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Slip effects on the stability of supersonic laminar flat plate boundary layer

Klothakis Angelos, Sawant Saurabh S., Quintanilha Helio, Theofilis, Vassilis, Levin Deborah A.

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Summary

During the past years joint efforts have been exerted by different researchers for the development of high speed air vehicles as well as hypersonic systems in general, for a wide range of applications. However, such systems involve rarefied gas flows, which appear to be significantly different comparing to flows at the continuum regime; it is this the reason the Navier-Stokes equations fail to simulate such phenomena without further modification. To this end, the enhancement of an in-house academic Computational Fluid Dynamics solver to encounter such simulations is reported in this study. In case of rarefied gas flows and specifically for flows in the slip regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip and temperature jump boundary conditions have to be used instead. (Short description and some difficulties an SBL code can face). The obtained results are compared with those obtained with the parallel open-source code SPARTA, based on the Direct Simulation Monte-Carlo method. According to this last approach, the flow domain is divided into a finite number of computational cells. The required sample macroscopic flow properties are retrieved assuming inter-molecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by SBL and SPARTA. The effect of wall-slip velocity and temperature distributions on the linear stability of supersonic and hypersonic laminar boundary layers developing on a semi-infinite flat plate is investigated for Knudsen numbers, corresponding to flight altitudes of 35km - 65 km and, at first instance, low Reynolds numbers. The steady laminar base flow is obtained using the Direct Simulation Monte Carlo (DSMC) method. Results on the mean-free-path and wall-normal velocity and temperature gradients obtained are used to construct slip-velocity and temperature-jump boundary conditions along the plate surface, following recent updates of the Maxwell / von Smoluchowski theory. These wall boundary conditions, alongside the pertinent streamwise pressure gradient, extracted from the DSMC simulations at the edge of the boundary layer, are used to obtain similar compressible boundary layer profiles, the linear stability characteristics of which are compared with well-known results delivered by Navier-Stokes methods along a range of altitudes, Mach and Reynolds numbers.

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