Low Magnetic Reynolds Number Research Articles

A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.

Effects of a spanwise magnetic field on the exact coherent states in a channel flow

The primary objective of this study is to examine the effect of a uniformly constant spanwise magnetic field on exact coherent states and their structures in channel flow. Exact coherent states represent nonlinear solutions to the Navier–Stokes equations, bearing significant importance in the prediction and control of flow with and without magnetic field. Despite the recent extensive research which have reported the influences of magnetic fields with respect to fluid dynamics, the specific effect of a spanwise magnetic field on the exact coherent states remain ambiguous. To investigate the influence of magnetic field on exact coherent states in channel flow, our study encompasses Reynolds numbers ranging from 3000 to 10 000, with variations in the size of computational domains. High-precision direct numerical simulations, coupled with a Fourier–Chebyshev spatial pseudospectra discretization, are employed to solve the governing equations under the assumption of low magnetic Reynolds number. Starting from laminar flow, we utilize a bisection method on the amplitude of perturbations to track the exact coherent states in the channel. In a smaller computational domain 2π × 2.4 × 2, the spanwise magnetic field expedites the self-sustaining process of exact coherent structures, accelerating the transition from streamwise vortices to streamwise streaks. In a larger computational domain, the exact coherent states are bifurcated from relative periodic orbit solutions to traveling wave solutions. Furthermore, as the spanwise computational domain expands, localization coherent structures persist and steadily propagate downstream in the channel.

Time dependent magnetic field effects on the MHD flow and heat transfer in a rectangular duct

AbstractWe consider the effect of time dependent magnetic field on the natural convection magnetohydrodynamic flow in a rectangular duct. The flow is two‐dimensional, unsteady, laminar and the fluid is electrically conducting and incompressible. The heat transfer is taken into account using the Boussinesq approximation and the buoyancy force is included in the momentum equations for the thermal coupling. The flow is considered at low magnetic Reynolds number setting and hence, the induced magnetic field is neglected. The proposed model in which the governing equations are given in terms of stream function, vorticity and temperature, is approximated by using a Chebyshev spectral collocation method for the spatial discretisation coupled with a backward difference scheme that is unconditionally stable for the temporal integration. The flow and heat transfer characteristic are analysed for several definitions of applied time varying magnetic field. Increase of the Hartmann number and the time variation of the applied magnetic field, changes the flow behaviour, especially at transient time levels and at the steady‐state.

Numerical Simulation of the Chemical Reaction on Faraday MHD Accelerator

Magnetohydrodynamic (MHD) is one of the most promising novel propulsion technologies with the advantages of no pollution, high specific impulse, and high acceleration efficiency. As the carrier of this technology, the MHD accelerator has enormous potential for applications in hypersonic wind tunnels, supersonic ramjet engines, and deep space propulsion. In this study, a three-dimensional numerical simulation of an ideal Faraday magnetohydrodynamic (MHD) accelerator is conducted to assess the effect on performance with respect to applied potential and magnetic field intensity. The study is performed by employing a low magnetic Reynolds number MHD model coupled with a 7-component chemical reaction model to simplify the impact of real gas effects. The chemical reaction exhibits an increasing trend with rising applied potential and a decreasing trend with diminishing magnetic field strength. This variation influences the gas conductivity, subsequently affecting the velocity and thrust of the system. Specifically, at a magnetic field intensity of 2.0 T and an applied potential of 600 V, the accelerator exhibits maximum velocity and thrust growth rates of 18.6% and 59.8%, respectively.

Numerical Computation of Williamson Hybrid Nanofluid Flow Over the Curved Surfaces With Effects of Thermal Radiation

Abstract The current investigation is based on Williamson's features of a hybrid nanofluid flow over a curved surface made mixture of silver (Ag) and titanium dioxide (TiO2) with engine oil. Under the presumption of a low magnetic Reynolds number, a constant homogenous magnetic field is applied. Consideration is given to the ramping temperature and the time-varying surface concentration. Thermal absorption and first-order consistent chemical reaction are also taken into account. To create a hybrid nanofluid, silver (Ag), and titanium nanoparticles are dispersed in a base fluid made of water and engine oil. Quasi-linearization technique and Finite difference scheme are employed on the nondimensional partial differential equations. All physical parameters of practical importance, such as velocity, temperature, and concentration profile are analyzed and provided in tables and graphs along with the impact of physical parameters. As the Williamson parameter (W) increases, the surface velocity of the steep plate decreases. Also, as the parameter temperature ratio of Nt and Rd increases, the forces opposing the flow field reduce the friction force, and the thermal field increases with temperature effects.

