Flow over a backward facing step

Problem Statement:

• Setting up a case in converge to for modeling flow over a backward facing step.
• Verifying the grid independence of the solution by running it on three different base grid sizes.

Setting up a case in converge for modeling flow over a backward facing step

A steady-state flow is simulated over backward facing step with an intention of capturing the effects of turbulence.

Geometry Setup:

The geometry for this simulation is created from scratch in Converge studio. The diagram utilized as a reference is given below: The resulting geometry in converge studio is:

After completing the diagnosis of the geometry created we move on to boundary flagging where boundaries are assigned to various geometric locations like inlet, outlet so that we can define boundary conditions at these locations.

Boundary Conditions:

• Inlet: Pressure - 110325 Pa and Velocity - Zero Normal Gradient.
• Outlet: Pressure - 101325 Pa and Velocity - Zero Normal gradient.
• Front and Back: For the simplification of the problem into 2-D we have defined the front and back boundaries as 2-D.
• Top and Bottom: Wall boundary with the law of condition.

Grid Setup:

The base grid has dimensions of 0.02 in all directions. For this particular geometry, a base grid of 0.002 produces approximately 1,96,000,00 cells which result in a memory overflow. Therefore the base grid was chosen to be 0.02 which produces an estimation of 20,000 cells. In addition to this, we also use fixed embedding to capture the flow much more effectively near the top and bottom walls.

Case setup prominent issues:

• Here we have chosen a pressure based steady-state solver.
• We have selected the minimum time step to be 1e-06 and maximum timestep as 1s.
• Maximum convection CFL limit: 1
• Maximum diffusion CFL limit: 2
• Maximum Mach CFL limit: 50.
• The turbulence model selected is the RNG k-epsilon model.

Results:

Velocity profile:

Pressure profile :

Vector Plot:

Streamline:

Mass-Flow rate at inlet and outlet:

Average velocity at inlet and outlet:

Pressure at inlet and outlet:

Inferences from the results:

• From the analysis of the velocity profile, a generation of the recirculating zone is created just after the step.
• The pressure profile reveals the effects of recirculation, as we can observe regions of low pressure being formed downstream of the flow.
• The vector profile which is colored by velocity further elucidates this phenomenon.
• The streamlines which are generated by using a high-resolution line source in paraview paints a clear picture of the areas under the influence of recirculation

Verifying the grid independence of the solutions by running it on three different base grid sizes.

Base Grid 0.01:

The base grid size of 0.01 produces approximately 156800 cells along with fixed embedding of scale 1 and embedded layers.

Base Grid:

Velocity Profile:

Base Grid 0.015:

Base grid of 0.015 gives approximately 50,000 cells with the fixed embedding of 1 scale and 1 embedded layer.

Base Grid:

Velocity Profile:

Base grid 0.025:

Base grid of 0.025 produces approximately 10,000 cells with the fixed embedding of scale 1 and embedded layer 1.

Base Grid:

Velocity Profile:

Base Grid-0.005:

Base grid of 0.005 produces approximately 1254500 cells with the fixed embedding of scale 1 and fixed embedded layer.

Velocity Profile:

Pressure profile:

Vector Plot: