Magnetohydrodynamic Turbulent Flows Research Articles

Numerical Modeling of Melt Flow and Mixing in an Inductively Stirred Ladle and Comparison with Gas and Mechanical Stirring

Fluid flow and mixing in an inductively stirred ladle are modeled mathematically. The effect of two modes of electromagnetic stirring on motion is simulated; one produces a predominantly swirling motion (as in mechanical, paddle‐stirred ladle), while the other generates an upwelling, toroidal motion (as in gas‐stirred ladle). Two different ANSYS software programs, namely, Maxwell‐3D and Fluent, are applied to carry out numerical simulations. In the former, 3D Maxwell's equations are solved to estimate, a priori, the distribution of Lorentz force within the melt phase due to the imposed three‐phase, alternating current excitation of copper coils, while in the latter, time‐averaged magnetohydrodynamic (MHD) turbulent flow equations are solved to yield the electromagnetically driven flow field. Model predictions are validated against published results and it is shown that the electromagnetic as well as turbulent‐MHD models developed in this work are robust and perform sufficiently accurately. Finally, numerically predicted results together with relevant published work indicated that at equivalent specific input stirring power and identical vessel shape and volume, mixing is fastest in electromagnetic stirring with a traveling magnetic field (producing an upwelling toroidal motion), followed by mechanical agitation, gas stirring, and electromagnetic stirring with a rotating magnetic field (inducing swirling flow).

Passive scalar small-scale anisotropy and mixing characteristics in magnetohydrodynamic turbulent channel flow

In wall-bounded turbulent flows, both velocity and scalar fluctuations exhibit inhomogeneity and anisotropy. This study investigates the statistical properties of the small-scale scalar fluctuations in a turbulent channel flow at Reτ≈585 using direct numerical simulations with and without a magnetic field. The influence of the Hartmann, Ha, and Prandtl, Pr, numbers on turbulent velocity and passive scalar fields is examined at Ha=0, 20, and 40 and Pr=0.7 and 1.4. Small-scale dynamics of the passive scalar and velocity fields are studied, analyzing their probability density functions and higher-order moments, as well as their gradients. We observed that the magnetic field substantially changes flow dynamics such as the typical cliff-and-ramp type structures. The presence of the magnetic field led to statistical anisotropy, even at small-scale gradient fields. The findings reveal that the skewness of the normal derivative of scalar fluctuations remains at the order of 2. We investigated mixing characteristics by analyzing scalar dissipation rates. Scalar dissipation rates near the wall remain close to unity and decrease sharply toward the channel center, reaching a minimum value. Moreover, an increase in scalar dissipation rates leads to a decrease in the corresponding mixing timescale of the flow. This could suggest a connection between an increase in the Lorentz force and potential adjustments in the mixing timescale, potentially contributing to enhance overall mixing. Additionally, we argue that combined effects of strong intermittency and persistency of anisotropy at small scales can influence the mixing characteristics of magnetohydrodynamic turbulent flow.

Application of the visual boundary recurrence plots to magnetohydrodynamic turbulence channel flow

The visual boundary recurrence plot (VBRP) method is used in this analysis to study time series of fluctuating velocities in turbulent magnetohydrodynamic channel flow that were studied in our previous study using the theory of the recurrence plots. The VBRP is a new graphical tool, which visualizes each point of the recurrence plot with colors depending on whether the neighboring points are recurrent or not and enhances, thus, the study of the stability of the textures of the recurrence plots, viewing them as geometrical shapes. We calculate the VBRPs of the turbulent velocity time series of a simulated channel flow monitored at constant streamwise and spanwise positions and at a number of positions along the wall-normal direction. We further estimate the visual boundary recurrence plot rates to indicate the change of the dynamics of the flow. The results highlight the flow dynamics under the influence of the magnetic field and identify additional correlations/similarities between the flow point positions within the channel. In this study, we show that these areas correspond to perturbations due to strikes that are created close to the boundary and move toward the centerline. It also seems that we have more often creation of streaks in the case of absence of magnetic field.

