Shock wave on a ramp
Mesh structure
The mesh is generated on Gambit and then imported on StarCD (c.f. the work that was done in a previous MICP task named SCCC).
The domain is composed of 40 cells on the horizontal part,
40 cells on the ramp and 40 cells on the vertical.
Finally there is one cell on Z direction. This is because
StarCD does not compute 2D-flows, however, the Z component of the variables
are not calculated.
The size of the cells is 0.05 m.
Simulation on StarCD
The domain consists in:
Mach number
Pressure
Density
Temperature
Total temperature
As we can see on the previous profiles, a shock appears
at the bottom of the ramp.
The Mach number goes from 2 before the shock, to 1.629
after the shock.
The density varies from 1.189 to 1.757 .
The shock generates a rise in temperature.
The simulation is done with constant enthalpy, which
is here called total temperature. We can notice on the last graph
that this value does remain constant( the all scale of color correspond
to the value 526.9)
We can notice that the shock is pretty thick, effectivly
there is only 4 or 5 cells where the shock occurs , what might not be enough.
As a consequence we decided to use a fine mesh.
Pressure Profil
The pressure is represented as a relative value taken
from 1.10^5.
On the graph, the minimum value is equal to the reference.
As we can see on the pressure graph, there is a higher
pressure zone behind the shock. This can also be observed on a 2D profil.
This is not physical but it is a consequence of the differencing schemes.
The pressure is drawn at x=3.625m (middle of a cell).
There is a first constant value behind the shock, than comes the higher
pressure (between y=1.0 and 1.2). During the shock, the pressure gets smaller
to get to a constant value 0, above the shock .
Angle of the shock
We can now calculate the angle of the shock.
Effectivly, we consider the middle of the difference
of pressure during the shock, this value appears for y=1.33.
We now know two points on the shock:
Xa=2 ; Ya=0 (Bottom of the ramp)
Xb=3.625 (middle of a cell) ; Yb=1.33
The angle of the shock is given by:
alpha=arctan[(Yb-Ya)/(Xb-Xa)]=39.299
Comparision with the theory
We can compare these results with the ones given by a fortran program found on the internet (listing) to the following address :
http://www.grc.nasa.gov/www/wind/valid/wedge/wedge.html
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