臺灣博碩士論文加值系統

此研究探討一個逆向流之渦捲式熱交換器中徑向與渦流向(流體流動方向)之固體熱傳導對熱傳效率之影響，此熱交換器由四組渦線所建構。數值分析模式中熱傳效率( )乃表示為熱傳單位指數(NTU)、熱容率比值(C)、無因次化管壁厚度( )、比爾數(Bi1 or Bi2)、渦線圈數(Nt)與無因次渦線起始角度( )之函數，經由與不具熱傳導效應之熱傳效率( )比較後，一個熱傳效率減少量之性能指標( )乃被定義且解答之。分析結果顯示， 與 值受 值之影響極為輕微，但兩者均會隨著Nt值之增加而增大；同時無論於平衡流(C = 1)或非平衡流(C ≠ 1) 之操作下，此熱交換器均存在一個最佳之Bi1值與一個最佳之Bi2值，兩者均介於10-4至10-2之間，操作於此最佳值之下，所得到之 值為最大值，而 值則會接近0。在熱力學第二定律之分析中，一個最佳之冷熱流之熱容率比值乃被發現，在廢熱之回收過程中，欲得到較大之有效功之回收率，此熱交換器之NTU值須大於2.0，且操作於接近平衡流之狀態。研究中亦針對此熱交換器於氣體－氣體、液體－液體與氣體－液體之應用分別進行最大可能 值之評估。在所規劃之實驗中，一個氣體－液體之渦捲式熱交換器乃被製作，並用於氣體側之熱傳與壓降資料之量測，在雷諾數(Re)於4447至32017之範圍內，量測之結果經參數相關性分析後，而提出一組平均紐塞數(Nu)與平均摩擦因子(f)之經驗公式。

The effect of radial and spiral-direction solid heat conduction on the heat transfer effectiveness of a counter-current spiral heat exchanger constructed by four Archimedes spirals was investigated. The heat transfer effectiveness ( ) is a function of number of transfer units (NTU1 and NTU2), ratio of flow capacity rates (C), dimensionless wall thickness ( ), Biot number (Bi1 or Bi2), number of spiral turns (Nt) and dimensionless start-point angle of spiral ( ). By comparing to the effectiveness of the heat exchanger without the solid heat conduction effect ( ), a performance evaluation factor called the decrement in heat transfer effectiveness ( ) was defined and numerically evaluated. The and the values are weakly dependent on the value, but moderately increase with the Nt value. Either at the balanced-flow operation or at the unbalanced-flow operation, the heat exchanger has an optimum Bi1 value and an optimum Bi2 value ranging from 10-4 to 10-2. At the optimum Bi1 or Bi2 values, the value is a maximum and the value nears zero. In the thermodynamic second-law analysis, an optimum hot flow-to-cold flow capacity-rate ratio was found. For obtaining a large net recovered exergy rate, the spiral heat exchanger needs to possess a large number of transfer units (greater than 2.0) and be operated at a near balanced-flow condition. For gas-to-gas, liquid-to-liquid and gas-to-liquid waste heat recovery applications, the maximum possible values of the spiral heat exchanger at balanced-flow operation were estimated. In the experiment, a gas-to-liquid spiral heat exchanger was manufactured and used for measuring the heat transfer and pressure drop data in the gas channel. Empirical equations for the Nusselt number (Nu) and Darcy friction factor (f) were established for the Reynolds number (Re) in the range of 4447 to 32017.

