大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱圓盤之混合對流渦流特性研究

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國立交通大學

機械工程學系

碩士論文

大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一

加熱圓盤之混合對流渦流特性研究

Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

研究生 : 陳奎銘

指導老師: 林清發博士

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大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱

圓盤之混合對流渦流特性研究

Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

研究生：陳奎銘 Student：Kuei-Ming Chen

指導教授：林清發 Advisor：Tsing-Fa Lin

國立交通大學

機械工程學系

碩士論文

A Thesis

Submitted to Institute of Mechanical Engineering

Collage of Engineering

National Chiao Tung University

In Partial Fulfillment of the Requirements

For the degree of

Master of Science

In

Mechanical Engineering

June 2007

Hsinchu, Taiwan, Republic of China

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誌謝

時光飛逝，回首在新竹這兩年來的點點滴滴，交大這充滿學術氣息的環境下似乎讓我在知識上成長茁壯許多。本論文之所以可以順利完成，首先要感謝的是指導老師林清發教授嚴謹及殷切的指導，使學生能培養出獨立思考、釐清並自行解決問題的能力；更在學生撰寫論文時，不辭辛勞逐字斧正文稿，在此獻上最高謝意。在研究所期間，要特別感謝謝汎鈞及羅文賢學長在實驗設備設計、架設上的協助指導，亦要感謝博士班郭威伸、賴佑民、陳尚緯、張文瑞等博士班學長在生活及課業上指導與建議，使我受益匪淺，謝謝您們。凱文、政陞、峻樟這群不只是求學中的同學，更是生活上的好朋友。研究所之所以能在緊湊忙碌又充滿歡樂中的氣氛中度過，即是靠這些同學兼好友的夥伴們相互協助幫忙，令我永生難忘。另外也要感謝壹龍、永龍、長志、浚圩等一群努力的學弟妹幫忙及合作，希望你們能繼續保持實驗室優良傳統，並帶著實驗室進步。最後更要感謝父母及家人對於我無怨無悔付出及支持，使我可以無後顧之憂的專注於研究，並且可無憂無慮過求學生活。並特別要感謝女友自華的陪伴與體恤，生活最精采的部分是妳陪我渡過，不管在課業上或生活上的關心與支持使我有勇氣面對一切的困難挑戰。能與妳相處是我這輩子最大的幸福。最後，僅以本文獻給我所關心的人和所有關心我的人。奎銘謹致 2007/6/30 于風城交大

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大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱圓盤之混

合對流渦流特性研究

研究生：陳奎銘指導老師：林清發博士國立交通大學機械工程學系中文摘要本篇論文利用實驗流場觀測方法及溫度場量測方法探討在較大的噴流到圓盤的距離對於在垂直圓柱容器中一空氣圓形噴流衝擊至一加熱圓盤的穩態及非穏態渦流結構之流場特性進行研究。由於在較大的高度下，慣性力及浮力所驅動的渦流相對的比較強烈，所以本實驗主要的研究重點是在探討噴流到圓盤的距離對於穩態及非穏態的慣性力及浮力渦流結構流場之臨界發生點與特徵，除此之外，由慣性力及浮力所造成的非穏態流場也將會註明。在本實驗研究操作範圍分別是：噴流到圓盤的距離 40～60 mm，噴流的直徑固定為 10 mm，流量變化 0 ～12.0 slpm，加熱圓盤與入口冷空氣間的溫度差範圍 0～25.0℃，所相對的噴流雷諾數變化為 0～1,623，相對於雷利數 0～507,348。由流場觀測及溫度場量測可以清楚顯示噴流到圓盤的距離對於一次渦流、二次渦流、三次渦流及浮力渦流的臨界發生雷諾數有顯著的影響。其中一次渦流只有在噴流到圓盤的距離比上噴流的直徑HDj為 6 且非常高的浮慣比之下會消失，而二次流在HDj為 5 及 6 下不會出現。除此之外，我們定義了四種典型的不穩定現象，分別是慣性力、渦流相互推擠、第一類浮力、第二類浮力所造成的不穩定渦流流場，其中第二類浮力所造成的不穩定渦流流場發生在HDj等於 4 到 6 且非常低的雷諾數下。而在HDj等於 4 時

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流譜主要是由渦流相互推擠這種不穩定渦流流場所主導，而當HDj由 4 增加到 6

時，流譜則漸漸轉由非週期性的慣性力所造成的不穩定渦流流場主導。除此之外，當HDj增加時，流譜中的穩定渦流流場區域逐漸縮小。

最後，我們對由慣性力及浮力所造成的渦流及各類的渦流流場不穩定性的實驗結果做分析，求得經驗公式。

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Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

Student: Kuei-Ming Chen Advisor: Prof. Tsing-Fa Lin Institute of Mechanical Engineering

National Chiao Tung University

ABSTRACT

An experiment combining flow visualization and temperature measurement is carried out in the present study to investigate how the jet-disk separation distance H affects the steady and time-dependent vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber when H is large. The study is motivated by the fact that at the large H the interactions between the inertia and buoyancy driven vortex rolls are relatively strong. Particular attention is paid to examining the effects of H on the onsets and characteristics of steady and time-dependent inertia and buoyancy driven vortex flows. Besides, the onsets of the inertia and buoyancy driven vortex flow instabilities affected by H will be inspected. In the present experiment three jet-disk separation distances are considered with H = 40.0, 50.0, and 60.0 mm for a fixed injection pipe diameter with Dj = 10.0 mm. The jet flow rate is varied from 0 to 12.0 slpm (standard

liter per minute) for the jet Reynolds number Rej ranging from 0 to 1,623. The

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temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0 for the Rayleigh number Ra ranging from 0 to 507,3℃ 48.

The results from the flow visualization and the measured temperature data clearly show the significant effects of the jet-disk separation distance on the critical Rej for the onset of the primary, secondary and tertiary inertia-driven rolls, and the

buoyancy-driven roll. The primary inertia-driven roll disappears only at a very low Rej and at a very high buoyancy-to-inertia ratio for HDj =6. Besides, the secondary

inertia-driven roll does not appear at larger jet-disk separation distance for HDj =5 &

6.

Moreover, we identify four different types of vortex flow instabilities (inertia-driven, mutual roll-pushing, type-1 buoyancy-driven, and type-2 buoyancy-driven) when HDj is varied from 1 to 6. It is noted that the type-2

buoyancy-driven vortex flow instability only occurs at very low Rej with a large

jet-disk separation distance for HDj =4 to 6. Furthermore, the mutual roll-pushing

unstable vortex flow almost occupies the flow regime map for HDj =4 and the region

dominated by the nonperiodic inertia-driven unstable vortex flow becomes larger in the flow regime map as HDj is raised from 4 to 6. Furthermore, the region of the

stable vortex flow in the flow regime map becomes smaller at increasing HDj.

Finally, empirical correlations are proposed for the critical conditions for the onsets of the inertia and buoyancy driven vortex rolls and for the onsets of various vortex flow instabilities.

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ABSTRACT i

iii

LIST OF TABLES

v

LIST OF FIGURES

vi

NOMENCLATURE

xiv

CHAPTER 1 INTRODUCTION

1.1 Motivation 1.2 Literature Review

1.3 Objective and Scope of Present Study

1

2

6 CHAPTER 2 EXPERIMENTAL APPARATUS AND

PROCEDURES

2.1 Experimental Apparatus 2.2 Experimental Procedures

8

11 CHAPTER 3 DIMENSIONLESS GROUPS AND

UNCERTAINTY ANALYSIS

3.1 Dimensionless Groups 3.2 Uncertainty Analysis

16

iii

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CHAPTER 4 RESULTS AND DISCUSSION

4.1 Typical Vortex Flow Patterns

4.2 Effects of HDj on Onsets of Inertia and Buoyancy

Driven Vortex Rolls

4.3 Effects of HDj on Steady Vortex Flow Characteristics

4.4 Effects of HDj on Vortex Flow Instabilities

4.5 Effects of HDj on Time-Dependent Vortex Flow

Characteristics

20

21

23

28

30

38 CHAPTER 5 CONCLUDING REMARKS

161 REFERECES 164

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LIST OF TABLES

Table 3.1 Summary of uncertainty analysis. --- 19 Table 4.1 Critical condition for appearance of the inertia-driven vortex flow

