Shock Tube Simulation

Objective:

To setup a transient shock tube simulation and plot the:

• Pressure and temperature history in the entire domain
• Cell count as a function of time.

Introduction:

Shock tube is a device which is used to produce and confine shock waves. It contains a diaphragm that separates a high pressure and a low pressure section. When the pressure ratio between the two sections is maintained at sufficient levels and the diaphragm is ruptured, a shock wave propagates through the low pressure region.

When the diaphragm bursts, it creates compression waves which propagate in the low pressure section and expansion waves which traverse in the high pressure section. After a short interval of time, the compression waves in the low pressure region will merge to form a shock wave. The stationary gases in the low pressure area will experience raise in pressure and temperature due to the formation of shock waves and they will start moving towards the walls of the tube. Since the shock wave travel at supersonic speeds, it generates an expansion fan. An expansion fan consists of infinite number of mach waves that diverge from a sharp corner. Both the expansion fan and the shock waves are reflected from the closed ends of the tube. When the shock wave hits the closed end of the tube, it gets reflected back. This reflected shock wave cancels the motion of the gases in the low pressure section initiated by the primary shock wave. The strength of the shock wave and expansion fan depends on the initial pressure ratio across the diaphragm and physical properties of the gases present in the tube.

Regions in Shock Tube:

The following are the regions situated in a typical shock tube :

Region 1: This is the region infront of the primary shock.
Region 2: It is the region between contact surface and primary shock.
Region 3: This is the region between tail of the expansion fan and contact surface.
Region 4: It is the region ahead of the leading expansion wave.
Region 5: It is the region behind the reflected shock.

Geometry:

The pre-modelled geometry was imported into Converge and the geometry was inspected for any surface errors or open edges. After fixing all the errors, the boundaries were flagged and the case was setup.

Shock Tube Dimensions:

Length of the tube (along x axis) = 0.2 m

Height of the tube (along y axis) = 0.01 m

Width of the tube (along z axis) = 0.01 m

Initial conditions and Regions:

Region 0 – High Pressure Region [ Green Region]

Medium = N2

Temperature = 300 K

Pressure = 600000 Pa

Region 1 – Low Pressure Region [ Brown Region]

Medium = O2

Temperature = 300 K

Pressure = 101325 Pa

Events:

At 0 sec,

High pressure and Low Pressure →→ Closed

At 0.001 sec,

High Pressure and Low Pressure →→ Open

This type of event is defined to replicate the action of diaphragm rupture.

Boundary Conditions:

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 – 2 D

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 – 2 D

Simulation Time Parameters:

Start Time: 0 sec

End Time: 0.03 sec

Solver: Transient Solver

Physical Models: Turbulence Model – RNG k-εε

Running the Simulation Using Cygwin:

Results:

• Mesh: The geometry was meshed using Cartesian mesh elements. Mesh size of 1mm was provided in X, Y, Z directions.

When the flow concentration or species concentration is high in certain areas of the geometry, Automatic Mesh Refinement (AMR) is performed in such areas. In our project, Species AMR was provided with a maximum embedding level of 3 and sub-grid scale criteria as 0.001.

• Pressure Contour

• Temperature Contour

• Velocity Contour

Plots:

• Temperature vs Time Plot for entire Domain

• Pressure vs Time Plot for entire Domain

• Pressure vs Time plot for High Pressure and Low Pressure region

From the above plot, the variation of pressure with time is shown. The pressure is maintained at the respective regions when the event is closed. After 0.001 seconds, the event opens and the flow takes place from the high pressure region to the low pressure region. This results in the expansion of N2 and the pressure of N2 decreases. Then the N2, gas expands and tends to reach the wall of O2 thereby compressing O2. This increases the pressure of O2. Then this wave gets reflected back to N2 region. The reflected shock waves comes back and prevents mixing thereby causing a recirculation zone.

• Temperature vs Time plot for High Pressure and Low Pressure region

From the above plot, the variation of mean temperature with time is shown. The temperature is maintained at 300K as per the initial condition when the event is closed. After the event opens at 0.001 seconds, the temperature (like pressure) increases in the driven region O2. It does not happen exactly at 0.001 seconds, it takes some time to increase. This movement of gas at the event opening causes increase in temperature and pressure producing shock waves. After the shock waves gets reflected from the wall, the flow is backward towards the driver region. Hence the temperature of the driven region decreases and reaches the initial temperature at about 0.0023 seconds. For the N2 species the case is vice-versa.

• Total Cell Count vs Time Plot

The total cell count as a function of time is plotted. For the first 0.001 sec where the diaphragm is intact, the total cell count remains constant at 2000 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 around 10,000 was recorded.

The Shock Tube Simulation can be Visualized below

Conclusion:

The shock tube is a versatile experimental facility for the study of gaseous phenomena at elevated temperature and pressure. By replicating the flow of gases in the presence of a shock wave, we can measure parameters such as rates of chemical kinetics, dissociation energies etc. By modifying the design of the shock tube, we can also simulate hypersonic flow that occurs during cases such as atmospheric re-entry of spacecraft etc.