Acknowledgement i
Chinese abstract ii
Abstract iii
Table of Contents iv
List of Tables ix
List of Figures xi
Nomenclature xvi
Chapter 1 Introduction 1
1.1 Preface 1
1.2 Literature survey 2
1.3 Objective of the work 12
Chapter 2 Geometric Analysis of Archimedes’ Spiral and Heat
Transfer Area in a Spiral Heat Exchanger 14
2.1 Length of a curve in polar coordinates 14
2.2 Length of Archimedes’ spiral in polar coordinates 16
2.3 Geometric analysis of a spiral heat exchanger 18
2.3.1 Length of inner surface of a wall (dashed line) 18
2.3.2 Length of outer surface of a wall (solid line) 19
2.3.3 Heat transfer area of a wall 22
2.3.4 Heat transfer area for a channel flow in the spiral heat exchanger 23
Chapter 3 Energy Equations for a Spiral Heat Exchanger
with Consideration of Solid-Side Heat Transfer 27
3.1 Mathematical modeling 27
3.1.1 Energy balance for inner wall of cold flow (dashed lines) 27
3.1.2 Energy balance for inner wall of hot flow (solid lines) 32
3.1.3 Energy balance for hot flow channel 37
3.1.4 Energy balance for cold flow channel 38
3.2 Dimensionless energy equations 39
3.2.1 Dimensionless energy equations for walls 41
3.2.2 Dimensionless energy equations for hot and cold flows 43
3.3 Heat transfer effectiveness of heat exchanger 45
3.4 Decrement in heat transfer effectiveness 46
3.5 Heat transfer effectiveness at Bi1 → 0 and Bi2 → 0 46
Chapter 4 Numerical Analysis 49
4.1 Finite-difference equations for the solid walls 49
4.1.1 Finite-difference equations for the inner wall
of the cold-flow channel 50
4.1.2 Finite-difference equations for the inner wall
of the hot-flow channel 65
4.2 Finite-difference equations for the channel flow 80
4.2.1 Finite-difference equations for the hot flow 80
4.2.2 Finite-difference equations for the cold flow 81
4.3 Computer simulation program 82
4.4 Error analysis of numerical scheme 83
Chapter 5 Heat Transfer and Exergy Analysis of a Spiral Heat Exchanger without Solid-Wall Heat Conduction Effect 85
5.1 Heat transfer area of a spiral heat exchanger without solid-wall heat conduction effect 85
5.2 Energy equations 87
5.2.1 Energy balance for hot flow 88
5.2.2 Energy balance for cold flow 89
5.3 Dimensionless energy equations 90
5.3.1 Dimensionless energy equations for the hot flow 90
5.3.2 Dimensionless energy equations for the cold flow ( ) 91
5.4 Numerical scheme and heat transfer effectiveness 92
5.5 Second-law analysis 94
5.5.1 Exergy change rate in a flow 94
5.5.2 Exergy change rate in a flow in the spiral heat exchanger 96
5.5.3 Net recovered exergy rate 97
5.5.4 Results of exergy analysis and discussion 99
5.5.5 Numerical example 101
Chapter 6 Results and Discussions for the Effect of Solid-Wall
Heat Conduction on the Heat Transfer Effectiveness 105
6.1 Heat transfer effectiveness of the spiral heat exchanger
at C* = 1.0 and NTU1 = NTU2 105
6.1.1 Temperature distributions 106
6.1.2 Heat transfer effectiveness of the spiral heat exchanger 107
6.1.2.1 Effect of Nt on 107
6.1.2.2 Effect of Bi1 on 107
6.1.2.3 Comparison between two different models 108
6.2 Decrement in heat transfer effectiveness ( ) at balanced-flow operation (C* = 1) 110
6.2.1 Effects of Bi1, , NTU1 values on value 110
6.2.1.1 value at small Bi1 values (Bi ≤ 10-4) 110
6.2.1.2 value at intermediate Bi1 values (10-4 < Bi1 < 0.1) 111
6.2.1.3 value at large Bi1 values (Bi1 ≥ 0.1) 112
6.2.2 Effect of Nt value on value 113
6.2.3 values at unequal NTU1 and NTU2 values 113
6.3 Decrement in heat transfer effectiveness ( ) at unbalanced-flow operation (C* ≠ 1) 114
6.4 Possible values at C* = 1 in practical applications 115
6.4.1 Gas-to-gas applications 116
6.4.2 Liquid-to-liquid applications 117
6.4.3 Gas-to-liquid applications 119
6.5 Regression analysis for at C* = 1 and large Bi
values (Bi1 = Bi2 = Bi) 121
Chapter 7 Measurement of Heat Transfer and Fluid Friction Data 124
7.1 Geometry of the spiral heat exchanger using in the experiment 124
7.2 Experiment on fluid friction correlation 125
7.2.1 Experimental setup and apparatus for pressure drop measurement 125
7.2.2 Pressure drop and Darcy friction factor 125
7.3 Experiment on heat transfer characteristics 127
7.3.1 Experimental setup and apparatus for temperature measurement 127
7.3.2 Data acquisition system in temperature measurement 128
7.3.2 Temperature distribution in the air-flow channel 130
7.3.3 Convective heat transfer coefficient and average Nusselt number 130
7.4 Uncertainty analysis of experimental data 133
7.4.1 Uncertainty analysis for the Nusselt number 133
7.4.2 Uncertainty analysis for the Darcy friction factor 135
7.5 Nu and f values in the literature 136
7.6 Comparison of the Nu and f values 138
7.7 Heat transfer effectiveness at various flowrates 139
Chapter 8 Conclusions 141
References 144

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