(ΔT=0℃). --- 41 Table 4.2 Critical condition for the onset of the Buoyancy-driven vortex roll for

various H. ---42 Table 4.3 Critical condition for appearance of the primary inertia-driven vortex

roll at H = 60.0 mm. ---43 Table 4.4 Critical condition for the onset of the inertia-driven time-dependent

vortex flow for various H. ---44 Table 4.5 Critical condition for the onset of the mutual roll-pushing vortex flow

instability for various H. ---45 Table 4.6 Critical condition for the onset of nonperiodic type-2 buoyancy-driven

time-dependent vortex flow. ---46

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LIST OF FIGURES

Fig. 1.1 Flow regimes associated with a circular jet impinging onto a flat plate. --- 7 Fig. 2.1 Schematic diagram of the experimental apparatus.--- 13 Fig. 2.2 The heater consists of three parts: resistance heating element, holder and

insulator.--- 14 Fig. 2.3 The locations of the detection points on the upper copper plate. --- 15 Fig. 4.1 Steady vortex flow pattern in the chamber with H = 40.0 mm for Rej =

541 (Qj = 4.0 slpm) and Ra = 0 (∆T = 0℃)： (a) side view flow photo

taken at the vertical plane θ = 0° & θ = 180° and (b) the corresponding

schematically sketched cross vortex flow. --- 47 Fig. 4.2 Vortex flow pattern in the chamber with side view flow photo taken at

the vertical plane θ = 0° & θ = 180° and the corresponding schematically sketched cross vortex flow for Rej = 947 (Qj = 7.0 slpm)

and Ra = 0 (∆T = 0℃)：(a) H = 30.0 mm (b) H = 50.0 mm. --- 48 Fig. 4.3 Steady vortex flow pattern in the chamber with H = 40.0 mm for Rej =

406 (Qj = 3.0 slpm) and Ra = 30,065 (∆T = 5℃) for (a) side view flow

photo taken at the vertical plane θ = 0° & θ = 180° and (b) the

corresponding schematically sketched cross vortex flow. --- 49 Fig. 4.4 Steady side view flow photos taken at the cross plane θ 0 & 180= o oat

Qj = 3.0 slpm (Rej = 406) and ΔT=5℃ for (a) H = 20.0 mm and (b) H =

40.0 mm. --- 50 Fig. 4.5 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) for H = 40.0 mm. --- 51 Fig. 4.6 Steady side view flow photos taken at the cross plane θ=0° & 180° for

various HDj at ΔT=0℃(Ra=0) and Qj=2.0 slpm(Rej=270). --- 52

Fig. 4.7 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) for H = 50.0 mm. --- 53 Fig. 4.8 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) for H = 60.0 mm. --- 54 Fig. 4.9 Side view flow photos taken at the cross plane for various HDj and Rej

with the disk unheated (ΔT=0℃). --- 55 Fig. 4.10 Side view flow photos taken the cross plane θ=0° & 180° for various jet

Reynolds numbers at Ra=0 (ΔT=0℃) for (a) H = 40.0 mm and (b) H =

50.0 mm. --- 56 Fig. 4.11 Side view flow photos taken at the cross plane θ=0° & 180° for various

HDj and Rej at ΔT=5℃. --- 57

Fig. 4.12 Side view flow photos taken at the cross plane θ=0° & 180° for

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Rej=1,623 (Qj=12.0 slpm) with various Ra at H=30.0 mm. --- 58

HDj and Rej at ΔT=5℃. --- 59

Fig. 4.14 Unsteady side view flow photos taken at the cross plane for various jet

Reynolds numbers at Ra=202,939 (ΔT=10℃) for H = 60.0 mm. --- 60 Fig. 4.15 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) for H = 40.0 mm. --- 61 Fig. 4.16 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) for (a) H = 50.0 mm and (b) H

= 60.0 mm. --- 62 Fig. 4.17 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at ΔT=10℃ for (a) H = 40.0 mm, (b) H = 50.0

mm, and (c) H = 60.0 mm.--- 63 Fig. 4.18 Steady side view flow photos taken at the cross plane θ=0° & 180° for

