Shock Tube Simulation

• Given Problem:-

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

• Software used-

1. Converge CFD Software

2. Cgywin

3. Paraview

• Geometry -

• Steps Involved while solving this challenge-

1. We first download the required geometry from the website of skill lync.

2. Set the case setup according to the given problem in the challenge. We first need to prepare the geometry by deleting unnecessary parts from geometry and make sure that it dont have any error.

3. We will flag the bounaries and regions. Basically we will define two regions in this case i.e. High pressure region and low pressure region. High pressure region contains nitrogen and low pressure contains oxygen.

4. Prepare the case setup and export the files into cgywin for further use an computation.

5. Cgywin willl create the output files of the case by solvig them.

6. Now we will open paraview software and open the case there.

7. Now by using Converge software line plotting option, we will plot the graphs for Temperature and pressure.

• Case setup Important Parameters:-

1. Application- General Flow

2. Solver- Transient

3. Start Time- 0

4. End time- 0.003 sec

5. Initial time step and minimum time step- 1e-9 sec

6. Pressure at N2 region- 6 Bar

7, Pressure at O2 region- 101326 Pa

8. Turbulence Model- RNG k-e

9. Base Grid- 0.00075 m

10. Boundary conditions- High Pressure Region- Stationary Wall with Slip condition.(300k)

Low Pressure Region- Stationary wall with law of wall

Rest boundary are 2d.

• Shock Tube Discription:-

• The shock tube is divided into two regions mainly i.e. low pressure and high-pressure region.

•When the diaphragm is broken then there is no interface between the fluid in the high-pressure zone and low pressure zone ,so the high pressure fluid is directly going to enter the low-pressure zone.

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

• Because of pressure differences, the shock waves develops quickly. Then the fuel and air mixture mixes and then shock waves occur and then auto ignition happens.

• From the shock tube data, the fuel and air mixture takes some minimal time to start ignition. This is known as ignition delay.

• Base Grid, Pressure and Temp condition-

Fig.1.1 Mesh Profile of geometry

Fig.1.2 Two regions of N2 and O2 in shock Tube

Fig.1.3 Initial pressure condition in shock tube condition before diagphram Broken

Fig.1.4 Pressure condition just when diagphram broken

Fig.1.5 final Pressure condition in shock tube after time completion

Fig.1.6 Graph of pressure vs time

Explanation-

The total run time for the case is 0.003 sec. The separartion is there for 0.001 seconds and after it the mixing took place. Let\'s understand the case in points-

1. Fig. 1.2, Green side is nitrogen part whereas purple part is oxygen part. The diaphragm is separating the mixture.

2. Fig. 1.3, Pressure of nitrogen is quite high(6 Bar) which is quite high compare to oxygen (1 bar).

3. Fig. 1.4, The diaphragm gets broken after 0.001 seconds and hence the nitrogen will push the oxygen to the right side due to its high pressure.

4. Fig. 1.5, It is the final time step of process. After breaking of diaphragm high pressure N2 will try to fill the low pressure space. Therefore there is a drop in the pressure in the high-pressure region accompanied by a rise of pressure in low-pressure-refer . However, this forward motion of N2 is thwarted by the retreating shock wave which also prevents the further mixing of N2 and 02 by creating a recirculating zone at the far end of the low-pressure region. Thus there is a backflow of N2 in the high-pressure region resulting in pressure rise which is accompanied by a corresponding pressure drop in the low-pressure region-refer figure below. The phenomenon gives rise to fluctuations in pressure which we can observe the pressure vs time plot.

5. Fig. 1.6, The graph shows the fluctuations in pressure due to shock waves.

Temperature-

Fig.1.7 Initial Temp. condition in shock tube condition before diagphram Broken

Fig.1.8 Temperature condition just when diagphram broken

Fig.1.9 final Temperature condition in shock tube after time completion

Fig.1.10 Graph of Mean Temp vs time

Explanation-

The total run time for the case is 0.003 sec. The separartion is there for 0.001 seconds and after it the mixing took place. Let\'s understand the case in points-

2. Fig. 1.7, Temperature is identical at both sides.

3. Fig. 1.8, The diaphragm gets broken after 0.001 seconds and hence temperature starts changing due to pressure difference of gases.

4. Fig. 1.9, It is the final time step of process. As the pressure decreases in the high-pressure region immediately after 0.001s there is the corresponding decrease in the temperature of that region . Similarly with rise of pressure in the low-pressure region is accompanied by increases in temperature of the low-pressure region-refer figure below. This oscillation in temperature and pressure are caused due to the shock wave which continuously travels back forth in the channel.

5. Fig. 1.10, The graph shows the fluctuations in temperature due to shock waves. Due to fluctuation in pressures due to shock waves we will see the variation in temperature. Due to this we can see the fluctuations in the graph.

Cell Count-

Cell count is constant i.e. near 4000 till 0.001 seconds. We are keeping the fluids from mixing with each other upto 0.001 seconds.

But after 0.001 secons things goes interesting though. We are using AMR in this case. When mixing happens the N2 present in the higher pressure regions penetrates into the lower pressure region, therefore, its concentration increases in the low- pressure region. Now the converge which is actively monitoring the subgrid-scale N2 concentration increases the cell count as per AMR. As the N2 penetrates further into the low- pressure region the cell count increases accordingly. However, this increase in cell count is not absolute, because as the shock wave created due to the initial pressure difference propagates forward it hits the end wall of the low-pressure region and is reflected back. This retreating shock front mitigates the mixing process by creating a recirculating zone. As a result, the rise of species concentration of N2 in the low pressure is curtailed and therefore the rise of cell count is also modified proportionately.

Velocity-