非牛頓流體與我們的生產和生活息息相關，因此深入研究非牛頓流體有很大的實用價值。目前有很多種流體的數值模擬方法，但用晶格波茲曼方法處理非牛頓流體問題還沒有引起廣泛的關注。從工業上常見的流體問題背向階梯流場模擬入手，針對非牛頓流體各個特性進行研究和分析。
本文是使用D2Q9 模型來模擬背向階梯流場中的廣義非牛頓流體—冪律型流體，展開研究和分析牛頓流體、剪切變稀流和剪切增稠流三種不同類型流體之間的速度場和溫度場。
首先，選取一個範圍內一系列的參數，例如：冪次指數、雷諾數、普朗特數、階梯擴張比，來分析剪切變稀流和剪切增稠流的流動情形和溫度分布隨參數的變化。之後在流道中置入方形柱體障礙物，其中柱體障礙物在流場中扮演擾動的角色，改變了物體的流線方向，且在障礙物後側形成環狀迴流區影響通過的流體進而改變部區域內的熱傳，而選取不同冪次指數n值，造成黏度的變化，而流動現象和溫度變化也越複雜。

While there is close relationship between non-Newtonian fluids and our poduction and living .Thus further study of non-newtonian fluid has great practical value. We know, there are a variety of fluid numerical simulation method for research, but the method using lattice Boltzmann for non-newtonian fluid problem hasn't caused wide spread concern. By simulating the general problems of backward-facing step fluids in industry. Then analyzing the properties of non-Newtonian fluids.
In this paper with D2Q9 model to simulate a generalized non-Newtonian power-law backward-facing step fluids, we mainly used to study and analysis different types of flow phenomena among Newtonian fluids and shear thinning fluids and shear thickening fluids.
Firstly, selecting a range of parameters like power-law index numbers, Reynold number, Prandtl number, and ER number. Then we can compare and analysis flow phenomena of shear thinning fluids and shear thickening fluids when the parameters changes . The built-in obstacle in channel include square cylinder, and the cylinder obstacle plays the role of causing interruption within the fluid field. The direction of fluid flow toward was changed by cylinder obstacle, and the recirculation region formed behind cylinder obstacle influence the fluid pass through. As mentioned above, heat transfer was different in local region. For choosing different power-law indexes causes the viscosity changed. And the flow phenomenon and variation of temperature become more complex.

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