Week 7: Shock tube simulation project

AIM:

               To do a transient state simulation of a shock tube.

OBJECTIVES:

• To setup a transient state shock tube simulation.
• To plot the pressure and temperature plot history in the entire domain
• To plot the cell count as a function of time.
• To show the mesh generation using PARAVIEW.

INTRODUCTION:

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 build up of high pressures which cause diaphragm(s) to burst and a shock wave to propagate down the shock tube (compressed-gas driven).

THEORY:

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 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 for safety reasons, with 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 test begins with the bursting of the diaphragm. Several methods are commonly used to burst the diaphragm.

• A mechanically-driven plunger is sometimes used to pierce it or an explosive charge may be used to burst it.
• Another method is to use diaphragms of plastic or metals to define specific bursting pressures. Plastics are used for the lowest burst pressures, aluminium and copper for somewhat higher levels and mild steel and stainless steel for the highest burst pressures. These diaphragms are frequently scored in a cross-shaped pattern to a calibrated depth to ensure that they rupture evenly, contouring the petals so that the full section of the tube remains open during the test time.
• Yet another method of rupturing the diaphragm utilizes a mixture of combustible gases, with an initiator designed to produce a detonation within it, producing a sudden and sharp increase in what may or may not be a pressurized driver. This blast 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.

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 rarefraction wave, often referred to as the Prandtl-Meyer wave, travels back in to the driver gas.

The interface, across which a limited degree of mixing occurs, separates driven and driver gases is referred to as the contact surface and follows, at a lower velocity, the lead wave.

A 'Chemical Shock Tube' involves separating driver and driven gases by a pair of diaphragms designed to fail after pre-determined delays with an end 'dump tank' of greatly increased cross-section. This allows an extreme rapid reduction (quench) in temperature of the heated gases.

GEOMETRY SETUP:

• IMPORT GEOMETRY:

        Geometry is imported to the workspace from the stl file given.

                     

• NORMAL ORIENTATION:

        The orientation of normal are checked and its changed such that the normal points inwards by going to transform > normal

        

• CREATING BOUNDARIES:

        The boundary are created for the geometry under boundary flag tab.

         

         The boundaries are assigned to the faces and the name of the boundaries are edited and click apply.

• DIAGNOSIS:

        The diagnosis is runed and checked for problems for the geometry.

         

BEGIN CASE SETUP:

• APPLICATION TYPE:

        On the right panel go to the case setup tab, select begin case setup.

         

         Select the application type as time-based and select apply and done.

• MATERIALS:

        Select materials and select the checkbox reaction mechanism then select the predefined mixture as air then click apply and done.

        

• GAS SIMULATION:

         

         The default values are selected and press ok.

• GLOBAL TRANSPORT PROPERTIES:

        Select global transport properties, keep the default values and press ok.

         

• SPECIES:

         In species tab, add O2 and N2 as species in the gas species tab.

         

• RUN PARAMETERS:

        Under solver tab select solver as transient solver.

        

• MISC TAB:

        Under misc tab uncheck use shared memory option and click ok.

        

• SIMULATION TIME PARAMETERS:

         

        Set the start time, end time, initial, minimum and maximum time steps as shown above.

• SOLVER PARAMETERS:

         

         Select the Navier-stokes solver type as density based and click ok.

• REGIONS AND INITIALIZATIONS:

         

         A high pressure region is created and pressure of 600000 pa is defined and N2 is defined as species.

         

         In low pressure region, pressure is defined as atmospheric pressure and O2 is defined as species. 

• BOUNDARY CONDITIONS:

        HIGH PRESSURE BOUNDARY:

         

         Under high pressure boundary, the boundary type is defined as wall and velocity boundary condition is defined as slip and specified value of 300k is defined as temperature boundary condition.

         LOW PRESSURE BOUNDARY:

          

          Under low pressure boundary condition boundary type is set to wall and velocity boundary condition is set to slip and temperature boundary condition as zero normal gradient.

• EVENTS:

        When 2 regions are in contact with each other with no boundary in-between them, it is necessary to use events. The events flag creates triangles in the place between the 2 regions called as disconnect triangles.

        The events flag can be turned on before the case set-up, by navigating to the initial conditions window and checking the events option.

        After turning on the events flag, the event can be set by selecting the events option in the case set-up tree. 

        Events can be cyclic, permanent or sequential.

        Based on how the event should occur, the type of event can be chosen from the options available. 

        The event can repeat itself over cycles, in a sequence or can be set permanently. Based on this setting, Converge creates what is called as disconnected triangles. These are triangles that Converge creates and do not show up in post processing as they are temporarily created for the purpose of simulating the event.

