空化水动力学非定常特性研究进展及展望
季斌
, 程怀玉
Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation
JI Bin, CHENG Huaiyu
中图分类号: O352
文献标识码: A
通讯作者:
收稿日期: 2017-05-18
接受日期: 2018-04-3
网络出版日期: 2019-01-15
版权声明: 2019 开云棋牌官方 This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
基金资助:
作者简介:
作者简介：季斌, 1982年生, 武汉大学水利水电学院副教授.主要从事空化水动力学应用基础研究. 主持国家自然科学基金项目3项,发表SCI论文49篇(第一作者或通讯作者29篇), 6篇论文入选ESI高被引论文,1篇论文被评为``2015年中国百篇最具影响国际学术论文'',1篇论文获 J. Hydrodyn.2014年高被引论文奖,1篇论文被列为 Int. J. Multiphase Flow期刊主页统计近5年被引用次数最多的论文, 获省部级科技奖励3项,2015年入选湖北省``楚天学者计划'', 2017年获湖北省杰出青年基金,2018年获国家自然科学基金优秀青年科学基金.
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摘要
空化作为一种重要的复杂水动力学现象,具有明显的三维流动特征与剧烈的非定常特性,在水力机械、船舶推进器、水利工程中广泛存在,且通常会带来不利的影响,长期以来一直是水动力学领域研究的重点与难点课题之一.本文首先从实验测量和数值模拟两个角度,综述了空化水动力学非定常特性研究的发展概况, 分析了当前存在的问题.在空化实验研究中,主要介绍了空化水洞、空化流场测量以及多物理场同步测量等方面所取得的进展.在数值模拟方法中, 对目前的空化模型和湍流模型进行了分类介绍,并重点讨论了大涡模拟、验证和确认等在空化流模拟中的应用.之后以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等,梳理了其研究中存在的几个关键科学问题,包括空化演变、空化流动的三维结构、失稳机制、空化不稳定性及其与低频压力脉动的联系、空化与旋涡的相互作用、空化与弹性水翼的流固耦合、空化对尾流场影响等.最后展望了空化水动力学的研究方向和未来发展趋势.
关键词：
Abstract
Cavitation is an important kind of complex multiphase flow with strong three-dimensional characteristic and high unsteadiness, which frequently occurred in a wide range of fluid machinery, marine propulsor, and hydraulic engineering and can generate the destructive behavior. Cavitation has been one of the most difficult and key problems in the area of hydrodynamics for quite a long time. In this paper, the research progress of unsteady hydrodynamics characteristics for cavitation is reviewed from the viewpoints of experimental and numerical investigations, respectively. And the existing problems in the cavitation research are also discussed. For the experimental study, the progress of the cavitation mechanism tunnel, measurement technology for cavitating flow and simultaneous sampling technique are introduced. For the numerical investigations, some of the most popular cavitation models and turbulence models are introduced by categorization, and the applications of large eddy simulation (LES) approach and validation & verification in cavitation simulations are discussed in detail. Then, mainly based on attached cavity but also other kinds of cavitation, such as cavitation cloud, cavitation erosion, and vortex cavitation, several basic but important problems are discussed. Problems discussed herein includes the evolution of attached cavity, the three dimensional structures of cavitation, the shedding mechanism of attached cavity, the unsteadiness mechanism of cavitation and its connection with the pressure fluctuations, the interaction between cavitation and vortex, the fluid-structure interaction in the cavitating flow around a flexible hydrofoil, influence of cavitation on the wake flow, and so on. Finally, prospects of the direction and trends of cavitation hydrodynamics research are discussed.
Keywords：
1 引 言
水动力学是一门研究水和其他液体的运动规律及其与边界相互作用的学科,与空气动力学一样, 水动力学是流体力学的一个重要分支(刘桦等 2007),在流体力学、甚至整个力学学科中均占据着非常重要的地位.空化作为水动力学的一种特有现象, 包含了几乎所有的复杂流动问题,如湍流(王一伟等 2012)、相变(潘森森 1979)、可压缩流动(Ceccio 2009)等,一直是水动力学研究的重点、难点课题之一.
一般认为,空化是一种因流体动力学因素作用而在液体内部或在液体与固体界面上发生的液体与其蒸汽的相变过程与现象(张博等2009, Arndt 2012, 潘森森和彭晓星 2013, 高远等 2015, Prosperetti 2017).对空化现象的认识和研究可追溯到19世纪.有记载的是Besant在1839年、Reynolds在1873年就已经开始在实验室对空化现象进行研究.1902年在英国Cobra号驱逐舰螺旋桨上首次发现空蚀损伤,接着在水工建筑物和水力机械上也发现了同样的现象.由于空化在水力机械中广泛存在, 且通常会带来不利的影响(计志也 1992, 王一伟等2012), 因而一直是研究人员关注的重点(Arndt 1981, 2002, Aw et al. 2016, Luo etal. 2016, Zhang et al. 2016, Zima 2016).
需要注意的是, 由于目前对空化的认识尚不全面, 对其分类也比较混乱,大体有以下几种分类方式: 产生空化的原因、空化的流动特性和空化的发展阶段等.
按空化产生的原因划分. 根据空化产生的主要因素,可以将空化分为水力空化、振荡性空化、声致空化、光致空化及非相变型空化(潘森森和彭晓星2013). 本文前述的空化定义严格而言指的就是水力空化,因其在日常生活中最为广泛、流动机理最为复杂, 一般可以将空化理解为水力空化.振荡型空化是指由于持续的高频高幅压力脉动引起的空化,如柴油机汽缸冷却套管的水中空化;声致空化指的是由多个声传感器或声波发生器发出的声束聚焦、形成驻波而激发的空化现象,如超声空化; 光致空化与声致空化类似, 是由于激光能量集中而激发的空化现象;非相变空化本质上并不是空化现象,该流动中的气泡长大、缩小主要是由于外界压力的变化导致其内部不可凝结气体的膨胀、收缩或者由于水中游离气体的扩散溶解.在气泡的长大缩小过程中, 存在少量的相变过程, 但并不是主导因素,因此也称为`` 空化'', 如通气空化等.
按空化的流动特性划分. 按照空化流动性质,可以将空化分为游移空化、固定空化、旋涡空化和振荡空化.游移空化主要由单个小空泡构成, 会随着液体一起向下游运动, 如图1(a) 所示. 在运动的过程中, 往往伴随着扩展、收缩、溃灭等过程.固定空化的位置则比较确定, 一般会依附于绕流固体表面.其长度与当地的压力关系较为紧密, 压力越小, 长度越大.旋涡空化主要发生在旋涡内部的强剪切区域, 如螺旋桨的梢涡.由于旋涡结构的离心作用, 会在涡心处形成低压区域,当其压力低于饱和蒸汽压时, 即会诱发旋涡空化.这类空化可以发生于任何具有足够强的剪切力使得当地压力降至饱和蒸汽压的区域.
按空化的发展阶段划分. 这种分类方式主要根据空化的表观进行分类,主要可以分为初生空化、片空化、云空化、超空化(Brennen 1995, Wang etal. 2001).初生空化是指水中的微小气核在流场中低压的作用下出现的爆发性生长现象.初生的空化因周围压力与饱和蒸汽压比较接近, 空化程度较轻,多为单个或多个的气泡. 影响初生空化的因素繁多, 一般认为,空化初生与当地压力(潘森森 1979)、湍流强度(Arakeri 2006)、气核分布(潘森森 1985)及当地流动结构(Katz 1984)等密切相关,且各因素之间也会存在一定的相互影响,这使得人们对于空化初生的认识依然比较有限(Arakeri 1979).进一步降低空化数, 空泡的数量逐渐增加并相互融合, 形成片状结构,即为片空化, 如图1(b) 所示. 片空化具有较为明显的不稳定性,尾部会产生准周期性的生长脱落过程(何友声等 1997).这一不稳定性随着空化数的降低会进一步得到加强,尾部的空泡脱落现象更为剧烈, 形成云空化, 如图1(c)所示.与片空化的较为清晰的汽液交界面不同, 在云空化流动中,由于流动的不稳定性, 其内部为含有大量微小液滴的汽液混合物,汽液交界面也变得十分模糊.云空化的发生使得伴随其发生的片空化行为更加具有准周期性,会经历完整的空化生长、脱落、溃灭过程,并会导致整个流场的流动结构也呈现出一定的准周期性, 如压力脉动等,因而一直受到研究人员的关注. 目前, 对于其准周期性的行为, 尤其是尾部脱落, 主要有两种解释:反向射流理论和激波理论. 云空化的长度会随着空化数的降低而生长,当空化数足够低时, 云空化的尾部,即空化的闭合区将移至绕流固体的下游,即绕流物体的尾部完全包裹在空泡内, 这种空化称之为超空化, 如图1(d)所示. 超空化因可将绕流物体完全包裹在气泡内部,隔绝了与外界液体的接触, 因而可以显著减小绕流物体所受到的阻力,在军事、民用领域均具有很好的应用前景(曹伟等 2006, 赵新华等 2009).
片空化及其向下游发展形成的云空化一般统称为附着型空化.附着型空化演变规律非常复杂, 且其在工程实际中最为常见,与工程实践联系最为紧密, 其相关研究成果可以直接产生工程应用价值,相关的研究最为活跃(时素果等 2011, 阎超等 2011, 时素果和王国玉2012, 赵宇等 2014). 因此, 本文将以附着型空化为例,同时兼顾其他空化类型, 介绍近年来空化流研究的进展及尚存在的问题.
本文的主要结构如下: 第2节对空化研究的相关实验技术发展进行介绍,在第3节对近年来空化数值模拟方面的研究进行总结,在第4章对空化研究中几个关键的科学问题进行阐述,最后在第5节对本文的主要内容进行总结, 并对今后的发展方向提出建议.
2 空化实验平台与实验技术进展
2.1 空化实验平台
水洞是空化实验的重要平台. 1895年, CharlesParsons建造了世界上第一座空泡水筒(见图2),观察了空化发展过程, 并通过增加螺旋桨盘面推迟空化初生,将船速从20节增加到了32.75节. 目前, 世界上已建成的水洞约200余座,分布于近30个国家的科研单位(徐海兵 2004).其中以美国宾州大学超高速水洞流速最大, 实验段流速可达83.8m/s.此外, 宾州大学还拥有2座小型水洞,这些优良的实验平台使得该校在空化领域取得了诸多进展(McCormick 1962,Arndt & Ippen 1968, Lamson et al. 1991, Meyer et al. 1992).我国第一座水洞于1957年在上海建成, 国内现在拥有水洞13座左右.其中北京理工大学王国玉、黄彪等利用其小型空化水洞对水翼空化进行了大量的实验研究,并且取得了较多成果(Huang et al. 2014b, Wang et al. 2015, Wu et al.2015). 2013年,中国船舶科学研究中心颜开、彭晓星研究员等设计并建成了一个小型多功能高速空泡水洞,最高流速可达25m/s. 该水洞配备了快速除气和播核装置,是目前国内唯一可以独立控制和测量水中溶解气体和自由气核的实验设备.该水洞还可在实验段上游安装来流振荡机构以获取非定常来流,是进行空化机理研究的理想设备. Peng 等 (2017)利用该水洞对梢涡空化的涡唱现象进行了深入实验研究与理论分析(见图3), 指出涡唱现象是一种自然频率的共振问题,并且给出了涡唱频率的预测表达式. Song 等 (2017)则进一步提出了一个基于噪声水平的梢涡空化初生判断方法.彭晓星等还利用该水洞对比了不同含气量对空化的影响(见 图4),其初步结果表明含气量对空化的脱落会产生较为明显的影响,随着水中含气量的降低, 空泡的脱落频率逐渐减小.
图 4 不同含气量对空化的影响. (a) 攻角$\theta =1^\circ$,来流速度$V=7$\,m/s, 空化数$\sigma =1.3$, 含气量$\alpha /\alpha_{\rm s}=91{\%}$; (b) 攻角$\theta =1^\circ$, 来流速度$V=7$\,m/s, 空化数$\sigma =1.3$, 含气量$\alpha /\alpha _{\rm s}=70{\%}$
霍普金森压杆(Split Hopkinson Pressure Bar,SHPB)发射系统也是一类重要的空化实验研究平台,尤其是对于高速航行体水下发射水动力学问题的研究具有非常好的适用性(王一伟和黄晨光2018,Bustamante et al. 2018, Wei et al. 2011).中国科学院力学研究所搭建的SHPB发射系统可以在200m/s内将发射物体从静止加速至30m/s,结合高速摄影、压力测量系统等测量方法,可以较为全面地对高速运动物体表面的空化绕流进行实验研究. Wang 等(2012)基于该实验平台对通气空化的脱落机制进行了较为系统的研究与分析.其研究结果发现, 在通气空化中,注入的气体与反向射流的相互作用会引起空泡的大尺度脱落,这是该类空化流动中一种特有的空泡脱落机制. 王一伟等 (2013)对水下回转航行体的附着型空化行为进行了实验与数值研究.基于实验与数值结果, 其深入探讨了该流动中空化非稳态演化的物理机制,对反向射流的生成机理进行了分析, 揭示了其对空泡演化的诱导作用.于娴娴等 (2014) 研究了轴对称航行体通气空化的非定常演化行为.研究结果表明, 该流动中空泡脱落的主要原因为边界层衍生二次涡,其在发展过程中将会切断主涡涡面进而引起尾部主涡结构的脱落. 此外,通气量的大小对空泡的形态会产生明显的影响, 一般而言,通气量的增加会引起空泡长度与厚度的增加, 脱落位置也会向下游移动.
2.2 空化流动压力场测量技术
压力作为影响空化的重要因素(Arndt 1981, 2002),很早就受到了研究人员的重视(Astolfi et al. 2000, Wang et al. 2001).Kawanami 等 (1997) 为了研究附着型空化流动机理及其控制方法,在水翼表面布置了多个压力测点, 其响应频率可达2.8kHz.借助这些压力传感器,其准确测得了脱落的空化云向下游运动过程中诱发的剧烈压力脉动,并提出了一种经典的空化云脱落机制, 即反向射流机制,大大促进了人们对于空化云脱落的理解,并提出了控制空化不稳定性的方法. Callenaere 等 (2001)则创造性地利用一个超声波发生器和一个压力传感器对附着型空穴内部的反向射流的厚度进行了测量.根据实验结果,他们指出空穴尾部的逆压梯度、反向射流与空穴厚度的比值是影响空化发展稳定性的两个关键参数,这是人们对于空化的不稳定特性理解的重要一步. 但是,由于空化发生时压力很低,而空化溃灭时局部压力又可以达到数百个大气压,流场中存在着非常剧烈的压力脉动, 因而对压力传感器提出了很高的要求.Foeth 等 (2008) 为了测量扭曲水翼表面的压力分布,在水翼吸力面及压力面布置了多个测点. 为了尽可能避免压力传感器损坏,其将压力传感器布置于水翼内部的小腔室内, 通过小孔与外界流场接触,进而捕捉流场中的压力脉动. 即便如此, 吸力面多个传感器依然被损坏.Singh 等 (2013) 为了对空化射流的压力场进行测量,在空化射流冲击区域布置了一个压力传感器,该传感器响应频率高达500kHz, 感应区面积为19.63mm$^{2}$.为了防止其被空化破坏,他们特意用一个有机玻璃薄片将感应区进行部分遮盖,使其有效面积减小至3.14mm$^{2}$, 最终成功测量到了该处的压力脉动.然而, 应当注意的是,通常而言压力传感器感应区面积比空泡大、响应频率比空泡溃灭频率低,这意味着传感器采集得到的压力信息可能是不准确的(Carnelli et al.2011). 就当前压力传感器技术而言,如何在测量空泡区压力脉动的同时尽可能保护压力传感器不被损坏依然是一个急需解决的问题.
2.3 空化流动速度场测量技术
在空化实验的早期, 流速信息的测量主要依靠探针等侵入式测量技术(Stutz & Reboud 1997a, 2000). 此类方法虽然简单、易于实施,但是也会在较大程度上直接影响当地流场,使得其测量信息的可靠性受到影响. 基于光学原理的LDV (laser dopplervelocimetry)测量技术则可以很好地解决这一问题,其测量数据精度也较高, 在空化机理的研究中起到了重要的作用(Arndt etal. 2000, Chesnakas & Jessup 2003, Sou et al. 2007).但是无论是侵入式的探针测量还是无侵入的LDV,其测量的数据均是某个空间点的信息,更为重要的整个流场的瞬态信息无法获取. 为此, Zhang 等 (1998)在前人工作的基础上(Adrian 1994, Westerweel 1997), 发展了PIV(particle image velocimetry)技术并首次将其应用于空化流动测量.该方法可以较为精确地测量流场中某个断面的流速分布,因而可以提供丰富的流场信息. Gopalan和Katz (2000)采用PIV技术对附着型空化的闭合区结构进行了大量观测,获取了速度、涡流等物理量的瞬态及时均分布,其结果表明闭合区蒸汽泡的溃灭是涡量生成的主要原因. Iyer和Ceccio(2002)则利用该技术得到了空化流动的剪切应力、雷诺应力分布,分析了空化对剪切层的影响. 国内学者Huang 等 (2014a)利用PIV技术对Clark-Y水翼空化绕流进行了一系列的实验测量,其工作表明附着型空化的准周期性生长、发展、脱落、溃灭等过程对涡量的输运具有非常重要的影响.随着技术的进步, 传统的PIV技术也得到了长足的发展, 逐渐演化出TR-PIV(Foeth et al. 2006, Wosnik et al. 2006), stereo-PIV (Dreyer et al.2014) 等新的测量手段. 但是, 应当注意的是,这些PIV方法均无法获得空化区域内部的速度场.
为了解决该问题, 近年来一些研究者提出了PLIF (planer laser inducedfluorescence)技术,该技术利用激发态激光在跃迁时释放光子来显示流场信息,不再依赖于示踪粒子, 因而可以直接对空穴内部进行测量,并且具有很高时间分辨率(纳秒级)与空间分辨率(小于1mm).Friedrichs和Kosyna (2003)利用PLIF对离心泵内部的旋转空化进行了测量,获得了空化区域内部的速度分布,其分析表明叶片空化与相邻叶片导边的相互作用是旋转空化的主导性因素.Dular 等 (2005)利用PIV及PLIF技术也对离心泵内部的空化流场进行了测量,得到了叶片周围瞬态、时均的速度场与蒸汽体积分数分布 (如图5所示) . 此外, Bachert 等 (2003) 及Dular 等 (2007)还利用该技术对绕水翼空化流动进行了实验观测,得到了较为精确的空化结构外形. PIV/PLIF作为一种无侵入式的测量技术,可以同时获得空化区域内外的流场信息,可以大大促进人们对于空化外部及内部结构的认识,在今后的实验研究方面应当得到重视与发展.
2.4 空化流动蒸汽含量测量技术
流场蒸汽含量作为一个可以直接表征空化程度的物理量,一直是实验研究人员关注的重点. 早在1997年,Stutz等就尝试对文丘里管内部空化流动中的蒸汽含量分布进行测量(Stutz& Reboud 1997a, Stutz & Reboud 1997b). 在实验中,他们利用光学探针成功获得了云空化脱落区域及附着型空化区域中某些监测点的时均蒸汽含量及速度,其测得最大的时均蒸汽含量分别为0.21和0.8左右. 随后, Stutz和Legoupil (2003)利用X射线密度测量仪对类似的文丘里管内部空化流场的蒸汽含量进行了测量.实验中, 他们使用了一个发射源和24个线性排列的接收探头,以获取对应的24个空间位置上的瞬时蒸汽含量, 其采样频率可达1000帧,测得的最大蒸汽含量为0.25. Coutier-Delgosha 等 (2007)用同样的装置对水翼空化绕流进行了测量,其测得的时均蒸汽含量和最大的瞬时蒸汽含量分别为0.6和0.85.但是应当注意的是, 这些测量方法尽管可以获得流场蒸汽含量,但其仍然只是获取部分空间点的含气率. Makiharju 等 (2013)进一步发展了该测量技术, 使其可以对一个平面的蒸汽含量进行测量(见图6), 这大大丰富了可获取的流场蒸汽含量信息,是空化流场测量技术的一大突破, 对空化的实验研究将发挥重大作用.Ganesh 等 (2016) 利用该技术对文丘里管空化流动进行了细致地测量,首次从实验的角度发现了空化流动中的激波现象,揭示激波现象为空化脱落的一个重要机制,大大加深了人们对于空化脱落机理的理解.
2.5 多物理场同步测量技术
值得注意的是, 随着实验技术的不断发展以及空化研究的不断深入,空化流动多物理场同步测量技术越来越多地得到应用与推广 (Wang et al.2017). 利用多物理场同步测量技术,可以实时对多个物理量(如压力、速度、噪声等)进行同步测量,这使得分析空化流动中各流场参数的瞬时相互作用成为可能. 陈广豪(2016) 利用同步测量系统(见图7),将高速全流场显示系统和压力测量系统结合在一起, 进行同步采集,可以获得较高的同步精度. 基于该同步测量系统获得的实验数据,其对空穴形态与压力脉动进行了深入分析,揭示了空穴演变与流体动力的相互作用. 张孝石 (2017)在研究水下航行体空化流动过程中,构建了空化流动多场同步测量系统,可以同时获取高速图像、压力信号、通气量等实验数据,对自然空泡和通气空泡的形态演变过程及其表面压力脉动特性进行了系统的研究,揭示了空泡脱落模式、频率及壁面压力脉动的变化规律.空化流动具有非常强的非定常性,其演变又会引起流场中其他物理量如压力、速度的剧烈变化,与流场中的漩涡、湍流结构具有密切的相互联系,这意味着空化流场中多物理量瞬态相互作用的研究对揭示空化机理具有重要价值,多物理场同步测量技术在空化流动研究中也必将愈发重要. Reuter 等(2017)利用多场同步测量技术对单个空泡发展过程中的流场的速度及空泡的形态进行了同步观测,发现壁面效应对空泡溃灭过程具有非常强的影响,不同的壁面距离会诱发两种不同的漩涡结构.
3 空化数值模拟方法的进展
实验研究尽管为人们认识附着型空化及其流动机理提供了丰富的数据,促进了人们对该流动的理解. 但是随着研究的不断深入,实验手段本身的实验周期长、实验费用高昂、获取数据有限等缺陷逐渐暴露出来,附着型空化的高度非定常性与三维流动特性更是加剧了这一矛盾. 另一方面,计算机性能的不断提升使得数值模拟技术在空化流动领域中的应用越来越广泛,已经成为空化研究中一个重要的研究手段(Hidalgo 2015, Peng G Y et al. 2016).在空化流动的数值模拟中,空化模型与湍流模型对模拟结果的精度起着非常重要的作用.
3.1 常用的几种空化模型
空化模型是用于描述气、液两相之间质量输运的数学模型,
对空化流动的模拟精度起着决定性的作用. 目前,
应用较为广泛的空化模型主要分为两类: 一类为基于正压流体状态方程的空化模型,
一类为基于质量输运的空化模型.
3.1.1 基于正压流体状态方程的空化模型
正压流体状态方程模型最初由Delannoy和Kueny (1990) 提出. 在该模型中,气液混合物的密度可以采用状态方程描述, 即认为是压力与密度的函数.通常在空化流动中, 温度的效应可以忽略. 忽略热力学效应后, 在该模型中,混合物的密度可以简化为当地压力的单值函数, 即
$$ \rho _{\rm m} =f(p)(1)$$
式中, $\rho _{\rm m}$为混合物密度, $p$为当地压力.为了更加方便地表述混合物密度$\rho _{\rm m}$与压力的关系,定义参数$\Delta p_{\rm v}$
$$ \Delta p_{\rm v} = \pi c_{\min }^2 \dfrac{\rho _{\rm l} - \rho _{\rm v} }{2}(2) $$
式中, $\rho _{\rm l}$和$\rho_{\rm v}$分别为液态水和水蒸汽密度, $c_{\min}$为流场中的最小声速.则$f(p)$可以写为
$$ \rho _{\rm m} = f(p) = \left\{ \begin{array}{ll} \rho _{\rm ref} \left( {\dfrac{p + p_0 }{p_{\rm ref}^{\rm T} + p_0 }} \right)^{1 / n}, &\ p > p_{\rm v} + 0.5\Delta p_{\rm v} \\ \dfrac{\rho _{\rm l} + \rho _{\rm v} }{2} + \dfrac{\rho _{\rm l} - \rho _{\rm v} }{2}\sin \left( {\pi \cdot \dfrac{p - p_{\rm v} }{\Delta p_{\rm v} }} \right), &\ p_{\rm v} - 0.5\Delta p_{\rm v} < p < p_{\rm v} + 0.5\Delta p_{\rm v} \\ \dfrac{p}{RT} , &\ p < p_{\rm v} - 0.5\Delta p_{\rm v} \\ \end{array} \right.(3) $$
式中, $p{\rm ref}^{\rm T}$为参考压力, $\rho {\rm ref}$为参考密度, $p_{0}=300$\,MPa, $n=7$. 从式(3)可以看出,在该模型中: (1) 当压力较大 $(p>p_{\rm v}+0.5\Delta p_{\rm v})$ 时,混合物被视为纯液态水, 其密度与压力的关系服从Tait方程; (2)当压力较小 $(p<p_{\rm v}-0.5\Delta p_{\rm v})$ 时,认为当地流动介质为纯水蒸汽,流体密度与压力的关系满足理想气体状态方程; (3) 当压力大小适中$(p_{\rm v}-0.5\Delta p_{\rm v}<p<p_{\rm v}+0.5\Delta p_{\rm v})$时, 当地流场由汽、液两相混合物组成,其密度与压力的关系按正弦曲线描述.关于该空化模型的理论分析及实际应用已经有了较为详细的研究(Goncalves & Patella 2009, 谭磊和曹树良 2010, 黄彪 2012).该模型可以较好地模拟稳定的附着型空穴,对压力等参数的预测与实验结果也比较吻合. 需要注意的是,空化的本质是相变, 而基于正压流体状态方程的空化模型,并没有体现相变过程,这暗示着该空化模型在捕捉空化流动细节时必然存在着一定的缺陷.实际上, Katz (1984)和Lerouxd 等 (2004) 的实验结果表明,在空化流动中旋涡的产生及其运动对空化的演变产生着重要的作用.而在空化流场中,由于密度与压力梯度不平行导致的斜压矩项在旋涡演变过程中的作用不可忽略.但是在基于正压流体状态方程空化模型中,由于将密度简化为压力的单值函数, 其密度与压力梯度始终保持平行,因而无法反映斜压矩项的影响.该空化模型在预测空化的对流和输运现象方面存在明显的缺陷.
