臺灣博碩士論文加值系統

本論文之主要目的為發展具週期移動邊界之容器內可壓縮流體之數值模擬方法，並應用至具隔板、移動壁及浮力的封閉系統等不同問題的流體與熱傳評估上。本研究提出並修正兩階段壓力修正的數值方法，以在系統啟動期間或達週期性穩定後，同時求解可壓縮流體之絕對壓力、密度、溫度和速度分布。在數值計算上採移動且局部或整體變形的交錯式非均勻網格以調適系統體積的變化，來求解積分式的統御方程式。此方法在本論文中已應用於求解下列問題，包括: (1)方形容器內具一振動壁之熱對流，(2)具兩個週期移動邊界之容器內之熱流場，(3)具隔板及兩個週期移動邊界之容器內之熱流場，(4)容器內具non-Boussinesq’s 流體的自然對流問題。網格分配視情況需要在局部區域採靜止或移動的交錯式網格，同時其整體網格亦透過變形來反應因振動產生的體積變化。
本論文探討了在各種熱邊界條件下，壁面的振動對於含有空氣之容器內熱流場Nusselt number的影響。結果顯示振動壁導致容器內熱流場產生週期性變化，且在各不同物理條件下皆有不同的特性。本研究考慮的參數包括振動壁的頻率、壁面衝程和兩振動壁面間相差。對於中間具絕熱隔板的問題，更加入了中間間距大小對整體效應的探討。

The aim of this thesis is to develop a numerical method for analysis of thermal and flow fields of compressible flow in an enclosure with periodically moving boundary. The combined influence of the partitions, movement of the walls, and the buoyancy as well on the flow pattern and heat transfer performance is evaluated. The two-stage pressure correction scheme is developed and modified for simultaneously determining the distributions of absolute pressure, density, temperature, and velocity of the compressible flow field in the enclosure during the start-up and periodically stable periods. The compressible-flow model is adopted, and the governing equations are expressed in integral form and discretized on the staggered grids which may locally or globally deform in resonance with the walls to accommodate the variation in the volume of the enclosure.
The application of this method has been extended to the following topics: (1) thermal convection in a square enclosure with a vibrating wall, (2) flow and thermal fields in an enclosure with two periodically vibrating walls, (3) flow and thermal fields in an enclosure with partitions and two periodically vibrating walls, and (4) pressure effects on natural convection for non-Boussinesq fluid in a rectangular enclosure.
Effects of wall vibration in a rectangular enclosure containing air under various thermal boundary conditions are investigated. The vibrating wall leads to periodic variations in the flow and thermal fields, and also in Nusselt numbers, within the rectangular enclosure, and hence results in remarkable different features in different situations. Major parameters, including frequency, stroke, and the phase angle of the wall vibrations on the flow, are evaluated. For particular situations, the effects of height of aperture formed by adiabatic partitions are added to study.

ENGLISH ABSTRACT …………………………………………………………….…i
CHINESE ABSTRACT……………………………………………………………….ii
ACKNOWLEDGEMENT………………………………………………...………….iii
TABLE OF CONTENTS………………………………………..……………………iv
LIST OF TABLES………………………………………….…………………..........vii
LIST OF FIGURES ……………………………………………………….……...…viii
NOMENCLATURE ………………………………………..…………………….….xii

CHAPTER
1. INTRODUCTION….……………….....................................………………...…….1
1.1 Background…………..……………..……………..…………………..……1
1.2 Objective.................………..…........………………………………..…..….8
1.3 Scope of Present Thesis……………………………………………...……14
Figures……………………..…………………………………….…….……...16
2. THEORETICAL ANALYSIS…...........................................…….…..………......21
2.1 Governing Equations ……….……….…………………………………....21
2.1.1 Space conservation …………………..……………………….….22
2.1.2 Mass conservation …………………………..…..……….………23
2.1.3 Momentum conservation ……………………….………..………24
2.1.4 Energy conservation ……..…………………...….…………..……25
2.2 Initial Conditions ……………………………..……..………….…………27
2.3 Dimensionless Form …………….….……………………………………..28
Tables………………………………………………………………………….32
3. NUMERICAL METHODS AND SOLUTION PROCEDURES ……….….……33
3.1 Grid Layout …………………..…………..…………………….………....33
3.2 Discretization Equations .……..…………………..……...…………….….35
3.2.1 Space conservation law ……………………………………..........35
3.2.2 Continuity equation ………………………………………….…....36
3.2.3 Momentum equation ………….……………………….……...…..37
3.2.4 Energy equation ………………………..…………………..…..…40
3.3 Two-Stage Pressure Corrections …………………………………..….…43
3.4 Solution Procedures ……………………………………………..…….….49
Figures……………………..…………………………………………...……..52
4. THERMAL CONVECTION IN A RECTANGULAR ENCLOSURE WITH A
VIBRATING WALL……….…………………………………..…………….……54
4.1 Initial and Boundary Conditions………..…………………………………55
4.1.1 Initial conditions……………………..………………………….…55
4.1.2 Boundary conditions………………………………………......…..56
4.3 Results and Discussion………………………………………….....…...…57
Tables and Figures………………………………………………...…...…..….65
5. FLOW AND THERMAL FIELDS IN AN ENCLOSURE WITH TWO
PERIODICALLY VIBRATING WALLS …..………………………..….……..….78
5.1 Boundary Conditions………………………...…………………..………..79
5.2 Results and Discussion………………………………………………...….80
Tables and Figures………………………………………………………...…..87
6. FLOW AND THERMAL FIELDS IN AN ENCLOSURE WITH PARTITIONS
AND TWO PERIODICALLY VIBRATING WALLS……………………..……...94
6.1 Boundary Conditions………………………...………………………..…..95
6.2 Results and Discussion………………………………………………...….96
Tables and Figures……………………………………………..…………….104
7. PRESSURE EFFECTS ON NATURAL CONVECTION FOR NON-
BOUSSI NESQ FLUID IN A RECTANGULAR ENCLOSURE…………...…...117
7.1 Theoretical Analysis……………………….….….………………..…......117
7.2 Results and Discussion….………………………………………………..120
Tables and Figures …………………………………………….……….....….126
8. CONCLUDING REMARKS…….……………………………….…….….….....133
REFERENCES…………………………….………………..………….…...………139
AUTHOR………………………………………………………………...…………146

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