本文以數值模擬方法探討具等熱通量紊流強制對流之空氣流過穿孔圓柱鰭片散熱器的流場與熱傳特性。根據雷諾平均納維-斯托克斯(RANS)近似的三種紊流模型，使用有限體積法求解紊流統御方程式。在所研究範圍內，整體性能而言，standard k-epsilon 模型較其它兩種模型佳(RNG k-epsilon 模型和realizable k-epsilon 模型)。而本文之研究參數分別為：圓柱鰭片直徑(D)、穿孔直徑(d)、穿孔間距(s)及雷諾數(Re)。Re,D,d與s對於摩擦因子與平均紐賽數的影響也作了詳細地討論。
將數值計算結果與參考文獻之實驗數據比較，結果顯示standard k-epsilon 模型所得之結果與參考實驗數據較為吻合，故本文採用standard k-epsilon 模型進行往後的計算。為了探討各研究參數對流場流動行為及熱傳之影響，本文針對不同研究參數組合進行模擬，並計算對應之摩擦因子及平均紐賽數。結果顯示，摩擦因子及平均紐賽數皆隨著D之增加而增加，穿孔圓柱鰭片相較於固體鳍片有較大的平均紐賽數約高出8%，數值結果顯示使用穿孔圓柱鰭片導致熱傳增益。另外發現於 d=1.5mm 及 s=4mm 時，摩擦因子出現最小值，且於 d=1mm 及 s=2.75mm 時，平均紐賽數出現最大值。
此外，數值結果驗證後，本文應用反應曲面法(RSM)結合基因演算法(GA)進行數值模擬最佳化，並藉由迴歸分析得到本文之目標函數，熱性能係數之迴歸方程式，其設計參數分別為：圓柱鰭片直徑(D)、無因次之穿孔直徑(e)及無因次之穿孔間距(f)。最後以基因演算法求得最佳的熱性能係數及對應之最佳設計參數組合。最佳化結果顯示，迴歸方程式與CFD求得的最佳性能係數之誤差小於2%，且本研究中熱性能係數之增益可達34%。

In this study, the fluid flow and heat transfer characteristics of turbulent forced convection of air flow through perforated circular pin fin heat sinks with constant heat flux are investigated numerically. The parameters studied are diameter of circular pin fins, diameter of perforations, space of perforations and Reynolds number. The effects of D, d, s and Re on friction factor and averaged Nusselt number are also discussed in detail. Subsequent numerical computations are performed with standard k-epsilon model for the parameters studied and the theoretical model developed is validated with the available experimental data in the literature.
In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using Response surface methodology (RSM) coupled with Genetic algorithm (GA). The objective function is defined as thermal performance factor with three design parameters, diameter of circular pin fins, non-dimensional diameter of perforations and non-dimensional space of perforations, and is obtained by using regression analysis. Finally, the maximum thermal performance factor and the optimal sets of design parameters are obtained by using Genetic algorithms (GA). The difference of optimal thermal performance factor between which is calculated by regression function and obtained by using CFD is less than 2%, and the numerical optimization shows that the enhancement of the objective function can achieve 34% in this study.

 
INTRODUCTION

With the advancement of technology, many industrial systems and personal equipment gradually trend toward small size and high power development. It is an important issue on the development of the cooling system that how to cope the large heat flux at the limit of size of cooling system. It is a common application in cooling problem of electronic device that using axial fan coupled with heat sink to perform forced air convection cooling. This method is simple and effective, but it requires the reserved flowing space for air at working environment of heat sink. Therefore, many researchers are researching that how to enhance the cooling efficiency of the heat sink in the working space is limited. There are many different types of fins were invented, such as flat fins, serrated fins, circular and square pin fins and so on. Different types of fin caused different pressure drop and different disturbance mixing ability of the channel, and the corresponding coefficient of performance was also different. Moreover, many researchers proposed that perforations on the pin fin will cause larger total heat transfer area on the heat sink and smaller region of wake that reduced pressure drop of the channel. Thus the simulations and optimizations of turbulent flows through perforated circular pin fin heat sinks are performed, and the results are investigated in this study.

MATERIALS AND METHODS

In this study, the turbulent governing equations based on Reynolds-averaged Navier-Stokes (RANS) approach are discretized using control volume method, and the solution procedure based on SIMPLE algorithm are carried out. The computational results obtained by employing three turbulence models (standard k-epsilon model, RNG k-epsilon model and realizable k-epsilon model) are validated with the available experimental data in the literature to obtain the appropriate selection of turbulence model. The parameters studied are diameter of circular pin fins, diameter of perforations, space of perforations and Reynolds number. Finally, a multi-parameters constrained optimization procedure integrating the computational fluid dynamic (CFD), response surface methodology (RSM) and genetic algorithm (GA) is proposed to design the geometric configuration for the perforated circular pin fin heat sinks.

RESULTS AND DISCUSSION

According to the computation results, overall performance of standard k-epsilon model is better in comparing with other models (RNG k-epsilon model and realizable k-epsilon model) in the studied ranges, so subsequent numerical computations are performed with standard k-epsilon model for the parameters studied. The results show that the larger circular pin fin diameter leads to larger total heat transfer area and size of wake, which cause the increasing of averaged Nusselt number and friction factor. When the perforation diameter increases, the smaller size of wake causes the lower friction factor, and the variation of averaged Nusselt number is less than that of friction factor. When s=2.75mm and s=1.5mm, the visible vortexes near top and bottom wall of channel have the better mixing the energy in the fluid behind pin fin and lead to higher averaged Nusselt number. However, the variation of friction factor is less than that of averaged Nusselt number in this case. Moreover, the presence of perforation causes the increasing of total heat transfer area and decreasing of size of wake region behind the fin. It is the reason that perforations on fin cause the enhancement of performance factor. Finally, the maximum thermal performance factor and the optimal sets of design parameters are obtained by using Genetic algorithms (GA). The difference of optimal thermal performance factor between which is calculated by regression function and obtained by using CFD is less than 2%, and the numerical optimization shows that the enhancement of the objective function can achieve 34% in this study.

CONCLUSION

The results show that the averaged Nusselt number calculated on the basis of projected area and friction factor increase with increasing the diameter of circular pin fins. The circular perforated pin fins are shown to have 8% larger averaged Nusselt number than corresponding solid pin cases, which means the use of circular perforated pin fins lead to the heat transfer enhancement. Moreover, the minimum friction factor is observed at d=1.5mm and s=4mm, and the maximum averaged Nusselt number is found at d=1mm and s=2.75mm. Finally, the numerical optimization shows that the enhancement of the objective function can achieve 34% in this study.

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