Week 7: Shock tube simulation project

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 bursted 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 backin to the driver gas.

We can see the expansion wave, shock wave and slip line in the above diagram.

This diagram shows the pressure variation as the diaphragm breaks the pressure at slip line/contant line is equal, the

pressure increases as it passes through expansion wave, and the prssure is atmospheric in front of shock wave.

Different waves that are formed in the tube as diaphragm ruptures:

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 turrbine 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 apllication type.

Step :2 - Material to be choosed 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 shocktube 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 pressuer 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 inbetween 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 colour(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