Basil F. Picologlou

Linear stability analysis for high-velocity boundary layers in liquid-metal magnetohydrodynamic flows

Abstract This paper presents a linear stability analysis for the fully developed liquid-metal now in a constant-area rectangular duct with thin metal walls and with a strong, uniform, transverse magnetic field. For the steady flow, there are large velocities inside the boundary layers adjacent to the sides which are parallel to the applied magnetic field. There are two independent eigenvalue problems for the linear stability of the high-velocity side layers. The first problem involves disturbance vorticity which is perpendicular to the magnetic field, and these disturbances decay for all wavelengths and Reynolds numbers. The second problem involves disturbance vorticity which is parallel to the magnetic field, and the critical Reynolds number for these disturbances is 313. The critical disturbance involves a short axial scale and a high velocity in the direction perpendicular to the side. Both of these characteristics have positive implications for the heat transfer through this boundary layer. This heat transfer is important in liquid-lithium cooling systems or “self-cooled blankets” for magnetic confinement fusion reactors. In such blankets, a high-velocity boundary layer occurs adjacent to the “first wall”, which faces the fusing plasma.

Experimental and Analytical Investigations of Magnetohydrodynamic Flows Near the Entrance to a Strong Magnetic Field

ABSTRACTAn experimental program on liquid metal MHD phenomena relevant to blanket engineering is being carried out at ANL’s ALEX facility. The experiments carried out at the facility are aimed towards detailed measurements of 3-D MHD flow characteristics to enlarge the existing data base and to provide validation of exisiting analytical approaches. Results of the first series of experiments, dealing with three dimensional MHD effects in a circular thin conducting wall duct in the fringing field of a strong transverse magnetic field, are reported. Comparison of the experimental data with the predictions of pretest analysis both supports the basic premises on which the analysis is based and suggests possible improvements.

Liquid-metal MHD flow in rectangular ducts with thin conducting or insulating walls: laminar and turbulent solutions

Abstract This paper treats the steady, fully-developed flow of a liquid metal in a rectangular duct of constant cross-section with a uniform, transverse magnetic field. Thin conducting wall boundary conditions at the top/bottom walls (perpendicular to the magnetic field) are extended to allow electrical currents to return through either the wall or the Hartmann layers. Hence, a unified analysis of flows in ducts with wall conductance ratios in the range of interest of fusion blanket applications, namely, from thin conducting to insulating wall ducts, is conducted. The flow in laminar and turbulent regimes is investigated through a composite core-side-layer spectral collocation solution which explicitly resolves the flow in the side layers (parallel to the magnetic field) even for very large Hartmann numbers. Turbulent profiles are obtained through an iterative scheme in which turbulence is introduced through an eddy viscosity model from the renormalization group theory of turbulence [Yakhot, V. and Orsag, S.A., J. Sci. Comput. , 1986, 1 (1), 3]. The transition from a flow in a duct with thin conducting walls to one with insulating walls is clearly displayed by varying the wall conductance ratio from 0.05 to 0 for Hartmann numbers in the range 10 3 –10 5 . In turbulent regime, Reynolds numbers vary in the range 5 × 10 4 –5 × 10 5 . For thin conducting wall duct flows, turbulence is concentrated in the increased side layers while the core remains unperturbed. In insulating wall ducts, the flow remains in the laminar regime within the considered range of Reynolds numbers.

MHD considerations for a self-cooled liquid lithium blanket

The magnetohydrodynamic (MHD) effects can present a feasibility issue for a self-cooled liquid metal blanket of magnetically confined fusion reactors, especially inboard regime of a tokamak. This pressure drop can be significantly reduced by using insulated wall structure. A self-healing insulating coating has been identified, which will reduce the pressure drop by more than a factor of 10. The future research direction to further quantify the performance of this coating is also outlined.

Magnetohydrodynamic Flow in a Manifold and Multiple Rectangular Coolant Ducts of Self-Cooled Blankets

AbstractThe magnetohydrodynamic flow of a liquid metal through a manifold that feeds an array of electrically coupled rectangular ducts with thin conducting walls is investigated. This geometry is typical of an inlet/outlet manifold servicing arrays of poloidal coolant channels in tokamak self-cooled blankets. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, which are relevant to liquid-metal flows in self-cooled tokamak blankets, viscous and inertial effects are confined to very thin boundary layers adjacent to the walls. The analysis for obtaining three-dimensional solutions outside these layers is described, and numerical solutions are presented. Electrical coupling between the common manifold and the coolant ducts, as well as coupling among the coolant ducts themselves, necessitates simultaneous solutions for the multiple channels, and uniquely determines the partition of the total flow rate amo...