3.1.2 基于质量输运方程的空化模型
为了捕捉空化过程中的相变过程,人们发展出了一套基于质量输运方程的空化模型(transportequation-based model, TEM). 通过添加适当的源项,对质量或体积分数采用传输方程来控制汽液两相之间的质量传输过程.与基于正压流体状态方程的空化模型类似, 在这类空化模型中,一般也忽略热力学效应的影响. 目前,通常采用基于体积分数的输运方程来描述相变过程
$$ \dfrac{\partial (\rho _{\rm v} \alpha _{\rm v} )}{\partial t} + \dfrac{\partial (\rho _{\rm v} \alpha _{\rm v} u_i )}{\partial x_{\rm i} } = \dot {m}^ + - \dot {m}^ -(4) $$
式中, $\alpha $$_{\rm v}$为气相体积分数, $\dot {m}^ + $表示蒸发过程中单位时间内由液相转为汽相的液体质量, $\dot {m}^ - $则表示反向的凝结过程. 根据不同的$\dot {m}^ + $和$\dot {m}^ - $的构建方式, 此类模型又可分为两大类, 即基于Rayleigh-Plesset方程(R-P方程) 的空化模型和基于界面动力学的空化模型.
(a)基于R-P方程的空化模型
R-P方程描述的是一个单泡在内外压差作用下的生长或溃灭过程, 其形式为
$$ \rho _{\rm l} \left( {\dfrac{3}{2}\dot {R}^2 + R\ddot {R}} \right) = p_{\rm v} - p + p_{\rm g0} \left( {\dfrac{R_0 }{R}} \right)^{3\gamma } - \dfrac{2S}{R} - 4\mu \dfrac{\dot {R}}{R}(5) $$
式中, $R$为空泡的半径, $R_{0}$为空泡的初始半径, $\dot {R}$ 和$\ddot {R}$分别为空泡半径对时间的一阶导、二阶导数. $p_{\rm v}$为泡内压力, $p_{\rm g0}$为泡内不可凝结气体分压,$S$为表面张力系数, $\mu $为液态水的黏性系数.若忽略二阶项、表面张力、液体黏性、不可凝结气体的影响,可以得到空泡半径变化与压力之间的关系
$$ \dfrac{{\rm d}R}{{\rm d}t} = \pm \sqrt {\dfrac{2}{3}\dfrac{\left| {p_{\rm v} - p} \right|}{\rho _{\rm l} }}(6) $$
若认为发生改变的体积由水体的蒸发产生水蒸汽充满(或由水蒸汽凝结而腾出),则可以得到如下的表达式
$$ \dot {m} = \pm \rho _{\rm v} \dfrac{\rm d}{{\rm d}t}\left( {\dfrac{4}{3}\pi R^3 } \right) = \pm 4\pi \rho _{\rm v} R^2 \sqrt {\dfrac{2}{3}\dfrac{\left| {p_{\rm v} - p} \right|}{\rho _{\rm l} }}(7) $$
式(7)的符号取决于具体的相变过程,蒸发取正值, 凝结反之.上式建立了单个气泡膨胀或收缩过程中相间质量传输速率与压力的关系,并成为多个基于质量输运方程的空化模型的源项基础.
基于式(7), Schnerr和Sauer (2001)提出了第一个不需要经验常数的质量输运空化模型, 在该模型中
$$ \left. {\begin{array}{ll} \dot {m}^ + = \dfrac{3\rho _{\rm v} \rho _{\rm l} }{R\rho _{\rm m} }\alpha _{\rm v} \left( {1 - \alpha _{\rm v} } \right) \sqrt {\dfrac{2}{3}\dfrac{\left( {p - p_{\rm {sat}} } \right)}{\rho _{\rm l} }} ,&\quad p > p_{\rm {sat}} \\ \dot {m}^ - = - \dfrac{3\rho _{\rm v} \rho _{\rm l} }{R\rho _{\rm m} }\alpha _{\rm v} \left( {1 - \alpha _{\rm v} } \right) \sqrt {\dfrac{2}{3}\dfrac{\left( {p_{\rm {sat}} - p} \right)}{\rho _{\rm l} }} ,&\quad p < p_{\rm {sat}} \\ \end{array}} \right\}(8) $$
2002年, Singhal 等 (2002) 提出了第一个被商用化的空化模型,即全空化模型(full cavitation model), 其源项定义为
$$ \left. {\begin{array}{ll} \dot {m}^ + = C_{\rm p} \dfrac{\sqrt k }{\sigma }\rho _{\rm l} \rho _{\rm v} \sqrt {\dfrac{2}{3}\dfrac{\left( {p - p_{\rm {sat}} } \right)}{\rho _{\rm l} }} f_{\rm v} ,&\quad p > p_{\rm {sat}} \\ \dot {m}^ - = - C_{\rm d} \dfrac{\sqrt k }{\sigma }\rho _{\rm l} \rho _{\rm v} \sqrt {\dfrac{2}{3}\dfrac{\left( {p_{\rm {sat}} - p} \right)}{\rho _{\rm l} }} (1 - f_{\rm v} - f_{\rm g} ),&\quad p < p_{\rm {sat}} \\ \end{array}} \right\}(9) $$
在该模型中,当地湍动能、表面张力系数、不可凝结气体的影响也被考虑在内,因而得名为``全空化模型''. Singhal 等 (2002)利用该模型对绕NACA66水翼空化流动、浸没式圆柱空化绕流、锐边圆孔空化流进行了模拟计算,部分计算结果见 图8,模拟与实验的对比较好地验证了该模型的有效性.
图 8 Singhal模型预测值与实验值的对比. (a) NACA66水翼压力,(b)浸没式圆柱压力系数, (c)锐边圆孔出流系数 (
Zwart 等 (2004) 于2004年提出了一个更为简单的空化模型
$$ \left. {\begin{array}{ll} \dot {m}^ + = C_{\rm p} \dfrac{3\alpha _{\rm v} \rho _{\rm v} }{R}\sqrt {\dfrac{2}{3}\dfrac{\left( {p - p_{\rm {sat}} } \right)}{\rho _{\rm l} }} ,&\quad p > p_{\rm {sat}} \\ \dot {m}^ - = - C_{\rm d} \dfrac{3\rho _{\rm v} \left( {1 - \alpha _{\rm v} } \right)\alpha _{\rm {nuc}} }{R}\sqrt {\dfrac{2}{3}\dfrac{\left( {p_{\rm {sat}} - p} \right)}{\rho _{\rm l} }} ,&\quad p < p_{\rm {sat}} \\ \end{array}} \right\}(10) $$
并利用该模型对水翼空化、诱导轮空化及文丘里管空化进行了数值模拟.结果表明, 该模型较好地捕捉到了空化流动细节.该模型在目前的空化模拟中应用得较为广泛.
Niedziedzka 等 (2016)较为系统地介绍了以上这3种空化模型的发展历史,并对其各自的适用性进行了归纳总结.此类空化模型对于大尺度空泡团的旋涡脱落现象有较好的体现,但其过早预测了空穴的断裂.
(b)基于界面动力学的空化模型
尽管基于R-P方程的空化模型能够对汽液两相间的质量输运进行较好的描述,但是其通常涉及到蒸发与凝结源项的经验常数,且模型的经验系数取值并不相同, 此类空化模型具有一定的局限性.为了消除经验常数带来的局限性, Senocak和Shyy (2004)不再从传统上的R-P方程着手来推导汽液相间的蒸发与凝结源项,转而从空泡界面动力学的运动机理着手, 推导汽液相间的质量传输速率,提出了基于界面动力学的质量传输模型(interfacial dynamic model,IDM). 在该模型中, 源项的表达式定义为
$$ \left. {\begin{array}{ll} \dot {m}^ + = \dfrac{\left( {1 - \alpha _{\rm l} } \right)\left( {p - p_{\rm {sat}} } \right)\rho _{\rm v} }{\left( {u_{\rm {v,n}} - u_{\rm {I,n}} } \right)^2\left( {\rho _{\rm l} - \rho _{\rm v} } \right)t_\infty },&\quad p > p_{\rm {sat}} \\ \dot {m}^ - = - \dfrac{\left( {p_{\rm {sat}} - p} \right)\rho _{\rm l} \alpha _{\rm l} }{\left( {u_{\rm {v,n}} - u_{\rm {I,n}} } \right)^2\left( {\rho _{\rm l} - \rho _{\rm v} } \right)t_\infty },&\quad p < p_{\rm {sat}} \\ \end{array}} \right\}(11) $$
利用该模型, Senocak 等 (2004)对圆柱空化绕流、绕NACA66水翼空化流动及文丘里管空化流动进行了模拟计算,数值结果与实验数据吻合较好. 理论上,在空化模型中消除了经验系数对空化模型的影响, IDM空化模型具有更普遍的适用性.该模型对低汽相体积分数的混相区域逐渐过渡到高汽相体积分数的纯汽相区域的动态交界面有很好的表现,可清晰的模拟出附着空穴中, 不同含汽量区域的空穴界面,但是对空穴的断裂及大尺度空泡团脱落现象的预测能力存在明显的不足(黄彪 2012).
2012年, 黄彪 (2012) 在对上述两类基于质量输运空化模型的认识基础上,提出了一种基于混合密度分域的空化模型(density modify basedcavitation model, DMBM). 其源项的表达式为,
$$ \left. {\begin{array}{l} \dot {m}^ - = \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)\dot {m}_{\rm k}^ - + \left[ {1 - \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)} \right]\dot {m}_{\rm s}^ - \\ \dot {m}^ + = \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)\dot {m}_{\rm k}^ + + \left[ {1 - \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)} \right]\dot {m}_{\rm s}^ + \\ \end{array}} \right\}(12) $$
$$ \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right) = 0.5 + \tanh \left[ {\dfrac{C_{\rm 1} \left( {C_{\rm 3} \rho _{\rm m} / \rho _{\rm l} - C_2 } \right)}{C_4 \left( {1 - 2C_2 } \right) + C_2 }} \right] \bigg/ \left( {2\tanh C_1 } \right)(13) $$
其中$\chi (\rho _{\rm m} / \rho _{\rm l} )$为桥接函数,通过该函数将两个空化模型进行桥接, 以便对空化行为进行更好的预测.与实验结果的对比表明,该模型不但可以准确地模拟出附着在翼型前端的稳定的含汽量相对较大的空穴,还可以捕捉到空泡脱落时刻翼型尾部的不稳定脉动,其预测得到的时均速度等流场结构和水动力学特性也与实验结果有较好的吻合.
Zhao 等 (2016) 则基于Zwart模型, 将旋涡对空化的影响考虑在内,提出了LVC空化模型. 该模型在模拟间隙空化流动时,可以较好地反映旋涡空化的长度,与实验数据吻合较好, 如 图9所示.
3.2 空化模型的新进展
值得注意的是,尽管上述空化模型可以在一定程度上揭示空化流动机制,但是这些模型均只能在宏观层面对蒸汽体积分数分布进行求解,因而无法反映空化演变的微观机理. 现有的空化理论均表明,空化演变涉及多个微观物理过程,气核的大小及数量对空化的发展均会产生重要的影响.
为了能更好地反映空化的微观行为, Hsiao 等 (2017) 和Ma 等 (2017)提出了一种基于欧拉--拉格朗日耦合方法的多尺度空化模型,以捕捉片状空化的形成、发展、破碎及云空化的脱落过程.该模型不需要对相间的质量输运进行任何假设,转而对自由空化核和固壁空化核进行模化处理. 在该模型中,采用了一个小尺度模型以追踪微观空泡的轨迹,利用大尺度模型描述大空泡团的动力学特性,两者通过一个过渡函数进行桥接.该模型可以清晰地反映小空化核生长成为宏观空泡、并相互融合形成片状空化的过程,如 图10所示.该模型在各种类型的空化(如绕水翼空化、绕钝体空化、螺旋桨空化等)均具有令人满意的预测,具有较好的应用潜力.
图 10 基于欧拉--拉格朗日耦合观点空化模型对空化典型行为的捕捉(
Du 等 (2016)指出,不同的空泡大小与空泡数量密度可能会导致一样的蒸汽体积分数,但是其对空化溃灭过程的影响差别巨大,这种差别是传统基于R-P方程的空化模型所无法捕捉的.为了考虑空泡大小、数量密度及泡群效应对空化的影响,他们基于修正的全空化模型,将空泡数量密度变化作为一个重要因素考虑在内,提出了一个全新的空化模型. 数值计算表明,该模型可以较好地反映空泡密度对云空化溃灭压力的影响,不同的空泡密度可能会引起不同的当地云空化溃灭速度, 见 图11.空泡密度还会影响当地的溃灭强度, 密度越大, 溃灭越剧烈.该模型证明泡间的相互作用在云空化中不可忽略, 应当引起足够的重视. Ye和 Li (2016)基于修正后的R-P方程,提出了一个可以考虑二阶导数项与泡--泡相互作用的空化模型.当考虑二阶导数项与泡--泡相互作用的影响后,除蒸汽体积分数非常小的区域外, 蒸汽泡的生长速度会显著降低.凝结主要发生于泡簇边界附近, 二阶导数项会在一定程度上加速凝结.该模型的计算结果与实验值、采用ZGB模型计算的数值结果进行了对比,验证了该模型的有效性. 张凌新等(2013)在群泡溃灭方面也做了大量的理论分析与数值计算,细致分析了泡--泡相互作用、泡群溃灭行为等,并提出了基于群泡理论的空化模型,为此类模型的发展做出了很多重要的工作.
此外, 为了更好地反映真实的空化流动现象,最近研究者还逐渐将可压缩性对空化的影响考虑在数值计算中(Liu et al.2012, Gropper et al. 2016). Srinivasan 等(2009)为了更好地预测空泡动力学行为,在其提出的空化模型中将气相视为可压缩流动介质,成功精确捕捉到了涡空化发生、云空化脱落及空穴的摆动. Wang 等(2014)则将汽相、液相的可压缩型均用状态方程进行描述并求解,并利用该模型对空化射流进行了数值计算, 验证了该模型的有效性.Schnerr 等 (2008)在考虑可压缩性的影响后,在水翼附近捕捉到了激波诱发的10.5MPa局部高压. Örley 等(2015)为精确求解自由空化射流在溃灭阶段诱导的压力波,考虑了所有流动相的可压缩性.他们发现除了经典的Kelvin-Helmholtz不稳定性会引起射流的失稳外,空化溃灭引起的湍流脉动、被卷吸的空气以及汽液交界面附近射流内部的溃灭也会引起射流的不稳定性行为.考虑流动的可压缩性在捕捉这些流动机理过程中发挥了重要作用.Gnanaskandan和Mahesh(2015)则发展了一套基于非结构化网格的空化流动求解方法. 在该方法中,他们考虑了汽液混合物可压缩性的影响,并且给出了不同组分含量混合物的声速表达式. 利用该模型,他们对水翼空化绕流及楔形空化绕流 (见 图12) 进行了细致地计算,数值结果与实验吻合很好, 且较好地捕捉到了空化流动的细微结构.实际上,由于空化的可压缩性引起的激波现象及其对空化发展的影响已经在实验中得到验证(Ganeshet al. 2016). 因此某种意义上而言,基于不可压缩流动的空化模型存在着天然的缺陷,可以考虑可压缩效应的空化模型应当是今后空化模型发展的一个重要方向.
3.3 湍流模型在空化流动中的应用与发展
湍流模型在空化流动模拟中同样占据着非常重要的作用(王福军 2016).近年来, 随着计算机性能的飞速发展, 大涡模拟(large eddy simulation,LES)逐渐在空化模拟领域得到应用. 在LES中,对于大尺度的旋涡结构利用直接数值模拟(direct numerical simulation,DNS) 进行直接求解, 对小尺度的旋涡结构利用亚格子模型进行模化处理,因而具有较高的模拟精度. 但是, LES对于计算资源的消耗较大,难以在工程实践中得到推广. 标准$k$-$\varepsilon $模型尽管对计算资源的要求较低, 且具有较好的计算稳定性,但是因其将湍流黏度视为湍动能与耗散率的函数, 过高地预测了湍流黏度,因而低估了空化流动的不稳定性(Wu et al. 2005, Wang & Ostoja-Starzewski 2007, Huang et al. 2014a).为了修正标准$k$-$\varepsilon $模型在空化预测中的缺陷,人们提出了多种修正方法, 如滤波器模型(FBM)(Johansen et al.2004)、基于密度修正的湍流模型(DCM) (Reboud et al. 1998)等.
随着对湍流模型认识的加深, 近年来, 在空化流动模拟中,求解分辨率可变的湍流模式逐渐得到关注,其主要思想是根据流场信息自动调整湍流的求解尺度,仅对必要的湍流结构进行求解, 进而大幅降低计算资源的消耗. 目前,这类模型主要可以分为两大类: 分域模型(zonalmodel)和桥接模型(bridging model) (Jeong & Girimaji 2010).
3.3.1 分域模型
分域模型主要有分离涡模型(Travin et al. 2000)、非稳态雷诺时均模型(Khorrami et al. 2002)以及多种RANS/LES混合模型等. 此类模型主要通过某种方式,对计算域进行划分, 并分别利用不同求解精度的湍流模型进行求解计算,以此降低对计算资源的要求.
Huang 等 (2014a)在FBM和DCM的基础上,提出了一种基于密度分域的滤波器模型(filter-based density correction model, FBDCM). 他们指出, 尽管FBM 模型和DCM 模型在一定范围内,均能降低流场中的湍流黏性系数, 但两种模型的物理内涵存在明显的差异:在云状空化流动中, 空穴尾部流场存在大尺度的旋涡运动,随着速度梯度的增加, 湍动能迅速变大. FBM模型没有考虑空化多相流动特性的影响, 主要对远离壁面,水汽含量较高的空化云旋涡脉动区域进行滤波修正,以捕捉大尺度涡流所造成的非定常特性. 而DCM模型主要通过对空化区域的混合密度进行修正,影响范围主要集中在近壁空化核心区域内, 以考虑汽液混相的压缩性,在远离壁面区域, 由于无明显的空化现象产生, 其作用效果欠佳. FBM模型和DCM模型的作用区域存在明显的差异,两者分别顾及了不同区域的流动特性. 基于上述认识, 针对FBM 模型和DCM模型在空化流动模拟应用中的特点,对空化流场基于混合密度的分布进行分域,在不同区域采用不同的湍流黏性修正方式,形成一种基于混合密度分域的湍流模式(FBDCM), 充分发挥FBM 模型和DCM模型的优势, 以捕捉湍流和空化之间的交互作用和动态行为:在翼型前缘含汽量较大的区域, 应用DCM模型,以体现附着型空穴的可压缩特性.在翼型尾部的含汽量较大的雾状空泡团区域, 应用FBM 模型,以捕捉大尺度的空泡涡团结构. 为了保证湍流黏性系数的光滑过渡,两种湍流黏性系数通过下面的混合函数进行桥接, 其表达式为
$$ \mu _{\rm {T\_hybrid}} = \dfrac{C_{\rm \mu } \rho _{\rm m} k^2}{\varepsilon }f_{\rm {hybrid}}(14) $$
$$ f_{\rm {hybrid}} = \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)f_{\rm {FBM}} + \left[ {1 - \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right)} \right]f_{\rm {DCM}}(15)$$
$$ \chi \left( {\rho _{\rm m} / \rho _{\rm l} } \right) = 0.5 + \tanh \left[ {\dfrac{C_{\rm 1} \left( {C_{\rm 3} \rho _{\rm m} / \rho _{\rm l} - C_2 } \right)}{C_4 \left( {1 - 2C_2 } \right) + C_2 }} \right] \bigg/ \left( {2\tanh C_1 } \right)(16)$$
FBDCM模型巧妙地联合FBM与DCM模型, 充分发挥各模型的优点,FBDCM成功地以与RANS模型接近的计算消耗对附着型空化进行了较为理想的精确模拟,以很小的计算代价捕捉到了反向射流、空泡脱落、旋涡演变等诸多流动细节(Huang et al. 2014a, Chen et al. 2015).
3.3.2 桥接模型
与分域模型不同, 桥接模型在整个计算域中采用同一套湍流模型(Speziale1997. Batten et al. 2004). 通过定义适当的参数,该模型可以从RANS模型无缝过渡到DNS,并以此针对任何一套网格均能获得计算精度与计算资源消耗之间的平衡.此类模型的挑战在于: (1)对于任意给定的物理分辨率均能提供尽可能好的闭合模式; (2)随着求解物理分辨率的提高, 能够产生更高的预测精度.物理分辨率由桥接参数控制, 这与大涡模拟中的滤波尺度的作用比较类似.实际上, 可以将此类模型视为一种LES,其闭合模式对任意滤波尺度均适用(Jeong & Girimaji 2010).
此类模型以PANS (partial-averaged Navier Stokes)模型为代表(Girimaji et al. 2003). 在该模型中, 定义了两个关键参数,模化湍动能与总湍动能之比$f_{\rm k}$、模化耗散率与总耗散率之比$f_{\varepsilon }$, 其表达式为
$$ f_{\rm k} = \dfrac{k_{\rm u} }{k},\quad f_{\rm \varepsilon } = \dfrac{\varepsilon _{\rm u} }{\varepsilon }(17) $$
式中, $k_{\rm u}$和$\varepsilon _{\rm u}$为模化处理的湍动能、耗散率, $k$和$\varepsilon $分别为总湍动能、耗散率. 随着这两个参数的减小,未求解的湍动能、耗散率逐渐下降, 由DNS直接求解的部分逐渐升高,进而获得更高的精度. 该模型最初基于标准$k$-$\varepsilon$模型中推导而来(Girimaji et al. 2003), 因形式简单,可以很容易地推广至其他模型(Krajnovic et al. 2012, Davidson 2014,Bie et al. 2015), 且易于在商用软件平台上实现,因而应用较广(Basara et al. 2011). Ji 等(2012)应用PANS模型对绕NACA66的空化流动进行了模拟分析. 利用该模型,以较小的计算资源消耗成功捕捉到了由于大尺度空化云脱落诱发的水翼壁面附近压力脉动.
然而, PANS模型由于对整个域的流动均会在一视同仁地进行求解,这使得其在空化数值模拟中并不能完全发挥其优势. 实际上,在空化流动数值模拟中, 重点关注的区域主要集中于空化发生附近,因此仅需提高该区域的物理求解分辨率即可. 基于这种想法, Hu 等(2014)针对空化流动的特点, 提出了一种基于密度分域的修正 PANS模型.在该模型中, 整个计算域的桥接参数不再设为统一值,而是依据当地的空化状态进行动态调整, 在关心的空化区域降低$f_{\rm k}$的值, 以提高该区域的求解精度; 对于无空化区域, 则提高$f_{\rm k}$的值, 以便更大程度上采用RANS模型进行计算, 降低对计算资源的要求.与原始PANS模型相比, 该模型不需要人为地调整$f_{\rm k}$的值,具备更好地通用性, 并且可以在进一步降低对计算资源的消耗的同时,保证计算精度(图13). 该模型针对空化流动问题的特点,将分域模式及桥接模式的思想有机地结合在一起,这为今后空化流动领域湍流模型的改进提供了一个新的思路. 利用该模型,Hu 等 (2014)对绕回转体空化流动进行了数值研究,对其中U型旋涡结构的生成与发展机理做了深入的分析与讨论,促进了人们对于空化流动旋涡演变机制的认识.
图 13 Clark-Y水翼空化绕流的实验图像 (
3.4 大涡模拟在空化流动方面的应用
随着计算机技术的飞速发展, 计算资源越来越充分,对计算资源消耗较大的大涡模拟 (LES)也越来越多地在空化流动模拟中得到应用(Xiao et al. 2014, Egerer etal. 2016, Wosnik et al. 2006). Wang 和Ostoja-Starzewski(2007)对NACA0015水翼空化绕流进行了大涡模拟,较为系统地研究了不同攻角、不同空化数下的空化形态,较为准确地捕捉到了漩涡与空泡的演变行为. Bensow 和Bark(2010)提出了一种隐式LES亚格子模型, 并对螺旋桨空化进行了预测.模拟结果成功捕捉到了诸多空化流动现象, 他们认为基于该模型,对空化的危害如空蚀、噪声等, 进行数值评估或许成为可能. Gnanaskandan和Mahesh(2016)利用LES对不同雷诺数下的圆柱非定常空化绕流进行了详细的研究.他们发现空化会显著改变漩涡的脱落频率与涡量的斜压矩项,对近尾流场区域的雷诺数、湍流强度均会体现一定程度的抑制,并且延迟了三维卡门涡街的破裂. Huang 等 (2014b)为了研究空化对水翼水动力学性能及水翼周围流场结构的影响,对Clark-Y水翼附着型空化及云空化进行了实验研究与大涡分析.LES数值结果与实验结果吻合很好,充分表明了大涡模拟在空化流动预测中的优越性. 他们的工作表明,水翼的宏观水动力学性能与空化发展的状态具有很强的相关性:在附着型空化的初生阶段,随着导边空化的发展水翼的升力系数会逐渐增大; 随着空化的进一步发展,空化本身的不稳定性使得升力系数也呈现了很强的脉动特征;在空化的最后阶段,空穴的完全脱落会使得水翼的升力系数存在一个剧烈的下降. Roohi 等(2013)则基于OpenFOAM平台利用VOF模型对Clark-Y水翼空化流动进行了LES计算分析,并将其与Kunz、Sauer空化模型进行了对比. 结果也与实验吻合得较好,可以较好地预测空化的起始位置、空穴大小、升力系数等重要参数.大涡模拟方法在空化问题中的逐步应用(Luo et al. 2012, Salvador etal. 2013, Sou et al. 2014, Gavaises et al.2015)使得其相对与RANS模型的优势也体现得更加明显. 虽然理论上而言,直接数值模拟 (DNS) 对空化流动的细微结构具有更好的预测能力,近年来DNS也取得了较大的进展(Marquillie et al. 2008, Linh Van etal. 2015, Iyer & Mahesh 2016). ŽnidarČiČ等 (2015)为了将DNS应用于空化流动的数值计算,基于Kim-Moin投影法提出了一个新的算法,利用影响矩阵技术及本征分解使得并行计算效率得到提高,进而降低了对计算资源的消耗. 尽管该方法尚存在一些问题,但依然非常值得肯定与关注. 不过, 就目前而言,考虑到空化流动通常雷诺数较高, 需求的计算资源很难得到满足,因此DNS在空化流动的推广应用依然会受到较强的限制. 总体而言,LES方法是在计算精度与效率中一个较好的平衡点, 可以预测的是,在今后的空化数值研究中, LES将会扮演着非常重要的角色.
