values of its aerodynamic coefficients have to be determined for those three regimes. Experimentation of low-density flows being both complex and expensive, a numerical approach is preferred. Z
X
Z
Y
X
Mach 14 12 10 8 6 4 2
(a)
Z
Y
X
Mach 22 18 14 10 6 2
(b)
Y
Mach 25 21 17 13 9 5 1
(c)
Figure 3.1: Effect of the rarefaction on the Mach number flow field for the flower geometry, respectively at Kn = 30.2 (a), Kn = 2.14 (b) and Kn = 0.345 (c). Rarefied flows are clearly different from continuous flows, in this case the bow shock is thicker and the wake is barrely present
3.2 Direct Simulation Monte Carlo Several approaches exist for numerical modelling of rarefied gas flows: direct Boltzmann equation solution methodology, gas kinetic Navier-Stokes schemes, moment methods, and direct simulation Monte Carlo (DSMC). Among those, DSMC is the most widely used technique. It has a high degree of accuracy, is conceptually simple, and is easily applicable to complex geometries. The method was developed in the early 1960’s by Prof. Graeme Bird, from the University of Sydney, and has been continuously developed and improved since then. It is valid for any gas flow for which the collision cross section is smaller than the distance between atoms or molecules. Unfortunately, the memory and computing performance requirements increase much faster than the number of simulated particles. Therefore, it is only used for rarefied and transitional flows simulation. Computational fluid dynamics (CFD), which is not applicable to flows with a certain degree of non-equilibrium, is preferred for continuum flow simulation, where DSMC methods would require too important computational power. [22] Basically, the DSMC performs a probabilistic simulation on a limited number of simulated particles, each of them representing a large number of molecules or particles, in order to reproduce the physics of the Boltzmann equation. Operations are performed in two sequences. The particles are first moved through the computational domain, according to their velocity vector, and assigned to a new cell if necessary. Particles leaving the computational domain are removed. The particles are then organized into pairs and collisions are performed. Collisions between particles and between particles and a surface are calculated using specified probabilistic, phenomenological models. The simulation begins in vacuum, and ends when steady state conditions have been reached. When the simulation is finished, the field and surface quantities are sampled. [23] The simulations presented in this study were performed with the Rarefied Gas Dynamics Analysis System (RGDAS), developed by the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences. It is an extended 18