Numerical Prediction of Cavitating MHD Flow of Electrically Conducting Magnetic Fluid in a Converging-Diverging Nozzle

2004 ◽  
Vol 71 (6) ◽  
pp. 825-838 ◽  
Author(s):  
Jun Ishimoto
Keyword(s):  
Magnetic Field ◽  
Magnetic Fluid ◽  
Mhd Flow ◽  
Cavitating Flow ◽  
Numerical Results ◽  
Nonuniform Magnetic Field ◽  
Working Fluid ◽  
Two Dimensional ◽  
Two Phase ◽  
Electrically Conducting

The fundamental characteristics of the two-dimensional cavitating MHD flow of an electrically conducting magnetic fluid in a vertical converging-diverging nozzle under a strong nonuniform magnetic field are numerically predicted to realize the further development and high performance of a two-phase liquid-metal MHD power generation system using electrically conducting magnetic fluids. First, the governing equations of the cavitating flow of a mercury-based magnetic fluid based on the unsteady thermal nonequilibrium multifluid model are presented, and several flow characteristics are numerically calculated taking into account the effect of the strong nonuniform magnetic field. Based on the numerical results, the two-dimensional structure of the cavitating flow and cavitation inception phenomena of the mercury-based magnetic fluid through a converging-diverging nozzle are shown in detail. The numerical results demonstrate that effective two-phase magnetic driving force, fluid acceleration, and high power density are obtained by the practical use of the magnetization of the working fluid. Also clarified is the precise control of the cavitating flow of magnetic fluid that is possible by effective use of the magnetic body force that acts on cavitation bubbles.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Broad Class ◽  
Mhd Flow ◽  
Two Dimensional ◽  
Energy Principle ◽  
Inviscid Flows ◽  
Virtual Displacement ◽  
Euler Flows ◽  
Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

scholarly journals Experimental and CFD analysis of MHD flow around smooth sphere and sphere with dimples in subcritical and critical regimes

2020 ◽  
pp. 197-197
Author(s):  
Jasmina Bogdanovic-Jovanovic ◽  
Zivojin Stamenkovic
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Bluff Body ◽  
Slight Modification ◽  
Mhd Flow ◽  
Stationary Flow ◽  
Working Fluid ◽  
Detached Eddy Simulation ◽  
Reynolds Stresses ◽  
Smooth Sphere

An overview of previous researches related to the problem of flow around a bluff-body, using experimental and numerical methods, is presented in the paper. Experimental investigation was performed by a Laser Doppler Anemometer (LDA), measuring velocity components of the water flow around a smooth sphere and a sphere with dimples in square channels. Measurement results in subcritical velocity flow field, velocity fluctuation components, lift, drag and pressure coefficients, and 2D Reynolds stress at quasi-stationary flow are conducted using 1D LDA probe. The obtained experimental results are compared with numerical simulations, which are performed using the ANSYS-CFX software. For the numerical simulations of quasi-steady-state flow, k-? turbulent model was used, while for numerical simulation of unsteady fluid flow and for the comparison of results related to the eddy structures, vortex shedding and Reynolds stresses, Detached Eddy Simulation were used. Since the obtained results of experimental and numerical investigation of flow around smooth sphere and sphere with dimples showed good agreement, the considered flow problem was expanded by introducing the influence of a transverse magnetic field with a slight modification of the electrical conductivity of the working fluid. The other physical properties of the fluid remained the same, which also corresponds to realistically possible physical conditions. Numerical simulations were performed for three different values of Hartmann number and very small values of Reynolds magnetic number (inductionless approximation). Comparisons and analyzes of the results were made for the cases containing a magnetic field and those with an absence of a magnetic field.

scholarly journals Analytical Solution for MHD Flow of a Magnetic Fluid within a Thick Porous Annulus

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shihhao Yeh ◽  
Tsai-Jung Chen ◽  
Jik Chang Leong
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Angular Velocity ◽  
Analytical Solution ◽  
Magnetic Fluid ◽  
Mhd Flow ◽  
Induced Magnetic Field ◽  
State Problem ◽  
Closed Form Solutions ◽  
Steady State Problem

The steady-state problem of a magnetic fluid filling a porous annulus between two cylindrical walls under the influence of a nonuniform radially outward magnetic field has been investigated. The cylindrical walls are either electrically perfectly insulated or electrically perfectly conducting. The permeability of the porous annulus increases with its radial location. The governing partial differential equations were derived carefully and closed form solutions for the profiles of the velocity component and the induced magnetic component were obtained. The effect of the strength of the externally applied magnetic field, the permeability of the porous annulus, and the conductivity of the cylindrical walls were examined through the angular velocity components, as well as the induced magnetic field.

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