Showing papers on "Hartmann number published in 2003"

Hartmann wave-front measurement at 13.4 nm with lambdaEUV/120 accuracy.

Abstract: We report, for the first time to our knowledge, experimental demonstration of wave-front analysis via the Hartmann technique in the extreme ultraviolet range. The reference wave front needed to calibrate the sensor was generated by spatially filtering a focused undulator beam with 1.7- and 0.6-microm-diameter pinholes. To fully characterize the sensor, accuracy and sensitivity measurements were performed. The incident beam's wavelength was varied from 7 to 25 nm. Measurements of accuracy better than lambdaEUV/120 (0.11 nm) were obtained at lambdaEUV = 13.4 nm. The aberrations introduced by an additional thin mirror, as well as wave front of the spatially unfiltered incident beam, were also measured.

Nonlinear peristaltic transport of mhd flow through a porous medium

Abstract: In order to determine the characteristics of peristaltic transport of magnetohydrodynamic flow through a porous medium, the motion of a hydromagnetic (electrically conducting), viscous, and incompressible fluid in planer channel filled with a homogeneous porous medium and having electrically insulated walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength was analyzed using a perturbation expansion in terms of a variant wave number. We obtain an explicit form for the velocity field, a relation between the pressure rise and flow rate, in terms of Reynolds number, wave number, Hartmann number, permeability parameter, and the occlusion. The effects of all parameters of the problem are numerically discussed and graphically explained. 2000 Mathematics Subject Classification: 76S05. 1. Introduction. Peristalsis is now well known to the physiologists as one of the major mechanisms for fluid transport in many biological systems. In particular, peristaltic mechanism may be involved in swallowing food through the oesophagus, urine transport from kidney to bladder through the ureter, movement of chyme in the gastrointestinal tract, transport of spermatozoa in the ductus efferents of the male reproductive tracts and in the cervical canal, movement of the ovum in the fallopian tubes, and in the vasomotion of small blood vessels as well as blood flow in arteries. In addition, peristaltic pumping occurs in many practical applications involving biomechanical systems. Also, finger and roller pumps are frequently used for pumps corrosive or very pure materials so as to prevent direct contact of the fluid with the pump’s internal surfaces. A number of analytical [3, 5, 7, 9, 11, 12, 16, 23], numerical, and experimental [2, 10, 19, 20, 21] studies of peristaltic flow of different fluids have been reported. Several review articles have been written [8, 14]. Also a summary of analytical papers up to 1984 has been presented in [18]. Most of the analytical studies use perturbation series in a small parameter such as Reynolds number or a dimensionless wave number, which, unfortunately, limits the range of validity of the results. However, a perturbation method does provide explicit information about the physical effects of that parameter. Also, the analytical results can be used to check the calculations of wider-range numerical methods.

Non-linear peristaltic transport of magnetohydrodynamic flow in an inclined planar channel

Abstract: In order to determine the characteristics of the peristaltic transport of magnetohydrodynamic gravity flow, the motion of a hydromagnetic (electrically conducting), viscous and incompressible fluid in an inclined planar channel having electrically insulated walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength was analyzed using a perturbation expansion in terms of a variant wave number. We obtain explicit form for the velocity field, a relation between the pressure rise and flow rate, in terms of Reynolds number, wave number, Hartmann number, Froud number, inclined angle, and the occlusion. The effects of all parameters of the problem are discussed numerically and explained graphically. ﺔــﺻﻼﺨﻟا

Heat transfer and hydromagnetic control of flow exit conditions inside oscillatory squeezed thin films

Abstract: The influence of fluids inertia and the effects of the presence of a magnetic field normal to the direction of the flow of an electrically conducting fluid are studied on flow and heat transfer inside a nonisothermal and incompressible thin film undergoing oscillatory squeezing. The governing equations have been nondimensionalized and solved numerically. Further, the influence of the squeezing Reynolds number, thermal squeezing number, Hartmann number, and the squeezing frequency are determined. It is shown that flow instabilities appear at large squeezing Reynolds numbers and that the Nusselt number is affected by inertia effects as a result of increased squeezing Reynolds number. Further, it is found that flow instabilities are reduced when the magnetic field is introduced.

Magneto‐hydrodynamic squeeze film characteristics for finite rectangular plates

Abstract: The squeeze‐film characteristics between two parallel rectangular plates with an electrically conducting fluid in the presence of a transverse magnetic field are analyzed. The squeeze‐film Reynolds equation applicable to the curved surfaces is derived using the continuity equation and the magneto‐hydrodynamic (MHD) motion equations. A closed‐form solution is obtained for the squeeze‐film pressure of parallel rectangular plates, and applied to predict the squeeze‐film behavior. According to the results, the presence of magnetic fields signifies an enhancement in the squeeze‐film pressure. On the whole, the magnetic‐field effect characterized by the Hartmann number provides an increase in value of the load‐carrying capacity and the response time as compared to the classical non‐conducting lubricant case, especially for larger values of the aspect ratio or smaller values of film height.

