SHOCK-TUBE SIMULATION
ABSTRACT: This report contains a study on the shock tube simulation containing oxygen and nitrogen. Inside the shock tube, initially Nitrogen resides in the high pressure region and the Oxygen resides in the low pressure region. The setup was arranged in Converge Studio and the results were post processed using Paraview and Converge.
THEORY: A shock tube is a tube closed at both ends divided into two section of high pressure(driver) and low pressure(driven) seperated by a diaphragm. This diaphram is designed to collapse after a certain time and the gas at high pressure tends to mix with low pressure gas with high velocity. This is not a case of diffusion. High pressure gas mixing with low pressure at high velocities caused by shock waves inside the tube and it reflects from the surface. This shock causes temperature and pressure to rise in the specimen and shock causes a flow.
The driving gas is usually the one with low molecular weight and the driven gas is usually the one with high molecular weight. Pressure at driven section is kept below the atmospheric pressure usually.
Applications: Shock tube can be used to study chemical kinetics of a reaction. In automobiles industry they are used to calculate ignition delay in the IC engine. They are also used to setup wind tunnel. The hypersonic velocites achieved from it can be used to study the effect of atmosphere on the space shuttle on its entry in atmosphere.
CASE SETUP: The case was setup in Converge Studio according to following parameters.
Application: General flow
Materials: Air
Simulation Parameters: Transient, full Hydrodynamic simulation, start time=0.0 sec, end time=0.003 sec, initial time step= min time step= 1e-09 step.
Boundary: 1. High-pressure-boundary- type is wall, velocity boundary conditions is slip
2. Low-pressure-boundary- type is wall, velocity boundary condition is slip, Temp is 300K
Rest all boundaries are 2-D type.
Initial conditions and Events: Regions-ID-0 N2, pressure= 600000 Pa, temp=300 K
Id-1 O2, pressure= 101325 Pa, temp=300 K
Events- Sequential-1. High pressure and low pressure closed at 0.0 sec
2. High pressure and low pressure open at 0.001 sec
Physical model: default
Grid control: Base Grid- dx=dy=dz=0.001m
Adaptive Mesh refinement- Species: N2, Active Regions= High pressure and low Pressure, sgs embed level=0.001
Output/Post Processing: Time interval for 3D and text output is 1e-05
User defined function default
Geometry: The geometry was a rectangular tube divided into two sections of high pressure and low pressure.
RESULTS: After the case was setup in converge, cygwin was used to run the exported files and generate post processing files. Paraview and Converge Studio were used for post processing which include temperature and pressure analysis. Following results were obtained:
1. CELL COUNT:
Here the id region in blue(0.0e+00) color corresponds to high pressure region and the id region red(1.0e+00) corresponds to low pressure.
The plot shows the cells after 0.001 sec increases rapidly because the events triggered the opening of the high pressure and low pressure region at 0.001 sec. It can be seen that the load balancing is done by the two processors used in the simulation.
These disturbances in the graph is caused by the excessive variation of parameters of the species. This results in the adaptive mesh refinement creating more cells in the regions to capture the results. The cell count increases rapidly after 0.001 sec. This happens because the high pressure and low pressure region are open after 0.001 sec. A shock is generated and the pressure varies due to this shock.
There is frequent disturbance in the number of cells for time upto 0.0015 sec. Then there is a slight converge of the number of cells for some duration and then again the rapid changes in the number of cell occur. The decreased variation is caused because the flow tries to attain stability and the physical parameters of species do not vary with great deal. These rapid changes after a short span of some stability is caused when the waves reflect from the end of the shock tube. The quantities change very rapidly in this duration. This keeps on repeating throughout the simulation and the flow never attains stability. An animation is shown below which clearly displays the changes in the mesh at all intervals.
2. PRESSURE:
Max pressure region id-00
Max pressure region id-01
Mean pressure region id-00
Mean pressure region id-01
Animation of Pressue over all time steps in shock tube simulation.
The graph of pressure vs time and the animation shows follwing things:
1. The graph and animation is constant upto a time interval. In graph, this is constant upto 0.001 second as this is the time upto which the diaphragm is closed and high pressure and low pressure regions do not mix with eachother.
2. After 0.001 sec in plots and 4 sec(approx) in animation there is disturbance observed and its due to the event setup. High pressure and low pressure regions are opened and can mix, this is analogous to breaking of diaphragm.
3. The pressure increases rapidly. This is due to the generation of shock waves which propagates inside the tube. From the animation it can be observed that the shock waves have a leading head and a trailing head. The pressure ahead of the leading head is lower and behind the trailing head is lower comparatively. There is a flow of mass in the same direction as of the shock wave due to this pressure difference.
4. The graph of mean pressure is not increasing over all time steps. It attains its local maximum value first at 0.0016 sec(approx) and then there is a decrease in pressure. When the shock waves reflect from the end of the shock tube they basically compress the gas at that end to a high pressure. The peak pressure is attained during this compression. The compressed gas prevents the mass of two gases from mixing with eachother and is reflected back. This is when the pressure of the gas starts to drop. The wave then reaches out the other end and the pressure decreses further. It is then reflected from that end and the process is repeated.
5. The ignition delay can be calculated from the graph of pressure vs time. Ignition delay is the time lag between the reflection of shock from the boundary and the onset of temperature. It can be obtained by linearly extrapolating the steepest curve line back in time to the pre-ignition baseline.
3. TEMPERATURE:
Max temperature-region id-00
Max temperature-region id-01
Mean temperature-region id-00
Mean temperature-region id-01
Animation of temperature over all time step in shock tube simulation.
Following things can be inferred from the plots of temperature and animation:
1. The temperature is constant upto 0.001 sec in plots and upto 4 sec(approx) in animation. This is due to the event defined for first 0.001 sec. Physically this signifies that the high pressure and low pressure region do not mix with eachother.
2. There is disturbance in graph as well as in animation after that time. This happens due to the event defined at the time interval of 0.001 sec. The high pressure and the low pressure regions are open to mix with eachother. This is physical analogous of the diaphragm breaking at the time 0.001 sec.
3. The temperature in the region id-01 increases. This is due to the pressure wave propagating in the region of low pressure. This pushes the the mass of the low pressure region and compresses it adiabatically. The work is done on the system, volume decreases and hence the temperature rises.
4. The temperature in the region id-00 decreases. The shock wave travels from high pressure to low pressure region and the work is done by the system of high pressure gas. There is adiabatic expansion and hence the temperature decreases.
5. The temperature in high pressure and low pressure region reaches local minima and local maxima respectively at 0.0016 respectively. Then there is a decline in temperature. This is due to the reflection of shock from the tube.
Below is the velocity animation of shock tube over all time steps.
From the velocity animation it is observed that the shock's leading head has lower velocity as compared to the trailing head. This is due to the inverse relationship between pressure and velocity. The pressure in leading and trailing heads is high and low respectively. The animation shows that the velocity reaches as high as 1300 m/s, thus the supersonic shock waves are developed inside the tube.