Turbulent Flow Of Liquid Metal Research Articles

Ultrasound Localization Microscopy in Liquid Metal Flows

Liquid metal convection plays an important role in natural and technical processes. In experimental studies, an instrumentation with a sub-millimeter spatial resolution is required in an opaque fluid to resolve the flow field near the boundary layer. Using ultrasound methods, the trade-off between the frequency and imaging depth of typical laboratory experiments limits the spatial resolution. Therefore, the method of ultrasound localization microscopy (ULM) was introduced in liquid metal experiments for the first time in this study. To isolate the intrinsic scattering particles, an adaptive nonlinear beamformer was applied. As a result, an average spatial resolution of 188 μm could be achieved, which corresponded to a fraction of the ultrasound wavelength of 0.28. A convection experiment was measured using ULM. Due to the increased spatial resolution, the high-velocity gradients and the recirculation areas of a liquid metal convection experiment could be observed for the first time. The presented technique paves the way for in-depth flow studies of convective turbulent liquid metal flows that are close to the boundary layer.

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.

Electrical voltage by electron spin-vorticity coupling in laminar ducts

A tiny electrical voltage can be generated by the collective coupling of the electron spins to the flow vorticity in laminar and turbulent liquid metal flows. Here, we demonstrate a linear scaling law between electrical voltage and pressure drop for laminar flows through capillaries with different cross sections, both, analytically and experimentally.

Numerical Simulation of the Plasma Arc Melting Cold Hearth Refining Process (PAMCHR)

In order to improve our understanding of the PAMCHR process applied to the processing of Ti alloys, a 3D numerical simulation of the thermal and hydrodynamic behavior of the metal flowing in the refining hearth has been set up, based on Ansys-Fluent CFD software. The solid and liquid phases are governed by a set of transport equations expressing the conservation of mass, momentum, heat, and solutes. The turbulence of the liquid flow is modeled through the standard k–e model. Heat input and tangential shear stress caused by the plasma jet originating from the torches, as well as the themocapillary effect, are accounted for as boundary conditions. Their effects on the turbulent liquid metal flow have been modeled together with the displacement of the torches. Simulation results are presented for a pilot furnace and representative operating conditions. Turbulent fluid flow in the Ti64 molten pool is analyzed in detail and the role of each momentum source is examined. Comparison between the measured and calculated pool profiles is also reported and reveals a satisfactory agreement.

Numerical Study on the Potential of Cavitation Damage in a Lead⁻Bismuth Eutectic Spallation Target.

To perform basic Research and Development for future Accelerator-driven Systems (ADSs), Japan Proton Accelerator Research Complex (J-PARC) will construct an ADS target test facility. A Lead–Bismuth Eutectic (LBE) spallation target will be installed in the target test facility and bombarded by pulsed proton beams (250 kW, 400 MeV, 25 Hz, and 0.5 ms pulse duration). To realize the LBE spallation target, cavitation damage due to pressure changes in the liquid metal should be determined, preliminarily, because such damage is considered to be very critical, from the viewpoint of target safety and lifetime. In this study, cavitation damage due to pressure waves caused by pulsed proton beam injection and turbulent liquid metal flow, were studied, numerically, from the viewpoint of single cavitation bubble dynamics. Specifically, the threshold of cavitation and effects of flow speed fluctuation on cavitation bubble dynamics, in an orifice structure, were investigated in the present work. The results showed that the LBE spallation target did not undergo cavitation damage, under normal nominal operation conditions, mainly because of the long pulse duration of the pulsed proton beam and the low liquid metal flow velocity. Nevertheless, the possibility of cavitation damage in the orifice structure, under certain extreme transient LBE flow conditions, cannot be neglected.

Buoyancy impact on secondary flow and heat transfer in a turbulent liquid metal flow through a vertical square duct

Direct Numerical and Large-Eddy Simulations of the turbulent flow through a vertical square duct at different Reynolds and Richardson numbers are presented for a fluid with low Prandtl number. Buoyancy substantially affects the flow field, Reynolds stresses and heat transfer. A strong coupling between secondary flow and buoyancy effects is found and a double vortex pattern develops with increasing Richardson number which transports hot fluid from the hot to the cold wall. The alterations in the balance of the individual Reynolds stress components leading to the development of this vortex pattern are highlighted. An analysis of the global scaling of secondary flow strength and other quantities identifies the onset of the mixed convection regime.

