A numerical model of annular linear induction pump with a full-scale pump channel is created to study the scale-dependent instability of the magnetohydrodynamic flow. The magnetic-fluid coupling effect is implemented by modifying the underlying governing equations and constraints. The model authenticity is validated by comparing the simulated pressure difference, as well as the pressure pulsation, with the previous experimental data. The flow patterns at different flow rates corresponding to different magnetic Reynolds numbers are depicted from both the azimuthal and meridian viewpoints, and the periodicity of the occurring vortex flows is found in the pump. By analyzing the different mechanisms contributing to the fluid kinetic energy, it is found the competition between the axial components of the Lorentz force and pressure gradient dominates the flow evolution in the pump channel. The magnetic-fluid coupling effect is found to amplify the disturbances in either the magnetic field or the fluid field. It is even effective within the uniform externally imposed magnetic field and inlet velocity only if a disturbance exists in the initial flow. Increase in the cycle number of disturbance can enhance the flow stability and induce smaller vortex flows. Finally, different mechanisms of energy conversion in the pump are analyzed and it is found that the sudden occurrence of vortex flows can induce large current density, which significantly increases the Ohmic dissipation and decreases the efficiency of energy conversion from magnetic field into the fluid. The relatively large Ohmic dissipation in the fluid is the main reason for the low efficiency of such a device.

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Flow instability is the intricate phenomenon in the Annular Linear Induction Pump when the pump runs at off-design working condition. A 3D numerical model is built to simulate the flow in the pump channel. The pump heads at different flow rates are accurately predicted by comparing with experiment. The simulation results show the fluid velocity is circumferentially non-uniform in the pump channel even at the nominal flow rate. The flow in the middle sector continuously decelerates to nearly zero with the reducing flow rate. Reversed flow occurs in the azimuthal plane, followed by vortex flow. The reason for the heterogeneous velocity field is attributed to the mismatch between non-uniform Lorentz force and relatively even pressure gradient. It is seen that the flow in the region of small Lorentz force has to sacrifice its velocity to match with the pressure gradient. An analytic expression of the axial Lorentz force is then developed and it is clearly demonstrated the Lorentz force could be influenced by the profiles of velocity and radial magnetic flux density. The coupling between velocity and magnetic field is studied by analyzing the magnitudes of different terms in the dimensionless magnetic induction equation. It is found the dissipation term is determined not only by the magnetic Reynolds number but the square of wave number of the disturbance in each direction. The smaller disturbing wave number weakens the dissipating effect, resulting in the larger non-uniform magnetic field and axial Lorentz force.