本文採用晶格波茲曼方法(Lattice Boltzmann Method，LBM)，並結合大渦模擬來模擬高雷諾數(Reynolds number，Re)並具有熱傳效應的強制對流紊流場。晶格波茲曼方法由於數值穩定性的原因，大部分的研究都在低雷諾數的流場，
而本文利用了特殊的邊界條件處理方法及大渦模擬來解決此問題，因此可以模
擬高雷諾數的流場。

目前模擬紊流有三種方式，分別為直接數值模擬(Direct Numerical Simulation，DNS)、大渦數值模擬(Large Eddy Simulation，LES)及雷諾平均模擬(Reynolds Average Navier-Stokes Simulation，RANS)。本文採用大渦數值模擬(LES)，其基本的理念是將物理量分成大尺度與小尺度的量，主要求解大尺度的物理量，而小尺度的擾動則建立模型來近似，此模型稱為亞格子模型。亞格子模型目前有數種模型，本文採用最簡單的亞格子渦黏及渦擴散模型，並使用Smagorinsky模式來得到渦黏及渦擴散系數，此模型的準確度在大多數的工程應用上是可被接受的。

本文模擬的問題包含頂蓋驅動流、背向階梯流場、波形渠道。流場皆假設為二維不可壓縮流，模擬的範圍涵蓋了層流及紊流。由於晶格波茲曼方程式為非穩態方程式，在求解紊流的時候無法得到穩態解，因此本文採用時間平均的方式得到時間平均解。本文研究的問題與已知文獻的實驗及模擬結果相比較，均非常吻合。

在頂蓋驅動流中，當Re≦7500時為層流，Re≧10000時為紊流，模擬結果與已有文獻進行渦中心位置的比較，結果非常吻合。在背向階梯流場中，當Re≦1200時為層流，1200< Re <6600時為過渡區，Re≧6600時為紊流，模擬結果與已有文獻進行再接觸點長度的比較，結果非常吻合。此外，並觀察其熱傳效應，在雷諾數高時有較好的對流熱傳效應。在波形渠道中，當Re≦500時為層流，Re≧3000時為紊流，並討論振幅波長比、雷諾數及普朗特數對表面摩擦係數與紐賽數的影響，結果顯示增加振幅波長比與提高雷諾數會提高表面摩擦係數，而提升雷諾數及普朗特數可以增加對流熱傳效應。

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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