Solution of the convective heat transfer problem in a screw coordinate system

The problems of hydrodynamics and heat transfer in a screw channel flow are considered in a screw coordinate system. In particular, we consider an upward flow of liquid metal in a heated annular channel with a screw edge. The problem is related to the heat exchange in the flow around the fuel cell in the active zone of a nuclear reactor with a liquid-metal coolant. Differential equations of mass, momentum and energy conservation for a liquid metal flow are written in terms of tensor variables for a curvilinear (screw) coordinate system. The well-known equations for the cylindrical system are taken as a basis. They are supplemented with additional terms which arise due the transition to the screw coordinate system. The method of numerical calculation in the helical coordinate system greatly simplifies the description of the geometry and boundary conditions, the construction of the computational grid, the representation and subsequent processing of the results. Numerical simulations of velocity, pressure and temperature fields in a turbulent flow of liquid metal in an annular channel with a screw edge are carried out. Two problems are studied numerically and compared: channels with straight and twisted (screw) edge. Analysis of the results revealed significant influence of the edge twist on the flow and heat transfer characteristics. The presence of a gap between the edge and the outer pipe enhances the twist effects.

Semi-empirical heat transfer correlations for turbulent tube flow of liquid metals

PurposeThe purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 106.Design/methodology/approachThe energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number.FindingsThe inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data.Research limitations/implicationsHeat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low.Originality/valueUnified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

Influence of thermo-gravitational convection in the flow of liquid metal in a horizontal pipe with a longitudinal magnetic field

The direct numerical simulation (DNS) of MHD-heat transfer problems in turbulent flow of liquid metal (LM) in a horizontal pipe with a joint effect of the longitudinal magnetic field (MF) and thermo-gravitational convection (TGC). The authors calculated the effect of TGC in a strong longitudinal MF for a homogeneous heating. Investigated the averaged fields of velocity and temperature, heat transfer characteristics, the distribution of wall temperature along the perimeter of the cross section of the pipe. The effect of TGC on the velocity field is affected stronger than in the temperature field.

Thermo-hydraulic flow in a sudden expansion

The paper deals with the turbulent flow of liquid metal directed upwards in a vertical channel featuring a backward-facing step. The vertical wall behind the step is heated at various rates thereby inducing forced and mixed convection. Due to the low Prandtl number of liquid metal flow a data basis for this technically relevant flow type did not exist so far. Here, DNS and LES results are presented to provide detailed information about the statistics of the turbulent motion, budgets of turbulent kinetic energy and other quantities. This information is then further used to develop suitable statistical turbulence models capable of properly covering this flow and similar ones, i.e. forced, mixed and free convection of liquid metals. Finally, the paper reports on the construction of an experiment conceived for exactly the same configuration as simulated, with the purpose of close cross validation between the different approaches.

Direct numerical simulation of Mhd heat transfer of the liquid metal in a horizontal pipe with the joint effect of the longitudinal magnetic field and thermo-gravitational convection

The results of the direct numerical simulation (DNS) of the MHD heat transfer in turbulent flow of liquid metal (LM) in a horizontal pipe under the joint influence of a longitudinal magnetic field (MF) and thermo-gravitational convection (TGC) are presented. Discusses the characteristics of hydrodynamics and heat transfer in the longitudinal MF in the absence of TGC. Suppression of turbulent transport is observed with an increase in the Hartmann number: the heat transfer coefficients, the friction coefficient. The authors calculated the effect of TGC in a strong longitudinal MF for a homogeneous heating. Investigated the averaged fields of velocity and temperature, heat transfer characteristics, the distribution of wall temperature along the perimeter of the cross section of the pipe. The effect of TGC on the velocity field is affected stronger than in the temperature field.

Surface waves propagating on a turbulent flow

We study the propagation of monochromatic surface waves on a turbulent flow of liquid metal, when the waves are much less energetic than the background flow. Electromagnetic forcing drives quasi-two-dimensional turbulence with strong vertical vorticity. To isolate the surface-wave field, we remove the surface deformation induced by the background turbulent flow using coherent-phase averaging at the wave frequency. We observe a significant increase in wavelength, when the latter is smaller than the forcing length scale. This phenomenon has not been reported before and can be explained by multiple random wave deflections induced by the turbulent velocity gradients. The shift in wavelength thus provides an estimate of the fluctuations in deflection angle. Local measurements of the wave frequency far from the wavemaker do not reveal such systematic behavior, although a small shift is visible. Finally, we quantify the damping enhancement induced by the turbulent flow and compare it to the existing theoretical predictions. Most of them suggest that the damping increases as the square of the Froude number, whereas our experimental data show a linear increase with the Froude number. We interpret this linear relationship as a balance between the time for a wave to cross a turbulent structure and the turbulent mixing time. The larger the ratio of these two times, the more energy is extracted from the wave. We conclude with possible mechanisms for energy exchange.

