Week 7: Shock tube simulation project

AIM:

• Setup a transient shock tube simulation
• Plot the pressure and temperature history in the entire domain
• Plot the cell count as a function of time

shock tube:

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. Shock tubes (and related impulse facilities such as shock tunnels, expansion tubes, and expansion tunnels) 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. More recently, shock tubes have been used in biomedical research to study how biological specimens are affected by blast waves.

Operation:

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 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.

Applications of shock waves:

shock tubes have been used to measure dissociation energies and molecular relaxation rates they have been used in aerodynamic tests. The fluid flow in the driven gas can be used much as a wind tunnel, allowing higher temperatures and pressures there in replicating conditions in the turbine sections of jet engines. However, test times are limited to a few milliseconds, either by the arrival of the contact surface or the reflected shock wave.

They have been further developed into shock tunnels, with an added nozzle and dump tank. The resultant high temperature hypersonic flow can be used to simulate atmospheric re-entry of spacecraft or hypersonic craft, again with limited testing time

Importing Geometry and Assign the boundary:

Import the geometry into the Converge studio and clean up the geometry by using some tools which are available in the converge.

Enable the vectors on the geometry make sure that all the normals should be facing inside the fluid domain The below figure shows the vectors outside the domain convert them into inside where the fluid is going.

Now check for the errors in the geometry by opening the diagnosis dock and then find if no errors are there means we can proceed to the case setup.

Now Assign the boundaries name to the geometry

Case setup for Simulation:

• Application Type – Time Based
• The flow is general flow which contains the air as a Material.
• Air contains a Species mixture of O2 and N2 which will flow through the required geometry.
• Global Transport Parameters the Prandtl number is 0.9 and the Schmidt number is 0.78.

Simulation Parameters:

• In the Run Parameter: Solver we used is Transient state and the simulation mode = Full hydrodynamic in the mic state we enable the Solver Momentum, Solve Species.
• In Simulation time Parameters we set the values for start time as 0 Seconds and end time as 0.003 Seconds and the initial and Minimum time setup for 1e-9 and Maximum time setup is 1 sec and remaining values are put to default.
• In the Solver Parameters, the Navier stock equation should be Pressure based solver and remaining should be default.

Initialization and Boundary Conditions:

• In the initialization region we have to create the two regions and initialized with the valves.
• The name of the Region as a High Pressure Region and the values assigned for the temperature and pressure is 300k and 600000 Pascal and add the species N2 with the mole fraction of 1.
• The name of the another Region as a Low Pressure Region and the values assigned for the temperature and pressure is 300k and 101325 Pascal and add the species O2 with the mole fraction of 1.

Events:

CONVERGE uses events to active or deactivate the disconnect triangles, which control when and where flow between regions is allowed. An OPEN event deactivates the disconnect triangles and thus allow flow between the specified regions. A CLOSE event activates the disconnect triangles and thus prohibits flow between the specified regions. When disconnect triangles are activated, they act as a SYMMETRY boundary condition.

The Events must be CYCLIC, SEQUENTIAL, PERMANENT, or NO_DIS_TRIANGLES

In this we used the Event as Sequential which is shown below

• At 0 seconds the diaphragm between the High Pressure Region and Low Pressure Region is closed
• After 1 milli second the diaphragm between the High Pressure Region and Low Pressure Region is open

High Pressure Region Boundary Conditions:

• For high pressure region the boundary type should be wall
• Velocity Boundary Condition should be the Slip Condition.
• Temperature Boundary Conditions should be the Zero Normal Gradient.

Low Pressure Region Boundary Conditions:

• For Low pressure region the boundary type should be wall
• Velocity Boundary Condition should be the Slip Condition.
• Temperature Boundary Conditions should be the Zero Normal Gradient.

Physical Models:

• In the physical models enable the Turbulence Modelling and the solver should be selected as RNG K-e and put the remaining values as a default.

