Week 7: Shock tube simulation project

                                                                   TRANSIENT STATE SIMULATION OF FLOW VIA SHOCK TUBE USING CONVERGE CFD

                                                                                                                (WEEK-7 CHALLENGE)

1. AIM

Our aim is to setup a transient shock tube simulation in converge, simulate it using Cygwin terminal and post process in Paraview and check the results.  

2. THEORY/EQUATIONS/FORMULAE USED

Structure of CONVERGE CFD simulations

The basic steps for a simulation are as follows,

1. Pre-processing [Converge Studio v3.0] – It is a leading CFD package for simulating 3D fluid flow. It is a user friendly interface which provides high productivity and easy-to-use workflows. Its features includes autonomous meshing, state of the art physical models, robust chemistry solver, and the ability easily accommodate complex moving geometries.
2. Solving [Cygwin] – It is a large collection of GNU and Open Source tools which provide functionality similar to a Linux distributionon Windows.
3. Post-processing [ParaView 5.9.0] – It includes analyzing the results by plotting the results as charts, contour, and exporting the data, also validating the results both qualitatively and quantitatively.

Shock Tube

Shock tube is an instrument to produce plane propagating shockwaves by rupturing a diaphragm which separates high and low pressure regions inside a tube. It is used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale. Shock tubes (and related impulse facilities such as shock tunnels, expansion tubes, and expansion tunnels) can also be used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. Shock tubes are also used to investigate compressible flow phenomena and gas phase combustion reactions.

A shock wave inside a shock tube may be generated by a small explosion (blast-driven) or by the buildup of high pressures which cause diaphragm(s) to burst and a shock wave to propagate down the shock tube (compressed-gas driven).

A simple 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 some form of 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 low-pressure gas, referred to as the driven gas, is subjected to the shock wave. The high pressure gas is known as the driver gas. The corresponding sections of the tube are likewise called the driver and driven sections. The driver gas is usually chosen to have a low molecular weight, (e.g., helium or hydrogen) for safety reasons, with high speed of sound, but may be slightly diluted to 'tailor' interface conditions across the shock. To obtain the strongest shocks the pressure of the driven gas is well below atmospheric pressure (a partial vacuum is induced in the driven section before detonation).

The test begins with the bursting of the diaphragm. There are several methods are commonly used to burst the diaphragm.

1. A mechanically-driven plunger is sometimes used to pierce it or an explosive charge may be used to burst it.
2. Use diaphragms of plastic or metals to define specific bursting pressures. Plastics are used for the lowest burst pressures, aluminum and copper for somewhat higher levels and mild steel and stainless steel for the highest burst pressures. These diaphragms are frequently scored in a cross-shaped pattern to a calibrated depth to ensure that they rupture evenly, contouring the petals so that the full section of the tube remains open during the test time.
3. A mixture of combustible gases, with an initiator designed to produce a detonation within it, producing a sudden and sharp increase in what may or may not be a pressurized driver. This blast 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.

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 rarefaction wave, often referred to as the Prandtl-Meyer wave, travels back in to the driver gas.

The interface, across which a limited degree of mixing occurs, separates driven and driver gases is referred to as the contact surface and follows, at a lower velocity, the lead wave.

A 'Chemical Shock Tube' involves separating driver and driven gases by a pair of diaphragms designed to fail after pre-determined delays with an end 'dump tank' of greatly increased cross-section. This allows an extreme rapid reduction (quench) in temperature of the heated gases.

Problem – Shock Tube

The challenge includes transient state simulation of flow through a shock tube with Adaptive Mesh Refinement (AMR), and to check the results.   

Mesh Size -   dx = dy = dz = 0.002 m   AMR – Species N2 based with embedding level 3

3. PROCEDURE

• Firstly all the softwares are downloaded and installed in the system.
• Geometry is imported in converge studio, boundary is flagged, and boundaries are checked for normals and orientation is done as per the requirement and finally diagnosis check is carried out to check for any errors such as intersections, open edges, non-manifold edges, overlapping triangles etc.
• Case setup is done using setup wizard, then the input files are exported to a specific directory and also converge executable application are also copied into the directory.
• The simulation is run using Cygwin commands and post converted the output files so that it is compatible for post processing in Paraview.

4. NUMERICAL ANALYSIS
   • Geometric Model

The 3D geometry file of shock tube is imported in Converge Studio as per the figure given below.   

