VERIFICATION OF ELECTRICALLY CONDUCTIVE FLUID FLOW CALCULATION IN CIRCULAR PIPES

Magnetohydrodynamics (MHD) treats the phenomena that arise in fluid dynamicsfrom the interaction of an electrically conducting fluid with the electromagnetic field. Thedevelopment of computational hydrodynamics has significantly improved the accuracy ofcalculations on mathematical models, but it is still difficult to choose the optimal turbulence models,mesh quality, model parameters to solve a particular problem. The aim of the work is to verify thecalculation of the conducting fluid flow in circular pipes and to determine the optimal error of theturbulence model calculation and the parameters of its use. The study was conducted on the basis ofa comparison of experimental studies by the PIV-method of velocimetry with the results of numericalcalculations. The liquid is considered viscous, incompressible, and electrically conducting. Controlnonlinear momentum equations are solved numerically using the method of control volumes.Comparison of velocity profiles showed that almost all models show a fairly good match with theresults of the experiment. Analysis of the sum of squares residuals of calculation points fromexperimental shows that the BSL Reynolds Stress turbulence model is the best for the flow withoutthe influence of the magnetic field, and the k-ɛ model is the best in the presence of a magnetic field.The SST k-ω model has quite enough results regardless of the Hartmann number. The number ofmesh elements has little effect on the ac-curacy of the pressure drop calculation. For simplegeometries it is enough to use meshes with the number of elements that does not exceed the 500000elements. According to all criteria, it is rational to choose the k-ɛ turbulence model for furthercalculations. This model has some shortcomings in the calculation of wall layers, but allows to obtainhigh-quality and adequate results for the flow of conducting fluid with a limit on the mesh elementsnumber.

Viscous micropump of immiscible fluids using magnetohydrodynamic effects and a power-law conducting fluid

Small-scale fluid transport methods have grown significantly in recent years, mainly in applications in microfluidic systems. Therefore, the present study analyzes the movement of two-layers of immiscible fluids within a parallel flat plates microchannel. The fluid layers are composed of a Newtonian fluid and a power-law fluid. The pumping is produced by magnetohydrodynamics effects that act on the non-Newtonian conducting fluid dragging the non-conducting Newtonian fluid by viscous forces. Under the consideration of a laminar, incompressible, and unidirectional flow, the dimensionless mathematical model is established by the momentum equations for each fluid, together with the corresponding boundary conditions at solid-liquid and liquid-liquid interfaces. The problem formulation is semi-analytically solved using the Newton-Raphson method. The results are presented as a function of the velocity profiles and flow rate, showing interesting behaviors that depend on the physical and electrical properties of each fluid and flow conditions via the dimensionless parameters such as the flow behavior index, a magnetic parameter related to Lorenz forces, the fluids viscosity ratios and the dimensionless liquid-liquid interface position. This work contributes to the understanding of the various immiscible non-conducting fluids pumping techniques that can be used in microdevices.

Analysis of the Magnetohydrodynamic Behavior of the Fully Developed Flow of Conducting Fluid

Important industrial applications are based on magnetohydrodynamics (MHD), which concerns the flow of electrically conducting fluids immersed in external magnetic fields. Using the Finite Volume Method, we performed a 3D numerical study of the MHD flow of a conducting fluid in a circular duct. The flow considered was laminar and fully developed. Along the initial section of the duct, there were magnets placed around the duct producing magnetic fields in the radial direction. Two arrangements of magnetic field orientation were considered: fields pointing toward and away from the duct’s center alternately, and all fields pointing toward the duct’s center. For each arrangement of magnets, various intensities of magnetic fields were considered to evaluate two effects: the influence of the magnetic field on the flow velocity, and the influence of the flow velocity on magnetic field induction. It was found that for the second arrangement of magnets and Hartmann numbers larger than 10, the flow velocity was reduced by as much as 35%, and the axial magnetic induction was as high as the field intensity applied by each magnet. Those effects were negligible for the first arrangement and low fields because of the distribution of field lines inside the duct for these situations.