Week 7: Shock tube simulation project

Aim: Shock tube simulation project

Objective: 

• Setup a transient shock tube simulation
• Plot the pressure and temperature history in the entire domain - Explain the result
• Plot the cell count as a function of time - Explain the result

It is expected to show the mesh generation using ParaView.

Also, create animation and upload it on Youtube and provide the Youtube link for animation in your report.

Introduction

The shock wave is an instrument used to direct and replicate shock waves in order to simulate the actual explosion and its effects usually on a smaller scale. It is also used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. They are also used to investigate compressible flow phenomena and gas-phase combustion reactions. More importantly, they are used in biomedical research to study how biological specimens are affected by blast waves.

The plot shows the different types of waves that are produced after the diaphragm is ruptured.

Shock waves are produced by using a high-pressure build-up that causes the diaphragm to burst resulting in shock waves traveling down the tube.

Application

It is used to measure the rates of chemical kinetics. It is also used in aerodynamic tests. It is also used to measure the dissociation energies and molecular relaxation rate.

Case-setup

Case-setup

The shock_tube. STL file is loaded into the Converge-CFD set-up. 

The diagnosis dock is selected from the "View" option and the "Find" option is selected. It is found that there are ("Intersections(0)","Nonmanifold Problems(12)","Open Edges(0)", "Overlapping Tris(0)","Normal Orientation(0)","Isolated tris (0)".

Therefore the diaphragm connecting the two regions is deleted to remove the non-manifold error.

The "Normal Toggle" is selected from the ribbon, upon selecting the normal toggle it was observed that the normal is pointing outside the volume, technically the normal should point inside the volume where the fluid is flowing. Therefore in the geometry dock, the "Transform" option is clicked. The "Normal" tab is selected from the geometry dock and one of the triangles containing the normal pointing outward is selected. The "Apply" option is selected for removing the normals.

The "Case Setup Dock" is selected from the "View" and "Begin Case Setup" is executed.

The "Time" based "Application" type is selected. The "Material" is selected and the predefined mixture is selected as air. The "Reactant mechanism" is checked off because it is not a combustion problem. The species is selected and the "Apply" is clicked. Under "Gas simulation" the Equation of state is selected as "Redlich Kwong", the critical temperature is 133K and the critical pressure is 3770000Pa. The Turbulent Prandtl number is 0.9 and the Turbulent Schmidt number is 0.78 under Global Transport parameters. The `O_2` and the `N_2` are selected as species. Under "Run parameters" the "Transient-state solver" is selected. The "Temporal type" is Time-based simulation. The "simulation mode" is selected as "Full Hydrodynamic" because the geometry is simple so while creating the mesh inside the geometry it solves the NS equation as well, but if the geometry is complex "No hydrodynamic solver" is selected as such if there is an error it will point out immediately while creating the mesh, otherwise if the hydrodynamic solver is selected then it will be very tedious to identify the error in the simulation case set up.

Under "Simulation time parameters" end time is chosen as 0.003s (steady-state). The initial and minimum time step is 1e-09 s. The maximum time step is 1s, and the maximum convection CFL limit is 1 and the rest are default values.

The "Pressure" "Equation" is selected under the "Solver parameter"  and the "Preconditioner" is selected to "None". The "Maximum convection CFL limit (final stage)" is set to 0.5. The "Density-based solver" is selected it is suitable for even low Mach numbers to avoid extrapolating temperature calculations and the PISO coupling scheme is selected.

Boundary Selection

The boundary flagging was done and tabulated as under

Regions and initialization

The present challenge requires us to create the region based on low pressure and high-pressure region. The low pressure and high-pressure region were defined and tabulated as under 

Setting up of Turbulence model

The Realisable `k-epsilon` model is selected from the case-setup tree for the above-said simulation. Since the size of the eddies is restricted near the wall and the maximum size of the eddies is formed away from the wall. It is well suitable for resolving flows in the logarithmic flow region where y+ ranges from 30 to 300 and flows involving a high Reynolds number.

Events 

When two regions are connected with each other but without any boundary in between them then it is necessary to create the events which result in the creation of triangles which are called disconnect triangles.

The events can be cyclic, permanent, or sequential depending upon the simulation which is to be executed. In the present challenge, the sequential type is selected. At 0s there is no flow in between the two regions, therefore the event is closed. Now at 0.001s the rupturing of the diaphragm takes place and there is a flow between the high-pressure region and the low-pressure region.

Base-grid

The following grid sizes were used in the simulation

Adaptive Mesh Refinement

Adaptive mesh refinement is a technique that is used to refine the grids automatically based on fluctuating and moving conditions such as temperature or velocity. The feature is used to refine the grid in the flow region of interest such as flame propagation or high velocity without slowing down the simulation with a globally refined grid. There are two types of AMR, mainly sub-grid scale-based and value-based.  The AMR type and criteria are chosen in such a way that the embedding is added where the flow field is most unresolved. In the present challenge, I have used species type AMR which is tabulated as under

Results

Mesh-0

Mass fraction of N2

Pressure

Temperature

Animation file 

Mass fraction of N2

Pressure

Temperature

Line plots

Pressure

Region_0

Region_1

Mean temperature

Region_0

Region_1 

Total cells

Mesh-1

Mass fraction of N2

Pressure

Temperature

Animation file 

Mass fraction of N2

Pressure

Temperature

Line plots

Pressure

Region_0

Region_1

Mean temperature

Region_0

Region_1 

Total cells

Mesh-2

Mass fraction of N2

Pressure

Temperature

Animation file 

Mass fraction of N2

Pressure

Temperature

Line plots

Pressure

Region_0

Region_1

Mean temperature

Region_0

Region_1 

Total cells

 Summarizing all the values

 Conclusion

• The transient-state simulation of the shock tube was performed successfully using Converge-CFD software and the Cygwin command prompt terminal.
• The event was created to connect the high-pressure region and the low-pressure region by a triangle which is called a disconnected triangle.
• The bursting of the diaphragm occurs which results in the creation of shock waves. The compression waves propagate in the low-pressure region whereas the expansion waves propagate in the high-pressure region.
• The mixing of the fluid was also observed as a result of the shock waves get refracted back.
• The fluctuation is observed in the pressure and the temperature plots during mixing.
• The cell count varies once the shock wave is created this is primarily because of AMR.

Source

Shock tube:[https://en.wikipedia.org/wiki/Shock_tube]

Concept of EVENTS:[https://skill-lync.com/knowledgebase/week-6-concept-of-events]