Shock Tube Simulation
- Objective:
- To set-up a transient shock tube simulation in Converge CFD and analyse the results.
- Procedure:
- The geometry of a shock tube is downloaded and imported into Converge CFD software.
- The geometry is diagnosed for any surface imperfections, such as open edges, non-manifold edges,etc.[Note:A shock tube consists of 2 regions, a high pressure region and a low pressure region, and a diaphragm separating the two. The diaphragm is also present in the geometry, which causes the non-manifold edges error, so it is deleted as it is simulated using 'events' option in case set-up.]
- The boundaries are flagged based on the regions to which they belong to, i.e., high pressure and low pressure region. This is done as there is neither inlet nor outlet for this simulation as the fluid is stored at a particular pressure similar to a pressurized container.
- The inputs for the simulation are given by means of case set-up. The inputs include the selection of material, here, the `N_2` and `O_2` are chosen as the species. Then the simulation time parameters are selected for transient simulation(Here, simulation time=0.003s).
- Then, under the Regions and Initialization, the 2 regions and the corresponding initial conditions such as the pressure and the species present in the region are specified. Furthermore, the boundary conditions of the two boundaries are given as stationary slip walls.
- The most important step is the addition of 'Events' feature under the 'Regions and Initialisation'. Here, the virtual diaphragm is created using this feature. The time period when the 2 regions should remain closed(0s to 0.001s) and when it should open(0.001s to 0.003s) are specified.
- The base grid size(dx=dy=dz=0.003m) of the mesh is given and the species AMR(Adaptive Mesh Refinement) feature is used to refine the mesh for the critical regions of `N_2`.
- The physical models, post-processing and output parameters are selected.
- The input files are exported to a folder and the converge executable is run to generate the output files.
- The output files are post-converted and various parameters are viewed using Paraview software.
- Note: Shock tube, as discussed earlier, consists of a high pressure(driver side), a low pressure(driven side) and a thin metallic diaphragm. Once the diaphragm ruptures, shock wave is generated, which compresses the low pressure gas. Thus, the shock wave travels throughout the constant area shock tube, which causes a drastic change in the velocity, pressure,etc. Shock tube is used to study the chemical kinetics of gases. It is also used to find the ignition delays in engines, and various other parameters related to ignition, as ignition is dependant on the pressure, temperature and various physical variables of gas which could be influenced by shock waves. It has varied applications in the field of aerospace for production of high speed flows in laboratories for experimenting. The below picture shows a shock tube setup for an experiment.
- Observations and Inferences:
- Animation of mass fraction and corresponding pressure variation in Shock tube:
- Observation:
- The red portion denotes the presence of `N_2` and blue portion denotes `O_2` in the Mass fraction contour. Similarly the red portion denotes high pressure and blue portion denotes low pressure in Pressure contour.[This is specified for clarity as the two contours are combined]
- As the diaphragm ruptures the high pressure `N_2` compresses the low pressure `O_2` and then retracts back after a certain limit. Also the mixing of the two entities take place to an extent.
- This continues till the end of simulation.
- Inference:
- As the diaphragm breaks there is a formation of normal shock wave, which propagates along the length of the tube until the end(end of the driven section). Then it gets reflected by the wall and hence returns back, which can be noted as the `N_2` gas retracts back, and the wave furthers towards the left end. The same is depicted in the pressure contour, when the right part of the tube is observed precisely. [Note:A drastic state variation, such as pressure, which moves rightward and gets reflected signifies the presence of shock wave.]
- Now, at the same instant when the shock wave is created, the expansion or rarefaction waves are created. These expansion waves move in the direction opposite to that of the shock wave with the speed of sound causing continuous or smooth changes in the state of the gas. Then they get reflected by the end wall of the driver side and cause the expansion along the length of the shock tube as they move.[Note:The expansion and other changes in state of gas happens in the direction opposite to the direction of propagation of expansion wave.]
