Shock Tube
Introduction:
All shock tubes consist of at least two sections: one called the driver section and the other called the driven section. We will cover the basics of two-section shock tube operation below.
In two-section shock tube operation, the driver and driven sections are filled with gases at different
pressures and are initially separated by a thin diaphragm. The pressure in the driver section is greater than in the driven section and is slowly increased until the diaphragm ruptures. The rupture of the diaphragm creates a shock wave propagating in the driven section and an expansion wave propagating in the driver section. The moving boundary between the shock-processed fluid and the expanded fluid is called a contact surface. The conditions across the contact surface are constant pressure and constant velocity. The incident shock wave travels all the way along the test section until it reflects off of the end wall. Similarly, the expansion wave reflects at the end of the driver section. The reflected shock then interacts with either the contact surface and/or the reflected expansion wave (whichever it hits first).
High Pressure zone- Green
Low Pressure zone- Brown
Boundary Condition and Initial condition:
High Pressure zone- 600000 Pa, 300k, Filled with N2.
Low Pressure zone- 101325 Pa, 300k, Filled with O2.
Turbulence Modeling- RNG K epsilon.
Time Frame- 0 to 0.03 sec.
Diaphragm- breaks at 0.01 sec.
Solution:
1. Cell count
The cell count remains stationary till 0.001 sec because the diaphragm is still attached. Once the seperation between high pressure and low pressure zone opens up, the cell count starts varying rapidly. Since the high pressure zone pushes the gas/ fluid in low pressure zone, shock waves are generated and this results in rapid variation in pressure, temperature and species concentration in specific regions. The shock waves reflect back and forth from the walls casuing continuous variation in cell counts.
2. Pressure:
The above graph shows the variation in pressure values of N2 and O2. Once the diaphragm breaks the shock wave generation causes rapid variation in pressure of both N2 and O2. The high pressure N2 expands in the low region causing a decrease in the pressure of N2, while the low pressure region (O2) experiences a push/ compression from the N2 molecules causing their pressure to rise. Now, since we also have reflection from the walls, there is an increase in pressure of N2 as the reflected waves try to compress the expansion waves downstream of the diaphragm. Even the O2 molecules expand because of the reflected waves, which allows a decrease in their pressure. This process goes on till the time limit provided in the simulation. Determining the ime required for a steady simulation is beyond the scope of this challenge.
https://www.youtube.com/watch?v=hKo5YVPEJIw
3. Temperature:
The temperature profile for N2 and O2 behaves in the same manner as pressure. As soon as the diaphragm breaks, the temperature for N2 goes down due to its expansion, while the temperature for O2 goes up due to compression. When the waves start reflecting, opposite thing happens and this goes on until 0.03 sec.