Shock Tube Simulation Using Converge CFD

Shock Tube is an experimental apparatus that is widely used to study chemical kinetics. Shock Tube consists of two regions, one that is at a high-pressure and the other at low-pressure both separated by a diaphragm. The high-pressure zone is known as the driver section and the low-pressure zone is known as the driven section. The pressure at driver zone is increased steadily with respect to the driven zone and after a certain point, the diaphragm breaks, resulting in the fluid or gas from the high-pressure zone to rush towards the low-pressure zone as a result of which compression waves are generated. These compression waves coalesce in the driven zone to form shock waves which raise the stationary driven zone\'s pressure and temperature on arrival of the shock wave whereas in the driver zone expansion waves are generated because the fluid or gas expands in this region. The motion of the fluid that was initiated because of the primary shocks get cancelled by the reflected shock waves. One domain where shock tube find its application is in the study of Ignition Delay of a fuel-air mixture. The setup relies on the same principle where the generation of shocks lead to the fuel-air mixture getting ignited and the data obtained can be used to compare against experimental data.

Shock Tube can be simulated using Converge CFD software where different properties like pressure, temperature variation can be analysed. The geometry of the tube is imported and the case is set up by assigning the high-pressure zone as filled with N2 gas at a pressure of 6 bar and the low-pressure zone as filled with O2 gas at atmospheric pressure. Having a diaphragm in the simulation isn\'t possible so instead, a concept known as \'Events\' is utilised. A Sequential event where the high-pressure and low-pressure zones are kept disconnected from each other until 0.001 milliseconds and then opened after 1 millisecond is initialised. Using this technique makes it possible to simulate the diaphragm inside the flow chamber. The solver used is Transient with simulation end time of 0.003 seconds and Adaptive Mesh Refinement (AMR) is used to refine the mesh to capture the data more accurately. AMR works by locally refining the mesh locally by monitoring an assigned property. In this simulation, Species Adaptive Mesh Refinement technique with N2 as the species, SGS embed level of 0.001 with type Permanent and maximum cell count of 200000 is assigned. In order to create a smooth animation, the output files are written every 1e-05 second and text output every 1e-6 second. The images shown below represent how AMR works to refine the mesh as the simulation progresses. Note that the timestamp used is not in seconds.

At t=0,

At t=30,

At t=209,

During the start of the simulation the two pressure regions are disconnected from each other and no mixing of the gases takes place. When the simulation crosses time-step of 0.001 second, sequential event that was initialised to simulate the diaphragm connects the two regions thus letting high-pressure N2 gas to rush towards the driven zone. Adaptive Mesh Refinement technique increases the number of cells rapidly and as the simulation progresses it keeps on updating the cell count. When the solution starts to attain equilibrium the number of cells start to drop and thus reach a steady-state value. To capture this steady-state phenomenon the simulation should be run for longer than 0.003 seconds.

Pressure Variation Across the Driver Region:

Pressure Across the Driven Region:

Pressure Across the Tube:

• At the start of simulation the pressure difference between the two regions is 5 bar and as the simulation crosses 0.001 seconds the diaphragm breaks and the gas in hihg-pressure zone rushes towards the low pressure zone creating a rapid pressure-differential drop. The generation of shock waves due to compression cancel the incoming shocks and thus pressure difference between the two zones rises again. This phenomenon repeats again but this time the magnitude of reduction in pressure difference reduces and as the simulation progresses the shocks eventually stabilise and start to reach steady-state value.
• As N2 gas in the high-pressure region expands after the breaking of diaphragm, the pressure in that zone drops rapidly and after the shock waves get reflected back, the re-circulation zone create a rise in pressure. The flow again rushes towards the low-pressure region but the reduction of pressure due to expansion is less than in the earlier cycle. This variation in pressure eventually starts to attain equilibrium and reach a steady-state point. At the driven zone, the opposite effect takes place where the pressure rises and drops in a cycle and then reaches a steady-state after a few cycles.

Temperature Variation Along the Tube: A similar effect is observed with respect to temperaure where the value of temperature reduces as the gases start to mix after 0.001 seconds and rises again when re-circulation zone is created to eventually reach steady-state when the generated shocks attain equilibrium.

Temperature of Driver Region: Expansion of N2 gas in the high-pressure region leads to the inital decrease in temperature as a consequence of decrease of pressure in that region.

Temperature in Driven Zone:

Temperature Animation in Shock Tube:

To visualise how the pressure and velocity of flow varies as the simulation progresses at every time step, the results are post-processed and viewed using ParaView.

Pressure Variation Along the Tube at different time-step:

At t=0,

At t=20, (diaphragm breaks)

At t=35, the broken diaphragm lets N2 gas to rush towards the low pressure region leading to a decrease in the difference of pressures between two zones

At t=60, the compression of gases creates a high pressure region in the driven zone

At t=90, the generated shock waves start to reflect back the oncoming waves creating a re-circulation zone

At t=150, the pressure in the driver zone rises however the difference in pressure between the two zones is reduced

At t=209, due to the re-circulation in the above time-step,the solution starts to attain a steady-state value,however, the high-pressure and low-pressure regions get switched

Variation of Velocity Across the Tube for each Time-Step:

At t=0,

At t=20,

At t=190,

At t=209,

Pressure and Velocity Animation of Shock Tube: