Shock tube simulation project
AIM : To setup a shock tube simulation and observe how the shock waves, refraction waves are getting developed over a period, when the diaphragm is broken.
OBJECTIVE :
- Setup a transient shock tube simulation
- Plot the pressure and temperature history in the entire domain
- Plot the cell count as a function of time
SIMULATION-SETUP :
- Case setup : CONVERGE CFD STUDIO
- Commanad editor : Cygwin
- Post-processor : Paraview
THEORY ( SHOCK TUBE)
Shock tubes are important devices and plays an important role in the field of chemical kinetics. In our case shock tube is seperated by two regions ie,,, the high pressure region and the low-pressure region. Well in real-life situations what people actually do is they fill the high pressure region with fuel and the low pressure region with air, so as to observe how the auto-ignition is taking place and the delay time for auto-ignition.
above figure shows a shock-tube
o
theoretical development of shok, expansion, and reflected waves.
Shock tubes
Shock tubes are particularly useful in gas-phase work, since high temperatures can be produced in a relatively short time (of the order of a few molecular collisions), and subsequent chemical changes can be studied. A shock tube suitable for kinetic studies consists of a metal tube some 6 inches in diameter and 20 ft long. This is divided into a high-pressure section, containing driver gas, and a low-pressure section containing the gas or gases to be reacted. The two are separated by a thin diaphragm of metal foil or cellophane. When the latter is burst by a suitably controlled needle, the expansion of the high-pressure gas produces a shock wave which passes through the low-pressure gases. These are adiabatically compressed and are carried to the far end of the low-pressure section where subsequent changes can be followed (observation stations).
With an inert gas, the shock wave produces a heating effect and then thermal ionization. If the low-pressure section contains a diatomic gas, other things can happen. Starting with a weak shock wave, travelling only a little faster than sound, changes in rotational and vibrational enegries can be observed. The gas is suddenly heated to a new temperature, but it takes many collisions before the molecular rotaions and vibrations come to thermal equilibrium with the translational motion. With stronger shock waves, temperatures are reached at which the diatomic molecule begins to dissociate into radicals, and since this is a relatively slow process, rates can often be measured. At higher temperatures still, ionization can occur, and rates of ionization and recombination can be measured.
Basic concept:
- High-pressure driver gas expands upon diaphragm opening creating shock waven
- Test gas is instantaneously compressed and heated to combustion temperaturesn from incident and reflected shocks
- High-temperature experiments monitored at end wall
CASE-SETUP
The given geometry was imported to the converge studio and the diagnosis was done to check for any errors in the geometry.
SURFACE CLEAN-UP
When the geomtry was imported and the diagnosis was done, there was a non-manifold error that popped up. Non-maniflod error is the error that occurs when any one edge of the triangle is shared by more than one triangle in the geometry.
Non-manifold error
In the above figure the edge of triangle 1 is shared by more than one triangle ie,, triangle 2 & 3. Similarly triangle 1 also contributes it edge to triangle 4 & 5. Hence 4*3 = 12 non-manifold errors.
The surface clean up was done and the errors were solved in the converge studio itself.
MATERIALS FOR SIMULATION
Air (fluid) consists of O2 and N2. Since the shock-tube has two regions ie,,, the high-pressure region and the low pressure region, the high-pressure one was filled with N2 gas and the lower one with O2 gas.
There is no mixing happening until the diaphragm is broken.
As air consists of O2 and N2, were added as a species for the simulation.
SIMULATION PARAMETERS
The simulation we are concerned here is the transient-state simulation with simulation mode being full-hydrodynamic, ie…. we are solving for parameters like temperature, pressure, velocity and so on.
The simulation was ran for a total of 3ms. Starting with an initial time step of 1e-6 to maximum time step of 1s.
WRITING TIME INTERVALS (3D OUTPUT FILES)
Around 300 3d output files were dumped in the output folder. Since we are running the simulation for 3ms, the time interval for writing the 3d output files is
BOUNDARY FLAGGING AND CONDITIONS
The shock-tube was divide into 6 different boundary High-pressure boundaries, high-pressure boundaries with front and back 2D and similarly the Low-pressure boundary, low-pressure boundaries with front and back 2D.
The high-pressure boundary was assigned to a wall – type boundary condition with no-slip and temperature condition being the Nueman boundary (NE) condition.
