Efficient simulation of internal multiscale gas flows

We develop, validate, and apply an efficient multiscale method for the simulation of a large class of low-speed internal rarefied gas flows, which are critical to a range of future technologies. The method is based on an existing multiscale approach for the simulation of small-scale dense-fluid flows of high-aspect ratio, but has been extended to support fluid compressibility, non-isothermal conditions, three dimensional domains, and transience. Furthermore, the method is able to treat a broader range of flows: periodic, non-periodic, body-force-driven, pressure-driven, thermally-driven, and shear-driven. It also incorporates pseudospectral methods, and so boasts excellent convergence characteristics and accuracy. All verification cases presented herein are designed to be amenable to solution by a full molecular treatment (where scale separation is not exploited). The computationally demanding simulation technique known as direct simulation Monte Carlo (DSMC) is employed to obtain reference solutions, allowing for comparison with those computed by the multiscale method: excellent agreement is observed throughout. The unsteady (time-marching) implementation of the method, which allows for the resolution of transient flows, is validated by comparison with time dependent experimental data. Again, agreement is excellent. The computational efficiency of the multiscale method is exceptional. It provides efficiency gains of multiple orders of magnitude, relative to full molecular simulations (by the DSMC method); in some cases, the multiscale method allows for the solution of otherwise computationally intractable problems. Note, highly scale-separated systems are simulated with even greater efficiency. Following the experimental validation of the method, it is applied to the study of thermal-transpiration compressors (and implicitly Knudsen compressors). We characterise the effectiveness of these devices by considering the maximum pressure difference attainable for various combinations of (realistic) thermodynamic and geometric conditions. The development time required to obtain this pressure difference, which is also considered as a performance indicator, is also computed.