Week 7: Shock tube simulation project

Aim :- Shock tube simulation using Converge CFD package and post processing.

Objective :-

• Setup a transient shock tube simulation in Converge.
• Plot the pressure and temperature history in the entire domain.
• Plotting the cell count as function of time.

Introduction :-

Shock tube :-

A simple shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in which a gas at low pressure and a gas at high pressure are separated using some form of diaphragm.

The low-pressure gas, referred to as the driven gas, is subjected to the shock wave. The high pressure gas is known as the driver gas. The corresponding sections of the tube are likewise called the driver and driven sections. The driver gas is usually chosen to have a low molecular weight, for safety reasons, with high speed of sound.

To obtain the strongest shocks the pressure of the driven gas is well below atmospheric pressure.

The driven section contains the gas mixture of interest - We generally consider N2 as our driver gas in simulation. The driver section is pressurized with an inert gas (e.g. Helium) until the diaphragm ruptures, thereby creating a shock wave that travels through the test gas in the driven section.

For test the diaphragm is burst using mechanical plunger, voltage or just by increasing pressure if material is plastic or some metal.

The bursting diaphragm produces a series of pressure waves, each increasing the speed of sound behind them, so that they compress into a shock propagating through the driven gas. This shock wave increases the temperature and pressure of the driven gas and induces a flow in the direction of the shock wave but at lower velocity than the lead wave. Simultaneously, a rarefaction wave, often referred to as the Prandtl-Meyer expansion wave, travels backing to the driver gas.

Applications :-

• The fluid flow in the driven gas can be used much as a wind tunnel, allowing higher temperatures and pressures therein replicating conditions in the turbine sections of jet engines.
• The resultant high temperature hypersonic flow can be used to simulate atmospheric re-entry of spacecrafts or hypersonic craft.
• Shock tubes to both create and direct blast waves at a sensor or an object in order to imitate actual explosions and the damage that they cause on a smaller scale.

CASE SETUP :-

Step :1 - Setting up the application type.

Step :2 - Material to be chosed is air and species we will include 'O2' and 'N2'.

Step :3 - In simulation parameter we will run transient case for time period of 0.03 seconds.

Step :4 - For boundary we have generally two boundaries in shock tube one is high pressure boundary and other is low pressure boundary.

• High pressure boundary type - Slip

• Low pressure boundary type - Slip

Step :5 - For regions we have mainly 2 regions

• High pressure region - Pressure = 6 bar

Species = N2

• Low pressure region - Pressure = 1 bar

Species = O2

Step :6 - We specify events in this simulation to replicate the popping diaphragm situation.

In events section we generally define the time frame until which the flow in between 2 region should be stopped, and time frame at which the flow should start.

We can apply the events for boundaries, and regions.

Step :7 - In physical modelling we specify turbulence modelling.

Step :8 - In Grid control section we define base gris size and also adaptive mesh refinement which is required to capture the shock wave accurately.

Step :9 - Specify the species in post variable selection.

Step :10 - Time to save output data should be kept as small such that we can get required output files for smooth animation of shock wave.

RESULTS :-

Velocity contour :-

This is the velocity profile right after the diaphragm pops down we can see the shockwave with red color (higher velocity) propagating towards the wall. and the blue region in high pressure side is due to expansion wave since the velocity temperature and density decreases passing through the expansion wave.

Mass fraction(N2) contour :-

Mass fraction of N2 when the diaphragm pops down we can see the diffusion of N2 into O2.

Temperature contour :-

In case of temperature its greater at shock front and decreases behind it, and everything coming inside the stationary shock front gets heated up and there is increase in temperature of gases.

Mesh grid :-

Adaptive mesh refinement can be seen when the wave travel across the shock tube.

Plots of Pressure, total cell count, mass of species in low pressure region, and velocity :-

Conclusion :-

• From pressure plot we can say that as the diaphragm pops the pressure in region 0 (high pressure region) decreases due to diffusion into the low pressure region and variation of pressure is due to reflection of flow by the wall of the shock tube.
• In case of cell count it increases and decreases according to the adaptive mesh refinement criteria to extraploate accurate results.
• From mass of the species in low pressure region plot we can see how the N2 concentration increases in low pressure region after the diaphragm is broken.
• The velocity profile shows how the velocity is increased and decreased successively in shock tube.