Rarefied Hypersonic Flow over a Sharp Flat Plate: Numerical and Experimental Results

The flow over a flat plate located in a rarefied hypersonic flow (Ma « 20, Re = 2790 and 8208) has been investigated numerically [solving NavierStokes equations (NS) and using direct simulation Monte Carlo method (DSMC)] as well as experimentally (measuring density flowfield, wall pressure and wall heat transfer). Large translational and rotational nonequilibrium effects were present and could not be reproduced by NS equations, even when accounting for velocity slip and temperature jump in the wall boundary conditions. The discusssion of results leads to information on the molecular parameters to be used for modeling collisional cross sections, R-T energy exchange, and gas-surface interaction in DSMC method. Introduction A number of studies have been carried out at the Laboratoire d'Aerothermique, consisting of considering, both experimentally and numerically, rarefied hypersonic flows over different obstacles. Numerical approaches consisted of both Navier-Stokes (NS) and direct simulation Monte Carlo (DSMC) calculations. Different objectives were assigned to these studies: checking the sensitivity of DSMC results to a number of numerical parameters (space and time discretization), checking the validity of a continuum (NS) vs a molecular (DSMC) approach of rarefied flows at the rarefaction Copyright ©1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Senior scientist, Centre National de la Recherche Scientifique (CNRS) t Research Engineer, Societe d'Etudes de constructions et de Services pour Souffleries et Installations Aerothermodynamiques (SESSIA) * Assistant-professor, Institut Universitaire de Technologic (IUT), Evry 276 FLAT PLATE WITH SHARP LEADING EDGE 277 level considered, checking the sensitivity of DSMC results to a number of physical parameters governing rotational -translational (R-T) energy exchange, gas -gas and gas -surface interaction and trying to determine these parameters from comparison between DSMC and experimental results, and clarifying the interpretation of some experimentally measured quantities (e.g. wall pressure). The discussion relative to the first objective has been presented in Ref. 1 and will not be repeated here. Description of the Work Test Cases and Experimental Work The present paper is devoted to flat plates with sharp leading edges. A companion paper submitted to this symposium discusses flat plates with truncated leading edges. The flow conditions were chosen among those that could be obtained in the SR3 low -density facility of the laboratory. Four test cases (see Table 1) were considered by combining two operating conditions of the facility (low Reynolds number for cases A and B, medium Reynolds number for C and D) and two angles of attack (i = 0 deg for B and D, i = 10 deg for A and C). Nitrogen was used as working gas. Stagnation temperature To was equal to 1100K and the length of the plate was L = O.lm. The experimental work consisted of flowfield surveys by an electron beam fluorescence probe, yielding the flowfield density distribution, wall pressure measurements, and wall heat transfer measurements using thermocouples imbedded in a thin wall. The model used for pressure measurements was made of brass. The other models were covered with black graphite paint. Heat transfer measurements were performed before any significant warming up of the model, i.e. the model wall was at room Table 1 Freestream conditions Mach number Ma^ Pressure p^ , N/m Number density rioo, m~ Temperature TOO, K Velocity Voo , m/s Mean free path AOO (m) Reynolds number Re^ — pooV^L/ p,^ Reynolds number* Re^ = /? ooVoo£//^oo Reynolds number Rew = p 2 equal to wall and stagnation temperatures, respectively. All flow parameters were non-dimensionalized by their freestream values, or derived FLAT PLATE WITH SHARP LEADING EDGE 279 Table 2 Direct simulation Monte Carlo computational parameters Test case i (deg) a f VHS fitting Number of cells Al A 10 0.8 0.5 VH A2 A 10 1 0.5 VH B2 B 0 0.8 0.5 VH w B3 B 0 1 0.5 VH 3000 B4 B 0 1 0.5 VL ti5 B 0 1 1 VH C2 C 10 1 0.5 VH 1 w Dl D 0 1 0.5 VH 6000 quantities [pooV^ for skin-friction and pooVooCp(TQ -Tw) for heat transfer rate, where />oo and Cp have their usual meaning]. Using reduced quantities, results relative to cases A and B are thus expected to be identical to results relative to cases C and D, respectively. DSMC results were obtained from a number of computer runs. The corresponding parameters are given in Table 2. Two values of the accommodation coefficient were used (0.8 and 1). Two values of the fraction / of inelastic collisions were used (1 and 0.5). Fraction / = 1 is more favorable to R-T equilibrium and more comparable to the NS hypothesis (Tt = Tr). Fraction / = 0.5 was considered to be consistent with a realistic value of the rotational collision number Zr equal to a few units. Because it was impossible to make VHS model reproduce the