Flow over a backward facing step

Flow over a backward facing step

The backward facing step is an interesting case for studying the performance and solution strategy of a turbulence model. 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.

Spatial variations in the velocity field cause production of turbulence outside the wall region and its interaction with the mean flow influences the size of the separation bubble. The size of the bubble, or the re-attachment length, is one of the quantities that must be predicted accurately by a turbulence model. Now a lot of intensive studies both experimental as well as theoretical studies based on the experimental results have been done in the past, and people have been successful in knowing the phenomenon in detail. A lot of published results are available for people to compare their own results obtain from numerical simulations based on newly proposed schemes and code. But at the same time this very problem also provides an opportunity for CFD software user to get acquainted with its environment, which is the sole purpose here.

Domain:

Problem Statement: To simulate and analyse flow in channel with a backward facing step.

A little background on the problem: This particular flow has been extensively studied in the past. A plenty of research done on it and a lot of experimental data is available for this very problem. This is why this problem finds a space for CFD software learners as well as for developer.

This flow is setup in Converge Studio 3.0.12 and post processed in ParaView 5.4.

Mesh:

Shown above is the mesh with grid sizing of 2e-3,1.5e-3 and 1e-3 mm respectively.

Boundary Conditions:

Inlet: Inflow Pressure: 111325 Pa

Temperature: 300K

Specie: Air (with O2 and N2 at usual concentrations)

Turbulent Kinetic Energy: 0.02% intensity

Turbulent Dissipation: 0.003 m

Outlet: Outflow Pressure: 101325 Pa

Backflow temperature: 300K

Backflow specie: Air (with O2 and N2 at usual concentrations)

Turbulent Kinetic Energy: 0.02% intensity

Turbulent Dissipation: 0.003 m

Top-Bottom: Wall using law of wall for velocity.

Solver Details:

Physical Model: RANS- Reynolds Averaged Navier Stokes

Turbulence Model: K-Epsilon RNG

Solver: Steady-State solver, Full Hydrodynamic, Compressible.

Simulation time: 15000 cycles

Initial time step: 1e-8

Minimum time step: 1e-8

Maximum time step: 1.0

Discretisation Schemes:

Navier Stokes Solver Scheme: PISO

Navier Stokes Solver Type: Pressure-Based

Convective Flux Scheme: Flux blending

Specie: Flux blending

Turbulence: Flux blending

Initialization: domain: Air

Pressure: 101325 Pa

Temperature: 300K

Grid Size: Three grid sizes were used 2e-3, 1.5e-3, 1e-3 and an extra 2e-4.

Results:

Average Velocity Vs Cycles

Total Count

Total Pressure

Static Pressure

Mass Flow Rate

Inferences and Conclusion:

• From the above graph we can see that all the parameters show convergence.
• Mass flow rate from inlet and outlet boundaries show very good match showing that the solution to the physical equations was solved perfectly.
• For all the parameters shown above values for grid size 1.5e-3 and 1e-3 are very close to each other.

• The figure above shows the formation of separation bubble and the reattachment length was found to be around 0.115mm which falls within limits with the theoretical results and with the available data on the internet for comparison.
• Although the basic RANS with K-epsilon model will not be able to predict the exact losses that may occur for such a flow but it definitely gives an idea to the designer for the values to expect for with the edge of have considerably lower computational effort and ease.
• Next is an image of velocity contour at 10^th cycle where the high velocity red zone and recirculating low velocity fields can clearly be seen for three different grid size domains.
• Just after it is an image showing the contours of pressure fields in the domain at 50th cycle, as the domain was initialized at 1bar and the inlet it set at a total pressure of 111325Pa or 1.1 bar as the flow starts the pressure drops to 0.94bar owing to high velocities at inlet which finally reaches to maximum of 160m/s as the flow attains steady state.

Formation of separation bubble:

As from the figure above it is evident that static pressure at inlet is lower than that at the outlet giving rise to an adverse pressure gradient which will give rise to separation of flow depending upon the Reynolds number the height of the step and factors like viscous dissipation, Etc.

Now because of adverse pressure gradient the fluid layer in the vicinity of the wall and above the viscous layers change the direction from positive x direction to negative x direction which is further supported by the existing viscous layer just next to wall and grows in size, in y direction. This can be seen from the line plot shown below for one of the three cases at 8th cycle.

Interpret the graph by the following annotations

This topic is actually very vast to discuss on and so any further discussion will take us away from the intent of this project. So, to sum-up separation bubbles from because of adverse pressure gradient and are further supported by the viscous nature of the fluid. The separation bubble length is mainly a characteristic parameter of such a study whose values generally depend on some major factors like Reynolds number, the step height and various others.

References:

1. Fluid Mechanics and Hydraulic Machine, Sukumar Pati, IIT Kharagpur- Mechanical Engineering Department.
2. A Numerical study of Flow over a confined Backward Facing Steps, I.E. Barton, Internal Journal for Numerical Methods in Fluids.
3. Simulation of Backward Facing Step flow using OpenFoam, A. S. Kumar, A. Singh and K. B. Thaigarajan, AIP Conference Proceedings 2204.
4. LAMINAR SEPARATION BUBBLES, M. Gaster, Queen Mary University of London.