Turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field in the region of hydrodynamic stabilization

Numerical simulation is performed of turbulent pipe flow in the vicinity of entry to longitudinal magnetic field. Use is made of the model of turbulence developed by the present author and previously employed for performing calculations in the region of stabilized flow and heat transfer. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on the hydraulic drag coefficient and longitudinal component of velocity vector.     

The calculation of heat transfer and resistance under conditions of stabilized turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field

The model of turbulence, developed previously for a flow in the field of mass forces (buoyancy, Coriolis) and for an unsteady flow, is applied to the case of liquid flow in magnetic field. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on heat transfer and resistance obtained in the region of stabilized flow and heat transfer.     

Hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic time variation of the flow rate

The available experimental and theoretical studies of hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic increase or decrease of the flow rate are reviewed and analyzed. The reason is found why the effect of hydrodynamic nonstationarity on heat transfer and skin friction coefficient turns out to be different from that in the case of laminar flow. The differences in this effect on heat transfer and drag are treated. The experimentally observed effects are reproduced most accurately when simulated on the basis of equations for turbulent stresses and heat fluxes.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 2, 2005, pp. 212–222.Original Russian Text Copyright © 2005 by E. P. Valueva.     

Heat transfer and resistance to movement in a rotationally advancing flow of conducting liquid in the presence of a magnetic field

Conclusions The functional relationships thus obtained for the resistance and heat-transfer coefficients in a rotationally-advancing flow of a conducting liquid in a pipe with a constant internal axial magnetic field and small Reynolds magnetic numbers (Re_m1) contains only a single longitudinal magnetic field strength component equal in the above case to the external magnetic field strength. It follows from the above that the formulas thus obtained hold both in the case when the flowing liquid does not perform any useful work, i.e., when electrical energy is not tapped off (or injected) in the form of a current, and for the case when it is tapped off (or injected).The difference consists only in the fact that in the second instance the velocity of the liquid drops along the pipe according to the amount of the work thus obtained (and, obviously, to the work in overcoming the resistance forces). In the first instance the reduction in the velocity is due only to the overcoming of the resistance forces.It is appropriate to note that formulas (17), (18), (20), and (21) for H_o=0 are converted into corresponding formulas for a rotationally-advancing liquid flow in a pipe without a magnetic field. The latter formulas are adequately confirmed by practical experience (see [2]). This provides grounds for assuming that the formulas will also be fully confirmed in practice.Translated from Izmeritel'naya Tekhnika, No. 5, pp. 41–45, May, 1968.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Pulsating high-frequency flow

An integral method is suggested for approximate calculation of oscillation-period average heat transfer and drag under conditions of pulsating high-frequency flow of gas in a pipe with constant density of heat flux to the wall. It is found that the flow rate oscillation superimposed on the flow has little effect on the period average Nusselt number and coefficient of friction drag; these quantities may be calculated by the method developed for a steady-state flow of liquid of variable properties. The oscillation affects significantly the period average coefficient of hydraulic drag whose values increase with the amplitude of superimposed oscillation.     

Heat transfer in turbulent non-Newtonian flow

The effect of non-Newtonian Prandtl number on the distribution of resistance to heat transfer is examined. Two new analogies between heat and momentum transfer are developed, one of which is shown, by comparison with experiment, to be superior to another more complex and recently published analogy-type expression. It is concluded that more accurate information is needed on conditions near the wall before reliable characterization of heat transfer can be made in such systems.     

Heat transfer on the middle generatrix of a horizontal pipe in the turbulent flow of low-temperature helium

Results are presented from an experimental study of heat transfer in a turbulent helium flow under conditions of forced and mixed convection in horizontal pipes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 3, pp. 357–362, March, 1984.     

On the space-charge longitudinal wake field in perfectly conducting pipe of planar geometry

Longitudinal space-charge wake field is considered for a beam of rectangular cross-section propagating between two perfectly conducting planes. It is shown that the forces driving negative mass instability are weaker compared to circular configuration. A similar effect takes place for a flattened (ribbon) beam.     

Free-surface flow of liquid oxygen under non-uniform magnetic field

The paramagnetic property of oxygen makes it possible to control the two-phase flow at cryogenic temperatures by non-uniform magnetic fields. The free-surface flow of vapor-liquid oxygen in a rectangular channel was numerically studied using the two-dimensional phase field method. The effects of magnetic flux density and inlet velocity on the interface deformation, flow pattern and pressure drop were systematically revealed. The liquid level near the high-magnetic channel center was lifted upward by the inhomogeneous magnetic field. The interface height difference increased almost linearly with the magnetic force. For all inlet velocities, pressure drop under 0.25 T was reduced by 7–9% due to the expanded local cross-sectional area, compared to that without magnetic field. This work demonstrates the effectiveness of employing non-uniform magnetic field to control the free-surface flow of liquid oxygen. This non-contact method may be used for promoting the interface renewal, reducing the flow resistance, and improving the flow uniformity in the cryogenic distillation column, which may provide a potential for enhancing the operating efficiency of cryogenic air separation.     

Heat transfer under conditions of plane potential flow past obstacles

An exact solution is given of the equation of convective heat transfer (mass transfer) under conditions of plane potential flow of incompressible liquid along a wall which has a bend in the form of a half-ellipse to present an obstacle to incident flow. The temperature of the obstacle surface is arbitrary, and the temperature of the rest of the wall coincides with that of incident flow. Particular cases of the constant temperature of the obstacle and of the sine distribution of its surface temperature are treated.     

Investigation of heat transfer and hydrodynamic drag in the turbulent flow of a gas in the field of a longitudinal pressure gradient of variable sign. I

We present results from a study of heat transfer and hydrodynamic drag in the turbulent flow of a gas through a channel formed by a series of flat nonsymmetric diffusers with a divergence angle of 12° and a series of converging diffuser sections, for the interval Re =(10–80)·10³.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 4, pp. 581–591, April, 1969.     

Heat transfer during film boiling of a subcooled liquid under conditions of forced flow through channels

An experimental study of heat transfer during the film boiling of subcooled liquid nitrogen in pipes with the Reynolds number Re=80,000-1,500,000 and=0.20–0.95 is reported.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 4, pp. 610–613, April, 1972.     

The Lorentz forces on an electrically conducting sphere in analternating magnetic field

A method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic field is developed. The crux of this method lies in expressing the external magnetic held and the eddy current density in the sphere in terms of a “source function” of the current sources and a “skin depth dependent function”. The general formula for the Lorentz force is used to derive the special case of a sphere in an axisymmetric stack of circular current loops. Numerical results for this case are presented as a function of the stack geometry. Approximations of the skin depth functions for practical situations are presented. Finally, a procedure to determine the magnetic pressure distribution on the surface of a levitated liquid metal droplet is given     

An experimental investigation of liquid metal flow past a cylinder in longitudinal magnetic field

The distribution of pressure on the surface of a cylinder is obtained as a result of experimental investigation; this distribution significantly varies with increasing magnetic induction compared to the flow past a cylinder in the absence of magnetic field. In so doing, the pressure drag coefficient of the cylinder significantly increases. The measurements of velocity profiles reveal that the extent of the region of stagnant flow before the cylinder (the so-called “leading” wake) increases with magnetic induction. The dependence of axial defect of velocity on the MHD interaction parameter is obtained; this dependence under conditions of flow in a strong magnetic field is unaffected by the shape of the body subjected to flow, as is confirmed by the results of experiment involving the flow past a plate.