Large eddy simulation of magnetohydrodynamic turbulent flow in an electrically conducting circular pipe with V-shaped strips

Pressure drops and velocity distributions of liquid metal MHD flow in pipes are closely related to the geometry of the cross-section. Liquid metal flows in two types of electrically conducting circular pipes under a uniform magnetic field applied transversely to the flow are investigated numerically using large eddy simulation with a coherent structure model developed in the OpenFOAM environment. One pipe has a typical circular cross-section (N-pipe), whereas the other has four V-shaped strips at the wall parallel and perpendicular to the magnetic field (F-pipe). The increasing transverse magnetic field causes a turbulent MHD flow evolves into a single-sided turbulent flow and a laminar flow in the N-pipe. The V-shaped strips on the Hartmann wall generate a low-velocity belt along the magnetic field direction in the center of the pipe and weak high-velocity jets near the V-shaped strips. Furthermore, the inflection points in the velocity profile improve instability and turbulence. The root mean square of the velocity fluctuation, in particular, the transverse components increase with the Hartmann number increasing along the magnetic field direction in the F-pipe. The V-shaped strips delay the MHD turbulent-laminar transition. However, the skin friction coefficient is slightly higher in the F-pipe than in the N-pipe, with the same dimensionless parameters. The research results can be applied to the turbulence promoter in the MHD pipe flow. Key words: Magnetohydrodynamic turbulent flow, large eddy simulation, pipe, V-shaped strips. Tables 5, Figs 9, Refs 23.

Local fluxes in magnetohydrodynamic turbulence

Using highly resolved direct numerical simulations we examine the statistical properties of the local energy flux rate $\varPi _\ell (x)$ towards small scales for three isotropic turbulent magnetohydrodynamic flows, which differ in strength and structure of the magnetic field. We analyse the cascade process in both kinetic and magnetic energy, disentangling the different flux contributions to the overall energy dynamics. The results show that the probability distribution of the local energy flux develops long tails related to extreme events, similar to the hydrodynamic case. The different terms of the energy flux display different properties and show sensitivity to the type of the flow examined. We further examine the joint probability density function between the local energy flux and the gradients of the involved fields. The results point out a correlation with the magnetic field gradients, showing, however, a dispersion much stronger than what is observed in hydrodynamic flows. Finally, it is also shown that the local energy flux shows some dependence on the local amplitude of the magnetic field. The present results have implications for subgrid-scale models, which we discuss.

On the Inertial Range Bounds of K-41-like Magnetohydrodynamics Turbulence.

The spectral slope of magnetohydrodynamic (MHD) turbulence varies depending on the spectral theory considered; is the spectral slope in Kraichnan–Iroshnikov–Dobrowolny (KID) theory, in Marsch–Matthaeus–Zhou and Goldreich–Sridhar theories, also called Kolmogorov-like (K-41-like) MHD theory, the combination of the and scales in Biskamp, and so on. A rigorous mathematical proof to any of these spectral theories is of great scientific interest. Motivated by the 2012 work of A. Biryuk and W. Craig (Physica D 241(2012) 426–438), we establish inertial range bounds for K-41-like phenomenon in MHD turbulent flow through a mathematical rigor; a range of wave numbers in which the spectral slope of MHD turbulence is proportional to is established and the upper and lower bounds of this range are explicitly formulated. We also have shown that the Leray weak solution of the standard MHD model is bonded in the Fourier space, the spectral energy of the system is bounded and its average over time decreases in time.

Effects of electrically conductive walls on turbulent magnetohydrodynamic flow in a continuous casting mold

In the present study, we have performed a series of numerical simulations of the turbulent liquid metal flow in a laboratory-scale setup of the continuous casting. The liquid metal flow was subjected to an external non-uniform magnetic field reproducing a realistic electromagnetic brake (EMBr) effect. The focus of this research was on the effects of the finite electrical conductivity of Hartmann walls on the flow and turbulence in the mold. To be able to simulate distributions of the electric potential and current in both the fluid and solid wall domains, we applied our recently developed and validated in-house conjugate MHD solver based on the open-source code OpenFOAM. The dynamic Large Eddy Simulation (LES) method was used to simulate the turbulent flow. The results obtained for the neutral (non-MHD) and MHD cases over a range of the imposed EMBr strengths – all for the perfectly electrically insulated walls – were compared with the available Ultrasound Doppler Velocimetry (UDV) measurements. A good agreement between simulations and experiments was obtained for all simulated cases. Next, we completed a series of simulations including a wide range of the finite electric conductivities (ranging from a weakly to perfectly conducting wall conditions) of the Hartmann walls for a fixed value of the imposed EMBr. The obtained results demonstrated a significant influence of the electric wall conductivities on the flow and turbulence reorganization. It is expected that here provided insights can be applicable for the new generation of the laboratory- and real-scale continuous casting setups.

