Week 7: Shock tube simulation project

AIM:-

• Setup a transient shock tube simulation
• Plot the pressure and temperature history in the entire domain - Explain the result
• Plot the cell count as a function of time - Explain the result

THEORY:-

Introduction:

Shock tubes are the devices which are mostly used to study chemical kinetics. It basically is a tube with two chambers and a diaphragm separating the chambers. On one side is a high-pressure gas and on the other side is a low-pressure gas. Mixing occurs when the diaphragm is removed and as a result of the pressure difference, shock waves develop and are reflected from the walls and we obtain compression and expansion waves.

A real-life example of a shock tube is to study the auto-ignition system. The tube is filled with fuel and air in the two chambers. Due to the shock waves and a rise in temperature, the air-fuel mixture is going to auto-ignite. The shock tube data can be used to see how long the mixture takes to combust i.e. the ignition delay. So, a shock tube simulation can be very useful to compare the analytical and experimental data.

The brown region is the High-pressure region and the skyblue one is the low-pressure region.

Dimensions of the shock tube:

• in X-direction- 0.2 m
• in Y-direction- 0.01 m
• in Z-direction- 0.01 m

Simulation setup:

The following Simulation tools will be incorporated:

1.Converge studio:- To pre-process the data that needs to simulate the case. It plays an important role in generating important 3d input files only using GUI. It does not run simulation directly, however it generates inputs files which use to run the simulation.

2. Cygwin:- Cygwin is a collection of GNU and open-source tools that provide functionality similar to Linux distribution on windows.
3. Paraview:- To post-processing to obtain the contour, plots, etc. It is an open-source, multi-platform data analysis and visualization software.

Case Setup/Simulation Setup:

MATERIAL:

Gas Simulation:

• As only air is our working medium hence uncheck Reaction Mechanism.
• Predefined mixture: air
• Enable species(not in mech.dat) as we want to assign the participating species of Air like O2 and N2

Global Transport Properties

• Turbulent Prandtl number: 0.9
• Turbulent Schmidt number: 0.78

Species:

• Click on Gas species and add O2 and N2

SIMULATION PARAMETER:

Run Parameter:

• Solver: Density-based Transient
• Simulation Mode: Full Hydrodynamic
• Gas flow Solver: Compressible (as air is working medium)

Simulation Time Parameter:

• End time: 0.003s
• Start time: 0s
• Initial time step: 1e-09 s
• Minimum time step: 1e-09 s
• Maximum time step: 1 s

REGION & INITIALIZATION:

• Click on Region and Initialization and add 2 Regions.
• Region 0 as High Pressure region-Stream ID 0: temperature 300k; Pressure 6bar
• Species Air
• Region 1 as Low pressure- Stream ID 1:
• Species Air.

Events (to connect or disconnect the flow between two regions):

The flow is restricted till 0.001s and the flow will be taking place after 0.001s to the end time.

Turbulence model:

• RNG k-epsilon

Base grid:

• dx=0.0015m; dy=0.0015m; dz=0.0015m.

Enable Adaptive Mesh Refinement- (to capture the small change in flow by the automatic refinement of the grid at only where there is a small change in flow):

• Select High and Low-pressure Regions in Active Regions under AMR group 1.
• Maximum cells: 200000 (the maximum number of cells possible in the mesh).
• Enable species parameter.
• Embed type: Subgrid-scale(SGS)- SGS is used to show the small change in flow parameter (using subgrid criteria) by scale it down, depends on Max embedding level.
• Max embedding level: 2
• Formula for subgrid : Grid size after subgrid(smallest cell size after subgrid)=Base grid size/(2^Max embedding level)=0.004/(2^2)=0.8/4=0.001metre.
• Timing control type: PERMANENT.

Post-variable selection:

Output files:

The time interval for writing 3d output data files=3e-05 s

The time interval for writing restarting output=3e-05 s

Export input files and Running the Simulation:

Now we have successfully set up the Case and need to export the input files to run the Simulation.

Run the Simulation in Cygwin using a parallel processor.

Post Converting:

Now we need to convert all the output files which are processed by converge msmpi into the files which will be readable for post-processing in Paraview

Paraview:

We need to Post-process the output files to obtain the contour.

Results:

Pressure Plots for High and Low-pressure regions:

Conclusion:

• As the pressure in the high-pressure region exceeds maximum diaphragm pressure the diaphragm gets ruptured, and due to this, there is a pressure difference created. The high-pressure regions tend to more towards the low-pressure region which leads to formation of shock waves in that region which increases sudden pressure and Temperature on that low pressure region. On the other side, in the high-pressure region, the expansion waves will be created due to pressure relaxation, where Pressure and Temperature decrease.
• Both the Shock and Expansion waves are interacting with each other after reflecting from the wall due to the Slip Boundary condition of the Wall.

Youtube links:
pressure:- https://youtu.be/NxYjlXkJksA

Temperature:- https://youtu.be/iPm6uryDUxM