Week 7: Shock tube simulation project

Objective:-

To simulate transient simulation over a shock tube and determine the temperature, pressure plot and cell count as the function of time.

Theory:-

Shock Tube

• Shock tube is an instrument used to replicate and direct blast wave at a sensor or a model in order to simulate actual explosion and their effect usually on a smaller scale.
• Shock tube can also be used to study aerodynamics flow under a wide range of temperature and pressure that are difficult to obtain in other type of testing facilities.
• Shock tube are also used to investigate compressible flow phenomena and gas phase combustion reaction.
• A shock wave inside a shock tube may be generated by a small explosion of high pressure which cause diaphragm to burst and a shock wave to propogate down the shock tube.

Diaphragm :-

• Partition between pressure stage in a turbine casing are called as diaphragms.
• They hold the vane shaped nozzle and seals between the stages.
• Usually Labyrinth type seal are used, one half of the diaphragms is fitted into the top of the casing and the other half into the bottom.

GEOMETRY:-

A shock tube geometry where the brown region is High Pressure region and light blue region is Low Pressure Region and Diaphragm is in between them which separate both the region.

CASE SETUP:-

1. Application Type:-

1. Time Based

2. Material:-

1. Gas simulation - On
2. Reaction Mechanism - On

3. Global Transport Parameters:-

1. Turbulent Prandtl Number - 0.9
2. Turbulent Schmidt Number - 0.78

4. Run Parameter:-

1. Solver - Transient Based Solver

5. Simulation Time Parameter:-

1. Start time - 0.0
2. End time - 0.05
3. Initial time step - 1e-9
4. Minimum time step - 1e-9
5. Maximum time step - 1

6. Region and Initialization:-

1. High Pressure Region:-

1. Temperature - 300 K
2. Pressure - 600000 Pa
3. Species - N2 (Mass Fraction - 1)

2. Low Pressure Region:-

1. Temperature - 300 K
2. Pressure - 101325 Pa
3. Species - O2 (Mass Fraction - 1)

7. Event :-

8. Boundary Condition:-

1. High Pressure Wall - Wall type ( HIGH PRESSURE REGION)
2. High Pressure Front 2D - TWO_D (HIGH PRESSURE REGION)
3. High Pressure Back 2D - TWO_D (HIGH PRESSURE REGION)
4. Low Pressure Wall - Wall type (LOW PRESSURE REGION)
5. Low Pressure Front 2D - TWO_D (LOW PRESSURE REGION)
6. Low Pressure Back 2D - TWO_D (LOW PRESSURE REGION)

9. Physical Model:-

1. Turbulance Model - RNG k-epsilon

MESH:-

Grid size:-

dx = dy = dz = 5e-4 m

Mesh without AMR

Adaptive Mesh Refinement:-

Mesh with AMR

RESULT:-

A. Temperature variation:-

1. Temperature Contour:-

2. Temperature variation with time:-

1. The mean temperature at the high pressure region, low pressure region and shock tube are plotted as the function of simulation time.
2. It is observed that respect to the temperature where temperature reduce as the gases start to mix after 0.001 sec and rises again when the recirculation zone is created to eventually reach steady state when the generated shock attain equilibrium.
3. At the end of the simulation, the low pressure region had a mean temperature about 295 K and high pressure region has temperature about 278 K .

3. Temperature Animation:-

B. Pressure variation:-

1. Pressure Contour:-

2. Pressure change with time:-

1. The pressure is maintained its stability till 0.001 sec with a pressure difference of nearly to 5 bar.
2. As the diaphragm break and the gas in high pressure zone rushes toward the low pressure zone creating a rapid pressure differential drop.
3. The initial pressure of 6 bar in high pressure region and 101325 Pa in low pressure region reaches steady state of 1.2 bar at the end of 0.05 sec.
4. The generation shock wave due to compression cancel the incoming shock and thus pressure difference between the two zones rises again.
5. This phenomenon repeat again but the magnitude of reduction in pressure difference reduce and as the simulation progress and the shock eventually stabilies and start to reach state value.

C. Cell Count:-

1. The total cell count as a function of time is plotted for first 0.001 sec where the diaphragm is closed, the total cell count remain constant at 8000 cell.
2. After which the diaphragm, is broken and the effect of species adaptive mesh refinement can be observed.
3. The total cell count varies continuously during this period and a maximum cell count of 127000 was recorded.
4. When the shock is stablies and reach the steady state value the cell count also remain constant around 9500 cell.

D. Mass Fraction for O2:-

E. Mass Fraction for N2:-

F. Velocity Animation:-

CONCLUSION:-

Hence, we have study transient simulation over shock tube and variation of mass fraction of O2 and N2

• A