Shock Tube Simulation

Shock Tubes:

These are simple ducts containing a high pressure and a low pressure region, which is separated by a diaphram (usually metal). They are used to study the chemical kinetics of ignition of fuel inside a high pressure chamber. They mimic the environment which occurs inside the combustion chamber of the IC engine (like Direct inj. systems, where auto ignition occurs). Hence, they can also be used to determine the ignition delay along with the chemical kinetics.

Working:

The Duct containing the High pressure and Low pressure Fluids are separated physically by a diaphram. The driver gas is usually filled until the diaphram ruptures on is own. Hence, the driver gas is at the highest pressure. Once the diaphram is broken, the Fluid at high pressure region starts to mix with the low pressure region. Due to the high pressure difference, a shock wave is occurs.

We can observe an expansion wave occuring at the High pressure region and a compression wave occuring at the low pressure region. We are also able to observe the reflections of the shock wave that gradually slows down the mixing process of the two fluids.

Background of the Project:

This project is intended to introduce about shock tubes, its working and the need of using a shock tube. Following are few applications:

1. To study the Chemical Kinetics.
2. Can be used as Wind tunnels which replicate high pressure and high temperature environments (as in Turbine sections of Jet Engines).
3. The possibility of simulating a hypersonic flow inside a shock tube allows us to study things like atmospheric entry of spacecrafts.

The experimental durations are limited to few microseconds. However, this is suffieicnt for most of the studies.

Another exposure through this project is the concept of regions and events in ConvergeCFD. Regions are the volumes containing the fluids. The regions with respect to the shock tube are the high and low pressure regions. At t = 0 seconds, the two regions are physicslly separated. As in experiment, it is required to break the diaphram separating the regions. This is achieved by utilising the Events functionality. This enables us to realise the breaking of diaphram by connecting the two regions at the user defined time.

Mesh Generation

The Adaptive Mesh Refinement is done based on the concentration of N2. As the N2 Conc. decreases locally, the mesh is also refined.

Pressure & Temperature of the Shock tube Domain:

Once the region opens up, the pressure difference creates a shockwave. The movement of shock wave can be noticed by seeing the distinction between the high and low pressure. As the wave progresses, it hits the wall and reflects backwards and this continues. While the wave travels to the opposite wall, the pressure inside the tube is rougnly between 3 bar to 4.5 bar. Once the wave hits the wall, it undergoes compression and the pressure again increases to 6 bar.

The Temperatures can be seen increasing on the right side once the regions Open up. The high pressure region compresses the fluid in the low pressure region due to which is the tempreature rise. Similarly, as the pressure of the high pressure region decreases, there is an expansion observed and this causes the decreasing temperature. The Change is temperature is mostly due to compression/ expansion of fluids as the initial temperatures for both regions have been set same at 300K.

Cell Count History:

The Cell count stays constant till few instant after 0.001 seconds. Because the mixing of high pressure and low pressure region is about to start, which can be attributed to the delay. This delay can be shortened while the Pressure difference between the two regions are higher.

The cell count increases once the mixing starts and the shock wave occurs. We have defined the AMR based on the Species concentration. Hence, due to mixing, the ratio of N2 gets lowered which enables the AMR to refine the mesh at those locations. This leads to the increase in the cell count suddenly.

After the first reflection of shock wave at right wall, the wave pushes the O2 to the left side, which enables mixing with N2 - resulting in higer refinement of mesh and increased cell count from 0.0015 seconds till 0.0024 seconds.

After this, the wave undergoes second reflection at the left wall and this pushes the N2 as well as O2 to the right. This reduces the level of mixing which increases the N2 conc. to higher level that reduces the mesh refinement. This leads to reducing cell count later on.

References:

1. Shock Tube Investigations of High Temperature Reaction Kinetics (http://www1.phc.uni-kiel.de/cms/index.php/en/research-m-gfr/147-shock-tube-investigations-of-high-temperature-react-kin.html)

2. Fundamentals of Shock Tube (https://nptel.ac.in/courses/112103021/35)

Google Drive Link to Sim Files: (https://drive.google.com/open?id=1GcAZUWXNq-uiSU9bh3Lr-1cJk7b5gih4)