Week 7: Shock tube simulation project

AIM :- To simulate the shock tube and provide the temperature history of entire domain.

OBJECTIVES :-

• To understand the working of shock tube.
• To understand the concept of 'Events' in the converge studio.
• Setup the transient shock tube simulation.
• Plotting the temperature and pressure for entire domain.
• Plotting the cell count as a function of time.
• Creating the animation files for each contour.

THEORY AND INTRODUCTION :-

# Shock tube setup and working :-

The shock tube is a simple duct closed at both ends. A diaphragm devides this duct into two compartments called as driver (high pressure) and driven (low pressure) sections. These two sections are seperated by a metal diaphragm. A high pressure driver gas reservoir is connected with the driver section. However a vaccume pump is connected to the driven section to arrive at the accurate driven section pressure. Pressure sensors are generally mounted along the driven tube for pressure measurment. A shock wave inside a shock tube may be generated by a small explossion(blast-driven) or by the build up of high pressure which cause diaphragm to burst and a shock wave to propogate down the shock tube (compressed gas driven).

In our case we are implementing compressed gas driven method. By slowly increased the driver gas pressure for a given driven pressure untill the diaphragm gets ruptured. Burst of the diaphragm creates a compression waves which propogate in the driven section and expansion waves traversing in the driver section. In a short interval of time, compression waves colapse to form the 'shock wave' which propogate in the driven section. The stationary low pressure driven gas raises it's pressure and temperature on arriaval of the shock waves. Driver gas at the same time encounters the expansion in the presence of expansion waves. The contact surface moves in the driven section which seperates the driver and driven gasses and provides the position of diaphragm. Expansion waves do not coalesce, so they form an 'Expansion Fan'. Both the expansion fan and shock reflect from the closed ends of the shock tube. Reflected shock cancels the motion of the driven fluid initiated by the primary shock, thus providing more resistance against mixing. Collision and boundary layer effect results in small pressure loss, as the energy gets transfered in the form of waves.

# Uses of shock tube :-

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 tube can also be used to study aerodynamic flow under a wide range of temperatures and pressure that are difficult to obtain in other types of testing facilities. Shock tubes are also used to investigate compressible flow phenomenon and gas phase combustion reactions.

# Shock tube simulations :-

We are setting up 1D quasi transient (for 0.003 sec) shock tube simulation using converge studio and using Paraview to post process the results.

Pressure difference of 6 bar is initialy set between high and low pressure regions and 300k as initial temperature in the domain. N2 is used in the region of high pressure zone, therefore no need of enabling the 'Reaction Mechanism' dialogue box species (N2) based Adaptive mesh refinement is used with 0.001 Sgs embed and permanent type. By using the option 'Events', flow is allow to takeplace between the two regions after 0.001 sec. To make this happen, we used 'Sequential' option in the Event's tab.

GEOMETRY :-

Geometry for the given challenge are as follows-

In converge V3.0, there have no need of 2D boundaries, here require only 3D boundaries. In this geometry left tube is a high pressure tube and right tube is a low pressure tube. At middle there have no any interference so that shock can be trnsfer from one end to other end. All normal are inside the domain because our system is inside the domain as shown in figure above.

I set the case setup for shock tube challenge project as bellow-

1. GAS SIMULATION :-

Here, I set the gas simulation so that shock must be observe and simulation run successfully.

2. GLOBAL TRANSPORT PROPARTIES :-

These are by default value which consider converge itself.

3. GAS SPECIES :-

As air as a pre-mixture there have two gasses i.e. oxygen and nitrogen and I consider that are gas species.

4. RUN PARAMETERS :-

Converge itself consider solver as a transient here for fully hydrodynamic flow.

5. SIMULATION TIME PARAMETERS :-

Due to the shock tube problem I consider here very small time to show up the clear results as shown above.

6. SOLVER PARAMETERS :-

Here used density based solver bacause in shock tube problem there have sudden impact.

7. REGION NAME :-

Here gives the region name for each boundary.

8. HIGH PRESSURE BOUNDARIES :-

High pressure boundary is wall type and use slip function because, there have slip inside the walls and also specified the temperature.

9. LOW PRESSURE BOUNDARIES :-

Same as that of high pressure boundary because both are region attached with each other in opposite directions.

10. HP REGION AND INITIALIZATION :-

In high pressure region specified pressure is 6 bar and nitrogen as a species with mass fraction is 1.

