Shock tube simulation

Imagine a calm pool of water. Now what do you think will happen when a stone is thrown in the centre of it? It will generate concentric ripples from the point of impact, right? This is what a shock wave looks like. In this project, we are going to set up the geometry of a shock tube and simulate a shock wave inside it to study its movement patterns and how it affects the gasses inside the tube.

Main 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

Theoretical background:

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.

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

Geometry 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.

The adaptive mesh refinement can be observed from the below mesh animation.

 Results:

1. Velocity and Nitrogen Mass Fraction variation across the shock tube

The above animation manages to capture the effect of the shock and expansion fans on the motion of the Nitrogen gas.

The shock waves generated due to diaphragm rupture, pushes the nitrogen gases towards the low pressure region. But before the gases could reach the other end of 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 opposite direction. The process continues till the intensity of the shock waves abates.

2. Pressure Variations

The initial pressure of 6 bar in high pressure region and 1 bar in 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.

3. Temperature Variations

The mean temperatures at the high pressure region (Region 0), Low pressure region (Region 1) and the shock tube was 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.

4. Total Cell Count

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 14200 was recorded.

Conclusion:

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.