Stability Analysis of Thin Electrically-Conductive Viscoelastic Fluid Film Flow Along a Rotating Cylinder in a Magnetic Field

受磁場影響的導電粘彈性流體沿旋轉圓柱側流動的薄膜穩定性分析

劉悟慢(Wu-Man Liu) ； 陳朝光(Cha'o-Kuang Chen)

《中國機械工程學刊》 43卷5期 (2022/10) Pp. 411-420

摘要

In this study, stability of thin electrically-conductive viscoelastic fluid film flow along the side of a rotating vertical cylinder with the effect of magnetic field is discussed in this paper. This paper applied long-wave perturbation method to solve generalized nonlinear motion equation of thin film. The criteria for linear thin film stability can be obtained by normal mode method, then the multiple-scales method is applied to confirm the nonlinear stability. By the coefficient in Ginzburg-Landau equation, different states of the thin film can be determined. From this study, in order to enhance the stability of the thin film, it can be achieved by either increasing the effect of the magnetic field, decreasing the viscoelastic effect or decreasing the rotational velocity. Meanwhile, increasing radius under large Rossby number can lead to losing stability easier, such as the dimensionless radius is more than 50. It is worth noting that this phenomenon is leaded by the radius, and the influence is stronger than other parameters.

關鍵字

Hydromagnetic stability analysis ； Hartmann number ； Rossby number

並列摘要

本文介紹了在磁場影響下的導電粘彈性流體薄膜沿旋轉垂直圓柱外側流下的流體穩定性研究。本文使用長波微擾法推導了液膜的廣義非線性運動方程。線性的薄膜穩定性條件會應用正模分析法來確定。最後使用多重尺度法來檢驗非線性穩定性。通過Landau方程式的不同係數判斷不同的流體薄膜狀態。由此可以得出，增加磁場強度，降低粘彈性效應，或者降低圓柱體旋轉速度可以增強流體薄膜的穩定性。與此同時，隨著圓柱半徑在大羅斯貝數（Rossby number）下的增加，如大於50，流體薄膜會更容易失去穩定性，從而主導流體薄膜的狀態，導致其他參數對穩定性的影響降低。