Flow over a Background facing step

Aim:

• To simulate the Backward step flow for three different mesh grid sizes by using convergent science and paraview.
• To show various velocity and pressure contours for the different mesh.
• To show the various plot of velocity, pressure, mass flow rate and total cell count for different mesh grids.
• To steady the turbulent flow characteristics in Backward step flow

Introduction:

What is Backward Facing Step Problem?

Figure: Flow Features of Backward Facing Step Flow

Fully developed flow enters the domain from left. When the flow reaches the step, because of expansion of flow channel, pressure gradient exists, it detaches and a recirculation zone is formed. A turbulent boundary layer encounters a sudden back step, causing flow separation. Later the flow eventually reattaches to the bottom wall.

Backward-Facing Step (BFS) flow is one representative model for separation flows, which can be widely seen in aerodynamic flows (airfoil, spoiler, high attack angle process), engine flows, condensers, vehicles (cars, boat), heat transfer systems, and even the flow around buildings, etc. The flow separation after a simple stage will introduce separation bubble formation, evolution and re-attachment process, which is dependent on the Backward Facing Step geometric design, the inlet and outlet conditions, turbulent intensity, as well as heat transfer conditions. It is shown that the step size (duct expansion ratio) will define the basic re-circulation and re-attachment process.

It is a basic model involving the most important feature of a separated flow –a free shear flow separation, vortex generation and reattachment.

A backward step flow includes an inflow of uniform velocity,laminar or turbulent from a channel to a step on the either sides with a step height of h .The flow fluid is divided into four regions namely separated Shear layer ,the recirculation region under the shear layer,the reattachment region, and the recovered boundary layer.

Flow with separation and reattachment has long been a subject of fundamental fluid dynamics research. The presence of a separated flow, together with a reattaching flow, gives rise to increased unsteadiness, pressure fluctuations, structure vibrations and noise, as it also exhibits an unsteady structure with a large scale vortex in the separated shear layer and low-frequency motion around the reattachment region with fluctuation of an instantaneous reattachment point.

Turbulent flow over a backward-facing step is one of the classical tests to validate turbulence models in CFD. In the present work, steady-state turbulent flow over a backward-facing step was simulated using Converge with the Renormalization-group (RNG) k-ε model to account for turbulent viscosity

Turbulent flows occur in a variety of industrial problems. A flow is termed as turbulent when the inertial forces of the fluid are greater than the viscous forces resulting in chaotic fluctuations in the flow.

Importance of Backward Facing Step Problem

Separation and reattachment of turbulent flows occur in many practical engineering applications. It is seen both in internal flow systems such as diffusers, combustors and channels with sudden expansions, and in external flows like flow around airfoil and building. In these situations, the flow experiences an adverse pressure gradient, which causes the boundary layer to separate from the solid surface. The flow subsequently reattaches downstream forming a recirculation bubble. The presence of a separated flow, together with a reattaching flow, gives rise to increased unsteadiness, pressure fluctuations which may lead to structure vibrations and noise.

Procedure for Generation of Geometry:

We have to create the geometry of the Backward step flow in the Converge by using the Commands provided in the geometry box.The dimensions of the geometry is shown in the below image.

Go to the create geometry and by using vertices method enter the Co-Ordinates of the vertices and then join them by using the 3 vertices triangle method and then copy the geometry by using the angle method and copy the geometry at the distance of -0.02 meters in the direction of Z-axis then by using the loft command we can complete the 3d geometry of the Backward step.The below figure shows the geometry in 3D view

Now enables the normal/Vectors of the geometry and transform the normal in one direction.

Now check for the errors in the Diagonsis Dock.Check for the errors in Intersections, Open edges,Over lapping triangles and for isolated triangles if there was no errors means we can forward for the case setup.

case setup for Simulation:

• Application Type – Time Based
• The flow is general flow which contains the air as a Material.
• Air contains a Species mixture of O2 and N2 which will flow through the required geometry.
• Global Transport Parameters the Prandtl number is 0.9 and the Schmidt number is 0.78.

Simulation Parameters:

• In the Run Parameter: Solver we used is Steady state and the simulation mode = Full hydrodynamic in the mic state we enable the Solver Momentum, Solve Species and Steady state Monitor.
• In the Steady State Monitor, we keep the minimum number of Cycles to be execute for Steady State solver is 15000 and we add the monitor variables of Mass flow rate and average velocity.
• In Simulation time Parameters we set the values for start time as 0 cycles and end time 15000 cycles and the initial and Minimum time setup for 1e-9 and remaining values are put to default
• In the Solver Parameters, the Navier stock equation should be Pressure based solver and remaining should be default.
• The number of cycles for the 2e-4 mesh, 1.5e-4 and 1.2e-4 is 15000 in order to converge the solution.

