Control of Wake Structure Behind a Square Cylinder by Magnetohydrodynamics

In this paper, a two-dimensional (2D) numerical simulation has been performed for an unsteady magnetohydrodynamics (MHD) flow around a solid square cylinder placed in a channel. Computational simulations were done for the ranges of Reynolds and Stuart numbers of 1–250 and 0–10, respectively. Finite volume method (FVM) has been used to solve the unsteady Navier–Stokes equations. The effects of streamwise magnetic field on the flow separation and suppress of the vortex shedding are studied in detail for the above ranges. Additionally, four new empirical equations for wake length and Stuart number are suggested. Finally, a comparison is performed between the cases of with and without a channel to study the effect of channel walls. The obtained results revealed that Strouhal number decreases linearly with increasing Stuart number. Also, the flow distribution pattern changes from time-dependent pattern to steady-state by increasing Stuart number.

Numerical investigation of the Lorentz force effect on the vortex transfiguration in a two-dimensional lid-driven cavity

Numerical calculations of the two-dimensional unsteady incompressible driven cavity flow in the presence of the Lorentz body force are presented. The Navier—Stokes equations in vorticity-stream function formulation are solved numerically using a uniform grid mesh of 201×201. A second-order central difference approximation is used for spatial derivatives and the solutions march in time with a fourth-order Runge—Kutta method. The unsteady driven cavity flow solution is computed for a Reynolds number of Re=1000. The effects of the Stuart number (ratio of the electromagnetic forces to inertial forces) and penetration depth of the Lorentz force on the lid-driven cavity vortices are investigated. Two new quaternary vortices at the bottom corners of the cavity are observed in the flow field as the Stuart number and penetration depth increase. The primary vortex size also dwindles and eventually breaks down into two tertiary vortices as these parameters increase. The velocity component profiles are also considerably sensitive with respect to these parameters. It should be emphasized that on the basis of extensive comparisons and validations, which are made with benchmark solutions found in the literature, the numerical computations are repeated considering the Lorentz body force effect in the lid-driven cavity. Detailed results are presented in the article.

On the interaction between Tollmien-Schlichting and Rayleigh-Bénard instabilities in the presence of a longitudinal magnetic field

The method used by Gage and Reid(10) to investigate hydrodynamic stability of thermally stratified fluid is extended to hydromagnetic stability to study the effect of aligned magnetic field on the stability of unstable thermal stratification under the assumption of small magnetic Reynolds number. The interaction between the Tollmien–Schlichting–Stuart mechanism of instability due to shear and magnetic field and Rayleigh–Bénard–Thompson mechanism of instability due to thermally unstable stratification and magnetic field is brought out in detail. It is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, Squire's theorem is not valid. This conclusion follows from the fact that in our analysis the Richardson number Ri ( < 0) will not be greater than the value −0·92 × 10−6. In particular, it is shown that for the values of stratification parameter n ≤ 0·6 the effect of magnetic field for small values of Stuart number N is to augment instability and impose the restriction on the validity of our numerical procedure. However, for η = 0·8 a sharp transition from unstable to stable flow takes place at N = 0·3. A physical explanation for this based on eddies is given.