GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES

The classical Reynolds analogy relation fail on blunt-nosed bodies, as the distributions of skin frictions on curved wall surfaces differ from that on heat fluxes. With a theoretical research background on hypersonic Reynolds analogy relations, numerical simulations are presented in this paper to study the general Reynolds analogy relation on blunt-nosed bodies, as circular cylinder and power-law body, under different incoming flows. A linear relation of Reynolds analogy is obtained by theoretical analysis on the boundary layer along those surfaces. Also, numerical methods are applied to obtain solutions of N-S equations, from which skin frictions and heat fluxes and their analogy coefficients around cylinders and power-law bodies are calculated. The methods are validated by comparing the distribution of Reynolds analogy coefficients and the stagnation point heat transfer rate with former numerical and theoretical results. The convergence and grid independence are verified for the TVD method. The variation of Reynolds analogy relations are investigated in the range of Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6 and M_\infty = 3\sim 12. The present study shows that the general Reynolds analogy relation predicts the ratio between skin frictions and heat fluxes on regimes near the stagnations point for hypersonic flows. Downstream the stagnation point of circular cylinders (where \theta > 60^\circ), the Reynolds analogy relation deviates from the theoretical linear relationship in varying degrees with the growing of Reynolds number. Numerical results demonstrate that, comparing with the general Reynolds analogy relations on circular cylinders, Reynolds analogy coefficients are lower and fit linear distributions better for power-law bodies. Analyses indicate that modifications based on the shape of noses or the Reynolds number may improve the accuracy of theoretical predictions.