Investigation of Continuum Breakdown in Hypersonic Flows Using a Hybrid DSMC-NS Algorithm

Abstract

A new method of determining continuum breakdown in hypersonic flows that is part of a modular particlecontinuum numerical method is presented. The modular particle-continuum method loosely couples direct simulation Monte-Carlo and Navier-Stokes methods which operate in different regions, use different mesh densities, and are updated using different sized timesteps. The hybrid method includes overlapping regions where both particle and continuum methods are used. The new method of detecting continuum breakdown involves the direct comparison of particle and continuum solutions within such overlapping regions. Such a method of continuum breakdown detection eliminates the use of a breakdown parameter and associated empirical cutoff value used in the majority of prior hybrid research. Hybrid simulations of hypersonic flow over a cylinder using this new method are shown to accurately reproduce the flowfield properties and heating rates of full DSMC simulations. The new method of continuum breakdown detection is more computationally expensive than computing a breakdown parameter and is more sensitive to statistical scatter. EHICLES traveling at hypersonic speeds and at high altitudes may generate flowfields that contain a mixture of near-continuum and nonequilibrium regions. Near-continuum flow is present in highly compressed regions downstream of strong shock waves, in stagnation regions, and in the far-wake of the vehicle. Nonequilibrium flow is present in the interiors of shock waves and thin hypersonic boundary layers, as well as in rapidly expanding regions in the near-wake of the vehicle. The continuum assumption inherent in the Navier-Stokes (NS) equations is known to break down for nonequilibrium flow and kinetic methods must be used to accurately model such regions. The most popular kinetic method for hypersonic flows is the direct simulation Monte-Carlo (DSMC) particle method. The cell size and timestep required for an accurate DSMC simulation are limited to the local mean-free-path (λ) and mean-free-time (τc) respectively. Although the DSMC method provides an accurate model for both continuum and nonequilibrium flow, simulation of continuum regions where λ and τc are typically very small becomes computationally intensive. However, it is precisely in such near-continuum regions where the NS equations provide an accurate physical model and can be solved efficiently (without such cell size and timestep rest rictions) using methods from computational fluid dynamics (CFD). For this reason, significant research has been devote d to the development of hybrid particle-continuum numerical methods. The goal of such hybrid methods is to use efficie nt CFD methods to solve the NS equations where they are accurate and restrict use of the kinetic particle method to nonequilibrium regions only. Various hybrid methods applied to a range of applications are detailed in Refs. 1‐7. A concise summary of this prior research as well as a complete description of the hybrid algorithm used for this arti cle, called the modular particle-continuum (MPC) method, can be found in Ref. 8. The major considerations involved in the development of a hybrid DSMC-NS method include information transfer between DSMC and NS regions (requiring the control of statistical scatter), the numerical cycle that dictates when to transfer information (the coupling cycle), and determinin g in which regions the DSMC method is required (continuum breakdown). Reference 9 presents a discussion of these considerations and Ref. 8 discusses these issues in context with the MPC method used to generate the hybrid results in this article. Typically, continuum breakdown is assumed