Week 5: Prandtl Meyer Shock problem
AIM:
Prandtl Meyer Shock problem
objectives:
1. Shock flow boundary conditions
Do a literature search on what BC's are typically used for shock flow problems
2. What is a shock wave?
In your own words, describe the physics behind shock waves
3. Effect of SGS parameter on shock location
In the Prandtl Meyer shock problem, look at the effect of SGS temperature value on cell count and the shock location
theory:
shock wave-
when an aeroplane flying welll below the speed of the sound creates a disturbance in the air and sends out pressure pulses in all directions as shown in below figure (a) . air ahead of aeroplane receives these messages before the aeroplane arrives and the flow seprates around the aeroplane, but as the aeroplane approaches the speed of the sound. the pressure pulses merge closer and closer together as shown in below figure (b) in front of aeroplane and little time elapses between the time the air gets the waning of the aeroplane approch and aeroplane's actual arrival time. at the speed of the sound the pressure pulses move at the same speed as the aeroplane as shown in below figure (c). they merge together a head of aeroplane into a shock wave which is an almost instantaneous line of change in pressure, temperature and density..
the air has no warning of the impending approach of the aeroplane and abrutply passes through the shock system. there is a tendency for the air to break away from the aeroplane and not flow smoothly about it. as a result there is a change in aero dynamic forces from those experienced at low incompressible low speeds.
prandtl meyer expansion fan-
As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of the sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum and energy. As the speed of the object increases towards the speed of sound, we must consider compressibility effects on the gas. The density of the gas varies locally as the gas is compressed by the object. When an object moves faster than the speed of the sound, and there is an abrupt decrease in the flow area, shock waves are generated. If the flow area increases, however, a different flow phenomenon is observed. If the increase is abrupt, we encounter a centered expansion fan. The word "expansion" denotes that the area is increasing. There are some marked differences between shock waves and expansion fans. Across a shock wave, the Mach number decreases, the static pressure increases, and there is a loss of total pressure because the process is irreversible. Through an expansion fan, the Mach number increases, the static pressure decreases and the total pressure remains constant.