Flow rate measurements in turbulent liquid metal channel flow using Time-of-Flight Lorentz force velocimetry

Non-contact flow control and flow measurements in hot and aggressive metal melts are big challenges in metallurgical applications. Time-of-Flight Lorentz force velocimetry (ToF LFV) is an electromagnetic measurement technique to meet these challenges. Our experimental results demonstrate that this method is well suited to measure flow rate in turbulent liquid metal channel flow without knowledge of both melt and magnetic field properties. Moreover, the measured flow profiles are in very good agreement with predictions of numerical simulations using the commercial program Package FLUENT MHD. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromorphic description of turbulent channel flow

The simple microfluid theory of Eringen is employed to determine the velocity profile and microgyrations in a steady flow of viscous fluids between two parallel walls. The shearing stress, microrotations, microinertia and Reynold stresses are determined. The results are compared with the experimental work of Laufer.     

Statistical modeling of compressible turbulent channel flow

Several questions that are relevant to turbulence modeling are addressed on the basis of recently obtained direct numerical simulation results of turbulent supersonic channel flow. In particular, this concerns the turbulence frequency production mechanism, wall damping effects on turbulence model parameters, and the relevance of compressibility effects. Limited support is found for usually applied models for the turbulence frequency production and wall damping effects. In contrast to that it is shown that turbulence frequency production mechanisms and wall damping effects may be explained very well on the basis of a frequency scaling that characterizes mean flow changes. The influence of compressibility is found to be relevant. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of contraction on turbulent channel flow

Summary Measurements in an effectively two-dimensional channel indicate that flow acceleration at constant Reynolds Number can have appreciable effects on the turbulence structure. As in wakes, the structure approaches equilibrium exponentially after the acceleration. The effect of acceleration appears to be (at least qualitatively) of the same kind as is observed when turbulence is subjected to rapid distortion.

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Zusammenfassung Messungen in einem effektiv zwei-dimensionalen Kanal zeigen, daß eine Strömungsbeschleunigung bei konstanter Reynolds-Zahl einen wesentlichen Einfluß auf die Turbulenz-Struktur haben kann. Nach der Beschleunigung findet man eine exponentielle Annäherung an das Gleichgewicht, wie bei Dellen. Der Beschleunigungs-Effekt auf die Turbulenz erscheint, wenigstens qualitativ, von der gleichen Art zu sein wie der Einfluß von raschen Verformungen.

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Symbols c _f skin-friction coefficient = - D half-width of the channel - L length of contraction=12 inches - dp/dx pressure gradient - V mean velocity in thex-direction,U=U ₀ aty=D - U mean velocity - average of the mean velocity - U ^* friction velocity = (₀/)^± - root mean square value of the turbulent velocity fluctuations inx, y andz directions - X coordinate in the direction of the flow;X=0 at the end of contraction - Y coordinate perpendicular to the surface of the wall on which measurements are madey=0 at the wall andy=D at the centre of the channel - ₀ Wall shear stress - density of the fluid - viscosity of the fluid - kinematic viscosity of the fluid=/     

Simulation of bubbly flow in a vertical turbulent channel

The paper presents results of Direct Numerical Simulation of bubbly flow to analyse the interaction between the turbulent fluid and the bubbles. The simulations aim to investigate the effect of the bubble Reynolds number, related to the bubble size, and the void fraction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-Reynolds-number effects on turbulent scalings in compressible channel flow

The effect of the Reynolds number in a supersonic isothermal channel flow is studied using a direct numerical simulation (DNS). The bulk Mach number based on the wall temperature is 1.5, and the bulk Reynolds number is increased up to Re_τ ≈︁ 1000. The use of van Driest velocity transformation in the presence of heated walls has been questioned due to the poor accuracy at low Reynolds number. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi-local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-layer asymptotic analysis of turbulent channel flow

