Turbulent Flow Over a Backward-Facing Step

In this application, AcuSolve is used to simulate fully developed turbulent flow over a backward-facing step. AcuSolve results are compared with experimental results as described in Driver (1985) and on the NASA Langley Research Center Turbulence Modeling Resource web page. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow that forms a shear layer, recirculates and then reattaches downstream of the divergent step.

Problem Description

The problem consists of a fluid with material properties close to air flowing through a channel containing a sharp expansion, as shown in the following image, which is not drawn to scale. The step causes the flow to recirculate before reattaching downstream of the step. The inlet height of the channel is 8.0 m and expands as a step function to 9.0 m at a distance 20.0 m downstream of the inlet. This expanded section of the channel extends 50 m downstream of the step. The inflow of the channel is defined as fully developed at a Reynolds number (Re) of 36,000, based on the step height to match the experimental conditions. The density of the flow medium is 1.1837 kg/m3 and the dynamic viscosity is 1.457 X 10-3 kg/m-s. The simulation was conducted with the Reynolds Averaged Navier-Stokes equations using four turbulence models, Spalart Allmaras, Shear Stress Transport (SST), K-ω and K-ε.


Figure 1. Critical Dimensions and Parameters for Simulating Turbulent Flow Through a Channel with a Backward-Facing Step
The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements extruded in the cross stream direction, normal to the flow plane and by imposing symmetry boundary conditions on the extruded planes. The upper and lower walls are specified as no-slip, the inlet velocity and eddy viscosity are specified to match the conditions in the experiment (Driver 1985) at a distance of 20 m upstream of the step.


Figure 2. Detail of Mesh Near the Backward-Facing Step


Figure 3. Finer Detail of Mesh Near the Backward-Facing Step

AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. As the fully developed turbulent flow enters the divergent section, the expansion of the cross sectional height causes a shear layer to develop above the lower wall. The expansion causes two recirculation zones; one immediately near the step wall and one that extends further downstream near the lower wall. The recirculation region eventually recovers downstream and the flow reattaches. The following images show the flow solution within the channel, demonstrating the recirculation region and reattachment point.


Figure 4. Velocity Contours Showing Low Velocity Near the Step Wall


Figure 5. Close-Up View of Velocity Vectors and Contours in the Cross-Stream Plane Near the Step
Upstream of the expansion section, the streamwise velocity increases as the distance from the lower wall increases until it reaches the centerline of the channel and then begins decreasing until it reaches zero at the top wall. As the flow passes the step, it expands into the region directly downstream of the step wall, separating from the wall and recirculating until it recovers further downstream. The image below shows the coefficient of pressure along the lower wall of the step compared against experimental results. The non-dimensional values are defined by the integrated inlet pressure and the magnitude of the inlet velocity. The image shows black circles representing the experimental measurements (Driver 1985), a solid red line for the SA model, a solid blue line for the SST model, a solid green line for the K-ω model and a solid cyan line for the K-ε model, representing the AcuSolve results. The resulting pressure coefficient within the channel demonstrates minor differences between the three turbulence models. The SA model predicts a slightly larger recirculation region, and does not reach the peak pressure in the wake of the step, compared to the SST model.


Figure 6. Coefficient of Pressure Plotted Against Location Along the Lower Wall Before and After the Step

Summary

In this application, a fully developed turbulent flow at a Reynolds number of 36,000 is studied and compared against experimental data. The AcuSolve results compare well with the experimental data for pressure coefficient. The performance of the Spalart Allmaras turbulence model was found to be consistent with previously published results for flow over a backward facing step (NASA 2015). The K-ω model appears to perform the best out of the three, predicting the reattachment and pressure distribution most accurately. AcuSolve demonstrates the ability to predict the shear layer in this type of application, the recirculation that occurs downstream of the step, as well as the reattachment point within the channel.

Simulation Settings for Turbulent Flow over a Backward-Facing Step

AcuConsole database file: <your working directory>\backstep_turbulent\backstep_turbulent.acs

Global

  • Problem Description
    • Analysis type - Steady State
    • Turbulence equation - Spalart Allmaras
  • Auto Solution Strategy
    • Max time steps - 100
    • Relaxation Factor - 0.5
  • Material Model
    • Air
      • Density - 1.183 kg/m3
      • Viscosity - 1.4575e-3 kg/m-sec

    Model

  • Volume
    • Fluid
      • Element Set
        • Material model - Air
  • Surfaces
    • +Z
      • Simple Boundary Condition
        • Type - Slip
    • -Z
      • Simple Boundary Condition
        • Type - Slip
    • Inlet
      • Simple Boundary Condition - (disabled to allow for nodal boundary conditions to be set)
      • Advanced Options
        • Nodal Boundary Conditions
          • X-Velocity
            • Type - Linear
            • Precedence - Always
            • Curve fit variable - Y reference coordinate
            • Curve fit values - (included in .acs)
          • Y-Velocity
            • Type - Linear
            • Precedence - Always
            • Curve fit variable - Y reference coordinate
            • Curve fit values - (included in .acs)
          • Z-Velocity
            • Type - Zero
          • Eddy Viscosity
            • Type - Linear
            • Precedence - Always
            • Curve fit variable - Y reference coordinate
            • Curve fit values - (included in .acs)
    • Outlet
      • Simple Boundary Condition
        • Type - Outflow
    • Wall - Lower - Downstream
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Low Reynolds Number
    • Wall - Lower - Upstream
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Low Reynolds Number
    • Wall - Step
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
    • Wall - Upper
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Low Reynolds Number

References

D. M. Driver and H. L. Seegmiller. "Features of Reattaching Turbulent Shear Layer in Divergent Channel Flow". AIAA Journal, 23(2): 163-171. Feb 1985.

NASA Langley Research Center Turbulence Modeling Resource webpage. http://turbmodels.larc.nasa.gov/backstep_val.html. Accessed May 2015.