When compressed gas is ejected from a nozzle into a low-pressure environment, the shock wave diffracts around the nozzle lip and a vortex loop will form. The phenomenon has been widely investigated in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has not received as much attention. It is necessary to understand this transient flow in rarefied environments to improve thrust vector control and avoid potential contamination and erosion of spacecraft surfaces. This work provides numerical results of the vortex loop formation caused by shock wave diffraction around a 90° corner using the direct simulation Monte Carlo method and the compressible Navier–Stokes equations with the appropriate Maxwell velocity slip and the von Smoluchowski temperature jump boundary conditions. The Mach number and rarefaction effects on the formation and evolution of the vortex loop are discussed. A study of the transient structures of vortex loops has been performed using the rorticity concept. A relationship of mutual transformation between the rorticity and shear vectors has been discovered, demonstrating that the application of this concept is useful to understand vortex flow phenomena.

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Numerical investigation of rarefied vortex loop formation due to shock wave diffraction with the use of rorticity

Hypersonic re-entry vehicles aerothermodynamic investigations provide fundamental information to other important disciplines like materials and structures, assisting the development of thermal protection systems (TPS) efficient and with a low weight. In the transitional flow regime, where thermal and chemical equilibrium is almost absent, a new numerical method for such studies has been introduced, the direct simulation Monte Carlo (DSMC) numerical technique. Verification and validation efforts are needed to lead to its acceptance. In this work, the Monte Carlo simulator OpenFOAM and Sparta have been studied and benchmarked against numerical and theoretical/experimental data for inert and chemically reactive flows. The results show the validity of the data found with the DSMC. It is shown how a simulation with a mean value of one particle per cell gives sufficiently good results with very low computational resources. This achievement aims to reconsider the correct investigation method in the transitional regime where both the direct simulation Monte Carlo (DSMC) and the computational fluid-dynamics (CFD) can work, can work, but with a different computational effort.

Francesco Pellicani

Papers

Atmosphere Re-Entry Simulation Using Direct Monte Carlo Method (DSMC)