Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 1. Hydrodynamic flow

2011 ◽  
Vol 674 ◽  
pp. 120-131 ◽  
Author(s):  
C. MISTRANGELO
Keyword(s):  
Scaling Laws ◽  
Topological Analysis ◽  
Metal Flow ◽  
Three Dimensional ◽  
Homogeneous Magnetic Field ◽  
Sudden Expansion ◽  
Reattachment Length ◽  
Flow Topology ◽  
Starting Point ◽  
Liquid Metal Flow

Numerical simulations are performed to study three-dimensional hydrodynamic flows in a sudden expansion of rectangular ducts. Separation phenomena are investigated through the analysis of flow topology and streamline patterns. Scaling laws describing the evolution of the reattachment length of the vortical areas that appear behind the cross-section enlargement are derived. The results discussed in this paper are required as a starting point to investigate the effects of an applied homogeneous magnetic field on separation phenomena in a geometry with a sudden expansion.

Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow

2011 ◽  
Vol 674 ◽  
pp. 132-162 ◽  
Author(s):  
C. MISTRANGELO
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Scaling Laws ◽  
Numerical Study ◽  
Topological Analysis ◽  
Metal Flow ◽  
Magnetohydrodynamic Flow ◽  
Sudden Expansion ◽  
Internal Layers ◽  
Flow Topology

A numerical study has been carried out to analyse liquid metal flows in a sudden expansion of electrically conducting rectangular ducts under the influence of an imposed uniform magnetic field. Separation phenomena are investigated by selecting a reference Reynolds number and by increasing progressively the applied magnetic field. The magnetic effects leading to the reduction of the size of separation zones that form behind the cross-section enlargement are studied by considering modifications of flow topology, streamline patterns and electric current density distribution. In the range of parameters investigated, the magnetohydrodynamic flow undergoes substantial transitions from a hydrodynamic-like flow to one dominated by electromagnetic forces, where the influence of inertia and viscous forces is confined to thin internal layers aligned with the magnetic field and to boundary layers that form along the walls. Scaling laws describing the reattachment length and the pressure drop in the sudden expansion are derived for intense magnetic fields.

Numerical Simulation of Three-Dimensional Molten Pool Temperature Field and Flow Field for Laser Melt Injection Based on Fluent

2012 ◽  
Vol 538-541 ◽  
pp. 1837-1842 ◽  
Author(s):  
Long Zhi Zhao ◽  
Zi Wang ◽  
Xin Yan Jiang ◽  
Jian Zhang ◽  
Ming Juan Zhao
Keyword(s):  
Temperature Field ◽  
Liquid Metal ◽  
Molten Pool ◽  
Metal Flow ◽  
Three Dimensional ◽  
Transient Temperature ◽  
Transient Temperature Field ◽  
Liquid Metal Flow ◽  
Fluent Software ◽  
Thermo Physical Properties

According to the characteristics of laser melt injection, a numerical model for a simplified 3D transient temperature field in molten pool was established using FLUENT software in this paper. In the model, many factors were considered such as liquid metal turbulence, latent heat of phase transformation and material thermo physical properties depending on temperature. The results show that the model can be developed well by FLUENT software. And the results also show that the driving force of the liquid metal flow mechanism.

Numerical Simulation of Steady Liquid-Metal Flow in the Presence of a Static Magnetic Field

2004 ◽  
Vol 71 (6) ◽  
pp. 786-795 ◽  
Author(s):  
Amnon J. Meir ◽  
Paul G. Schmidt ◽  
Sayavur I. Bakhtiyarov ◽  
Ruel A. Overfelt
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dissipative Heat ◽  
Novel Approach ◽  
Liquid Metal Flow

We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven, steady liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell’s equations, Ohm’s law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy forces, and convective and dissipative heat transfer. Employing the electric current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the fluid with the surrounding media. A finite element method based on this approach was used to simulate the flow of a metallic melt in a cylindrical container, rotating steadily in a uniform magnetic field perpendicular to the cylinder axis. Velocity, pressure, current, and potential distributions were computed and compared to theoretical predictions.

scholarly journals Why, how and when MHD turbulence at low becomes three-dimensional

2014 ◽  
Vol 761 ◽  
pp. 168-205 ◽  
Author(s):  
Alban Pothérat ◽  
Rico Klein
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Opposite Wall ◽  
Liquid Metal Flow ◽  
Dc Current ◽  
The Magnetic Field

AbstractMagnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-two-dimensional, three-dimensional or in any intermediate state. To this end, forcing is applied by injecting a DC current $I$ through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality. Flow dimensionality is characterised in several ways. First, we show that when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_{b}\sim I^{2/3}$. Second, we show that when the distance $l_{z}$ over which momentum diffuses under the action of the Lorentz force (Sommeria & Moreau, J. Fluid Mech., vol. 118, 1982, pp. 507–518) reaches the channel width $h$, the velocity near the opposite wall $U_{t}$ follows a similar law with a correction factor $(1-h/l_{z})$ that measures three-dimensionality. When $l_{z}<h$, by contrast, the opposite wall has less influence on the flow and $U_{t}\sim I^{1/2}$. The central role played by the ratio $l_{z}/h$ is confirmed by experimentally verifying the scaling $l_{z}\sim N^{1/2}$ put forward by Sommeria & Moreau ($N$ is the interaction parameter) and, finally, the nature of the three-dimensionality involved is further clarified by distinguishing weak and strong three-dimensionalities previously introduced by Klein & Pothérat (Phys. Rev. Lett., vol. 104 (3), 2010, 034502). It is found that both types vanish only asymptotically in the limit $N\rightarrow \infty$. This provides evidence that because of the no-slip walls, (i) the transition between quasi-two-dimensional and three-dimensional turbulence does not result from a global instability of the flow, unlike in domains with non-dissipative boundaries (Boeck et al. Phys. Rev. Lett., vol. 101, 2008, 244501), and (ii) it does not occur simultaneously at all scales.

Characterization of the flow past a truncated square cylinder in a duct under a spanwise magnetic field

2011 ◽  
Vol 691 ◽  
pp. 341-367 ◽  
Author(s):  
Vincent Dousset ◽  
Alban Pothérat
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Homogeneous Magnetic Field ◽  
Steady Flows ◽  
Square Cylinder ◽  
Electrically Conducting ◽  
Truncated Cylinder ◽  
The Magnetic Field

AbstractWe study the flow of an electrically conducting fluid past a truncated square cylinder in a rectangular duct under the influence of an externally applied homogeneous magnetic field oriented along the cylinder axis. Our aim is to bridge the gap between the non-magnetic regime, where we previously found a complex set of three-dimensional recirculations behind the cylinder (Dousset & Pothérat, J. Fluid Mech., vol. 653, 2010, pp. 519–536) and the asymptotic regime of dominating Lorentz force analysed by Hunt & Ludford (J. Fluid. Mech., vol. 33, 1968, pp. 693–714). The latter regime is characterized by a remarkable structure known as Hunt’s wake in the magnetohydrodynamics community, where the flow is deflected on either side of a stagnant zone, right above the truncated cylinder as if the latter would span the full height of the duct. In steady flows dominated by the Lorentz force, with negligible inertia, we provide the first numerical flow visualization of Hunt’s wake. In regimes of finite inertia, a thorough topological analysis of the steady flow regimes reveals how the Lorentz force gradually reorganizes the flow structures in the hydrodynamic wake of the cylinder as the Hartmann number $\mathit{Ha}$ (which gives a non-dimensional measure of the magnetic field) is increased. The nature of the vortex shedding follows from this rearrangement of the steady structures by the magnetic field. As $\mathit{Ha}$ is increased, we observe that the vortex street changes from a strongly symmetric one to the alternate procession of counter-rotating vortices typical of the non-truncated cylinder wakes.

Liquid-metal flow in an insulated rectangular expansion with a strong transverse magnetic field

1995 ◽  
Vol 305 ◽  
pp. 111-126 ◽  
Author(s):  
John S. Walker ◽  
Basil F. Picologlou
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Boundary Layers ◽  
Applied Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Metal Flow ◽  
Constant Area ◽  
Large Expansion ◽  
The Magnetic Field

This paper concerns a steady liquid-metal flow through an expansion or contraction with electrically insulated walls, with rectangular cross-sections and with a uniform, transverse, externally applied magnetic field. One pair of duct walls is parallel to the applied magnetic field, and the other pair diverges or converges symmetrically about a plane which is perpendicular to the field. The magnetic field is assumed to be sufficiently strong that inertial effects can be neglected and that the well-known Hartmann-layer solution is valid for the boundary layers on the walls which are not parallel to the magnetic field. A general treatment of three-dimensional flows in constant-area ducts is presented. An error in the solution of Walker et al. (1972) is corrected. A smooth expansion between two different constant-area ducts is treated. In the expansion the flow is concentrated inside the boundary layers on the sides which are parallel to the magnetic field, while the flow at the centre of the duct is very small and may be negative for a large expansion slope. In each constant-area duct, the flow evolves from a concentration near the sides at the junction with the expansion to the appropriate fully developed flow far upstream or downstream of the expansion. The pressure drop associated with the three-dimensional flow increases as the slope. increases.

Linear three-dimensional instability of a magnetically driven rotating flow

2002 ◽  
Vol 463 ◽  
pp. 229-239 ◽  
Author(s):  
I. GRANTS ◽  
G. GERBETH
Keyword(s):  
Cross Section ◽  
Metal Flow ◽  
Three Dimensional ◽  
Low Frequency ◽  
Rotating Magnetic Field ◽  
Finite Cylinder ◽  
Liquid Metal Flow ◽  
Characteristic Features ◽  
Rotating Boundary ◽  
Dimensional Instability

The instability of a rotating-magnetic-field-driven liquid metal flow in a finite cylinder with respect to infinitesimal azimuthally periodic perturbations is studied numerically. This instability is observed to set in prior its axisymmetric counterpart with relatively low frequency at diameter-to-height ratios between 0.5 and 2. The axisymmetric and three-dimensional instabilities have similar characteristic features. The instability originates in the cross-section of the horizontal and vertical rotating boundary layers and excites inertial waves in the inviscid core.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

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