Week 7: Shock tube simulation project

Shock Tube Simulation:

Objectives:

• Setup a transient shock tube simulation
• Plot the pressure and temperature history in the entire domain - Explain the result
• Plot the cell count as a function of time - Explain the result

Theory:

The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale. Shock tubes (and related impulse facilities such as shock tunnels, expansion tubes, and expansion tunnels) can also be used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. Shock tubes are also used to investigate compressible flow phenomena and gas phase combustion reactions. More recently, shock tubes have been used in biomedical research to study how biological specimens are affected by blast waves.

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).

Generally, there are two types of Shock tubes:

Both compression-driven and blast-driven shock tubes are currently used for scientific as well as military applications. Compressed-gas-driven shock tubes are more easily obtained and maintained in laboratory conditions; however, the shape of the pressure wave is different from a blast wave in some important respects and may not be suitable for some applications. Blast-driven shock tubes generate pressure waves that are more realistic than free-field blast waves. However, they require facilities and expert personnel for handling high explosives.

Working:

A simple shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in which gas at low pressure and gas at high pressure is separated using some form of a diaphragm. The diaphragm suddenly bursts open under predetermined conditions to produce a wave propagating through the low-pressure section. The shock that eventually forms increases the temperature and pressure of the test gas and induces a flow in the direction of the shock wave. Observations can be made in the flow behind the incident front or take advantage of the longer testing times and vastly enhanced pressures and temperatures behind the reflected wave.

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, (e.g., helium or hydrogen) for safety reasons, with a high speed of sound, but may be slightly diluted to 'tailor' interface conditions across the shock. To obtain the strongest shocks the pressure of the driven gas is well below atmospheric pressure (a partial vacuum is induced in the driven section before detonation).

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 a lower velocity than the lead wave. Simultaneously, a refraction wave, often referred to as the Prandtl-Meyer wave, travels back into the driver's gas.

Applications:

Biomedical research like inserting of medicine · Military applications like missile launching · Mining purposes · Blockage removal in a Sewage plant.

Geometry:

Diagnosis result: (before case setup)

Boundary Flagging:

Simulation Case setup:

• Application type: Time based

• Materials:

        (a) Predefined mixtures = Air

        (b) Gas simulation

        (c) Global transport parameters

        (d) Species

• Simulation Parameters:

        (a) Run Parameters

        (b) Simulation Time Parameters:

        (c)  Solver Parameters [Transient-State]:

• Boundary Conditions:

        (a) High pressure

        (b) Low pressure

• Regions and Initialization:

        (a) High-pressure region

        (b) Low-pressure region

        (c) Select Events

• Physical Models:

        Click on Physical Models and select Turbulence Modeling.

• Turbulence modeling:

• Grid Control:

        (a) Base grid

        (b) Select Adaptive Mesh Refinement

• Output Processing:

        (a) Post variable selection

        (b) Output Files

Results:

• Meshing:

        (a) Base Mesh

        (b) Mesh with AMR

• Region Representation:

• Mass Fraction $N_2$ Contour:

• Pressure Contour:

• Pressure Plot:

• Temperature Contour:

• Temperature Plot:

• Velocity Contour:

• Cell Count Plot:

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 in dampness, 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 corresponds to expansion waves due to a 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. 
• The density variation, follows the same pattern as the pressure, as both of them are directly related to the ideal gas equation.
• Moreover, the shock increases the temperature, and the expansion wave decreases the temperature.