本文使用數值模擬分析三維模式下廢氣煙道熱回收熱電系統，探討不同熱擷取裝置(集熱塊與嵌入式鰭片)之流場、溫度場以及電場的分佈。研究中熱電模組之物理模型包含高溫壁面(煙道)、熱電發電模組(thermoelectric generator，TEG)、集熱塊或嵌入式鰭片，以及水冷散熱器等。在數值分析上使用那維爾-史都克(Navier-Stokes)方程式作為流場統御方程式，並配合能量守恆與電流守恆方程式，求解熱電模組中熱電耦合效應。由於煙道內廢氣具有高放射率氣體且屬於偏高溫環境，所以流場必須同時考慮對流及輻射熱傳。此外，本研究著重於最佳化設計，採用簡易共軛梯度法(Simplified Conjugate-Gradient Method，SCGM)作為最佳化搜尋器，結合商業計算流體力學(CFD)軟體進行最佳化分析。
首先在貼壁式熱電模組的部分，探討不同操作條件下(包括不同集熱塊材料、廢氣溫度、等效熱對流係數)改變集熱塊尺寸之影響，並計算熱電模組的發電功率(Pmax)與轉換效率(η)。再針對貼壁式熱電模組的排列間距(S)與集熱塊厚度(Hsp)，於不同操作條件中(包括冷熱側流體溫差ΔT = 200 – 800 K、等效熱對流係數heff = 20 – 80 W/m2•K)，探討熱電模組的發電功率(Pmax)與發電密度(Pmax/A)之變化。結果發現集熱塊的熱擴散效應增加熱傳路徑，進而減少系統整體熱阻，當熱電晶片加裝集熱塊後，最大功率可有效提升50%以上。最後利用最佳化方法-簡易共軛梯度法，以熱電模組之最大發電密度為其目標函數，搜尋貼壁式熱電系統中最佳的設計參數，且搜尋範圍分別為排列間距從40mm至300mm之間，以及集熱塊厚度從1mm至30mm之間。
在嵌入式熱電模組的部分，針對嵌入式熱電模組的鰭片高度(0mm < Hfin < 100mm)與鰭片支數(4 < N < 8)，於不同操作條件中(包括廢氣流速Vin = 3、5、10 m/s、廢氣溫度Tgas = 500、600、700 K)，以參數分析探討熱電模組的理想發電密度(PTEG/A)與鰭片所造成的額外泵功密度(Pfan/A)，以及模組淨發電密度(Pnet/A)之變化。結果顯示當高廢氣流速(Vin = 10m/s)與廢氣溫度(Tgas = 600K)，鰭片高度Hfin約50mm具有最大淨發電密度。隨後便針對廢氣速度與鰭片高度進行最佳化分析，探討不同廢氣溫度(Tgas = 500K、600K、700K)下最佳流速與鰭片高度設計。此外，貼壁式與嵌入式熱電模組研究中皆進行實驗比對，以自行架設的小型風洞實驗系統，量測各種不同條件下熱電模組測試本體之性能曲線(V-I與P-I曲線)，實驗結果顯示與數值分析具有良好的一致性，在熱電模組之最大發電量比較，貼壁式熱電模組誤差約8%，而嵌入式模組誤差約9%。
最後，在百葉窗型鰭片的部分，討論不同操作條件(包括廢氣溫度與入口風速)下，百葉窗角度(θ)與百葉窗間距(Lp)變化所造成熱傳因子(j)與壓降因子(f)之影響。並且使用簡易共軛梯度法進行最佳化搜尋，以熱交換器性能評價中最大面積縮減率(1-A/Aref)作為其目標函數，結合商業計算流體力學軟體，搜尋不同百葉窗間距(Lp = 0.7mm、1.0mm與1.3mm)下最佳的百葉窗型鰭片角度。結果表示當Lp = 1.0mm時，隨著不同的雷諾數百葉窗鰭片角度變化具有不同最佳面積縮減率，當雷諾數ReH從100至500，最大的面積縮減率分別是65.3%、66.9%、65.6%、63.7%和62.2%。並在文末將最佳百葉窗角度結果基於雷諾數迴歸出近似關係式。

This paper investigates the three-dimensional thermoelectric generator (TEG) are attached to a rectangular chimney used for venting flue gas from either a boiler or stove. The thermoelectric module consists of a hot plate, a flat spreader (or a built-in fin heat sink), a thermoelectric generator and a cold plate based on water cooling. In a thermoelectric analysis, the three-dimensional governing equations of heat and electric current in TEG at steady state are based on the conservation of energy and current. In addition, the flue gas flow is assumed to be a three-dimensional, steady, turbulent flow which is solved by mass, momentum (Reynolds-averaged Navier-Stokes equation), energy, turbulent - equations in the fluid region. Because of the high temperature flue gas flowing into the chimney tunnel, the radiation effect is considered. Moreover, the Simplified Conjugate-Gradient Method (SCGM) was used to search the optimal design. The approach is developed by using the commercial CFD code as the direct problem solver, which is able to provide the numerical solutions.
