Flow Over a Backward Facing Step

Introduction:

Flow over a backward facing step forms the basis of many real flow situations. It is often used as test cases for improvement of numerical schemes and is a classical problem in applied aerodynamics. The backward-facing step is a common test case for CFD codes. Although the geometry is very simple, the flow can feature interesting separation regions, which also makes it an ideal candidate for testing numerical boundary conditions as well. There are many studies in the literature for the backward facing step.In the below figure the 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.

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.

Objective:

• Analyze and simulate flow through a backward facing step.
• Plot contours for velocity and pressure to visualize how flow separation takes place.
• To understand how different quantities like velocity, pressure behave due to the sudden step.

Steps To Be Done:

1. Creating geometry.
2. Setting up case.
3. Boundary Flagging.
4. Assigning boundary conditions.
5. Assigning regions.
6. Post processing the results.
7. Plot the results.

1. Creating Geometry:

Software Used: CONVERGE Studio

We can create a backward step in any CAD software like SolidWorks and import them into CONVERGE or we can create a geometry in Converge directly. In this project, we have created a geometry directly in CONVERGE.

2. Setting Up Case:

We will then set up the case in CONVERGE Studio by flagging the boundary and assigning boundary conditions and initial conditions.

3. Boundary Flagging:

In this step, we take triangular structures and flag them together as boundaries which are marked with different colours. This is done so that the boundary conditions can be assigned to each triangular structure.

4. Assigning Conditions:

Once the boundaries have been flagged, we assign the different boundary conditions for the flow to take place within the geometry. In the series of snapshots below, you can see the various boundary conditions that are assigned to the geometry.

Inflow boundary conditions:

Outflow boundary conditions:

Front and back walls:

The front and back walls of the geometry are 2 dimensional since this is a 2 D simulation.

Top and bottom walls:

5. Assigning Regions:

Here, we will put the planes together and assign initial conditions in the volumetric region.Just like we group triangles to boundaries, we can group the boundaries to define individual volumes. These volumes are called as regions in CONVERGE Studio. In this case, we define only a single volume. Once defined, we set the initial values for pressure, temperature and turbulence in this region.

We will now run the case in the Command line window (CYGWIN).

6. Post-Processing The Results:

Software Used: ParaView

As the simulation is binary files called “post” files are generated inside the output folder. These files have an extension *.out. Now these files are written by CONVERGE. These files contain information regarding the 3D flow field. We use a special software called Paraview that can read this flow information. However, before ParaView can do this, the files have to be converted to a form that ParaView can understand. This is done using a tool called post_convert.After the conversion, we load the files into ParaView.

Simulation Results:

Case 1: dx = 2e-3m, dy = 2e-3m, dz = 2e-3m

• Mesh

• Velocity Contour

• Pressure Contour

7. Plotting the Results:

• Velocity Plot

• Pressure Plot

• Mass Flow Rate Plot

• Total Cell Count Plot

Case 2: dx = 1.5e-3m, dy = 1.5e-3m, dz = 1.5e-3m

• Mesh

• Velocity Contour

• Pressure Contour

Plotting the Results:

• Velocity Plot

• Pressure Plot

• Mass Flow Rate Plot

• Total Cell Count Plot

Case 3: dx = 1.2e-3m, dy = 1.2e-3m, dz = 1.2e-3m

• Mesh

• Velocity Contour

• Pressure Contour

Plotting the Results:

• Velocity Plot

• Pressure Plot

• Mass Flow Rate Plot

• Total Cell Count Plot

Discussions:

• From the above plots of velocity,pressure and mass flow rate for all the three different base mesh sizes, it is clear that the inlet and outlet plots are almost the same.
• After some intial cycles all the plots achieve the steady stade condition.
• As the base grid size decreases, the number of grid points in the mesh increases and it gives more fine mesh.
• The decrease in the mesh size gives the results with increased accuracy.
• Simulation time also increase as the number of cycles increase.

Comparing The Plots:

• Velocity Plot:

We will now create line probes in the computational domain to obtain the velocity profile at a given x location.When fluid flows through a pipe, it tends to slow down as you approach a wall. This layer of slowed-down fluid is what we typically call as the boundary layer. To see this, all we need to do is create a line probe in any region upstream of the step.

Line probe before step

• Here we can see that there is a kind of parabolic profile for velocity.
• Since the mesh is coarse, the profile doesn’t appear exactly parabolic but still there is a similar trend.
• Once the fluid encounters the step, it sees a larger area. This causes a decrease in the velocity.

Line probe after step

• Pressure Plot:

At the same location, there is also an increase in static pressure – the increase occurs over a distance, away from the step, which is proportional to the size of the wake region. This increase in pressure results in flow reversal. This can be visualized in the plot below.

Line probe before step

Upon plotting the pressure in the pipe, we notice a sudden dip in the curve which indicates to the low pressure in the re-circulation region. Once the fluid flows to the low pressure region, it starts recirculating and its pressure increases again, as indicated in the graph

Line probe after step

• Location Of Flow Separation:

In this case, the flow is subjected to a sudden increase of cross-sectional area, resulting in a separation of flow starting at the point of expansion.

• Reason For The Flow Separation:

A fluid climbs the uphill portion of the curved surface with no problem, but it has difficulty remaining attached to the surface on the downhill side. At sufficiently high velocities, the fluid stream detaches itself from the surface of the body. This causes the flow separation. Flow can separate from a surface even if it is fully submerged in a liquid or immersed in a gas as in the case of backward facing step. The location of the separation point depends on several factors such as the Reynolds number, the surface roughness, and the level of fluctuations in the free stream, and it is usually difficult to predict exactly where separation will occur unless there are sharp corners or abrupt changes in the shape of the solid surface. At recirculation zone pressure is going to be higher.

• Recirculation Zone/Wake Region:

At the step, the flow gets detached from the wall and is separated.At the separation point, there is a low pressure region created which causes flow to recirculate. This gives rise to what we call as the recirculation zone or wake region.For more clarity, let’s have a look at the image below, here we are showing you the flow vectors. This helps in understanding the direction of flow at any given location.

You can view the animation here:

• Conclusion:

By performing a fluid flow simulation through the backward step, we can get a grasp on understanding how fluids flow through shapes which have a sudden change in their geometries. Industrially speaking, this can also help us understand how the static pressure drops and vortex shedding happens when fluids flow through structures that have a sudden change in their geometric shapes.