大渦數值模擬結合沉浸邊界法及壁面函數分析複雜幾何形狀紊流流場

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研究生：	張伯華 Chang, Po-Hua
論文名稱：	大渦數值模擬結合沉浸邊界法及壁面函數分析複雜幾何形狀紊流流場 Large eddy simulations of complex geometry flows with wall function and Immersed Boundary Method
指導教授：	林昭安
口試委員:	崔燕勇黃智永
學位類別：	碩士 Master
系所名稱：	工學院 - 動力機械工程學系 Department of Power Mechanical Engineering
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	58
中文關鍵詞：	紊流、沉浸邊界法、大渦數值模擬
相關次數：	點閱：3 下載：0
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Immersed boundary method and wall models are adopted to simulate the laminar and turbulent flows over periodic hills with large eddy simulation. The Reynolds numbers based on the hill hight are 25∼100 for the laminar flow, whereas are
2800, 5600 and 10595 for the turbulent flows. The results show that the flow over periodic hills consists of separation, recirculation and reattachment for the laminar and turbulent flows. The locations of separation and reattachment points are linear with the Reynolds number for laminar flows, but exhibit slightly difference with the Reynolds number for turbulent flows. For the simulation of turbulent flow over periodic hills, the results reveal that the present numerical treatment with grid resolutions (200 × 95 × 96) are sufficient for capturing the turbulence quantities compared with the DNS data of Breuer et al. [1] at lower Reynolds number Re = 2800. However, due to the inappropriate implement of wall model, the near wall turbulence is fail to be predicted as Reynolds number increased. It indicates that the adopted wall model with velocity correction could not accurately capture the near wall Reynolds stresses on the curvature wall boundary.

Introduction 1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Immersed Boundary Method . . . . . . . . . . . . . . . . . . . 2
2.2 Large Eddy Simulation . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Wall Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Turbulent Periodic Hills Flow . . . . . . . . . . . . . . . . . . 6
3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Mathematical Models 8
1 Immersed Boundary Method . . . . . . . . . . . . . . . . . . . . . . . 8
2 Governing Equations for Large Eddy Simulation . . . . . . . . . . . . 9
2.1 The filtering operation . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The filtered Navier-Stokes equations . . . . . . . . . . . . . . 10
3 Sub-grid Scale Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Smagorinsky Model . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Dynamic Smagorinsky Model . . . . . . . . . . . . . . . . . . 13
4 Wall Models for near-wall treatment . . . . . . . . . . . . . . . . . . 15
4.1 Schumann’s approach and Grotzbach’s approach . . . . . . . . 16
4.2 The Werner-Wengle wall law . . . . . . . . . . . . . . . . . . . 16
4.3 Turbulent boundary layer equations . . . . . . . . . . . . . . . 17
Numerical Solution 19
1 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Discretization of the Transport Equation . . . . . . . . . . . . . . . . 22
2.1 Spatial discretization . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Temporal discretization . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Direct momentum forcing procedure . . . . . . . . . . . . . . 26
3 The Pressure Poisson Equation . . . . . . . . . . . . . . . . . . . . . 29
3.1 Direct fast Fourier transform solver . . . . . . . . . . . . . . . 31
Numerical results 34
1 Channel flows with wall models . . . . . . . . . . . . . . . . . . . . . 34
2 Laminar flow over periodic hills . . . . . . . . . . . . . . . . . . . . . 38
3 Turbulent flow over periodic hills . . . . . . . . . . . . . . . . . . . . 41
Conclusions
                                

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