On bioconvective chemically reactive flow involving applications of magnetohydrodynamic and radiation

Background and objectiveBioconvective flow of Reiner-Rivlin liquid subject to motile microorganism is communicated. Concept of magnetohydrodynamics for low magnetic Reynolds number is highlighted. Convective constraints for heat and mass are implemented. Thermal expression consists of dissipation and radiation. Joule heating and heat generation/absorption impacts are entertained. Brownian motion and thermophoresis behaviors are studied. Binary chemical reaction and motile microorganisms are taken. MethodologyNonlinear expressions are converted into dimensionless equations through appropriate transformations. Nonlinear differential system is numerically computed. ResultsSolutions are analyzed for velocity, microorganisms’ field, concentration and temperature. Coefficient of skin friction, microorganism density number, heat transport rate and concentration gradient via emerging variables are examined. Higher magnetic field has opposite impact on coefficient of skin friction and velocity. An increase in thermal field is detected for radiation and magnetic variables. Larger thermal Biot number intensifies the temperature. Larger approximation of solutal Biot number leads to enhance concentration. There is a reverse trend for heat transfer rate through radiation and random motion variables. Brownian motion and thermophoresis variables for concentration have opposite impacts. An increasing trend of solutal Biot number and Sherwood numbers is observed. Larger bioconvective Lewis number corresponds to boost up microorganism density number.

Mean flow and Convective instability analysis of the BEK and related rotating boundary layer flows subject to a uniform static magnetic field

This study examines the convective instability of the hydromagnetic Bödewadt, Ekman, and von Kármán (BEK) rotating system under the low magnetic Reynolds number approximation. The computations for the mean flow are carried out for different magnetic parameters using MATLAB for several flows of the BEK family. The equations for the linear instability are derived and then solved through the Chebyshev-spectral method for both Type-I (Inviscid) and Type-II (viscous) modes. It is observed that the Rossby number, the Reynolds number, and the magnetic parameter characterize the stability of the hydromagnetic BEK flows. The Reynolds number is based on the dimensionless radial location at the disk while the Rossby number is the ratio of the difference between the angular speeds of fluid and disk and the angular speed of the disk. The magnetic number is the ratio of magnetic field strength and the system rotation rate. The analysis reveals a stabilizing effect of the magnetic parameter on the Type-I modes for Rossby numbers in the range [−1,1]. Further, the Type-II modes disappear upon elevating the magnetic parameter in the aforementioned range of the Rossby number. The growth rates, |αi|, also diminish upon increasing the magnetic parameter. The computations for mean flow reveal that the radial wall shear stress diminishes upon elevating the strength of the applied magnetic field. However, a reverse trend is noted for the azimuthal wall shear stress which indicates an increase in the torque on the disk with enhancing the intensity of the magnetic field.

Double multiple-relaxation-time model of lattice-Boltzmann magnetohydrodynamics at low magnetic Reynolds numbers

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on the central-moment (CM) and multi-relaxation-time (MRT) collision models. The simulation of the magnetic induction equation within the lattice-Boltzmann approach to MHD has been usually devised along the lines of the simplest phenomenological description—the single relaxation time (SRT) model to solve the complete induction equation. In order to deal with well-known stability difficulties of the SRT framework for larger magnetic relaxation time scales, we introduce, alternatively, a MRT technique for the solution of the magnetic induction equation, which proves to be efficient in extending the domain of applicability of the lattice-Boltzmann method to MHD problems. We also put forward a novel and practical boundary condition method to cope with the subtleties of magnetic Boltzmann-like distributions on curved boundaries. As supporting applications, we discuss the performance of the CM–MRT algorithm to describe the complex dynamics of the 3D Orszag–Tang vortex problem and open issues related to transient flow regimes in MHD pipe flows, subject to uniform and non-uniform magnetic fields.

