Showing papers on "Hartmann number published in 2008"

Influence of magnetic field and Hall currents on blood flow through a stenotic artery

Abstract: A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis (stenosis throat), have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hall parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.

Large eddy simulation of magnetohydrodynamic turbulent duct flows

Abstract: Turbulent duct flows in a uniform magnetic field are examined at low magnetic Reynolds number. Large-eddy simulation is conducted to reveal a sidewall effect on the skin friction. The duct has a square cross section and entirely insulated walls. The duct flow has two kinds of boundary layers: Hartmann layer and sidewall layer. The Hartmann layer is located on the wall perpendicular to the magnetic field, while the sidewall layer exists on the wall parallel to the magnetic field. As the magnetic field increases in the range of turbulent flows, the Hartmann layer becomes thin because of the “Hartmann flattening”—a flattening effect of the flow by the Lorentz force. The sidewall layer, however, becomes thick because of the turbulence suppression until the laminarization takes place. When the Reynolds number, Re, based on the hydraulic diameter, molecular viscosity, and bulk velocity is 5 300, the Hartmann and sidewall layers are laminarized at the same Hartmann number that is proportional to the magnetic fie...

Magnetohydrodynamic turbulence in a channel with spanwise magnetic field

Abstract: The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of a low magnetic Reynolds number. Direct numerical simulation (DNS) and large eddy simulation (LES) computations are performed for two values of the hydrodynamic Reynolds number (104 and 2×104) and with the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near the wall decrease, and the typical horizontal dimensions of the coherent structures enlarge upon increasing the Hartmann number. Comparison between LES and DNS results shows that the dynamic Smagorinsky model accurately reproduces the flow transformation.

The Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

Abstract: Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on Patankar's simpler method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0.733. At low Rayleigh number regime with weak magnetic field, a circulating flow is formed in the cavity. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer. The average Nusselt number decreases as Hartmann number increases. The results are presented for Rayleigh number from 104 up to 106 and are in form of streamlines, isotherms as well as Nusselt number for various Rayleigh and Hartman numbers.

MHD turbulence in a channel with spanwise magnetic field

Abstract: The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of low magnetic Reynolds number. DNS and LES computations are performed for two values of the hydrodynamic Reynolds number (10^4 and 2\times 10^4) and the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near the wall decrease, and the typical horizontal dimensions of the coherent structures enlarge upon increasing the Hartmann number. Comparison between LES and DNS results shows that the dynamic Smagorinsky model accurately reproduces the flow transformation.

Optimal growth and transition to turbulence in channel flow with spanwise magnetic field

Abstract: Instability and transition to turbulence in a magnetohydrodynamic channel flow are studied numerically for the case of a uniform magnetic field imposed along the spanwise direction. Optimal perturbations and their maximum amplifications over finite time intervals are computed in the framework of the linear problem using an iterative scheme based on direct and adjoint governing equations. It is shown that, at sufficiently strong magnetic field, the maximum amplification is no longer provided by classical streamwise rolls, but rather by rolls oriented at an oblique angle to the basic flow direction. The angle grows with the Hartmann number Ha and reaches the limit corresponding to purely spanwise rolls at Ha between 50 and 100 depending on the Reynolds number. Direct numerical simulations are applied to investigate the transition to turbulence at a single subcritical Reynolds number Re = 5000 and various Hartmann numbers. The transition is caused by the transient growth and subsequent breakdown of optimal perturbations, which take the form of one or two symmetric optimal modes (streamwise, oblique or spanwise modes depending on Ha) with low-amplitude three-dimensional noise added at the moment of strongest energy amplification. A sufficiently strong magnetic field (Ha larger than approximately 30) is found to completely suppress the instability. At smaller Hartmann numbers, the transition is observed but it is modified in comparison with the pure hydrodynamic case.

Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field

Abstract: The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with one conducting and one insulating pair of opposite walls under an external magnetic field parallel to the conducting walls, is investigated. The MHD equations are coupled in terms of velocity and magnetic field and cannot be decoupled with conducting wall boundary conditions since then boundary conditions are coupled and involve an unknown function. The boundary element method (BEM) is applied here by using a fundamental solution which enables to treat the MHD equations in coupled form with the most general form of wall conductivities. Also, with this fundamental solution it is possible to obtain BEM solution for values of Hartmann number (M) up to 300 which was not available before. The equivelocity and induced magnetic field contours which show the well-known characteristics of MHD duct flow are presented for several values of M.

Hall effects on MHD flow past an accelerated plate

Abstract: The simultaneous effects of rotation and Hall current on the hydromagnetic flow past an accelerated horizontal plate relative to a rotating fluid is presented. It is found that for given values of m (Hall parameter), M (Hartmann number) and an imposed rotation parameter Ω satisfying Ω = M 2m/(1 + m2), the transverse motion (transverse to the main flow) disappears and the fluid moves in the direction of the plate only. The effects of the parameters m, M and Ω on the axial and transverse velocity profiles are shown graphically, whereas the effects of the parameters on the skin-friction components are shown by tabular values.

