Effects of magnetic field on the shape of a bubble in a uniaxial straining flow

Abstract

In some processes such as the Liquid Metal MagnetoHydroDynamic (LMMHD) generator, an inert gas is blown into an electrically conducting fluid to control the behavior of the liquid metal in a magnetic field. In the present work, the effects of magnetic field on the deformation and breakup of a bubble in a uniaxial straining flow of conducting fluid are investigated by using the numerical analysis. Specifically, the steady bubble shape is first determined as a function of three dimensionless parameters: the Reynolds number (Re), the Weber number (W), and the magnetic interaction parameter (N). Then, the critical phenomena such as bubble breakup are studied based on the concept of existence of steady solutions. Finally, a full unsteady numerical code is adopted for verification of the critical phenomena in the bubble dynamics. In all computations, as a reference, the far field velocity distribution is assumed to be fixed. From the numerical results, it is found that the steady bubble deformation increases with the strength of the magnetic field for small N. When N is increased further with fixed Re and TV, the bubble shows distinct deformation characteristics depending on the value of W. If W is larger than a certain threshold value (Wh), there exists a critical range of N, N-c1 (TV) < N < N-c2 (W), for which no converged steady-state solution has been obtained. However, if W < W-th, the steady bubble deformation increases monotonously with the increase of N and no such a critical phenomenon has been observed. Unsteady numerical analysis shows that a bubble extends indefinitely in the critical range of the parameters found by the steady analysis. Based on the numerical results, the diagram for stability and breakup is prepared for a bubble in a linear flow of conducting fluid under magnetic field. The diagram is expected to provide a valuable information on the bubble size estimation which is essential in two-phase flow modeling. (C) 2001 Elsevier Science Ltd. All rights reserved.