In terms of TEG modules with flat spreader, the optimization of TEG module spacing and its spreader thickness as used in a waste heat recovery system is investigated and solved numerically using the finite difference method along with a simplified conjugate-gradient method. The power density for a thermoelectric module is the objective function to be maximized. A search for the optimum module spacing (S) and spreader thickness (Hsp), ranging from 40mm < S < 300mm and 1mm < Hsp < 30mm, respectively, is performed. The effects of different operating conditions, including the temperature difference between the waste gas and the cooling water (ΔT = 200 – 800 K), and effective waste gas heat transfer coefficients (heff = 20 – 80 W/m2•K) are discussed in detail. It was demonstrated that the proper size of a heat spreader can decrease the thermal resistance and that the maximum power Pmax with a spreader can be significantly increased (up to 50%) as compared to TEG without spreader. The predicted numerical data for the power versus current (P–I) curve are in good agreement (within 8%) with the experimental data.
In terms of TEG modules with built-in fin heat sink, the study investigates the power output performance of the TEG module, three-dimensional numerical simulations combining convection and radiation effects, including the chimney tunnel, TEG modules, plate-fin heat sinks and cold plates, based on water cooling are developed and solved simultaneously. The effects of operational parameters such as the flue gas velocity (Vin = 3, 5 and 10 m/s) and flue gas temperatures (Tgas = 500, 600 and 700 K) on the flow and heat transfer are determined. The influences of the plate-fin height (Hfin) and number of fins (N), ranging from 0mm < Hfin < 100mm and 4 < N < 8, on the power output and pressure drop are also described in detail. It is worthy of note that the net electric power (Pnet) of the TEG module was obtained using the ideal electric power (PTEG) minus the extra pumping power (Pfan). The numerical results for the power versus current (P–I) curve are in good agreement with the experimental data within an error of 9%.
In terms of louver fin, this study suggests a method for finding the optimal louver angle of a fin heat exchanger by use of a simplified conjugate-gradient method (SCGM) and a three-dimensional computational fluid dynamics model. The search for optimum louver angles ranging from θ = 15 to 45 for suitable louver pitches and fluid input velocity are carried out for Reynolds number ReH (based on the fin spacing 1.5 mm and the frontal velocity 1 - 5 m/s) ranging from 100 to 500. The maximum area reduction of using louver surface relative to the plain surface is the objective function to be maximized. The model calculates optimum performance of the heat-exchanger by means of finding the fin angle which would give the biggest reduction in area of the louvered surfaces relative to plain fin surfaces required to give equivalent performance. The numerical optimizer adjusts the angle of the louvered fin toward the maximization of the performance of the heat exchanger. Additionally, the correlations of the optimal louver angle as function of Reynolds number ReH are obtained.

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