Week 7: Shock tube simulation project

Introduction:

Shock tubes are particularly useful in gas-phase work since high temperatures can be produced in a relatively short time and subsequent chemical changes can be studied. It consists of a high and low-pressure section. Those two sections are separated by a thin diaphragm of metal foil or cellophane. High pressure contains driver gas whereas in the low-pressure region contains the gases to be reacted. When the diaphragm is burst suddenly by any controlled action, the expansion of the pressure gas produces shock wave which is passing through the low-pressure zone. These shock waves are hit the wall at back and forth which results in adiabatic compression of the gas. It leads to a rise in temperature in a chamber which can be monitored by thermocouples. Species reaction can be observed by laser monitors.

Stages of shock wave after bursting of the diaphragm

The direction of Shock waves

Objective:

To conduct the shock flow simulation inside the shock tube with the help of Regions and Events using CONVERGE.

Problem definition:

In this challenge, the high-pressure Nitrogen gas kept in the high-pressure region with 6 bar pressure whereas in the low-pressure region the oxygen gas kept in atmospheric pressure. These 2 regions are separated by diaphragm as per theory but in simulation bursting of the diaphragm simulated with help of Events and Regions. After 0.001 s the diaphragm is broken, then Nitrogen from the high-pressure region enters the low-pressure region in the form of the shock wave. Adaptive Mesh Refinement was used to capture the accurate profile of wavefront.

Mesh Details:

• dx = dy = dz = 2 mm
• AMR details:

Species: N2

SGS value = 0.001

Embed scale = 3

Timing type: Permanent

Animation of AMR meshing

Boundary Condition:

1) High pressure: Wall with slip BC

Wall motion type: Stationary

Surface Movement: Fixed

Temperature Boundary Condition: Zero normal Gradient (NE)

1) Low pressure: Wall with slip BC

Wall motion type: Stationary

Surface Movement: Fixed

Temperature Boundary Condition: Zero normal Gradient (NE)

Regions and Initialization:

There are two types of regions used those are High pressure and Low-pressure region.

1) High-Pressure region: Pressure = 6 bar

Species: N2

2) Low-pressure region: Pressure = 1 atm

Species: O2

Events:

Events are used to create diaphragm virtually which means it will open or close the separation. For this challenge, two events are created.

Starts (sec)	Region A	Region B	Event
0	High Pressure	Low Pressure	Close
0.001	High Pressure	Low pressure	Open

Solver Parameters:

1) Solver: Transient

Simulation mode: Full hydrodynamic

2) Turbulence Model: Reynolds Averaged Navier Stokes (RANS)

RNG K-ε">K−ε

3) Simulation Time Parameters:

Start time = 0 s

End time = 0.003 s

Initial time step = 1e-9 s

Minimum time step = 1e-9 s

Maximum time step = 1 s

Procedure:

1) The above condition has been given to Converge Studio to create input data files.

2) 12 input data files are accessed by using the Cygwin terminal.

3) The simulation has been performed by using Converge-3.0 executable. To decrease the simulation time, 2 cores are used with the help of MSMPI.

4) The output files are converted into Paraview VTK in-line binary format by using Converge Studio Post Processing 3D to see the results in Paraview.

Results:

1) Mass fraction of N2 and Velocity Contour Animation:

Inference:

• From the above velocity contour animation, it was clear that the shock wave produced after opening the event. It hits the wall at back and forth and then shock waves lose its momentum which means the velocity of the shock wave front gradually reduced after some time.
• From the mass fraction of N2 contour animation, It was clear that the N2 gas starts move from the high-pressure region to low pressure region in the direction of a shock wave for some particular time. When the shock wave hits the wall in the low-pressure region and came back, It disturbs the N2 gas distribution in the low-pressure region. The shock wave pulled back the N2 gas distribution before it reaches the low-pressure region wall.

2) Pressure Contour Animation and plots:

Pressure plot in High-pressure region

Pressure plot in the low-pressure region

Inference:

• From the above plots, It was evident that the pressure in the High-pressure region starts to reduce and the pressure in the low-pressure region starts to increase when the diaphragm opens after 0.001 s.
• When the shock wave hits the wall, the gas starts to compress locally. This phenomenon was captured as the fluctuation of pressure in both the plots.
• Pressure contour animation clearly shows that the propagation of the pressure field. It shows clearly that the pressure raise occurs when the shock wave hits the wall. And gradually the pressure of the gas starts reduced.

3) Temperature contour Animation and Plots:

Maximum Temperature plot in the High-pressure region

Maximum Temperature plot in the Low-pressure region

Inference:

• From the above contour and plots, it was evident that the temperature reached the maximum when the shock wave hits the wall. It happened because of the compression of a gas.
• The maximum temperature was attained at the low-pressure region which is 500 K. That hot gas in the low-pressure region again gets compressed due to the shock wave which comes from the high-pressure region.

4) Cell count vs Time step plot:

Inference:

• Automatic Mesh Refinement was used to capture the shock wave front accurately which leads to an increase in cell counts. Maximum 200000 cells were used in this simulation.

Conclusion:

• Events and Regions were useful to simulate the shock tube problem with an accurate time interval.
• The shock wave produced a maximum temperature of 500 K at 0.0003 s after the diaphragm opened.