Week 7: Shock tube simulation project

Aim: The main objective of this analysis is to perform shock tube simulation using the transient solver method and animate the pressure and temperature changes inside the tube.

Theory:-

The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale. Shock tubes (and related impulse facilities such as shock tunnels, expansion tubes, and expansion tunnels) can also be used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. Shock tubes are also used to investigate compressible flow phenomena and gas-phase combustion reactions. More recently, shock tubes have been used in biomedical research to study how biological specimens are affected by blast waves.

Basic Concept:-

1. High-pressure driver gas expands upon diaphragm opening, creating a shock wave
2. Test gas is instantaneously compressed and heated to combustion temperatures
   by the incident and reflected shocks.
3. High-temperature experiments monitored near end wall.

Shock Tube Characteristics:-

1. Instantaneous heating/compression from shock waves
2. Accurately known incident- and reflected-shock conditions (from incident shock MS)
3. Wide range of post-reflected shock Temperature and Pressure (600-4000 K, 0.1-1000 atm)

Geometry:-

To set up a shock tube problem, consider a rectangular tube having a diaphragm at the middle of the path of the tube, separating the tube into two equal volumes. As we cannot simulate the problem with a face separating the two volumes, the disconnection face is not taken into account in the geometry. As the disconnecting face is present in the given geometry, let us delete the faces connecting the two volumes of the shock tube.

Diagnosis:- Upon running a diagnosis check, it was noted that there were a number of Non-manifold edge problems.

This was due to the presence of a diaphragm inside the tube.

As we hide the side faces of the tube, we can see the disconnecting faces between the two volumes. To move forward with the simulation, we can delete the faces using the delete repair tool.

Transform Normal:- The normals of the geometry were pointing outwards. This was transformed to ensure the normals were pointed inwards.

Normals pointing inwards

Case Setup

a) Materials:- Predefined mixture was set to Air, Gas and species selected

b) Global Transport Properties:- Default values retained

c) Species:- O2 and N2 entered.

Simulation Parameters:-

i) Run Parameters:- Transient enabled

ii) Simulation Time Parameters:- Values set as shown below.

iii) Solver Parameters:- Solver scheme set to PISO

Initial Conditions and Events:-

Regions and Initialization:

High-Pressure Region:- Pressure set to 6 bar. Mass fraction of N2 set to 1.

Low-Pressure Region- Pressure set to atm, Mass fraction of O2 is 1.

Events:- Events are used when two boundaries are in contact with each other and there is no boundary between them. the event flag creates triangles in between two regions called disconnect triangles

Events can be cyclic, sequential, or permanent. Triangles are created when there is supposed to be no interaction between two regions and disconnected when there is supposed to be an interaction.

Boundary:-

High-Pressure region. Wall motion type set to Stationary. The surface movement is set to fix.

Low-Pressure Region: Wall motion type set to Stationary. The surface movement is set to fix.

Physical Models:-

Turbulence modelling set to RNG_K_EPS_epsilon.

Grid Control:-

Base Grid:

Adaptive Mesh Refinement:- Adaptive mesh refinement feature in Converge was enabled. This was done to increase mesh resolution in the vicinity of the boundary such that cell size is sufficient to predict the boundary layer effects.

Output:-

In order to execute the simulation, the directory in which these input files were stored was accessed in Cygwin and the following command was typed "mpiexec.exe -n 4 converge.exe restricted". After the Simulation was executed, the results were converted into a form that would be compatible with Paraview. This was done using the "post_convert.exe" command.

Results:-

1) Base Mesh:- Mesh with dx=dy=dz=1mm is shown below.

1. Nitrogen mass fraction contours + Velocity contours

The animation attached below shows the evolution of the following variables with time:

(a) Nitrogen mass fraction contours

(b) Velocity contours

It can be seen that after the event is triggered (at t=0.001s) compression waves are generated in the Low_Pressure Region (Oxygen gas) and expansion waves are formed in the High_Pressure Region (Nitrogen gas). The compression waves combine together to form a shock-front in the Oxygen gas, which is moving towards the end of the Low_Pressure Region. Simultaneously, due to the presence of expansion waves in the High_Pressure region, the Nitrogen gas begins to enter the Low_Pressure Region due to which the gas interface begins advancing into the Oxygen gas. Hence both the gas interface and the shock-front are moving through the Oxygen gas. However, the shock-front travels at supersonic speed (greater than the speed of the gas interface). Hence before mixing commences at the gas interface, the reflected shock-front pushes it (gas interface) in the opposite direction. This retreating gas interface again interacts with the shock-front after it gets reflected from the end of the High_Pressure Region. This time the shock-front pushes the gas interface back towards the Oxygen gas. In this manner the back and forth movement of the shock-front between the two regions causes the gas interface to oscillate. The motion of the shock-front through the shock tube can be easily observed by looking at the velocity contours whereas its effect on the motion of gas interface is clearly evident in the Nitrogen mass fraction contours.

Pressure:-

The animation attached below shows the evolution of pressure contours in the domain with time.

The plot attached below shows the variation of the following parameters with time:

(a) Mean pressure in the High_Pressure_Region

(b) Mean pressure in the Low_Pressure_Region

(c) Mean pressure in the domain

The results show that pressure in both regions remains constant until the event is triggered (at t=0.001s). After the event, compression waves are generated in the Low_Pressure_Region whereas expansion waves are formed in the High_Pressure_Region. The compression waves combine together to form a shock-front. The shock-front travels towards the end of the Low_Pressure_Region whereas the expansion waves travel towards the end of the High_Pressure_Region. Due to this, pressure in the Low_Pressure_Region increases whereas pressure in the High_Pressure_Region decreases. The shock-front and the expansion waves get reflected at the ends of the shock tube and reverse their direction of motion. Eventually, the shock-front enters the High_Pressure_Region and the expansion waves enter the Low_Pressure_Region. Consequently, pressure in the High_Pressure_Region increases and pressure in the Low_Pressure_Region decreases. In this manner, the alternating presence of shock-front and expansion waves in a particular region results in cyclic rise and fall of pressure. This is clearly evident in the plot which also indicates that the peak pressure in a particular region decreases with each cycle. This is because the energy contained in the shock-front is continuously dissipated in heating and compressing the gas through which it travels. After a sufficient amount of time, when the energy contained in the shock is dissipated completely, pressure in both regions attains an equilibrium value.

Temperature:-

The animation attached below shows the evolution of temperature contours in the domain with time.

The plot attached below shows the variation of the following parameters with time:

(a) Mean temperature in the High_Pressure_Region

(b) Mean temperature in the Low_Pressure_Region

(c) Mean temperature in the domain

The results show that similar to pressure, the mean temperature in a particular region rises and falls alternatively. This can again be attributed to the alternating presence of shock-front and expansion waves in a particular region as the passage of shock-front over a region increases its temperature and the passage of expansion waves over a region decreases its temperature.

Cell count:-

The plot attached below shows the number of computational cells in the domain as a function of time.

Conclusion:-

The following conclusions can be made based on the simulation results:

1. The gas interface oscillates inside the shock tube due to the back and forth movement of the shock-front between the two regions.

2. In each region, mean pressure rises and falls cyclically and with each cycle, the peak pressure decreases.

3. In each region, the mean temperature rises and falls cyclically.

4. The total cell count: remains equal to 20000 (constant) before the event and varies with time after it.