Shock tube simulation project

In this project, the 3D Shock tube is simulated using Converge 3.0.

Shock tubes are used to replicate and direct blast waves in order to simulate actual explosions and their effects on a smaller scale. Moreover, they are 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). The burst of the diaphragm creates a compression wave that propagates in the low-pressure section and expansion waves traversing in the high-pressure section. However, in a short interval of time, compression waves coalesce to form the shock wave which propagates in the low-pressure section. The stationery low-pressure gases experience a rise in pressure and temperature due to the arrival of shock waves as shown in the figure below. Both the expansion fan and the shock waves are reflected from the closed ends of the tube. Reflected shock counters the motion of the low-pressure section initiated by the primary shock. The strength of the shock wave and expansion fan depends on the initial pressure ratio across the diaphragm and physical properties of the gases in the sections.

image credit: ScienceDirect.com

Geometry:

A box of length 0.2m, with breadth and height of 0.01m, is modeled with two regions as shown below.

Region Green - High-Pressure Region (N2 gas)

Region Brown - Low-Pressure Region (O2 gas)

Both regions are operated by events to act as a diaphragm to obtain the shock during the simulation and to separate the regions before the explosion (i.e., the opening of the diaphragm).

Physical Setup:

General	Transient Pressure Based
Model	RNG k-ε
Materials	O2 & N2
Simulation Time	0-0.003 s
Boundary Conditions	walls (slip) High-Pressure Region ( N2, 6e5 Pa, 300K) Low-Pressure Region ( O2, 101325 Pa, 300K)
Events	0-0.001s (close) 0.001-0.003s (open)
Adaptive Mesh Refinement	Base Grid 0.001m N2 species SGS - 0.001

Mesh:

A base grid of 0.001m is used along all the directions. As far as, Adaptive mesh refinement is concerned, the sub-grid scale criterion of 0.001 for 3 embedded layers is used for N2 species.

AMR is activated if the below criterion is met.

`(d^2[N2])/(dt^2) > 0.001`

If the above criterion is true, then the 3 embedded layers adjacent to the cell are halved as no scaling is used.

`Embedded Size = (Base Grid Size)/2`

Mesh refinement during the simulation time is as shown below.

Grid Dependency Test:

Here two base grids of sizes 0.002m and 0.001m are considered to perform the grid dependency study. Total cells, the variation of mean pressure, and temperature over the simulation time in both the regions are compared for both the grid sizes.

Total Cells:

Variation of Pressure in the flow region:

Variation of Temperature in the flow region:

From the above figures, it is clear that the results obtained with a base grid of 0.002m vary with the base grid of 0.001m within 1%. The number of cells during the simulation time with the base grid of 0.001m is much higher. So, we can opt for the base grid of 0.002m. Anyhow, in this project I did choose a size of 0.001m for the base grid.

Flow of Project in Converge:

1. Provided 3D geometry is dropped in the Converge workspace.
2. Boundaries are named using appropriate names.
3. Normal directions are checked to be in line with the geometry and flow.
4. Diagnosis is performed to check any discrepancies in geometry.
5. Then appropriate species are selected for the regions.
6. Simulation Parameters along with the appropriate time steps are set.
7. Boundary conditions are set to the appropriate regions and their corresponding values.
8. The base grid of the considered step size is inserted along with respective directions and AMR of 3 embedded layers with species SGS of 0.001 is used.
9. Variables for post-processing and time intervals for writing the output and restart files are set and selected.
10. All the input files are stored at the desired location.
11. All the stored input files are executed using the command editor. These input files are executed by Converge Solver in the background.
12. Then the executed files generate the output folder in which data files after every selected cycle intervals are stored which are post-processed for the graphical results.

Total Cells:

Here the number of total cells over the simulation time is shown as below.

Effect on Mass Fraction and Pressure:

Effect on Mass Fraction and Velocity:

Variation of Temperature in Shock Tube:

Variation of Density in Shock Tube:

Mean Temperature over Flow Time:

Mean Density over Flow Time:

Mean Pressure over Flow Time:

Discussion:

• The process of generation of shock and expansion waves continues till the pressure difference in the domain dies out, therefore AMR keeps on refining the mesh in the wavefront until the rate of change of concentration of N2 is below the SGS value.
• To observe the pressure difference to damp, we need to run the simulation for a longer duration.
• The diaphragm breaks at 0.001s (activated by events). As soon as, it breaks, the pressure in the High-pressure region reduces and increases the pressure on the Low-pressure region, this sudden increase in pressure in the Low-pressure region causes the shock in the Low-pressure region and corresponding expansion waves due to decrease in pressure, flow in the High-pressure region.
• The shock waves are reflected when the gases in the Low-pressure region are compressed and the pressure in the Low-pressure region is higher than the Shock front. This sinusoidal behavior of damping is observed until the pressure difference becomes zero.
• For the density variation, it follows the same pattern as the pressure, as both of them are directly related from the ideal gas equation.
• Moreover, the shock increases the temperature, and the expansion wave decreases the temperature.