Heat transfer in laminar and turbulent liquid-metal MHD flows in square ducts with thin conducting or insulating walls

Abstract The heat transfer in fully-developed liquid-metal flows in a square duct with a uniform, transverse magnetic field is analyzed. Velocity profiles obtained for laminar and turbulent regimes [Cuevas, S., Picologlou, B. F., Walker, J. S. and Talmage, G., Int. J. Engng Sci. , 1997, 35 , 485] are employed to solve the heat transfer equation through finite differences, in a duct with one side wall (parallel to the magnetic field) uniformly heated and three adiabatic walls. Turbulent effects are introduced through eddy viscous and thermal diffusivity models from the renormalization group theory of turbulence [Yakhot, V. and Orszag, S. A., J. Sci. Comput. , 1986, 1 (1), 3]. Analysis focuses in determining how the structure of the side-layer flow, influenced by the wall conductance ratio and Hartmann and Peclet numbers in the ranges of interest of fusion blanket applications, affects the heat transfer processes. Numerical calculations for liquid lithium show that for thin conducting wall duct cases, the laminar MHD heat transfer mechanism, characterized by high-velocity side-wall jets, appears to be more efficient than turbulent mixing in the boundary layer for a given Peclet number.

Liquid-metal flow in a rectangular duct with thin metal walls and with a non-uniform magnetic field

Abstract This paper treats the steady flow of an electrically conducting, incompressible liquid in a duct with a constant rectangular cross section, with thin, electrically conducting walls and with a non-uniform transverse magnetic field which is parallel to two duct walls. With the x axis along the centerline of the duct, the dimensionless magnetic field B = B x (x, y) x + B x (x, y) y , where x and ŷ are Cartesian unit vectors, while Bx and By are odd and even functions of y, respectively. For a small magnetic Reynolds number, Bx and By satisfy the Cauchy-Riemann equations and boundary conditions at the pole faces of the external magnet. Previous treatments have used a simplified magnetic field B = B y (x) y , even though this field does not satisfy the Cauchy-Riemann equations. We consider a magnetic field in which By at the plane of symmetry varies from 0.98 to 0.54 over a short axial distance. For this field the maximum values of Bx and of the y variation of By are 0.25 and 0.125 in the liquid-metal region. These values are certainly significant, but they are neglected in the simplified magnetic field model. Nevertheless the results for the simplified and complete magnetic fields are virtually identical, so that the simplified field gives excellent results. Previous treatments have also assumed that the Hartmann number M is large. A possible error arises from the implicit assumption that α = cM 1 2 ⪢1 , where c is the wall conductance ratio, while realistic values of a are generally not particularly large. Comparison of the three-dimensional results for α⪢1 and for α = O(1) reveals that the results for α⪢1 can be corrected with simple scaling factors derived from much simpler solutions for fully developed flow.

Techniques for measurement of velocity in liquid-metal MHD flows

Three instruments for measuring local velocities in liquid-metal MHD experiments for fusion blanket applications are being evaluated. The devices are used in room-temperature NaK experiments to measure three-dimensional flow field patterns anticipated in complex blanket geometries. Hot film anemometry, a standard technique in ordinary fluids, is being used, as well as two developmental devices. One is called the Liquid Metal Electromagnetic Velocity Instrument (LEVI), and performs essentially as a local dc electromagnetic flow meter. The third device, a Thermal Transient Anemometer (TTA) is a rugged, yet relatively simple device, which measures local velocity through the mechanism of convective heat transfer, in some ways similar to hot-film anemometry. Results are presented showing the kinds of data collected this far with each instrument. Measurements include both local velocity measurements and some preliminary frequency analyses of the fluctuating signals from both a hot-film sensor and the LEVI device.

Experimental Facility for Studying MHD Effects in Liquid Metal Cooled Blankets

AbstractThe capabilities of a facility, brought into service to collect data on magnetohydrodynamic (MHD) effects pertinent to liquid-metal-cooled fusion reactor blankets, are presented. The facility, designed to extend significantly the existing data base on liquid metal MHD, employs eutectic NaK as the working fluid in a room-temperature closed loop. The instrumentation system is capable of collecting detailed data on pressure, voltage, and velocity distributions at any axial position within the bore of a 2 Tesla conventional electromagnet. The axial distribution of the magnetic field can be uniform or varying with either rapid or slow spatial variations. The magnet gap dimensions, for the uniform field of 2T, are 15.3 cm high × 0.76 m wide × 1.83 m long. NaK was circulated in December 1984 and the magnet was energized in March 1985. Shakedown tests in a round pipe test section are currently underway.

Experimental Investigations of MHD Flow Tailoring for First Wall Coolant Channels of Self-Cooled Blankets

Results of experiments on the concept of flow tailoring, the use of salient features of MHD flows in strong magnetic fields to create desirable velocity profiles in the coolant ducts of the first wall and the blanket, are reported. Proof-of-principle testing of flow tailoring has been chosen as the first joint activity on liquid metal MHD between Argonne National Laboratory (ANL) and Kernforschungszentrum Karlsruhe (KfK) because flow tailoring offers the possibility of significant improvement in blanket design and performance. The joint tests are conducted at ANLs ALEX facility on a test article fabricated at KfK. A 3-D MHD thermal hydraulic code developed at ANL is used to demonstrate the increased thermal performance of first wall coolant channels with flow tailoring. Sample results of detailed measurements of velocity and voltage distributions are compared to theoretical predictions provided by analytical tools developed at ANL with the collaboration of the University of Illinois.