Numerical Study Of Thermally Driven Flows Using Unstructured Mesh Discrete Unified Gas Kinetic Scheme

Non-equilibrium gas flows driven by non-uniform temperature filed are interesting phe-nomena occurring at micro or rarefied condition.As these flows are driven purely by inho-mogeneous temperature fields without requiring external force nor pressure difference or moving parts,they have shown unique advantages in various industrial fields,especially in the microelectromechanical systems?MEMS?industry.Numerical studies of these non-equilibrium flows can provide a better understanding of the underlying flow mechanisms and as well as the forces associated,thus offer guidance to the engineering applications em-ploying the flows.With the rapid advance of computing power and memory size,numerical methods based on directly solving the gas-kinetic equation have become wildly used in sim-ulations of low-speed non-equilibrium flows.Among these methods,the recently proposed Discrete Unified Gas Kinetic Scheme?DUGKS?by Guo et al.is a novel method that can efficiently simulate flows in the full range of flow regimes.However,DUGKS still lacks systemic validations for different kinds of non-equilibrium flows including the thermally driven flows.In addition,as a finite-volume based method,DUGKS can take the advan-tage of geometrical flexibility best on unstructured meshes.In this thesis,we developed the unstructured mesh DUGKS,and investigated the properties of DUGKS in simulating low Knudsen number flows,and also studied several typical thermally driven flows in the full range of Knudsen number using the unstructured mesh DUGKS.The main works in this thesis are summarized as follows:Firstly,we proposed the arbitrary unstructured-mesh based DUGKS and developed the general-purpose parallel solver.The effectiveness of DUGKS for simulating multi-scale(with Knudsen number from 10^-4to 10¹)non-equilibrium gas flows has been demonstrated by various testing cases covering from high-speed to low-speed,and continuum to rarefied flows.We also investigated the performance of DUGKS for simulating continuum flows as a finite-volume lattice Boltzmann method and analyzed the reason of its superiorities over other non-regular-grid lattice Boltzmann methods in terms of accuracy and stability.The theoretical analysis is validated by numerical testing cases.The numerical results demon-strated the superior stability of DUGKS?maximum CFL number allowed is 1.1 instead of0.7?over the characteristics based off-lattice Boltzmann scheme proposed by Bardow et al.,and with the same mesh resolution,the DUGKS gives results closer to the LBM's results.Secondly,we studied the thermal creep flow in a channel with a ratchet surface and its mechanical performance as a conceptual heat engine.The effects of gas rarefaction,tem-perature difference and geometrical parameters on the mechanical performance have been analyzed systemically.The numerical results indicate that the maximum output power and thermal efficiency can be achieved in the early transitional regime?Kn?0.2?and they both approach to zero at free molecular flow regime.In addition,the counter-intuitive reversed flow in the channel has been observed in the free molecular flow regime.Thirdly,we studied the thermal creep flow in a cuboid-like enclosure induced by the temperature gradient along the wall.It is the first full three-dimensional numerical study of such flows.The effects of the Knudsen number,temperature configuration and geometry aspect ratio on the flow structures and heat transfer have been explored.The reverse of thermally induced flow direction has been observed at Knudsen number around 0.2,and special vortex flow structures have been uniquely identified that have no counterparts in the two-dimensional case.Finally,we investigated the radiometric flow induced by a one-side-heated plate in a two-dimensional enclosure and analyzed the effect of wall proximity on the flow structures and radiometric force.We found that wall proximity in the direction perpendicular to the temperature gradient direction has significant affections to the vortex flow structures as well as the radiometric force.A closer distance between the heated plate and the wall leads to a much larger radiometric force.In summary,the work in this thesis extends the applicability of DUGKS to complex geometries and particularly focuses on the simulations of thermally induced flow.The ef-fectiveness of DUGKS as a finite-volume lattice Boltzmann method is demonstrated and the reason is explained through theoretical and numerical analyses.By using the newly de-veloped algorithm and solver,three types thermally induced flows are simulated and new phenomenons have been observed,which helps deepen our understanding of such non-equilibrium flows.These work laid the foundation for the further applications of DUGKS.