Transient flow simulation in a Shock-tube using Converge CFD

Transient flow simulation of a shock tube

The project deals with the study of transient flow simulation in a shock tube using Converge CFD software. The shock tube is dealt with pressure variation which produces the shock and the case is done with the transient flow. The variation of pressure and temperature in the shock tube is shown. For the grid, Adaptive mesh refinement technique is used by the Converge software which is explained in the report and the plot of cell count as a function of time is plotted.

Shock Tube:

Shock tubes are the devices for studying the flow of high-temperature and high-velocity compressible gas. In this present project, the high-temperature supersonic gas flow is initiated in a shock tube as a result of rupture of the diaphragm separating two gases in high-pressure and low-pressure chambers. Figure 1 shows the shock tube used for the simulation. The high-pressure chamber has N2 gas and the low-pressure chamber is full of O2 gas.

Fig 1: Shock tube with N2 high pressure and O2 low pressure

Initially, the shock tube which consists of two regions i.e. high pressure and low pressure is separated by the diaphragm. When the diaphragm breaks, fluid flows from a high-pressure region to low pressure region. Due to the pressure difference, the shock waves can reflect from the walls and get refraction waves. i.e. compression and expansion waves occur in this process. As an application part, in the case of IC Engine, the chamber will be filled with fuel and air. Because of these shock waves, there is going to be auto-ignition. i.e. the fuel and air are going to auto-ignite. From this, Combustion time for the fuel and air can be determined which is mainly called as ignition delay. Hence, shock tubes are extremely useful in chemical kinetics.

Initial and Boundary conditions:

Since the shock tube is divided into two regions, the initial conditions take place with respect to the value of the pressure.

Region Gas Pressure value(Pa)

High-pressure N2 600000

Low-pressure O2 101325 (atm)

The pressure difference occurs only when the diaphragm is removed from the tube. To do this during simulation, a case called \"Event\" is used in Converge. For the present project, the following event conditions are used on the diaphragm based on the time.

Start(s) Region A Region B Event

0 High-pressure Low-pressure CLOSE

0.001 HIgh-pressure Low-pressure OPEN

Open and close refers to the diaphragm movements depending on which the fluid flow travels from high to low pressure creating shock waves.

Since the simulation is 2D, mirror or two-D boundary condition is applied to the non-interacting direction and \"wall\" boundary condition is applied to the high pressure and low-pressure zone.

Time parameters:

The simulation is run from 0 to 0.003 sec with initial and minimum time-step of 1e-09. This minimal time-step is used since Converge has the capability to adapt to new larger time step once the initial and boundary conditions are perfect in the next time-step. The files are extracted with a time-step interval of 1e-5s which leads to 209 frames until the end of time.

Meshing:

The base mesh used for the shock tube domain is 1e-3 for all the x, y and z directions. In order to capture the shock and flow accurately, Adaptive mesh refinement(AMR) is adapted to N2 gas from the time once the diaphragm starts to open i.e. from 0.001 s. This AMR technique is unique in Converge and reduces the time to mesh for the geometry. Figures from 2 to 4 represents the mesh for different time zone. We can observe the changes in the mesh as the shock front moves which is due to the AMR applicability. The theory of AMR is given below.

Adaptive mesh refinement:

1. AMR is a technique which automatically increases the grid resolution based on the curvatures or second derivatives in the field variables. It can be activated on a region-by-region basis. It can be activated for velocity, temperature, void fraction, species, passives and/or y+ values.

2. In the present project, this AMR is technique is used on the species based. The type is used as permanent starting from the time of 0.001(SGS embed) which is done to capture the shock and flow accurately.

3. SGS is nothing but sub-grid scale which is calculated as:

ϕ\' = ϕ - ϕ\"

where,

ϕ\' is the sub-grid scalar field

ϕ is the actual field and,

ϕ\" is the resolved field.

From this equation, the ϕ\' is evaluated using truncated infinite series.

Fig 2: Base mesh grid at t=0 (Without AMR)

Fig 3: Mesh at time frame = 30 (AMR can be observed)

Fig 4: Mesh at time frame = 150. (AMR observation as the wavefront moves).

Result:

Based on the mesh adaptation, the total cell counts in the flow domain for the complete simulation is shown in Figure 5.

Fig 5: Time vs total cell variation

It can be observed that from time 0 to 0.001 sec, there is no variation in the cell count as it takes only the base mesh into account. Since from 0.001s, AMR is implemented, the cell count in the geometry is increased and as the wavefront moves, at around 0.0022s, the wavefront moves and reflects back which adapts to maximum cell count in the domain. And as the simulation progresses, the flow inside the domain tends to steady flow and hence the amount of cell reduces and reaches a steady-state as the flow progresses.

The pressure and the temperature profile for the entire domain are shown in Figure 6 and Figure 7.

Fig 6: Pressure variation

Fig 7: Temperature variation

From figure 6, the pressure is maintained its stability till 0.001s with a pressure difference of 5 bar. As the diaphragm breaks and the gas in high-pressure zone rushes towards the low- pressure zone creating a rapid pressure-differential drop. The generation of shock waves due to compression cancel the incoming shocks and thus pressure difference between the two zones rises again. This phenomenon repeats again but the magnitude of reduction in pressure difference reduces and as the simulation progresses and the shocks eventually stabilise and start to reach a steady-state value.

In Figure 7, A similar effect is observed with respect to the temperature where the value of temperature reduces as the gases start to mix after 0.001 seconds and rises again when the re-circulation zone is created to eventually reach steady-state when the generated shocks attain equilibrium.

The pressure and the temperature variation for the entire time is shown in below video.

The Figures below shows the variation for different time frames.

Fig 8: Variation as the diaphragm breaks (time frame = 20)

Fig 8: Variation as the high pressure moves to low (timeframe = 34)

Fig 9: Variation as the wavefront hits the wall and reflects back(timeframe = 90)

Fig 10: Variation for the end of time (timeframe = 209)

Below video represents the variation in velocity for the domain.

Below figure represents the velocity variation at different timeframes in the shocktube.

Fig 11: Velocity once the diaphragm breaks (timeframe = 20)

Fig 12: Observation of shock waves as the wave front hits wall and reflects back(tf = 58)

Fig 13: Clear-cut observation of the shockwave (tf = 75)