11. LP REGION AND INITIALIZATION :-

In low pressure region specified atmosperic pressure and oxygen as a species with mass fraction is 1.

12. EVENTS :-

Events is used to join or contact of two same or different region. At start fluid goes from HP to LP region which are closed end and at 0.001 sec fluid goes from HP to LP region which are open. This is sequential events because fluid flows inline manner.

13. TURBULENCE MODELLING :-

It's by default setting of converge studio.

14. BASE GRID SIZE :-

It's a base grid size where total 20,000 cells are estimated.

15. ADAPTIVE MESH REFINEMENT :-

In adaptive mesh refinement minimum cells is 1 and Maximum cells are 200000. Also I specifies here species.

16. OUTPUT FILES :-

Time interval for writting 3D output files is very less because showing the clear animation of shock wave.

RESULT PLOTS :-

I plotted the results from above setting are as follows-

# Pressure, temperature, velocity and density contour for different time are as follow-

a) At t=0 sec.

b) At t=50 sec

c) At t=100 sec

d) At t=150 sec

e) At t=200 sec

f) At t=250 sec

g) At t=300 sec

From the above contours it can be also observed that the reflected shocks resist the upcoming flow, thus preventing the two species to mix and as the time progresses, the proparties of the species in the domain tend to attain equilibrium.

# Pressure, temperature, velocity and density plots for different time are as follows-

a) At t=100 sec

b) At t=150 sec

c) At t=200 sec

Here, as time increases temperature and vellocity increases but pressure and density decreases from above plot with respect to time.

# Converge plots are as follows-

a) Total cell plot :-

After the rupture of the membrane, compression waves coalesce to form a shock wave which trvels in the driven section of the chamber, whereas an expansion fan is generated and it moves in the driver section of the chamber. Major portion of the shocks are in the driver section which consists of N2 species. We used N2 species based on AMR. Due to the expansion fan compression waves and reflected waves sudden change in the proparties of the medium is observed, at certain locations in the domain. Species based AMR refine the mesh in the N2 filled region at the places where sudden change in the proparties exist. The process of generation of shock and expansion waves contineous till the pressure difference in the domain dies out, therefore AMR option keeps on refining the mesh in the new region of the wave front generation, which results in increasing number of cells in the domain.

b) Total mass plot :-

c) Density plot :-

d) Mean temperature plot :-

e) Pressure plot :-

f) Species mass for N2 plot :-

g) Species mass for O2 plot :-

h) Subgrid scale for N2 :-

From the Ideal gas low, it is evident that pressure, density and temperature are directly proportional to each other.

It can be noted from the above plots that the amplitude of the fluctuations gets reduced as time progresses.

Eventually, the fluctuations die out leading to a steady value of pressure, density and temperature after a considerable time. To view those results the simulation time should be increased.

Pressure difference are the driving force for the formation of shocks, so as the pressure diference reduces, the magnitude of the wave front generated will be low, thus leading to the gradual reduction in the amplitude of the fluctuation as time progresses.

In the form of waves, energy gets transfered with the goal of attaining equilibrium. Shocks are formed due to the coaleasce of the wave during the process of ataining equilibrium. Eventually steady state is obtained after considerable time of simulation, which can be evident from the pressure contour , in which pressure difference reduces as the time progresses.

Similar pattern is observed in the low pressure region but in the opposite sense. After a considerable time, fluctuation die out leading to a steady state solution even in this case.

# Animation files :-

CONCLUSIONS :-

A similar pattern of consecutive maxima and minima can be observed for temperature too. This is because the pressure is directly proportional to the temperature.

In high pressure region the temperature initially starts to decrease and it is vice versa for the low pressure region.

When we observe the above video it's clear that when diaphragm ruptures expansion and compression takes place in the HP region and LP region respectively at the initial stage. Then the shock wave gets reflected back from the boundary resulting in compression and expansion in HP region and LP region respectively for pressure animation. In the high pressure region, we have N2 species and in the low pressure region, we have O2 species which are at 1 bar and ambient pressure respectively. The containts of the species remain the same untill 0.001 sec where the flow transfer happens causing shock to propogate. The simulation runs for only 0.003 sec and therefore if we allow the simulation to run any further it will reach the steady state value as the concentration decreases periodically.

The fineness of shock tube is depends on mesh quality i.e. base grid size.

In this way I setup the case, plot the required plots, contours through paraview and convergent studio and describe it details as above, and finally showing the animation file to conclude the results of setting case.