We study the flow in a layer of conductive liquid under the influence of surface tension, gravity, and Lorentz forces due to imposed potential differences and transverse magnetic fields, as a function of the Hartmann number, the Bond number, the Reynolds number, the capillary number and the height-to-width ratio A. For aspect ratios A 1 and Reynolds numbers Re≤A, lubrication theory is applied to determine the steady state shape of the liquid surface to lowest order. Assuming low Hartmann (Ha ≤ O(1)), capillary (Ca ≤ O(A4)), Bond (Bo ≤ O(A2)) numbers and contact angles close to 90°, the flow details below the surface and the free surface elevation for the complete domain are determined analytically using the method of matched asymptotic expansions. The amplitude of the free surface deformation scales linearly with the capillary number and decreases with increasing Bond number, while the shape of the free surface depends on the Bond number and the contact angle condition. The strength of the flow scales linearly with the magnetic field gradient and applied potential difference and vanishes for high aspect ratio layers (A → 0). The analytical model results are confirmed by numerical simulations using a finite volume moving mesh interface tracking method, where the Lorentz force is calculated from the equation for the electric potential. It is shown that the analytical result for the free surface elevation is accurate within 0.4% from the numerical results for Ha2 ≤ 1, Ca ≤ A4, Bo ≤ A2, Re ≤ A and A ≤ 0.1 and within 2% for A=0.5. For A=0.1, the solution remains accurate within 1% of the numerical solution when either Ha2 is increased to 400, Ca to 200A4 or Bo to 100A2.@en

Control of self-sustained jet oscillations in confined cavities is of importance for many industrial applications. It has been shown that the mechanism underlying these oscillations consists of three stages: (i) growth of the oscillation, (ii) amplitude limitation and (iii) delayed destruction of the recirculation zone bounding the jet. It has also been shown that oscillations may be enhanced or suppressed by applying (e.g. electromagnetic) body forces. In the current paper we study the influence of electromagnetic forces oriented aligned with or opposite to the direction of the jet on the oscillation mechanism. The influence of the forcing is found to depend on the Stuart number N in relation to a critical Stuart number Ncrit. We demonstrate that for |N| < Ncrit , the oscillation mechanism is essentially unaltered, with moderate modifications in the jet oscillation amplitude and frequency compared to N=0N=0. For N > Ncrit, electromagnetic forcing leads to total suppression of the self-sustained oscillations. For N < Ncrit , electromagnetic forces dominate over inertia and lead to strongly enhanced oscillations, which for N≪−NcritN≪−Ncrit become irregular. As was earlier demonstrated for N=0,N=0, the present paper shows that for −6Ncrit<N<Ncrit−6Ncrit<N<Ncrit the oscillatory behaviour, i.e. frequencies, oscillation amplitudes and wave shapes, can be described quantitatively with a zero-dimensional model of the delay differential equation (DDE) type, with model constants that can be a priori determined from the Reynolds and Stuart number and geometric ratios. @en

The influence of electromagnetic forcing on self-sustained oscillations of a jet issuing from a submerged nozzle into a thin vertical cavity (width W much larger than thickness T) has been studied using particle image velocimetry. A permanent Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field from three permanent magnets across its thickness. As a working fluid a saline solution is used. The magnetic field is in the north-southnorth configuration, such that the Lorentz force can be applied in an up-down-up configuration or in a down-up-down configuration by switching the direction of the electrical current. A critical Stuart number N-c was found. For N N-c and an oscillation enhancing up-down-up configuration of the Lorentz force, St grows with N as St. v N. In contrast, for N > N-c and an oscillation suppressing down-up-down configuration of the Lorentz force, all jet oscillations are suppressed. (C) 2014 AIP Publishing LLC.@en

The influence of electromagnetic forcing on self-sustained oscillations of a jet issuing from a submerged nozzle into a thin vertical cavity (width W much larger than thickness T) has been studied using particle image velocimetry. A permanent Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field from three permanent magnets across its thickness. As a working fluid a saline solution is used. The magnetic field is in the north-southnorth configuration, such that the Lorentz force can be applied in an up-down-up configuration or in a down-up-down configuration by switching the direction of the electrical current. A critical Stuart number N-c was found. For N N-c and an oscillation enhancing up-down-up configuration of the Lorentz force, St grows with N as St. v N. In contrast, for N > N-c and an oscillation suppressing down-up-down configuration of the Lorentz force, all jet oscillations are suppressed. (C) 2014 AIP Publishing LLC.@en

The influence of electromagnetic forcing on self-sustained oscillations of a jet issuing from a submerged nozzle into a thin vertical cavity (width W much larger than thickness T) has been studied using particle image velocimetry. A permanent Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field from three permanent magnets across its thickness. As a working fluid a saline solution is used. The magnetic field is in the north-southnorth configuration, such that the Lorentz force can be applied in an up-down-up configuration or in a down-up-down configuration by switching the direction of the electrical current. A critical Stuart number N-c was found. For N N-c and an oscillation enhancing up-down-up configuration of the Lorentz force, St grows with N as St. v N. In contrast, for N > N-c and an oscillation suppressing down-up-down configuration of the Lorentz force, all jet oscillations are suppressed. (C) 2014 AIP Publishing LLC.@en