Fig. 4.19 Steady side view flow photos taken at the cross plane θ=0° & 180° for

various HDj at ΔT=0℃(Ra=0) and Qj= 3.0slpm(Rej=406). --- 66

various HDj at ΔT=0℃(Ra=0) and Qj= 4.0slpm(Rej=541).. --- 67

various HDj at ΔT=5℃ and Qj=1.0 slpm(Rej=135). --- 68

various HDj at ΔT=5℃ and Qj=2.0 slpm(Rej=270).. --- 69

various HDj at ΔT=5℃ and Qj=3.0 slpm(Rej=406).. --- 70

various HDj at ΔT=10℃ and Qj=1.0slpm(Rej=135). --- 71

various HDj at ΔT=10℃ and Qj=2.0 slpm (Rej=270).--- 72

Fig. 4.30 Radial variation in non-dimensional steady air temperature with Rej =135

(Qj=1.0 slpm) and ΔT=5.0℃ at Z = 0.5 on the vertical plane θ =0o for

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HDj = 4, 5 , and 6.--- 76

various jet Reynolds numbers at Ra=30,065 (ΔT=5℃) for H = 40.0 mm. --- 77 Fig. 4.32 Steady side view flow photos taken at the cross plane θ=0° & 180° for

various jet Reynolds numbers at Ra=60,130 (ΔT=10℃) for H = 40.0

mm. --- 78 Fig. 4.33 Steady side view flow photos taken at the cross plane θ=0° & 180° for

various jet Reynolds numbers at Ra=58,721 (ΔT=5℃) for H = 50.0 mm. --- 81 Fig. 4.36 Steady side view flow photos taken at the cross plane θ=0° & 180° for

various temperature difference at Rej=135 (Qj=1.0slpm) and H = 40.0

various temperature difference at Rej=135 (Qj=1.0slpm) and H = 50.0

mm. --- 85 Fig. 4.40 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) and H = 20.0 mm. --- 86 Fig. 4.41 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=7,520 (ΔT=10℃) and H = 20.0 mm.--- 87 Fig. 4.42 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=0 (ΔT=0℃) fo H = 60.0 mm. --- 91 Fig. 4.46 Unsteady side view flow photos taken at the cross plane θ=0° & 180° for

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mm. --- 92 Fig. 4.47 Unsteady side view flow photos taken at the cross plane θ=0° & 180° for

mm. --- 93 Fig. 4.48 Unsteady side view flow photos taken at the cross plane θ=0° & 180° for

mm. --- 94 Fig. 4.49 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=117,442 (ΔT=10℃) for H = 50.0 mm.--- 95 Fig. 4.50 Unsteady side view flow photos taken at the cross plane θ=0° & 180°

for various jet Reynolds numbers at Ra=176,162 (ΔT=15℃) for H =

50.0 mm. --- 96 Fig. 4.51 Unsteady side view flow photos taken at the cross plane θ=0° & 180° for

mm. --- 97 Fig. 4.52 Unsteady side view flow photos taken at the cross plane θ=0° & 180°

for various jet Reynolds numbers at Ra=293,604 (ΔT=25℃) for H =

50.0 mm. --- 98 Fig. 4.53 Unsteady side view flow photos taken at the cross plane θ=0° & 180°

for various jet Reynolds numbers at Ra=202,939 (ΔT=10℃) fo H =

60.0 mm. --- 102 Fig. 4.57 Time-periodic vortex flow for H = 20.0 mm and Ra = 0 (ΔT=0℃) at

Rej=839 (Qj=6.2slpm) illustrated by side view flow photos taken at the

cross plane θ=0° & 180° at selected time instants in a typical periodic

cycle (tp = 1.45 sec). --- 103

Fig. 4.58 Time-periodic vortex flow for H = 20.0 mm and Ra = 18,790 (ΔT=25℃) at Rej=1,028 (Qj=7.6slpm) illustrated by side view flow photos taken at

the cross plane θ=0° & 180° at selected time instants in a typical

periodic cycle (tp = 1.58 sec).--- 104

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Fig. 4.59 Time-periodic vortex flow for H = 40.0 mm and Ra = 0 (ΔT=0℃) at Rej=676 (Qj=5.0slpm) illustrated by side view flow photos taken at the