Similarly, high-pressure boundaries with front and back 2D were assigned to TWO_D – type boundary condition. Now in the same way Low-pressure boundary was assigned to a wall – type boundary condition with no-slip and temperature condition being the Nueman boundary (NE) condition.
Similarly, low-pressure boundaries with front and back 2D were assigned to TWO_D – type boundary condition.
INITIAL CONDITIONS AND EVENTS
REGIONS AND INITIALIZATION
The shock tube was divided into two different regions, ie…. the high-pressure region and the low-pressure region.
grouping boundaries into regions
A pressure of 600000 Pa or 6 bar was provided to high-pressure region and the lower one was at atmospheric pressure ie… at 101.325 kPa or 1 bar.
EVENTS
Sequential type event was added where the following conditions were assigned.
At time t = 0s, the high-pressure and low-pressure region were separated by the diaphragm.
At time t = 0.001s or 1ms, the diaphragm is made to open and there is a mixing of N2 and O2 gases, that is taking place due to the broken diaphragm and thus due to this pressure difference there will be development of the shock waves.
TURBULENCE-MODELLING :
The turbulence model taken here is RNG K-Ɛ.
MESHING
Converge predicted around 2500 cells (without AMR) initially for a base grid of 2mm. But since we have enabled the Adaptive mesh refinement (AMR) with regards to species the cell count however varies accordingly.
mesh at time t = 0 sec (without AMR)
The minimum number of cells in AMR is assigned to 1 and the maximum number of cell are 200000.
High-pressure and Low-pressure regions were assigned under active regions so that the converge is able to predict the species present under these regions. The maximum embedding level was set to 3.
And hence the size of cells present in the AMR is
Grid size = (base grid)/2^(embedding level) = 0.002/(2^3)=0.25 mmIn AMR we have enabled species type of mesh refinement with a sgs of 0.001, it means that converge is going to refine the mesh when the concentration of N2 is 0.001. Thus we have the varying cell-count in the result with AMR enabled.
RESULTS
PRESSURE IN SHOCK-TUBE DOMAIN
Above fig shows the variation of pressure in the shock-tube domain. Initially the pressure is 6 bar (of N2) or 0.6 MPa. When the diaphragm breaks after 0.001s or 1 ms, the pressure drops rapidly and the diaphragm opens up, which will lead to slight increase in pressure of the low-pressure region, as we can see from the graph the pressure of the lower region is increased to 0.15 MPa from 0.1 MPa. As the mixing occurs of N2 and O2 gases the pressure again in high-pressure region decreases and due to this pressure difference there will be a development of shock waves (diamond pattern) and this shock waves when it hits the wall it will travel back and forth, and gets reflected from wall as expansion and compression waves.
CELL-COUNT IN SHOCK-TUBE DOMAIN (as a function of time)
As discussed above converge predicted around 2500 cells without AMR. Since we have enabled AMR, the cell count is varying and converge is refining the cells according to the condition of sgs of 0.001, the mesh is refined and new elements are created.
TEMPERATURE IN SHOCK-TUBE DOMAIN
In the above figure the variation of temperature in high-pressure and low-pressure region is shown.
When the diaphragm breaks the temperature at the region 0 drops from 300K to around 200K, this is because due to the mixing of the N2 and O2 gases and the development of shock wave in the domain is responsible for the decrease in temperature of region 0 and 1, as the shock wave travels back and forth.
ANIMATION LINKS :
Mass-fraction of N2 variation in the domain.
Velocity profile in shock-tube domain.
Pressure profile in shock-tube doamin.
Mesh-refinement with AMR.
CONCLUSION
- The initial pressure difference between the two regions is 5 bar ie,, (6-1 = 5). but as the mixing occurs, the pressure difference reduces in both regions.
- As the high-pressure gas mix with the low-pressure gas, there is a formation of shock wave due to a pressure difference. These shock waves travel back and forth in the domain due to reflection from walls in the form of compression and expansion waves.
- Initially, the pressure of N2 drops due to expansion and that of O2 rises due to compression of the gas. Here we get the first instance of minima and maxima of the graph.
- After this, the shock wave gets reflected from the wall causing an increase in pressure. And this cycle gets repeated with diminishing values of maximum and minimum pressure.
- After every cycle, it can be seen that the high -pressure and low-pressure regions get interchanged. To attain a steady-state, the simulation time should definitely be greater than 0.003 sec or 3 ms.