The flow from a submerged bifurcated nozzle into rectangular liquid-filled cavities with width-to-thickness ratios W/T = 6.5, 11, and 18 has been studied using free surface visualization and particle tracking. When W/T = 11 and when W/T = 18, self-sustained oscillations of the submerged jets and the free surface are present. When W/T = 6.5, the self-sustained oscillations are no longer present, but oscillations with the frequency of gravity waves occur. We propose a critical value of W/T above which self-sustained jet oscillations occur, based on the spreading angle of turbulent jets. When W/T is larger than this critical value, the shear layers of the jet reach the front and back wall of the cavity before the jet can impinge the side wall, resulting in semi two-dimensional flow in the plane between the front and the back wall. Two-dimensional recirculation zones form alongside the jet leading to the jet oscillations. When W/T is smaller than this critical value, the jet can develop like a free turbulent jet up to an impingement point at the narrow side wall. When the jet impinges the side wall, flow in the directions parallel and perpendicular to the front and back walls is possible, resulting in complex three-dimensional flow patterns. The critical value for W/T, based on the known 12 deg spreading angle of turbulent jets is W/T = 10, which is in good agreement with the experimental results@en

The effect of Lorentz forcing on self-sustained oscillations of turbulent jets (Re = 3.1 x 10(3)) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (F-L <0) or upward (F-L > 0), to weaken or strengthen the self-sustained jet oscillations. The low frequency self-sustained jet oscillations induce a free surface oscillation. When F-L <0 the amplitude of the free surface oscillation is reduced by a factor of 6 and when F-L > 0 the free surface oscillation amplitude is enhanced by a factor of 1.5. A large fraction of the turbulence kinetic energy k = 1/2 (u) over bar (i)' (u) over bar (i)' is due to the self-sustained jet oscillations. A triple decomposition of the instantaneous velocity was used to divide the turbulence kinetic energy into a part originating from the self-sustained jet oscillation k(cos), and a part originating from the higher frequency turbulent fluctuations k(turb). It follows that the Lorentz force does not influence k(tub), in the measurement plane, but the distribution of k(cos), can be altered significantly. The amount of energy contained in the self-sustained oscillation is three times lower when F-L <0 compared to the situation with F-L > 0. (C) 2014 Elsevier Inc. All rights reserved.@en

The effect of Lorentz forcing on self-sustained oscillations of turbulent jets (Re = 3.1 x 10(3)) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (F-L <0) or upward (F-L > 0), to weaken or strengthen the self-sustained jet oscillations. The low frequency self-sustained jet oscillations induce a free surface oscillation. When F-L <0 the amplitude of the free surface oscillation is reduced by a factor of 6 and when F-L > 0 the free surface oscillation amplitude is enhanced by a factor of 1.5. A large fraction of the turbulence kinetic energy k = 1/2 (u) over bar (i)' (u) over bar (i)' is due to the self-sustained jet oscillations. A triple decomposition of the instantaneous velocity was used to divide the turbulence kinetic energy into a part originating from the self-sustained jet oscillation k(cos), and a part originating from the higher frequency turbulent fluctuations k(turb). It follows that the Lorentz force does not influence k(tub), in the measurement plane, but the distribution of k(cos), can be altered significantly. The amount of energy contained in the self-sustained oscillation is three times lower when F-L <0 compared to the situation with F-L > 0. (C) 2014 Elsevier Inc. All rights reserved.@en

The effect of Lorentz forcing on self-sustained oscillations of turbulent jets (Re = 3.1 x 10(3)) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (F-L <0) or upward (F-L > 0), to weaken or strengthen the self-sustained jet oscillations. The low frequency self-sustained jet oscillations induce a free surface oscillation. When F-L <0 the amplitude of the free surface oscillation is reduced by a factor of 6 and when F-L > 0 the free surface oscillation amplitude is enhanced by a factor of 1.5. A large fraction of the turbulence kinetic energy k = 1/2 (u) over bar (i)' (u) over bar (i)' is due to the self-sustained jet oscillations. A triple decomposition of the instantaneous velocity was used to divide the turbulence kinetic energy into a part originating from the self-sustained jet oscillation k(cos), and a part originating from the higher frequency turbulent fluctuations k(turb). It follows that the Lorentz force does not influence k(tub), in the measurement plane, but the distribution of k(cos), can be altered significantly. The amount of energy contained in the self-sustained oscillation is three times lower when F-L <0 compared to the situation with F-L > 0. (C) 2014 Elsevier Inc. All rights reserved.@en

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