Hybrid DSMC-CFD Simulations of Hypersonic Flow over Sharp and Blunted Bodies

A hybrid particle-continuum computational framework is developed and presented for simulating hypersonic interacting flows, aimed to be faster and more accurate than conventional numerical methods. The framework consists of the direct simulation Monte Carlo-Information Preservation (DSMC-IP) method coupled with a Navier-Stokes solver. Since the DSMCIP method provides the macroscopic information in each time step, determination of the continuum fluxes across the interface between the particle and continuum domains becomes straightforward. Numerical experiments of hypersonic flows over a simple blunted cone and a much more complex hollow cylinder-flare are conducted. The solutions for the two geometries considered from the hybrid framework are compared in detail with pure particle calculations. It is concluded that the hybrid method basically works very well. Numerical accuracy improvement is achieved in simple flows but unclear in complex flows. It is also concluded that the numerical efficiency obtained with the hybrid method is far from satisfactory. Overall, the hybrid framework provides a foundation for future development. Introduction The flow around a space vehicle during its atmospheric re-entry always spans a very wide range of flow regimes, from the continuum to the transition, depending upon the flight altitude and the characteristic length scale of the fuselage. For many years, efforts have been undertaken on developing a particlecontinuum coupled numerical method that is fast and at the same time physically accurate. Among many particle-based schemes, the direct simulation Monte Carlo (DSMC) method is the most common one. The DSMC method emulates the nonlinear Boltzmann equation by simulating the real molecule collisions with collision frequencies and scattering velocity distributions determined from the kinetic theory of a dilute gas. On the other hand, among many ∗Graduate Student Research Assistant, AIAA Student Member, E-mail: ([email protected]) †Professor, AIAA Associate Fellow, E-mail: ([email protected]) Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. continuum schemes, the computational fluid dynamics (CFD) method that solves the Navier-Stokes (NS) equations can be regarded as the most popular approach for these flows. A major issue in making a combination of the two numerical methods comes from the information exchange at the interface between the particle and continuum domains. At the interface, macroscopic flow properties have to be provided to the CFD method to evaluate the net fluxes and to the DSMC method to initialize the particles entering from the continuum domain into the particle domain. Several attempts have been considered, such as the Marshak condition, the kinetic flux-vector splitting (KFVS) scheme, and adaptive mesh and algorithm refinement (AMAR) embedding a particle method. To date, a robust, multi-dimensional scheme that is capable of handling nonequilibrium, hypersonic compressed flows has not yet been accomplished. Since the DSMC technique inherits very strong statistical fluctuations, it always needs several steps of sampling before smooth macroscopic flow properties can be obtained. A hybrid approach in this fashion is considered as weakly coupled and is inadequate for complex nonequilibrium flows. To overcome the fluctuations, Fan and Shen first proposed an Information Preservation (IP) technique. The technique was later further developed by others for low speed rarefied gas flows, such as micro-electro-mechanical systems (MEMS). In the latest development by Sun and Boyd, an additional temperature term is introduced in the energy model to balance the translational energy carried by a particle moving from cell to cell. Another issue regarding the development of a hybrid method is to know when to switch between the methods. Since it is well known that the NS equations are not valid under rarefied conditions, it is general to use a continuum breakdown parameter as the switching criterion. For the hypersonic flows mentioned above, this issue has been investigated in our previous work and it is concluded that a proposed parameter Knmax ≡ max (KnD,KnT ,KnV ) (1) with a threshold value of 0.05 can best predict the regions where the Navier-Stokes equations fail. The 1 of 13 36th AIAA Thermophysics Conference 23-26 June 2003, Orlando, Florida AIAA 2003-3644 Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Knudsen number in Eq. 1 is expressed as