Hall and Ion Slip Impacts on Unsteady MHD Convective Flow of Ag-TiO2/WEG Hybrid Nanofluid in a Rotating Frame

Background: The radiative magnetohydrodynamic (MHD) flow of an incompressible viscous electrically conducting hybrid nanofluid over an exponentially accelerated vertical surface under the influence of slip velocity in a rotating frame taking Hall and ion slip impacts is discussed. Methods: Water and ethylene glycol mixture have been considered as a base fluid. A steady homogeneous magnetic field is applied under the assumption of a low magnetic Reynolds number. The ramped temperature and time-varying concentration at the surface are taken into consideration. The first-order consistent chemical reaction and heat absorption are also regarded. Silver (Ag) and titania (TiO2) nanoparticles are disseminated in base fluid water and ethylene glycol mixture to be formed a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations for the closed form solutions. Results: The phrases for non-dimensional shear stresses, rates of heat, and mass transfer are also evaluated. The graphical representations are presented to scrutinize the effects of physical parameters on the significantflow characteristics. The computational values of the shear stresses, rates of heat and mass transports near the surface are tabulated by a range of implanted parameters. Conclusion: The resultant velocity grows by an increase in thermal and concentration buoyancy forces, Hall and ion-slip parameters, whereas rotation and slip parameters have overturn outcome on them. The temperature of hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Ag-WEG nanofluid. Species concentration of hybrid Ag-TiO2/WEG nanofluid decreases due to an increase in Schmidt number and chemical reaction parameter.

Effect of MHD Control on Turbulent Boundary Layer Separation Flow in Scramjet Inlet

In order to study the effect of MHD control on the separation flow of turbulent boundary layer in the scramjet inlet based on the assumption of low magnetic Reynolds number, considering the source term of turbulent electromagnetic dissipation, the numerical simulation method is developed for electromagnetic field coupled with flow field. A Mach 4 plate is adopted as the basic configuration to assess the accuracy of the solver’s source term of turbulent electromagnetic dissipation. On this basis, numerical simulation of MHD control on the separation flow of boundary layer in scramjet inlet is carried out to study the influence of different electric field strengths and magnetic induction intensity on it. The results show that applying MHD local control alleviates the boundary layer separation in the scramjet inlet. Under different electric field strengths and magnetic induction intensity, the separation vortex’s scale significantly changes. The scale of the separation zone continues to decrease when the electric field strength or magnetic induction intensity increases, and the effect of MHD control is more significant.

Thermochemical non-equilibrium and electromagnetic effects of double-cone in hypervelocity flow

Hypervelocity flows generated over a 25°/55° double-cone are numerically investigated, characterized by a complex shock wave/boundary layer interaction. Based on the low magnetic Reynolds number assumption, the coupled model is established for the thermochemical non-equilibrium flow field and the externally applied magnetic field. The aim of the study is on one hand to evaluate the high temperature effects and on the other to investigate the electromagnetic effects of such an interaction. The results indicate that the thermochemical non-equilibrium effects become relevant and significantly affect the flow structure and surface properties in the case of high-enthalpy flows. The performance of shock wave/boundary layer interaction flows magnetohydrodynamic control is mainly determined by the Lorentz force near the triple point and the separated flow region. Furthermore, the modification of the flow field due to the applied magnetic field causes the mitigation of the aerodynamic heating. This is enhanced with the increase of magnetic field strength.

A Formal Verification and Validation of a Low Magnetic Reynolds Number MHD Code for Fusion Applications

As the nuclear fusion research advances, researchers and engineers focus more on the design of the required systems that complement the nuclear fusion reaction in the plasma of a Tokamak. Some proposals for breeding blankets as well as plasma-facing components’ protection systems are based in liquid metal flows under the Tokamak intense magnetic fields. This creates the situation where induced magnetic field can be neglected and the low magnetic Reynolds number (Re) electric potential formulation can be used to close the magnetohydrodynamic (MHD) system of equations. In the last few years, many different laboratories have developed their own MHD codes to study the liquid metal flow. A formal verification and validation of such codes is necessary to enhance the reliability of the numerical results and to make sure that design decisions are based on safe grounds. The fusion community has made the effort of proposing standardized benchmark cases through which any MHD code should demonstrate its reliability. This work contains the formal validation and verification activities of the MHD code developed some years ago in the Universitat Politecnica de Catalunya (UPC) and currently candidate to contribute to the research done at the Princeton Plasma Phyisics Laboratory (PPPL). The code is implemented over OpenFOAM which makes it easily modifiable. Among these benchmark cases, there are high Hartmann number (Ha), 3-D flows, and magneto-convective interaction cases.