Time‐domain BEM solution of convection–diffusion‐type MHD equations

Abstract: The two-dimensional convection–diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time-domain BEM solution procedure is tested on some convection–diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time-dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd.

Effect of Magnetic Field on MHD Pressure Drop Inside a Rectangular Conducting Duct

Abstract: The effect of increasing Hartmann number and duct wall conductivity on the incompressible laminar flow of a liquid metal (Pb-17Li) in a rectangular duct under a transverse magnetic field has numerically been studied using usual equations of fluid dynamics coupled with the electromagnetic equations of the appropriate form. Simulations have been performed for ducts with and without electrical insulation, and the pressure drop is evaluated in each of the cases. The results of the simulation are compared with the analytical relations found in the literature. Finally, the applicability of different insulation coatings vis-a grave-vis their effect in reducing the magnetohydrodynamics pressure drop has been examined.

Numerical Study of Oscillatory Natural Convection During Solidification of a Liquid Metal in a Rectangular Enclosure with and without Magnetic Field

Abstract: A numerical investigation of the two-dimensional, oscillatory natural convection during the solidification of a liquid metal contained in a rectangular cavity, having an aspect ratio equal to 4 and submitted to an external uniform magnetic field, is presented. The numerical approach is based on the finite-volume approximation with an enthalpy formulation. A computer program based on the SIMPLER algorithm is developed. The results show that the oscillatory flow in the liquid part of the enclosure appears by the formation of the principal and secondary cells, and periodic oscillations in the hydrodynamic and thermal fields. The effect of a magnetic field with different orientation provides a notable change on the flow and thermal structures. A discrete Fourier transform is used to determined the critical frequencies F cr of oscillations. Stability diagrams show the dependence of the critical Grashof number Grcr and the dimensionless critical frequency F cr with the Hartmann number Ha. The strongest stabiliz...

A Differential Quadrature Solution of MHD Natural Convection in an Inclined Enclosure With a Partition

Abstract: Magnetohydrodynamics natural convection in an inclined enclosure with a partition is studied numerically using a differential quadrature method. Governing equations for the fluid flow and heat transfer are solved for the Rayleigh number varying from 10 4 to 10 6 , the Prandtl numbers (0.1, 1, and 10), four different Hartmann numbers (0, 25, 50, and 100), the inclination angle ranging from 0 deg to 90 deg, and the magnetic field with the x and y directions. The results show that the convective flow weakens considerably with increasing magnetic field strength, and the x-directional magnetic field is more effective in reducing the convection intensity. As the inclination angle increases, multicellular flows begin to develop on both sides of the enclosure for higher values of the Hartmann number if the enclosure is under the x-directional magnetic field. The vorticity generation intensity increases with increase of Rayleigh number. On the other hand, increasing Hartmann number has a negative effect on vorticity generation. With an increase in the inclination angle, the intensity of vorticity generation is observed to shift to top left corners and bottom right corners. Vorticity generation loops in each region of enclosure form due to multicelluar flow for an x-directional magnetic field when the inclination angle is increased further. In addition, depending on the boundary layer developed, the vorticity value on the hot wall increases first sharply with increasing y and then begins to decrease gradually. For the high Rayleigh numbers, the average Nusselt number shows an increasing trend as the inclination angle increases and a peak value is detected. Beyond the peak point, the foregoing trend reverses to decrease with the further increase of the inclination angle. The results also show that the Prandtl number has only a marginal effect on the flow and heat transfer.

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

Abstract: The directional effect of a magnetic field on the onset of oscillatory convection is studied numerically in a confined three-dimensional cavity of relative dimensions 4:2:1 (length:width:height) filled with mercury and subject to a horizontal temperature gradient. The magnetic field suppresses the oscillations most effectively when it is applied in the vertical direction, and is the least efficient when applied in the longitudinal direction (parallel to the temperature gradient). In all cases, however, exponential growths of the critical Grashof number, Grc (Gr, ratio of buoyancy to viscous dissipation forces) with the Hartmann number (Ha, ratio of magnetic to viscous dissipation forces) are obtained. Insight into the damping mechanism is gained from the fluctuating kinetic energy budget associated with the time-periodic disturbances at threshold. The kinetic energy produced by the vertical shear of the longitudinal basic flow dominates the oscillatory transition, and when a magnetic field is applied, it increases in order to balance the stabilizing magnetic energy. Moreover, subtle changes in the spatial distribution of this shear energy are at the origin of the exponential growth of Grc. The destabilizing effect of the velocity fluctuations strongly decreases when Ha is increased (due to the decay of the velocity fluctuations in the bulk accompanied by the appearance of steep gradients localized in the Hartmann layers), so that an increase of the shear of the basic flow at Grc is required in order to sustain the instability. This yields an increase in Grc, which is reinforced by the fact that the shear of the basic flow naturally decreases at constant Gr with the increase of Ha, particularly when the magnetic field is applied in the vertical direction. For transverse and longitudinal fields, the decay of the velocity fluctuations is combined with an increase of the shear energy term due to a sustained growth in stabilizing magnetic energy with Ha.