        Triangles are created for when there should be no interaction between the 2 regions and these triangles are deactivated when there is supposed to be an interaction between the 2 regions. It is important to note that no triangles must be created by the user, only events must be defined in order to have no intersecting triangles.

        

• GROUP COLOUR BY REGION:

        when the group color by region is selected the model is grouped by regions.

        

• PHYSICAL MODEL:

        

        The RNG K-epsilon is selected for turbulence model and the values are kept default.

• GRID CONTROL:

        

        In grid control the adaptive mesh refinement is selected.

• BASE GRID:

         The base grids are defined as 0.002 m and press ok.

          

• ADAPTIVE MESH REFINEMENT:

         In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'.

         

         The species N2 is added as species and timing type is set to permanent and bed type as SGS.

• POST VARIABLE SELECTION:

         

         Keep the default values in typical variables tab.

          

          Under combustion/turbulence the values are kept default.

          SPECIES/PASSIVE:

           

           Mass fraction is checked and O2 and N2 are added in the mass fraction tab.

• OUTPUT FILES:

         The interval for writing 3d output data files and restarting outputs are defined.

          

• Exporting the input files to a folder
• Then the executable is pasted inside the folder
• The simulation is run in Cygwin.
• The postconvert executable is pasted in the output folder.
• The post conversion is done on Cygwin and converted into the type that paraview reads.
• The results are then post processed using paraview.

 RESULTS:

MESH:

Due to adaptive mesh refinement, mesh is refined at regions where there is more change in slope of N2 mass fraction.

MESH WITH REGION:

This image shows the mesh and the regions.

PRESSURE CONTOUR;

As the diaphragm breaks the oblique shock wave is generated and it enters and reach the downstream end of the driven section. The shock wave increases the static properties in the low pressure region. This results in expansion of N2  and hence pressure decreases. The moment when it hits the downstream end and gets reflected, their pressure value changes respectively and the flow pattern occurs till the shock intensity is decreased.

PRESSURE PLOT ALONG THE LENGTH OF DOMAIN:

The pressure keep on increases along the length of the domain.

PRESSURE PROFILE VS TIME:

The pressure stable untill the diaphragm gets breaks. once the diaphragm breaks and decreases and increases the pressure thus forming a wave like structure.

ANIMATION OF PRESSURE CONTOUR:

https://drive.google.com/file/d/1yP6v0TC9fRCjZynzz9A3CF3aMsHvbKT0/view?usp=sharing

TEMPERATURE CONTOUR:

When the diaphragm is broken the shock wave is generated and temperature in O2  region increases and when the shock wave gets reflected then the temperature in O2 region decreases and vice versa until the shock intensity is decreased.

TEMPERATURE PLOT ALONG THE LENGTH OF THE DOMAIN:

The temperature first decreases and then increases and reaches the steady state.

TEMPERATURE PROFILE VS TIME:

Temperature also increases and decreases continuosly untillit reaches steady state once diaphragm breaks.

ANIMATION OF TEMPERATURE CONTOUR:

https://drive.google.com/file/d/1jQpRUsuijSAXTw96y5nIvr0XHCWLLnOa/view?usp=sharing

DENSITY CONTOUR:

ANIMATION OF DENSITY CONTOUR:

https://drive.google.com/file/d/1On5A7sLIB-S01Rer2v6Zko95VgAzsZ36/view?usp=sharing

 MASS FRACTION OF N2:

As the diaphragm breaks the high pressure N2 region pushes the low pressure O2 region and then the low pressure regions pushes the waves towards the N2 region and continues until the pressure reaches the converged value.

ANIMATION OF MASS FRACTION OF N2:

https://drive.google.com/file/d/1WA7_OSjoH5qKj0oCbqWjh6sm14LODlfP/view?usp=sharing

MASS FRACTION OF O2:

VELOCITY CONTOUR:

As the diaphragm breaks the velocity increases and decreases continuosly untill the shock gets reduced.

ANIMATION OF VELOCITY CONTOUR:

https://drive.google.com/file/d/1FY6YyEJtx6LVZKv-W9n46hA8GIGCGqML/view?usp=sharing

TOTAL CELLS:

 

As we set the diaphragm to burst at 0.001s after that the total number of cells increases and decreases continuosly.

CONCLUSION:

• As the diaphragm breaks the gas from the high pressure region tried to enter the low pressure region. But since the low pressure region already had another gas, the high pressure gas pushed behind to its original region during which we can see shock waves produced. This is because when both the gases were pushed to one side high pressure developed due to which these shock waves are formed until the pressure gets stabilized.
• We can see that from the point where the diaphragm breaks the mesh seemed to be refined and travels with the flow.