cross plane θ=0° & 180° at selected time instants in a typical periodic

cycle (tp = 4.3 sec).--- 105

Fig. 4.60 Nonperiodic vortex flow for H = 40.0 mm and Ra = 60,130 (ΔT=10℃) at Rej=1,352 (Qj=10.0slpm) illustrated by side view flow photos taken at

the cross plane θ=0° & 180° at selected time instants.--- 106 Fig. 4.61 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=60,130 (ΔT=10℃) and H = 40.0 mm. --- 108 Fig. 4.63 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=90,195 (ΔT=15℃) and H = 40.0 mm. --- 109 Fig. 4.64 Side view flow photos taken at the cross plane θ=0° & 180° for various

temperature difference at Rej=270 (Qj=2.0slpm) and H = 40.0 mm.--- 112

jet Reynolds numbers at Ra=58,721 (ΔT=5℃) for H = 50.0 mm. --- 114 Fig. 4.69 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=117,442 (ΔT=10℃) for H = 50.0 mm.--- 115 Fig. 4.70 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=101,470 (ΔT=5℃) fo H = 60.0 mm. --- 118 Fig. 4.73 Time-periodic vortex flow illustrated by side view flow photos taken at the

cross plane θ=0° & 180° at selected time instants for H = 40 mm and Ra

= 90,195 (ΔT=15℃) at Rej=676 (Qj=5.0 slpm) with tp = 1.82 sec.--- 119

Fig. 4.74 Time-periodic vortex flow for H=20.0 mm and Ra=11,270 ( ℃) at Re 0 . 15 T= Δ

j=135 (Qj=1.0 slpm) illustrated by side view flow photos taken

at the vertical plane θ 0 & = ° 180° at selected time instants.--- 120 Fig. 4.75 Nonperiodic vortex flow for H = 40.0 mm and Ra = 90,195 (ΔT=15℃)

at Rej=41 (Qj=0.3 slpm) illustrated by side view flow photos taken at

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the cross plane θ=0° & 180° at selected time instants.--- 121 Fig. 4.76 Nonperiodic vortex flow for H = 40.0 mm and Ra = 90,195 (ΔT=15℃)

the cross plane θ=0° & 180° at selected time instants.--- 122 Fig. 4.77 Nonperiodic vortex flow for H = 40.0 mm and Ra = 120,260 (ΔT=20℃)

the cross plane θ=0° & 180° at selected time instants.--- 123 Fig. 4.78 Nonperiodic vortex flow for H = 50.0 mm and Ra =58,721 (ΔT=5℃) at

Rej=54 (Qj=0.4 slpm) illustrated by side view flow photos taken at the

cross plane θ=0° & 180° at selected time instants. --- 124 Fig. 4.79 Nonperiodic vortex flow for H = 50.0 mm and Ra =58,721 (ΔT=5℃) at

Rej=68 (Qj=0.5 slpm) illustrated by side view flow photos taken at the

cross plane θ=0° & 180° at selected time instants. --- 125 Fig. 4.80 Nonperiodic vortex flow for H = 50.0 mm and Ra =117,442 (ΔT=10℃)

the cross plane θ=0° & 180° at selected time instants.--- 126 Fig. 4.81 Nonperiodic vortex flow for H = 60.0 mm and Ra =202,939 (ΔT=10℃)

the cross plane θ=0° & 180° at selected time instants.--- 127 Fig. 4.82 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=30,065 (ΔT=5℃) for H = 40.0 mm. --- 128 Fig. 4.83 Side view flow photos taken the cross plane θ=0° & 180° for various jet

Reynolds numbers at Ra=60,130 (ΔT=10℃) for H = 40.0 mm.--- 129 Fig. 4.84 Side view flow photos taken at the cross plane θ=0° & 180° for various

jet Reynolds numbers at Ra=120,260 (ΔT=20℃) fo H = 40.0 mm.--- 131 Fig. 4.86 Side view flow photos taken at the cross plane θ=0° & 180° for various

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jet Reynolds numbers at Ra=507,348 (ΔT=25℃) for H = 60.0 mm.--- 141 Fig. 4.96 Flow regime map delineating the temporal state of the vortex flow for H

= 40.0 mm

.

--- 142 Fig. 4.97 Flow regime map delineating the temporal state of the vortex flow for H

= 50.0 mm

.

= 60.0 mm

.

= 10.0 mm

.

