MHD Duct Research Articles

Element-free Galerkin analysis of MHD duct flow problems at arbitrary and high Hartmann numbers

Element-free Galerkin analysis of MHD duct flow problems at arbitrary and high Hartmann numbers

The effects of boundary roughness on the MHD duct flow with slip hydrodynamic condition

In this paper we present the analytical study of the magnetohydrodynamic (MHD) flow through a rectangular duct driven by the pressure gradient and under the action of the transverse magnetic field. Motivated by various MHD applications in which hydrodynamic slip naturally occur, we prescribe the slipping boundary condition on the upper boundary which contains irregularities as well. Depending on the period of the boundary roughness, we derive three different limit problems by using rigorous analysis in the appropriate functional setting. This approach also enables us to determine the relative contribution of the MHD effect and the slip itself in the governing coupled system satisfied by the velocity and induced magnetic field.

Performance analysis of thermoacoustic plasma MHD generation

We develop a quasi-one-dimensional theoretical model describing the oscillatory plasma MHD conversion in a channel with parallel electrodes. Based on the model, a thermoacoustic plasma MHD generation system with a looped configuration is proposed and the characteristics of the operation of the system are investigated. Our results show that, for efficient oscillatory MHD generation, the channel dimension of the MHD duct should be much larger than the penetration depth (a proper Womersley number is above 100), otherwise the thermoacoustic effect will play a major role and consume considerable energy. Further, the electromagnetic induction parameter should be larger than 100S⋅T2/m, so that a majority of the kinetic energy of the oscillatory plasma can be harnessed for energy conversion. Moreover, a load ratio between 0.6 to 0.8 is suggested for the presented system, with which an efficiency above 20% can be achieved when the electromagnetic induction parameter is 500S⋅T2/m. In the optimal case, an efficiency of 24% can be obtained, with the corresponding output electricity of 1644 W. These results shed light on the feasibility of the closed-cycle MHD generation without any moving part, which endows the system with advantages of high reliability and long lifetime.

Chebyshev spectral collocation method for MHD duct flow under slip condition

The magnetohydrodynamic problem of a fully developed flow of an incompressible and electrically conducting fluid is solved numerically by a Chebyshev spectral collocation method in a square duct with walls of variable electric conductivities under a slip condition for velocity. The flow is driven by a constant pressure gradient under the effect of an externally applied oblique magnetic field. The efficiency of the method that is implemented in the physical space on preassigned collocation points is exploited to discretise the governing equations. The corroboration and validation of the proposed technique are carried out by means of a case study with published results substantiating that its implementation results in satisfactorily good agreements. Novel results are presented graphically, and the combined effects of the most characteristic magnetohydrodynamic flow parameters such as the slip length, conductivity parameter, and Hartmann number on the velocity and induced magnetic field are investigated.

Chebyshev spectral collocation method for MHD duct flow under slip condition

Chebyshev spectral collocation method for MHD duct flow under slip condition

3D modelling of MHD mixed convection flow in a vertical duct with transverse magnetic field and volumetric or surface heating

Understanding phenomena associated with the multiple effects/interactions of the fusion nuclear environment on liquid metal flow is required to correctly design liquid metal (LM) blankets for fusion facilities. These effects are investigated in the present work by numerically simulating 3D LM MHD flow. The simulated geometry consists of a straight, vertical duct which runs perpendicular to a strong, fringing applied magnetic field. There is also a region of applied heating as the primary goal is to explore buoyancy effects in MHD duct flows. Results are presented for both buoyancy assisted (upwards) and buoyancy opposed (downwards) flows in conducting and insulating ducts for a range of Hartmann numbers (Ha) up to 100, Reynolds numbers (Re) from 103 to 104 and Grashof (Gr) numbers from 107 to 108. While increasing Gr or decreasing Re increases buoyancy effects, increasing Ha was shown to increase maximum temperature through turbulence reduction. The extent to which the MHD mixed convection flows are quasi-2D is analyzed and buoyant effects, in competition with electromagnetic forces, are shown to bring about 3D flow features not seen in purely MHD flows. Volumetric nuclear heating with steep gradients is applied to the vertical MHD flows for comparison to flows with surface heating only. Surface heating generates stronger buoyancy effects than volumetric heating of the same total power; however, many of the same phenomena occur. Therefore, surface heating, the only option for lab experiments, can provide indication of the effects of volumetric heating in MHD flows.

