氣體可壓縮性對微管道內強迫對流之研究

Study on the influence of gas compressibility on forced convection in a microtube

簡育欽(Yu-Chin Chien)

指導教授 ： 翁輝竹

中原大學/工學院/機械工程研究所/碩士(2015年)

https://doi.org/10.6840/cycu201500853

摘要

本論文完成氣體在微管道內熱流場及其特性之分析。主要目的在探討稀薄氣體可壓縮性對流速、壓力、溫度、滑移、躍變、平均流阻及總熱通量之影響。首先，應用Navier-Stokes方程式、能量方程式及一階滑移與躍變邊界條件，完成發展流與完全發展流之熱流模式的建立。完全發展解係半解析獲得，發展解則利用前進隱含(MI)法數值獲得。接著，設置一熱流測試系統，藉由理論結果及實驗數據之比較以驗證本數學模式。最後，對稀薄氣體在微管道內熱流場及其特性作一分析。
研究結果發現，實驗質量流率與總熱通量數據皆隨氣體稀薄化程度增加而減少，而氣體可壓縮性可導致總熱通量達負值，亦即氣體出口溫度低於環境溫度。在特定切線動量及熱調和係數下，透過理論預測可得到與實驗量測相近之行為。結果進一步發現，氣體可壓縮性致使延著管道流速增加、溫度減小、滑移增強、躍變增強、平均流阻減少、總熱通量減少及壓力呈非線性分布，而此可壓縮效應可隨出入口壓降增加而更趨明顯。

關鍵字

微流體學 ； 稀薄氣體 ； 可壓縮流 ； 對流熱傳 ； 強迫對流

並列摘要

This thesis conducts an analysis of the flow and thermal fields and their corresponding characteristics of gas flow in a microtube. The main purpose is to investigate the influence of rarefied gas compressibility on the fluid velocity, pressure, temperature, slip, jump, average flow drag, and net heat flux. First, the Navier-Stokes and energy equations subject to the first-order slip and jump boundary conditions are used to establish the thermal-flow modes of developing and fully developed flows. The fully developed solution is semi-analytically obtained, and the developing solution is numerically obtained by using a marching implicit (MI) procedure. Further, a thermal-flow test system is designed to verify the mathematical models by comparing theoretical results with experimental data obtained. Finally, the thermal-flow fields and the corresponding characteristics of rarefied gases in a microtube are further analyzed.
It is found that both the mass flow rate and net heat flux experimental data decrease with the increase of rarefaction degree; moreover, gas compressibility may result in a negative net heat flux; that is, the gas outlet temperature is lower than the ambient temperature. The present theoretical predictions can be in agreement with the experimental measurements by setting particular tangential momentum and thermal accommodation coefficients. The result further reveal that gas compressibility leads to the increases in fluid velocity, velocity slip, and temperature jump, the decreases in temperature, average flow drag, net heat flux, and the non-linear distribution of pressure along the microtube. Such compressible effects could be further enhanced by increasing the pressure drop between inlet and outlet.

並列關鍵字

microfluidics ； rarefied gases ； compressible flow ； convective heat transfer ； forced convection

參考文獻

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