Cylinder Flow

 We now consider the effect of a uniform magnetic field that is aligned with the velocity field at the inflow to flow past a cylinder. We have already verified that the incompressible code obtains the correct answer for the case without magnetic field. This provides us with a baseline for comparison. The farfield boundary conditions are straightforward to provide for the magnetic streamfunction. The condition at the wall was chosen (somewhat arbitrarily) so that the magnetic streamfunction is set to zero there. This condition sets the normal component of the magnetic field to zero at the cylinder. A summary of the simulation parameters is given in table 6.4.

 

Parameter Value

Dimension 2d

S_v 100

S_r 100

V_A 0.1

$$\Delta t$$ 0.005

N-Range 10

K_Tri 460

Method Galerkin

  

Figure 6.6: Incompressible flow past a cylinder with inflow magnetic fields. From the top: (1) x component of the velocity field, (2) y component of the velocity field, (3) x component of the magnetic field, (4) y component of the magnetic field

The instantaneous primitive variable fields are shown in figures 6.6 and 6.7. We see from figure 6.7 that the shedding pattern at the cylinder is only slightly perturbed but that the vortex street has been destabilized downstream from the cylinder. The wake has also become more complicated with more small scale structures appearing than before.

  

Figure 6.7: Incompressible flow past a cylinder with inflow magnetic fields aligned with inflow velocity. Top: Pressure field, Middle: Vorticity, Lower: Stream function of the magnetic field