Shock Tube simulation

Objective:

• Setup a trasient shock tube simulation.
• Plot the pressure and temperature history in the entire domain.
• plot the cell count asa function of time - Exolain the result.

Introduction:

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 two regions are seperated by diaphgram ,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. Observations can be made in the flow behind the incident front or take advantage of the longer testing times and vastly enhanced pressures and temperatures behind the reflected wave.

In addition to measurements of rates of chemical kinetics shock tubes have been used to measure dissociation energies and molecular relaxation rates they have been used in aerodynamic tests.

A real-life example of a shock tube is to study the auto-ignition system. The tube is filled with fuel and air in the two chambers. Due to the shock waves and a rise in temperature, the air-fuel mixture is going to auto-ignite. The shock tube data can be used to see how long the mixture takes to combust i.e. the ignition delay. So, a shock tube simulation can be very useful to compare the analytical and experimental data.

Geometry:

Above Mentioned geometry the green is high pressure region and red is low pressure region.

Dimennsions of shock tube

X-axis 0.2 m

y-axis 0.001 m

z-axis 0.01 m

Mesh Size:

• x- direction = 0.004
• y-direction = 0.004
• z-direction = 0.004

The Adaptive Mesh Refinement option is enabled. It refines the mesh of a selective region. For this simulation, the AMR is enabled for species criteria. The properties of AMR are kept as follows -

• Maximum cells = 200000
• Maximum embedding level = 3
• Sub-grid criteria = 0.001

Mesh size at 0 sec:

Mesh size 0.001 sec:

As we can see above after 0.01 sec the grid size is refining along with simulation this is happend when AMR value given 0.01 sec . The AMR is refining each cell leveal 3.

Boundary Conditions:

The boundaries are grouped into two regions-

• High-pressure region
• Low-pressure region

The set of boundary conditions in both these regions are identical.

• As the case is 2-dimensional, the front and the back wall of the tube are kept TWO_D.
• The sidewall has a boundary type WALL with No-slip boundary condition. The Temperature and Turbulent Kinetic Energy have Dirichlet boundary condition at this wall.
• The Upper and Lower walls have a boundary type WALL with Law of Wall boundary condition. The Temperature and Turbulent Kinetic Energy have Dirichlet boundary condition at this wall.

Initial Conditions:

For the High-pressure region

• Pressure = 6 Mpa
• Temperature = 300 K
• Mass fraction of N2 = 1

For the Low-pressure region

• Pressure = 1.013 Mpa
• Temperature = 300 K
• Mass fraction of O2 =1

The Events option was enabled for this simulation. Using this option, we can simulate the function of a diaphragm as a physical diaphragm could not be accommodated in the geometry.

• The Diaphragm remains closed till 0.001 sec.
• After 0.001 sec, the diaphragm is opened and the gases start to mix in the domain.

Result:

Cell count: 0.004

cell count 0.001:

In that the cell count is 895 where the simulation reached 0.03 sec and after 0.001 sec the AMR starts to refine each cell at leavel 3 to get cell count is 1800. If the base grid size finer cell count is increase.If base grid size is 0.001 the starting cell count is 2000 After 0.001 sec AMR starts to refine the cell count is reached 14800.

Pressure:

The pressure in High and Low-pressure zones (Region 0: High-pressure, Region 1: Low-pressure)

Pressure at shock tube:

Animation :

Conclusion:

• As we can see above graph between high pressure and low prssure intial the pressure differnce is 5 bar. the difference of pressure its going to mix both condtion as per bernoulies principle.
• The high pressure gas mix with low gas pressure due to produce shock waves because of presure difference. the shock waves are travelled both front and back in domine due to reflection from the walls compression and expression of gases.
• At the walls produces high pressure due to compression of gases its will take when the fluid reaches steady state.
• After 0.015sec the pressure reaches steady state before that the pressures are interchanged repetedly and gets staedy state.
• Above as we see the aninmation of pressure produceing shock waves when the pressure reflection from walls due to pressure difference.

Temperature:

The temperature in High and Low-pressure zones (Region 0: High-pressure, Region 1: Low-pressure)

Shock tube temperature

Animation:

Conclusion:

• A similar pattern of consecutive maxima and minima can be observed for temperature too. This is because the pressure is directly proportional to temperature.
• In High-pressure region, the temperature initially starts to decrease and it is vice-versa for the Low-pressure region.
• At the walls pressure reached high reached so temperature increases thias can usesful to combution process for auto ignition.

Pressutre vs Mass fraction of N2:

Velocity: