在此篇研究中，首先，Zigzag流道之三個幾何設計變數: 入口長度、彎管角度和導圓角半徑。本研究利用數值求解連續方程式，Navier Stokes方程式和能量方程式，Zigzag流道之熱傳與水力性能表現可藉由有效性和無因次壓力降來評估。接著將討論三種幾何設計變數對性能表現之影響，考慮目標函數為壓力降和冷端出口溫度時，兩者無法同時改善。由於二次流動的發生，其擾動之機制減少了熱邊界層之厚度並增加通過壁面之熱通量。於是三個幾何設計變數對於二次流動強度表明出熱傳性能將為隨著較小之彎管角度、導圓角半徑和較大之入口長度。
然而，為了研究Zigzag 流道設計之多樣性，利用NSGA-II 演算法求解出考慮冷端出口溫度和壓力降為目標函數之多目標最佳化問題。其柏拉圖解將根據支配等級和擁擠距離被排列。而柏拉圖其中之特定一解(無因次壓力降6.169和有效性0.201) 和單直管流道進行比較。而最後，將直管型、Zigzag型和蛇形狀之印刷式迴路熱交換器利用有效性和壓力降進行評估。和實驗數據相比驗證後，可以發現出Zigzag型PCHE相比於其餘兩者，其熱傳性能較高。而結果顯示出，柏拉圖特定一解之PCHE 提升有效性(239%)的同時增加了最少的壓力降。

In the present study, firstly, the zigzag channel is investigated with three design variables: length of entrance (L_e), bending angle (θ_b) and radius of fillet (R_f ). The results are numerically investigated by solving the steady state continuity equation, Navier-Stokes equations and energy equation. Therefore, the heat transfer and hydraulic performance of zigzag channel can be estimated by effectiveness (Feff) and non-dimensional pressure drop (Fp). Secondly, the effect of geometric parameters is discussed, respectively. Considering the objective function as non-dimensional pressure drop and effectiveness can not be improved without degrading the other objective, it means that two objective functions can’t be simultaneously enhanced. Then, owing to the secondary flow occurring, the mixing mechanism decreases the thickness of the thermal boundary layer which enlarges the heat flux to pass through the wall. Consequently, the variation of secondary flow intensity of three design variables reveals that heat transfer performance increases with the lower θ_b and R_f also larger L_e. However, to investigate the diversity of zigzag channel design, the multi-objective optimization problem that considering the effectiveness and non-dimensional pressure drop as the objective function is implemented by Non dominated Sorting Genetic Algorithm II. The Pareto fronts are sorted by the dominating rank and crowding distance. The particular solution of Pareto fronts (with non-dimensional pressure drop equals 6.169 and the effectiveness is 0.201) is compared with the single straight channel. Lastly, the PCHE is equipped with straight channels, zigzag and serpentine flow channels, allowing us to numerically investigate the PCHE performance in terms of the effectiveness and non-dimensional pressure drop. With the validation by the previous experimental data, it is found that the PCHE with zigzag flow channels, compared with the PCHE with the low passages or with the serpentine flow channels, possesses significant heat transfer enhancement by the generation of the so-called mixing effect accompanied with eddy structures accomplishing the heat transfer enhancement. In conclusion, the zigzag channels PCHE with the Pareto front gets the effect of improving effectiveness by increasing less pressure drop penalty.

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