Turbulent Flow Past a Wall-Mounted Hump

In this application, AcuSolve is used to simulate fully developed turbulent flow past a smooth hump on the lower wall of a flow domain. AcuSolve results are compared with experimental results as described in Seifert and Pack (2002) 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 moving past a wall protrusion resulting in flow separation and recovery.

Problem Description

The problem consists of a fluid with material properties close to air flowing through a flow domain containing a well-defined smooth hump with a slit opening at approximately 65 percent of the hump chord. The inlet of the domain is defined with an inflow velocity in the streamwise direction that develops into fully turbulent flow at a Reynolds number (Re) of 936,000, based on the hump chord length of 1.0 m. The density of the flow medium is 1.0 kg/m3 and the dynamic viscosity is 1.0684 X 10-6 kg/m-s. The simulation is conducted with the Reynolds Averaged Navier-Stokes equations using the Spalart Allmaras turbulence model, shear stress transport (SST) model, the K-ω model and Realizable K-ε model to evaluate the performance of the turbulence models. The flow predictions from AcuSolve are compared against experimental data and previously published turbulence model performance for pressure and friction coefficients within the domain.
Figure 1. Critical Dimensions and Parameters for Simulating Turbulent Flow Through a Domain with a Wall-Mounted Hump


The upper walls of the domain are specified as slip (inviscid) and the lower walls are specified as no-slip. The inlet velocity and appropriate turbulence parameters are specified in the streamwise direction to match the desired Reynolds Number of 936,000. The outflow pressure is set to zero, and the lower wall on cavity below the hump is set to slip. The problem is simulated as two dimensional with a single layer of elements extruded in the cross stream direction and by defining the side walls as slip.
Figure 2. Three Views of the Mesh Used for Simulating Turbulent Flow over a Wall-Mounted Hump (Full Mesh is Shown on the Bottom, with Increased Resolution in Clockwise Views)


AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions within the domain. The images below show contours of velocity within the domain as well as the recirculation region directly downstream of the hump. As the flow enters the domain with a bulk velocity, it begins to develop a turbulent boundary layer near the lower wall prior to reaching the hump. As the flow approaches the hump section, the velocity near the lower wall decreases, but does not recirculate in front of the hump. It then accelerates over the top of the hump and separates immediately after reaching the cavity opening. The recirculation region propagates downstream, before the flow recovers and reattaches to the lower wall.
Figure 3. Velocity Contours on the Boundaries of the Domain, Showing Velocity Magnitude


Figure 4. Close up View of Velocity Contours Showing the Recirculation Region with Streamlines (White Lines) Representing the Region of Backflow


The images below show the coefficient of pressure and coefficient of skin friction along the lower wall of the flow domain plotted with experimental results. The non-dimensional values are defined by the integrated inlet pressure and the magnitude of the inlet velocity. The images show black circles representing the experimental measurements (Seifert and Pack 2002), solid red lines for the SA model, solid blue lines for the SST model, solid green lines for the K-ω model and solid cyan lines for the Realizable K-ε model, representing the AcuSolve results. The resulting pressure coefficient within the domain demonstrates that there are minor differences between the four turbulence models. All four models are shown to perform accurately in predicting the increase in surface pressure on the front of the hump but tend to over predict the skin friction in the wake of the hump, leading to a minor over prediction of the reattachment location. The SA model predicts a slightly larger recirculation region and does not meet the expected recovery pressure compared to SST, K- ω and K-ε models. This performance was found to be consistent with comparisons to other one equation models (NASA 2015).
Figure 5. Coefficient of Pressure Along the Lower Wall as the Flow Moves Past the Hump, Where c is the Hump Chord Length and 0.0 is the Reference Location at the Front of the Hump in the X-Direction (Streamwise)


Figure 6. Skin Friction Coefficient Along the Lower Wall as the Flow Moves Past the Hump, Where c is the Hump Chord Length and 0.0 is the Reference Location at the Front of the Hump in the X-Direction (Streamwise)


Summary

In this application, a bulk turbulent flow at a Reynolds number of 936,000 within a flow domain containing a wall-mounted hump is studied and compared against experimental data. The AcuSolve results compare well with the experimental data for pressure coefficient and skin friction coefficient near the hump and downstream. The performance of the four turbulence models were found to be consistent with previously published results for flow over a wall-mounted hump (NASA 2015). For this application, the two equation models appear to outperform the one equation turbulence model, with better agreement for the downstream pressure on the wall. This application demonstrates AcuSolve's ability to predict the distribution of pressure and shear stress on protruding bodies within a turbulent flow field and serves to validate current turbulence modeling capabilities.

Simulation Settings for Turbulent Flow past a Wall-Mounted Hump

SimLab database file: <your working directory>\wall_mounted_hump_turbulent\wall_mounted_hump_turbulent.slb

Global

  • Problem Description
    • Flow - Steady State
    • Turbulence equation - Spalart Allmaras
  • Auto Solution Strategy
    • Max time steps - 100
    • Convergence tolerance - 0.001
    • Relaxation factor - 0.4
  • Material Model
    • Fluid
      • Density - 1.0 kg/m3
      • Viscosity - 1.0684e-6 kg/m-sec

    Model

  • Volumes
    • Fluid
      • Element Set
        • Material model - Fluid
  • Surfaces
    • +Y
      • Simple Boundary Condition
        • Type - Slip
    • -Y
      • Simple Boundary Condition
        • Type - Slip
    • Cavity walls
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
    • Hump walls
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
    • Hump walls - downstream
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
    • Inlet
      • Simple Boundary Condition
        • Type - Inflow
        • Inflow type - Velocity
        • Inflow velocity type - Cartesian
        • X Velocity - 1.0 m/sec
        • Turbulence input type - Direct
        • Kinetic energy 1.2615e-5 m2/s2
        • Dissipation rate 0.00106 m2/s3
    • Lower slip
      • Simple Boundary Condition
        • Type - Slip
    • Lower wall
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
    • Nozzle walls
      • Simple Boundary Condition
        • Type - Wall
        • Turbulence wall type - Wall Function
  • Outlet
    • Simple Boundary Condition
      • Type - Outflow
  • Slip
    • Simple Boundary Condition
      • Type - Slip

References

A Seifert and L.G. Pack. "Active Flow Separation Control on Wall-Mounted Hump at High Reynolds Numbers". AIAA Journal. 40(7). 2002.

NASA Langley Research Center Turbulence Modeling Resource web page. http://turbmodels.larc.nasa.gov/nasahump_val.html. Accessed June 2015.