慣性效應影響二階非牛頓流體微粒附著率之研究

A Study of Inertial Effect on Particle Deposition Rates of a Second-Grade Non-Newtonian Fluid Past a Wedge Plate

焦傳宗(Chuan-Tsung Chaio)

指導教授 ： 蔡瑞益

中原大學/工學院/機械工程研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400358

摘要

本文探討二階非牛頓流體受慣性效應與布朗擴散作用對其微粒附著速度所產生影響之研究。當流體具有彈性時，其微粒運動受慣性效應與彈性之影響甚大。在高分子塑膠加工過程與化學工業程序中，非牛頓流體之應用已十分普遍，其中二階非牛頓流體與懸浮微粒流經物體表面，而微粒附著沉積在一般工業界上也是常見的現象。
統御方程式為二階非牛頓流體之連續方程式、動量方程式、能量方程式及濃度方程式，並且定義彈性參數（E）。對統御方程式做無因次化相似轉換後，以微擾法展開。在數值計算的部分，以四階Runge-Kutta積分法與射擊法求得。結果包含零階與一階速度場、溫度場、濃度場分布，並且計算微粒附著速度。
在零階的部分與一般牛頓流體有相同之結果；一階的部分受角度的影響較大。另外我們可以發現當微粒粒徑很小時，受布朗擴散與熱泳機制所支配；當微粒粒徑增加，則受慣性效應與彈性參數所支配。在m=1時，角度的影響遠大於流體流動的影響，以至於在近壁區產生微粒堆積；在m=0時，角度的影響較小，而彈性參數的影響使邊界層內速度顯著地改變，因而使微粒附著速度有極大的變化。此外彈性參數加強了慣性效應的效果。

關鍵字

二階非牛頓流體 ； 微粒附著率 ； 慣性效應

並列摘要

Combined effects of inertial and Brownian diffusion on particle deposition of a second-grade non-Newtonian fluid onto wedges are reported. When the fluid flows elastically, the motion of particles has a great effect upon the inertia and elastic. Particles suspended in the non-Newtonian fluids deposition onto a surface in plate flow are of significance in a wide range of physical applications, such as the polymer welding and chemical industry processes.
The governing equations include the continuity, momentum, energy and concentration equations of a second-grade non-Newtonian fluid and define the elastic parameter (E). The solution methods are used not only similar transformation but perturbation technique for the governing equations. In numerical analysis, the equations are solved by the fourth-order Runge-Kutta integration and shooting method. The results include zero-grade and first-grade velocity profiles, temperature and concentration distributions then calculate particle deposition velocity.
In the zero-grade part, the physics phenomenon is alike the Newtonian fluid; in the first-grade part, it has a greater effect on angle. In addition, we can find that the particle deposition rates are controlled by Brownian diffusion and thermophoresis effect for ultra-small particle sizes. However, when the particle size increases, the inertial and elastic effect become more and more important and Brownian diffusion effect maybe negligible. Finally, at m=1, the effect of angle is more than the effect of fluid flow, thus it piles up the particles near the wall. At m = 0, the effect of angle is smaller and the effect of elastic parameter makes velocity profiles change apparently in boundary layer. As the result, the particle deposition velocity varies very much. Furthermore, the elastic parameter enhances the effect of inertia.

並列關鍵字

second-grade Non-Newtonian fluid ； particle deposition rates ； inertial effect

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