Investigation of rarefied flow over backward-facing step in different rarefaction regimes using direct simulation Monte Carlo

Hypersonic aerothermodynamics for a re-entry vehicle approaching the earth’s atmosphere is critical in the exploration of space. These vehicles often encounter various flow regimes due to the density variations and have surface abnormalities. The backward-facing step (BFS) is one such simplified configuration for modeling anomalies around such space vehicles. The present work examines rarefied hypersonic flow over a BFS using the direct simulation Monte Carlo (DSMC) method. The purpose of this research is focused on exploring the various loads encountered by a re-entry vehicle passing through different altitudes covering different rarefaction regimes. The fluid considered was non-reacting air, with the free-stream Mach number as 25, and the Knudsen number considered ranged from 0.05-21.10. The influence of the Knudsen number on flow characteristics has been elucidated graphically in various streamwise directions. The normalised flow properties such as velocity, pressure, temperature and density showed an increasing trend with the Knudsen number due to compressibility and viscous heating effects. In all flow regimes, there was an appearance of flow recirculation. With rarefaction, the recirculation lengths decreased, whereas the boundary layer thickness showed an increase. The aerodynamic surface properties such as pressure coefficient, skin friction, and heat transfer coefficient, by and large, showed an increase with the Knudsen number. When the chemical reactions were accounted for and compared against the non-reacting flows, the velocity, pressure, and density field showed no marked variation; however, considerable variations were observed in the temperature field. Furthermore, the present study also depicts the compressibility factor contour, showing the flow regions that diverge from the ideal gas behaviour.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.

Data-Driven Nonlinear Constitutive Relations for Rarefied Flow Computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed firstly through machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between discrepancies of stress tensors and heat flux and feature vectors is established after training phase. Through the obtained off-line training model, new test case excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through a various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make DNCR method to be an effective tool in rarefied gas community, especially for hypersonic engineering applications.