Effects of the magnetic field direction and of the cross-sectional aspect ratio on the mass flow rate of MHD duct flows

In the present study, numerically analyzed are the effects of the applied magnetic field direction and of the cross-sectional aspect ratio on the mass flow rate of 3D MHD duct flows, by utilizing commercial code CFX. Flows are driven by a constant pressure gradient in rectangular ducts with different cross-sectional aspect ratios and under various orientations of the applied magnetic field in different cases, and the variation of the mass flux in a fully developed fluid region in the above situations is discussed. Here, the mechanism causing the variation of the mass flux for different magnetic field directions and for different cross-sectional aspect ratios is discussed in particular. The features of the axial velocity distributions in the cases when the magnetic field is dis-aligned with the duct walls are presented closely.

Effect of vortex promoter shape on heat transfer in MHD duct flow with axial magnetic field

The heat transfer from the side-wall of a duct through which an electrically conducting fluid flows within a strong transverse magnetic field is numerically investigated using high-resolution numerical simulation. Parameter ranges considered are 0≤Ha≤2400 and 100≤Re≤3000 for a constant blockage ratio of 1/4. The gain in the heat transfer using obstacles of different geometric shapes are compared. For Ha=320, a maximum heat transfer enhancement of 78% is obtained when using the square cylinder at a modes Re=1000, while the triangular cylinder outperformed the various other vortex promoter geometries at Re = 2000 yielding a 75% improvement.. However, at a higher Hartmann number of Ha=2400, a maximum heat transfer augmentation of 16% and 40% is obtained for the triangular cylinder at Re=1000 and 2000, respectively. This suggests that for a duct flow under the influence of a strong magnetic field, the triangular obstacle is a superior heat transfer promoter geometry compared to the square or circular cylinders. A further net power analysis reveals that the heat transfer enhancement dominates over the pumping power to produce net benefits for even a modest heat transfer enhancement.

DRBEM solution of the Cauchy MHD duct flow with a slipping perturbed boundary

In this study, the MHD flow direct and Cauchy problems are solved in a rectangular duct with a perturbed, curved, and slip upper boundary. The aim is to recompute the slipping velocity and the slip length by using the asymptotic analysis with respect to the perturbation parameter ϵ and solving MHD flow equations for the first order and the corrector solutions in the rectangular duct. Hence, without discretizing the curved boundary, we are able to obtain the solution of MHD flow in the duct with curved perturbed boundary. The dual reciprocity boundary element method (DRBEM) is utilized for solving the coupled MHD equations as a whole. The discretization of Cauchy problems leads ill-conditioned systems of linear algebraic equations, hence a regularization technique is necessary. In this study, the Tikhonov regularization is used to obtain the solution of the Cauchy MHD problems. The main advantage of the DRBEM is discretizing only the boundary and providing both the velocity and its normal derivative values on the boundary. This enables us to recover the slip length on the perturbed boundary through the slip boundary condition.

Local iRBF-DQ method for MHD duct flows at high Hartmann numbers

Local iRBF-DQ method for MHD duct flows at high Hartmann numbers

Instability of MHD Flow in the Duct with Electrically Perfectly Conducting Walls

The stability problem of conducting fluid flow in a square duct with perfectly conducting walls is investigated. A homogeneous and constant static magnetic field is applied along the vertical direction of the flow. Nonmodal linear stability analysis is performed on this problem for the first time and the effect of the imposed magnetic field is also taken into account. The amplification and distribution of primary optimal perturbations are obtained by solving iteratively the direct and adjoint governing equations with respect of perturbations. Four modes of perturbations with different symmetries in the space are investigated. Computational results show that, the MHD duct flow is stable at either small or large Hartmann number, but unstable at moderate one. The primary optimal perturbations are in the form of streamwise vortices, which are located inside the thin sidewall layers parallel to the magnetic field. The size of the vortices is decreased with the growing of Hartmann number Ha, meanwhile the amplification of the perturbations is reduced due to the magnetic damping effect. The Hartmann layer perpendicular to the magnetic field seems to be irrelevant to the stability of the MHD duct flow. The most unstable perturbation is in the form of Mode I, which having co-rotating vortices at opposite sidewalls and the vortices tend to enhance each other.

