DSMC simulations of rarefied hypersonic flows

Abstract

When the conditions of the flow are rarefied and hypersonic, a more suitable alternative to the use of Navier-Stokes equations for developing a numerical solution is the Direct Simulation Monte Carlo method (DSMC). The method was developed about 50 years ago by Graeme Bird [1] and now is a well-established technique for modelling low density gas flows. DSMC is a particle method, which employs a large number of particles in modelling a rarefied gas. In this thesis the application and performance of a new open-source DSMC computational kernel, called SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) (as described in [2]) is reported. Four cases are examined: a) a hypersonic flat plate simulation and comparison with DAC (DSMC Analysis Code) [3]; b) a Mach 20.2 flow over a 70-degree planetary probe; and c) a Mach 15.6 flow over a flared cylinder d) a hypersonic flow around a biconic. Those test cases were selected in order to investigate the ability of the SPARTA open-source code in reproducing the fine features of the complicated flow phenomena connected with shock-boundary and shock-shock interactions, and its computational efficiency in a parallel computation environment. Moreover, additional objectives of this assessment procedure were the establishment of a “best-practice” for the construction of the computational grids around the examined bodies, and the gain of know-how on the optimal use of the open-source code.

The aforementioned test cases, along with their variants, have been previously used by other researchers to validate some of the very well-known parallel DSMC solvers, such as DAC [3], SMILE [4], MONACO [5], ICARUS [6], MGDS [7] and dsmcFoam [8]. For example, dsmcFoam solver, among other test cases, was also validated against the flow over the 70-degree blunt cone [9]. DAC solver, which is NASA’s code for DSMC simulations, has been validated against a 25/65 degrees sharp cone [10]. Furthermore, MONACO has been tested on a flow over a blunt cone, along with other validation cases, such as a blunt cone at an angle of attack [11]. Some important characteristics of the flows developed around the test objects are very steep gradients of velocity, temperature and density, shock/shock interaction, compression and rapid expansion. Such features render the numerical simulation of these complex flows very demanding so that a special study on the simulation parameters (number of particles, grid density, time step, etc.) is needed.

For the flat plate test case, simulation experiments have been conducted in a free-jet expansion tunnel [12], forming a database to be used for code validation purposes. Regarding the planetary probe test case, its form was decided by the AGARD Group 18 [13], while the experimental results, to be used for code validation, can be found in [13], [14]. Regarding the flared cylinder test case, a large number of experiments have been conducted in order to acquire accurate aero-thermodynamic results. The experiments were conducted on the SR3 wind tunnel, using nitrogen as the flow gas. The flared cylinder and the biconic experiments, used in this study, were conducted at the Buffalo Research Center (CUBRC) wind tunnel [15], [16]. These test cases were selected because the shapes used have the ability to reproduce shock/shock and shock/boundary interactions.