臺灣博碩士論文加值系統

在此次的研究中，利用大渦數值模擬 (LES) 和Van Driest阻尼函式 (damping function) 來預測受限壁面的無限平板管流和旋轉圓盤內的流場。數值程序是基於有限體積和交錯型網格，空間上和時間上的方法分別是用二階精確度的中央差分和ADI。
本次研究主要的工作之一是去平行大渦數值模擬的程式。所採用的環境是單一程式和多個資料 (SPMD) 的型態，所用到的平行機器為16個節點 (node) 的IBM SP2、16個節點的IBM SMP和32個節點的叢集式電腦 (PC clusters)。結果可發現在程式陣列較大時，其加速表現 (speed-up) 有線性甚至超線性的現象發生，尤其在IBM SMP的機器上，但是叢集式電腦的加速爬升能力則較IBM的機器差。然而，叢集式電腦對於科學計算上的確提供了一經濟有效能的方法。
另外，完全發展的無限平板管流（其以剪應力速度uτ為準的雷諾應力Reτ等於180）和旋轉圓盤內的流場（其最大旋轉雷諾應力Reθ為 ）皆被用來檢測此次所採用的大渦數值方法，所比較的數據為直接數值模擬 (DNS) 的計算結果和一些可以獲得的量測結果。

In the present study, large eddy simulations with Van Driest damping function is used to predict wall bounded channel flows and rotor-stator cavity flows. The numerical procedure is based on the finite volume approach with staggered grid arrangement. The spatial and temporal schemes adopted are center differencing and ADI, which are second order accurate.
One of the major efforts of the present research is to parallelize the LES programs. In the present parallel implementation, the single program multiple data (SPMD) environment is adopted. The target machines are a 16-node IBM SP2 (power 2), a 16-node IBM SMP (power 3) and a 32-node PC clusters. Linear or even super linear results are obtained for the large problem size using IBM SP2 and SMP machines. The scalability of the PC cluster is not compatible with the IBM machines. However, the PC clusters does provide a cost effective way of scientific computations.
The fully developed channel flows with Reynolds number of and the rotor-stator cavity flows are adopted to examine the capability of the LES scheme. The results are examined by comparing the predicted flow quantities with DNS data and available measurements.

Abstract ………………………………………………………………...…………….. i
Acknowledgment ……………………………………………………………….…… ii
Nomenclature ……………………………………………………………………..… iii
List of Tables …..…………………………………………………………………..... vi
List of Figures ………………………………………………………………….….... vi
Chapter 1 Introduction 1
1.1 Introduction ……………………………………………………………..….……. 1
1.1.1 Turbulent flows scales …………………………………………………….…… 2
1.1.2 Turbulence models ……………………………………………………….……. 3
1.1.3 Remedy methods ………………………………………………………..…….. 5
1.2 Literature survey …………………………………………………………….…... 5
1.3 Objectives ………...……………………………………………………………... 8
Chapter 2 Mathematical Model 10
2.1 Governing equations ………………………………………………………….... 10
2.1.1 The filtering operation …………………………………………………….…. 10
2.1.2 Filtered Navier-Stokes equations …………………………………………….. 11
2.2 Sub-grid scale modeling ………………………………………………………... 12
2.2.1 Smagorinsky model …………………………………………………………... 13
2.2.2 Other related models …………………………………………….…………… 14
Chapter 3 Numerical Algorithm 15
3.1 Discretisation of the transport equation ………………………………….…….. 15
3.1.1 Spatial discretisation ……………………………………………………...….. 16
3.1.2 Temporal discretisation ……………………………………………….……… 18
3.2 Pressure correction ……………………………………………………………... 19
3.2.1 Sequence of operations ……………………………………………………….. 21
Chapter 4 Parallel Algorithm 23
4.1 Domain decomposition …………………………..…………………………….. 24
4.2 Basic functions and the parallel region construct ……………………..……….. 25
Chapter 5 Results and Discussion 27
5.1 Parallel efficiency ………..………………………..…………………...……….. 27
5.2 Fully developed channel flow ….………………..…………………….……….. 29
5.3 Rotor-stator cavity flow ….………………………..……………………...…….. 30
Chapter 6 Conclusion and Future Works 32
6.1 Conclusion ………….…..………………………..…………………….……….. 32
6.2 Future works …..………..………………………..…………………….……….. 33
Bibliography …..…………………………………………………………………… 35
Tables ……………………………………………………………………………….. 38
Figures ……………………………………………………………………….……... 39
Appendix …...………………………………………………………………………. 55

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