應用各種最佳化技術於完全限制狀況下高性能散熱座之散熱最佳化研究

Thermal Optimal Design for Fully-Confined Compact Heat Sinks by Using Various Optimization Methods

洪振聰(JENN-TSONG HORNG)

指導教授 ： 洪英輝 ； 傅建中

國立清華大學/工學院/動力機械工程學系/博士(2008年)

https://doi.org/10.6843/NTHU.2008.00174

摘要

本論文研究針對在水平渠道內完全限制狀況下高性能散熱座之流體流阻與熱傳特性作一系列的實驗研究與理論分析。依據實驗資料與理論分析結果，發現局部有效紐賽數在展向(Spanwise)具對稱性，而沿著流向(Streamwise)而遞減。在探討之影響參數中格拉雪夫數(GrH )、散熱座基板高度與整體散熱座高度比值( Hb/H)或鰭片與基座(Fin/Base)材料不同組合對局部有效紐賽數的影響不顯著；但發現此紐賽數會隨著雷諾數(ReD)的增加而增加。上述的參數對於平均紐賽數、局部與平均外部熱導，亦呈現相同的影響趨勢。根據實驗結果，本研究進一步地提出包含有效摩擦因子、平均外部熱阻與平均總熱阻之熱流特性經驗公式。
在進行最佳化研究之前，本研究有效地運用反應曲面法(RSM) 獲得的二階函數與類神經網路(ANN)推論獲得的三階函數兩種模式精確地預測總熱阻、壓降與質量的值。以RSM獲得的二階函數模式預測值與實驗值相比，在總熱阻、壓降與質量預測上之最大誤差分別為7.3%、1.7%與6.3%；利用ANN方法產生的三階函數模式預測值與實驗值相比，在總熱阻、壓降與質量預測上之最大誤差分別為3.2%、3.8%與6.3%。另外，本研究應用倒傳遞(Back-propagation)訓練方法，建立輸出之性能與輸入之設計參數間更精確的隱含性ANN函數；以此函數預測值與實驗值作比較，在總熱阻、壓降與質量預測上之最大誤差分別為2.6%、2.8%與4.3%。
最後，本研究針對水平渠道內完全限制狀況下高性能散熱座之熱傳特性最佳化的探討上，分別使用RSM-SQP、ANN-GA、RSM-GA與ANN-SQP等四種不同的最佳化方法，成功地完成在壓力，質量與空間等多重限制狀況下散熱最佳化的評估設計。經由上述四種不同最佳化方法的比較，可以發現RSM-SQP方法與ANN-GA方法兩者較RSM-GA方法與ANN-SQP方法兩者優異。當與ANN-GA方法之最佳化結果作比較，發現使用RSM-SQP方法在Case I 與Case II時，由於最佳化的設計參數均遠離可操作的區域，故其最佳化的結果產生了顯著的誤差；相對的，在Case III 與Case IV 因為最佳化的設計參數位於可操作的區域內，因此RSM-SQ方法亦可獲得滿意的結果。總而言之，使用RSM-SQP方法的優點是在本研究中僅需77組測試資料，它遠少於ANN-GA方法 所需的320 組測試資料，故操作上顯著地節省電腦計算時間。如最佳化的設計參數在可操作的範圍內(如Case III 與Case IV)，即可得到滿意的結果。至於使用ANN-GA方法的優點，由於ANN網路的訓練樣本是選取在整個求解的領域內均勻分佈的樣本中隨機選取，其最佳化的解可涵蓋整體有興趣的區域，而非僅止於可操作的區域，因此ANN-GA方法可以求得精確的整體最佳化解，這種結論可由在本研究中Case (I)至Case (IV)最佳化的結果獲得印證。

關鍵字

最佳化設計 ； 高性能散熱座 ； 完全限制 ； 類神經網路 ； 基因演算法

並列摘要

In the present study, a series of experimental investigations and theoretical analyses on the fluid flow friction and heat transfer behavior for fully-confined compact heat sinks in a ducted flow have been performed. From the experimental data and theoretical results, the distribution of local effective Nusselt number is symmetric along the spanwise direction; and the local effective Nusselt number decreases along the streamwise direction. The local effective Nusselt number is insignificantly affected by GrH, Hb/H or Fin/Base material; while, it increases with increasing ReD. Similar trends can be found for the effects of relavant influencing parameters on other heat transfer characteristics such as average effective Nusselt number, local and average external thermal conductance. New correlations for fluid flow friction and thermal performance, including the effective friction factor, average effective Nusselt number, average external thermal resistance and overall thermal resistance, in terms of relevant influencing parameters have been presented.
Prior to the execution of thermal optimization, two numerical models such as the RSM with a quadratic explicit formula and the ANN with a third-order explicit formula are effectively employed to accurately fit the data of overall thermal resistance, pressure drop and mass. As compared with the actual experimental data and theoretical results, the maximum deviations of the predictions for overall thermal resistance, pressure drop and mass by using the RSM method with a quadratic explicit formula are 7.3%, 1.7%, and 6.3%; those by using the ANN method with a third-order formula are 3.2%, 3.8% and 5.2%, respectively. In addition, with an effective back-propagation training algorithm, a more accurate implicit correlation between the performance outputs and design variables has been obtained. As compared with the actual experimental data and theoretical results, the maximum deviations of the predictions by this implicit correlation for overall thermal resistance, pressure drop and mass are 2.6%, 2.8%, and 3.4%.
Furthermore, four types of optimization technique such as RSM-SQP, ANN-GA, RSM-GA and ANN-SQP methods have been successfully employed for the optimal evaluation on the thermal performance of fully-confined compact heat sinks in a ducted flow under multi-constraints such as pressure drop, mass, and space limitations. Among these four optimization methods, the superiority of using either the RSM-SQP or ANN-GA method can be found as compared with using the ANN-SQP or RSM-GA method. As compared with the optimal results obtained by the ANN-GA method, a significant deviation evaluated by using the RSM-SQP method for Cases I and II is found because the optimal values of the design variables are located beyond the region of operability. In contrast, a satisfactory agreement is achieved by the RSM-SQP method for Cases III and IV because the optimal values of the design variables are located within the region of operability. In summary, the advantage of using the RSM-SQP method with a smaller number of test cases, say 77 instead of 320 in the ANN-GA method, can be significantly found in the saving of computation time for some design cases with multi-constraints in the region of operability, e.g. Cases III and IV. As for the advantage of using the ANN-GA method, although more test cases are needed for the ANN-GA method as compared to that for the RSM-SQP method, the ANN-GA method which has randomly uniform-distributed training patterns in the whole solving domain can be applied to the global region of interest, not just in the region of operability; a globally precise optimal solution can be achieved with the ANN-GA method for all the cases (i.e., Cases I through IV) explored in the present study.

並列關鍵字

optimal design ； compact heat sink ； fully-confined ； ANN ； GA

參考文獻

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