Numerical Investigation on Mechanisms of MHD Heat Flux Mitigation in Hypersonic Flows

Numerical simulations of hypersonic magnetohydrodynamics (MHD) flow over a typical sphere–cone blunt body are carried out based on the assumption of a low magnetic Reynolds number. The effects of an external dipole magnetic field on the surface heat flux are analyzed in detail, and multiple mechanisms of the MHD heat flux mitigation are revealed systematically for the first time. The following is found: (1) The external magnetic field can effectively reduce the stagnation point heat flux, and the increase in the boundary layer thickness due to the effect of counter-flow Lorentz force, which is equivalent to adding an adverse pressure gradient, is the main reason. (2) In the head region of the blunt body, the relative surface heat flux shows a complex trend of rising and falling because there are two mechanisms which could produce the opposite effects on the surface heat flux. One is that the counter-flow Lorentz force results in an increase in the boundary layer thickness, and the other is that the Joule heating increases the static temperature behind the shock wave. (3) In the shoulder region of the blunt body, the Lorentz force component, normal to streamline, could change the flow direction of the fluid elements, causing the streamline to deviate from the wall or even separate, thus affecting the surface heat flux. (4) In the large area downstream of the blunt body, the surface heat flux could still be reduced by more than 30% due to the “upstream historical effect”.

Onset of instability with collapse observed in relatively high density and medium beta regions of LHD

Edge MHD instabilities with pressure collapse are found in relatively high beta and low magnetic Reynolds number regions with a magnetic axis torus outward-shifted configuration of the large helical device (LHD), and characteristics and onset conditions of the instability are investigated. The instability has a radial structure with an odd parity around the resonant surface, which is different from that of the interchange instability typically observed in the LHD. The onset condition dependence on the magnetic axis location shows that the onset beta increases as the magnetic axis location moves more torus inwardly, and the instability appears only in limited configurations where the magnetic axis is located between 3.65 and 3.775 m. In such configurations, the resonant surface location is close to an index of the plasma boundary. This fact suggests that the distance between the resonant surface location and the plasma boundary plays an important role in the onset, and a possibility that the instability is driven by an external mode.

Effect of a localized MHD body force on near-wall turbulence

The present study focuses on the response of a near-wall turbulent flow subjected to a spatially localized body force. Characteristics of a turbulent channel flow under a Lorentz force distribution are analysed through Direct Numerical Simulation at a low turbulent Reynolds number (4200) and a low magnetic Reynolds number. It is found that streamwise or spanwise magnetic fields alter only slightly the wall layer when the magnetic fields are constrained within the buffer layer. Yet, the turbulent wall layer is greatly affected once the edge of the localized Lorentz force reaches the logarithmic layer. Furthermore, the spanwise magnetic field results in flow relaminarization at much lower magnetic severity parameters than the streamwise magnetic field. We further show that this is basically coming from the specific MHD terms appearing in the shear-stress transport equations. Tables 1, Figs 6, Refs 5.

Formation of Bow Shock Waves Around a Blunt Body in Magnetohydrodynamics Flows

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes, which are well suited to studies of hypersonic magnetohydrodynamic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, based on the low magnetic Reynolds number assumption and dipole magnetic field distribution, the influence of magnetic field on the diffraction of an incident shock wave over a sphere was studied numerically. The incident shock Mach number ranges from 11 to 15 under different magnetic field intensities. Time histories of the shock-detached distance and stagnation pressure were first obtained. Moreover, the time needed to establish the steady flows over the sphere was also displaced against the magnetic interaction parameter. The larger the magnetic interaction parameter, the longer the time needed to establish a steady bow shock for experiments, which further challenges the facilities to have sufficient test times for conducting hypersonic magnetohydrodynamic flow experiments.

Dynamos driven by modified Beltrami flows, and a search for related planar flow dynamos

