Steady-state simulation of or flow over a backward facing step using Converge CFD
Objective:
To simulate flow over a backward-facing step using Converge CFD for three different mesh sizes as stated below and to compare the results.
1. Mesh1 - dx = dy = dz =2e-3m
2. Mesh2 - dx = dy = dz =1.5e-3m
3. Mesh3 - dx = dy = dz =1.0e-3m
Problem Definition:
The geometric specification for the backward-facing mesh is as shown;
The working fluid is air. It is flowing into the backward-facing step from the left at an inlet total pressure of 110325 Pa and exiting from the outlet at a static pressure of 101325 Pa.
Simulation Results:
1. Mesh Comparison
Mesh1
Mesh2
Mesh3
Inference:
From the above plots and figures, it can be observed that the total cell count increases as the mesh becomes finer. A mesh with a higher cell count would require more computational power/time.
2. Mass flow rate variation with cycle count
Mesh1
At inlet boundary
At outlet boundary
Mesh2
At inlet boundary
At outlet boundary
Mesh3
At inlet boundary
At outlet boundary
Inference:
In the above plots, it can be observed that all the three meshes converge to very similar values (about 1.4 kg/s) but the inlet and outlet values have opposite signs to ensure the conservation of mass. Mass flow rate at inlet boundary is negative as it aligns with the direction of its normal and positive at the outlet boundary as it travels against the direction of the normal. As far as accuracy is concerned a finer mesh gives out fewer errors.
3. Total Pressure variation with cycle count
Mesh1
At inlet boundary
At outlet boundary
Mesh2
At inlet boundary
At outlet boundary
Mesh3
At inlet boundary
At outlet boundary
Inference:
The inlet boundary values for total pressure show the specified value i.e., 110325 Pa. As a result of the pressure drop due to the resistance offered by the pipe, this pressure decreases to around 103800 Pa at the outlet boundary as shown in the plots above.
4. Static Pressure variation with cycle count
Mesh1
At inlet boundary
At outlet boundary
Mesh2
At inlet boundary
At outlet boundary
Mesh3
At inlet boundary
At outlet boundary
Inference:
The static pressure at the outlet was specified as 101325 Pa as is evident from the above static pressure plots for outlet boundary. At the inlet boundary, the static pressure values are around 98000 Pa. It can be seen that the static pressure has increased rather than decrease because of the decrease in velocity due to a suddenly increased area. This creates an adverse pressure gradient as the outlet static pressure is higher than the inlet one which leads to the flow separation.
5. Velocity variation with cycle count
Mesh1
At inlet boundary
At outlet boundary
Mesh2
At inlet boundary
At outlet boundary
Mesh3
At inlet boundary
At outlet boundary
Inference:
In all the above plots for three meshes, the inlet velocity is close to -140 m/s and the outlet velocity is close to 60 m/s. Even though the outlet velocity is smaller than the inlet velocity, the conservation of mass still holds true because the outlet area is bigger than the inlet area so that the mass flow rate (density * velocity * area) remains constant.
6. Velocity Profiles
Mesh1
Mesh2
Mesh3
Inference:
It can be clearly observed that all three meshes have the same trends. In the velocity profile along the vertical axis before separation, it can be noted that the velocity is minimum near the walls and maximum at the central axis. The profile looks like a square wave instead of a parabola because of the inadequate amount of cells present to capture the velocity gradient accurately.
However, in the velocity profile along the vertical axis after separation, it can be observed that near the bottom edge where there is a sudden increase in area, the flow is traveling in the negative x-direction. This means that recirculation is taking place in that region. This is due to the adverse pressure gradient the leads to flow separation and formation of vortices that increase drag.
The boundary layer separation increases the drag, meaning it resists the motion of a body relative to the fluid flow hence decreasing the velocity of the fluid. This is evident from the velocity profile along the horizontal axis that shows a decrease in velocity after flow separation. Since, before the flow separation, the velocity was steadily increasing, it can be concluded that the boundary separation is the reason for the decrease in velocity of the flow.
7. Pressure Profiles
Mesh1
Mesh2
Mesh3
Inference:
The above plots show the variation of static pressure along the horizontal axis for the three mesh sizes. In all three, the static pressure starts at around 98000 Pa at the inlet boundary and ends at the specified 101325 Pa. And in the region where sudden expansion occurs, the static pressure stoops low to around 96000 Pa. This is because the velocity at this point is the highest, therefore the more dominant pressure at this region is the dynamic pressure. However, with the suddenly increased area, the velocity reduces which leads to an increase in static pressure at the outlet boundary.
8. Animation
All the above explanations can be better understood by viewing the following animations that show the steady-state velocity and pressure distribution in the backward-facing step.
Steady-State velocity distribution animation with 2d glyphs
Steady-State pressure distribution animation