- Then again, as the shock wave, after reflection from the left end, travels thro' the length of the tube causing the gases moving leftward to move rightward to an extent.
- Meanwhile, the contact surface has moved thro' a distance from its initial position due to the motion of the gases and the influence of pressure.
- Based on the above inferences the shock tube could be divided into 4 regions as shown below:
- Region 1: It is the region between the shock and the right end of the wall, where the gas is at rest and the shock wave has not affected it yet.
- Region 2: It is the region between the shock wave and the contact surface, which is affected by the initial shock wave.
- Region 3: It is the region between the contact surface and the tail of the expansion fan, which is under expansion and the gas is moving in the direction of the shock.
- Region 4: It is the region between the head of the expansion wave and the left end of the wall, where the gas is at rest and is yet to be affected by the expansion wave.
- Observation:
- Animation of Velocity variation in Shock tube:
- Observation:
- The above shows the variation of velocity in the shock tube.
- The variation in velocity is very drastic all over the domain.
- Inference:
- The drastic variation in velocity is attributed to the formation of the shock wave.
- There is no considerable change in velocity of the gases near the ends, which denotes that the gases are at rest at these locations.
- Observation:
- Animation of Temperature variation in Shock tube:
- Observation:
- The above shows the variation of temperature in the shock tube.
- There is smooth variation in a particular section and drastic in some sections.
- Inference:
- The drastic variation in temperature is attributed to the formation of the shock wave.
- The contact surface and its motion can be identified clearly from the above contour by means of the temperature discontinuity prevailing in the contour in the rightward of the tube. As the shock wave cause drastic increase in the temperature as it passes by, the contact surface is found to have completely different projections of temperature than the other regions.
- Observation:
- Pressure Variation in the entire domain:
- Observation:
- The pressure is constant until 0.0011s and it varies in cyclic manner as the flow furthers.
- The amplitude and wavelength of the pressure curve decreases gradually as the simulation continues.
- Inference:
- The pressure is constant until the diaphragm is closed.
- As the diaphragm ruptures the average pressure over the entire domain first decreases as the high pressure side mixes with the low pressure side and the shock wave travels towards the low pressure side in addition to expansion wave travelling towards the high pressure side reducing the pressure there.
- Then it increases as the shock wave travels towards the high pressure region and rises the pressure furthermore. This continues till the simulation ends.
- Moreover, this would reach a steady state(equillibrium state) if the simulation continues further beyond this time frame.
- Observation:
- Temperature Variation in the entire domain:
- Observation:
- The temperature is constant until 0.0011s and it varies in cyclic manner similar to that of pressure.
- The amplitude and wavelength of the temperature curve decreases gradually as the simulation continues.
- Inference:
- The temperature also varies in the same fashion as that of the pressure curve.
- The same reasons are accounted for this too.
- Observation:
- Cell Count Variation in the entire domain:
- Inference:
- The total number of cells is lesser in the beginning until 0.0011s.
- It increases to a very high number after that. This is because the species AMR feature is enabled only after 0.001s. With the influence of this feature the meshing is made autonomous.
- In species AMR, the `N_2` is selected, which means that the critical areas of `N_2` are refined upon satisfaction of a particular condition after 0.001s.
- This leads to the above non-linear change in the number of cells as the simulation progresses.
- Inference:
- Mesh when AMR feature is realised:
- Inference:
- The above shows the refinement taking place in the shock tube as the diaphragm ruptures.
- As a three-layer refinement is selected, the meshing is found to be in the above pattern.
- Inference:
- Animation of Mesh generation for Shock tube simulation:
- Inference:
- The above animation of the mesh generation shows how the mesh refinement takes place as the simulation proceeds.
- It can be concluded that the mesh-refinement is done in and around the contact surface in order to capture the variations taking place in this location in far clear manner.
- Inference:
- Animation of mass fraction and corresponding pressure variation in Shock tube:
- Result:
- Thus, the transient shock tube simulation has been done and the inferences derived.