Effects of small boundary perturbation on the MHD duct flow

In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude ? is applied on cross-section of the duct. Using the asymptotic analysis with respect to ?, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.

Heat transfer augmentation of a quasi-two-dimensional MHD duct flow via electrically driven vortices

ABSTRACTThe fluid dynamics and heat transfer characteristics of magnetohydrodynamic duct flow often degrade the laminarization caused by the magnetic field. The present work evaluates the performance of a system featuring alternating current injection from a point electrode as a vortex promoter for enhancement of the thermal-hydraulic characteristics. It is found that the vortices generated by the current injection alone generally induce a greater thermal-hydraulic performance with a significantly smaller additional pressure loss than configurations featuring a physical obstacle. A maximum overall efficiency index of 1.83 was recorded within the parameter space investigated.

Combining an obstacle and electrically driven vortices to enhance heat transfer in a quasi-two-dimensional MHD duct flow

The design of vortex promoters in a heated-wall duct is often limited by the considerations of practicality, especially in complex systems such as fusion blankets. The present study investigates the use of current injection to invoke a street of vortices in quasi-two-dimensional high transverse magnetic field magnetohydrodynamic duct flows to enhance instability behind a cylinder. The intent is to generate intensive flow vorticity parallel to a magnetic field downstream of a field-aligned cylinder. Electric current enters the flow through an electrode embedded in one of the Hartmann walls, radiates outward, imparting a rotational forcing around the electrode due to the Lorentz force. The quasi-two-dimensional nature of these flows then promotes a vortical rotation across the interior of the duct with axis aligned to the magnetic field. The hot and cold walls are parallel to the magnetic field. Electric current amplitude and pulse width, excitation frequency and electrode position are systematically varied to explore their influences on the convective heat transport phenomenon. This investigation builds on a recommendation from previous work of Bühler (J. Fluid Mech., vol. 326, 1996, pp. 125–150) dedicated to understanding of the flow stability in a similar configuration. This study provides supportive evidence for the use of current injection as an alternative to the conventional mechanically actuated turbuliser, with heat transfer almost doubled for negligible additional pumping power requirements.

A hybrid finite difference–boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds number

A conservative coupled finite difference–boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulated. The co-evolution of the velocity and magnetic fields as described respectively by the Navier–Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting domain and the non-conducting exterior, is solved using the magnetic field formulation. The aim is to simulate localized magnetic fields interacting with turbulent duct flow. Detailed verification of the implementation of the numerical scheme is conducted in the limiting case of low magnetic Reynolds number by comparing with the results obtained using a quasistatic approach that has no coupling with the exterior. The rigorous procedure with non-local magnetic boundary conditions is compared with simplified pseudo-vacuum boundary conditions and the differences are quantified. Our first direct numerical simulations of turbulent Hartmann duct flow at moderate magnetic Reynolds numbers and a low flow Reynolds number show significant differences in the duct flow turbulence, even at low interaction level between the flow and magnetic field.