Initialization and Boundary Conditions:

• In the initialization region change the name of the Region as a volumetric region and the values assigned for the temperature and pressure is 300k and 101325.0 Pascal and add the species O2 and N2 with the mole fraction of 0.23 and 0.77.
• The pressure at the inlet is 110325 Pascal and the temperature should be 300 k and the boundary type is INFLOW
• The pressure at the outlet is 101325 Pascal and the temperature should be 300 k and the boundary type is OUTFLOW.
• For the Top and Bottom boundary should be the wall type with a Law of wall boundary condition and temperature should be 300k.
• The front_2d and back_2d and the boundary type is 2D wall.
• The number of cycles for the 2e-4 mesh, 1.5e-4 and 1.2e-4 is 15000 in order to converge the solution.

Physical Models:

• In the physical models enable the Turbulence Modelling and the solver should be selected as RNG K-e and put the remaining values as a default.

Grid Control:

• In the Grid control enable the Fixed Embedding and Base grid
• Enter the base grid values and then go to the fixed Embedding add the
• Entity type=Boundary
• Boundary ID=Top and Bottom
• Mode =Permanent
• Scale=1
• Embedded layers=1

After entered all the values click on apply.

Output and Post Processing:

• Post variable Selection and Output files are the default values.
• In the output files we have given time interval to write the output data=1000 cycles, thus the outputs of the simulation files be stored after 1000 cycles.

Post-Processing:

I have done the post processing of the results for all three cases using the converge studio and paraview. Post processing is actually used in order to get the desired Output by running the simulation

Results:

Case-I: dx = dy = dz =2e-3m Mesh size

Mesh Profile:

Velocity Contours:

The velocity contours represents the flow in the backwardstep.The velocity is higher at the inlet with a 150 m/sec and at the outlet the velocity is gradually decline with a approximately of 60 m/sec due to the increased in the geometry and at the step the velocity is very low due to the divergent nozzle and the flow is turbulent so the pressure droping takes places so that the velocity starts decreasing from this point only.

In the velocity counturs with the vectors the velocity after the step is recirculating because of the separation in the flow and form the boundary layer with the shear zone and at distance forming a vortex which is the region for recirculating the flow.

Velocity Animation:

Velocity plot:

From this graph we observed that the velocity of the flow is low in the step region beacuse of the flow is turbulent and the velocity is changed enormously and reached the highest velocity of 150 m/sec in the middle where we can observe graph as it rises after that decrease in the velocity at the wall region .

Pressure Contours:

Initially the pressure is high at the inlet and it goes on increasing utill it reaches the step region and after that the pressure gradually changed it becomes lower in the step region due to the turbulence,the flow experiences an adverse pressure gradient, which causes the boundary layer to separate from the solid surfaces and after that there is a tremendous growth in the pressure untill it reaches the outlet and attains the maximum pressure.

Pressure Animation:

Pressure plot :

Mass Flow rate at the inlet and outlet:

The mass flow rate is same for both inlets and outlets they are liked mirror image.The convergence is achieved after the 3500 cycles and value for the mass flow rate is 1.35 kg/sec.

Total Pressure at the inlet and outlet:

The pressure is constant at the inlet and the pressure at the outlet is gradually increased from the starting cycles and achieved the convergence after the 2000 cycles and reamins the same value throughout the simulation.

Average Velocity at the inlet and outlet:

The Velocity at the inlet is -140 m/sec and the velocity at outlet is 60 m/sec.The velocity is high in the inlet and low at the outlet because of the increased cross sectional area for the outlet when compared with the cross sectional area of the inlet.

Total Count Cells:

The total number of cells is around 1960 cells.The number of cells are low and the outputs of all graphs and plots are not smooth.

Case-II: dx = dy = dz =1.2e-3m Mesh size

Mesh Profile:

Velocity Contours:

The velocity contours represents the flow in the backwardstep.The velocity is higher at the inlet with a 150 m/sec and at the outlet the velocity is gradually decline with a approximately of 60 m/sec due to the increased in the geometry and at the step the velocity is very low due to the divergent nozzle and the flow is turbulent so the pressure droping takes places so that the velocity starts decreasing from this point only.

In the velocity counturs with the vectors the velocity after the step is recirculating because of the separation in the flow and form the boundary layer with the shear zone and at distance forming a vortex which is the region for recirculating the flow.

Velocity Animation:

Velocity plot:

From this graph we observed that the velocity of the flow is low in the step region beacuse of the flow is turbulent and the velocity is changed enormously from the point 0.011 meters and reached the highest velocity of 150 m/sec in the middle where we can observe graph as it rises after that decrease in the velocity at the wall region .

