Simulation of Compressible Flow - Shock Wave

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.