= 20.0 mm

.

= 30.0 mm

.

--- 147 Fig. 4.102 Time-periodic vortex flow for H = 30.0 mm and Ra = 38,051 (ΔT=15℃)

Fig. 4.103 Time-periodic vortex flow for H = 40.0 mm and Ra = 90,195 (ΔT=15℃) at Rej=676 (Qj=5.0 slpm) illustrated by side view flow photos taken at

Fig. 4.104 Time-periodic vortex flow for H = 50.0 mm and Ra = 176,162 (ΔT=15 ℃) at Rej=676 (Qj=5.0 slpm) illustrated by side view flow photos taken

at the cross plane θ=0° & 180° at selected time instants in a typical

Fig. 4.105 Nonperiodic vortex flow for H = 60.0 mm and Ra = 304,409 (ΔT=15℃) at Rej=676 (Qj=5.0 slpm) illustrated by side view flow photos taken at

periodic cycle. --- 151 Fig. 4.106 The time records of non-dimensional air temperature for

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Ra=90,195(ΔT=15.0℃) and Rej=676 (Qj=5.0 slpm) with H=40.0 mm

measured at selected locations on the vertical plane θ 0 at Z = 0.67 = ° for R = r/Rc = (a) 0.17, (b) 0.45, (c) 0.62, (d)0.76, and (e) 0.96 (tp=1.82

sec). --- 152 Fig. 4.107 The time records of non-dimensional air temperature and the

corresponding power spectrum densities for Ra=90,195 ( ℃) and Re 0 . 15 T= Δ

j=676 (Qj=5.0 slpm) with H=40.0 mm measured at selected

locations on the vertical plane θ 0 at Z = 0.67 fo R = r/R= ° c = (a)0.45,

(b)0.62, (c)0.76,and (d)0.96 (tp=1.82 sec).--- 153

Fig. 4.108 The time records of non-dimensional air temperature and the corresponding power spectrum densities for ΔT=15.0℃ and Rej=676

(Qj=5.0 slpm) with measured at selected locations on the vertical plane

at Z = 0.67 and R = r/R °

=

θ 0 c = 0.62 for various HDj = (a)4, (b)5, and

(c)6. --- 154 Fig. 4.109 The time records of non-dimensional air temperature for

Ra=176.162(ΔT=15.0℃) and Rej=1,488 (Qj=11.0 slpm) with H=50.0

mm measured at selected locations on the vertical plane at Z = 0.67 for R = r/R

° = θ 0

c = (a) 0.34, (b) 0.62, and (c) 0.96.--- 155

Fig. 4.110 The time records of non-dimensional air temperature for ℃ and Re 0 . 15 T= Δ

j=1,488 (Qj=11.0 slpm) with measured at selected locations on

the vertical plane θ 0= ° at Z = 0.67 and R = r/Rc = 0.62 for HDj = (a)4,

(b)5, and (c)6.--- 156 Fig. 4.111 The time records of non-dimensional air temperature for ℃

and Ra=234,883 at H = 50.0 mm with measured at selected locations on the vertical plane at Z = 0.67 and R = r/R

0 . 20 = ΔT ° = θ 0 c =0.89 for Rej = (a) 1,190, (b) 1,352, (c) 1,488, and (d) 1,623. --- 157 Fig. 4.112 The time records of non-dimensional air temperature for Ra=176,162

(ΔT=15.0℃) and Rej=47 (Qj=0.3 slpm) with H=50.0 mm measured at

selected locations on the vertical plane θ 0 at Z = 0.33 for various R = °

= r/Rc = (a) 0.07, (b) 0. 17, (c) 0.48, and (d) 0.79. --- 158

Fig. 4.113 The time records of non-dimensional air temperature for ℃ and Re 0 . 15 T= Δ

j=47(Qj=0.3 slpm) with measured at selected locations on the

vertical plane θ 0= ° at Z = 0.33 and R = r/Rc = 0.17 for HDj = (a)4,

(b)5, and (c)6.--- 159 Fig. 4.114 The time records of non-dimensional air temperature for ℃

and Ra=234,883 at H = 50.0 mm with measured at selected locations on the vertical plane at Z = 0.33 and R = r/R