Turbulence suppression and regeneration in a magnetohydrodynamic duct flow due to influence of arbitrary electrically conductive walls

In the current study, we present a series of numerical simulations describing a turbulent magnetohydrodynamic flow subjected to a transverse magnetic field in a square duct with arbitrary electrically conductive walls. The characteristic flow and electromagnetic non-dimensional parameters (Reynolds and Hartmann number, respectively) were fixed, while the wall conductivity ratio (Cd) was varied from the perfectly electrically insulated (Cd = 0) to perfectly electrically conducting (Cd→∞). We have assumed the one-way coupling between the flow of an electrically conducting fluid and the imposed magnetic field. The influence of the electrically conducting walls was imposed by simulating additional finite solid domains coupled with the channel interior. The turbulence was simulated by applying the large eddy simulation approach with the dynamic Smagorinsky sub-grid scale model. The obtained results confirmed a significant impact of the conductivity of the surrounding walls on the flow and turbulence reorganization. We have observed that the initially fully developed turbulence regime was gradually suppressed in the 0≤Cd<0.15 range, while the fully laminarized state was obtained at Cd=0.15. We found that the process of turbulence suppression was accompanied by the appearance of the patterned turbulence phenomenon in the proximity of the walls parallel to the magnetic field direction. With a further increase in the wall conductivity parameter (0.15<Cd<∞), we have observed a complete turbulence regeneration. We found that this turbulence regeneration was caused by the local reorganization of the total current density loops near the electrically conducting walls.

Verification and Validation of COMSOL Magnetohydrodynamic Models for Liquid Metal Breeding Blankets Technologies

Liquid metal breeding blankets are extensively studied in nuclear fusion. In the main proposed systems, the Water Cooled Lithium Lead (WCLL) and the Dual Coolant Lithium Lead (DCLL), the liquid metal flows under an intense transverse magnetic field, for which a magnetohydrodynamic (MHD) effect is produced. The result is the alteration of all the flow features and the increase in the pressure drops. Although the latter issue can be evaluated with system models, 3D MHD codes are of extreme importance both in the design phase and for safety analyses. To test the reliability of COMSOL Multiphysics for the development of MHD models, a method for verification and validation of magnetohydrodynamic codes is followed. The benchmark problems solved regard steady state, fully developed flows in rectangular ducts, non-isothermal flows, flow in a spatially varying transverse magnetic field and two different unsteady turbulent problems, quasi-two-dimensional MHD turbulent flow and 3D turbulent MHD flow entering a magnetic obstacle. The computed results show good agreement with the reference solutions for all the addressed problems, suggesting that COMSOL can be used as software to study liquid metal MHD problems under the flow regimes typical of fusion power reactors.

Observation of a novel flow regime caused by finite electric wall conductance in an initially turbulent magnetohydrodynamic duct flow.

We present results of a series of numerical simulations of an initially fully developed turbulent flow of a liquid metal in a long duct under the influence of a constant uniform transverse magnetic field and various wall conductances (ranging from perfectly insulated to perfectly conducting walls). The changes in the wall conductance caused the appearance of novel flow regimes characterized by the coexistence of locally turbulent or laminar flow regions and a nonmonotonic behavior of the corresponding wall-friction coefficients. In contrast to the situation where an increase in the imposed magnetic field will lead to continuous suppression of turbulence and final complete relaminarization of the flow in a specific range of wall-conducting parameters, we also observe an apparent partial and complete turbulence regeneration from the magnetohydrodynamic-suppressed laminar state.

Analysis of magnetohydrodynamic channel flow through complex network analysis.

Velocity time series of hydrodynamic and magnetohydrodynamic (MHD) turbulent flow are analyzed by means of complex network analysis in order to understand the mechanism of fluid patterns modification due to the external magnetic field. Direct numerical simulations of two cases are used, one for the plane hydrodynamic turbulent channel flow at the low Reynolds number of 180, based on the friction velocity, and the corresponding MHD flow with an external streamwise magnetic field with a magnetic interaction number of 0.1. By applying the visibility graph algorithm, we first transformed the time series into networks and then we evaluated the network topological properties. Results show that the proposed network analysis is not only able to identify and detect dynamical transitions in the system's behavior that identifies three distinct fluid areas in accordance with turbulent flow theory but also can quantify the effect of the magnetic field on the time series transitions. Moreover, we find that the topological measures of networks without a magnetic field and as compared to the one with a magnetic field are statistically different within a 95% confidence interval. These results provide a way to discriminate and characterize the influence of the magnetic field on the turbulent flows.