In the classical theory for large-Reynolds number fully developed channel flow, the solutions obtained by asymptotic-expansion techniques for the outer Karman defect layer and the inner Prandtl wall layer are demonstrated to match through the introduction of an intermediate layer, based on a general intermediate limit. From an examination of the results for this general intermediate layer, the distinguished intermediate limit and the corresponding intermediate layer for which the turbulent and laminar contributions to the difference of the Reynolds stress from the wall stress are of the same order of magnitude are identified. The thickness of this distinguished intermediate layer is found to be of the order of the geometric mean of the thicknesses of the outer and inner layers     

Subcritical instability of liquid metal channel flow in the presence of a spanwise magnetic field

The linear and nonlinear evolution of perturbations is investigated in a magnetohydrodynamic channel flow with electrically insulating walls. The applied magnetic field is parallel to the walls and orthogonal to the stream. Linear optimal perturbations and their maximum amplifications over finite time intervals are computed using a scheme based on the direct and adjoint governing equations. It is shown that dominant optimal perturbations are no more the classical streamwise modes and how the flow is two-dimenzionalized for high enough Hartmann numbers. For fixed Reynolds and Hartmann numbers, direct numerical simulations are applied to investigate how the transition to turbulence is affected by the magnetic field. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of bed load transport in turbulent open channel flow

The paper reports on direct numerical simulations of a particle-laden open channel flow carried out to investigate the interaction between the dispersed and the continuous phase. The dispersed phase is represented by an immersed boundary method. The particle-particle collisions are accounted for by a physically motivated collision model. Two cases, one with shear stress below the threshold of mobilization and the other with shear stress above the threshold are considered. The different density ratios lead to different types of modification of the flow field by the formation of density-specific patterns of the particles. Light particles do not attain resting states but saltate evenly distributed in span-wise direction. Heavy particles tend to form stream-wise clusters of inactive particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of mass loading on particle-laden turbulent channel flow

Results are presented for the behavior of particle-laden gases in a moderate Reynolds number vertical channel down flow. The effects of mass loading on the gas-phase turbulence and particle concentration are studied. A direct numerical simulation including models of wall-particle interaction is conducted. It is confirmed that particle feedback causes the turbulence intensities to become more non-isotropic as the particle loading is increased. The particle concentration exhibits a maximum close to the wall and a slight increase in the middle of the channel. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hot-wire measurement in turbulent flow behind a parallel-line heat source

An interaction of the free turbulent shear flow and the steady temperature field, which develops to the homogeneity, was studied. The temperature field was generated by parallel thin heated wires. The isotropic grid turbulence is supposed. Heated wire generates large cross temperature gradients and development of the temperature field was investigated experimentally. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow

In the present study, a theoretical model is proposed to predict the vertical distribution of suspended sediment in open channel turbulent flow. We derive our mathematical model based on the six prominent hydrodynamic mechanisms, which are upward sediment flux due to the turbulent diffusion, downward gravitational settling of the sediment, hindered settling phenomenon, secondary current, fluid induced lift force on the suspended particles and the gradient of Reynolds normal stress of the suspended sediment. The importance of the hydrodynamics is described by the changes of suspended sediment concentration profile in terms of the particle-flow interaction caused by those mechanisms. We also address the significance of the co-existence of those mechanisms for estimating the suspended sediment concentration profile. The present model agrees satisfactorily with a wide spectrum of experimental data in available literature. Unlike the previous researchers, we select a broad range of previously published models of vertical sediment concentration distribution for comparison analysis, and the proposed model shows better prediction accuracy which is confirmed by error analysis.     

Characterisation of bubble clusters in simulations of upward turbulent channel flow

The paper reports on Direct Numerical Simulations of bubble-laden flows performed to investigate the interaction of bubbles with turbulence in an upward flow between two parallel vertical plates. Two simulations are presented with uniform bubble diameter and a third one with bi-disperse bubbles. Three different approaches are used to characterize bubble clustering in the investigated configuration. Horizontal pairing and tendency to form cluster has been found for all reported cases, slightly less pronounced in the bi-disperse swarm. Among other results, a 60°-alignment has been found by means of the angular pair correlation function for the mixed pairs in the bi-disperse swarm. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS and scaling law analysis of compressible turbulent channel flow

