Towards Development of a Hybrid DSMC-CFD Method for Simulating Hypersonic Interacting Flows

A preliminary hybrid particle-continuum computational framework for simulating hypersonic interacting flows is proposed. The framework consists of the direct simulation Monte Carlo-Information Preservation (DSMC-IP) method coupled with a NavierStokes solver. Since the DSMC-IP 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. A hypersonic flow over a two-dimensional wedge is considered as an example and compared with pure particle calculations. The results show that this preliminary hybrid framework is promising but several issues are yet to be resolved. Introduction Hypersonic flows are of great interest in space vehicle design because the interactions of shock/shock and shock/boundary layer create high localized temperatures and associated extremely high heating rates in the interaction region. Experimental measurements under realistic conditions are difficult to conduct due to the technical difficulties and tremendous costs. Therefore, it is in general required to analyze hypersonic flows by means of computational methods. Recently, for a set of hypersonic free stream conditions, biconic configurations and hollow cylinder/flares were extensively studied with different numerical approaches. In comparisons with experimental data, it was evident that the computational fluid dynamics (CFD) techniques based on the Navier-Stokes (NS) equations have better performance than the direct simulation Monte Carlo (DSMC) method in terms of the ∗Graduate Student Research Assistant, AIAA Student Member ([email protected]) †Graduate Student Research Assistant, AIAA Student Member ([email protected]) ‡Associate Professor, AIAA Senior Member ([email protected]) Copyright c © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. capture of flow structures and the prediction of the separation region size. However, it was shown that the CFD methods constantly over predict the heat transfer on the fore body ahead of where separation occurs. Furthermore, it was demonstrated in Ref. 8 that adjacent to the body wall, especially near the cone tip, there is a strong thermal nonequilibrium effect, that is inconsistent with the basic assumptions of the NS equations. In addition, Roy et al. showed that DSMC and CFD do agree for conditions that are more rarefied than the experiments. Therefore, the objective of the present work is to develop a combined DSMC-CFD computational method for the physically accurate and numerically efficient analysis of this class of hypersonic flows. Two primary issues must be taken into account in developing a combination of DSMC and CFD methods. We first need to know when to switch between the methods. Since it is well known that the NS equations are not valid under rarefaction conditions, it is general to use a continuum breakdown parameter as the 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 Knudsen number in Eq. 1 is expressed as