Rarefied gas flows in microscale geometries : a hybrid simulation method

  • Stephanie Docherty

Student thesis: Doctoral Thesis


Accurate predictions of the flow behaviour in microscale geometries are needed, for example, to design and optimise micro devices, and to ensure their safety/reliability. Rarefied gas flows in such geometries tend, however, to be far from local thermodynamic equilibrium, meaning that the flow behaviour cannot be described by conventional fluid mechanics. Alternative approaches for modelling 'non-equilibrium' gas flows have been proposed in recent years; because analytical solution methods are subject to significant limitations, the direct simulation Monte Carlo (DSMC) method is, at present, the most practical numerical simulation tool for dilute gases. Unfortunately, the computational expense of tracking and computing collisions between thousands (or perhaps millions) of DSMC particles means that simulating the scales of realistic flow problems can require months (or even years) of computing time. This has resulted in the development of continuum-DSMC 'hybrid' methods, which aim to combine the efficiency of a conventional continuum-fluid description with the detail and accuracy of the DSMC method. This thesis focuses on the development of a continuum-DSMC method that offers a more general approach than existing methods. Using a heterogeneous framework with a field-wise coupling strategy, this new method is not subject to the limitations of the well-known domain decomposition framework, or the restrictions of the heterogeneous point-wise coupling approach. The continuum-fluid description is applied across the entire flow field, while the DSMC method is performed in dispersed micro elements that can be any size and at any location; these elements then provide the continuum description with updated constitutive and boundary information. Unlike most methods in the literature, the coupling strategy presented here is able to cope with heat transfer, and so non-isothermal flows can be simulated. Testing and validation of this new continuum-DSMC method is performed by simulating a number of benchmark cases and comparing the results with full DSMC solutions of the same cases. Two 1D flow problems are considered: a micro Fourier flow problem tests the energy coupling procedure of the method, and a high-speed micro Couette flow problem demonstrates the full coupling algorithm. In general, the method's accuracy is found to depend on the arrangement of the micro elements - with sufficient micro resolution, good agreement with the equivalent full DSMC simulations can be obtained. Although the hybrid method offers no computational speed-up over the full DSMC simulations for several of these 1D test cases and only modest speed-ups for the others, both of these 1D ow problems are simulated only to validate the coupling strategy of the method. Considerable speed-ups are offered by the method when simulating a larger and more realistic flow problem: a microchannel with a high-aspect-ratio cross-section acts as a representative geometry for modelling a gas flow through a narrow microscale crack. While the limitations of existing hybrid methods preclude their use for this type of high-aspect-ratio geometry, the new hybrid method is able to model this problem under isothermal and non-isothermal conditions. The implementation of the method is simplified to 2D by assuming that the flow variation in the streamwise direction is negligible, i.e. the method is applied to the microchannel cross-section only. Accurate predictions of the mass flow rate and the streamwise velocity field are obtained for a number of test cases; accurate predictions of the temperature field are also obtained when there is a temperature difference between the bounding walls.
Date of Award7 Oct 2015
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)

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