Parallel, Steady/Unsteady DSMC Simulations of the Aerodynamics of Sounding Rockets

Abstract

Over the past several decades, atomic oxygen (AO) measurements taken from sounding rocket sensor payloads in the Mesosphere and lower Thermosphere (MALT) have shown marked variability. AO data retrieved from the second Coupling of Dynamics and Aurora experiment (CODA II) have shown that the data is highly dependent upon rocket orientation. Many sounding rocket payloads including CODA II, contain AO sensors that are located in close proximity to the payload surface and are thus significantly influenced by compressible, aerodynamic effects. These effects serve to inhibit the AO sensors’ ability to accurately determine undisturbed atmospheric conditions. The present research numerically models the influence caused by these aerodynamic effects using a newly developed parallel, steady/unsteady, three-dimensional, DSMC solver entitled foamDSMC. The solver’s parallel capabilities as well as it’s unsteady functionality demonstrates significant improvements over previous research conducted by the present authors’. The solver is used to simulate the steady flow regime at two kilometer intervals along both the up-leg and down-leg trajectories. Unsteady results are also presented and simulated near apogee. The results are used to create correction functions based on the ratio of undisturbed to disturbed flowfield concentrations. The numerical simulations verify the experimental results showing the strong influence of rocket orientation on concentration. The correction functions, when applied to uncorrected CODA II data sets, show a significant improvement in terms of minimizing the effects of compressible flow aerodynamics. A rarefied gas may be divided into several different flow regimes in accordance with its level of rarefaction as quantified by the Knudsen number (Kn). A significantly large number of flows may be classified within the transition regime (0.1 < Kn < 10), and constitute numerical simulation limits well outside that of conventional NavierStokes, continuum based solvers. Traditionally, the Boltzmann equation, based on kinetic theory, remained the only viable option for solution of these high Kn number flows. Recently however, direct particle simulation methods, not relying on the quantification of the velocity distribution function have become mainstay. Particularly relevant, is the direct simulation Monte Carlo (DSMC) method of G.A. Bird. The DSMC method is a direct simulation method based on kinetic theory, and may be regarded as a numerical solution to the Boltzmann equation in the limit of very large numbers of simulated molecules. 1,2 The method, as its name connotes may be categorized as a Monte Carlo method in that it makes extensive use of random numbers to help in the stochastic generation of continuum variables. The primary objective of the method is to approximate these variables by means of modeling the interactions of a statistically significant number of simulated molecules, each representing a much larger subset of the real, un-modeled gas. The deterministic motions and probabilistic collisions of these simulated molecules are modified over sufficiently small time steps, which is governed by the mean collision frequency. Since the tracking and molecular interactions are conducted on a particle by particle basis, the conservation of mass, momentum, and energy may be enforced to machine accuracy. 3