                                                                                                               Fig: 3D Geometry – Shock Tube

• Mesh

                                                             Fig: Mesh at time t = 0 s                                        Fig: Mesh at time t = 0.003 s with AMR

• Boundaries

                                                                                         Fig: Boundaries of the domain grouped as regions

• Case Set-up

1. In Materials tab, materials – Air, species – O2, N2 and global transport parameters are selected.

    2. In Simulation Parameters tab, Run parameters such as Solver type, Simulation Mode and Gas flow Solver are set. In Misc. Tab uncheck the shared memory and steady state monitor.

3. Simulation time parameters such as total number of cycles, time step, CFL limits etc are set as shown in the figure below.

    4. Solver parameters such as the Navier stokes solver type, equations preconditions type, solver controls are set.

    5. Boundary Conditions and Initial Conditions

6. Regions and Initialization – High and Low Pressure Region is created and the initial condition, species are added to the respective regions.

Also the events are created in such a way that a diaphragm is intact between both high pressure and low pressure regions till 0.001 seconds and then the diaphragm breaks and the species are open to flow till the end.

7. Turbulence Modelling – Reynolds Averaged Navier Stokes – RNG K-epsilon Model

    8. Base Grid – Mesh sizes are entered as per the problem and AMR is done based on species.

    9. Post Variable Selection - Select all the necessary variables and the location that needs to be checked while post processing.

    10. Output Files – Output files writing time intervals, restart files are set as per the requirement.

     11. After the setup is done click on “Validate all” option to check for any issues with the case setup. If everything is correct then green tick will appear for all tabs as shown in the figure below. Once the Setup is done, export the input files.

     12. With input and executable files, navigate to the specific directory in Cygwin and run the simulation using "exe -n 4 converge.exe restricted </dev/null> logfile &"

     13. After the run is completed Post convert the output files using “exe -n 4 post_convert.exe” into binary inline vtk format.

     14. Using the vtm group files, post processing is done in ParaView in order to study the results.

5. RESULTS

                                                                                                       Fig: Total Cell Count

                                                                                                       Fig: Pressure Plot    

                                                                                              Fig: Pressure Contour at t = 0.003 s

                                                                                                          Fig: Temperature Plot 

                                                                                                  Fig: Temperature Contour at t = 0.003 s

                                                                                                        Fig: Velocity Contour at t = 0.003 s

                                                                                            Fig: Mass Fraction – N2 contour at t = 0.003 s

                                                                                            Fig: Mass Fraction – O2 contour at t = 0.003 s

Animation Link

             Mesh – https://youtu.be/wPAxlcn6fP4

             Velocity – https://youtu.be/jGBZhyMhSuc

             Pressure – https://youtu.be/QqRQVjhS0YA

             Temperature – https://youtu.be/CCvaQImNvn8

             Mass Fraction of N2 – https://youtu.be/6MviknsQcxg

    6. CONCLUSION

• The transient state flow simulation through a shock tube is carried out for 3 milliseconds.
• Events are created in such a way that a diaphragm is intact between both high pressure and low pressure regions till 0.001 seconds and then the diaphragm breaks and the species are open to flow till 0.003 seconds.
• Adaptive Mesh Refinement is used along with base grid size of 0.002 m with embed type - sub grid scale, max embed level – 3, sub grid criterion based on permanent species (N2) time – 0.001.
• The total cell count keeps changing according to the set timing as shown in the animation respectively. This type of refinement helps to capture the characteristic of the flow accurately. The maximum cell count attained is 200000 as the limit was set.
• Plots and Contours shows that the diaphragm is kept intact between both high pressure (600000 Pa) and low pressure (101325 Pa) regions till 0.001 seconds and when the diaphragm breaks fluid in the high pressure zone enters the low pressure zone and ultimately reaches a equilibrium state.
• Pressure difference creates the shock waves are developed and it gets reflected back and forth on the walls.
• Contours also shows that the reflected shock resists the oncoming flow which in turn prevents from mixing of the two species.
• These shock waves, reflected waves creates sudden change in the properties of the medium as seen the plots. These waves are generated till the pressure difference dies out.

    7. REFERENCES

• https://skill-lync.com/knowledgebase/week-6-concept-of-events
• https://thermopedia.com/content/1124/#:~:text=Shock%20tubes%20are%20devices%20for,pressure%20and%20low%2Dpressure%20chambers.
• https://en.wikipedia.org/wiki/Shock_tube