3.5 数值计算的验证确认在空化模拟中的应用
目前,基于RANS方法和LES在附着性空化流动的数值模拟研究中均取得了很大进展,但是对其数值模拟结果的准确性却没有一个比较有说服力的评判方法.当前常规的做法是采用几套人为加密的网格与实验数据进行比较,定性地得到数值模拟结果的精确性,并不能完全形成系统的、令人信服的结论.对于数值模拟结果准确性的研究------验证和确认 (verification andvalidation, V&V), Roache (1998)的方法已经在单相流动中广泛运用,并且形成相应的规程. 他们提出的网格收敛指数法(GCI)和Stern 等(2001)提出的相关因子法(CF)分别被美国机械工程师学会(ASME)和国际拖曳水池会议(ITTC)采用.近来, Xing 和Stern(2010)提出的安全系数法(FS)也显示出了较好的适用性,正在逐步得到推广应用. 然而,空化流动模拟结果的验证与确认方面的工作却依然较少,如何将验证和确认的方法运用到空化数值计算方面的工作也比较缺失.近来, Long 等 (2017)对空化数值模拟的验证和确认方法进行了初步探索.结果表明, 非定常的空化流动会对验证过程产生较大困难,空化的非定常性增大了模型确认的难度. 他们对基于GCI,CF和FS发展而来的7种不确定度估计方法进行了研究.结果发现改进的安全系数法(FS1)、安全系数法(FS)和网格收敛指数法(GCI)相对其他方法可能更适合运用于基于RANS方法的空化数值模拟不确定度估计.而即便在单相流动中, 大涡模拟的验证和确认依然处于初步摸索阶段(Klein 2005, Freitag & Klein 2006, Tao 2015),空化流动方面的相关工作更是鲜见报道.
验证和确认是系统评估数值模拟结果的基本流程,对提高数值模拟可信度和促进数值模拟方法的进步作用重大,是当前和今后研究者进行空化流动数值模拟研究值得重视和采用的内容.考虑到大涡模拟在空化流动研究中的重要地位,空化流动大涡模拟的验证和确认会是当前和今后一段时间内研究的难点和热点.
4 空化研究几个关键科学问题进展
4.1 附着型空化绕流的演变
附着型空化往往伴随着准周期性的空穴生长、空泡脱落、溃灭等过程,尽管对于不同形状的水翼其具体的空化形态存在着一定的差别,但是其一个典型的演化周期通常均会经历这三个阶段(Huang et al. 2014a,Zhao et al. 2016). 本文以绕Clark-Y水翼的空化演变为例,简要介绍绕水翼附着空化的典型演变过程, 如 图14所示.在该模拟中, 水翼攻角为8$^\circ$, 空化数为0.8. 从 图14可以看到, 在$t=T/8$ $(T$为该空化的发展周期),在水翼前缘处形成透明状附着型空穴, 并处于持续的增长状态,该过程中空穴相对而言比较稳定, 维持着一个较为清晰的汽液交界面;在$t=3T/8$ 时刻, 附着型空穴逐渐覆盖了水翼的整个吸力面,并开始在空穴尾部产生逆时针的空化旋涡,并诱导产生了一股指向水翼导边的反向射流,空穴的尾部受到较大程度的扰动, 汽液交界面被破坏,取而代之的是充满着大量微小气泡的汽液混合物; 在$t=4T/8\sim 7T/8$期间, 反向射流持续向上游运动, 水翼尾部的汽液混合区域逐渐扩大,而透明状的汽相空穴区域则逐渐缩小. 最终, 在$t=T$ 时,反向射流到达空穴前缘附近, 与主流相遇, 两股方向相反的流动相互作用,随即切断了附着空穴并引起大尺度空泡的旋涡脱落.脱落的空化云被主流向下游输运, 并逐渐溃灭. 与此同时,一个新的附着空穴在导边处再次生成并向下游发展, 如此周而复始,构成了附着空化的准周期性行为.
4.2 附着型空化的三维流动特性
空化流动具有高度的三维流动特性. 即使绕流物体为二维结构,其空化绕流也具有显著的三维流动特征, 如U形涡结构等. 但是,在二维水翼中, 空化流动三维结构的产生与发展具有一定的随机性,不便于对其展开研究. 为此, Foeth等 (Foeth et al. 2006, 2008; Foeth 2008) 设计了一种扭曲叶片, 该叶片几何形状较为简单,可诱发典型的三维流动结构( 图15),因而是一种研究空化流动三维特性的理想模型(Cheng et al. 2016, Chen et al. 2017).
Foeth发现除了与平直水翼空化流动中类似的反向射流外,还存在着一种侧向射流( 图16).反向射流的速度分量主要集中于流向,而侧向射流则具有较强的展向速度分量. Foeth等通过实验观察认为,反向射流与主流在导边附近的碰撞是引起空化云大尺度脱落的主要原因.但是由于扭曲水翼的几何结构,附着空化发展至最大长度时其闭合区呈凸出状,而非平直水翼中近似直线的闭合区,这使得反向射流实际上呈现一种向上游径向辐射式的运动.
本课题组的近期研究表明:这种运动形式在一定程度上会削弱反向射流流向上的强度,进而使得其与主流的碰撞可能会非常微弱,在某些情况下不足以切断附着空化, 整个流动也因此较为稳定.除了反向射流外, 侧向射流也会引起当地的空化云脱落.侧向射流在展向上的运动会在附着型空穴的两侧与汽液交界面发生碰撞,并引起相应的空化云脱落. 尽管侧向射流诱发的脱落强度较小,但是其显著改变了空穴的形状, 对空化的演变起着重要的作用.反向射流、侧向射流引起空化脱落的同时,也会对当地旋涡结构产生巨大的影响.随空化云一起脱落的涡结构会在主流的作用下向下游运动,其形状也会发生明显的改变, 最终形成U型涡结构(Peng et al.2016)(亦称为马蹄涡、发卡涡等), 如 图17所示.在此基础上课题组对扭曲水翼的空化流动进行了模拟研究,得到扭曲水翼的空化动态演变过程,并成功捕捉到了反向、侧向射流的动力学行为, 如 图18所示.需要注意的是, 在平直水翼空化绕流中也观察到了该旋涡结构的存在(Wang et al. 2001), 但是其强度、规律性均不如扭曲水翼中的明显.关于该结构的形成机理尚不十分清楚, 本课题组前期(Ji et al.2013)的研究表明该结构的产生与绕脱落空化云的环流存在较大的关系.本课题组的最新研究成果(Long et al.2018)则进一步揭示了其产生及发展机理:该结构的涡量来源主要为附着空穴内部的回流结构,脱离附着型空穴后的旋涡演变的主导因素为绕该旋涡结构的环量引起的升力.
图 17 不同空化数下的U型涡形态 (扭曲NACA16012, $\alpha =0^\circ$,$V_{\infty }=7 $m/s) (
图 18 Delft扭曲水翼空化绕流的一个典型演变周期 (中间: 实验(
4.3 附着型空化的脱落机制
附着型空化往往会具有较强的附着型空穴准周期性脱落行为,并引起流场产生相应的变化, 如速度和压力的低频脉动等.由于附着型空化脱落行为对流场的重大影响,人们对其脱落机理开展了长期的研究. 目前,一般认为附着型空化的脱落机制主要有两种, 即反向射流和激波.早在1955年, Knapp (1955)就发现了空化流动中的反向射流. Kawanami 等(1997) 则通过实验手段证明了反向射流在空化流动中的作用.他们在水翼吸力面放置了一个小障碍物,以阻碍由水翼尾部向水翼导边发展的反向射流, 如 图19所示.实验结果表明, 放置了障碍物后, 反向射流向上游的运动明显受到阻碍,无法运动到水翼导边附近与主流发生碰撞, 进而缓解了空化云的脱落,较大程度上降低了空化的不稳定性. Callenaere 等 (2001)认为反向射流相对于附着型空化厚度的大小在空化不稳定性分析中应当引起足够的注意.Laberteaux和Ceccio (2001)通过对平直水翼NACA0009的空化绕流研究指出,反向射流与汽液交界面的碰撞是引起空化云周期性脱落的主导因素. Foeth(2008)对扭曲水翼的研究表明,具有较强展向速度分量的侧向射流尽管引起的空化云脱落强度较小,但是其对附着型空穴的演变同样起着非常重要的作用.这些研究表明反向射流在空化脱落过程中具有很大的影响(Le et al. 1993,Arndt et al. 2000).
近年来研究者在实验中发现, 空穴断裂及脱落存在另外一种非定常机制,即激波效应(bubbly shock propagation induced shedding). Ganesh 等(2016)等采用高速摄像和$X$射线技术研究了片状空化向云状空化转变规律,在不同工况下, 存在两种非定常流动机制,即以空泡旋涡脱落为特征的回射流机制,和以大尺度空穴结构瞬间溃灭为表现形式的水汽激波机制, 如 图20所示. Reisman 等 (1998) 和Arndt 等 (2006)在研究绕水翼空化脱落机理时, 认为当$\sigma /2\alpha $较小时,在空化区域内的类似间断面的水汽激波是影响附着型空穴断裂及脱落的重要因素.已有的研究初步推断:水汽激波间断面产生于尾部大尺度空泡团的溃灭压力波,当压力波传播到附着型空穴前缘时, 会导致附着型空穴的断裂及空泡脱落.在附着型空穴内部, 其主要流动介质为汽液混合物,其声速显著低于纯水声速(Shamsborhan et al. 2010). 随着空化数的降低,空穴内部的含汽量会增大, 空化流体的声速会显著降低,当空化局部马赫数达到冲击波产生条件时,就会发生以大尺度空穴结构瞬间溃灭为特征的水汽激波机制.在水汽激波机制下,空穴内部可以观察到水汽激波面前后的含汽量有显著差异(Crespo 1969,Noordzij & Wijngaarden 2006), 水汽激波面厚度与空穴厚度相近.水汽激波在推进过程中, 附着型空穴瞬间整体溃灭,空穴的溃灭与脱落形式与回射流机制完全不同, 并且, 空泡溃灭过程中,旋涡结构并不显见. 由此可以推断,不同机制所体现出的质量传输过程是不一样的,对湍流场的影响机制也有显著的差异. 水汽激波在向上游推进过程中,间断面位置处会诱发显著的压力脉动尖峰,这与回射流机制有着本质的不同, 回射流持续向上游推进过程中,空穴始终附着在壁面上, 空穴内部混相介质比较稳定, 壁面压力脉动较小.针对水汽激波机制, 需进一步研究间断面前后瞬态湍流场,以及水汽间断面上、下游含汽量、水汽间断面推进速度以及局部湍流脉动压力之间的关系.
图 20 空化流动中的激波效应(
4.4 空化不稳定性与低频压力脉动
人们除了在实验和数值模拟中发现了附着型空化的非定常行为,还在理论层面对其不稳定性进行了分析. 理论分析表明,空化不稳定性实际上是空化流动的固有性质.
考虑一个固定在流道内部的水翼, 如 图21所示.假设在水翼吸力面存在一个体积为$V_{\rm c}$的空穴,入口体积流量$Q_{\rm in}$与出口压力$P_{\rm out}$为常数,则由连续性方程可知
$$ {Q'} = Q_{\rm {out}} - Q_{\rm {in}} = \dfrac{{\rm d}V_{\rm {cav}} }{{\rm d}t}(18) $$
式中, $Q_{\rm out}$为出口的体积流量, $Q$'为出口平面体积流量的脉动量.在一维简化流动模型中, 流域内各个断面的流动参数可以认为是相同的,则整个流域内的流动可以用一根流线上的流动参数进行描述,即为一维流动. 将该模型引入绕水翼空化流动, 根据动量守恒有
$$ p - p_{\rm {out}} = \dfrac{L}{A} \dfrac{{\rm d}{m'}}{{\rm d}t}(19) $$
式中, $m'$为出口平面的质量流量脉动,$p$为流场中某点的压力, $L$为该点到出口平面的距离,$A$为流道的横截面积. 由式(19)容易得到
$$p = p_{\rm {out}} + \rho _{\rm l} \dfrac{L}{A} \dfrac{{\rm d}{Q'}}{{\rm d}t}(20) $$
定义空化阻抗系数$C $ (Brennen & Acosta 1976)
$$ C = - \dfrac{{\rm d}V_{\rm {cav}} }{{\rm d}p}(21) $$
利用式(20)和式(21), 连续性方程可以写为
$$ {Q'} = \dfrac{{\rm d}V_{\rm {cav}} }{{\rm d}t} = \dfrac{{\rm d}V_{\rm {cav}} }{{\rm d}p} \dfrac{{\rm d}p}{{\rm d}t} = - \rho _{\rm l} C\dfrac{L}{A} \dfrac{{\rm d}^2{Q'}}{{\rm d}t^2}(22) $$
式(22)可以进一步写为
$$ \dfrac{{\rm d}^2{Q'}}{{\rm d}t^2} + \dfrac{A}{\rho _{\rm l} CL}{Q'} = 0(23)$$
式(23)解析解的类型取决于$C$的正负. 当$C>0$时,该式$Q$'的解会出现周期性的振荡, 其频率为
$$ \omega = \sqrt {\dfrac{A}{\rho _{\rm l} CL}}(24)$$
当$C<0$时, 式(23)的解析解会呈现指数型的增长, 这与实验观测是不符的.事实上, 对于空化流动而言, $C$一般均为正值(Franc & Michel 2005).这表明对于空化流动而言, 其本身便存在一个内在的不稳定性.以上这些理论推导在实验中已经得到了较好的验证(Tsujimoto 2007, Chen et al. 2008). 联合式(18)和式(20)可得(Ji et al. 2015)
$$ p = p_{\rm {out}} + \rho _{\rm l} \dfrac{L}{A} \dfrac{{\rm d}^2V_{\rm {cav}} }{{\rm d}t^2}(25) $$
式(25)表明空化流动中的低频压力脉动与空化体积对时间的二阶导数呈正比,揭示了空化流动中低频压力脉动的产生根源.这不但将空化状态与空化激振力的关系进行了定量描述,更为工程中控制空化激振力提供了新的思路,即控制空化体积对时间的二阶导即可, 并不需要严格要求处于无空化流动.该理论预测的结果与数值模拟结果吻合得很好, 如 图22所示,充分证明了该理论的正确性与适用性(Long et al. 2017)
4.5 空化--旋涡交互作用
附着型空化的周期性脱落与不稳定流动行为,不但会引起空化云形态的剧烈变化,还会显著增强当地的涡量分布,对旋涡结构的演变产生明显的影响.Ji 等 (2014) 为了进一步探究空化--旋涡作用,将密度可变的涡量输运方程引入空化流动的分析中
$$ \dfrac{{\rm d}\pmb \omega }{{\rm d}t} = (\pmb \omega \cdot \nabla )\pmb V - \pmb \omega (\nabla \cdot \pmb V ) + \dfrac{\nabla \rho _{\rm m} \times \nabla p}{\rho _{\rm m}^2 } + \dfrac{1}{Re}(\nabla ^2\pmb \omega )(26)$$
式中, $\pmb \omega $为涡量, $\pmb V $为速度矢量.方程左边表示涡量的变化率,右边四项分别为旋涡的拉伸扭曲项、膨胀收缩项、斜压矩项以及黏性耗散项.拉伸扭曲项表征的是由于速度梯度引起旋涡结构的拉伸与变形,膨胀收缩项反映的是流体微团膨胀或收缩对涡量的影响,斜压矩项主要由压力与速度梯度的不平行引起.黏性耗散项指的是由于流体黏性涡量会逐渐耗散. 需要注意的是,黏性耗散项与前三项相比很小, 可以忽略,因而在后续的讨论中没有考虑该项. 如 图23所示, Ji 等(2014)的研究表明, 在整个空化的演化过程中,拉伸扭曲项在片状空化尾部及云空化内部处于绝对主导地位.该项可以视为角动量守恒定理的体现(Wu et al. 2006),旋涡结构的扭曲变形会使得处于同一条流线上质点的动量较小、角动量增加,进而促进了涡量的生成. 对于密度不可变的流体而言,膨胀收缩项与斜压矩项对涡量基本没有影响. 但是在空化流动中,这两项对空化流动中旋涡的演化的作用不可忽略,其大小可以增长至扭曲项同一量级. 在空化流动中,蒸汽体积分数的输运方程可以表述为
$$ \dfrac{{\rm d}\alpha _{\rm v} }{{\rm d}t} = \dfrac{\partial \alpha _{\rm v} }{\partial t} + \left( {\pmb V \cdot \nabla } \right)\alpha _{\rm v} = \dfrac{\rho }{\rho _{\rm l} - \rho _{\rm v} }\nabla \cdot \pmb V(27)$$
图 23 Delft扭曲水翼空化绕流某个时刻的空化云形态及$Z=0.2C$平面上涡量输运方程各项的分布情况(
$$ \dot {m} = \dfrac{\rho _{\rm l} \rho _{\rm v} }{\rho _{\rm l} - \rho _{\rm v} }\nabla \cdot \pmb V(28)$$
由上式易得
式中$\dot { m}$为相间质量传输速度. 由该式可知,膨胀收缩项与相间质量输运速度呈正比,这意味着在空化流动中膨胀收缩项是一个非常重要的涡量来源.尽管斜压矩项的大小不如膨胀项, 但其影响同样不可忽略. 在空化流动中,混合物密度梯度与压力梯度并不总是相互平行(Laberteaux & Ceccio 2001), 这也会引起流场中涡量的增加. 实际上,实验观测与数值计算均表明, 斜压矩项主要集中于空化云的溃灭区,可能是云空化溃灭阶段主要的涡量来源.
4.6 附着型空化与弹性水翼的相互作用
随着人们对水力机械、船舶推进器等要求的日益提高,传统金属材料因重量大、阻尼性能较差等原因引起的振动、噪声和疲劳寿命等问题逐渐凸显.轻薄的弹性材料以及复合材料为解决这些困扰行业发展问题,尤其是振动和噪声, 提供了全新的契机. 但是与此同时,非定常水动力学空化和结构弹性变形之间的相互作用也更加复杂,其非定常性也表现出了明显的不同, 这对研究人员提出了更大的挑战.Ducoin等(Ducoin et al. 2009, 2010,2012)综合利用实验和数值模拟技术对聚甲醛(POM)材质的弹性水翼开展了系统的研究,并对其水弹性响应进行深入分析. 他们的工作表明,对于无空化的弹性水翼绕流问题,计算结构动力学(CSD)与计算流体动力学(CFD)的耦合算法可以很好地预测弹性水翼与流场之间的流固耦合问题.在无空化的弹性水翼绕流问题中,水翼的水动力学性能与水翼的形变具有明显的相关性,其升力系数、阻力系数与形变量紧密相关. 对于弹性水翼的空化绕流,空化会在很大程度上影响弹性水翼的固有振动频率,弹性水翼的振动反过来也会对空化形态产生很大影响.他们还针对弹性水翼空化流动的特点,提出了一个具有2自由度的水弹性响应计算方法, 并对其进行了验证.总体而言,该方法对刚性水翼和弹性水翼的全湿流动和空化流动行为均具有较好的预测.
Wu 等 (2015)发现, 与无空化流动相比, 空化会增强水翼的弯曲变形,并且会对水翼的水弹性响应产生明显的影响. 与刚性水翼相比,空泡、旋涡的脱落频率均会增大. 此外, 在弹性水翼空化绕流中,其升力系数及阻力系数的脉动更加剧烈,水弹性响应也呈现出高度的混沌性. Wu 等 (2015)认为,弹性水翼的空化绕流演变可以分为3个阶段: (1)附着型空穴的发展阶段,空穴逐渐向下游发展, 升阻力均在上升, 与刚性水翼绕流相比,弹性水翼形成的附着空穴长度更长, 覆盖区域更大,这主要是由于水翼变形攻角增大引起; (2)旋涡相互作用与空化脱落阶段,由于水翼的变形, 其水动力学性能参数产生了明显的脉动,并引起了更为复杂的空化形态; (3)残余空化脱落与新附着空穴生成阶段,残余的空穴将会彻底脱落, 并与初次脱落的空穴产生强烈的交互作用,形成一对反向的旋涡结构, 并引起水翼负载的急剧下降. 在此过程中,新的附着空穴在水翼导边附近生成, 并逐渐生长, 如此循环, 如 图24所示.
图 24 刚性水翼和弹性水翼空化绕流的一个典型演变周期 (
4.7 附着型空化对尾流场的影响
附着型空化的准周期性脱落行为不但会明显改变当地的流动结构,在其下游的尾流区也必然会引起强烈的速度与压力脉动(Hart 1993).顾巍等 (2001) 采用LDV对水翼空化尾流场的速度脉动进行了测量,并运用子波函数对其进行了分析,发现了尾流场脉动速度中特征频率的间歇性和特征相干子结构. Arndt 等(2006)利用TR-PIV对NACA0015水翼的空化尾流结构进行测量,发现大量的三维旋涡结构, 如 图25所示.
图 25 水翼空化尾流场结构观测 (
黄彪 (2012)应用DPIV等实验技术对绕Clark-Y水翼的尾流流场结构,包括速度场、湍流强度以及涡量场, 见 图26 $\sim $ 图 28.研究表明, 与无空化流动相比, 附着型空化会明显增加尾流低速区的范围,对其分布也具有一定的影响. 在无空化工况下, 尾流区呈现细长的窄带状,在向下游发展的过程中会逐渐倾向于压力面; 而在空化流动中,在水翼尾部存在大尺度空泡团的旋涡脱落现象,并逐渐向下游运动形成空化尾迹, 低速区域明显增大,时均尾迹角度有向水翼吸力面偏移的趋势. 与此同时,空化云的准周期性脱落现象还会对尾流区域的流动稳定性产生明显的扰动,进而大幅度增强水翼尾缘处的湍流脉动强度及其影响范围.空化云脱落的过程中也会引起当地旋涡结构的改变,使得涡量呈现数量级程度的增长. 进一步的实验数据显示,当没有产生空化时, 在水翼尾缘附近, 分别形成了正反向旋涡区,并向下游延伸成为涡带. 一旦空化发生, 旋涡结构强度得到明显的加强,并且上下涡带随着空化区域的延伸而向后拉长, 作用范围亦逐渐扩大,涡量聚集区由最初的涡带转化为大涡量团的分散分布, 并逐渐向下游耗散.附着型空化准周期性的大尺度空泡团脱落现象也加速了水翼尾部流场的动量交换.
图 26 水翼尾缘处沿主流方向上的时均速度分布 $(\alpha =8^\circ$, $ Re=7.0\times 10^{5})$. (a)无空化, (b)空化
图 27 水翼尾缘处的时均湍流脉动强度分布 $(\alpha =8^\circ$, $Re=7.0\times 10^{5})$. (a)无空化, (b)空化
4.8 其他类型空化流动的相关研究
附着型空化作为一种最贴近工程实践的空化流动,在水力机械运行过程中十分常见,相关的进展可以产生直接的工程应用价值,因而前文以附着型空化为主梳理了近年来空化领域的相关进展.但是应当注意的是, 各种类型的空化其背后的流动机理都是相同或相似的,在实际流动中各种类型的空化也经常同时出现. 在水翼的空化绕流问题中,随着空化数的降低,会依次经历初生空化、片空化、云空化、超空化等阶段(Wang et al.2001). 初生空化受到诸多因素的影响(Arndt & Ippen 1968, Morch 2015, Zhang et al. 2015), 其中水质是其中的关键影响因素之一,因此能够对水质进行控制的水洞,如中国船舶科学研究中心颜开、彭晓星研究员等建立的小型多功能实验水洞,是初生空化研究中非常重要的实验平台.初生空化通常伴随着噪声水平的大幅度提高(Arakeri 1979),这对舰船的隐身性能提出了重大挑战,如何对其进行准确预报及控制也是研究的重点(Cangioli & Manfrida 1997, Song et al. 2017).
云空化通常被认为是附着型空化失稳脱落而来, 由于测量技术的限制,其内部结构尚不清楚. Coutier-Delgosha 等 (2006)利用内窥镜观测了云空化内部形态, 发现其内部气泡并不呈球形,分布也并不均匀, 见 图29. 云空化与空蚀密切相关(De & Hammitt 1982), 但是其作用机理尚不清楚. 不过,最近空化数值模拟方面的进步使得对空蚀进行数值预报已经成为可能(Bensow& Bark 2010), 这将会大大促进空蚀方面的研究.