Bachtiar, Ivers and James [Planar velocity dynamos in a sphere. Proc. R. Soc. Lond. 2006, A462, 2439–2456]showed that a planar fluid velocity v can support dynamo action in a conducting sphere, however their modelp1Y22DM12 exhibited slow convergence. Seeking more planar flow dynamos, they also considered convertingsome historical flows to planar flows by a process they termed ‘planarising‘. In particular they studied oneof many flows considered by Pekeris, Accad and Shkoller [Kinematic dynamos and the earth's magnetic field. Phil. Trans. R. Soc. Lond. 1973, A275, 425–461]. This PAS flow was chosen because it produced adynamo at low truncation levels and low critical magnetic Reynolds number R c, properties enhanced bythe flow being a helical Beltrami flow. The original aim of the present project was to find a planar flowdynamo with faster convergence than p1Y22DM12. Whilst the PAS flow can only be partly planarised, wehave constructed two modifications, labelled biPAS and quasiPAS, which can be fully planarised. We havestudied 128 models using the PAS, biPAS, quasiPAS flows, and their part and full planarisations. We haveverified 12 known dynamos, found 84 new dynamos, but found no dynamos with fully planar flows. Thepartly-planarised PAS, and the biPAS- and quasiPAS-based flows are not Beltrami. But 20 (normalisedusing rms( v ), or 22 using max | v |) of the associated dynamos have lower R c than the original Beltrami PASdynamos from which they were derived, showing that the Beltrami property is not essential for low R c. Acomparison is also made herein with optimal enstrophy-normalised dynamos.

Mechanism analysis of magnetohydrodynamic control in hypersonic turbulent flow

Under the assumption of the low magnetic Reynolds number, the coupled model is established for the turbulent flow field and the externally applied magnetic field. The AUSMPW+ scheme and LUSGS method are used to solve turbulent magnetohydrodynamics (MHD) flow equations, in which the Spalart-Allmaras one-equation turbulence model is used. A series of numerical simulations over various geometry configurations, namely, a flat plate and a compression corner, is conducted by using an external electromagnetic field. Results show that the performance of MHD boundary layer flow control is determined mainly by the Lorentz force in the streamwise direction. With an external magnetic field used, the low velocity fluid in the boundary layer can decelerate and increase the static temperature locally. Moreover, the counter-flow Lorentz force always brings a negative effect on the turbulent skin friction coefficient, and the location for the MHD zone has a great influence on the control efficiency of the ramp-induced separation. A reasonable magnetic field layout scheme should be configured in practical engineering application.

Investigation of micro-shock waves in a planar magnetogasdynamic flow using the discontinuous Galerkin finite element method

The present work focuses on the numerical investigation of micro-shock wave propagation in a two-dimensional magnetogasdynamic flow in the framework of the Dis- continuous Galerkin-Finite Element Method (DG-FEM). The Lorentz force has been im- plemented in the compressible, viscous Navier–Stokes equations as a source term using first-order spatial and fourth-order temporal Runge–Kutta discretization schemes. To in- vestigate the effect of the electrical conductivity on the micro-shock wave propagation, a two-dimensional micro-shock channel problem with hydraulic diameter of 2.5 mm, length of 82 mm, and no-slip boundary conditions at the left and at the right wall is considered as a benchmark problem. In this case, acoustic waves are generated behind after the rupture of the membrane that separates two states of the same gas originally at different pressure and density and both initially at rest. The magnetic field is taken into account as uniform and stationary throughout the microchannel, and the numerical simulations are performed in a short physical time, before the reflection of the waves on the lateral wall. A detailed parametric study of the temperature, density, pressure, and u-velocity is carried out by a variation of the electrical conductivity of the magnetogasdynamic flow, under the assumption of low magnetic Reynolds numbers. It has been found that the jumps of the acoustic waves become significantly intensified when the electrical conductivity of the gas is increased. It has also been observed that the presence of the Lorentz force causes an acceleration in the gasflow towards the outlet section of the microchannel at the low Knudsen number of 0.05. The outcome of this research work could be relevant to biomedical applications where the ability to control the flow in a microchannel has a significant impact on the development of small devices aimed to deliver pharmaceutical drugs in specific locations.

Hall and ion slip effects on the MHD flow of Casson hybrid nanofluid past an infinite exponentially accelerated vertical porous surface

In the present investigation, the radiative MHD flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol combination should be formed by a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations to ensure closed-form analytical solutions. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters. For uniform and ramped wall temperatures, the resultant velocity grows by an increase in Hall and ion slip parameters. The resultant velocity increases by an increase in volume fractions of nanoparticles with uniform wall temperature, and a reverse effect is observed with ramped wall temperature. The temperature of Casson hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Casson Ag-WEG nanofluid. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid decreases with an increase in Schmidt number and chemical reaction parameters. The heat absorption increases the Nusselt number near the surface, while Ag and TiO2 nanoparticle volume fractions tend to lessen it.