Two-phase stratified MHD flows in rectangular ducts

Abstract

The characteristics of two-phase stratified magnetohydrodynamic (MHD) flow in horizontal rectangular ducts are investigated for a system consisting of a conductive liquid and a non-conductive gas. Numerical and analytical solutions of the governing equations for the velocity and induced magnetic field intensity of fully developed laminar MHD flow are obtained for various combinations of bottom- and side-wall conductivities and for different orientations of an externally applied transverse magnetic field. The relevant set of dimensionless parameters governing the problem is identified. Unlike in single-phase MHD flows, the presence of a non-conductive gas layer breaks the flow symmetry, leading to a significantly different dependence of the flow characteristics on duct aspect ratio, wall-conductivity configuration, and the strength and orientation of the applied magnetic field. Using mercury-air flow as a representative test case, the solutions are employed to quantify the influence of the gas phase on the in-situ liquid holdup, velocity field, pressure gradient, flow lubrication, and pumping-power requirements. It is shown that, regardless of the magnetic Reynolds number, these characteristics are strongly affected by the wall-conductivity configuration and by the orientation of the external magnetic field.

Figures (29)

• Figure 1: Stratified two-phase flow in a rectangular duct under external magnetic field. (a) Flow schematics and (b) cross-sectional view.
• Figure 2: Effect of the aspect ratio, $AR$, on the holdup in ducts with different wall conductivities. (a) $Ha=5.181$; (b) $Ha=103.625$. The red (blue) diamond represent the two-plate model value of the holdup in case of conductive (insulating) bottom wall Barmak25.
• Figure 3: Effect of $Ha$ and $Q_{21}$ on the mercury holdup (a) Fully insulating ($I_bI_s$, solid line) and perfectly conducting ($C_bC_s$, dashed line) square ducts. (b,c) Aspect ratio effect $AR=0.5,1,2$: (b) Fully insulating ducts (c) Perfectly conducting ducts.
• Figure 4: Effect of $Ha$ and $Q_{21}$ on the mercury holdup in ducts with perfectly conducting bottom wall and insulating side walls, ($C_bI_s$) (a) Comparison with perfectly conducting ($C_bC_s$, solid line, $C_bI_s$, dashed line) square ducts. (b) Aspect ratio effect, $AR=0.5,1,2$ in $C_bI_s$ ducts.
• Figure 5: Velocity contours in a square duct for $Q_{21} = 1$: (a,b) all walls insulating, $I_bI_s$. (c,d) all wall conducting, $C_bC_s$. (a,c) $Ha=5.181$, the velocities are scaled by the maximal velocity, which is located in the air layer. (b,d) $Ha=103.625$, only the velocity contours in the mercury are shown (scaled by its maximal velocity). The corresponding $U_\text{max}$ values used for scaling are dimensionless (normalized by $U_{1S}$ ). (e,f) Single phase mercury flow in a conducting square duct, $Ha=103.625$. (e) Velocity contours and (f) comparison of the single-phase velocity profile flow along the horizontal centerline ($y=0.5$) with the interfacial velocity profile ($y=h$) in mercury-air flow.