此外, 梢涡空化作为在螺旋桨绕流中最先出现的一类空化,也引起了研究者的诸多关注(Young & Kinnas 2003, Lu et al. 2014).而随着各国对喷水推进泵的重视, 间隙空化流动, 作为其内部的典型流动,也已经迅速成为研究的热点问题(Higashi et al. 2002, Peng et al.2017). Dreyer 等 (2014)针对水翼间隙空化流动开展了一系列的实验研究,细致测量了其速度、压力、涡量等分布, 获得了大量的珍贵实验数据,已经成为很多相关数值计算结果的验证基准.
这些研究成果, 连同附着型空化的相关研究,极大地促进了人们对于空化的认识与理解.
5 总结与展望
本文以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等为对象,较为系统地回顾了近年来空化水动力学非定常特性研究方面的进展及尚存在的问题.
(1) 由于当前对于空化的认识尚不全面, 空化的分类也比较混乱.附着型空化绕流具有明显的准周期性,会经历空化初生、发展、脱落、溃灭等阶段.附着型空化在工程应用中最为常见, 其流动机理尚存在诸多问题,因而在今后的空化研究中应当继续引起重视.
(2) 实验技术的发展, 包括空化实验平台及各类空化流场测量技术等,大大促进了人们对空化流动机理的认识. 可以控制水质的水洞在空化,尤其是初生空化的研究中将发挥重要的作用.SHPB发射系统是一种较为理想的水下高速航行体空化绕流的实验平台.如何在测量空泡区压力脉动的同时尽可能保护压力传感器不被损坏依然是空化实验中一个急需解决的问题;PIV/PLIF同时获得空化区域内外的流场信息,在今后的实验研究方面应当得到重视与发展; 此外,蒸汽分布的测定对分析空化内部结构具有重要意义,以X射线密度测量系统为代表的蒸汽分布测量方法将极大便利对空化内部流动结构的辨识与分析.
(3) 数值模型, 包括空化模型和湍流模型的发展,对空化流动的数值研究具有重要的作用. 目前而言,对于传统的基于质量输运方程的空化模型而言,如何选取合适的源项是决定该模型模拟精度的关键.如何在空化模型中考虑空化行为的多尺度性、群泡效应、可压缩性,应当是今后空化模型的重要方向. 湍流模型方面, 对于工程问题,寻求一个既对计算资源消耗较小、又能满足空化流动计算精度要求的湍流模式依然是今后的重点,分域与桥接两种模式为适用于工程应用的湍流模型发展提供了大致的方向;对于空化机理研究, 随着计算机性能的不断提高, LES的优势逐渐得到突显,但网格对计算结果的影响(如求解尺度是否达到了惯性子区、网格的验证和确认等)还需仔细校验.基于密度基的求解器在高速空气动力学中已发展较为成熟,特别是高速空气动力学中激波的捕捉方法,可为水动力学空化提供很多借鉴,为此今后开发基于密度基的空化流动求解器也是一个发展方向.
(4) 附着型空化流动的机理研究取得了较大的进展.附着型空化流动行为的定性描述已经较为完善,典型三维流动结构如U形涡等的产生与发展机理也取得了较大的进步,这促进了人们对于空化流动演化的认识. 此外,空化流动的不稳定性与低频压力脉动方面的进展对于工程实践也有着重要的指导意义.
(5) 附着型空化的脱落机制也取得了重大进展, 即反向射流和激波效应.反向射流的作用很早就在实验和数值模拟中被观察到,对其流动行为的分析也比较全面.但是激波现象直到最近才在实验中得到证实,对其认识尚缺乏足够的实验数据与分析. 现有的研究表明,激波效应在空化数较低的流动中影响较大.这意味着对于低空化数流动的数值模拟准确性应当提高警惕,也对数值模拟提出了新的要求, 即如何在空化流动模拟中捕捉激波现象.
(6) 空化与漩涡的相互影响机理仍不明确. 空化与旋涡的相互作用,应当成为今后空化分析中需要关注的重点;弹性水翼在水力机械中的应用或许是解决水力机械、船舶推进器等目前发展困境的一个方向,但是绕弹性水翼空化流动的行为也更加复杂,其中的流固耦合问题会对空化云及水翼自身产生较大的影响,在今后的研究中将会是一个热点与难点问题.附着型空化也会对尾流场产生较大的影响, 当予以足够的重视.
(7) 其他空化相关方面的研究也取得了很多成果.云空化的内部结构及其与空蚀之间的联系依然是一个尚未解决的难题;梢涡空化及间隙空化因其极强的工程应用背景与复杂的流动机理,在后续的研究中将会受到大量的关注.
致 谢 衷心感谢清华大学吴玉林教授、北京理工大学王国玉教授、中国船舶科学研究中心潘森森研究员、美国明尼苏达大学Roger E.A. Arndt教授在本论文研究和撰写过程中给予的指导和帮助.
The authors have declared that no competing interests exist.
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绕水翼空化流动及振动特性的实验研究 .
Cavitation is a kind of complex and unsteady hydrodynamics phenomenon occurred in hydraulic machinery. The cavity shedding leads to structure vibration which a ects the e ciency, noise and safety of hydraulic machinery, so it is important to study the structure vibration in cavitating flow. The characteristics of the cavity shape around a NACA66 hydrofoil and the vibration response are analyzed experimentally. A high-speed video camera is used to visualize the unsteady cavitating flow patterns and a laser doppler vibration meter is used to measure the vibration velocity. The highspeed video camera and the laser doppler vibration meter can be triggered synchronously by a synchronization system. The characteristics of cavity shape and vibration in di erent cavitation stages are analyzed both in time field and frequency field. Synchronous results of cloud cavitation are studied. It is found that as the cavitation number decreases, four stages of cavitation are visualized in which are non-cavitation, cavitation inception, sheet cavitation and cloud cavitation. The vibration amplitude of the hydrofoil increases as the cavitation number decreases. Cavities shedding leads to vibrations whose dominant frequencies are same with the frequencies of cavities shedding at sheet cavitation and cloud cavitation stages. At the cloud cavitation stage, the vibration is high-frequency and low-amplitude when the attached cavity develops. At the stages of cavity pulsation and cavity shedding, the vibration is low-frequency and high-amplitude.
Experimental investigationof the vibration characteristics of hydrofoil in cavitating flow .
Cavitation is a kind of complex and unsteady hydrodynamics phenomenon occurred in hydraulic machinery. The cavity shedding leads to structure vibration which a ects the e ciency, noise and safety of hydraulic machinery, so it is important to study the structure vibration in cavitating flow. The characteristics of the cavity shape around a NACA66 hydrofoil and the vibration response are analyzed experimentally. A high-speed video camera is used to visualize the unsteady cavitating flow patterns and a laser doppler vibration meter is used to measure the vibration velocity. The highspeed video camera and the laser doppler vibration meter can be triggered synchronously by a synchronization system. The characteristics of cavity shape and vibration in di erent cavitation stages are analyzed both in time field and frequency field. Synchronous results of cloud cavitation are studied. It is found that as the cavitation number decreases, four stages of cavitation are visualized in which are non-cavitation, cavitation inception, sheet cavitation and cloud cavitation. The vibration amplitude of the hydrofoil increases as the cavitation number decreases. Cavities shedding leads to vibrations whose dominant frequencies are same with the frequencies of cavities shedding at sheet cavitation and cloud cavitation stages. At the cloud cavitation stage, the vibration is high-frequency and low-amplitude when the attached cavity develops. At the stages of cavity pulsation and cavity shedding, the vibration is low-frequency and high-amplitude.
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| [4] |
空泡尾流场中的速度脉动与子波分析 .
空泡流在特定的条件下会发生强烈的周期性振荡，并由此在尾流场中产生大规模的空泡云脱落，在整个脱落过程中激发了多种尺度涡结构的形成和发展，直接对空泡尾流速度场产生了极大的影响，在试验中采用激光测速的方法记录了空泡尾流场中的脉动速度，并利用子波变换对时域和频域双分析的特点发现和分析了其中的特征相干子结构，为频谱分析补充了大量时域的信息。
Velocity fluctuation inthe cavitating wake and its wavelet analysis .
空泡流在特定的条件下会发生强烈的周期性振荡，并由此在尾流场中产生大规模的空泡云脱落，在整个脱落过程中激发了多种尺度涡结构的形成和发展，直接对空泡尾流速度场产生了极大的影响，在试验中采用激光测速的方法记录了空泡尾流场中的脉动速度，并利用子波变换对时域和频域双分析的特点发现和分析了其中的特征相干子结构，为频谱分析补充了大量时域的信息。
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| [5] |
二维空泡流的脉动性态研究 .
采用高速摄影技术对定常来流中ＮＡＣＡ４４１２翼的不稳定的空泡流形态特征进行了水洞试验研究．试验结果揭示了由于空泡形态断裂而产生的低频脉动现象．这一现象在跨空泡流（Ｔｒａｎｓ－ｃａｖｉｔａｔｉｎｇｆｌｏｗ）情况下尤为明显，常使空泡长度和厚度在大幅范围内拟周期地变动，其频率特性比较稳定，有别于空泡末端局部泡团脱落而产生的脉动
A study onpulsation of two-dimentional cavitation flow .
采用高速摄影技术对定常来流中ＮＡＣＡ４４１２翼的不稳定的空泡流形态特征进行了水洞试验研究．试验结果揭示了由于空泡形态断裂而产生的低频脉动现象．这一现象在跨空泡流（Ｔｒａｎｓ－ｃａｖｉｔａｔｉｎｇｆｌｏｗ）情况下尤为明显，常使空泡长度和厚度在大幅范围内拟周期地变动，其频率特性比较稳定，有别于空泡末端局部泡团脱落而产生的脉动
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| [6] |
非定常空化流动机理及数值计算模型研究.[博士论文] .Physical andnumerical investigation of unsteady cavitating flows. [PhDThesis] . |
| [7] |
空蚀研究现状 .Some recent advances in cavitation damage research . |
| [8] |
``十一五''水动力学发展规划的建议 .
水动力学是流体力学的一个重要分支,有着悠久的研究与发展历史,形成了比较完整的学科体系.进入21世纪以来,资源开发、环境保护、国家安全已成为世界各 国普遍关注的战略问题.我国的海防建设、海洋资源开发与海洋空间利用、海岸带综合规划和水环境保护、水资源开发与利用等为水动力学研究提出了新的迫切需 求.本文阐述了水动力学研究的国家需求、国内外水动力学研究的现状和发展趋势,提出了近期有待研究的主要科学问题.
Suggestion on the researchframe programme on hydrodynamics for the eleventh five year plan .
水动力学是流体力学的一个重要分支,有着悠久的研究与发展历史,形成了比较完整的学科体系.进入21世纪以来,资源开发、环境保护、国家安全已成为世界各 国普遍关注的战略问题.我国的海防建设、海洋资源开发与海洋空间利用、海岸带综合规划和水环境保护、水资源开发与利用等为水动力学研究提出了新的迫切需 求.本文阐述了水动力学研究的国家需求、国内外水动力学研究的现状和发展趋势,提出了近期有待研究的主要科学问题.
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| [9] |
空化机理的近代研究 .
正 一、引言 人们对于空化问题的认识和探讨已有近百年的历史。上世纪末勇敢号鱼雷艇推进器出事以后,Barnaby首先注意到空化问题的严重性。在这以后,不仅在船用螺旋桨上,而且在水轮机、离心泵、流量计、控制阀、水下通讯设备、水下武器等凡是液体和物体之间存在着相对高速运动的场合,都发现空化现象所带来的严重影响。这些影响可能是动力特性的改变和工件效率的损失,或是噪音的增加和材料的剥蚀,或是部件严重的振动,等等。因而从很早的时候起,
Modern research of cavitation mechanism .
正 一、引言 人们对于空化问题的认识和探讨已有近百年的历史。上世纪末勇敢号鱼雷艇推进器出事以后,Barnaby首先注意到空化问题的严重性。在这以后,不仅在船用螺旋桨上,而且在水轮机、离心泵、流量计、控制阀、水下通讯设备、水下武器等凡是液体和物体之间存在着相对高速运动的场合,都发现空化现象所带来的严重影响。这些影响可能是动力特性的改变和工件效率的损失,或是噪音的增加和材料的剥蚀,或是部件严重的振动,等等。因而从很早的时候起,
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| [10] |
空化核最新研究评述 .
正 大家知道,空化核的存在是液体空化的内因,压力场的作用是液体空化的外因,二者同为近10多年来空化研究领域中最活跃的两个方面,80年代以前的工作已有专文作了总结,本文将主要评述1980—1984年空化核研究的动态与成果,包括核的模型、核的测量、核的相似、核的播种、核的作用等,所有现有的核模型都没有跳出寻找游离气体在液体中稳定存在的机构的框子,无法克服“气核悖理”,核测量上的主要困难,是如何既正确又简便地
Critical review on cavitation nucleiresearch .
正 大家知道,空化核的存在是液体空化的内因,压力场的作用是液体空化的外因,二者同为近10多年来空化研究领域中最活跃的两个方面,80年代以前的工作已有专文作了总结,本文将主要评述1980—1984年空化核研究的动态与成果,包括核的模型、核的测量、核的相似、核的播种、核的作用等,所有现有的核模型都没有跳出寻找游离气体在液体中稳定存在的机构的框子,无法克服“气核悖理”,核测量上的主要困难,是如何既正确又简便地
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| [11] |
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| [12] |
绕栅中水翼空化流动的数值和实验研究 .
The unsteady dynamics of cavitating flows around ahydrofoil and in a cascade hydrofoil are investigated by numerical andexperimental methods. Experiments around a hydrofoil and on a cascadehydrofoil are carried out in a rectangular test section of a cavitationtunnel锛宎nd the lift and drag force are conducted and the frequencycharacteristics of lift signals are analyzed. The cavitation model incalculation is Kubota model which can describe the unsteady vortexcavitation accurately; the filter-based turbulence model can capture theunsteady characteristics in the flow more exactly; the reliability of thenumerical model is validated by the experiment of the cavitation tunnel. Theresults show that a good agreement is obtained between the experimental dataand the numerical simulation results. Compared the results around ahydrofoil, the cavitation thickness about the cascade hydrofoil is thinner;the adverse pressure gradient near the wall of the cascade hydrofoil issmaller; the intensity of the re-entrant jet and the velocity gradient inthe mixing field are smaller and the shedding time is longer.
The structure analysis aboutthe cavitation flow around the cascade hydrofoil by numerical andexperimental study .
The unsteady dynamics of cavitating flows around ahydrofoil and in a cascade hydrofoil are investigated by numerical andexperimental methods. Experiments around a hydrofoil and on a cascadehydrofoil are carried out in a rectangular test section of a cavitationtunnel锛宎nd the lift and drag force are conducted and the frequencycharacteristics of lift signals are analyzed. The cavitation model incalculation is Kubota model which can describe the unsteady vortexcavitation accurately; the filter-based turbulence model can capture theunsteady characteristics in the flow more exactly; the reliability of thenumerical model is validated by the experiment of the cavitation tunnel. Theresults show that a good agreement is obtained between the experimental dataand the numerical simulation results. Compared the results around ahydrofoil, the cavitation thickness about the cascade hydrofoil is thinner;the adverse pressure gradient near the wall of the cascade hydrofoil issmaller; the intensity of the re-entrant jet and the velocity gradient inthe mixing field are smaller and the shedding time is longer.
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| [13] |
一种修正的低温流体空化流动计算模型 .
In order to predict the cavitating flow characteristics in cryogenic fluids more exactly, a revised cavitation model considering the thermal effect with modified the evaporation and condensation source terms is established, which is based on Kubota cavitation model. The computations for cavitating flows in liquid nitrogen are conducted around an axisymmetric ogive by employing Kubota cavitation model and the revised cavitation model, respectively. The computational results are compared with the experimental data to evaluate the revised cavitation model. It is found that for the results of the revised cavitation model due to considering the thermal effects, the evaporation becomes smaller and the condensation becomes larger, the cavity length is shorter and the cavity interface becomes more porous compared with the results of original Kubota model. The results of the revised cavitation model are more accordant with the experimental data, and it dictates that the revised cavitation model can describe the process of mass transport more accurately in the cavitation process in cryogenic fluids and it is applicable for computations of cavitating flows in cryogenic fluids flow.
A modifiedkubota cavitation model for computations of cryogenic cavitatingflows .
In order to predict the cavitating flow characteristics in cryogenic fluids more exactly, a revised cavitation model considering the thermal effect with modified the evaporation and condensation source terms is established, which is based on Kubota cavitation model. The computations for cavitating flows in liquid nitrogen are conducted around an axisymmetric ogive by employing Kubota cavitation model and the revised cavitation model, respectively. The computational results are compared with the experimental data to evaluate the revised cavitation model. It is found that for the results of the revised cavitation model due to considering the thermal effects, the evaporation becomes smaller and the condensation becomes larger, the cavity length is shorter and the cavity interface becomes more porous compared with the results of original Kubota model. The results of the revised cavitation model are more accordant with the experimental data, and it dictates that the revised cavitation model can describe the process of mass transport more accurately in the cavitation process in cryogenic fluids and it is applicable for computations of cavitating flows in cryogenic fluids flow.
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| [14] |
基于滤波器湍流模型的水翼空化数值模拟 .
采用界面捕获法,在均相流模型假设下,引入滤波函数修正了RNG k-ε湍流模型,基于正压流体假设的状态方程空化模型.采用SMPLEC算法,数值求解雷诺平均的Navier-Stokes方程,模拟了二维 NACA66(Mod)翼型的定常、非定常空化流动.计算得到的翼型表面压力分布与试验结果基本一致,较好地模拟了非定常空化云的初生、发展、断裂和脱落 的周期性过程,非定常流动的斯特劳哈数与试验结果相吻合.给出了2个时刻的翼型表面速度矢量场,分析了空泡内部流动结构,结果发现翼型空泡尾部的反向射流 是引起翼型表面局部压力升高,进而导致空泡发生断裂及空化云脱落的重要原因.
Numerical simulation of hydrofoil cavitation based on filter-basedmodel .
采用界面捕获法,在均相流模型假设下,引入滤波函数修正了RNG k-ε湍流模型,基于正压流体假设的状态方程空化模型.采用SMPLEC算法,数值求解雷诺平均的Navier-Stokes方程,模拟了二维 NACA66(Mod)翼型的定常、非定常空化流动.计算得到的翼型表面压力分布与试验结果基本一致,较好地模拟了非定常空化云的初生、发展、断裂和脱落 的周期性过程,非定常流动的斯特劳哈数与试验结果相吻合.给出了2个时刻的翼型表面速度矢量场,分析了空泡内部流动结构,结果发现翼型空泡尾部的反向射流 是引起翼型表面局部压力升高,进而导致空泡发生断裂及空化云脱落的重要原因.
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| [15] |
流体机械旋转湍流计算模型研究进展 .
旋转湍流是泵、水轮机、风力机和压缩机等流体机械中的典型流动现象,其三维随机脉动特性很强,具有逆压梯度高、流线曲率大、壁面影响突出等特点。目前存在多种湍流模型,但都有各自的适用范围,尚不存在一个通用的湍流模型。现有湍流模型在物理和数值方面的预测性能还未达到流体机械实际需求。针对强旋转和大曲率流动,本文阐述了湍流模型的发展。从湍流核心区的高雷诺数流动、近壁区低雷诺数流动和层流到湍流的转捩流动等不同方面,分析了现有湍流模型在流体机械中的适用性。指出了典型湍流模型在求解旋转湍流时存在的问题,探索了针对不同求解目标引用不同湍流模型的有效途径和方法,对湍流模型的发展趋势及湍流模型在流体机械中的应用进行了展望。
Research progress ofcomputational model for rotating turbulent flow in fluidmachinery .
旋转湍流是泵、水轮机、风力机和压缩机等流体机械中的典型流动现象,其三维随机脉动特性很强,具有逆压梯度高、流线曲率大、壁面影响突出等特点。目前存在多种湍流模型,但都有各自的适用范围,尚不存在一个通用的湍流模型。现有湍流模型在物理和数值方面的预测性能还未达到流体机械实际需求。针对强旋转和大曲率流动,本文阐述了湍流模型的发展。从湍流核心区的高雷诺数流动、近壁区低雷诺数流动和层流到湍流的转捩流动等不同方面,分析了现有湍流模型在流体机械中的适用性。指出了典型湍流模型在求解旋转湍流时存在的问题,探索了针对不同求解目标引用不同湍流模型的有效途径和方法,对湍流模型的发展趋势及湍流模型在流体机械中的应用进行了展望。
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| [16] |
航行体垂直出水载荷与空泡溃灭机理分析 .
Pressure pulses generated by cavitation collapse when vehicles launching through the free surface will form the key load which decides the strength of structures. Consequently, it is very significant to investigate the mechanism of cavitation evolution and collapse. Firstly, a typical vertical launching process was simulated, and time sequences of pressure distribution gained were verified by experimental results. Through the analysis about flow fields, mechanism for the occurrence and evolution of cavitation collapse was investigated. Furthermore, a physical model of collapse pressure was established, by which influence of important factors such as cavity thickness, thickness of water layer, sound speed were studied. Finally, relative issues about the similarity law of scaled tests and load-reduction measurements were discussed.
Mechanismanalysis about cavitation collapse load of underwater vehicles ina vertical launching process .
Pressure pulses generated by cavitation collapse when vehicles launching through the free surface will form the key load which decides the strength of structures. Consequently, it is very significant to investigate the mechanism of cavitation evolution and collapse. Firstly, a typical vertical launching process was simulated, and time sequences of pressure distribution gained were verified by experimental results. Through the analysis about flow fields, mechanism for the occurrence and evolution of cavitation collapse was investigated. Furthermore, a physical model of collapse pressure was established, by which influence of important factors such as cavity thickness, thickness of water layer, sound speed were studied. Finally, relative issues about the similarity law of scaled tests and load-reduction measurements were discussed.
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| [17] |
水下回转航行体的云状空化回射流运动特征研究 .
该文针对典型的细长回转航行体 的水下航行过程,基于SHPB(霍普金森压杆)发射系统开展了机理性实验。相应基于单一流体/多相混合模型,结合空化模型及修正的RNG k湍流模式对该问题进行了数值模拟。并在实验与数值模拟结果的基础上,研究了回射流诱导的云状空化不稳定性问题,探讨了该现象中空化非稳态演化的物理机 制,分析了空泡末端回射流的产生原因以及它对空泡演化的诱导作用。进一步从压力梯度角度给出了回射流运动的动力学模型和空泡长度的预测表达式,并通过数值 结果验证了该模型和公式的有效性。
Characteristics of the re-entry jet in the cloud cavitatingflow over a submerged axisymmetric projectile .
该文针对典型的细长回转航行体 的水下航行过程,基于SHPB(霍普金森压杆)发射系统开展了机理性实验。相应基于单一流体/多相混合模型,结合空化模型及修正的RNG k湍流模式对该问题进行了数值模拟。并在实验与数值模拟结果的基础上,研究了回射流诱导的云状空化不稳定性问题,探讨了该现象中空化非稳态演化的物理机 制,分析了空泡末端回射流的产生原因以及它对空泡演化的诱导作用。进一步从压力梯度角度给出了回射流运动的动力学模型和空泡长度的预测表达式,并通过数值 结果验证了该模型和公式的有效性。
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| [18] |
高速航行体水下发射水动力学研究进展 .
高速航行体水下发射水动力学研究,是具有重大工程应用背景的前沿基础问题.与之紧密相关的非定常空化流动,特别是空泡稳定性、溃灭等问题,是影响发射载荷及安全性的关键.本文首先简述了这一领域的主要科学问题,归纳了主要控制参数和影响方式;之后针对非定常空化流动问题,综述了已有的实验观测手段及数值模拟方法;总结了空泡发展、稳定性、溃灭及流动控制等重要物理机制、模型及各因素相互作用规律;最后展望了该领域仍存在的主要科学问题与未来发展趋势.
Research progresson hydrodynamics of high speed vehicles in the underwaterlaunching process .
高速航行体水下发射水动力学研究,是具有重大工程应用背景的前沿基础问题.与之紧密相关的非定常空化流动,特别是空泡稳定性、溃灭等问题,是影响发射载荷及安全性的关键.本文首先简述了这一领域的主要科学问题,归纳了主要控制参数和影响方式;之后针对非定常空化流动问题,综述了已有的实验观测手段及数值模拟方法;总结了空泡发展、稳定性、溃灭及流动控制等重要物理机制、模型及各因素相互作用规律;最后展望了该领域仍存在的主要科学问题与未来发展趋势.
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| [19] |
空化水洞总体设计以及相关的几个问题.[硕士论文] .Collectivity designof cavitation tunnel and some relative problems. [Master Thesis] . |
| [20] |
CFD模拟方法的发展成就与展望 .
The achievements of CFD are summarized, especially on computational gasdynamics. The developments on numerical schemes, grid techniques, turbulence modeling, large eddy simulation are addressed. Also, problems as well as development trends in the above aspects are analyzed separately.
On theachievements and prospects for the methods of computational fluiddynamics .
The achievements of CFD are summarized, especially on computational gasdynamics. The developments on numerical schemes, grid techniques, turbulence modeling, large eddy simulation are addressed. Also, problems as well as development trends in the above aspects are analyzed separately.
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| [21] |
轴对称航行体通气云状空化非定常特征研究 .
物体在水下高速运动时会在局部区域产生低压而引起空化流动。在预期的空化区域通入气体是调节和控制空化流动的重要手段。文章基于水下水平发射装置观察了轴对称航行体通气空化的非定常演化现象并进行了相应的数值模拟,分析了演化过程和机制,探讨了通气量等主要参数的影响规律。研究表明,从边界层衍生的二次涡切断主涡涡面使尾部主涡脱离是空泡脱落的主要原因;此外,随着通气量的增加,空泡长度和厚度有所增加,脱落位置逐步后移。
Unsteady characteristicsof ventilated cloud cavity around symmetrical bodies .
