- 學位論文
以離散元素法探討旋轉鼓暫態乾顆粒流之流變性質
Transient Rheology Property of Dry Granular Flow in Rotating Drum using Discrete Element Method
摘要
本研究主要探討乾顆粒體在穩態流況下成立的摩擦定律於暫態顆粒流中是否也成立?摩擦定律即在描述摩擦係數隨慣性數單調遞增的現象，而此定律可視為顆粒流的組成率。 研究過程利用離散元素法(Discrete Element Method, DEM)模擬乾顆粒體於三維旋轉鼓中的流變行為，並利用其數據做後處理以計算相關流變參數，繼而改變三種轉速來確認轉速對摩擦定律以及其他參數之影響性。其中，本研究利用Virial應力概念來計算顆粒流內部的應力，並與解析解做驗證。 本研究在穩態流況找到符合摩擦定律的摩擦係數與慣性數關係。接著在暫態也同樣整理出摩擦係數與慣性數關係，並且與穩態相比較。由結果可以觀察到暫態摩擦係數與慣性數關係在顆粒流加速度不為零的時候，有偏離穩態摩擦定律的現象。因此，本研究分別將暫態每個瞬間的流變參數對流動層深度做圖，藉以瞭解暫態流變參數隨時間的變化趨勢，並試著釐清暫態摩擦係數與慣性數關係偏離穩態的原因。最後，推論在加速度大於零的狀況下，顆粒流的I值必須加上加速度造成的I值增量，形成有效慣性數I'，並以此有效慣性數對應至穩態摩擦定律中的摩擦係數，會發現在相同慣性數的狀況下，暫態加速區之摩擦係數會達到比穩態更高的值。
並列摘要
This research concerns whether the friction law in steady states of dry granular flow could extend to transient state.The friction law treated as constitutive law of granular flow in steady state depicts the phenomenon that effective friction coefficient increases monotonically with the growing inertial number(I).(The effective friction coefficient is the friction coefficient between bulks of granular materials and is calculated as the ratio of shear stress over normal stress. And inertial number is a non-dimensional number related to the shear rate of granular flow.) This research uses the Discrete Element Method(DEM) to simulate the rheological behavior of dry granular flow in a 3D rotating drum. Furthermore, the Virial stress is adopted to calculate the stress among the granular flow. In order to generate the related rheological parameters, a postprocessor is developed. And the results are used in reproducing friction law in steady state. Similarly, the relation between effective friction coefficient and I of transient state is calculated and compared with that of the steady state. The results of the relation between effective friction coefficient and I show that there is a discrepancy between both flow states. Therefore, this research analyzes the trend of rheological parameters by drawing the parameters versus depth profile at each instant. Finally, this research deduces that the acceleration of granular materials produces additional contribution to the inertial number. It is also found that, with the same value of the inertial number,effective friction coefficient value in the friction law of the transient state is higher than that of the steady state.