利用沉浸邊界法及離散元素法發展一數值黏度計之數值模擬分析

Abstract

對於稠密顆粒懸浮於流體中的整體流動行為，皆為非牛頓流體流動，因顆粒懸浮於流體中，導致整體黏滯性不再保持常數，而是隨著顆粒在流體中的體積分率增加而增加。這種流動行為在工業應用中由為常見，如塑膠顆粒的射出成型，混凝土灌漿等等。 本研究利用沉浸邊界法和離散元素法，設計出一個數值流變儀。透過模擬一個簡單剪切流驅動密集懸浮顆粒，分析整體流動的運動行為，計算整體流動的相對黏滯性及顆粒法向應力，並與過去相關研究結果進行比較。接著，為了確認此數值流變儀能夠模擬不同顆粒的材料性質，將透過調整顆粒碰撞模型中使用的模擬參數，如顆粒彈性恢復係數、動摩擦係數、靜摩擦係數等等，進行敏感度分析。使其能透過設定不同的顆粒條件，模擬出不同顆粒、流體的流變特性，來計算其相對應的本構關係。最後，為了模擬更複雜、真實的流動行為，我們將顆粒的外型修改為橢球形狀，首先修改拉格朗日標記點的佈點方式，接著模擬一中性浮力橢球顆粒放置於簡單剪切流中的運動行為。觀察橢球顆粒角速度，隨著橢球顆粒長軸與水平軸夾角的變化，並與過去相關的研究結果進行比較。

The bulk behavior of dense particles suspended in a fluid is characterized by non-Newtonian fluid flow, as the volume fraction of particles in the flow leads to a non-constant viscosity. Suspension of solid particles in liquid flows is a common phenomenon in various industrial flow systems, such as injection molding, concrete pumping, etc. The purpose of this study is to develop a numerical viscometer by using immersed boundary method and discrete element method. By simulating a simple shearing flow driving dense suspended particles, we analyzed the bulk flow behavior, calculated the relative viscosity and particle normal stresses, and compared the results with relevant previous studies. Furthermore, to verify the applicability of this numerical rheometer to different particle materials, sensitivity analysis was performed by adjusting simulation parameters, such as particle coefficient of restitution, coefficient of kinetic friction, and coefficient of static friction in the collision model. This allowed us to simulate various particle and fluid rheological properties and calculate the corresponding constitutive relationships. Additionally, to model more complex and realistic flow behavior, we modified the particle shape to be ellipsoidal. We adapted the Lagrangian marker distribution method and simulated the motion of an neutrally buoyant ellipsoidal particles immersed in a simple shearing flow. We observed the angular velocity of the ellipsoidal particles varying with the angle between the long axis and the horizontal axis, and compared the results with relevant past research findings.