物体在水下高速运动时会在局部区域产生低压而引起空化流动。在预期的空化区域通入气体是调节和控制空化流动的重要手段。文章基于水下水平发射装置观察了轴对称航行体通气空化的非定常演化现象并进行了相应的数值模拟,分析了演化过程和机制,探讨了通气量等主要参数的影响规律。研究表明,从边界层衍生的二次涡切断主涡涡面使尾部主涡脱离是空泡脱落的主要原因;此外,随着通气量的增加,空泡长度和厚度有所增加,脱落位置逐步后移。
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| [22] |
云状空化非定常脱落机理的数值与实验研究 .
The unsteady characterics of cloud cavitating flow arounda hydrofoil are investigated by the experimental and numerical methods.Experiments on a hydrofoils are carried out in a rectangular test section ofa cavitation tunnel. A high-speed video camera is used to visualize theunsteady flow structures. The caculations are conducted on thetwo-dimensional hydrofoil section, based on a single-fluid model of thecavitation: the liquid/vapor mixture is considered as a homogeneous fluidwhose compsition is regulated by mass tranfer equation. The RNG$k$-$\varepsilon $ turbulence model with modified eddy viscosity coefficient isused in the computation, and the coefficient is related to the vapor andliquid densities in cavitated regions for simulating the cavitating flow.The experimental and numerical results show the unsteady features of theperidical cloud cavity departure; the increasing of a local pressure is amain factor to induce ruture of a cloud cavity; an interaction between there-entrant jet and the cavity interface in the closure region can lead tothe increasing of the local pressure; the adverse pressure gradient ismainly responsible for the generation of the re-entrant jet.
Numerical andexperimental studies on unsteady shedding mechanisms of cloudcavitation .
The unsteady characterics of cloud cavitating flow arounda hydrofoil are investigated by the experimental and numerical methods.Experiments on a hydrofoils are carried out in a rectangular test section ofa cavitation tunnel. A high-speed video camera is used to visualize theunsteady flow structures. The caculations are conducted on thetwo-dimensional hydrofoil section, based on a single-fluid model of thecavitation: the liquid/vapor mixture is considered as a homogeneous fluidwhose compsition is regulated by mass tranfer equation. The RNG$k$-$\varepsilon $ turbulence model with modified eddy viscosity coefficient isused in the computation, and the coefficient is related to the vapor andliquid densities in cavitated regions for simulating the cavitating flow.The experimental and numerical results show the unsteady features of theperidical cloud cavity departure; the increasing of a local pressure is amain factor to induce ruture of a cloud cavity; an interaction between there-entrant jet and the cavity interface in the closure region can lead tothe increasing of the local pressure; the adverse pressure gradient ismainly responsible for the generation of the re-entrant jet.
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| [23] |
多泡相互作用对气泡溃灭的影响 .
空化常见于许多涉及液体的设备中。空化具有丰富的、多层次的非稳态特性,如片空化会有规律的低频振荡(脱落),形成云雾状的云空化;而云空化在新的压力环境下会迅速溃灭,导致高频噪声、高压冲击等。目前的研究表明,空化的这类高频特性与细观的气泡溃灭特别是泡群的耦合运动有关。对于单泡溃灭,其在自由流场或近壁面的运动特性已研究的比较充分,然而泡-泡耦合作用下的气泡溃灭过程比较复杂,涉及到气泡扭曲变形、局部射流以及压力传递等,其表现出来的整体特性还不十分清楚。本文对多泡流场中的气泡溃灭过程进行了直接数值模拟。气泡界面通过VOF方法进行捕捉,气泡内为可压缩理想气体,气泡的初始运动由气液间的压差驱动。研究着重于关注受周围气泡影响的中心气泡运动规律,研究结果表明:(1)与自由流场中的单泡溃灭相比,多泡中的中心气泡溃灭存在明显的延迟现象。周围气泡的增多或气泡间距的缩小,会增强中心气泡溃灭的延迟效应。延迟效应的产生主要与周围气泡诱导的压力场有关,当周围气泡首先溃灭时,在其溃灭周期内诱导产生了一个较长时间的负压场。(2)另外,多泡中的中心气泡溃灭时产生的高压峰值也远高于单泡溃灭,其中的机制也与周围气泡诱导的压力场有关,在周围气泡溃灭后期,其诱导的是一个正压场,从而增强了中心气泡周围的压差环境,导致中心泡溃灭产生更高的压力峰值。(3)周围气泡诱导的压力场性质主要与其界面运动的加速度有关,在其溃灭前期的一大段时间内,其诱导的是负压场,在其溃灭后期的一小段时间内,其诱导的是正压场。
Investigation of bubble-bubble interaction effect during thecollapse of multi-bubble system .
空化常见于许多涉及液体的设备中。空化具有丰富的、多层次的非稳态特性,如片空化会有规律的低频振荡(脱落),形成云雾状的云空化;而云空化在新的压力环境下会迅速溃灭,导致高频噪声、高压冲击等。目前的研究表明,空化的这类高频特性与细观的气泡溃灭特别是泡群的耦合运动有关。对于单泡溃灭,其在自由流场或近壁面的运动特性已研究的比较充分,然而泡-泡耦合作用下的气泡溃灭过程比较复杂,涉及到气泡扭曲变形、局部射流以及压力传递等,其表现出来的整体特性还不十分清楚。本文对多泡流场中的气泡溃灭过程进行了直接数值模拟。气泡界面通过VOF方法进行捕捉,气泡内为可压缩理想气体,气泡的初始运动由气液间的压差驱动。研究着重于关注受周围气泡影响的中心气泡运动规律,研究结果表明:(1)与自由流场中的单泡溃灭相比,多泡中的中心气泡溃灭存在明显的延迟现象。周围气泡的增多或气泡间距的缩小,会增强中心气泡溃灭的延迟效应。延迟效应的产生主要与周围气泡诱导的压力场有关,当周围气泡首先溃灭时,在其溃灭周期内诱导产生了一个较长时间的负压场。(2)另外,多泡中的中心气泡溃灭时产生的高压峰值也远高于单泡溃灭,其中的机制也与周围气泡诱导的压力场有关,在周围气泡溃灭后期,其诱导的是一个正压场,从而增强了中心气泡周围的压差环境,导致中心泡溃灭产生更高的压力峰值。(3)周围气泡诱导的压力场性质主要与其界面运动的加速度有关,在其溃灭前期的一大段时间内,其诱导的是负压场,在其溃灭后期的一小段时间内,其诱导的是正压场。
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| [24] |
水下航行体空化流动与压力脉动特性研究.[博士论文] .Study on thecavitating flows and pressure fluctuation for underwater vehicle .[ |
| [25] |
超空泡航行体控制问题研究进展 .
Advances in the studyof control technology of supercavitating vehicles are reviewed.The dynamics charateristics and control methods are analyzed, andtechnical difficulties related to hardware for maneuver control ofsupercavitating vehicles are presented. Finally the futureresearch trends in supercavitating vehicle control technology aresuggested.
Advances in supercavitationvehicle control technology .
Advances in the studyof control technology of supercavitating vehicles are reviewed.The dynamics charateristics and control methods are analyzed, andtechnical difficulties related to hardware for maneuver control ofsupercavitating vehicles are presented. Finally the futureresearch trends in supercavitating vehicle control technology aresuggested.
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| [26] |
非定常空化流动涡旋运动及其流体动力特性 .
=8 at a moderate Reynolds number, Re=7 10, for both noncavitating and sheet/cloud cavitating conditions. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, and the turbulence model utilizes the large eddy simulation (LES) approach with a classical eddy viscosity subgrid-scale turbulence model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The primary frequency, =0.85, of the hydrodynamic fluctuations can be observed for noncavitation. It is induced by the shedding of the vortex structures at the trailing edge of the hydrofoil. The primary frequency, =0.34, of the hydrodynamic fluctuations is induced by the growing up and shedding of the cavity, which can be observed for sheet/cloud cavitation. At the same time, some medium amplitude peaks are observed ranking from =0.5 to =1.5. These are due to the divergence influences from cavitation in different phases. These influences may lead to changes of vortex shedding frequencies at the trailing edge of the hydrofoil.
Study of turbulent vortex and hydraulic dynamics in transientsheet/cloud cavitating flows .
=8 at a moderate Reynolds number, Re=7 10, for both noncavitating and sheet/cloud cavitating conditions. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, and the turbulence model utilizes the large eddy simulation (LES) approach with a classical eddy viscosity subgrid-scale turbulence model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The primary frequency, =0.85, of the hydrodynamic fluctuations can be observed for noncavitation. It is induced by the shedding of the vortex structures at the trailing edge of the hydrofoil. The primary frequency, =0.34, of the hydrodynamic fluctuations is induced by the growing up and shedding of the cavity, which can be observed for sheet/cloud cavitation. At the same time, some medium amplitude peaks are observed ranking from =0.5 to =1.5. These are due to the divergence influences from cavitation in different phases. These influences may lead to changes of vortex shedding frequencies at the trailing edge of the hydrofoil.
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| [27] |
叶顶间隙旋涡空化数值计算模型与流动机理研究.[博士论文] .Numerical andphysical investigation of tip leakage vortex cavitating flows.[PhD Thesis] . |
| [28] |
Statistical properties of particle imagevelocimetry measurements in turbulent flow . |
| [29] |
Cavitation inception//Proceedings of theIndian Academy of Sciences Section C: Engineering Sciences , |
| [30] |
Viscous effects on the position ofcavitation separation from smooth bodies .
Flow visualization by the schlieren technique in the neighbourhood of a fully developed cavity on two axisymmetric headforms has shown the existence of laminar boundary-layer separation upstream of cavitation separation; the distance between the two separations to be strongly dependent on Reynolds number. Based on present results; a semi-empirical method is developed to predict the position of cavitation separation on a smooth body. The method applies only in the Reynolds-number range when the cavitating body possesses laminar boundary-layer separation under non-cavitating conditions. Calculated positions of cavitation separation on a sphere by the method show good agreement with experimentally observed positions.
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| [31] |
Rough surface effects oncavitation inception .
http://FluidsEngineering.asmedigitalcollection.asme.org/article.aspx?articleid=1433733
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| [32] |
Cavitation in fluid machinery andhydraulic structures .
Cavitation and its effects on fluid machinery and hydraulic structures were reviewed with emphasis on the mechanics of inception, the thermodynamic and gaseous diffusion factors on bubble growth, and resulting cavitation. Small amounts of free gas can change the water bulk modulus, with the speed of sound dropping to 15 m/s; this affects pump performance and stability. Most of the cavitation theory was formulated from experimental data which requires analysis of separation and transition to turbulence results; the influence of nuclei size and number density are important, along with the cavitation nuclei appearing in the form of small gas bubbles or solid particles with small quantities of gas.
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| [33] |
Instability of partial cavitation: a numerical/experimentalapproach//Proceedings of the 23rd Symposium on NavalHydrodynamics . |
| [34] |
Cavitation in vortical flows . |
| [35] |
Experimental andnumerical investigation of large scale structures in cavitatingwakes//36th AIAA Fluid Dynamics Conference and Exhibit, SanFrancisco, California . |
| [36] |
Some Remarks on Hydrofoil Cavitation .
This paper reviews numerical and experimental investigations of sheet/cloud cavitation carried out at the St. Anthony Falls Laboratory and at two collaborating facilities (Versuchsanstalt F r Wasserbau, Obernach, Germany and Osaka University, Japan) for more than a decade. Although significant advances have been made in the analysis of this flow several issues are still unresolved. The purpose of this paper is to examine the overall features of the problem, review the progress made to date and suggest avenues for new investigation.
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| [37] |
Anexperimental investigation of cavitation inception and developmenton a two-dimensional Eppler hydrofoil . |
| [38] |
The progressive role ofacoustic cavitation for non-invasive therapies, contrast imagingand blood-tumor permeability enhancement .
Abstract INTRODUCTION: Drug delivery pertaining to acoustic cavitation generated from ultrasonic (US) irradiation is advantageous for devising smarter and more advanced therapeutics. The aim is to showcase microbubbles as drug carriers and robust theranostic for non-invasive therapies across diverse biomedical disciplines, highlighting recent technologies in this field for overcoming the blood-brain barrier (BBB) to treat cancers and neurological disorders. Areas covered: This article reviews work on the optimized tuning of ultrasonic parameters, sonoporation, transdermal and responsive drug delivery, acoustic cavitation in vasculature and oncology, contrast imaging for real-time magnification of cell-microbubble dynamics and biomolecular targeting. Scholarly literature was sought through database search on key terminology, latest topics, reputable experts and established journals over the last five years. Expert opinion: Cavitation offers immense promise in overcoming current diffusion and convection limitations for treating skull/brain/vascular/tissue injuries and ablating tumors to minimize chronic/acute effects. Since stable cavitation facilitates the restoration of US-opened BBB and the modulation of drug concentration, US equipment with programmable imaging modality and sensitivity are envisaged to create safer miniaturized devices for personalized care. Due to differing biomedical protocols with regard to specific medical conditions, quantitative and qualitative controls are mandatory before translation to real-life clinical applications can be accomplished.
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| [39] |
Three-dimensional unsteady cavitation effects on a singlehydrofoil and in a radial pump--measurements and numericalsimulations//Fifth International Symposium on Cavitation . |
| [40] |
Near-wall formulation of the partially averaged Navier Stokesturbulence model .
RT Journal ArticleSR ElectronicID 152582A1 Basara, B.A1 Krajnovic, SinisaA1 Girimaji, S.A1 Pavlovic, Z.T1 Near-Wall Formulation of the Partially Averaged Navier-Stokes Turbulence ModelYR 2011JF Aiaa JournalSN 0001-1452VO 49IS 12SP 2627OP 2636AB The variable-resolution partially averaged Navier-Stokes bridging strategy is applied to the four-equation k-epsilon-zeta-f turbulence model. In this approach, the popular two-equation model is enhanced with an additional transport equation for the velocity scale ratio zeta and an equation for the elliptic relaxation function f for the purpose of improved near-wall behavior. By using the elliptic relaxation technique to model the wall blocking effect, the new four-equation partially averaged Navier-Stokes model retains the simplicity of the previous two-equation partially averaged Navier-Stokes versions but significantly improves predictions in the near-wall region. The proposed partially averaged Navier-Stokes k-epsilon-zeta-f model is evaluated in a turbulent channel flow and flow around a three-dimensional circular cylinder mounted vertically on a flat plate. The results clearly show benefits of the improved near-wall modeling and extend partially averaged Navier-Stokes applicability to a broader range of smooth bluff-body separated flows.LA engDO 10.2514/1.j050967LK http://dx.doi.org/10.2514/1.j050967OL 30
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| [41] |
Interfacingstatistical turbulence closures with large-eddy simulation . |
| [42] |
Implicit LES predictions of thecavitating flow on a propeller . |
| [43] |
Turbulencesimulations of flow past a circular cylinder based on a nonlinearpartially averaged Navier-Stokes (PANS) method .
A nonlinear partially averaged Navieru2013Stokes (PANS) method based on RNG ku2013u03b5 turbulence model is evaluated by a moderately high Reynolds number turbulence flow past a circular cylinder. The ratios of unresolved-to-total kinetic energy (fk) and unresolved-to-total dissipation (fu03b5) for PANS method are sensitive to the simulation result. Simulation results based on different fk are compared with the experimental data. The quantities including mean streamline velocity, mean normal velocity, streamlines, etc. are analyzed. The computational result is reasonable when fk is less than 0.6. The PANS method can be used in the simulation of high Reynolds number turbulence flow.
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| [44] |
The dynamic transfer functionfor a cavitating inducer . |
| [45] |
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| [46] |
PolymericHopkinson Bar-Confinement Chamber Apparatus to Evaluate Fluid Cavitation .
Mild traumatic brain injury associated with blast exposure is an important issue, and cavitation of the cerebrospinal fluid (CSF) has been suggested as a potential injury mechanism; however, physical
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| [47] |
Thecavitation instability induced by the development of a re-entrantjet .
The instability of a partial cavity induced by the development of a re-entrant jet is investigated on the basis of experiments conducted on a diverging step. Detailed visualizations of the cavity behaviour allowed us to identify the domain of the re-entrant jet instability which leads to classical cloud cavitation. The surrounding regimes are also investigated, in particular the special case of thin cavities which do not oscillate in length but surprisingly exhibit a re-entrant jet of periodical behaviour. The velocity of the re-entrant jet is measured from visualizations, in the case of both cloud cavitation and thin cavities. The limits of the domain of the re-entrant jet instability are corroborated by velocity fluctuation measurements. By varying the divergence and the confinement of the channel, it is shown that the extent of the auto-oscillation domain primarily depends upon the average adverse pressure gradient in the channel. This conclusion is corroborated by the determination of the pressure gradient on the basis of LDV measurements which shows a good correlation between the domain of the cloud cavitation instability and the region of high adverse pressure gradient. A simple phenomenological model of the development of the re-entrant jet in an adverse pressure gradient confirms the strong influence of the pressure gradient on the development of the re-entrant jet and particularly on its thickness. An ultrasonic technique is developed to measure the re-entrant jet thickness, which allowed us to compare it with the cavity thickness. By considering an estimate of the characteristic height of the perturbations developing on the interface of the cavity and of the re-entrant jet, it is shown that cloud cavitation requires negligible interaction between both interfaces, i.e. a thick enough cavity. In the case of thin cavities, this interaction becomes predominant; the cavity interface breaks at many points, giving birth to small-scale vapour structures unlike the large-scale clouds which are periodically shed in the case of cloud cavitation. The low-frequency content of the cloud cavitation instability is investigated using spectral analysis of wall pressure signals. It is shown that the characteristic frequency of cloud cavitation corresponds to a Strouhal number of about 0.2 whatever the operating conditions and the cavity length may be, provided the Strouhal number is computed on the basis of the maximum cavity length. For long enough cavities, another peak is observed in the spectra, at lower frequency, which is interpreted as a surge-type instability. The present investigations give insight into the instabilities that a partial cavity may undergo, and particularly the re-entrant jet instability. Two parameters are shown to be of most importance in the analysis of the re-entrant jet instability: the adverse pressure gradient and the cavity thickness compared to the re-entrant jet thickness. The present results allowed us to conduct a qualitative phenomenological analysis of the stability of partial cavities on cavitating hydrofoils. It is conjectured that cloud cavitation should occur for short enough cavities, of the order of half the chordlength, whereas the instability often observed at the limit between partial cavitation and super-cavitation is here interpreted as a cavitation surge-type instability.
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| [48] |
Improvements to acoustictechniques for the detection of cavitation inception . |
| [49] |
Application ofspherical nanoindentation to determine the pressure of cavitationimpacts from pitting tests .
This article focuses on the use of spherical nanoindentation measurements to estimate the pressure of cavitation impacts and its statistical distribution. Indeed, nanoindentation techniques are supposed to represent an effective tool in this field due to the similarities between substrate deformation under liquid impact and indentation testing. First, nanoindentation experiments were used to extract the mechanical parameters of a Nickel–Aluminum–Bronze alloy; second, pitting tests were performed at different operating pressures, and the geometrical characteristics of the pits were measured; and finally, the spectra of impact pressure and loads responsible for material erosion were obtained by coupling the findings of indentation tests with the analysis of pitting tests. Results assessed the capability of the proposed methodology to quantify the hydrodynamic aggressiveness of the cavitating flow. This procedure, which assumes the material itself as a sensor that is able to detect the impact loads, could represent an alternative solution to pressure transducers in estimating the cavitation intensity.
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| [50] |
Friction drag reduction of external flowswith bubble and gas injection .
The lubrication of external liquid flow with a bubbly mixture or gas layer has been the goal of engineers for many years, and this article presents the underlying principles and recent advances of this technology. It reviews the use of partial and supercavities for drag reduction of axisymmetric objects moving within a liquid. Partial cavity flows can also be used to reduce the friction drag on the nominally two-dimensional portions of a horizontal surface, and the basic flow features of two-dimensional cavities are presented. Injection of gas can lead to the creation of a bubbly mixture near the flow surface that can significantly modify the flow within the turbulent boundary layer, and there have been significant advances in the understanding of the underlying physical process of drag reduction. Moreover, with sufficient gas flux, the bubbles flowing beneath a solid surface can coalesce to form a thin drag-reducing air layer. The current applications of these techniques to underwater vehicles and surface ships are discussed.
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| [51] |
One-dimensional analysis of full load drafttube surge .
The effects of acoustic modes in the penstock on the self-excited oscillation in hydraulic power system were studied by assuming a finite sound velocity in the penstock. The flow in the draft tube is considered to be incompressible assuming that the length of the draft tube is smaller than the wavelength of the oscillation. It was found that various acoustic modes in the penstock can become unstable (amplified) by the diffuser effect of the draft tube or the effect of swirl flow from the runner. Their effects on each mode are discussed.
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| [52] |
Numerical investigation of dynamics of unsteady sheet/cloudcavitating flow using a compressible fluid model .
In this paper, a compressible fluid model is proposed to investigate dynamics of the turbulent cavitating flow over a Clark-Y hydrofoil. The numerical simulation is based on the homogeneous mixture approach coupled with filter-based density correction model (FBDCM) turbulence model and Zwart cavitation model. Considering the compressibility effect, the equation of state of each phase is introduced into the numerical model. The results show that the predicted results agree well with experimental data concerning the time-averaged lift/drag coefficient and shedding frequency. The quasi-periodic evolution of sheet/cloud cavitation and the resulting lift and drag are discussed in detail. Especially, the present compressible-mixture numerical model is capable of simulating the shock waves in the final stage of cavity collapse. It is found that the shock waves may cause the transient significant increase and decrease in lift and drag if the cavity collapses near the foil surface.
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| [53] |
Large eddysimulation and investigation on the flow structure of thecascading cavitation shedding regime around 3D twisted hydrofoil .
61Cascading shedding regime of cavitation on 3D hydrofoil is investigated using LES.61Cavity shape evolution and interlaced vortex structure of experiment were computed.61Interaction of re-entrant and side-entrant jets causes convex and cascading cavity.61Double peaks of lift or drag are caused by cavity break-up and ultimate collapse.61Relation of cavity size change and pressure disturbance is analytically clarified.
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| [54] |
Numericalinvestigation of unsteady cavitating turbulent flows aroundtwisted hydrofoil from the Lagrangian viewpoint .
Unsteady cavitating turbulent flow around twisted hydrofoil is simulated with Zwart cavitation model combined with the filter-based density correction model (FBDCM). Numerical results simulated the entire process of the 3-D cavitation shedding including the re-entrant jet and side-entrant jet dynamics and were compared with the available experimental data. The distribution of finite-time Lyapunov exponent (FTLE) was used to analyze the 3-D behavior of the re-entrant jet from the Lagrangian viewpoint, which shows that it can significantly influence the particle trackers in the attached cavity. Further analysis indicates that the different flow behavior on the suction side with different attack angle can be identified with Lagrangian coherent structures (LCS). For the area with a large attack angle, the primary shedding modifies the flow pattern on the suction side. With the decrease in attack angle, the attached cavity tends to be steady, and LCS A is close to the upper wall. A further decrease in attack angle eliminates LCS A in the boundary layer. The FTLE distribution also indicates that the decreasing attack angle induces a thinner boundary layer along the foil surface on the suction side.
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| [55] |
Tip-vortex inducedcavitation on a ducted propulsor//ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference, Hawaii , |
| [56] |
Internal structure and dynamics of sheetcavitation .
The internal structure and the dynamics of two-dimensional (2D) sheet cavitation on the suction side of a 2D foil section were investigated experimentally. Experiments were conducted in a cavitation tunnel and situations ranging from steady sheet cavitation to unsteady cloud cavitation were obtained by varying the foil incidence and the cavitation number. Using a novel endoscopic technique, coupled with x-ray attenuation measurements, the two-phase morphology and the void fraction within the sheet cavitation were investigated. Supplemental information on the instantaneous shape of the sheet cavity and its instability frequency were also obtained by visualization and pressure measurements, respectively. The investigations focused on (a) the void fraction distribution and (b) the frequency of the cavity oscillations. It was found that the void ratio can reach as much as 50% depending on the conditions of operation, and the Strouhal numbers are around 0.25 in the case of partial cavity instability and 0.12 in the case of transitional sheet cavitation. Finally, the visualization of the vapor structures within the sheet cavity for various stations along the chord gives a qualitative understanding of the process of vapor production and condensation.
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| [57] |
Analysis of cavitating flow structure by experimental andnumerical investigations .
The unsteady structure of cavitating flows is investigated by coupled experimental and numerical means. Experiments focus on the structure and dynamics of sheet cavitation on the upper side of a two-dimensional foil section in the ENSTA cavitation tunnel. Various flow conditions are investigated by varying the pressure, the flow velocity, and the incidence of the foil section. High-frequency local measurements of volume fractions of the vapour phase are performed inside the liquid/vapour mixture by a X-ray absorption method. The numerical approach is based on a macroscopic formulation of the balance equations for a two-phase flow. The assumptions required by this formulation are detailed and they are shown to be common to almost all the models used to simulate cavitating flows. In the present case we apply a single-fluid model associated with a barotropic state law that governs the mixture density evolution. Numerical simulations are performed at the experimental conditions and the results are compared to the experimental data. A reliable agreement is obtained for the internal structure of the cavity for incidence varying between 3 and 6 . Special attention is paid to the mechanisms of partial and transitional instabilities, and to the effects of the interaction between the two sides of the foil section.
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| [58] |
Sound and shock waves in liquids containingbubbles .
The propagation of infinitesimal sound waves in a liquid containing gas bubbles is considered. Relative motion of gas bubbles and liquid is explicitly allowed for, and it is shown that a significant error in the speed of waves may arise if the relative motion and fluctuations of mass fraction are neglected. The structure of steady shock waves is also derived.
