Shock tube simulation project

SHOCK TUBE

Introduction

Main goal of this challenge is to simulate shock tube problem, to see what happens when diaphragm is ruptured in the shock tube channel and to capture how the flow will be induced. Furthermore, we intend to understand how the "Events" work in "Converge Cfd".

Theory

The shock tube is an instrument to direct blast waves at a sensor or a model to simulate actial explosions and their effects. shock tubes, for instance, are used to study aerodynamics under a wide range of temperatures and pressures, also it is used to see compressible flow phenomena and gas phase combustion reactions. Recently, this devise is used in biomedical research to investigate how biomedical speciments are affected by blast waves.

A shock wave inside a shock tube could be generates by a little explosion (blast-driven) or by high pressure which causes a diaphragm to rupture (compressed-gas driven)

A simple shock tube is rectangular or circular in cross-section made of metal, in which low pressure and high pressure gas regions are separates by a diaphragm.

Low pressure gas region is called "driven", which is subjected to the shock wave. High pressure gas region is known as a "driver". The driver gas is usually chosen with low molecular weight (e.g Helium or Hydrogen) for safety reasons, but using these substances may slightly diluted to interface conditions across the shock. To achieve strongest shocks, pressure of the driven gas is well below to atmospheric pressure.

To start operating of the shock tube we need to rupture the diaphragm.

there are some methods bursting the diaphragm.

• A mechanically-driven plunger or explosive charge.
• Another way is to build up enough pressure in high pressure region to burst the diaphragm.

Exploding the diaphragm induses pressure waves, each increasing the speed of sound behind them. This shock wave increases pressure and temperature of the driven gas and produces a flow in the direction of the shock wave but at a lower velocity than the lead wave, Immediately, a rarefaction wave occurs, which is referred to as a Prandtl-Meyer expansion waves. This wave travels back to the driver gas region.

Geometry

As you see we have two regions: The green one is High pressure and The brown one is the Low pressure zones, which are separated from each other at the begining of the simulation (when time equals to zero).

SET UP

• Initial conditions

In our simulation as we said, there are two regions: High pressure and Low pressure. In high pressure zone we have N2 with the mass fraction of 1 and in the low pressure region there is O2 with the mass fraction of 1 as well.

In high pressure zone Initial pressure is set to be 6bar and in the low pressure zone it is an atmospheric pressure (1bar)

• Run Parameters

Our case is Transient full hydrodynamic compressible flow.

• Simulation time parameters

• Boundary Conditions

• Event

In order to eliminate separation between the high pressure and the low pressure zones we use "Events" in order to imitate a diaphragm explosion.

As we see at the begining of the simulation pressure zones are separates and when time reaches to 0.001sec the "virtual diaphragm" is opened.

MESH

In order to accurately capture mixing process we are using adaptive mesh refinement (AMR)

MESH GENERATION

As we see in the video above mesh is refined only in the mixing zone.

POST PROCESSING

As we see, mean pressure within the whole domain decreases initially due to convective flow dominance, when the diaphragm is ruptured we encounter shocks and high velocity flow between high pressure and low pressure zones causing decrease in static pressure, however along with the time marching the convective flow is decreased because the process is trying to establish equilibrium. finally mean pressure, according to the theory, if we take in account isentropic flow (not including losses), should be the same as the mean pressure at the beginning of the simulation.

`(P_h+P_l)/2` - where `P_h` is high pressure and `P_l` is the low pressure

According to the theory, mean pressure after the equilibrium is reached should be `(6+1)/2 = 3.5 (Bar)`. Fortunately we get the same results in Converge Cfd.

• High pressure zone

As we see temperature in high pressure zone is decreased, it is caused because of the flow generation in the low pressure zone direction, meaning, Initially in the high pressure zone static pressure is 6bar and when the diaphragm is opened flow is derived from high pressure to low pressure. according to the enegry conservation, due to increase in flow (dynamic pressure) and decrease in static pressure in the High pressure zone, temperature should also decrease.

• Low pressure zone

Due to static pressure increase in low pressure zone temperature is also increased. we should note that according to the thermodynamics these two fluid properties are dependent to each other.

• Total cell count

As we already described in set up we are using AMR in order to capture mixing structure properly, as wee see in the plots above total cell count is fluctuating within the simulation time, this is caused due to wave propagation, As the flow goes back and forth, meaing, when the wave is reflected from the edge of the domain, mixing zone is affected by the convection which changes the speed of the diffusion process of N2. This phenomenon is shown in the video below.

• N2 mass fraction and Velocity contours

Conclusion

We simulated shock tube successfully, learnt the working principle of the shock Tube, Furthemore we saw the purpose of the concept called "Events".