320
10. Compressible Flow
Fig. 10.2. Predicted Mach number contours for inviscid flow through a channel
with a circular arc bump in lower wall: subsonic flow at Ma;, = 0.5 (above), transonic flow at Ma;, = 0.675 (middle), and supersonic flow at Ma;, = 1.65 (bottom);
from Lilek (1995)
is supersonic, a shock is generated as the flow reaches the bump. This shock
is reflected by the upper wall; it crosses another shock, which issues from the
end of the bump, where another sudden change in wall slope is encountered.
Figure 10.3 shows distribution of Mach number along lower and upper
walls for the three cases, respectively. The solution error is very small on
the finest grid and subsonic flow; this can be seen from the effects of grid
refinement, as well as from the fact that the Mach numbers at both walls
at the outlet are identical and equal to the inlet value. The total pressure
error was below 0.25%. In the transonic and supersonic cases, grid refinement affects only the steepness of the shock; it is resolved within three grid