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| [59] |
The PANS k-epsilon model in a zonalhybrid RANS-LES formulation . |
| [60] |
New method for monitoring andcorrelating cavitation noise to erosion capability . |
| [61] |
Two phase flow approach inunsteady cavitation modelling//ASME Cavitation and Multiphase Flow Forum , |
| [62] |
Mind the gap: a new insight into the tip leakage vortexusing stereo-PIV .
The tip leakage vortex (TLV), which develops in the clearance between the rotor and the stator of axial hydro turbines, has been studied for decades. Yet, many associated phenomena are still not understood. For instance, it remains unclear how the clearance size is related to the occurrence of cavitation in the vortex, which can lead to severe erosion. Experiments are here carried out on the influence of the clearance size on the tip vortex structure in a simplified case study. A NACA0009 hydrofoil is used as a generic blade in a water tunnel while the clearance between the blade tip and the wall is varied. The 3D velocity fields are measured using Stereo Particle Image Velocimetry (SPIV) in three planes located downstream of the hydrofoil for different values of the upstream velocity, the incidence angle and a large number of tip clearances. The influence of the flow conditions on the structure of the TLV is described through changes in the vortex intensity, core axial flow, vortex center position and wandering motion amplitude. Moreover, high-speed visualizations are used to highlight the vortex core trajectory and clearance flow alteration, turning into a wall jet as the tip clearance is reduced. The measurements clearly reveal the existence of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation.
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| [63] |
A numericalmodel for the evolution of internal structure of cavitation cloud .
Bubble size distributions in cloud cavitation are important in cavitating flows. In this study, a numerical model was developed to study the evolution of the internal structure of cloud cavitation. The model includes (1) an evolution equation of bubble number density, which considers the bubble breakup effect and (2) the multiphase Reynolds-averaged Navier tokes equations with a modified cavitation model for background cavitating flows. The proposed model was validated with a flow over a projectile. Results show that the numerical model can predict the evolution of the internal structure of cloud cavitation. Comparisons of the proposed model and Singhal model were discussed. The effects of re-entrant jet and bubble number density on cavitating flows were also investigated.
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| [64] |
Anexperimental analysis of fluid structure interaction on a flexiblehydrofoil in various flow regimes including cavitating flow .
The structural response of a rectangular cantilevered flexible hydrofoil submitted to various flow regimes is analyzed through an original experiment carried out in a hydrodynamic tunnel at a Reynolds number of 0.75 106. The experiment considers static and transient regimes. The latter consists of transient pitching motions at low and fast pitching velocities. The experiments are also performed for cavitating flow. The structural response is analyzed through the measurement of the free foil tip section displacement using a high speed video camera and surface velocity vibrations using a laser doppler vibrometer. In non cavitating flows, it is shown that the structural response is linked to the hydrodynamic loading, which is governed by viscous effects such as laminar to turbulent transition induced by Laminar Separation Bubble (LSB), and stall. It is also observed that the foil elastic displacement depends strongly on the pitching velocity. Large overshoots and hysteresis effect are observed as the pitching velocity increases. Cavitation induces a large increase of the vibration level due to hydrodynamic loading unsteadiness and change of modal response for specific frequencies. The experimental results presented in this paper will help to develop high fidelity fluid tructure interaction models in naval applications.
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| [65] |
Numerical and experimental investigation of hydrodynamiccharacteristics of deformable hydrofoils .
The present paper is concerned with the numerical and experimental investigation of the hydroelastic behavior of a deformable hydrofoil in a uniform flow. The study is developed within the general framework of marine structure design and sizing. An experimental setup is developed in the IRENav hydrodynamic tunnel in which a cambered rectangular hydrofoil is mounted. An image-processing device enables the visualization of the foil displacement. As for the numerical part, the structure problem is solved with the finite element method, while the fluid problem is solved with the finite volume method using two distinct numerical codes that are coupled through an iterative algorithm based on the exchange of the boundary conditions at the fluid-structure interface. Results obtained from the coupled fluid-structure computations including deformation and hydrodynamic coefficients are presented. The influence of the fluid-structure coupling is evaluated through comparisons with "noncoupled" simulations. The numerical simulations are in very good agreement with the experimental results and highlight the importance of the fluid-structure coupling consideration. Particular attention is paid to the pressure distribution modification on the hydrofoil as a result of deformations that can lead to an advance of the cavitation inception, which is of paramount importance for naval applications.
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| [66] |
Hydroelasticresponses of a flexible hydrofoil in turbulent, cavitatingflow//ASME 2010 7th International Symposium on Fluid-StructureInteractions, Flow-Sound Interactions, and Flow-Induced Vibrationand Noise, Quebec , |
| [67] |
Investigation of a re-entrant jet reflection at an inclined cavityclosure line .
Cavitation on two-dimensional hydrofoils with swept leading edges always displays some 3-dimensional effects. It is well known that the cavity closure on such hydrofoil is not perpendicular to the channel walls, but is curved in a distinctive pattern. The cavitation pocket is longer in the region where the hydrofoil is the shortest. Also the dynamics of cavitation is very distinctive. In the region where the hydrofoil is the longest attached and steady cavitation with no cloud separation exists. On the other side, where the hydrofoil is the shortest, cavitation cloud separations occur.Different explanations for this pattern were proposed in the past but they have not jet been clearly confirmed neither experimentally nor by numerical simulation.In the present paper a clear explanation supported by the numerical simulation and also by experimental measurements, is given.
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| [68] |
Experimental evaluation of numerical simulation of cavitating flowaround hydrofoil .
Cavitation in hydraulic machines causes different problems that can be related to its unsteady nature. An experimental and numerical study of developed cavitating flow was performed. Until now simulations of cavitating flow were limited to the self developed n house CFD codes. The goal of the work was to experimentally evaluate the capabilities of a commercial CFD code (Fluent) for simulation of a developed cavitating flow. Two simple hydrofoils that feature some 3D effects of cavitation were used for the experiments. A relatively new technique where PIV method combined with LIF technique was used to experimentally determine the instantaneous and average velocity and void ratio fields (cavity shapes) around the hydrofoils. Distribution of static pressure on the hydrofoil surface was determined. For the numerical simulation of cavitating flow a bubble dynamics cavitation model was used to describe the generation and evaporation of vapour phase. An unsteady RANS 3D simulation was performed. Comparison between numerical and experimental results shows good correlation. The distribution and size of vapour structures and the velocity fields agree well. The distribution of pressure on the hydrofoil surface is correctly predicted. The numerically predicted shedding frequencies are in fair agreement with the experimental data.
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| [69] |
Efficient implicit LES method for the simulation of turbulentcavitating flows .
We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.
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| [70] |
Time resolved PIV and flow visualization of 3D sheetcavitation .
Time-resolved PIV was applied to study fully developed sheet cavitation on a hydrofoil with a spanwise varying angle of attack. The hydrofoil was designed to have a three-dimensional cavitation pattern closely related to propeller cavitation, studied for its adverse effects as vibration, noise, and erosion production. For the PTV measurements, fluorescent tracer particles were applied in combination with an optical filter, in order to remove the reflections of the laser lightsheet by the cavitation. An adaptive mask was developed to find the interface between the vapor and liquid phase. The velocity at the interface of the cavity was found to be very close to the velocity predicted by a simple streamline model. For a visualization of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil and cavitation structure. The time-resolved recordings reveal the growth of the attached cavity and the cloud shedding. Our investigation proves the viability of accurate PIV measurements around developed sheet cavitation. The presented results will further be made available as a benchmark for the validation of numerical simulations of this complicated flow
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| [71] |
The structure of three-dimensional sheetcavitation. [PhD Thesis] . |
| [72] |
On thecollapse structure of an attached cavity on a three-dimensionalhydrofoil . |
| [73] |
Fundamentals of Cavitation . |
| [74] |
An improved method to assess thequality of large eddy simulations in the context of implicitfiltering .
Large eddy simulations (LESs) of aero-optical effects in a turbulent boundary layer have been carried out at two Mach numbers (0.9 and 2.3) for an adiabatic wall boundary condition. This study is the continuation of previous work by the present authors using the temporal approximation. However, these temporal simulations have to cope with several drawbacks (thickening in time of the boundary layer, no temporal average and under-resolved statistics). In order to compensate these limits, spatially evolving simulations are performed by means of an extension to compressible flows of the rescaling method of Lund et al. Within this configuration, a blur image caused by phase distortion is the main aero-optical aberration undergone by the wave front. This aberration is due to density variations in turbulent flow. First, aerodynamic fields are proved to compare favourably with theoretical and experimental results. Once validated, the characteristics of the boundary layer allow us to obtain information concerning optical beam degradation. The link between index-of-refraction fluctuations and phase distortion fluctuations is then discussed. Also, the density field is used to compute variance of phase distortion, on the one hand, directly and, on the other hand, by means of the optical models. Therefore, LESs allow us to study these models and the validity of their assumptions. Furthermore, contrary to the temporal approximation, spatially evolving simulations enable us to perform a spectral analysis of phase distortion fluctuations. Finally, LES is proved to be considered as a reference tool for evaluating aero-optical effects.
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| [75] |
Unsteady PIV flow fieldanalysis of a centrifugal pump impeller under rotatingcavitation//Fifth International Symposium on Cavitation, Osaka,Japan . |
| [76] |
Bubbly shockpropagation as a mechanism for sheet-to-cloud transition ofpartial cavities .
Partial cavitation in the separated region forming from the apex of a wedge is examined to reveal the flow mechanism responsible for the transition from stable sheet cavity to periodically shedding cloud cavitation. High-speed visualization and time-resolved X-ray densitometry measurements are used to examine the cavity dynamics, including the time-resolved void-fraction fields within the cavity. The experimentally observed time-averaged void-fraction profiles are compared to an analytical model employing free-streamline theory. From the instantaneous void-fraction flow fields, two distinct shedding mechanisms are identified. The classically described re-entrant flow in the cavity closure is confirmed as a mechanism for vapour entrainment and detachment that leads to intermittent shedding of smaller-scale cavities. But, with a sufficient reduction in cavitation number, large-scale periodic cloud shedding is associated with the formation and propagation of a bubbly shock within the high void-fraction bubbly mixture in the separated cavity flow. When the shock front impinges on flow at the wedge apex, a large cloud is pinched off. For periodic shedding, the speed of the front in the laboratory frame is of the order of half the free-stream speed. The features of the observed condensation shocks are related to the average and dynamic pressure and void fraction using classical one-dimensional jump conditions. The sound speed of the bubbly mixture is estimated to determine the Mach number of the cavity flow. The transition from intermittent to transitional to strongly periodic shedding occurs when the average Mach number of the cavity flow exceeds that required for the generation of strong shocks.
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| [77] |
Visualisation and les simulation of cavitation cloudformation and collapse in an axisymmetric geometry .
Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90 and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the 'large-scale' cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development. (C) 2014 Elsevier Ltd. All rights reserved.
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| [78] |
PANS turbulencemodel for seamless transition between RANS and LES: fixed-pointanalysis and preliminary results//ASME/JSME 2003 4th Joint FluidsSummer Engineering Conference, Honolulu, Hawaii,
Partially-averaged Navier-Stokes (PANS) approach has been recently developed as a possible bridging model between Reynolds-averaged Navier-Stokes (RANS) method and large-eddy simulations (LES). The resolution control parameters in PANS are the fractions of unresolved kinetic energy () and unresolved dissipation ( ). We investigate the fixed-point behavior of PANS and present some preliminary results obtained using this model. By comparing the fixed-point behavior of PANS and URANS (unsteady Reynolds-averaged Navier-Stokes) methods, the possible advantage of the former over the latter is explained. Initial results from two-dimensional simulations of flow past square results are also presented.
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| [79] |
A numerical method tosimulate turbulent cavitating flows .
The objective of this paper is to develop a numerical method for simulating multiphase cavitating flows on unstructured grids. The multiphase medium is represented using a homogeneous mixture model that assumes thermal equilibrium between the liquid and vapor phases. We develop a predictor–corrector approach to solve the governing Navier–Stokes equations for the liquid/vapor mixture, together with the transport equation for the vapor mass fraction. While a non-dissipative and symmetric scheme is used in the predictor step, a novel characteristic-based filtering scheme with a second order TVD filter is developed for the corrector step to handle shocks and material discontinuities in non-ideal gases and mixtures. Additionally, a sensor based on vapor volume fraction is proposed to localize dissipation to the vicinity of discontinuities. The scheme is first validated for simple one dimensional canonical problems to verify its accuracy in predicting jump conditions across material discontinuities and shocks. It is then applied to two turbulent cavitating flow problems – over a hydrofoil using RANS and over a wedge using LES. Our results show that the simulations are in good agreement with experimental data for the above tested cases, and that the scheme can be successfully applied to both RANS and LES methodologies.
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| [80] |
Numerical investigation ofnear-wake characteristics of cavitating flow over a circularcylinder .
A homogeneous mixture model is used to study cavitation over a circular cylinder at two different Reynolds numbers ($Re=200$and 3900) and four different cavitation numbers (${\it\sigma}=2.0$, 1.0, 0.7 and 0.5). It is observed that the simulated cases fall into two different cavitation regimes: cyclic and transitional. Cavitation is seen to significantly influence the evolution of pressure, boundary layer and loads on the cylinder surface. The cavitated shear layer rolls up into vortices, which are then shed from the cylinder, similar to a single-phase flow. However, the Strouhal number corresponding to vortex shedding decreases as the flow cavitates, and vorticity dilatation is found to play an important role in this reduction. At lower cavitation numbers, the entire vapour cavity detaches from the cylinder, leaving the wake cavitation-free for a small period of time. This low-frequency cavity detachment is found to occur due to a propagating condensation front and is discussed in detail. The effect of initial void fraction is assessed. The speed of sound in the free stream is altered as a result and the associated changes in the wake characteristics are discussed in detail. Finally, a large-eddy simulation of cavitating flow at$Re=3900$and${\it\sigma}=1.0$is studied and a higher mean cavity length is obtained when compared to the cavitating flow at$Re=200$and${\it\sigma}=1.0$. The wake characteristics are compared to the single-phase results at the same Reynolds number and it is observed that cavitation suppresses turbulence in the near wake and delays three-dimensional breakdown of the vortices.
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| [81] |
Numerical simulation ofcavitating flows with homogeneous models .
The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models, an appropriate equation of state (EOS) is necessary to cover all possible fluid states (pure liquid, two-phase mixture and pure vapour). Moreover, the numerical method has to handle any Mach number accurately. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a preconditioning scheme. The cavitation phenomenon is modelled by two different liquid–vapour mixture EOS. The mathematical and thermodynamic properties are studied. Steady and unsteady numerical results are given for a Venturi geometry and comparisons are made with experimental data.
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| [82] |
Flow structure and modeling issuesin the closure region of attached cavitation .
Particle image velocimetry (PIV) and high-speed photography are used to measure the flow structure at the closure region and downstream of sheet cavitation. The experiments are performed in a water tunnel of cross section 6.35x5.08 cm[sup 2] whose test area contains transparent nozzles with a prescribed pressure distribution. This study presents data on instantaneous and averaged velocity, vorticity and turbulence when the ambient pressure is reduced slightly below the cavitation inception level. The results demonstrate that the collapse of the vapor cavities in the closure region is the primary mechanism of vorticity production. When the cavity is thin there is no reverse flow downstream and below the cavitation, i.e., a reentrant flow does not occur. Instead, the cavities collapse as the vapor condenses, creating in the process hairpin-like vortices with microscopic bubbles in their cores. These hairpin vortices, some of which have sizes as much as three times the height of the stable cavity, dominate the flow downstream of the cavitating region. The averaged velocity distributions show that the unsteady collapse of the cavities in the closure region involves substantial increase in turbulence, momentum, and displacement thickness. Two series of tests performed at the same velocity and pressure, i.e., at the same hydrodynamic conditions, but at different water temperatures, 35 00°C and 45 00°C, show the effect of small changes in the cavitation index (0306=4.69 vs. 0306=4.41). This small decrease causes only a slight increase in the size of the cavity, but has a significant impact on the turbulence level and momentum deficit in the boundary layer downstream. Ensemble averaging of the measured instantaneous velocity distributions is used for estimating the liquid void fraction, average velocities, Reynolds stresses, turbulent kinetic energy and pressure distributions. The results are used to examine the mass and momentum balance downstream of th...
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| [83] |
Hydrodynamiclubrication of textured surfaces: A review of modeling techniquesand key findings .
Understanding the influence of surface properties (roughness, grooves, discrete textures/dimples) on the performance of hydrodynamically lubricated contacts has been the aim of numerous studies. A variety of different numerical models have been employed by many researchers in order to find optimal texturing parameters (shape, size, distribution) for best performance enhancement in terms of load carrying capacity, film thickness, friction and wear. However, the large number of different modeling techniques and complexity in the patterns make finding the optimum texture a challenging task and have led to contrary conclusions. This article outlines the research effort on surface texturing worldwide, reviews the key findings and, in particular, provides a comparative summary of different modeling techniques for fluid flow, cavitation and micro-hydrodynamic effects.
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| [84] |
Cavitation and wake structure of unsteadytip vortex flows. [PhD Thesis] .
Unsteady flows are prevalent in virtually every fluid application yet, because of their intrinsic complexity, few attempts have been made to measure them or explain their behavior. This thesis presents an experimental study of one of the simplest unsteady flow induced effects, the periodic change in angle of attack of a lifting surface. Of particular interest is the influence this effect has on the tip vortex structure of a finite aspect ratio hydrofoil and the part it plays in the inception of cavitation. An aspect ratio 2.3 hydrofoil was reflection-plane mounted to the test section floor of the Caltech Low Turbulence Water Tunnel and harmonically oscillated in pitch near its center of pressure. Observations of the growth and collapse of surface and tip vortex cavitation were made along with detailed observations of the interaction of the tip vortex formation with the spanwise wake structure. Measurements of the cavitation inception number for surface cavitation and tip vortex cavitation were made relative to the phase of the hydrofoil and the reduced frequency, of oscillation. Studies of the oscillation-induced spanwise trailing vortex structures and the Karman vortex street generated by the boundary layer were made of a two-dimensional hydrofoil. Laser Doppler Velocimetry (LDV) measurements were taken of the tip vortex velocity profile and the flow at the trailing edge of both the two- and the three-dimensional hydrofoils.
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| [85] |
Implicit large eddy simulation of unsteady cloud cavitation arounda plane-convex hydrofoil .
The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation (ILES) is applied to analyze the three dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic-conditions, which were experimentally tested at the high speed cavitation tunnel of the cole Polytechnique F d rale de Lausanne (EPFL), clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasonably well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.
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| [86] |
Tip leakage vortexcavitation from the tip clearance of a single hydrofoil .
Focusing on the tip leakage vortex cavitation, experimental and numerical studies were carried out as the first step of the investigation of cavitations in tip leakage flow. For a single hydrofoil with a tip clearance, tip leakage vortex cavitations were observed for various cavitation numbers and angles of attack. To simulate the tip leakage vortex cavitation, a simple calculation of 2-D unsteady flow based on the slender body approximation with taking into account the effects of cavity growth was made. The results of calculations show qualitative agreement with the experimental results with respect to the location and size of the cavity. The influences of the cavitation number, angle of attack, blade loading distribution, and the size of tip clearance were simulated reasonably well.
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| [87] |
Multiscale tow-phaseflow modeling of sheet and cloud cavitation .
A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.
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| [88] |
A modified PANSmodel for computations of unsteady turbulence cavitating flows .
A modification to the PANS (partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter f k is modified to vary as a function of the ratios between the water density and the mixture density in the local flows. The objective of this study is to validate the modified model and further understand the interaction between turbulence and cavitation around a Clark-Y hydrofoil. The comparisons between the numerical and experiment results show that the modified model can be improved to predict the cavity evolution, vortex shedding frequency and the lift force fluctuating in time fairly well, as it can effectively modulate the eddy viscosity in the cavitating region and various levels of physical turbulent fluctuations are resolved. In addition, from the computational results, it is proved that cavitation phenomenon physically influences the turbulent level, especially by the vortex shedding behaviors. Also, the mean u-velocity profiles demonstrate that the attached cavity thickness can alter the local turbulent shear layer.
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| [89] |
Physical and numerical investigation of%unsteady cavitating flows. [PhD Thesis] .
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| [90] |
Detached-eddysimulation for time-dependent turbulent cavitating flows .
Abstract two-equation closures, have been very popular in providing good prediction for a wide variety of flows with presently available computational resource. But for cavitating flows, the above equations noticeably over-predict turbulent production and hence effective viscosity. In this paper, the detached eddy simulation (DES) method for time-dependent turbulent cavitating flows is investigated. To assess the state-of-the-art of computational capabilities, different turbulence models including the widely used RANS model and DES model are conducted. Firstly, in order to investigate the grid dependency in computations, different grid sizes are adopted in the computation. Furthermore, the credibility of DES model is supported by the unsteady cavitating flows over a 2D hydrofoil. The results show that the DES model can effectively reduce the eddy viscosities. From the experimental validations regarding the force analysis, frequency and the unsteady cavity visualizations, more favorable agreement with experimental visualizations and measurements are obtained by DES model. DES model is better able to capture unsteady phenomena including cavity length and the resulting hydrodynamic characteristics, reproduces the time-averaged velocity quantitatively around the hydrofoil, and yields more acceptable and unsteady dynamics features. The DES model has shown to be effective in improving the overall predictive capability of unsteady cavitating flows.
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| [91] |
Combinedexperimental and computational investigation of unsteady structureof sheet/cloud cavitation . |
| [92] |
Numerical simulationunsteady cloud cavitating flow with a filter-based densitycorrection model .
In this paper, various turbulence closure models for unsteady cavitating flows are investigated. The filter-based model (FBM) and the density correction model (DCM) were proposed to reduce the turbulent eddy viscosities in a turbulent cavitating flow based on the local meshing resolution and the local fluid density, respectively. The effects of the resolution control parameters in the FBM and DCM models are discussed. It is shown that the eddy viscosity near the cavity closure region can significantly influence the cavity shapes and the unsteady shedding pattern of the cavitating flows. To improve the predictions, a Filter-Based Density Correction model (FBDCM) is proposed, which blends the FBM and DCM models according to the local fluid density. The new FBDCM model can effectively represent the eddy viscosity, according to the multi-phase characteristics of the unsteady cavitating flows. The experimental validations regarding the force analysis and the unsteady cavity visualization show that good agreements with experimental visualizations and measurements are obtained by the FBDCM model. For the FBDCM model, the attached cavity length and the resulting hydrodynamic characteristics are subsequently affected by the detail turbulence modeling parameters, and the model is shown to be effective in improving the overall predictive capability.
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| [93] |
b. Large eddy simulation ofturbulent vortex-cavitation interactions in transient sheet/cloudcavitating flows .
The objectives of this study are to: (1) quantify the influence of sheet/cloud cavitation on the hydrodynamic coefficients and surrounding flow turbulent structures, (2) provide a better insight in the physical mechanisms that govern the dynamics and structure of a sheet/cloud cavity, (3) improve the understanding of the interaction between unsteady cavitating flow, vortex dynamics and hydrodynamic performance. Results are presented for a 3D Clark-Y hydrofoil fixed at an angle of attack of =8 degrees at a moderate Reynolds number, Re=7 105, for both subcavitating ( =2.00) and sheet/cloud cavitating conditions ( =0.80). The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, the turbulence model utilizes the Large Eddy Simulation (LES) approach with the Wall-Adapting Local Eddy-viscosity model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The detailed analysis of the vorticity transport equation shows strong correlation between the cavity and vorticity structure, the transient development of sheet/cloud cavitation has significantly changed the interaction between the leading edge and trailing edge vortices, and hence the magnitude as well as the frequency of the hydrodynamic load fluctuations. Compared to the subcavitating case, the sheet/cloud cavitation leads to much higher turbulent boundary layer thickness and substantial increase in velocity fluctuation.
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| [94] |
The influence of developedcavitation on the flow of a turbulent shear layer .
Developed cavitation in a shear layer was studied experimentally in order to determine the effect that the growth and collapse of cavitation have on the dynamics of shear flows. Planar particle imaging velocimetry (PIV) was used to measure the velocity field, the vorticity, strain rates, and Reynolds stresses of the flow downstream of the cavitating and noncavitating shear layer; the flow pressures and void fraction were also measured. The flow downstream of a cavitating shear flow was compared to the noncavitating shear flow. For cavitating shear layers with void fractions of up to 1.5%, the growth rate of the shear layer and the mean flow downstream of the shear layer were modified by the growth and collapse of cavitation bubbles. The cross-stream velocity fluctuations and the Reynolds stresses measured downstream of the cavitating shear layer were reduced compared to the entirely noncavitating flow. This result is inconsistent with a scaling of the shear stress within the shear flow based on the mean flow. The decrease in the cross-stream fluctuations and Reynolds stresses suggests that the cavitation within the cores of strong streamwise vortices has decreased the coupling between the streamwise and cross-stream velocity fluctuations.
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| [95] |
A numerical study of shear layercharacteristics of low-speed transverse jets .
Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et0002al.0002(J. Fluid Mech., vol. 593, 2007, pp. 93090009129) at velocity ratios ( ) of 2 and 4 and Reynolds number ( ) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ( ) is dominant along the length of the shear layer for , whereas the dominant frequencies change along the shear layer for . DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.
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| [96] |
Partially averagedNavier-Stokes (PANS) method for turbulence simulations-flow past asquare cylinder .
