Engineering Extrapolation to Flight Reynolds Number for Supercritical Airfoil Pressure Distribution Based on CFD Results

Abstract

Pressure distribution of supercritical airfoil at flight Reynolds number could not be fully simulated except in cryogenic wind tunnel such as NTF (National Transonic Facility) and ETW (European Transonic Wind tunnel), which is costly and time resuming. This paper aimed to explore an engineering extrapolation to flight Reynolds number from low Reynolds number wind tunnel data for supercritical airfoil pressure distribution. However, the extrapolation method requiring plenty of data was investigated based on the CFD results for the reason of low cost and short period. Flows over a typical supercritical airfoil were numerically simulated by solving the two dimensional Navier-Stokes equations, with applications of ROE scheme spatial discretization and LU-SGS time march. Influence of computational grids convergence and turbulent models were investigated during the process of simulation. The supercritical airfoil pressure distribution were obtained with Reynolds numbers varied from 3.0×106 to 30×106 per airfoil chord, angles of attack from 0 degree to 6 degree and Mach numbers from 0.74 to 0.8. Simulated results indicated that weak shock existed on the upper surface of supercritical airfoil at cruise condition, that the shock location, shock strength and trailing edge pressure were dependent of Reynolds number, attack angles and Mach numbers. A similar parameter describing the Reynolds number effects factors was obtained by analyzing the relationship of shock wave location, shock front pressure and trailing edge pressure. Based on the similar parameter, airfoil pressure distribution at Reynolds number 30×106 was obtained by extrapolation. It was shown that extrapolated result compared well with simulated result at Reynolds number 30×106, implying that the engineering method was at least promising applying to the extrapolation of low Reynolds number wind tunnel data.