Week 10.1: 2D Cavitation simulation

2D CAVITATION SIMULATION:

Aim: To carry out a simulation on a Winkl Hoffer Nozzle for fluid using Converge 3.0 CFD program and then post-process the results on Paraview.

Introduction: The simulation on a Winkle Hoffer Nozzle is the best way to simulate the conditions and effects of flow of high pressure and high velocity fuel when it enters the throat.

A phenomenon called ‘Cavitation’ occurs when the fuel passes through the throat of a fuel injector due to sudden change of area and pressure. As the static pressure drops of the fuel below the vapour pressure of the fuel, the fuel vaporizes due to which there is sudden variation in the flow rate, velocity and pressure which finally hampers the combustion process and causes erosion on the material. So in the above context the study and observation of Cavitation process is immensely important.

The Cavitation process is studied with the help of Volume of Fluid (VOF) Approach. This is used in case of multi-face flow such as liquid and gas phase in the simulation.

The transition from liquid to gas is described by the following:

dx / dt = [ x͞ - x ] / θ

Where:

dx / dt = represents the rate at which liquid converts to vapour.

θ = relaxation time scale

The fluids used in the simulation are as below:

Liquid Tetradecane = IC14H30 & Gas Tetradecane = C14H30

The parameters to be observed in the simulation are change in the velocity, pressure, mass flow rate through-out the flow and total cell count.

We used following pressure differences to run the simulation, which are as below:

1. Case 1: Pressure Difference = 30 Bar
2. Case 2: Pressure Difference = 70 Bar
3. Case 3: Pressure Difference = 100 Bar

Geometry:

- In the Converge Studio first we import the ‘STL’ file of the geometry.

- Then, we carry out a ‘Diagnosis’ on the shape created to check for any errors. If there is no error then the geometry is correct.

- Then we move to case set up.

Boundary Flagging:

Inflow Boundary:

Outflow Boundary:

Top-Bottom-Wall:

Side Wall-A:

Side Wall-B:

Throat:

Boundaries:

Final Geometry:

Case Set up Procedure:

- Application Type: Time-based

- Material: Predefined Mixture = Air

- Gas Simulation:

- Liquid Simulation:

- Global Transport Parameter:

- Species [Gas]:

- Species [Liquid]:

- Simulation Parameters:

- Run Parameter: Transient Solver.

- Simulation Time Parameter:

- Solver Parameters:

- Navier-Stokes Solver Type = ‘Density based’ selected.

- Boundary Conditions:

- Inflow Boundary Condition: [ For Case 1: 30 Bar Pressure Difference ]

- Outlet Boundary Condition: [ For Case 1: 30 Bar Pressure Difference ]

- Inflow & Outflow Boundary Conditions setup for Case 2 & 3 are as below :

- For Case 2: 70 Bar Pressure Difference:

Inlet Pressure = 10000000 Pa

Outlet Pressure = 3000000 Pa

- For Case 3: 100 Bar Pressure Difference:

Inlet Pressure = 12000000 Pa

Outlet Pressure = 2000000 Pa

- Top Bottom Wall Boundary Condition: Wall Motion = Stationary with Law of the Wall Condition.

- Wall Inlet Boundary Condition: Wall Motion = Stationary with Law of the Wall Condition.

- Side Wall A / B Boundary Condition: Wall Motion = Stationary with Law of the Wall Condition.

- Throat Boundary Condition: Wall Motion = Stationary with Law of the Wall Condition.

- Initial Conditions & Events:

- Regions: All boundaries defined to ‘Nozzle Region’.

- Physical Models:

- Turbulence Modelling= set to RANS [RNG K-Ɛ]

- Volume of Fluid (VOF) Modelling:

- Grid Control:

Base Grid Size:

- Adaptive Mesh Refinement: [Setup Similar For All Cases ]

- AMR with Velocity setup:

- AMR with Species setup:

- Fixed Embedding:

- Post Processing:

- Post variables Selection:

- Typical Variables/Geometry: Select desired variables such as Density, Velocity, pressure, temperature.

- Combustion / Turbulence: Select Turbulent Kinetic Energy (tke).

- Output Files:

Case setup is complete for all the cases.

- Export case setup: The case setup files are then ‘Exported’ to the destination folders to save the details.

- The destination folders should consist of following files in order to run the simulation and then post process the result on Paraview. The files are:

(i) converge.exe (name changed for the ease of run command on cygwin)

(ii) mpiexec.exe (name changed for the ease of run command on cygwin)

(iii) post_convert.exe (under output folder)

- Open Cygwin: Now the simulation is run using Cygwin. We navigate to the desired folder where the setup files were exported.

- Command to Run Simulation: The command to run simulation through Cygwin for Converge Studio 3.0 version is as below:

“ mpiexec.exe –n 2 converge.exe restricted “

- The simulation starts running, due to which output files are generated under a separate output folder.

- These output files are then post processed to convert the data in a format suitable for Paraview.

- Inline Plot: In the Converge Studio program, we can use Inline Plotting option to plot the curves during simulation run. We can observe the change in the plots and see the position of the simulation at the end of the time.

- Post Convert in Converge: To post process, we use file type as ‘Paraview VTK in-line binary format’. Now the files are post processed with a case name ‘test’.

- This generates ‘test.vtm’ group files which are generally used in Paraview to observe the results.

- Paraview: Open Paraview to check for the results.

Observations: For Case -1, 2, 3

Mesh Formation: For Case – 1, 2, 3

Mass Flow Rate Plot: For Case – 1, 2, 3

Total Cell Count: For Case – 1, 2, 3

Velocity Contour- Case-1:

Alpha Contour- Case-1:

Pressure Contour – Case-1:

Animation-Combined-Case-1: https://youtu.be/oEvv6cKcYyQ

Velocity Contour- Case-2:

Alpha Contour- Case-2:

Pressure Contour – Case-2:

Animation-Combined-Case-2: https://youtu.be/iKI3reNSQ3Q

Velocity Contour- Case-3:

Alpha Contour- Case-3:

Pressure Contour – Case-3:

Animation-Combined-Case-3: https://youtu.be/eB_9bQ3krqg

Results:

After running the simulation, the results can be observed as below:

1. In the Simulation Parameters setup, we used the Maximum CFL as 5. Since due to very high pressure difference the velocities become high. So a velocity based CFL which is convection based CFL was used as 0.5. It means that the velocity information propagates only half of a computational cell.
2. The simulation was run for 2 miliseconds which is how long an actual injection duration is.
3. Mesh Formations are shown for with the use of AMR (Adaptive Mesh Refinement).
4. The Mass flow rate plots are presented and we can infer that the mass flow has converged. Also the use of AMR effectively captures a fluctuation at the outlet in the graph.
5. An important parameter to be noticed is ‘Alpha (α)’ which is called a Void Fraction. When Alpha is ‘zero’ the fluid is in liquid phase and Alpha is ‘one’ then the fluid is in vapour state. The Alpha contour clearly shows that as the pressure difference increases the value of Alpha nears to the value of ‘one’ which represents the phenomenon of cavitation near the throat region.
6. From the pressure contour shows that the case setup used has effectively captured the effects of pressure difference.
7. The Total Cell Counts are shown in the graph and the cell counts increases with the increase in the pressure difference which has been captured effectively with the use of
8. Animations have been created for four major parameters which are Velocity, Alpha, Mass Faction for

Conclusion:

We can conclude with the use of Converge CFD program that the Simulation was run for three different valve lifts with Adaptive Mesh Refinements on the throat and observations are noticed.