The partially averaged Navier-Stokes (PANS) approach is a bridging closure model intended for any level of resolution between the Reynolds averaged Navier-Stokes (RANS) method and direct numerical simulations. In this paper, the proposed closure model is validated in the flow past a square cylinder. The desired ratio of the modeled-to-resolved scales in the PANS closure is achieved by appropriately specifying two bridging parameters: the ratios of unresolved-to-total kinetic energy (f k) dissipation (f epsiv). PANS calculations of different bridging parameter values are performed and the results are compared with experimental data and large-eddy simulations. The Strouhal number (S t), mean/root-mean-square (RMS) drag coefficient (C D), RMS lift coefficient (C L), mean velocity profiles, and various turbulent stresses are investigated. The results gradually improve from the RANS level of accuracy to a close agreement with the experimental results with decreasing value of the bridging parameter f k. Overall, the results indicate that the PANS method clearly satisfies the basic tenets of a bridging model: (i) provides a meaningful turbulence closure at any modeled-to-resolved scale ratio and (ii) yields improved accuracy with increasing resolution (decreasing modeled-to-resolved ratio).
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| [97] |
Unsteady cavitatingflow around a hydrofoil simulated using the partially-averagedNavier-Stokes model .
Numerical simulations of unsteady cavitating flow around a NACA66-mod hydrofoil were performed using the partially-averaged Navier tokes method with different values of the resolution control parameters (f= 1.0-0.2, f= 1). With decreasing f, the predicted cavitating flow becomes unsteady as the time-averaged turbulent viscosity at the rear part of the attached cavity is gradually reduced. For f= 0.9 and 0.8, the cavity becomes unstable and its length dramatically expands and shrinks, but the calculation fails to predict the vapor cloud shedding behavior observed experimentally. With smaller fless than 0.7, the cloud shedding behavior is simulated numerically and the predicted cavity shedding frequency increases. With f= 0.2, the whole cavitating flow evolution can be reasonably reproduced including the cavity growth/destabilization observed previously. The reentrant flow along the suction surface of the hydrofoil is the main trigger to cause the vapor cloud shedding. The wall pressure along the hydrofoil surface oscillates greatly due to the dynamic cavity shedding. Comparing the simulations and experiments, it is confirmed that for the PANS method, resolution control parameters of f= 0.2 and f= 1 are recommended for numerical simulations of unsteady cavitating flows. Thus, the present study shows that the PANS method is an effective approach for predicting unsteady cavitating flow over hydrofoils.
|
| [98] |
Numerical analysisof unsteady cavitating turbulent flow and shedding horse-shoevortex structure around a twisted hydrofoil .
Cavitating turbulent flow around hydrofoils was simulated using the Partially-Averaged Navier-Stokes (PANS) method and a mass transfer cavitation model with the maximum density ratio (rho(l)/rho(v,clip)) effect between the liquid and the vapor. The predicted cavity length and thickness of stable cavities as well as the pressure distribution along the suction surface of a NACA66(MOD) hydrofoil compare well with experimental data when using the actual maximum density ratio (rho(l)/rho(v,clip) = 43391) at room temperature. The unsteady cavitation patterns and their evolution around a Delft twisted hydrofoil were then simulated. The numerical results indicate that the cavity volume fluctuates dramatically as the cavitating flow develops with cavity growth, destabilization, and collapse. The predicted three dimensional cavity structures due to the variation of attack angle in the span-wise direction and the shedding cycle as well as its frequency agree fairly well with experimental observations. The distinct side-lobes of the attached cavity and the shedding U-shaped horse-shoe vortex are well captured. Furthermore, it is shown that the shedding horse-shoe vortex includes a primary U-shaped vapor cloud and two secondary U-shaped vapor clouds originating from the primary shedding at the cavity center and the secondary shedding at both cavity sides. The primary shedding is related to the collision of a radially-diverging re-entrant jet and the attached cavity surface, while the secondary shedding is due to the collision of side-entrant jets and the radially-diverging re-entrant jet. The local flow fields show that the interaction between the circulating flow and the shedding vapor cloud may be the main mechanism producing the cavitating horse-shoe vortex. Two side views described by iso-surfaces of the vapor volume fraction for a 10% vapor volume, and a non-dimensional Q-criterion equal to 200 are used to illustrate the formation, roll-up and transport of the shedding horse-shoe vortex. The predicted height of the shedding horse-shoe vortex increases as the vortex moves downstream. It is shown that the shape of the horse-shoe vortex for the non-dimensional Q-criterion is more complicated than that of the 10% vapor fraction iso-surface and is more consistent with the experiments. Further, though the time-averaged lift coefficient predicted by the PANS calculation is about 12% lower than the experimental value, it is better than other predictions based on RANS solvers. (c) 2012 Elsevier Ltd. All rights reserved.
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| [99] |
Numerical simulationof three dimensional cavitation shedding dynamics with specialemphasis on cavitation--vortex interaction .
613D cavitating turbulent structure around a twisted hydrofoil is simulated.61Three types of flow behavior along the hydrofoil suction side are illustrated.61The mechanism of cavitation–vortex interaction is discussed.
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| [100] |
Large EddySimulation and theoretical investigations of the transientcavitating vortical flow structure around a NACA66 hydrofoil .
Compared to non-cavitating flow, cavitating flow is much complex owing to the numerical difficulties caused by cavity generation and collapse. In this paper, the cavitating flow around a NACA66 hydrofoil is studied numerically with particular emphasis on understanding the cavitation structures and the shedding dynamics. Large Eddy Simulation (LES) was coupled with a homogeneous cavitation model to calculate the pressure, velocity, vapor volume fraction and vorticity around the hydrofoil. The predicted cavitation shedding dynamics behavior, including the cavity growth, break-off and collapse downstream, agrees fairly well with experiment. Some fundamental issues such as the transition of a cavitating flow structure from 2D to 3D associated with cavitation ortex interaction are discussed using the vorticity transport equation for variable density flow. A simplified one-dimensional model for the present configuration is adopted and calibrated against the LES results to better clarify the physical mechanism for the cavitation induced pressure fluctuations. The results verify the relationship between pressure fluctuations and the cavity shedding process (e.g. the variations of the flow rate and cavity volume) and demonstrate that the cavity volume acceleration is the main source of the pressure fluctuations around the cavitating hydrofoil. This research provides a better understanding of the mechanism driving the cavitation excited pressure pulsations, which will facilitate development of engineering designs to control these vibrations.
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| [101] |
LargeEddy Simulation of turbulent attached cavitating flow with specialemphasis on large scale structures in the hydrofoil wake andturbulence-cavitation interactions .
In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simulation (LES) method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.
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| [102] |
Filter-based unsteadyRANS computations .
The Reynolds-averaged Navier–Stokes (RANS) approach has been popular for engineering turbulent flow computations. The most widely used ones, such as the k61 ε two-equation model, have well-recognized deficiencies when treating time dependent flow fields. To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures, conditional averaging is adopted for the Navier–Stokes equation, and one more parameter, based on the filter size, is introduced into the k61 ε model. The sub-filter stresses are constructed directly by using the filter size and the conventional turbulence closure. The filter is decoupled from the grid, making it possible to obtain grid independent solutions with a fixed filter scale. The model is assessed in transient, planar turbulent wake flow simulations over a square cylinder utilizing progressively refined grid. In comparison to the standard k61 ε model, overall, the filter-based model is shown to improve the predictive capability considerably.
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| [103] |
Cavitation phenomena within regions of flowseparation .
The phenomenon of cavitation inception was studied on four axisymmetric bodies whose boundary layers underwent a laminar separation and subsequent turbulent reattachment. The non-cavitating flow was studied by holographic and schlieren flow-visualization techniques. Surface distributions on the mean and the fluctuating pressures were also measured. The conditions for cavitation inception and desinence were determined and holograms were recorded just prior to and at the onset of cavitation. The population of microbubbles and the subsequent development of visible cavitation was determined from the reconstructed image. In every case the appearance of visible cavitation was preceded by a cluster of microscopic bubbles in a small portion of the flow field providing clear evidence that cavitation is initiated from small nuclei. The inception zone was located within the turbulent shear layer downstream of transition and upstream of the reattachment region of the bodies with large separation regions. The location and the shape of this cavitation suggested a relation to the mixing-layer eddy structure. The inception region on the body with the smallest separation zone, a hemisphere-cylinder body, was located in the reattachment region, but the cavities were still detached from the surface. Instantaneous minimum-surface-pressure measurements do not account for observed cavitation-inception indices except for the hemisphere body, where the correlation is satisfactory. The rate of cavitation events was estimated from measurements of nuclei population, and fluctuating-pressure statistics in the portion of the flow susceptable to cavitation. It was demonstrated for the hemisphere body that at least one such cavitation event could occur every second. These findings are consistent with what is observed visually at the onset of cavitation and support the location of inception determined holographically.
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| [104] |
Mechanism and control of cloud cavitation . |
| [105] |
Time-accuratesimulations and acoustic analysis of slat free shear layer .
ABSTRACT A detailed computational aeroacoustic analysis of a high-lift flow field is performed. Time-accurate Reynolds Averaged Navier-Stokes (RANS) computations simulate the free shear layer that originates from the slat cusp. Both unforced and forced cases are studied. Preliminary results show that the shear layer is a good amplifier of disturbances in the low to mid-frequency range. The Ffowcs-Williams and Hawkings equation is solved to determine the acoustic field using the unsteady flow data from the RANS calculations. The noise radiated from the excited shear layer has a spectral shape qualitatively similar to that obtained from measurements in a corresponding experimental study of the high-lift system.
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| [106] |
An attempt to assess the quality of largeeddy simulations in the context of implicit filtering .
While methods for assessing the uncertainty of Reynolds–Averaged–Navier–Stokes (RANS) simulations have been well established in the past, the verification of Large Eddy Simulations (LES) is more difficult. One reason is that the numerical discretization error as well as the subgrid scale model contribution depend on the grid resolution and that both terms interact. In the present paper the accuracy of single-grid estimators to assess the amount of the unresolved turbulent kinetic energy is studied first. In the second part of the paper the sensitivity of the simulation results on the modeling error as well as the numerical error will be investigated in the context of LES with implicit filtering. This will be achieved by performing a systematic grid and model variation. The analysis is applied to an isothermal, turbulent, plane jet and a turbulent channel flow.
|
| [107] |
Recent investigations of the mechanics ofcavitation and cavitation damage . |
| [108] |
Superiority ofPANS compared to LES in predicting a rudimentary landing gear flowwith affordable meshes .
Results of simulations of the flow around a rudimentary landing gear are presented in the paper. A newly proposed improved Partially-Averaged Navier–Stokes (PANS) method using k61ε61ζ61f turbulence model is used for prediction of the flow. The results are compared with the experimental data but also with the results of two LES simulations performed using the PANS computational grids. PANS simulations predicted the flow in good agreement with the experimental data. LES predicted a non-physical creation of separation over the front wheels that does not exist in the PANS prediction and was not observed in the experimental oil film. PANS simulations showed low sensitivity to the grid refinement. They show clear advantage compared with the LES simulations when the computational grid is inadequate for resolution of the near-wall flow structures.
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| [109] |
Partial cavity flows. Part 1.Cavities forming on models without spanwise variation .
Partial cavities that formed on the vertices of wedges and on the leading edge of stationary hydrofoils were examined experimentally. The geometry of these test objects did not vary in the spanwise direction (i.e. two-dimensional). Open partial cavities formed on a series of two-dimensional wedges and on a plano-convex hydrofoil. These cavities terminated near the point of maximum cavity thickness, and small vapour-filled vortices were shed in the turbulent cavity wake. The turbulent flow in the wake of the open cavity was similar to the turbulent shear flow downstream of a rearward-facing step. Re-entrant flow was not observed in the cavity closure of open cavities, although recirculating flow associated with a region of flow separation was detected for some cases. Predictions of a two-dimensional free-streamline model of the cavitating wedge flows were compared to the experimentally observed cavities. The model predicted the profile of the open cavity only to the point of maximum cavity thickness. Examination of the flow field near the closure of the open cavities revealed adverse pressure gradients near the cavity closure. The pressure gradients around the open cavities were sufficient to cause large-scale condensation of the cavity. Unsteady re-entrant partial cavities formed on a two-dimensional NACA0009 hydrofoil. The interface of the unsteady closed cavities smoothly curved to form a re-entrant jet at the cavity terminus, and the re-entrant flow was directed upstream. The re-entrant flow impinged on the cavity interface and led to the periodic production of cloud cavitation. These cavities exhibited a laminar flow reattachment. The flow around the closed cavity was largely irrotational, while vorticity was created when the cloud cavitation collapsed downstream of the cavity. Examination of the flow field near closure of these cavities also revealed adverse pressure gradients near the partial cavity closure, but the rise in pressure did not lead to the premature condensation of the cavity.
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| [110] |
Partial cavity flows.Part 2. Cavities forming on test objects with spanwise variation .
Partial cavitation forming on the vertex of a wedge and on the leading edge of a stationary hydrofoil was experimentally examined. The geometry of these test objects varied in the spanwise direction (i.e. three-dimensional test objects). Closed cavities formed on these test objects. The interface of the closed cavities curved smoothly to form a re-entrant jet at the cavity terminus, and the re-entrant flow was directed spanwise, thus preventing its impingement on the cavity interface. The cavity shape and the pressure gradients near the closure of the closed cavities were qualitatively similar to those predicted with the two-dimensional free-streamline theory. These cavities had a steady, laminar flow reattachment. The flow around the closed cavity was largely irrotational.
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| [111] |
Real-time in vitro observation of cavitation in aprosthetic heart valve .
Abstract A technique for real-time in vitro observation of cavitation on a prosthetic heart valve operating in a ventricular assist device under normal physiologic conditions has been developed. Considering the documented observation of cavitation erosion in heart valve components from human explants, and the potential risk of blood damage that cavitation presents, the technique developed in this study may prove useful in the design of prosthetic heart valves and ventricular assist devices. Cavitation of a glycerol blood analog fluid has been documented for a Medtronic/Hall prosthetic heart valve operating in a Penn State Electric Ventricular Assist Device. The ventricular assist device was operated in a mock circulatory system under normal physiologic conditions. The valve was located in the mitral position, with the cavitation occurring on the inlet side after valve closure. Bubble cavitation was seen on the valve occluder face, and vortex cavitation was observed at two locations in the vicinity of the valve occluder and housing. The cavity growth and collapse cycle for these forms of vaporous cavitation was less than 1 msec. Stroboscopic photography and stroboscopic videography with frame grabbing were used to document the cavity life cycle. With beat rate held constant, the cavity duration time was found to decrease with increasing mean venous return pressure.
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| [112] |
Partial cavities:Pressure pulse distribution around cavity closure . |
| [113] |
An experimentalstudy of unsteady partial cavitation . |
| [114] |
A Bayesianfusion model for space-time reconstruction of finely resolvedvelocities in turbulent flows from low resolution measurements . |
| [115] |
Numerical investigation of the hump characteristic of apump-turbine based on an improved cavitation model .
For the safe and stable operation of a pump–turbine at pump mode, the hump characteristics must be studied and the hump region should be avoided. 3-D (three dimensional), compressible, cavitating flows in a pump–turbine at pump mode were numerically studied using SST k–ω turbulence model and mixture model. The decrease of the kinematic eddy viscosity in the region of high volume fraction of water vapor was considered in the calculation. The flow and external characteristic in the hump region were analyzed. Results show that the hump characteristic of a pump–turbine might be related to the cavity flow in the pump–turbine. It is the appearance of the cavitation that reduces the head of the pump–turbine. The cavitation incipience is thought to occur when the pump–turbine runs at the peak head and the cavitation is worse at 80% discharge of the pump–turbine. The cavitation regions locate at the inlet of the suction side. Calculation results are in good agreement with experimental data. The pressure fluctuation at the wave trough of hump characteristic is determined by the rotational speed. Numerical study of hump characteristics can provide a basic understanding for the improvement of stable operation of a pump–turbine.
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| [116] |
Numericalinvestigation of attached cavitation shedding dynamics around theClark-Y hydrofoil with the FBDCM and an integral method . |
| [117] |
Large eddy simulation and Euler--Lagrangian coupling investigationof the transient cavitating turbulent flow around a twistedhydrofoil . |
| [118] |
Verification and validation of URANS simulations of the turbulentcavitating flow around the hydrofoil .
In this paper, we investigate the verification and validation (V&V) procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model (DCM) coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety (FS1), the Factor of Safety (FS) and the Grid Convergence Index (GCI). The distribution of the area without achieving the validation at thevU level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.
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| [119] |
Large eddy simulation ofcavitation development on highly skewed propellers .
This paper deals with numerical simulations of the cavitating flow around two highly skewed propellers operating in open water and mounted on an inclined shaft. The aim of the study is to check the ability of our numerical method in distinguishing the variation in flow features resulting from different blade designs. Moreover, a secondary aim is also to improve the knowledge about the physics that control the growth and collapse of cavitation, and hence also the generation of cavitation noise and erosion on this type of propellers. The investigation is based on incompressible large eddy simulation (LES) in combination with a volume-of-fluid implementation to represent the two phases of liquid and vapour, and a transport equation-based method for the mass transfer between the phases. High-speed video recordings from experiments were made available for comparison. The simulations demonstrate that the current method makes it possible to analyse the main difference in flow features caused by modest design alternation. Furthermore, with suitable grid resolution, LES is demonstrated to be capable of capturing the mechanisms that are important in the cavitation development, and that numerical simulation is a reliable supplement to experiments in advanced propeller design.
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| [120] |
Numericalsimulation of cavity shedding from a three-dimensional twistedhydrofoil and induced pressure fluctuation by large-eddysimulation . |
| [121] |
A review of cavitation inhydraulic machinery. Journal of Hydrodynamics, Ser . |
| [122] |
A physics basedmultiscale modeling of cavitating flows .
Numerical modeling of cavitating bubbly flows is challenging due to the wide range of characteristic lengths of the physics at play: from micrometers (e.g., bubble nuclei radius) to meters (e.g., propeller diameter or sheet cavity length). To address this, we present here a multiscale approach which integrates a Discrete Singularities Model (DSM) for dispersed microbubbles and a two-phase Navier Stokes solver for the bubbly medium, which includes a level set approach to describe large cavities or gaseous pockets. Inter-scale schemes are used to smoothly bridge the two transitioning subgrid DSM bubbles into larger discretized cavities. This approach is demonstrated on several problems including cavitation inception and vapor core formation in a vortex flow, sheet-to-cloud cavitation over a hydrofoil, cavitation behind a blunt body, and cavitation on a propeller. These examples highlight the capabilities of the developed multiscale model in simulating various form of cavitation.
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| [123] |
Time-resolved two-dimensional X-ray densitometryof a two-phase flow downstream of a ventilated cavity .
To measure the void fraction distribution in gas-liquid flows, a two-dimensional X-ray densitometry system was developed. This system is capable of acquiring a two-dimensional projection with a 225 cm 2 area of measurement through 21 cm of water. The images can be acquired at rates on the order of 1 kHz. Common sources of error in X-ray imaging, such as X-ray scatter, image distortion, veiling glare, and beam hardening, were considered and mitigated. The measured average void fraction was compared successfully to that of a phantom target and found to be within 1 %. To evaluate the performance of the new system, the flow in and downstream of a ventilated nominally two-dimensional partial cavity was investigated and compared to measurements from dual-tip fiber optical probes and high-speed video. The measurements were found to have satisfactory agreement for void fractions above 5 % of the selected void fraction measurement range.
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| [124] |
Direct numericalsimulation of a separated channel flow with a smooth profile .
A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated not only near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.
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| [125] |
On cavitation produced by a vortextrailing from a lifting surface . |
| [126] |
Freestream nucleiand traveling-bubble cavitation . |
| [127] |
Cavitation inception from bubble nuclei .
Abstract The tensile strength of ordinary water such as tap water or seawater is typically well below 1 bar. It is governed by cavitation nuclei in the water, not by the tensile strength of the water itself, which is extremely high. Different models of the nuclei have been suggested over the years, and experimental investigations of bubbles and cavitation inception have been presented. These results suggest that cavitation nuclei in equilibrium are gaseous voids in the water, stabilized by a skin which allows diffusion balance between gas inside the void and gas in solution in the surrounding liquid. The cavitation nuclei may be free gas bubbles in the bulk of water, or interfacial gaseous voids located on the surface of particles in the water, or on bounding walls. The tensile strength of these nuclei depends not only on the water quality but also on the pressure-time history of the water. A recent model and associated experiments throw new light on the effects of transient pressures on the tensile strength of water, which may be notably reduced or increased by such pressure changes.
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| [128] |
Review ofnumerical models of cavitating flows with the use of thehomogeneous approach .
The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multi-fluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols.
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| [129] |
Relaxation effects,caused by relative motion, on shock waves in gas-bubble/liquidmixtures .
Abstract We observed a gradual change in the structure of a shock wave passing through a long tube of bubbly liquid, which we attribute to the motion of the bubbles relative to the liquid. We show that the effect of the motion on the structure of a shock wave is like that of thermal relaxation on gasdynamic shock waves: the pertinent relaxation time is the time viscous forces in the fluid take to alter the velocity of a bubble to that of the fluid. Our theory predicts certain changes in the speed of the shock wave and in its structure. We could not verify the prediction as to wave speed: in dilute mixtures it is too small to be measured. But we report experiments on the structure of the wave, which support our theoretical conclusion that the observed changes are due to the relative motion.
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| [130] |
Large-eddy simulation of cavitating nozzleflow and primary jet break-up .
We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics. The thermodynamic model is embedded into an implicit large-eddy simulation (LES) environment. The considered configuration follows the general setup of a reference experiment and is a generic reproduction of a scaled-up fuel injector or control valve as found in an automotive engine. Due to the experimental conditions, it operates, however, at significantly lower pressures. LES results are compared to the experimental reference for validation. Three different operating points are studied, which differ in terms of the development of cavitation regions and the jet break-up characteristics. Observed differences between experimental and numerical data in some of the investigated cases can be caused by uncertainties in meeting nominal parameters by the experiment. The investigation reveals that three main mechanisms promote primary jet break-up: collapse-induced turbulent fluctuations near the outlet, entrainment of free gas into the nozzle, and collapse events inside the jet near the liquid-gas interface.
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| [131] |
Numericalanalysis of cavitation cloud shedding in a submerged water jet .
Focused on the unsteady behavior of high-speed water jets with intensive cavitation a numerical analysis is performed by applying a practical compressible mixture flow bubble cavitation model with a...
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| [132] |
Combined experimental observation and numerical simulation of thecloud cavitation with U-type flow structures on hydrofoils .
[Display omitted]
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| [133] |
Generation ofabnormal acoustic noise: Singing of a cavitating tip vortex .
DOI: https://doi.org/10.1103/PhysRevFluids.2.053602
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| [134] |
Vapor Bubbles . |
| [135] |
Two phase flowstructure of cavitation: experiment and modeling of unsteadyeffects//3rd International Symposium on Cavitation . |
| [136] |
Observations ofshock waves in cloud cavitation . |
| [137] |
Flowfields and vortex dynamics of bubbles collapsing near a solidboundary .
DOI: https://doi.org/10.1103/PhysRevFluids.2.064202
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| [138] |
Verification and validation incomputational science and engineering . |
| [139] |
Numericalsimulation of cavitation around a two-dimensional hydrofoil usingVOF method and LES turbulence model .
In this paper simulation of cavitating flow over the Clark-Y hydrofoil is reported using the large eddy simulation (LES) turbulence model and volume of fluid (VOF) technique. We applied an incompressible LES modelling approach based on an implicit method for the subgrid terms. To apply the cavitation model, the flow has been considered as a single fluid, two-phase mixture. A transport equation model for the local volume fraction of vapour is solved and a finite rate mass transfer model is used for the vapourization and condensation processes. A compressive volume of fluid (VOF) method is applied to track the interface of liquid and vapour phases. This simulation is performed using a finite volume, two phase solver available in the framework of the OpenFOAM (Open Field Operation and Manipulation) software package. Simulation is performed for the cloud and super-cavitation regimes, i.e., =0.8, 0.4, 0.28. We compared the results of two different mass transfer models, namely Kunz and Sauer models. The results of our simulation are compared for cavitation dynamics, starting point of cavitation, cavity diameter and force coefficients with the experimental data, where available. For both of steady state and transient conditions, suitable accuracy has been observed for cavitation dynamics and force coefficients.
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| [140] |
Computational study of the cavitation phenomenon and itsinteraction with the turbulence developed in diesel injectornozzles by Large Eddy Simulation (LES) .
In the present paper, a homogeneous equilibrium model with a barotropic equation of state has been used for modeling cavitation in a real multi-hole microsac nozzle. The turbulence effects have been taking into account by Large Eddy Simulation (LES), using the Smagorinsky model as the sub-grid scale turbulent model and the Van Driest model for the wall damping. Firstly, the code has been validated at real operating diesel engine conditions with experimental data in terms of mass flow, momentum flux and effective velocity, showing that the model is able to predict with a high level of confidence the behavior of the internal flow at cavitating conditions. Once validated, the code has allowed to study in depth the turbulence developed in the discharge orifices and its interaction with cavitation phenomenon.
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| [141] |
Physical and numerical modelingof unsteady cavitation dynamics//Proceedings of 4th internationalConference on Multi-Phase Flow, New Orleans . |
| [142] |
Numericalinvestigation of three-dimensional cloud cavitation with specialemphasis on collapse induced shock dynamics .
The present paper focuses on a numerical approach based on the Riemann problem to simulate liquid flows with phase changes. Thereby, the flow properties include velocities from O(1) m/s to O(100) m/s and pressures from p ≈ 0 bar to O(1000) bar. The thermal and caloric behavior of liquid and vapor is described by suitable equations of state that keep the considered governing equations... [Show full abstract]
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| [143] |
Interfacial dynamics-basedmodelling of turbulent cavitating flows, Part-1: Model developmentand steady-state computations .
