Shock tube simulation using Converge CFD

Aim:-> To setting up shock tube simulation using Converge CFD.

Theory:-

The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale. Or in simple language shock tubes are devices for studying the flow of high-temperature and high-velocity compressible gas. Shock tubes can also be used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. Shock tubes are also used to investigate compressible flow phenomena and gas phase combustion reactions. An x-t diagram added below shows the horizontal axis indicating position along the shock tube, and the vertical axis indicating time elapsed since diaphragm rupture.

Fig: Typical shock tube diagram

A simple shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in which a gas at low pressure and a gas at high pressure are separated using some form of diaphragm. The low-pressure gas, referred to as the driven gas, is subjected to the shock wave. The high pressure gas is known as the driver gas. The corresponding sections of the tube are likewise called the driver and driven sections. The diaphragm suddenly bursts open under predetermined conditions to produce a wave propagating through the low pressure section. The shock that eventually forms increases the temperature and pressure of the test gas and induces a flow in the direction of the shock wave as the drivers gas flowing into the low pressure gas, pushing the gas in the low pressure chamber ahead of it.

Several methods are commonly used to burst the diaphragm.

• A mechanically-driven plunger is sometimes used to pierce it.
• Another method is to use diaphragms of plastic or metals to define specific bursting pressures. Plastics are used for the lowest burst pressures, aluminum and copper for somewhat higher levels and mild steel and stainless steel for the highest burst pressures.
• Yet another method of rupturing the diaphragm utilizes a mixture of combustible gases, with an initiator designed to produce a detonation within it.

~Pre processing:-

Geometry preparation:

Fig: Geometry

The above figure shows geometry of shock tube which includes two regions with different pressures. The region on left side is with high pressure i.e., 600000 Pa and right side region is with low pressure i.e., 101325 Pa. High pressure side is filled with N2 and low pressure side is filled with O2. Using 'Event' we need to create an event for so that membrane between low pressure and high pressure can be open or closed.

~Problem setting:-

Simulation parameters:-

• Type of simulation: Transient state
• Solver: Pressure based solver
• Mode: Full hydrodynamics
• Event: Enable

• Start time: 0 Seconds
• End time: 0.003 Seconds
• Time step: 1e-8
• Turbulence model: RNG K-epsilon
• Base grid: dx=dy=0.001m, dz=0.005m
• Region definition:
  
  • High pressure region
  • Low pressure region

Fig: High pressure definition	Fig: Low pressure definition

• Adaptive mesh refinement: Species based
  • Active region:- 1. High pressure region, 2. Low pressure region
  • Default embedding level:- 2
  • Sub-grid criterion:- 0.002

Initial and boundary conditions:-

• High pressure
  • Boundary type: Wall
  • Slip wall
  • Region: High_pressure
  • Temperature: 300k

• Low pressure
  • Boundary type: Wall
  • Slip wall
  • Region: Low_pressure
  • Temperature: 300k

In above figure the boundary flagging (defining boundary) is shown, the different color denotes different boundary in geometry. There are 2 boundaries considered in simulation which are high pressure zone and low pressure zone.

~Post processing:-

Mesh:

Fig: Mesh geometry

Fig: Enhanced mesh view due to AMR

Fig: Total cell count

The above figure shows mesh surface at initial state i.e., at time t=0 sec. The well structured mesh with 1mm height and 1mm width is generated. As time step increases, due to provided settings of AMR we get refined mesh at specific places. The refined mesh is shown in above 'enhanced view of mesh' figure.

For current problem the AMR setting is depended on species concentration. Where the species concentration gets changed by 0.002, solver automatically refined it with half of previous mesh element size. In setting of AMR, I have restricted number of maximum cells to 75000. So till 0.001 second the mesh elements are 5000 and after 0.001 seconds due to AMR the mesh counts increases. This can be seen in total cell count plot.

Fig: Variation of pressure wrt run time

Fig: Pressure contour

Fig: Variation of mean temperature wrt run time

Fig: Temperature contour

Fig: Variation of mass of N2 wrt run time

For all of the above plots it is visible that till 0.001 seconds, all the variables are remains unchanged. But after 0.001 seconds variable values are changing. The reason behind behavior of plot variables is event which we have generated while setting up problem. Due to event setting, the permeable membrane between high pressure region and low pressure region is present till 0.001 seconds and after 0.001 seconds it will tear down (open). As permeable membrane opens due high pressure region the N2 flows towards low pressure region and start mixing with O2 at low pressure region.

The function 'Event' present in converge allows us to open and close permeable membrane between low pressure region and high pressure region. The solver creates disconnect triangles between both regions. When we provide close condition, the disconnect triangles are present and does not allows N2 to flow towards O2. And when we provide open condition, the disconnect triangles gets delete, thus high pressurized N2 flows towards low pressurized O2.

In temperature contour it is seen that temperature in low pressure region is much higher than high pressure region. It happens due to compression of O2 species. As compression increases the temperature also increases.

Mass fraction animation:-

The above animation shows how shock wave is generated and propagate as soon as the permeable membrane breaks. It is also visible that after few milliseconds the shock wave reflects. At initial the membrane is present between high pressure zone and low pressure zone, it is present till 0.001 seconds. After 0.001 seconds the membrane gets break which allows high pressure fluid to flow towards low pressure zone.

Conclusion:- It can be concluded from above postprocessed data that-

1. Due to enabling AMR, number of mesh elements varying continuously.
2. Enabling AMR shows smooth and more accurate separation between N2 and O2 at their contact location.
3. High pressure N2 gas compress low pressure O2 gas, which increases temperature of O2 gas.
4. Generation of shock waves is due to pressure difference, and shock wave remains in motion (reflecting from end surfaces) till the pressure difference dies down.

Reference:-

1. Wikipedia