Magnetohydrodynamic Turbulence in the Earth’s Magnetotail From Observations and Global MHD Simulations

Magnetohydrodynamic (MHD) turbulent flows are found in the solar wind, the magnetosheath and the magnetotail plasma sheet. In this paper, we review both observational and theoretical evidence for turbulent flow in the magnetotail. MHD simulations of the global magnetosphere for southward interplanetary magnetic field (IMF) exhibit nested vortices in the earthward outflow from magnetic reconnection that are consistent with turbulence. Similar simulations for northward IMF also exhibit enhanced vorticity consistent with turbulence. These result from Kelvin-Helmholtz (KH) instabilities. However, the turbulent flows association with reconnection fill much of the magnetotail while the turbulent flows associated with the KH instability are limited to a smaller region near the magnetopause. Analyzing turbulent flows in the magnetotail is difficult because of the limited extent of the tail and because the flows there are usually sub-magnetosonic. Observational analysis of turbulent flows in the magnetotail usually assume that the Taylor frozen-in-flow hypothesis is valid and compare power spectral density vs. frequency with spectral indices derived for fluid turbulence by Kolmogorov in 1941. Global simulations carried out for actual magnetospheric substorms in the tail enable the results of the simulations to be compared directly with observed power spectra. The agreement between the two techniques provides confidence that the plasma sheet plasma is actually turbulent. The MHD results also allow us to calculate the power vs. wave number; results that also support the idea that the tail is turbulent.

Numerical investigation of the Lorentz force effect on two-point statistics in a turbulent channel flow

Effects of a uniform and static magnetic field in the streamwise direction with different Hartmann numbers on the average structure of velocity and pressure fluctuations in a magneto-hydrodynamic turbulent channel flow are investigated. Direct numerical simulations (DNSs) are performed at low magnetic Reynolds numbers and under subcritical conditions with the bulk Reynolds number Reb = 5600, based on the channel height, using a very long domain to analyze two-point velocity and pressure fluctuations. Comparisons are made with DNS data of channel flow with a spanwise magnetic field and also without a magnetic field. Results indicate a substantial increase in the large-scale flow anisotropy, more alignment of flow structures with the mean flow and substantial elongation of flow structures in the streamwise direction in case of the streamwise magnetic field. On the contrary, the spanwise magnetic field did not have a comparable influence on the large scale flow anisotropy. Streak spacing increased linearly with increasing Hartmann number with the magnetic field in the streamwise direction. The magnetic field in the spanwise direction was more effective in increasing the streak spacing at a lower Hartmann number. The mean size of the quasi-streamwise vortex rolls was not affected with the introduction of a magnetic field. The effect of the Hartmann number on turbulent scales shows that scales grow largely with increasing magnetic field strength. The influence of the magnetic fields on pressure fluctuations was similar in the two cases and confined to large-scale weak correlations, where their length was substantially increased, especially in the spanwise direction.

Spatio-temporal behavior of magnetohydrodynamic fluctuations with cross-helicity and background magnetic field

We study the spatiotemporal behavior of the Elsässer variables describing magnetic and velocity field fluctuations, using direct numerical simulations of three-dimensional magnetohydrodynamic turbulence. We consider cases with relatively small, intermediate, and large values of a mean background magnetic field and with null, small, and high cross-helicity (correlations between the velocity and the magnetic field). Wavenumber-dependent time correlation functions are computed for the different simulations. From these correlation functions, the decorrelation time is computed and compared with different theoretical characteristic times: the local nonlinear time, the random-sweeping time, and the Alfvénic time. It is found that decorrelation times are dominated by sweeping effects for low values of the mean magnetic field and for low values of the cross-helicity, while for large values of the background field or of the cross-helicity and for wave vectors sufficiently aligned with the guide field, decorrelation times are controlled by Alfvénic effects. Finally, we observe counterpropagation of Alfvénic fluctuations due to reflections produced by inhomogeneities in the total magnetic field. This effect becomes more prominent in flows with large cross-helicity, strongly modifying the propagation of waves in turbulent magnetohydrodynamic flows.