Weakly nonlinear stability of Hartmann boundary layers

Abstract: By means of a weakly nonlinear stability analysis it is shown that the Hartmann boundary layer presents subcritical instability in the proximity of the minimum linear critical Reynolds number. This gives further support to earlier speculations that finite amplitude effects account for the discrepancies between the results of the linear stability analysis and experimental evidence on laminarisation.

The MTOR LM-MHD Flow Facility, and Preliminary Experimental Investigation of Thin Layer, Liquid Metal Flow in a 1/R Toroidal Magnetic Field

Abstract: Fairly recently, a new experimental free surface liquid metal MHD facility, the so-called MTOR facility, has come on-line, and new data has been taken concerning flows of gallium alloy across a moderately strong toroidal field with characteristic 1/R field gradient. The purpose of these experiments has been two-fold: to gather data for benchmarking currently existing one and two dimensional free surface computational flow models (as well as 3D models currently under development), and to investigate phenomena not predicted by models, especially effects of nozzles, drains, waves and turbulence. Data is presented concerning MHD effects on the mean flow height and wave structure, both with and without the so-called Zakharov magnetic propulsion current added to help control and stabilize the flow. The test section is wide enough so that the characteristic factor (Hartmann Number * Aspect Ratio) is less than unity. In this case the Hartmann layer drag effects are small, allowing comparison of experimental data to two-dimensional axisymmetric models. Preliminary conclusions suggest that the field gradient in these experiments does not adversely affect the stability of the surface, and that magnetic propulsion current is effective in flattening and accelerating the liquid metal flow.

Toroidal flows in resistive magnetohydrodynamic steady states

Abstract: Ideal magnetohydrodynamics (MHD) still provides the mathematical framework and the textbook vocabulary in which the possible states of a toroidal plasma are discussed, generally regarded as static equilibria. This is so, despite the increasing realization that virtually all toroidal magnetofluids have nontrivial fluid flows (finite velocity fields) in them. A very different perspective results from nonideal MHD, including both resistivity and viscosity and invoking nonideal boundary conditions. There, it has been shown that if Ohm’s law and Faraday’s law are given equal importance with force balance, flows are an inevitable consequence of the assumptions of time independence and axisymmetry. Previous treatments of the toroidal steady states for such systems have been based on perturbation theory in which the flow velocity was assumed small, as a consequence of high viscosity (or in dimensionless terms, low Hartmann number H). Here, recently newly available numerical programs are used to lift this limitation and to solve nonlinearly for the allowed steady states of an axisymmetric, current-carrying, toroidal magnetofluid without such an expansion in the Hartmann number. Flow patterns for values of H from ≪1 to ≫1 have been calculated. As H is raised, the flow pattern goes from the predominantly poloidal pair of counter-rotating “convection cells” revealed by the perturbation theory to a pattern in which the toroidal kinetic energy of flow considerably exceeds the poloidal kinetic energy. In no case is the flow discovered a simple rotation.

Magneto-Hydrodynamic Squeeze Film Characteristics Between A Sphere and A Plane Surface

Abstract: Based upon the thin-film magneto-hydrodynamic (MHD) theory, this paper analyzes the squeeze-film characteristics between a sphere and plane surface lubricated with an electrically conducting fluid in the presence of a transverse magnetic field. The MHD Reynolds-type equation governing the squeeze-film pressure is derived using the continuity equation and the magneto-hydrodynamic motion equations. A closed-form solution for the squeezing film pressure is obtained, and applied to predict the MHD squeeze-film characteristics. According to the results obtained, the presence of externally applied magnetic fields signifies an enhancement in the squeeze-film pressure. On the whole, the magnetic-field effects characterized by the Hartmann number produce an increase in value of the load-carrying capacity and the response time as compared to the classical Newtonian-lubricant case. It improves the squeeze film characteristics of the sphere-plane surface system.

Application of Adomian's approximation to blood flow through arteries in the presence of a magnetic field

Abstract: The present investigation deals with the application of Adomian's decomposition method to blood flow through a constricted artery in the presence of an external transverse magnetic field which is applied uniformly. The blood flowing through the tube is assumed to be Newtonian in character. The expressions for the two-term approximation to the solution of stream function, axial velocity component and wall shear stress are obtained in this analysis. The numerical solutions of the wall shear stress for different values of Reynold number and Hartmann number are shown graphically. The solution of this theoretical result for a particular Hartmann number is compared with the integral method solution of Morgan and Young [17].

Rayleigh-Benard convection with magnetic field

Abstract: We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The magnetic field stabilizes, due to the Lorentz force, more or less Rayleigh- Benard convective cellular motion. The solution of the eigenvalue problem shows that the critical Rayleigh number increases with increasing Hartmann number while the corresponding wave length decreases. Interesting analogies to solar granulation and black spots phenomena are obvious. The influence of a horizontal field is stronger than that of a vertical field. It is easy to understand this by discussing the influence of the Lorentz force on the Rayleigh- Benard convection. This result corrects earlier calculations in the literature.

