Flow Past a Cylinder

As with the other applications we have developed using the spectral element toolkit we resort to cylinder flow as a test case. We see that the fields in figures 8.9 and 8.10 closely resemble the equivalent fields in the incompressible version of this simulation in section 6.5. This is no surprise since we chose a fairly low Mach number (Mach=0.5) to run this test at. We can also compare this to the compressible case without a magnetic field 7.2.2. We see that up-down symmetry of the x-component of velocity has been broken in the wake and the regular pattern of the y-component of velocity also breaks down ten diameters from the cylinder. This is clear evidence that the magnetic fields are indeed causing the von Karmann street to become unstable with time.

A summary of the simulation parameters is given in 8.3.

 

Parameter Value

Dimension 2d

S_v 100

S_r 100

A 0.1

Mach 0.5

$$\Delta t$$ 1e-4

N-Range 1 to 8

K_Tri 490

Method Discontinuous Galerkin

  

Figure 8.9: Instantaneous iso-contours of the simulation fields for flow past a cylinder LV=100,LB=100,A=0.1 with a magnetic field. From the top: (1) density, (2) pressure, (3) x component of the velocity field, (4) y component of the velocity field

  

Figure 8.10: Instantaneous iso-contours of the simulation fields for flow past a cylinder LV=100,LB=100,A=0.1 with a magnetic field. Top: x component of the magnetic field, Bottom: y component of the magnetic field