0 . 20 = ΔT ° = θ 0 c = 0.17 for Rej = (a) 135, (b) 108, (c) 68, and (d) 27. --- 160 xiii

(20)

NONMENCLATURE

Dj Diameter of jet at the injection pipe exit (mm)

Dw Diameter of disk (mm)

Gr Grashof number, _g_β_Δ_TH3 _ν2

g Gravitational acceleration (m/s2) H Jet-to-disk separation distance (mm)

HDj Ratio of the jet-disk separation distance to the jet diameter, H/ Dj

Qj Jet flow rate (Standard Liter per Minute, slpm) z

, ,

rθ Dimensional coordinates in cylindrical coordinate system

Z , ,

R Θ Dimensionless coordinates r R/ c, /360 , /θ ° z H

Ra Rayleigh number, _{gβΔTH αν}3

Rc Radius of cylindrical chamber (mm)

Rej _{Jet Reynolds number,}

j j

V D ν

Rew Local Reynolds number of the flow in the wall-jet region,

uH

/

ν

Rewe Local Reynolds number of the flow in the wall-jet region at disk

edge,

u H

_we

/

ν

Rw Radius of disk (mm)

Ta Ambient Temperature ( )℃

Tf Temperature of the heated disk ( )℃

Tj Temperature of jet at the injection pipe exit ( )℃

t Time (sec)

u Average radial velocity of the flow in the wall-jet region,

/(2 ) j

Q πrH

we

u _{Average radial velocity of the flow in the wall-jet region at disk}

(21)

edge, Q_j /(2πR H_w )

j

V Average velocity of the air jet at the injection pipe exit (m/s)

Greek symbols

α Thermal diffusivity (m2/s) β Thermal expansion coefficient (1/K)

ΔT Temperature difference between the heated disk and the air injected into the chamber (℃)

ν Kinematic viscosity (m2/s) Φ _{Non-dimensional temperature,}

(

_T₋_T_j

) (

_/_T_f ₋_T_j

)

ρ _{Density (kg/m}3₎ μ Dynamic viscosity (kg/ms) k Thermal conductivity (W/m

℃

) xv

大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱圓盤之混合對流渦流特性研究

國 立 交 通 大 學

機 械 工 程 學 系

碩 士 論 文

大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一

加熱圓盤之混合對流渦流特性研究

Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

研 究 生 : 陳 奎 銘

指 導 老 師: 林 清 發 博 士

大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱

圓盤之混合對流渦流特性研究

Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

研 究 生：陳 奎 銘 Student：Kuei-Ming Chen

指導教授：林 清 發 Advisor：Tsing-Fa Lin

國立交通大學

機械工程學系

碩士論文

A Thesis

Submitted to Institute of Mechanical Engineering

Collage of Engineering

National Chiao Tung University

In Partial Fulfillment of the Requirements

For the degree of

Master of Science

In

Mechanical Engineering

June 2007

誌 謝

大高度下之垂直圓柱容器中一空氣圓形噴流衝擊至一加熱圓盤之混

合對流渦流特性研究

Mixed Convective Vortex Flow Characteristics in a Round Jet of Air

Impinging onto a Heated Horizontal Disk Confined in a Vertical

Cylindrical Chamber with a Large Jet-disk Separation Distance

ABSTRACT

TABLE OF CONTENTS

ABSTRACT i

TABLE OF CONTENTS

iii

LIST OF TABLES

v

LIST OF FIGURES

vi

NOMENCLATURE

xiv

CHAPTER 1 INTRODUCTION

1

1

2

6

CHAPTER 2 EXPERIMENTAL APPARATUS AND

PROCEDURES

8

8

11

CHAPTER 3 DIMENSIONLESS GROUPS AND

UNCERTAINTY ANALYSIS

16

16

16

CHAPTER 4 RESULTS AND DISCUSSION

20

21

23

28

30

38

CHAPTER 5 CONCLUDING REMARKS

161

REFERECES 164

LIST OF TABLES

LIST OF FIGURES

.

.

.

.

.

國立交通大學

機械工程學系

碩士論文

研究生 : 陳奎銘

指導老師: 林清發博士

研究生：陳奎銘 Student：Kuei-Ming Chen

指導教授：林清發 Advisor：Tsing-Fa Lin

誌謝