Fully developed compressible turbulent channel flow (Ma = 0.8, Re = 3300) is numerically simulated, and the data base of turbulence is established. The statistics such as density-weighted mean velocity and RMS velocity fluctuations in semi-local coordinates agree well with those from other DNS data. High order statistics (skewness and flatness factors) of velocity fluctuations of compressible turbulence are reported for the first time. Compressibility effects are also discussed. Pressure-dilatation absorbs part of the kinetic energy and makes the streaks of compressible channel flow more smooth. The scaling laws of compressible channel flow are also discussed. The conclusions are: (a) Scaling law is found in the center area of the channel, (b) In this area, ESS is also found, (c) When Mach number is not very high, compressibility has little effect on scaling exponents.     

Electromagnetic flow control in liquid metals using Lorentz force techniques

Flow measurement and flow control in opaque and aggressive liquids such as metal melts are challenging tasks in industrial fluid mechanics. Optical measurement techniques as well as submerging probes or control units cannot be applied in case of highly severe environment; hence, contactless electromagnetic methods are of interest for practical flow control because of relatively high electrical conductivity of investigated materials. In this paper we present working principle and experimental results of two such contactless techniques. First, time-of-flight Lorentz force velocimetry (LFV), which allows to determine the flow rate of liquid metal without information about any fluid properties or magnetic field magnitude by cross-correlation of two Lorentz force signals. Secondly, Lorentz torque velocimetry (LTV) - a technique, which uses an electromagnetic pump with a torque sensor connected to the pump's shaft. In the methods so-called Lorentz force [1] is measured, which has electromagnetic nature and is proportional to velocity and flow rate of conductive liquid. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some studies on transition from laminar to turbulent flow in a two-dimensional channel

Zusammenfassung In einem Wasserkanal wurden Versuche über den laminar-turbulenten Umschlag einer zweidimensionalen Strömung durchgeführt. Geschwindigkeitsmessungen der vorderen und hinteren Randzonen von künstlich erzeugten Turbulenz-Kernen ergaben eine (auf die mittlere Strömungsgeschwindigkeit und die Kanaltiefe bezogene) kritische Reynolds-Zahl von 1025±25. Messungen der Intermittenz längs des Kanals bei den Reynolds-Zahlen 3460, 3570 und 3850 zeigten, dass die Umschlagstheorie nach Emmons auch für Kanalströmung sinnvoll ist.     

A study of effects of wall-normal rotation on the turbulent channel flow

The effects of the wall–normal rotation on the turbulence channel flow have been studied. A series of direct numerical simulations have been performed with various rotation rates for Reynolds number 180 based on the friction velocity in the non–rotating case. All remarkable changes are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of wall conductivity on turbulent channel flow under spanwise magnetic field

The effect of wall conductivity on turbulence in electrically conducting fluid in the presence of a constant magnetic field is considered. A channel flow with a spanwise magnetic field is analyzed using high-resolution direct numerical simulations performed for the case of low magnetic Reynolds number. It is found that the effect of suppression of wall-normal momentum transfer and reduction of wall friction identified earlier for the flow with perfectly insulating walls is enhanced if the walls are electrically conducting. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Simulation and analysis of turbulent MHD channel flow with a streamwise magnetic field

We perform large-eddy simulations of turbulent MHD channel flow with a streamwise magnetic field using a pseudo spectral method. The streamwise magnetic field leads to turbulent drag reduction due to the selective Joule damping of certain flow structures. Near the walls, the turbulent mean velocity profile retains the logarithmic layer but the von Karman constant decreases with increasing magnetic field strength. In the outer region, the flow is characterized by persistent streaky structures of large streamwise extent, which lead to a rather flat mean velocity profile. In addition, the streamwise velocity fluctuations develop a pronounced second peak upon increasing the magnetic induction as well as a second logarithmic layer that increases in steepness. We find that Prandtl's classical mixing-length model with a variable Kármán constant can describe the modified logarithmic layer reasonably accurately in a wide range of Reynolds and Hartmann numbers. However, the flow modification near the center of the channel is not properly captured by this approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)