EFFECT OF TRANSVERSE CURVATURE ON AXISYMMETRIC COMPRESSIBLE LAMINAR BOUNDARY LAYER

The thickness of the boundary layer over an axisymmetric slender body may be comparable to, or even of several times the local radius of the transverse curvature of the body. The practice of replacing distance of a point in the boundary layer from the axis by the local body radius, as in classical Prandtl boundary layer equatiions,is then no longer applicable.The present work discusses the effcet of the transverse curvature on the axisymmetric compressiboe laminar boundary layer flow,analogous to the work of Lighthill and Glauert for the incompressible case.The first part of the paper deals with the strong effect region, i.e., the region where the boundary layer thickness is much larger than the local body radius.The usual assumptions of perfect gas, Prandtl number equal to one and linear viscosity-temperature relation are made.Neglecting the pressure gradient,one may find a small parameter ε to characterize the transverse curvature effect.The reduced stream function is then expressed as a power series of ε and the asymptotic solutions for skin friction and heat transfer rate are found.It is shown that the singularity of the second approximation(the third term in series)near the wall may be removed by using the PLK method and the solution is then uniformly valid.For power-lawed bodies,r_w~xⁿ,the skin friction coefficient C_f and the Stanton number St in the strong effect region may be expressed as C_f=4C_e/R_ex T_w/T_e x/r_w cosφθ+0.577-In(1+2n)θ²+O(θ³,St=1/2C_f In the second part, the transverse curvature effect in the entire flow field is investigated by means of momentum integral method where the Crocco's independent variables x,μ are used.With a suitable choice of a relation between shearing stress τ and velocity μ,approximate solutions for C_f and St of the circular cylinder and circular cone, valid for the entire range of transverse curvature paameters Ω and Φ,are found Coparison of the results with the Probstein and Elliott's serics solution for the weak effect region and the solution for the strong effect region found in the first part is made.