Pressure Contours:

Initially the pressure is high at the inlet and it goes on increasing utill it reaches the step region and after that the pressure gradually changed it becomes lower in the step region due to the turbulence,the flow experiences an adverse pressure gradient, which causes the boundary layer to separate from the solid surfaces and after that there is a tremendous growth in the pressure untill it reaches the outlet and attains the maximum pressure.

Pressure Animation

pressure plot :

Mass Flow rate at the inlet and outlet:

The mass flow rate is same for both inlets and outlets they are liked mirror image.The convergence is achieved after the 6000 cycles and value for the mass flow rate is 1.35 kg/sec.

Total Pressure at the inlet and outlet:

The pressure is constant at the inlet and the pressure at the outlet is gradually increased from the starting cycles and achieved the convergence after the 6000 cycles and reamins the same value throughout the simulation.

Average Velocity at the inlet and outlet:

The Velocity at the inlet is -140 m/sec and the velocity at outlet is 60 m/sec.The velocity is high in the inlet and low at the outlet because of the increased cross sectional area for the outlet when compared with the cross sectional area of the inlet.

Total Count Cells:

The total number of cells is around 3300 cells.The number of cells are increased beacuse of the refinement of mesh and the outputs of all graphs and plots are little bit smoother.

Case-III: dx = dy = dz =1e-3m Mesh size

Mesh Profile:

Velocity Contours:

The velocity contours represents the flow in the backwardstep.The velocity is higher at the inlet with a 150 m/sec and at the outlet the velocity is gradually decline with a approximately of 60 m/sec due to the increased in the geometry and at the step the velocity is very low due to the divergent nozzle and the flow is turbulent so the pressure droping takes places so that the velocity starts decreasing from this point only.

In the velocity counturs with the vectors the velocity after the step is recirculating because of the separation in the flow and form the boundary layer with the shear zone and at distance forming a vortex which is the region for recirculating the flow.

Velocity Animation:

Velocity plot:

From this graph we observed that the velocity of the flow is low in the step region beacuse of the flow is turbulent and the velocity is changed enormously from the point 0.015 meters and reached the highest velocity of 150 m/sec in the middle where we can observe graph as it rises after that decrease in the velocity at the wall region .

Pressure Contours:

Initially the pressure is high at the inlet and it goes on increasing utill it reaches the step region and after that the pressure gradually changed it becomes lower in the step region due to the turbulence,the flow experiences an adverse pressure gradient, which causes the boundary layer to separate from the solid surfaces and after that there is a tremendous growth in the pressure untill it reaches the outlet and attains the maximum pressure.

Pressure Animation:

Pressure plot :

Mass Flow rate at the inlet and outlet:

The mass flow rate is same for both inlets and outlets they are liked mirror image.The convergence is achieved after the 7000 cycles and value for the mass flow rate is 1.35 kg/sec.

Total Pressure at the inlet and outlet:

The pressure is constant at the inlet and the pressure at the outlet is gradually increased from the starting cycles and achieved the convergence after the 8000 cycles and reamins the same value throughout the simulation.

Average Velocity at the inlet and outlet:

The Velocity at the inlet is -140 m/sec and the velocity at outlet is 60 m/sec.The velocity is high in the inlet and low at the outlet because of the increased cross sectional area for the outlet when compared with the cross sectional area of the inlet.

Total Count Cells:

The total number of cells is around 5500 cells.The number of cells are increased beacuse of the more refinement of mesh and the outputs of all graphs and plots are smooth and fine.

Conclusions:

velocity profile for 1e-3 mesh Backward flow

From the above images we can observe the general characteristics of the flow begins where the upstream boundary layer develops and the pressure gradient is developed into thin shear layer.

The turbulent structures in the shear layer catches the irrotational fluid from the non turbulent flow and this causes from the low velocity recirculation in the region.

The primary vertex is accured at the center from the step and the secondary vertex is formed at the corner of the step and the pressure gradient forms the shear layer curves(in the velocity image the sky blue color) goes down the wall and touches the wall.Some of the streams flow right and forms the recirculation region and some them goes right and reaches the outlet.

The reattachemnt length is the distance between the step and the reattachment point.After the both recirculation of flow occurs it flows towards the outflow direction in order to discharge from the channel.

Thus the all regions are formed in our simulation i.e. Shear layer,Primary recirculation,Secondray recirculation,Reattachment zone.This can be clearly observed in the case 3 velocity profile because more refinement of mesh

The total pressure loss is subdivided into irreversible pressure drops related to friction in the channels before and after the step, the reversible pressure rise at the expansion and an irreversible pressure drop occurring due to additional losses at the step.