Large-eddy simulation (LES) of compressible flow with wall modelling is assessed on a quasi-isothermal and supersonic plane channel. The derivation of a quasi-analytical wall model based on empirical laws appears very difficult for combined physical effects like compressibility with pressure gradient. A wall model based on the compressible thin boundary layer equations constitutes a more general approach toward the simulation of multiphysical wall bounded flows with LES. In this work, such a wall model is derived and solved thanks to a new meshless method. An adequate scaling of the wall distance is introduced in the Van-Driest damping function of the wall model to handle compressibility effects. The choice of the proper wall distance scaling is shown to be crucial as soon as compressibility effects become significant. Additionally, some sources of error inherent to this wall-modelling approach are treated by appropriate corrections, and show non-negligible impact on the results. On a quasi-isothermal plane channel flow, the mean wall fluxes, primitive variable profiles and velocity fluctuations compare well to Direct Numerical Simulation (DNS) and empirical correlations for a wide range of Reynolds number. Then the DNS of supersonic isothermal-wall plane channel of Coleman at Mach = 1.5 and Mach = 3 are used as a more discriminant test case. The results agree well with the DNS data in terms of mean wall friction and wall heat flux. Finally, a specific analysis of the wall model accuracy is performed outside of the LES solver. This analysis allows to discriminate the error due to the wall model itself from the error due to the interaction between the wall model and the LES solver.

This paper presents conceptual experiments and simulations aiming at controlling flow geometries. Such flow design is performed by driving electromagnetically a shallow layer of brine, the forcing being generated by a transverse electrical current and different combinations of permanent magnets placed underneath the brine supporting wall. It is shown how different basic flow characterisctics can be obtained with a single pair of magnets, by varying the angle with the electrical current. These basic flows are proposed as potential building blocks for advanced and complex flows studies. Three typical flow structures are presented to illustrate these building blocks. The discussion is then extended to multi-scale geometry by using blocks of various sizes. The flow is analysed using complementary experiments and numerical simulations. A good agreement is found between the 3D simulations and the experiments for both velocity and acceleration fields, which allows a higher degree of confidence in designing and modelling such flows. As the control of the flow geometry is important for mixing, in particular at low Reynolds number, we also illustrate the different stirring properties of the electromagnetically forced flows by comparing visualisations of passive scalars. They reveal complementary mixing properties for each of the building blocks.

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