Three-dimensional buoyant convection in a rectangular box with thin conducting walls in a strong horizontal magnetic field

Abstract: Three-dimensional buoyant convection in a rectangular box with electrically conducting walls in the presence of a strong, horizontal magnetic field has been considered. The electric conductance of the six walls is arbitrary. An asymptotic solution to the problem in the inertialess and small Peclet number approximations has been obtained for high values of the Hartmann number, Ha. The solution is valid for an arbitrary temperature distribution resulting from both differential heating of walls and internal heat sources. The three-dimensional flow is characterised by the presence of high-velocity jets at the vertical walls of the cavity. The velocity of the jets is O(Ha 1 / 2 ) times higher than in the bulk of the fluid. For sufficiently high boxes, comparison of the velocity profiles in the middle of a box with fully developed solutions developed previously for infinitely long rectangular ducts gives excellent agreement. Properties of convective flows have been investigated and examples for various temperature distributions have been presented. It has been shown that for wall conductance ratios ∼0.1, the three-dimensional effects are confined to about one value of the characteristic dimension of the duct cross-section at the top and the bottom of the box. The flow pattern has been shown to be very sensitive to symmetries of temperature and to variations of the wall conductance ratios. This property may be used to optimise the convective flow pattern. The numerical code developed on the basis of the asymptotic model is a flexible, fast tool to analyse and optimise convective flows in various blanket designs.

Wall functions for numerical modeling of laminar MHD flows

Abstract: A general wall function treatment is presented for the numerical modeling of laminar magnetohydrodynamic (MHD) flows. The wall function expressions are derived analytically from the steady-state momentum and electric potential equations, making use only of local variables of the numerical solution. No assumptions are made regarding the orientation of the magnetic field relative to the wall, nor of the magnitude of the Hartmann number, or the wall conductivity. The wall functions are used for defining implicit boundary conditions for velocity and electric potential, and for computing mass flow and electrical currents in near wall-cells. The wall function treatment was validated in a finite volume formulation, and compared with an analytic solution for a fully developed channel flow in a transverse magnetic field. For the case with insulating walls, a uniform 20×20 grid, and Hartmann numbers Ha={10,30,100}, the accuracy of pressure drop and wall shear stress predictions was {1.1%,1.6%,0.5%}, respectively. Comparable results were obtained also with conducting Hartmann walls. The accuracy of predicted pressure drop and wall shear stress was essentially independent of the resolution of the Hartmann layers. When applied also to the parallel walls, the wall functions reduced the errors by a factor two to three. The wall functions can be implemented in any general flow solver, to allow accurate predictions at reasonable cost even for complex geometries and nonuniform magnetic fields.

MHD simulation of the liquid metal/helium gas dual-cooled waste transmutation blanket for FDS

Abstract: Numerical simulation of magnetohydrodynamic (MHD) flow is implemented by using the commercial code package PHOENICS, in which the momentum source term of Lorentz force is added by applying FORTAN subroutine Assuming simplified condition of a square duct, the numerical approach is applied to simulate the velocity profile in MA-zone in the design of dual-cooled waste transmutation blanket (DWTB) for a fusion-driven sub-critical system (FDS) The high velocity of closing FW side will improve the heat transfer between liquid metal and the walls of duct, due to high Hartmann number, but the MHD pressure drop will be increased The compromise between the heat transfer and MHD pressure drop can be taken as reference for the design of the transmutation blanket

Current-induced instabilities of hydromagnetic flow in a small gap between rotating conducting cylinders

Abstract: In considering the stability of an electrically conducting fluid between rotating perfectly conducting cylinders with a current-induced pressure gradient acting in the azimuthal direction and with an applied axial magnetic field, the assumption of small-gap approximation is made and the governing equations with respect to both axisymmetric and non-axisymmetric disturbances are solved by a direct numerical procedure. A parametric study covering wide ranges of Q, the Hartmann number which represents the strength of the axial magnetic field, and β, a parameter characterizing the ratio of current-induced and rotation velocities, is conducted for the situation where the outer cylinder is stationary and the inner cylinder is rotating. It is found that the stability characteristics are thoroughly different from those of the case of weakly conducting walls. The variation of the onset mode is shown in the (β, Q)-plane, and the transition of the corresponding neutral curves is discussed in detail. Results for the critical Taylor number and wavenumber pertaining to the critical disturbances are presented. The critical values of radial current density required for the onset of instability are also determined.

Voltage-Driven Instability of Electrically Conducting Fluids

Abstract: This paper consists of two parts dealing with magnetohydrodynamic pinch instabilities in cylindrical and in planar geometry.