Abstract The merits of transport equation-based models are investigated by adopting an enhanced pressure-based method for turbulent cavitating flows. An analysis of the mass and normal-momentum conservation at a liquid–vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics-based cavitation model. The model offers direct interpretation of the empirical parameters in the existing transport-equation-based models adopted in the literature. This and three existing cavitation models are evaluated for flows around an axisymmetric cylindrical body and a planar hydrofoil, and through a convergent–divergent nozzle. Although all models considered provide qualitatively comparable wall pressure distributions in agreement with the experimental data, quantitative differences are observed in the closure region of the cavity, due to different compressibility characteristics of each cavitation model. In particular, the baroclinic effect of the vorticity transport equation plays a noticeable role in the closure region of the cavity, and contributes to the highest level of turbulent kinetic energy there. Copyright 08 2004 John Wiley & Sons, Ltd.
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| [144] |
Experimental determination of the speed of sound incavitating flows .
This paper presents measurements of the speed of sound in two-phase flows characterized by high void fraction. The main objective of the work is the characterization of wave propagation in cavitating flows. The experimental determination of the speed of sound is derived from measurements performed with three pressure transducers, while the void fraction is obtained from analysis of a signal obtained with an optical probe. Experiments are first conducted in air/water mixtures, for a void fraction varying in the range 0–11%, in order to discuss and validate the methods of measurement and analysis. These results are compared to existing theoretical models, and a nice agreement is obtained. Then, the methods are applied to various cavitating flows. The evolution of the speed of sound according to the void fraction α is determined for α varying in the range 0–55%. In this second configuration, the effect of the Mach number is included in the spectral analysis of the pressure transducers’ signals, in order to take into account the possible high flow compressibility. The experimental data are compared to existing theoretical models, and the results are then discussed.
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| [145] |
Characterization ofcavitation fields from measured pressure signals of cavitatingjets and ultrasonic horns . |
| [146] |
Mathematical basis and validation of the full cavitation model . |
| [147] |
An acoustic approach todetermine tip vortex cavitation inception for an ellipticalhydrofoil considering nuclei-seeding .
Tip vortex cavitation is usually the first type of propeller cavitation to appear with intense noise. The precise prediction of tip vortex cavitation inception is of great importance. In this paper, via an acoustic approach an experimental investigation on tip vortex cavitation inception for an elliptical hydrofoil has been done in a cavitation mechanism tunnel. For non-nuclei-seeding conditions, the sound level “collapses” when the tip vortex cavitation approaches desinence and there exists an inverse N-shape curve between the sound pressure level and cavitation number, drastically different from the generally known S-shape curve. Three nuclei-seeding conditions are then investigated to study the nuclei effects on the tip vortex cavitation inception. We propose an acoustic criterion to determine tip vortex cavitation inception applicable to both non-nuclei-seeding and nuclei-seeding conditions. The results confirm that the nuclei content and distribution in water indeed play an important role in the cavitation inception process. Supplemental observations from the high-speed video camera validate the proposed acoustic method.
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| [148] |
Effects of cavitationin a nozzle on liquid jet atomization .
Cavitation in two-dimensional (2D) nozzles and liquid jet in the vicinity of the nozzle exit were visualized using high-speed cameras to investigate the effects of cavitation on liquid jet under various conditions of cavitation and Reynolds numbers and Re. Liquid velocity in the nozzle was measured using a laser Doppler velocimetry to examine the effects of cavitation on the flow in the nozzle and liquid jet. As a result, the following conclusions were obtained: (1) cavitation in the nozzles and liquid jet can be classified into the four regimes: (no cavitation, wavy jet), (developing cavitation, wavy jet), (super cavitation, spray) and (hydraulic flip, flipping jet), (2) liquid jet near the nozzle exit depends on cavitation regime, (3) cavitation and liquid jet are not strongly affected by Re but by , and (4) strong turbulence induced by the collapse of cavitation clouds near the exit plays an important role in ligament formation.
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| [149] |
Numerical simulation ofincipient cavitation flow in a nozzle of fuel injector .
Cavitation clouds shedding in a nozzle of fuel injector for Diesel Engines play a dominant role in the fuel spray atomization process and the subsequent spray combustion. Since a high speed cavitation flow in a tiny nozzle with a complicated geometry is not easy to be visualized and measured, large efforts have been paid to carry out numerical simulations of the transient cavitating flow in the nozzle. Most of the previous simulations are based on the Homogeneous Equilibrium Model (HEM), a simplified bubble dynamics model or a barotropic equation, and the Reynolds-Averaged Navier–Stokes (RANS) turbulence model, which do not predict the cavitation cloud shedding. Cavitation in the nozzle takes various forms, such as a transparent cavitation sheet and clouds of cavitation bubbles, which makes its prediction difficult. As a first step to develop a cavitation model which can accurately treat both the sheet and cloud cavitations, in this study we propose a new combination of Large Eddy Simulation (LES), Eulerian–Lagrangian Bubble Tracking Method (BTM), and the Rayleigh–Plesset (RP) equation to simulate an incipient cavitation, in which only cavitation bubble clouds appear. A precursor simulation of a fully developed turbulent flow in a channel, in which periodic boundary condition is adopted for the inlet and exit, is carried out to generate inlet boundary condition for a nozzle simulation. To verify the validity of the model, transient cavitation motion and turbulent velocity in a rectangular nozzle are acquired by using a high speed camera and Laser Doppler Velocimetry (LDV). As a result, a recirculation flow and a cavitation cloud shedding are accurately predicted by LES using a fine grid, and the RP equation for all nuclei tracked in a Lagrangian manner.
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| [150] |
Computing non-equilibrium turbulentflows with time-dependent RANS and VLES//Fif- teenth InternationalConference on Numerical Methods in Fluid Dynamics , |
| [151] |
Numericalsimulation of cavitation dynamics using acavitation-induced-momentum-defect (CIMD) correction approach .
A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier tokes equations for the liquid phase supplemented with an additional vapor transport equation for the vapor phase. The novel cavitation-induced-momentum-defect (CIMD) correction methodology developed in this study accounts for cavitation inception and collapse events as relevant momentum-source terms in the liquid phase momentum equations. The model tracks cavitation zones and applies compressibility effects, employing homogeneous equilibrium model (HEM) assumptions, in constructing the source term of the vapor transport model. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG k model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Numerical simulations are carried out using a finite volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in good qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the CIMD approach. Our results indicate the profound influence of re-entrant jet motion and adverse pressure gradients on the cavitation dynamics.
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| [152] |
Comprehensive, approach to verification and validation of cfdsimulations---Part I: Methodology and procedures . |
| [153] |
a. Experiments on unsteadycavitation . |
| [154] |
b. Two-phase flow structure ofsheet cavitation .
An experimental study of flow within sheet cavities is performed in a cavitation tunnel equipped with a Venturi-type test section. The flow is investigated by means of a double optical probe allowing void fraction, velocity, and chord length of the vapor structures to be measured. Laser velocimetery, wall pressure measurements, and visualization techniques are also used to characterize the liquid flow around the cavity. The consistency of the experimental results was checked though mass and momentum balances. The effects of Reynolds and cavitation numbers are analyzed. Special attention is given to the dynamic behavior of the flow, and to the vapor flow rate within the cavities. The measurements show a complex two-phase flow characterized by the presence of an extended reversed flow occurring along the solid surface and a regular decrease in void fraction along the cavity. The phase transitions seem to be mainly restricted by the dynamic of the bubbles and thermodynamic effects.
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| [155] |
Measurements within unsteadycavitation . |
| [156] |
X-ray measurements withinunsteady cavitation .
A current method used to characterize the phase distribution within gas (or vapor)/liquid two-phase flows consists of using local probes. Two sensors placed in series enable void fraction, velocity, and chord length measurements. The choice of the data treatment method depends strongly on the unsteady behavior of the flow: the higher the velocity fluctuations, the more complex and time consuming the data treatments. Three different methods have been developed to study various cavitating flow conditions. They have been applied to characterize two-phase flows within sheet cavities using a double optical probe.
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| [157] |
Detached-eddy simulations past a circular cylinder .
The flow is calculated with laminar separation (LS) at Reynolds numbers 50,000 and 140,000, and with turbulent separation (TS) at140,000 and 3 10 6 . The TS cases are effectively tripped, but compared with untripped experiments at very high Reynolds numbers. The finest grid has about 18,000 points in each of 56 grid planes spanwise; the resolution is far removed from Direct Numerical Simulations, and the turbulence model controls the separation if turbulent. The agreement is quite good for drag, shedding frequency, pressure, and skin friction. However the comparison is obscured by large modulations of the vortex shedding and drag which are very similar to those seen in experiments but also, curiously, durably different between cases especially of the LS type. The longest simulations reach only about 50 shedding cycles. Disagreement with experimental Reynolds stresses reaches about 30%, and the length of the recirculation bubble is about double that measured. The discrepancies are discussed, as are the effects of grid refinement, Reynolds number, and a turbulence-model curvature correction. The finest grid does not give the very best agreement with experiment. The results add to the validation base of the Detached-Eddy Simulation (DES) technique for smooth-surface separation. Unsteady Reynolds-averaged simulations are much less accurate than DES for LS cases, but very close for TS cases. Cases with a more intricate relationship between transition and separation are left for future study.
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| [158] |
Stability analysis of cavitating flowsthrough inducers . |
| [159] |
Unsteady pressure fluctuation characteristics in the process ofbreakup and shedding of sheet/cloud cavitation . |
| [160] |
Dynamicsof attached turbulent cavitating flows .
Stationary and non-stationary characteristics of attached, turbulent cavitating flows around solid objects are reviewed. Different cavitation regimes, including incipient cavitation with traveling bubbles, sheet cavitation, cloud cavitation, and supercavitation, are addressed along with both visualization and quantitative information. Clustered hairpin type of counter-rotating vapor vortices at incipient cavitation, and finger-like structure in the leading edge and an oscillatory, wavy structure in the trailing edge with sheet cavitation are assessed. Phenomena such as large-scale vortex structure and rear re-entrant jet associated with cloud cavitation, and subsequent development in supercavitation are described. Experimental evidence indicates that the lift and drag coefficients are clearly affected by the cavitating flow structure, reaching minimum and maximum, respectively, at cloud cavitation. Computationally, progress has been made in Navier tokes (N ) based solution techniques. Issues including suitable algorithm development for treating large density jump across phase boundaries, turbulence and cavitation models, and interface tracking are discussed. While satisfactory predictions in wall pressure distribution can be made in various cases, aspects such as density and stress distributions exhibit higher sensitivity to modeling details. A perspective of future research needs in computational modeling is offered.
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| [161] |
Large eddy simulation ofa sheet/cloud cavitation on a NACA0015 hydrofoil .
A single fluid model of sheet/cloud cavitation is developed and applied to a NACA0015 hydrofoil. First, a cavity formation model is set up, based on a three-dimensional (3D) non-cavitation model of Navier–Stokes equations with a large eddy simulation (LES) scheme for weakly compressible flows. A fifth-order polynomial curve is adopted to describe the relationship between density coefficient ratio and pressure coefficient when cavitation occurs. The Navier–Stokes equations including cavitation bubble clusters are solved using the finite-volume approach with time-marching scheme, and MacCormack’s explicit-corrector scheme is adopted. Simulations are carried out in a 3D field acting on a hydrofoil NACA0015 at angles of attack 4°, 8° and 20°, with cavitation numbers σ = 1.0, 1.5 and 2.0, Re = 10 6, and a 360 × 63 × 29 meshing system. We study time-dependent sheet/cloud cavitation structures, caused by the interaction of viscous objects, such as vortices, and cavitation bubbles. At small angles of attack (4°), the sheet cavity is relatively stable just by oscillating in size at the accumulation stage; at 8° it has a tendency to break away from the upper foil section, with the cloud cavitation structure becoming apparent; at 20°, the flow separates fully from the leading edge of the hydrofoil, and the vortex cavitation occurs. Comparisons with other studies, carried out mainly in the context of flow patterns on which prior experiments and simulations were done, demonstrate the power of our model. Overall, it can snapshot the collapse of cloud cavitation, and allow a study of flow patterns and their instabilities, such as “crescent-shaped regions.”
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| [162] |
Simulatingcavitating liquid jets using a compressible and equilibriumtwo-phase flow solver .
In internal combustion engines the injection of high-pressure liquid fuel into a low-pressure gas through a nozzle passage is an important process to atomize the liquid and achieve optimal fuel–air mixing. A Computational Fluid Dynamics (CFD) model is developed in the present work to simulate the internal- and external-nozzle flow fields in an integrated way. The model assumes that the flow within and near the nozzle is continuous, and an Eulerian flow solver is developed using the general conservation laws of fluid dynamics. Differences in the thermodynamic states of the liquid and gas phases are modeled with a Stiffened Gas Equation of State (EOS). A practical phase equilibrium solver is developed, and is implemented into the Eulerian flow solver to predict phase changes in the flows – in particular, cavitation of the liquid within the injector nozzle passage. The combined equilibrium solver is applied to single-component and two component flows with one component being non-condensable air. A number of test problems are simulated to verify the numerical methods and validate the proposed models. These include two-phase shock tube problems, a converging–diverging nozzle flow problem, a submerged liquid jet problem, and a cavitating liquid jet problem.
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| [163] |
Shedding phenomenon of ventilated partial cavitationaround an underwater projectile . |
| [164] |
Experimental and numerical investigation of ventilated cavitatingflow with special emphasis on gas leakage behavior and re-entrantjet dynamics .
61Ventilated cavitating flow structure is studied by experimental and numerical methods.61The method with filter-based model is proposed to simulate the ventilated cavity.61The influence ofQvandFron the gas leakage behavior is discussed.61The mechanism of two types of re-entrant behaviors is illustrated.
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| [165] |
Ascaled underwater launch system accomplished by stress wavepropagation technique . |
| [166] |
Fundamentals of digital particle imagevelocimetry . |
| [167] |
Identification of largescale structures in the wake of cavitating hydrofoils using LESand time-resolved PIV//Proceedings of 26th Symposium on NavalHydrodynamics, Rome, Italy .
Large-scale three-dimensional cavitating structures exist in the wake of two-dimensional hydrofoils, as a result of sheet/cloud cavitation. This type of cavitation produces unsteady lift on most hydrofoils -- including the NACA 0015 studied here -- but is sufficiently periodic to have potential for control. A Large Eddy Simulation (LES) based on a virtual single-phase, fully compressible cavitation model captures the complex dynamical features of this highly unsteady cavitating flow well. The LES results are compared to Time-Resolved Particle Image Velocimetry (TR-PIV, recorded at 2000Hz) in the region immediately downstream of the hydrofoil, with particular attention to the predicted vortex shedding mechanisms. With a careful choice of photometric parameters and adaptive masking, the large, vortical, cavitating structures are identified quantitatively. The existence of the primary vortex pair predicted by the LES is confirmed by TR-PIV. This vortex pair produces large cross-stream velocities, with a general ejection direction of 3/4 to the free stream. However, the shedding pattern as recorded with TR-PIV is not nearly as regular as in the LES, due to the limited number of spanwise grid points in the simulation and the highly three- dimensional nature of cloud cavitation shedding in the experiment.
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| [168] |
Time-dependent turbulentcavitating flow computations with interfacial transport andfilter-based models .
Turbulent cavitating flow computations need to address both cavitation and turbulence modelling issues. A recently developed interfacial dynamics-based cavitation model (IDCM) incorporates the interfacial transport into the computational modelling of cavitation dynamics. For time-dependent flows, it is known that the engineering turbulence closure such as the original k - model often over-predicts the eddy viscosity values reducing the unsteadiness. A recently proposed filter-based modification has shown that it can effectively modulate the eddy viscosity, rendering better simulation capabilities for time-dependent flow computations in term of the unsteady characteristics. In the present study, the IDCM along with the filter-based k - turbulence model is adopted to simulate 2-D cavitating flows over the Clark-Y airfoil. The chord Reynolds number is Re =7.0 105. Two angles-of-attack of 5 and 8 associated with several cavitation numbers covering different flow regimes are conducted. The simulation results are assessed with the experimental data including lift, drag and velocity profiles. The interplay between cavitation and turbulence models reveals substantial differences in time-dependent flow results even though the time-averaged characteristics are similar. Copyright 2005 John Wiley & Sons, Ltd.
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| [169] |
Vorticity and VortexDynamics . |
| [170] |
Experimental andnumerical investigation of hydroelastic response of a flexiblehydrofoil in cavitating flow .
The objective of this paper is to investigate the hydroelastic response of a flexible NACA66 hydrofoil in cavitating flows by combined experimental and numerical studies. Experimental results are presented for rigid/flexible NACA66 hydrofoils fixed at α0=8° for subcavitating (σ=8.0) and cavitating flows (σ=1.4). The high-speed video camera and Laser Doppler Vibrometer are applied to investigate the flow patterns and vibration characteristics. The multiphase flow is modeled with the incompressible and unsteady Reynolds Averaged Navier–Stokes (URANS) equations. The k61ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that the cavitation has significant effect on the foil deformation and the unsteady characteristics of the hydroelastic response. The bending deformation is enhanced when the cavitation occurred. Meanwhile, the hydroelastic response has also affected the cavitation development and the vortex structure interactions. The cavity shedding frequency and vortex shedding and interacting frequency for the flexible hydrofoil are higher than that for the rigid hydrofoil. Compared to the periodic development of the hydrodynamic coefficients for the rigid hydrofoil, the hydrodynamic load coefficients of the flexible hydrofoil fluctuate more significantly, and the chaotic response of the flexible hydrofoil is mainly attributed to the disturbance caused by the flow-induced flutter and deformation of the foil. The evolution of the transient cavity shape and the corresponding hydrodynamic response can be divided into three stages: During the development of the attached cavity, the partial sheet cavity is formed and develops with the lift and drag coefficients increasing, while the maximum attached cavity formed on the suction side of the flexible hydrofoil is larger than that of the rigid hydrofoil, which is caused by the increase of the effective angle of attack due to the twist deformation. During the vortex structure interaction and cavity shedding process, the hydrodynamic loads for the flexible hydrofoil fluctuate because of the foil deformation, leading to a more complex cavitation pattern. During the residual cavity shedding and partial sheet cavity formation process, the cavities, together with the counter-rotational vortex structures, shed downstream totally and are followed by the formation of partial sheet cavities in next period, which is in advance for the flexible hydrofoil due to the larger effective angle of attack.
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| [171] |
LES investigationon cavity shedding of a Clark-Y hydrofoil under different attackangle with an integration method//IOP Conference Series:Earth and Environmental Science , |
| [172] |
Factors of safety for richardsonextrapolation .
A factor of safety method for quantitative estimates of grid-spacing and time-step uncertainties for solution verification is developed. It removes the two deficiencies of the grid convergence index and correction factor methods, namely, unreasonably small uncertainty when the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy and lack of statistical evidence that the interval of uncertainty at the 95% confidence level bounds the comparison error. Different error estimates are evaluated using the effectivity index. The uncertainty estimate builds on the correction factor method, but with significant improvements. The ratio of the estimated order of accuracy and theoretical order of accuracy P instead of the correction factor is used as the distance metric to the asymptotic range. The best error estimate is used to construct the uncertainty estimate. The assumption that the factor of safety is symmetric with respect to the asymptotic range was removed through the use of three instead of two factor of safety coefficients. The factor of safety method is validated using statistical analysis of 25 samples with different sizes based on 17 studies covering fluids, thermal, and structure disciplines. Only the factor of safety method, compared with the grid convergence index and correction factor methods, provides a reliability larger than 95% and a lower confidence limit greater than or equal to 1.2 at the 95% confidence level for the true mean of the parent population of the actual factor of safety. This conclusion is true for different studies, variables, ranges of P values, and single P values where multiple actual factors of safety are available. The number of samples is large and the range of P values is wide such that the factor of safety method is also valid for other applications including results not in the asymptotic range, which is typical in industrial and fluid engineering applications. An example for ship hydrodynamics is provided. [DOI: 10.1115/1.4001771]
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| [173] |
A general framework for verification andvalidation of large eddy simulations .
A general framework (methodology and procedures) for verification and validation (V&V) of large eddy simulations in computational fluid dynamics (CFD) is derived based on two hypotheses. The framework allows for quantitative estimations of numerical error, modeling error, their coupling, and the associated uncertainties. To meet different needs of users based on their affordable computational cost, various large eddy simulation (LES) V&V methods are proposed. These methods range from the most sophisticated seven equation estimator to the simplest one-grid estimator, which will be calibrated using factors of safety to achieve the objective reliability and confidence level. Evaluation, calibration and validation of various LES V&V methods in this study will be performed using rigorous statistical analysis based on an extensive database. Identification of the error sources and magnitudes has the potential to improve existing or derive new LES models. Based on extensive parametric studies in the database, it is expected that guidelines for performing large eddy simulations that meet pre-specified quality and credibility criteria can be obtained. Extension of this framework to bubbly flow is also discussed.
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| [174] |
Modelling of hydrodynamic cavitatingflows considering the bubble-bubble interaction .
A cavitation model considering the second-order derivative and bubble-bubble interaction is proposed. The bubble wall velocities are obtained by integrating the modified Rayleigh equation. The bubble-bubble interaction is measured by the coupling strength, which is modified for the hydrodynamic cavitating flows during the evaporation and decreases sharply at the cluster boundary during the condensation. The phase change rates are greatly reduced when the bubble-bubble interaction is considered, except at extremely low vapor volume fraction. Numerical results are given for the collapse of cavitation clusters and the unsteady cavitating flows around two NACA0015 hydrofoils. Comparisons are made with the experimental data and Zwart–Gerber–Belamri cavitation model.
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| [175] |
Numerical modeling ofsupercavitating propeller flows .
A three-dimensional boundary element method is used for the numerical modeling of supercavitating propellers subjected to nonaxisymmetric inflow. The method has been developed in the past for the prediction of unsteady sheet cavitation for conventional propellers. Toallow for the treatment of supercavitating propellers, the method is extended to model the separated flow behind trailing edges with nonzero thickness. The convergence of the method is studied. Results from numerical validation, as well as comparisons of predictions with experimental measurements, are provided.
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| [176] |
Areview of studies of mechanism and prediction of tip vortexcavitation inception .
The inception of the tip vortex cavitation (TVC) is a very important problem in cavitation researches. The study of the mechanism of the TVC inception is not only conducive to its prediction, but also helps to suppress or suspend the occurrence of cavitation. In this paper, the research progresses on the TVC inception including theoretical, experimental and numerical studies mainly in the last two decades are reviewed. It is shown that the TVC inception is affected by complicated factors, such as the water quality, the average pressure and the fluctuating pressure. In the scaling law for the determination of the TVC inception, all these factors are considered. To precisely describe the scaling law, more investigations are needed to understand the effects of the water quality and the fluctuating pressure.
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| [177] |
On the flow structure andturbulence in the closure region of attached cavitation//22thSymposium on Naval Hydrodynamics . |
| [178] |
A review ofmicroscopic interactions between cavitation bubbles and particlesin silt-laden flow .
Erosion through synergetic effects between cavitation erosion and particle abrasion in silt-laden flow seriously affects the safe operations of hydroturbines. In this review, recent advances of cavitation inception on particles and microscopic interactions between bubbles and particles are reviewed and discussed. For cavitation inception, influences of several paramount parameters (e.g. types, sizes, shape and surface structure of particles, pressurization and memory effects) have been revealed and discussed. The interaction mechanisms between cavitation bubbles and particles are demonstrated using experimental data obtained with a single particle. Through the microscopic interactions, the particles can be accelerated by the collapsing bubbles up to 40m/s and also be possibly split up by the cavitation, leading to deagglomeration of particle clusters.
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| [179] |
A cavitation model forcomputations of unsteady cavitating flows .
A local vortical cavitation(LVC) model for the computation of unsteady cavitation is proposed.The model is derived from the Rayleigh lesset equations,and takes into account the relations between the cavitation bubble radius and local vortical effects.Calculations of unsteady cloud cavitating fows around a Clark-Y hydrofoil are performed to assess the predictive capability of the LVC model using well-documented experimental data.Compared with the conventional Zwart's model,better agreement is observed between the predictions of the LVC model and experimental data,including measurements of time-averaged fl w structures,instantaneous cavity shapes and the frequency of the cloud cavity shedding process.Based on the predictions of the LVC model,it is demonstrated that the evaporation process largely concentrates in the core region of the leading edge vorticity in accordance with the growth in the attached cavity,and the condensation process concentrates in the core region of the trailing edge vorticity,which corresponds to the spread of the rear component of the attached cavity.When the attached cavity breaks up and moves downstream,the condensation area fully transports to the wake region,which is in accordance with the dissipation of the detached cavity.Furthermore,using vorticity transport equations,we also fin that the periodic formation,breakup,and shedding of the sheet/cloud cavities,along with the associated baroclinic torque,are important mechanisms for vorticity production and modification When the attached cavity grows,the liquid apour interface that moves towards the trailing edge enhances the vorticity in the attached cav-ity closure region.As the re-entrant jet moves upstream,the wavy/bubbly cavity interface enhances the vorticity near the trailing edge.At the end of the cycle,the break-up of the stable attached cavity is the main reason for the vorticity enhancement near the suction surface.
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| [180] |
Determination of frequencies of oscillations of cloudcavitation on a 2-D hydrofoil from high-speed camera observations .
A method is presented to determine significant frequencies of oscillations of cavitation structures from high-speed camera recordings of a flow around a 2-D hydrofoil. The top view of the suction side of an NACA 2412 hydrofoil is studied in a transparent test section of a cavitation tunnel for selected cloud cavitation regimes with strong oscillations induced by the leading-edge cavity shedding. The ability of the method to accurately determine the dominant oscillation frequencies is confirmed by pressure measurements. The method can resolve subtle flow characteristics that are not visible to the naked eye. The method can be used for noninvasive experimental studies of oscillations in cavitating flows with adequate visual access when pressure measurements are not available or when such measurements would disturb the flow.
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| [181] |
A new algorithm for DNS simulations of cavitating flowsusing homogeneous mixture approach//AIP Conference Proceedings , |
| [182] |
A two-phase flowmodel for predicting cavitation dynamics//Proceedings of the 5thInternational Conference on Multiphase Flow, Yokohama, Japan . |
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