Analytical and Numerical Study of Combined Effects of a Magnetic Field and an External Shear Stress on Soret Convection in a Horizontal Porous Enclosure

Abstract: The fluid flow induced by combined actions of Soret effect and shear stress applied on the top horizontal free surface (the lower one being rigid) in a horizontal porous layer, under an external magnetic field, is studied analytically and numerically. The horizontal walls of the porous layer are subject to uniform heat fluxes. The porous layer is sparsely packed then the flow is governed by the Brinkman model assuming the Boussinesq approximation. The governing parameters are the thermal Rayleigh number, RT, the Lewis number, Le, the separation parameter, ϕ, the effective Darcy number, Da, the Hartmann number Ha, the dimensionless shear stress, τ, and the aspect ratio of the enclosure, Ar. An analytical solution is derived on the basis of the parallel flow approximation, assuming enlarge aspect ratio layer, and validated numerically using a finite-difference method. The critical Rayleigh numbers for the onset of stationary, subcritical, and oscillatory convection are determined explicitly as functions of ...

Buoyant MHD flows in a vertical channel: the levitation regime

Abstract: Buoyant magnetohydrodynamic (MHD) flows with Joulean and viscous heating effects are considered in a vertical parallel plate channel. The applied magnetic field is uniform and perpendicular to the plates which are subject to adiabatic and isothermal boundary conditions, respectively. The main issue of the paper is the levitation regime, i.e., the fully developed flow regime for large values of the Hartmann number M, when the hydrodynamic pressure gradient evaluated at the temperature of the adiabatic wall is vanishing. The problem is solved analytically by Taylor series method and the solution is validated numerically. It is found that the fluid velocity points everywhere and for all values of M downward. For small M’s, the velocity field extends nearly symmetrically (with respect to the mid-plane) over the whole section of the channel between the adiabatic and the isothermal walls. For large values of M, by contrast, the fluid levitates over a broad transversal range of the channel, while the motion becomes concentrated in a narrow boundary layer in the neighborhood of the isothermal wall. Accordingly, the fluid temperature is nearly uniform in the levitation range and decreases rapidly within the boundary layer in front of the isothermal wall. It also turns out that not only the volumetric heat generation by the Joule effect, but also that by viscous friction increases rapidly with increasing values of M, the latter effect being even larger than the former one for all M.

Numerical Computation of Fluid Flow in a Magnetohydrodynamic Micropump

Abstract: A 2-dimensional model is developed to investigate fluid flow in a magneto-hydrodynamic (MHD) micropump. The transient, laminar, incompressible, and developing flow equations are numerically solved using the finite difference method and the SIMPLE algorithm. The micropump is driven using the Lorentz force, which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The effect of Hartmann number on the transient velocity profile and the entrance region length is studied. It is found that controlling the electrical conductivity and magnetic flux density will allow controlling the entrance region length.

Three-dimensional liquid metal flows in strong magnetic fields

Abstract: The prediction of three-dimensional MHD flows for applications in fusion engineering, where magnetic fields confining the plasma are very high, is still a challenging task since, up to the present day, numerical simulations for such conditions are beyond the capabilities of modern CFD tools. Also experimentally, on laboratory scales, these values of parameters are hard to reach. Asymptotic analyses instead are able to cover such regimes in which inertia and viscous forces play only a minor role in comparison with the strong electromagnetic forces. However, especially for geometries with sudden changes of cross section, inertia effects may still be present in thin viscous parallel layers, where relatively high values of velocity can occur. For such cases only numerical simulations and/or experiments can give the proper insight into the physics involved. Those methods are therefore applied to determine the relevant scaling laws for strong fields, which allow a physically meaningful extrapolation of data to the desired parameters for engineering applications. As an example the 3D MHD flow through a sudden expansion of rectangular ducts is considered; results have been obtained by asymptotic theory for strong magnetic fields, by numerical simulations up to moderate magnetic fields and they are compared with experimental data. It is possible to derive the relevant scaling laws for pressure drop, as a function of the Hartmann number Ha and the interaction parameter N. Results obtained by asymptotic analysis and numerical simulations show quite good agreement with experiments for the investigated parameters. Moreover, the numerical simulations allow analyzing the interesting 3D transitions and changes in the flow topology, occurring in the parameter range between the hydrodynamic case with Ha = 0 and the strong field case where Ha » 1, N » 1.