Shock tube simulation project   (Converge CFD, Skill Lync, Medium)
Aim:
To simulate the flow inside a shock tube using Converge CFD
Introduction:
Shock tube is an experiment setup which is used to find auto ignition conditions of fuel air mixture. It is one of the uses of shock tube. The shock tube setup consists of a tube divided in two parts, high pressure and low pressure region, using a diaphragm. The high pressure region is also called as driver region and low pressure region as driven region. The gases to be tested are filled in high and low pressure regions. The main part of experiment starts with rupture of diaphragm. The gases from high pressure region are released to low pressure region and this causes a shockwave. When this shockwave hits the opposite wall, there rise in temperature and pressure at that wall. The mixture depending on its reaction mechanism ignites and this is seen on pressure and temperature sensor values. This experiment is repeated for many values of pressure and equivalence ratios to get the output curve.
To simulate this experiment, we can use Converge CFD. The high pressure and low pressure regions are initialized with particular pressure, temperature and species and at a specified time the two regions are connected. This opening and closing of interface is handled by assigning them as events. When the regions are stated as closed, the software creates wall between them and flow doesn't pass. When the regions are opened, the wall is removed and regions get connected. For this report following geometry is used:
The dimensions are (0.2 x 0.01 x 0.01) metres in (X, Y, Z) directions.
Following are the details of case setup:
High pressure region walls (Red): Stationary no slip wall
Low pressure region walls (Cyan): Stationary no slip wall
Simulation time parameters:
Start time: 0 sec
End time: 0.015 sec
Initial timestep: 1e-9 sec
Minimum timestep: 1e-9 sec
Maximum timestep: 1 sec.
Max Conduction CFL number: 1
Max Diffusion CFL number: 2
Max Mach CFL number: 1
Region initialization:
High Pressure region: N2 at 600000 Pa and 300 K
Low Pressure region: O2 at 101325 Pa and 300 K
Events:
1) High and low pressure regions: Closed from 0 sec
2) High and low pressure regions: Open from 0.001 sec (simulating diaphragm rupture at 0.001 sec)
Mesh Settings:
Base mesh size = 0.001, 0.002, 0.01 m (200, 5, 1 elements along X, Y, Z directions)
(The Flow along X direction is important so there are more elements in that direction. The distribution along Y axis is not very important so less elements along Y direction. The flow along Z direction is neglected so only 1 element along Z direction)
Adaptive Mesh Refinement (AMR) Settings:
Start time: 0.001
Embedding based on N2 species
Embed layers: 2
Embed scale: 2
SGS.embed: 0.001
Maximum cells: 200000
Turbulence model: RNG k-e model with standard wall functions.
Solver: Transient, Density based, Compressible PISO solver.
Output files:
3D output saved at every 0.00005 seconds (Gives 300 files)
Text output written at every 0.000001 seconds.
Results:
1) Mesh:
Due to AMR, the mesh is refined at location where there more change in slope of N2 mass fraction. Three levels of mesh sizes can be seen.
2) Total cells:
When the diaphragm got ruptured (virtually removed), the cells started to get refined and we saw increase in cell count. When the first reflected shock wave passed from N2 - O2 boundary, the cell count was maximum.
The dynamic creation of mesh can be seen in next video.
3) N2 mass fraction and Velocity:
The video shows that N2 never got completely mixed with O2. This happened because their diffusion was governed by pressure difference. They would eventually get diffused based on density if gravity was present in the simulation.
The velocity plots show how the shock wave travels.
4) Pressure plots:
The above image shows pressures in High, low regions and mean pressure of entire domain. The pressures got eventually stable in pattern which showed the frequency of shockwave. In other words, the shockwave position can be determined based on pressure fluctuations of the region. The Shockwave which moves from HP to LP region can be seen from blue line and the expansion wave from LP to HP region can be seen from yellow curve.
The following video shows pressure contour over time values.
5) Temperature Plots:
The above grapg shows the max, mean and min temperatures in the domain. The location of low and high temperatures can be seen in contour plots. The region where there is high pressure, is the region where there would be autoignition.
The following video shows the transient temperature contour:
From the start of rupture of diaphragm, the first shockwave which hits the LP wall creates the maximum temperature. This is because there is maximum pressure difference. For later reflections of wave, the pressure difference becomes nearly equal.
The maximum temperature is seen when the first half of first shockwave gets reflected and interferes with second half of first shockwave.
Conclusion:
The Shock tube simulation is done using Converge CFD and flow features of shocktube problem were observed and post processed.