Nonlinear Transformations of the Kinetic and Magnetic Energies in Rotating Magnetohydrodynamic Turbulent Flows

Nonlinear Transformations of the Kinetic and Magnetic Energies in Rotating Magnetohydrodynamic Turbulent Flows

On the applicability of Taylor\u2019s hypothesis in streaming magnetohydrodynamic turbulence

We examine the range of applicability of Taylor’s hypothesis used in observations of magnetic turbulence in the solar wind. We do not refer to turbulence theory. We simply ask whether in a turbulent magnetohydrodynamic flow the observed magnetic frequency spectrum can be interpreted as mapping of the wavenumber turbulence into the stationary spacecraft frame. In addition to the known restrictions on the angle of propagation with respect to the fluctuation spectrum and the question on the wavenumber dependence of the frequency in turbulence which we briefly review, we show that another restriction concerns the inclusion or exclusion of turbulent fluctuations in the velocity field. Taylor’s hypothesis in application to magnetic turbulence encounters its strongest barriers here. It is applicable to magnetic turbulence only when the turbulent velocity fluctuations can practically be completely neglected against the bulk flow speed. For low flow speeds the transformation becomes rather involved. This account makes even no use of the additional scale dependence of the turbulent frequency, viz. the existence of a “turbulent dispersion relation”.

The effect of magnetic field advection on turbulent magnetohydrodynamic flow in a square duct

AbstractIn the field of magnetohydrodynamics, turbulent duct flows in a transverse magnetic field are of considerable interest. Their velocity fields exhibit electromagnetic boundary layers and anisotropy due to damping of turbulent fluctuations by the Lorentz force. The weak induced magnetic field is slaved to the velocity field (quasistatic limit) in laboratory experiments since the magnetic Reynolds number is small. Here we consider flow conditions with finite magnetic Reynolds number in direct numerical simulations, whereby the full induction equation needs to be solved. The modification of the imposed transverse field by the flow and other differences to the quasistatic results are briefly discussed.

Turbulent magnetohydrodynamic flow in a square duct: Comparison of zero and finite magnetic Reynolds number cases

The effect of finite magnetic Reynolds numbers ($R\phantom{\rule{0}{0ex}}m\ensuremath{\sim}{10}^{2}$) on MHD flow in a square duct was studied using direct numerical simulations. The structure of the secondary mean flow is modified significantly and the streamwise anisotropy is strongly enhanced away from the boundary layers.

Effect of an Electrically-Conducting Wall on Transient Magnetohydrodynamic Flow in a Continuous-Casting Mold with an Electromagnetic Brake

Large eddy simulation (LES) of transient magnetohydrodynamic (MHD) turbulent flow under a single-ruler electromagnetic brake (EMBr) in a laboratory-scale, continuous-casting mold is presented. The influence of different electrically-conductive boundary conditions on the MHD flow and electromagnetic field was studied, considering two different wall boundary conditions: insulating and conducting. Both the transient and time-averaged horizontal velocities predicted by the LES model agree well with the measurements of the ultrasound Doppler velocimetry (UDV) probes. Q-criterion was used to visualize the characteristics of the three-dimensional turbulent eddy structure in the mold. The turbulent flow can be suppressed by both configurations of the experiment’s wall (electrically-insulated and conducting walls). The shedding of small-scale vortices due to the Kelvin–Helmholtz instability from the shear at the jet boundary was observed. For the electrically-insulated walls, the flow was more unstable and changed with low-frequency oscillations. However, the time interval of the changeover was flexible. For the electrically-conducting walls, the low-frequency oscillations of the jets were well suppressed; a stable double-roll flow pattern was generated. Electrically-conducting walls can dramatically increase the induced current density and electromagnetic force; hence they contribute to stabilizing the MHD turbulent flow.

A New k-ω Model for Magnetohydrodynamic Turbulent Duct Flow

A solver for MHD turbulent flow and a new RANS model based on k-ω model in the open source toolbox OpenFOAM are developed to investigate magnetohydrodynamic (MHD) turbulent flow. Two electro-magnetic terms in the k and ω transport equations are added to include magnetohydrodynamic (MHD) effects. The modified k-ω is validated by simulating MHD turbulent duct flow. Time-averaged velocity and turbulent kinetic energy profiles simulated by standard k-ω and the modified k-ω in the fully developed section are both reported. The results compare fairly with those obtained from DNS data. A difference of 8.4% in is found between the modified k-ω and DNS, but the RANS model only uses 0.4% of the DNS computation time.