氣膠微粒在管流中熱泳附著之研究

Abstract

本研究探討管流中微粒的熱泳附著效率。當流場與溫度場皆是在發展狀態時，溫度梯度在圓管進口附近靠近管壁的位置是最高的，微粒的熱泳附著效率可能會增加。因此，本研究首先利用數值模擬的方法探討進口流效應對圓管中微粒熱泳附著效率的影響。而由於Romay 等人(1998)的紊流熱泳附著效率的實驗值與理論值不合，所以本研究接著用實驗的方法，探討微粒在圓管中的熱泳附著效率並與理論值比對。最後，工業上常用管壁加溫的方法來防止微粒的管壁附著，但是有效防止微粒附著的加熱溫度並未知，因此本研究利用數值模擬及實驗的方法探討微粒在層流圓管中的附著效率。

在發展中的流體對微粒熱泳附著效率影響的研究中，以數值方法來求取微粒在圓管中的臨界軌跡線，藉以計算出對應的熱泳附著效率。研究結果顯示，當流場是完全發展流而溫度場是正在發展中的狀態，微粒的熱泳附著效率只有在圓管進口的位置會稍微高於前述當流場與溫度場皆是完全發展流的案例，然而在Z>5的圓管中，最終的熱泳附著效率會一樣。當流場與溫度場皆是正在發展中的情況時，在Z>5的圓管中，微粒的熱泳附著效率大約是流場與溫度場皆是完全發展流案例的兩倍，而且在進口的位置附著效率會高出甚多。另外，本研究開發出可用在計算層流圓管中，流場與溫度場同時是完全發展流或同時是正在發展中的熱泳附著效率半經驗式。

在層流及紊流圓管的微粒熱泳附著效率實驗中，本研究使用單徑的氯化鈉微粒(微粒粒徑在0.038到0.498 mm之間)作為測試微粒，用來量測在一長1.18公尺，內徑為0.43公分圓管中微粒的熱泳附著效率。在Romay 等人(1998)的研究中，理論的熱泳附著效率和實驗值不合，然而在本研究中，考慮帶有Boltzmann靜電平衡微粒的靜電附著、微粒的紊流擴散及慣性衝擊等機制，所以微粒的熱泳附著效率可以準確地被量測出來。

在使用熱泳力來抑制微粒管壁附著這方面，我們將管壁加高溫度使其高於進氣氣流，係利用實驗及數值模擬的方法探討微粒在層流圓管內的附著效率。在數值分析這方面，求解包含熱泳項的對流擴散方程式，求得微粒在圓管內的濃度分佈及附著效率。實驗時使用單徑微粒(微粒粒徑為0.01, 0.02 and 0.04 mm)作為測試氣膠，量得的實驗值用來驗證數值解。研究結果顯示，微粒的附著效率會隨著管壁溫度的升高或是圓管內氣流量的增加而降低。本研究發展出一個半經驗式可以用來預測在層流圓管中，在給定的無因次附著參數下，求得所需要的無因次溫度差(亦即可求取所需的管壁加熱溫度)來達到零微粒附著效率。

This study investigates thermophoretic particle deposition efficiency in a tube flow. The highest temperature gradient near the wall occurs at the entrance of a tube when both flow and temperature are developing, thermophoretic deposition in the entrance region may be enhanced. Therefore, the effect of entrance flow on the thermophoretic deposition efficiency in laminar tube flow was first investigated numerically. In the previous study of Romay et al. (1998), the experimental data don’t agree well with theoretical results. In the present study, the thermophoretic particle deposition efficiency in tube flow was studied experimentally and compared with the theoretical predictions. To prevent particle deposition on tube wall, a common practice is to heat up the tube wall in industry. But the required wall temperature to effectively suppress particle deposition in tube wall is unknown. Thus the effect of tube wall temperature on particle deposition efficiency under laminar flow condition was investigated experimentally and numerically.

In the study of developing flow effect in a circular tube on thermophoretic particle deposition efficiency, the critical trajectory method was investigated numerically. The results show that when the flow is fully developed and temperature is developing, it is found that only near the thermal entrance region (or temperature jump region) of the tube the deposition efficiency is slightly higher than the combined fully developed case (flow and temperature), while the deposition efficiency remains the same for Z>5. When both flow and temperature are developing (or combined developing), the deposition efficiency is about twice of the combined fully developed case for Z>5 and is much higher near the entrance of the tube. Non-dimensional equations are developed empirically to predict the thermophoretic deposition efficiency in combined developing and combined fully developed cases under laminar flow condition.

In the experimental study of thermophoretic deposition of aerosols particles in laminar and turbulent tube flow. Thermophoretic deposition of aerosols particles (particle diameter ranges from 0.038 to 0.498 mm) was measured in a tube (1.18 m long, 0.43 cm inner diameter, stainless-steel tube) using monodisperse NaCl test particles under laminar and turbulent flow conditions. In the previous study by Romay et al. (1998), theoretical thermophretic deposition efficiencies in turbulent flow regime do not agree well with the experimental data. In this study, particle deposition efficiencies due to other deposition mechanisms such as electrostatic deposition for particles in Boltzmann charge equilibrium, and turbulent diffusion and inertial deposition were carefully assessed so that the deposition due to thermophoresis alone could be measured accurately.

In the aspect of suppression of particle deposition by thermophoretic force, flow through a tube with circular cross section was investigated numerically and experimentally for the case when the wall temperature exceeds that of the gas. Particle transport equations for convection, diffusion and thermophoresis were solved numerically to obtain particle concentration profiles and deposition efficiencies. The numerical results were validated by particle deposition efficiency measurements with monodisperse particles (particle sizes were 0.01, 0.02 and 0.04 mm). For all particle sizes, the particle deposition efficiency was found to decrease with increasing tube wall temperature and gas flow rate. An empirical expression has been developed to predict the dimensionless temperature difference needed for zero deposition efficiency in a laminar tube flow for a given dimensionless deposition parameter.