Navier–Stokes and Direct Simulation Monte Carlo Predictions for Laminar Hypersonic Separation

Axisymmetric direct simulationMonte Carlo (DSMC) and Navier–Stokes simulations are performed as part of a code validation effort for hypersonic ows. The ow eld examined herein is the Mach 11 laminar ow over a 25– 55-deg blunted biconic. Experimental data are available for surface pressure and heat ux at a Knudsen number Kn = 0.019 based on the nose radius. Simulations at a reduced freestream density (Kn = 0.057) are performed to explore the region of viability of the numerical methods for hypersonic separated ows. A detailed and careful effort is made to address the numerical accuracy of these simulations, including iterative and grid convergence studies for Navier–Stokes and temporal,grid,andparticle convergence studies for DSMC.Goodagreement is found between the DSMC and Navier–Stokes simulation approaches for surface properties as well as velocity pro les within the recirculation zone for the reduced density case. The results obtained indicate that the failure of earlier DSMC simulations atKn = 0.019 is due to insuf cient grid re nement within the recirculation zone. Furthermore, it is shown that accurate simulations of the biconic at the experimental conditionswith the DSMCmethod are not yet possible due to the extreme computational cost. Nomenclature d = molecular diameter, m f = general solution variable Kn = Knudsen number based on nose radius, ¸=RN L = characteristic length scale, m n = number density, particles/m3 p = pressure,N/m2, order of accuracy q = heat ux, W/m2 R = speci c gas constant, 296.8 for N2, J/kg ¢K Re = Reynolds number, V L= RN = nose radius, 0.00635m r = grid re nement factor T = translational temperature,K t = time, s u = axial velocity component, m/s V = velocity magnitude, m/s x = axial coordinate,m y = radial coordinate,m ° = ratio of speci c heats ¸ = mean free path, 1=[