From
the “grid permukaan” above, air with velocity of 500 m/s will flow from the
left side domain and exit from the right side. There is a narrowing in the
middle of the duct. Shock wave is expected to be happened. Before doing the iteration we should input
data in all cells with velocity of 500 m/s and temperature of 300K. From these
input, we can say that the flow is characterized as supersonic flow because the
value of the Mach number is greater than 1 along the duct.
Result
Density
is an important indicator in a compressible flow. The following picture is the density
distribution along the duct.
We
can see the increase of the density right after the air past the shock
wave and then decreases.
My
statement is correct. The flow is supersonic flow. We can see from the figure
above that the velocity is larger than velocity of sound. We can see that the
velocity decreases in the region right after the shock waves then increases in
the region where the density decreases as I mentioned above. The direction of
the velocity vector is from the left to the right for all distributed velocity.
The
following figure is the static relative pressure distribution.
From
the figure we can see that in the right-after the shock wave region the
pressure increases and then decreases as the density decrease as mentioned
above.
The
following figure is the temperature distribution.
Just
like the density, velocity and pressure, the temperature increases in the
region of right after the shock wave and then decreases.
Discussion
Shock
wave is an extremely thin region typically in an order of 10-5 cm,
across which the flow properties can change drastically. Anderson (2001)
explained that the pressure, density, temperature increase across the shock
wave, whereas the total pressure, Mach number and velocity decrease (1). This
is true for our case above. The flow ahead of the shock wave must be supersonic
(M larger than 1). Behind the shock wave (oblique shock wave, like in our case
above) the Mach number is larger than 1 but smaller than the Mach number ahead
of the shock wave. If we look at the result for velocity, we can see this
statement is true.
Shock
wave can give disadvantages to us. It can reduce the flow capacity. Because of
the shock wave, the drag can be large for application such as bullet/projectile, missile, and air
plane.
Ref.:
(1)
J.
D. Anderson Jr., Fundamentals of Aerodynamics, Third Edition, New York:
The Mc-Grawhill Companies Inc., 2001.
