Shock tube Simulation
AIM
- Setup a transient shock tube simulation
- Plot the pressure and temperature history in the entire domain.
- Plot the cell count as a function of time.
INTRODUCTION
Shock tubes are devices for studying the flow of high-temperature and high-velocity compressible gas.
High-temperature supersonic gas flow is initiated in a shock tube as a result of the rupture of a diaphragm separating two gases in high-pressure and low-pressure chambers. An unsteady rarefaction wave passes into the "driver" gas in the high-pressure chamber with a velocity a few kilometers per second. This results in the driver's gas flowing into the low-pressure gas, pushing the gas in the low-pressure chamber ahead of it. The shock wave propagates in the low-pressure chamber ahead of this flow of the studied gas. The velocity of the driven gas flow is equal to that of the driver gas flow. The wave (x − t) pattern, the schematic of the shock tube, and distribution of pressures p and temperatures T along the tube axis are presented in. The parameters are denoted by 0 in the low-pressure chamber of the shock tube, 1 behind the incident shock wave, 2 behind the contact surface, 3 in the rarefaction wave, 4 in the high-pressure chamber, and 5 behind the reflected wave. In order to generate a shock wave with the specified pressure ratio p1/p0 in a shock tube, it is necessary to provide the pressure ratio p4/p0 over the shock tube diaphragm, which satisfies the relation
where a is the velocity of sound, γ the adiabatic exponent, u1 the velocity of gas flow behind the shock wave producing the pressure ratio p1/p0. Varying the length of high- and low-pressure chambers, we can find a regime of shock tube operation under which the shock wave reflected from an end meets the tail of the rarefaction wave and the head of the reflected rarefaction wave at a fixed point. This regime known as the "joined" contact surface regime ensures the maximum time of undisturbed state behind the reflected wave. The maximum flow parameters achieved in shock tubes depend on the design of the high-pressure chamber. According to this, shock tubes can be divided into four groups.
- For this flow, air as a mixture of Nitrogen and oxygen is considered as a flow for the region.
- A transient state density-based solver is selected for the simulation and for algorithm PISO scheme is selected.
- Othe simulation parameters considered are :
Start time : 0 sec
End time: 0.03 sec
Minimum time step: 1e-7 sec
Maximum time step:1e-7 sec
- Two regions have been defined, one for the high-pressure region with a pressure of 600000 Pa, and consists of only Nitrogen, and low-pressure region which consists of only oxygen and atmospheric conditions.
- All boundaries are associated with it.
High-Pressure Region (Region 0)
At Top and End Walls:
Dirichlet Temperature Boundary Condition, T =300 K
Law of the wall Velocity Boundary Condition
At Front and Back Wall – Wall
Low-Pressure Region (Region 1)
At Top and End Walls:
Dirichlet Temperature Boundary Condition, T =300 K
Law of the wall Velocity Boundary Condition
At Front and Back Wall – Wall
- Converge uses events to activate to deactivate the disconnect triangle, which controls when and where flow between the regions is allowed.
- An OPEN event deactivates the disconnected triangle and thus allows flow between the specified regions.
- Close events activate the disconnect triangle and thus prohibit the flow between the disconnect triangle.
- It automatically refines the grid-based upon the fluctuating and moving conditions such as temperature and velocity.
- These features may be used to obtain a refined grid inflow region of interest allowing complex phenomena, such as flame propagation or high-velocity flow, without unnecessarily slowing the simulation with a globally refined grid.
Sub-Grid-Scale(SGS) AMR
For a scalar, the sub-grid field is denied as the difference between the actual field and the resolved field
where ϕ,is an actual scalar field, is resolved scalar field, and ϕ′ is a subgrid scalar field.
The dialog box AMR is shown below :
For our setup, we have set AMR, for Species, nitrogen, with a sub-grid-scale of 0.001.
RUNNING SIMULATIONS
- Once the case setup is done and files are exported and saved, then we will use external solver Cygwin to solve the problems using these input files.
- The command used to execute the solving process is shown below :
mpiexec.exe -n 4 "C:\Program Files\Convergent_Science\CONVERGE\3.0.12\bin\converge-intelmpi.exe" restricted
- This command should we run in the same folder where all the case data files are.
- This command is used to solve the problem in parallel with 4 cores.
- When the simulation is completed and converged, the header output files are converted to a suitable format for post-processing.
POST-PROCESSING
MESH
For our flow, we have selected a base grid of 2mm, and adaptive mesh refinement along with it, with SGS levels of 0.001.
The above image shows mesh with arm after running solution for 0.03 sec.
Animation of the above variation, with respect to time, is shown below.
Plot for the above variation with respect to time, as a change in nitrogen level, is shown below.
For the first 0.001 sec where the diaphragm is intact, the total cell count remains constant at 2500 cells. After which the diaphragm is broken and the effect of species adaptive mesh refinement can be observed. The total cell count varies continuously during this period and a maximum cell count of 200,000 was recorded.
PRESSURE-CONTOUR
The initial pressure of 6 bar in the high-pressure region and 1 bar in the low-pressure region reaches a steady pressure of 3.4 bar at the end of 0.02 sec. The same can be visualized from the below animation.
Nitrogen-Contour
The shock waves generated due to diaphragm rupture push the nitrogen gases towards the low-pressure region. But before the gases could reach the other end of the tube, the reflected shock wave pushes the N2 gases in the opposite direction, changing the flow of the N2 gases. That wave is again reflected from the other end of the tube pushing the N2 gases in the opposite direction. The process continues until the intensity of the shock waves abates.
Pressure Plot
The initial pressure of 0.6 MPa in the high-pressure region and 0.1 MPa in the low-pressure region reaches a steady pressure of 0.32MPa at the end of 0.02 sec. This can be visualized from the below plot.
Temperature -Plot
The mean temperatures at the high-pressure region (Region 0), Low-pressure region (Region 1), and the shock tube were plotted as the function of simulation time. At the end of the simulation, the Region 1 was at a mean temperature of 303k; the Region 0 at a mean temperature of 275 k and the entire shock tube was at a mean temperature of 286 K.
Conclusion
- Shock tube simulation has been performed successfully in Converge.
- It can be used to measure parameters such as rates of chemical kinetics, dissociation energies, etc.
- By modifying the geometry of our model be can model hypersonic flow also.