Week 7: Shock tube simulation project
Shock tube is a tube that has two regions separated by a diaphram. One side is the high pressure region and other side is a low pressure region. When the diaphram breaks, the flow happens from high pressure to the low pressure region. This results in generation of shocks in the low pressure region. When these walls strike the wall, they are reflected back and they push the incoming fluid in the opposite direction and this process continues until the pressure in the shock tube converges. Normally this is the phenomenon that happens in case of auto ignition of air and fuel in IC engines. Due to the generated shock waves, the fuel ignites by itself. Hence the shock tube problem helps us to understand such phenomenon.
In this case, we have taken a simple tube and divided it into two regions of nitrogen on the high pressure side and oxygen on the low pressure side.
Geometry
Left side is the high pressure region consisting of nitrogen and right side is the low pressure region consisting of oxygen
Boundary conditions:
The high pressure and low pressure walls are given wall with law of wall boundary condition and dirichlet boundary condition for temperature equal to 300K.
The remaining are given as walls with slip condition.
Regions:
The high pressure region has nitrogen and has a pressure of 600000pascal and temperature of 300K and the low pressure region has oxygen and has a pressure of 101325 pascal and temperature of 300k.
Adaptive mesh refinement was given as follows:
RANS K-epsilon turbulence model is used for the simulation and base grid size of 0.004m is taken.
Simulation time parameters: Transient solver is used to solve the problem inorder to know the time taken for the solution to converge.
initial time step= minimum time step= 1e-9
maximum time step=1
start time of simultion = 0s
end time of simulation= 0.03s
Results:
Mesh with adaptive mesh refinement
It can be seen from the graph that until 0.001 seconds, the presssure of the high and low pressure regions do not change. They remain constant which is equal to the pressure values given for the two regions as initial condition. After 0.001 second, the diaphram ruptures and the nitrogen expands from high pressure region to the low pressure region. As a result, oxygen in the low pressure region contracts. Therfore the pressure of the high pressure region decreases and that of the low pressure region increases.
Now after sometime, the pressure increases to a large extent in the low pressure region and hence this region now starts expanding leading to reduction of pressure in the low pressure region and increase of pressure in the high pressure region. This keeps on happening until the pressure in the entire shock tube reaches to a particular value.
Similar trend is observed with respect to the temperature of the two regions. The pressure starts to increase in the low pressure region as soon as the diaphram breaks and hence the temperature increases. The pressure starts to decrease in the high pressure region as the diaphram breaks and as a result the temperature also starts to decrease.
Animation of the pressure in the shock tube.
Animation for the concentration of nitrogen in the shock tube.
Cell count divided into different cores. The wavery pattern of the cell count with respect to time is due to the adaptive mesh refinement. Initially the mesh size is constant for 0.001 seconds as the diaphram is closed for 0.001s after that only it starts to change with respect to time.