| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 100 === In this study, the Large Eddy Simulation (LES) is introduced into the Lattice Boltzmann Method (LBM), and applied to numerically solving high Reynolds number (Re) turbulent flows with convective heat transfer. For LBM simulations, due to the numerically instability in simulating high Reynolds number flow, most studies were focused on low Reynolds number flow. Present work adopts special method for boundary condition and coupled with LES to solve this problem. Therefore, it can be used to simulate high Reynolds number flows.
Typically, there are three numerical methods to simulate turbulence, namely Direct Numerical Simulation (DNS), Large Eddy Simulation, Reynolds Average Navier-Stokes Simulation (RANS), respectively. The basic concept of Large Eddy Simulation is to decompose the turbulent flow field into large and small scale parts. The large scale part is solved by Navier-Stokes equation, while the small scale part is solved by sub-grid scale (SGS) model. The SGS model used in this study is based on the most convenient model : Smagorinsky model, which includes vortex viscous and vortex diffusive form.
Simulations of this article include driven cavity flow, backward facing step flow, and flows in a wavy channel. This flow fields are considered as two-dimensional incompressible flow, include laminar and turbulent flows. Due to Lattice Boltzmann Equation is an unsteady equation, the steady solution can’t be obtained in the simulation of turbulent flows. Therefore, the time average solutions are calculated the numerical simulations. The results are compared with other experimental and numerical results, and obtained good consistency.
In driven cavity flow, the flow is laminar for Re≦7500, turbulent for Re≧10000, the simulation results are compared with reference for the position of vortex center, and present results have good consistency. In backward facing step flow, the flow is laminar for Re≦1200, transition for 1200〈 Re 〈6600, and turbulent for Re≧6600, the simulation results are compared with reference for reattachment length, and present results have good consistency. In addition, we observe the heat transfer, the flow have good convective heat transfer in high Reynolds number. In wavy channel flow, the flow is laminar for Re≦500, turbulent for Re≧3000. Reynolds number, Prandtl number and amplitude-wavelength ratio on the skin-friction and Nusselt number have been studied, the results show the amplitudes of the Nusselt number and the skin-friction coefficient increase with an increase in the Reynolds number and the amplitude-wavelength ratio, and the Nusselt number increases with an increase in the Reynolds number and Prandtl number.
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