Week 7: Shock tube simulation project

                                                                    TRANSIENT SIMULATION OF A SHOCK TUBE USING CONVERGE CFD

OBJECTIVE

To set up a transient state shock tube simulation describe plots of cell count as a function of time, pressure and temperature throughout the domain.

INTRODUCTION (content taken from various websites)

• A shock tube compresses (and heats) a fuel mixture almost instantaneously and is used to study the chemical kinetics of various fuels under homogeneous conditions of temperature and pressure A shock tube is an instrument used to produce supersonic gaseous flows and have been used to investigate a wide range of problems in fluid dynamics as they provide a convenient method in which experimental shock waves are produced due to the rupturing of a diaphragm separating two chambers containing a gas or gases at differential pressure and are attractive because of their relative simplicity.

• The shock tube is a simple duct closed at both ends. A diaphragm divides this duct into two compartments called as driver and driven sections as shown in figures below. Driver section of the shock tube is the high pressure section which is supplied by the high pressure gas from the reservoir. Driven section of the shock tube is the low pressure section which contains the low pressure driven gas. These two sections are usually separated by a metal diaphragm.

WORKING PRINCIPLE & EXPERIMENTAL SETUP

The working principle of shock tube is that a diaphragm is a membrane separating high and low pressure regions in the shock tube. High pressure region is continuously pressurized by mean of compressor. When reaching a critical value for diaphragm stress, diaphragm burst and exposes high pressure gas to low pressure on removal of membrane high pressure particles move to low pressure regime, bombarding its particles to low pressure particles.

OPERATION

1. Set the metal diaphragm between the driver and driven section.
2. Fill the driven gas in the driven section from the driven gas reservoir. This step is not required for case of air as the driven gas.
3. Set the required pressure in the driven section using vacuum pump.
4. Start filling the driver gas (say helium) in the driver section from the highpressure reservoir.

Metal diaphragm bursts at a particular driver and driven gas pressure difference. Dynamics of operation of

shock tube after diaphragm burst is shown in steps in the following images:

1. On set of Diaphragm burst

2. Propagation of shock, expansion and contact surface in the shock tube

3. Reflection of shock and expansion from the ends of the shock tube

CLASSIFICATION OF REGIONS

The plot shows the high pressure and low pressure region with a diaphragm separating it. Different waves which are formed in the tube once the diaphragm is ruptured. Following are the notations of the regions between different waves in the shock tube

• Region 1: This is the region in front of the primary shock.

• Region 2: It is the region between contact surface and primary shock.

• Region 3: This is the region between tail of the expansion fan and contact surface.

• Region 4: It is the region ahead of the leading expansion wave.

• Region 5: It is the region behind the reflected shock

SIMULATION GEOMETRY

• The boundaries are flagged.
• The material chosen for simulation is air containing the species Oxygen and Nitrogen.

SIMULATION SETUP

INITIAL CONDITIONS

The simulation geometry is divided into high pressure (green) and low pressure (brown) as shown in the above figure.

HIGH PRESSURE REGION

• Pressure: 6 bar
• Temperature: 300K
• High Pressure Region is filled with Nitrogen

LOW PRESSURE REGION

• Pressure: 1.01325 bar
• Temperature: 300 K
• Low pressure Region is filled with Oxygen

BOUNDARY CONDITIONS

• High Pressure Walls: Type Wall. Slip condition.
• Low Pressure Walls: Type Wall. Slip condition.

SIMULATION TYPE

• Transient simulation. Starting time: 0s. End time: 5 ms.

EVENTS

• Events are entities that are used to connect or diconnect two regions at resired instant of time.
• Here, it is used to simulate the popping of the diapharm of the shock tube.
• High Pressure and low pressure region are kept till 1 ms.
• At 1 ms, the regions are opened allowing the gases to interact and thus simulating the rupture of diaharm.

TURBULENCE MODEL

• RNG k-epsilon turbulence model is used.

GRID SIZING

• 2 mm grid with AMR for species. Nitrogen is chosen for refinement with a SGS value of 0.001.

RESULTS

As the problem is of transient nature, we will study the flow physics with the hellp of animation videos and plots of Pressure, Temperature and Cell count against the time. 

1. MESH

• As can be inferred from the above video and plot, the mesh is created as per species (Nitrogen) AMR. 
• The diaphram is popped at 0.001s and it can be noted that the cell count remains constant upto that time.
• Oncet diaphram is opened the cell count varies and starts to increase. This is because the mixing of the nitrogen causes the concentration of Nitrogen to reduce and thus cause refinement of the cells.
• When the  wave reflects back, the nitrogen returns to the high pressure region, increasing the concentration of nitrogen, causing a reduction in cell count. The cell count thus increases and reduces again as the shock wave moves to and fro within the domain.

2. VELOCITY

 The variation of velocity contours and vectors can be seen in the above attached animation video.

3. PRESSURE

• When the two regions are allowed to interact at 0.001s, as the nitrogen expands into the low pressure region, an expansion wave can be sen to be formed in the high pressure region and a compression wave can be seen to be formed in the low pressure region.
• The pressure in both regions is seen to be fluctuating after 0.001s. 
• The pressure of the high pressure region falls as the nitrogen expands into the low pressure region and compresses the oxygen This results in a rise in pressure in the low pressure.
• The pressure in the high pressure region is then seen to ride again while that in the low pressure region falls. It can also be observed that the peak pressure attained reduces with each rise and fall cycle.

4. TEMPERATURE

The temperature in the low pressure region increases as the oxygen gets compressed when the region opens up, meanwhile the temperature of the high pressure region reduces due to the expansion of nitrogen.

CONCLUSION

• The shock tube is simulated and the variation of the pressures and temperatures in the domain through time are studied. 
• The refinement of the grid with the changing concentration of Nitrogen is also observed.