Development of an object-oriented three-dimensional Burnett equations solver for computing hypersonic flows in continuum-transition regime

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For computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen numbers (Kri) lie in the continuum-transition regime, a set of extended three-dimensional hydrodynamic equations are required which are more accurate than the NavierStokes equations and computationally more efficient than the Direct Simulation Monte Carlo (DSMC) computations. One such set is the Burnett equations which are obtained from the Chapman-Enskog expansion of the Boltzmann equation (with Knudsen number (Kri) as a small parameter) to O(Kn). In this paper, the threedimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn) and adding the augmented terms (linear third-order super Burnett terms with coefficients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances). The equations are solved using an explicit time-stepping scheme with Steger-Warming flux-vector splitting algorithm for the convective flux terms and second-order central differencing for the stress and heat flux terms. Maxwell-Smoluchowski slip boundary conditions are employed at the wall. 3-D augmented Burnett equations solver is developed both in FORTRAN?? and object-oriented JAVA. Both the FORTRAN and JAVA codes are applied to compute the three-dimensional hypersonic blunt-body flows for various range of Knudsen numbers and Mach numbers producing identical results. The focus of this paper is on development of a JAVA code for a very complex set of equations and its application to 3-D complex configurations. x Graduate Research Assistant * Bloomfield Distinguished Professor and Executive Director, Fellow AIAA Copyright © by authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. NOMENCLATURE et total energy per unit mass E total flux vector in x direction Ej convective flux vector in x direction EV viscous flux vector in x direction F total flux vector in y direction F! convective flux vector in y direction Fv viscous flux vector in y direction G total flux vector in z direction GI convective flux vector in z direction GV viscous flux vector in z direction Kn Knudsen number L reference length M Mach number Pr Prandtl number P pressure qt heat flux terms Q unknown vector in physical domain rn nose radius Re Reynolds number R gas constant T temperature Tw wall temperature u velocity components in x direction v velocity components in y direction w velocity components in z direction a accommodation coefficient for wall surface a/, P/ coefficients of stress terms in augmented Burnett equations y/ coefficients of heat flux terms in augmented Burnett equations K thermal conductivity K mean free path of gas molecules ILI viscosity 0, coefficients of heat flux terms in augmented Burnett equations p density a,y stress tensor a reflection coefficient for wall surface Y specific heat ratio co, coefficients of stress terms in augmented Burnett equations w circular frequency of perturbation American Institute of Aeronautics and Astronautics