Grid Control:

• Element size dx=dy=dz=0.003 m

Adaptive mesh refinement (AMR):

In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'. Many problems in numerical analysis, however, do not require a uniform precision in the numerical grids used for graph plotting or computational simulation, and would be better suited if specific areas of graphs which needed precision could be refined in quantification only in the regions requiring the added precision. Adaptive mesh refinement provides such a dynamic programming environment for adapting the precision of the numerical computation based on the requirements of a computation problem in specific areas of multi-dimensional graphs which need precision while leaving the other regions of the multi-dimensional graphs at lower levels of precision and resolution.

In our case we need more refinement of mesh at the shock were occur in that region we need more refinement of mesh in that area and the remaining should be the normal grid size mesh.

In converge we have the different methods which are used for the Adaptive Mesh Refinement Right now we are using the Species based method with the 3 embedded level. Thus the converge helps the curvature of temperature property provided in AMR and starts the refining of the mesh for the temperature curvature.

• In the Grid control enable the Adaptive Mesh Refinement
• In Adaptive Mesh Refinement the High_Pressure_region and Low_pressure_region is changed from the Available region to the Active Region.
• Then Go to Species
• Enter the number of Embedded level=3
• In the species window enter the details as per below figure:

Output and Post Processing:

• Post variable Selection and Output files are the default values.
• In the output files we have given time interval to write the 3D output data=0.00003 Seconds, thus the outputs of the simulation files be stored after 0.00003 seconds

Post-Processing:

I have done the post processing of the results for the case using the converge studio and paraview. Post processing is actually used in order to get the desired Output by running the simulation

Results:

Mesh Contour:

Mesh Animation:

Pressure Contour:

Pressure plot:

As the pressure difference between the two regions is 5 bar. As the mixing occurs the pressure difference occurs in both regions. As the high pressure gas starts mixing with the low pressure gas, thus it leads to the formation of shock waves due to the difference in the pressure. These shock waves travel to and fro in the domain due to the reflection from the walls

The pressure of N2 gets dropped due to the expansion and the pressure for the O2 gets increases due to the Compression of gas.when the wave gets back to its original position the pressure again increases and the pressure in low region decreases we can clearly observe this change in the graph for Maxima and Minimum graphs.This Process Continue still it reaches the simulation time.

Pressure Animation:

From the above animation we can see that the waves are travelling from higher pressure region to lower pressure region when it reaches the dead end it reflects back and travel in the opposite direction and the process repeats.

Velocity Contour:

Velocity Animation:

Temperature Contour:

Temperature plot:

From the graph,In the higher Pressure Region the temperature is constant at the initial stages after 1 milli seconds the temperature is declined a lot from 300 k to200 k due to the pressure decreases in the domain .At the same time the Temperature in lower region is increases due to the pressure increases ..we can see the fluctuations in the graph due to the shock wave as it moves front and back in the domain.when it moves backwards the temperature in high region starts increasing and decreases in the low region Simultaneously it happing as the flow waves are moving forward and backward.

Temperature Animation:

Mass Fraction of N2 Contour:

plot for Mass Fraction of N2:

Animation of Mass Fraction of N2:

From the animation we can observe that the as the diaphragm breaks the N2 gas is entered into the low pressure region and as soon as it reaches the end,the reflected shock waves pushes back the wave in the reverse direction and reflected back from the other end of the tube that pushes the N2 gases in the direction to the other end.This process is continue till the shock waves are declined.

Mass Fraction of O2 Contour:

Plot for Mass Fraction of O2:

Animation of Mass Fraction of O2:

Total Cell Count:

The total cells in the domain can be varied due to the brust of diaphragm and also we used the AMR technique for this so we can observe an increas in the number of cells in some regions.

The maximum cell count achieved in this case is 90,000 cells.

Conclusion:

• Successfully demonstrated the Transient Shock Tube Simulation.
• Also observed how the species is mixing in the Shock tube.