Week 7: Shock tube simulation project
Objective: To set up a transient shock tube simulation in Converge CFD and analyze the temperature and pressure history in the entire domain.
Shock Tube :
A shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in which a gas at low pressure and a gas at high pressure are separated using a diaphragm. The diaphragm suddenly bursts open under predetermined conditions to produce a wave propagating through the low pressure section. The shock that eventually forms increases the temperature and pressure of the test gas and induces a flow in the direction of the shock wave. Observations can be made in the flow behind the incident front or take advantage of the longer testing times and vastly enhanced pressures and temperatures behind the reflected wave. The test begins with bursting of diaphragm.
The bursting diaphragm produces a series of pressure waves, each increasing the speed of sound behind them, so that they compress into a shock propagating through the driven gas. This shock wave increases the temperature and pressure of the driven gas and induces a flow in the direction of the shock wave but at lower velocity than the lead wave. Simultaneously, a rarefraction wave, often referred to as the Prandtl-Meyer wave, travels back in to the driver gas.
Source: Wikipedia
Source: https://cefrc.princeton.edu/sites/cefrc/files/Files/2015%20Lecture%20Notes/Hanson/pLecture11.pdf
Geometry:
Dimensions of Shock Tube --->
Length: 0.2 m , Breadth: 0.01 m, Height: 0.01 m
Boundary Flagging:
Case Setup:
Time Based Transient Simulation (Pressure based)
Fluid: Air
Species: N2 and O2
Simulation Time Parameters:
Start Time: 0 s
End Time: 0.003 s
Initial Time-Step: 1e-09 s
Minimum Time-Step: 1e-09 s
Maximum Time Step: 1 s
Regions and Initialization:
High Pressure Region (Stream ID - 0):
Velocity : 0 m/s
Temperature: 300 K
Pressure: 600000 Pa
Species: N2 (Mass Fraction- 1)
Low Pressure Region (Stream ID - 0):
Velocity : 0 m/s
Temperature: 300 K
Pressure: 1 atm (101325 Pa)
Species: O2 (Mass Fraction- 1)
Boundary Conditions:
High Pressure --->
Wall Boundary
Velocity Bounadry Condition: Stationary
Temperature Boundary Condition: 300 K
Region: High Pressure Region
Low Pressure --->
Wall Boundary
Velocity Bounadry Condition: Stationary
Temperature Boundary Condition: 300 K
Region: High Pressure Region
Events:
In the given problem, the high pressure region and the low pressure region are seperated by a interface, which in reality is a diaphragm dividing the two regions. In Converge, in order to create this interface with no physical boundary in between, it is necessary to use events. The events flag creates triangles in the place between the two regions called as disconnect triangles which are are temporarily created for the purpose of simulating the event.The triangles are created there is no interaction between the two regions and are deactivated when there is an interaction between the two regions.
Turbulence Model: Reynolds- Averaged Navier-Stokes (RANS) with default settings
Adaptive Mesh Refinement:
A uniform mesh grid size over the entire shock tube geometry won't be able to accurately record the small fluid level interactions. Hence, in order to accurately capture the information where the shock occurs, the adaptive mesh refinement setting is used. It applies a refined mesh when the diaphragm breaks and the N2 concentration drops to a certain level after a time period of 0.001 s. Converge monitors the property specified in the AMR settings and refines the mesh when the temperature property between the consecutive grid is greater than the defined SGS value.
Post- Variable Selection: Mass Fraction- N2 and O2
Base Mesh Grid : 0.0025 m
The mesh refinement can be seen in the areas where the N2 concentration changes after the diaphragm breaks thus capturing the results accurately.
Results and Analysis:
Pressure variation --->
As seen from the plot,a pressure of 6 bar and 1 atm is maintained in the high pressure and lowe pressure region of the shock-tube respectively.After a time interval of 0.001 secs, the diaphragm breaks and there is a change in pressure across both the regions. The pressure in the high pressure region drops initially to a value lower than 2 bar and then after some fluctuations tries to converge to a mean pressure value of 3 bar. Similarly, in the low pressure region the pressure increeases to a value of 5 bar and then successively drops till it comes close to a mean value of 3 bar.
Velocity variation --->
Temperature Variation --->
In the above plot, after the diaphragm breaks at approximately 0.001 secs the temperature drops in the high pressure region drastically at first and stabilizes at later time intervals. The temperature in the low pressure region however region increases due to the entrainment of high pressure fluid thus compressing the low pressure fluid and increasing the temperature.
N2 and O2 Mass Fraction --->
From the above two plots, it can be seen that the mass fraction of N2 increases in the low pressure region after the diaphragm breaks with a decrease in the high pressure region gradually.
From the above two plots, it can be seen that the mass fraction of O2 increases in the high pressure region with a spike seen in the 1st plot after the diaphragm breaks with a decrease in the low pressure region gradually. The pressure waves reflect the fluid from the end walls, thus introducing a spike in the high pressure region.
Total Cell Count --->
In the above plot, it can be seen that the total cell count increases after the event of diaphragm breaking occurs at 0.001 secs creating shock waves inside the tube. Due to adaptive mesh refinement setting, the number of cells in the areas where the mesh refinement is higher than base grid mesh increases.