多孔性介質中自然對流與強制對流熱質傳現象之研究

Abstract

由於多孔性介質及流體蒸發、冷凝相變化對熱傳增益均有優異的表現，因此本研究擬以數值模擬方式探討一多孔性介質密閉空間中的自然對流，在系統中考慮同時存有水膜蒸發和蒸氣冷凝的狀態，以建立發生在一個充填多孔性介質的密閉空間所引發之自然對流熱質傳現象，更深入探討蒸發和凝結與多孔性介質間複雜的關係。本研究採用Darcy-Brinkman-Forchheimer多孔性介質模式進行分析，加以考慮等熱傳量的壁面條件和多孔性介質的孔隙率及滲透率等條件，以發展一套求解覆蓋流動水膜蒸發和蒸氣凝結的數值解法。另外，本文研究在有限長加熱平板(模擬電子元件上表面)加上多孔介質後，於層流槽道流場下的熱傳表現，考慮隨機孔隙率和人工排列孔隙率，並進而研究其設計參數以供實際應用於電子構裝熱傳改良或相關類似散熱機構之參考。 本研究之計算結果顯示蒸發現象對於加熱壁面之降溫效果非常顯著，特別在上方角落的位置。在高達西數的狀況下，潛熱熱傳在熱傳機制上扮演很重要的角色。在較小的達西-瑞利數時，平均紐塞數大約等於2.5，於一定值狀態與達西-瑞利數無關。在較高的達西-瑞利數時，平均紐塞數與達西-瑞利數之數學關係式在對數坐標下呈現線性之關係。 在考慮蒸發冷凝過程時，多孔性介質之孔隙率與銅粒粒徑大小對蒸發與冷凝之影響並不明顯。在較高瑞利數之下，潛熱熱傳在熱傳機制中比顯熱熱傳佔較大之比例。經過蒸發與冷凝相變化過程中且沒有乾涸狀況下，達西數 Da和水膜質量流率 對溫度的分布在的影響和瑞利數一樣都是輕微的。在有乾涸狀況下，在乾涸下方突然地失去液膜的保護，致使溫度迅速地增加且降低了熱傳遞速率。 在隨機孔隙率模式中，當標準差愈大時，孔隙率分布上的變動性愈大，致使流場形態變成非常紊亂不規則。應用隨機孔隙率模式之影響為導致局部紐塞數的局部之擾動變化非常明顯。在考慮水膜蒸發效應且高瑞利數之條件時，潛熱熱傳通量在整理熱傳機制中扮演非常重要之角色。當平均孔隙率大時，潛熱熱傳通量之貢獻也變得比較重要。對使用隨機孔隙率模式，X方向速度與Y方向速度為混沌不規則的且流場中在近高溫壁面處槽道效應並不明顯。 對具有多孔性鰭片狀之散熱片，在有較大孔隙率的條件下可獲得比全固體鰭片狀之散熱片較佳的熱傳效率。多孔性鰭片狀散熱片結構中固體顆粒粒徑太小或孔隙率太小時，會產生熱傳效能降低之不良結果。 但針對人工排列後，X方向速度 U 與，Y方向速度 V 皆變為平順且在人工排列模式A與人工排列模式B中可觀察出在近高壁面處之槽道效應。對具有多孔性凸塊，在有較大方孔隙率的條件下可獲得比全固體凸塊較佳的熱傳增益。多孔性凸塊結構中固體顆粒粒徑太小或孔隙率太小時，會產生熱傳效能降低之結果。多孔性凸塊之孔隙若經由人工排列後，更佳的熱傳效率是可預期的。

In general, porous medium, energy transfer of phase change with film evaporation and film condensation can enhance thermal performance. In this paper, a series of numerical simulations of natural and forced convection with porous medium are investigated. Darcy-Brinkman-Forchheimer’s formulation of momentum equation for the flow in the porous medium is adopted. The parameters of porosities, bead diameters and wall heat fluxes are taken into consideration to develop an algorithm combining the processes of the film evaporation, natural convection and film condensation. On the other hand, for enhancing heat transfer rate of channel flow, the square porous medium is mounted on the heated plate to improve the heat dissipation. The computed results are based on constant porosity model, random porosity model and artificial porosity model in the present study. The present results can be summarized as follows. The effect of the evaporation on the reduction of temperature of the hot wall is remarkable and especially in the upper corner. The latent heat flux plays an important role in heat transfer mechanism at a high Darcy number. The distribution of the ratio (Rl) in the lower Ra region is larger than that of in the higher Ra region as Da>10^(-5). The relationship of averaged Nusselt number with Darcy-Rayleigh number is almost linear in logarithmic scale as larger Darcy-Rayleigh number, and averaged Nusselt number is approximately 2.5 as small Darcy-Rayleigh number. Under evaporation and condensation situation, the effects of porosity, size of bead and mass flow rate for the without dryout situations on the evaporation and condensation are slight. In the dryout situation, the temperatures below the dryout position increases suddenly, and the heat transfer rate decreases rapidly. The latent heat flux plays an important role at a high Rayleigh number. The results are consistent well with the empirical form used for expressing the phenomenon of phase change. For the random porosity model, the distributions of velocities U and V are chaotic and disorder. The channelling effect is not apparent near the hot plate apparently under the random porosity model. The porous fin type heat sink under the larger porosity situation could obtain more heat dissipation than the traditional solid fin type one. The porous fin with a very small mean porosity or bead diameter Dp could result in reduction thermal performance. As for the artificial porosity model, the distributions of velocities U and V are smooth. The channelling effect is induced by the sparser porosities distributed near the hot plate apparently. The porous block under a larger porosity situation could obtain the thermal enhancement. As the porosity of porous block is artificially arranged, a higher heat transfer rate can be expected.