Heat Transfer in Turbulent Tube Flow of Liquid Metals

New heat transfer correlations for forced turbulent flow of liquid metals in the tubes have been proposed. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Four various turbulent number models developed by Aoki, Weigand et al., Kays, and modified Aoki's model were considered. Using the universal velocity profile determined experimentally by Reichardt and different relationships for the turbulent Prandtl number, the energy conservation equation was integrated. Subsequently, the Nusselt numbers for a broad range of Reynolds and Prandtl numbers were calculated using the Lyon integral. Based on the determined Nusselt numbers, new correlations for Nusselt number as a function of Reynolds and Prandtl numbers have been proposed for various relationships for the turbulent Prandtl number. Nusselt numbers calculated using the proposed correlations were compared with the experimental data. Constants in different models for the turbulent Prandtl number were adjusted so as to obtain good agreement between calculated and experimentally obtained Nusselt numbers.

Solid inclusions in an electromagnetically induced recirculated turbulent flow: Simulation and experiment

The paper presents the numerical and the experimental investigation of the particle-laden recirculated turbulent flow of liquid metal that is driven by electromagnetic force. Such flow is typical for induction metallurgical furnaces. The paper describes the behaviour of solid spherical particles that are mixed in the flow from a top surface of a melt and covers 3 stages of an admixing process as well as deposition of inclusions on the wall of a vessel. Experimental investigation of particles concentration at the quasi-stationary stage is fulfilled on the basis of a novel idea: ferromagnetic particles are proposed as a physical model of non-conductive inclusions in liquid metal at the presence of an alternative electromagnetic field. Such particles are separated from the samples of particle laden liquid by a permanent magnet. Such process resulted into investigation of a concentration field of inclusions. This investigation is the first known experimental work for the distribution of solid inclusions in a bulk of electromagnetically driven liquid metal flows. The experiment proves the relevance of the LES-based Euler-Lagrange numerical model under dilute conditions for modelling of the flows in induction furnaces.

Flow speeds and length scales in geodynamo models: The role of viscosity

The geodynamo is the process by which turbulent flow of liquid metal within Earth's core generates our planet's magnetic field. Numerical simulations of the geodynamo are commonly used to elucidate the rich dynamics of this system. Since these simulations cannot attain dynamic similarity with the geodynamo, their results must be extrapolated across many orders of magnitude of unexplored parameter space. For this purpose, scaling analysis is essential. We investigate the scaling behavior of the typical length scales, ℓ, and speeds, U, of convection within a broad suite of geodynamo models. The model outputs are well fit by the scalings ℓ∝E1/3 and U∝C1/2E1/3, which are derived from a balance between the influences of rotation, viscosity, and buoyancy (E is the Ekman number and C the convective power). Direct comparison with two previously proposed theories finds that the viscous scalings most favorably describe model data. The prominent role of viscosity suggested by these scaling laws may call into question the direct application of such simulations to the geodynamo, for which it is typically assumed that viscous effects are negligible.

Electromagnetic flow measurements in liquid metals using time-of-flight Lorentz force velocimetry

Time-of-flight Lorentz force velocimetry is a non-invasive electromagnetic measurement technique that can be used to determine both the flow rate and/or the local velocities in electrically conducting fluids like liquid metals. Using this technique, two identical so-called Lorentz force flow meters—each consisting of a permanent magnet system and an attached digital force sensor—are arranged in a row and separated by a defined distance. Each flow meter measures the Lorentz force that is generated within the melt when the electrically conducting liquid metal passes the magnetic field. This time-of-flight technique can be exploited for the flow measurement by purely cross-correlating the two force signals. Hence, the measurement becomes independent of any fluid properties and magnetic field parameters. We present results of two model experiments that demonstrate that time-of-flight Lorentz force velocimetry is feasible for non-contact measurement of both global flow rates and local surface velocity in turbulent liquid metal flow. In these experiments, we use the low-melting eutectic alloy Ga68In20Sn12 as a test melt. Moreover, to support these experimental findings, we present results of numerical simulations using the commercial codes FLUENT and MAXWELL. The numerical predictions are in good agreement with the experimental findings.

