Shock Tube Simulation

Objective:

Perform a shock tube simulation to detect shock waves formed due to bursting of a membrane that seperates a high pressure region and a low pressure region.

The intention is to provide the following:

1. Mesh refinement profile based on gradient (Adaptive-Mesh Refinement)
2. Pressure profile
3. Temperature Profile
4. Velocity Profile
5. Chemical Composition Profile

The purpose of simulating this shock-tube is to set up further simulations of chemical kinetics between fuel and air for auto-ignition caused by the pressure waves we will notice. This can also shed some light on how long it takes for the fuel and air to combust based on the shock tube data.

Introduction

Converge Studio was the software used to simulate the shock tube. The expected observations are a pressure wave propogating and reflecting across the tube due to the sudden interaction between a high pressure region and a low pressure region. 

To save on computational time, a useful feature of Converge Studio called adaptive mesh refinement (AMR) has been used. The main essence of AMR is to refine the mesh in places where there is a high gradient of something. This gradient can be chosen by the user to be pressure, temperature, velocity or chemical component. AMR has been activated for species, i.e. mesh will be refined where the interation of 2 chemical species is taking place.

Insight into the Problem

Shock tube is a simple duct closed at both ends, divded by a diaphragm that seperates a high pressure (driver) section and low pressure (driven) section. The physical set up is usually connected to a pressure reservoirs on both ends with sensors on the driven section to detect various properties. 

When the diaphragm breaks, the high pressure gas compresses gas in the low pressure region rapidly and giving rise pressure shock waves across the tube that reflects back and forth. This causes the temperature in the driven section to rise rapidly to near combustion temperatures, which helps with the ignition.

Geometry:

Case Setup:

The following parameters were used for the simulation on Converge Studio:

Post-processing:

Converge Studio plotting tools and Paraview was used to perform post-processing on the restults:

Variation of properties w.r.t time:

The cell count variation is observed as the number of cells increase when AMR is active in a certain part of the mesh. Higher cell counts leads to accurate capturing of mixture between N2 and O2.

A mirror oscialltion can be observed in mean temperature and pressure for the 2 species. This is because of the constant reflecting of the pressure shock wave that is causing the gas parameters to fluctuate. It can be observed that N2 specie starts of with a higher pressure than O2 specie and a mirroring effect can be seen. When N2 pressure drops, O2 pressure increases and vice versa. It can also be observed that the mean temperature of O2 increases well over its initial condition, a condition that can be exploited for ignition.

Animation:

1. Mesh Propogation

2. Pressure Fluctuations

3. Temperature Contours

4. Velocity Contours

5. Chemical Composition

Inferences

As we can see from the above contour plots, we have succesfully simulated a shock tube. As expected we can see shock waves propogated towards low pressure region and reflecting back. This is causing the gas in the low pressure region to compress to high temperatures and pressures. Phenomenon like this is useful to use in combustion and chemical kinetics studies.