傾斜容器內顆粒加速沉降之數值研究

Numerical simulation of enhanced sedimentation in an inclined vessel

張晏誠(Yen-Cheng Chang)

指導教授 ： 周逸儒

國立臺灣大學/工學院/應用力學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201702802

摘要

本研究使用雙向耦合之固液二相流Eulerian-Lagrangian三維數值模式，對於Boycott effect問題進行模擬與探討。在Eulerian-Lagrangian模式中，流體相以尤拉描述法在尤拉網格解析Navier-Stokes方程式，固體相則以拉格朗日描述法追蹤每顆顆粒的運動。為了模擬顆粒在邊界的堆積，本模式引入了新的碰撞模型，使顆粒在此碰撞機制下達到隨機緊密堆積。而原本的史托克阻力模型已不再適用於此高濃度流場，故本研究參考其他阻力模型，考慮流場中的顆粒濃度，進行阻力係數修正，建立本模式模擬高濃度流場之能力。
本文以Boycott effect物理問題作為範例，將容器與垂直軸傾斜一角度，模擬顆粒在傾斜容器中加速沉降現象，並以PNK theory驗證其準確性，其模擬結果非常接近理論值。接著改變不同容器傾角，觀察沉降過程中之克耳文-亥姆霍茲不穩定性(Kelvin-Helmholtz instability)，且發現此界面不穩定性的形成與容器內清水層厚度有很大的關係，清水層厚度愈大，沉降過程愈穩定，反之愈容易發生不穩定性。最後改變顆粒的直徑與流場初始濃度，分析在不同的參數設定下的顆粒沉降效率，當粒徑愈大，不穩定性的影響愈弱，沉降效率愈好;當初始濃度較低時，也有類似的效果。然而，比較容器傾角、顆粒直徑、流場初始濃度三個參數之影響，改變容器傾角與顆粒直徑的效果優於改變流場初始濃度。模擬結果顯示Boycott effect的確可有效加速顆粒沉降，說明傾斜板或傾斜容器對於顆粒沉降的重要性。

關鍵字

固液二相流 ； Boycott effect ； 克耳文-亥姆霍茲不穩定性

並列摘要

This article presents a three dimensional Eulerian-Lagrangian model to simulate the enhanced sedimentation in an inclined vessel which called Boycott effect. The model solves the governing equation of fluid phase on the Eulerian mesh and calculate the motion of Lagrangian particles by Newton’s second law. In order to simulate the depositing particles at the wall, a soft-sphere collisional method is introduced so that the volume fraction reaches a random closed packing limit by the collisional mechanism. Additionally, Stokes’ drag, the previous drag model, is unsuitable for the denser suspension. A drag reduction model that considering the concentration of the fluid is employed. Ultimately, the two-phase model is capable of calculating the motion of fluid and particles in the dense flow.
This model is then used to study the Boycott effect. The result is validated against the PNK theory and agrees well with the theoretical values. The Kelvin-Helmholtz instability is observed during the settling process at different tilted angles. We find that the instability on the interface is related to the thickness of clear fluid layer. The greater the thickness of the clear fluid layer, the more stable the settling process is. Finally, the present work simulate under different parameters such as the diameter of the particles and the initial concentration of the flow field. While the diameter of particles are larger, the instability is weaker, and it leads to the better sedimentation efficiency. It also results in the same performance while setting the less concentration in the initial flow field. However, the effect of the tilted angle and the diameter of particles is more sensitive than the initial concentration. The simulation results show that Boycott effect does enhance the sedimentation in the inclined vessel or under tilted plates.

並列關鍵字

Solid-liquid two-phase flow ； Boycott effect ； Kelvin-Helmholtz instability

參考文獻

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