Measurement and analysis of turbulent liquid metal flow in a high-power spallation neutron source—EURISOL

The European Isotope Separation On- Line (EURISOL) design study completed in 2009 examined means of producing exotic nuclei for fundamental research. One of the critical components identified in the study was a high-power neutron spallation source in which a target material is impacted by a proton beam producing neutrons by a process known as spallation. Due to the high heat power deposition, liquid metal, in this case mercury, is the only viable choice as target material. Complex issues arise from the use of liquid metal. It is characterised by an unusually low Prandtl number and a higher thermal expansivity than conventional fluids. The turbulence structure in LM is thereby affected and still an object of intense research, hampered in part by measurement difficulties. The use of Computational Fluid Dynamics (CFD) allowed a satisfactory design for the neutron source to be found rapidly with little iteration. However it was feared that the development of the boundary layer and associated turbulence would not be correctly represented by the CFD since the codes were developed for standard fluids. Therefore, an experiment and associated measurements were carried out to assess the reliability of the computations and to validate the design of the target. System level measurements such as cavitation noise, target structural vibrations and cover gas pressure were recorded as local pressure fluctuations in the fluid. In this manner, both the macroscopic effect of the turbulence on the target structure, and the liquid metal turbulence itself could be measured and serve as a benchmark for assessing the reliability of the computations. The current work shows how the Shear Stress Transfer (SST) and Large Eddy Simulation (LES) turbulence models were used to simulate the liquid metal flow. LES was proved more accurate than SST in predicting large and small turbulent structures in the liquid. The prediction of the turbulence intensity generated by large eddy structures in the fluid proved to be in agreement with experimental data at frequencies lower than 40 Hz and at speeds up to 6 m/s in the liquid metal.

Turbulent liquid metal flow in rectangular shaped contraction nozzles for target applications

Owing to the high beam power densities envisaged in advanced nuclear targets, liquid metal-operated free surface targets are conceived as one feasible option. There, the free surface is formed by an adequately shaped upstream located nozzle. Target boundary conditions necessitate a detailed knowledge on the turbulent flow in contraction nozzles in order to identify turbulence models accurately predicting experimental findings within the velocity range of interest for nuclear target and hence can then act as design optimisation tools. In this context, a combined experimental and numerical study is conducted on the basis of the turbulent flow in the contraction nozzle of the Super-FRS target. Two aspects determining the turbulent flow in the nozzle have been investigated. The first is a potential relaminarisation of the boundary layer caused by the acceleration within the contraction and the second is a development of the secondary flows due to the pressure gradient in the rectangular shaped ducts cross-section. Regarding the three different turbulence models investigated here only the V2F model exhibited the capability to predict the relaminarisation of the turbulent boundary layer both qualitatively and quantitatively. All turbulence models are able to predict the development of secondary flows induced by pressure gradients in transverse direction with an acceptable accuracy.

High-speed imaging and CFD simulations of a deforming liquid metal droplet in an electromagnetic levitation experiment

Electromagnetic levitation of a liquid metal droplet is of great interest to study gas–liquid metal reactions. An important prerequisite for the evaluation of the overall mass transfer between the gas and metal is to characterize the geometry of the deforming molten droplet, which determines the interfacial reaction area. In this article, the free surface shape and dynamics of a molten 80%Ni–20%Cr droplet is investigated both experimentally and numerically. The frequencies associated to the oscillatory translational motions of the drop and to the vibrations of its free surface are measured using high-speed video image analysis. A 2D transient model is then presented, in which three interacting phenomena are considered: electromagnetic phenomena, the turbulent flow of liquid metal in the drop and the change in the drop shape. The numerical results presented demonstrate the capabilities of the model.

The limits and pattern of the onset of the effect of thermogravitation on the flow and heat transfer in pipes

The available recommendations and solution of the problem on heat transfer under conditions of turbulent flow of liquid metal in a horizontal pipe with a low effect of thermogravitation are refined, and relations are suggested for the calculation of the onset of the effect of lifting forces on heat transfer under conditions of laminar and turbulent flows of liquid metals, gases, and dropping liquids in horizontal and vertical pipes.