Transient shock tube simulation using CONVERGE CFD

INTRODUCTION:

Shock-tubes are widely used to study the ignition delay for a particular reaction. The process involves two stages:

1. Two reactants are kept separate from each other in different regions, separated by a diaphragm, one at a very high pressure and one at low or atmospheric pressure.
2. The diaphragm is suddenly burst, which initiates the flow from the high pressure region into the low pressure region, leading to heavy mixing and chemical reaction.

The initiation of the chemical reaction takes place in a very short amount of time (milliseconds) and hence difficult to quantify exactly through experiments. Hence, simulations are performed for the same process with a very small time-step to identify the ignition delay.

For a CFD simulation, the diaphragm cannot be modeled as it would increase the complexity of the problem. Hence, "Event" are used in CONVERGE CFD to specify whether the regions are connected or not in a particular step.

For this project, we will be setting up a simple 2D simulation, which only involve mixing between two species and no chemical reaction. The purpose of this project is to visualize the transient behavior of the flow immediately after the diaphragm is burst.

COMPUTATIONAL GEOMETRY AND MESH:

The computational geometry simply involves two regions filled with two different species with a pressure difference.

The green colored region indicates the high pressure region filled with `N_2` and the brown colored region indicates low pressure region filled with `O_2`. There are no inlets and outlets in this model, and both the gases are stationary at the start of the simulation. The front and back walls are flagged as 2D boundaries while the rest of the faces are flagged as no-slip walls. The interface between the two regions is not modeled since it would be much more complex to delete them while the simulation is ongoing. Instead, it is controlled by "Sequential Events".

The base size of the mesh is taken to be `2.5` `mm`. Adaptive mesh refinement (AMR) is used with the mass fraction of `N_2` as the sub-grid parameter and a maximum embedding level of `3`. The sub-grid scale is taken to be `0.001`.

SETTING UP THE FLOW PHYSICS:

The simulation is set-up as a transient simulation with an initial time-step of `1times10^{-9}` `sec` and a total run-time of `0.01` `sec`. Two volumetric regions are initialized:

1. The first region (green) is initialized with `N_2` as the material and a pressure of `6` `ba r` (`600,000` `Pa`).
2. The second region (brown) is initialized with `O_2` as the matrial and a pressure of `1` `atm` (`101,325` `Pa`).

Corresponding surfaces are assigned to their respective regions to which they belong. "Events" are set up in CONVERGE CFD to accurately determine the transient behavior of the process. For the first `0.001` `sec` of the simulation, the two regions are set as "Closed" or disconnected. The regions are "Opened" up after `0.001` `sec`. No reaction mechanisms are set for this simulation. The total pressure in the entire domain is monitored during the simulation to visualize how it reaches a pseudo-steady state (pressure becomes uniform - but mixing may still not be entirely complete). The simulation is run in parallel with `4` processors.

RESULTS AND DISCUSSION:

Mesh

Pressure

Velocity

Mass Fraction of `N_2`

The total cell count shows a maximum of around `3700` cells. From the animation, the effects of the adaptive mesh refinement can be clearly seen. From the pressure and velocity animations, we can clearly see the formation of the shock waves. Since there are no outlets in the domain, the shock waves keep bouncing off the walls of the tube, which in turn, generates secondary shock waves. The total pressure plot in the entire domain shows the pressure fluctuation starting after `0.001` seconds, which marks the bursting of the diaphragm. The pressure fluctuates till it reaches a uniform value of around `340,000` `Pa`. The shock waves also affect the flow of the gases inside the tube, as we can see from the `N_2` mass fraction contours. As the shock wave bounces from the right wall, it pushes back on the `N_2` mixing with the `O_2`, and during its return journey from the other side of the tube, it pushes the `N_2` further towards the right. If any reaction mechanism was included in the simulation, the reaction would start in the mixing region of the two gases and propagate through the domain based on the characteristics of the reaction.