Velocity Distribution Characteristics Of Sea Water In Conductiv Magnetohydrodynamic (MHD) Homopolar Ducts

Abstract Shortcomings of conventional propeller propulsion can theoretically be removed by using a modern technology - unconventional hydroelectromagnetic propeller or magnetohydrodynamic (MHD thruster), that highlights an application of great interest about physical phenomena that occur in the interaction between electromagnetic fields and electrically conductive fluids. In application to marine propulsion, investigations of a variety of physical phenomena was carried out, including the flow characteristics in a MHD duct, thrust efficiency and optimum shape of the duct. This paper presents related interaction phenomena between a magnetic induction, created by a d.c. electromagnet and d.c. current, perpendicular to the field, imposed by a voltage difference between two electrodes in the conductive sea water. The fluid is forced to the direction perpendicular to the plane where magnetic and electric fluxes are intersecting, this force is called the Lorentz force. Experimental and theoretical studies were carried out on small magnetohydrodynamic model (DC homopolar model) having two channels arranged in series or parallel. Each time the speed distribution was followed over the channel axis and perpendicular to channel axis.

Experimental study of instabilities in magnetohydrodynamic boundary layers

Heat and mass transport phenomena in liquid metal blankets are strictly related to velocity distributions near the walls. It is known that the thin boundary layers, which form along walls parallel to an imposed magnetic field, can lose their stability due to the presence of high velocity jets with inflection points. This can lead to the formation of complex vortical structures whose size and features depend on mean flow rate and magnetic field strength. With the aim of investigating experimentally flow instabilities in liquid metal MHD duct flows, a loop has been manufactured and fully instrumented, in which GaInSn is used as model fluid. The circuit is inserted in a large dipole magnet that is strong enough to reach flow parameters close to those in ITER applications. Electric potential distributions are detected on the surface of the test section and in the liquid metal by means of a movable 4-pole potential probe. Detection of time-dependent signals allows identifying the critical Reynolds number for the onset of instabilities. Time-averaged measured data gives further information about the mean velocity distribution in the duct. Those results can be directly compared with numerical simulations, which support the physical interpretation of the observed MHD phenomena.

Patterned turbulence and relaminarization in MHD pipe and duct flows

AbstractWe present results of a numerical analysis of relaminarization processes in MHD duct and pipe flows. It is motivated by Julius Hartmann's classical experiments on flows of mercury in pipes and ducts under the influence of magnetic fields. The simulations, conducted both in periodic and non‐periodic settings, provide a first detailed view of flow structures that have not been experimentally accessible. The main novelty of the analysis is very long (tens to hundreds of hydraulic diameters) computational domains that allows to discover new flow regimes with localized turbulent spots near the side walls parallel to the magnetic field. The computed critical parameters for transition as well as the friction coefficients are in good agreement with Hartmann's data. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study of instabilities in a quasi-2D MHD duct flow with an inflectional velocity profile

The mechanisms responsible for instabilities and a transition to turbulence in liquid metal duct flows of a fusion blanket are not understood very well, which limits predictive capabilities for heat and material transport in a blanket. In order to elucidate such mechanisms in quasi-two-dimensional (Q2D) magnetohydrodynamic flows with inflection points, an experimental and computational effort is underway to electromagnetically induce a Q2D turbulent flow through the injection of current at the Hartmann walls. In such a flow, inflectional instabilities arise at the two locations where current is supplied. In the experiments, Hartmann wall inductive velocimetry is employed as the main flow diagnostics. The electric potential field is measured using an array of small probes embedded in the wall material, and the fluctuating velocity field is reconstructed from the potential data using Ohm's law. First experimental data have been taken, which are in qualitative agreement with the pre-experimental analysis, where the flows are numerically simulated using a Q2D flow model.

Wavelet optimized finite difference mesh for MHD flow in a circular duct

There is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest. Magnetohydrodynamic flow problems belong to this category. Treatment of such problems numerically, therefore, requires a non-uniform mesh, which is very fine near the boundary. The determination of the size of the grid in different parts of the domain is, therefore, a challenging problem. Some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh. The method has mostly been used for one dimensional problems. The present paper investigates the problem for fully developed MHD duct flow problems which are basically two dimensional. The boundary layer character is more pronounced in one direction as compared to the other. The governing equations comprise a coupled system of two partial differential equations with Dirichlet boundary conditions. Wavelet based adaptive mesh is first created and then the system is discretized over this mesh. Computations have been carried out at different precision levels for various Hartmann numbers for a pipe of circular section. Contours are also drawn to depict the core and the boundary layer region.