Shock tube simulation using Converge
Shock tube is an instrument used to study supersonic flows, shockwaves, expansion waves and chemical gas reactions. Usually one portion of the tube is increased to a high pressure and the other side of the tube which is relatively in a much lower pressure is seperated from the high pressure portion of the tube by a diaphragm. The diaphragm is broken to start the supersonic flow. The shockwaves and expansion waves propagating through the tube are then observed.
In this project the workings of a shock tube is simulated using Converge CFD and the post processing is done using Paraview, the dimensions of the shock tube used for the simulation are 0.2m, 0.01m, 0.01m (x,y,z).
One portion/region of the shock tube is kept at a high pressure of 6 bar (600000 Pa) filled with nitrogen and the other portion/region of the tube is kept at atmospheric pressure (101325 Pa) filled with oxygen. RNG k-epsilon is used as the model for turbulence.
The boundary conditions used for the simulation are:
For both front and back of high pressure region of the tube : 2D boundary is used.
For both front and back of low pressure region of the tube : 2D boundary is used.
For boundaries other than the front and back : Assigned as stationary wall with Law of the wall condition is applied.
In order to simulate the breaking of diaphragm event functionality of the Converge is utilised. An event is set up such that high pressure region opens to the low pressure region at exactly 0.001s. The simulation is carried out using transient solver up to 0.003s for two mesh sizes and the results are captured using Paraview.
The mesh 1 is of size of 0.001m and the mesh 2 is of the size 0.0005m. For both the meshes species based adoptive mesh refinement for nitrogen is carried out with max embedding level of 3 with sub-grid criterion taken as 0.001 i.e., minimum mass fraction of the selected species that will trigger Adoptive mesh refining (AMR) is 0.001.
Animation showing mesh 1 with AMR:
Total cell count for mesh 1:
Animation showing mesh 2 with AMR:
Total cell count for mesh 2:
The cells counts are suddenly increasing afte 0.001s which is clearly the indication that the high pressure has opened and the nitrogen has started mixing with oxygen in the lower pressure region, to maintain the high accuracy the AMR kicks in wherever nitrogen is present.
Pressure comparison between two meshes:
Mean temperature comparison between two meshes:
When the high pressure region opens at 0.001s, due to a large difference in pressure the flow will reach supersonic velocities which results in a shockwave getting emitted from the interface of high and low pressure region towards the direction of the low pressure region. From the graphs we can observe that the pressure and temperature after the event of the high pressure region opening at 0.001s falls, this is due to release of pressure by opening of high pressure region. But shortly after both pressure and temperature begin to rise, this increase is the result of shockwave getting reflected back. The reflected shockwave increases the pressure but not as high as it was originally, which results in a weaker shockwave getting generated and the pattern continues until the pressure difference across the tube becomes constant.
As explained before, the shockwave rises the temperature, this rise in the temperature will result in combustion if nitrogen and oxygen are replaced with combustible gases, therefore useful in studying chemical kinetics of combustion.
For demonstration the animations of changes pressure, velocity, temperature and the species are attached below:
Animation showing N2 variation in the shock tube:
Animation showing pressure variation in the shock tube:
Animation showing temperature variation in the shock tube:
Animation showing velocity variation in the shock tube: