Laminar to Turbulent Transition Over an Airfoil

Problem Description

The problem consists of a fluid having material properties close to air with density of 1.0 kg /m3 and molecular viscosity specified to produce a Reynolds number of 2.0e6, assuming a chord length of 1.0 m and an inlet velocity of 1.0 m/s, as is shown in the following image, which is not drawn to scale. The inflow velocity is oriented to simulate a 1 degree angle of attack. The model is simulated as steady state with constant inflow conditions using the farfield boundary condition. The two equation gamma-ReTheta (γ- Reθ) transition model, used with the one equation Spalart Allmaras turbulence model, is validated against experimental data obtained from the experimental studies conducted by Somers, 1997.

Figure 1. Critical Dimensions and Parameters used for Simulating Transitional Flow over the S809 Airfoil

Figure 2. Mesh Used for Simulating Transitional over the S809 Airfoil

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 airfoil walls are specified as no-slip and the the inlet velocity and eddy viscosity are specified at the farfield boundary.

AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions over the airfoil. The simulation results show that the flow field is laminar at the leading edge until approximately 50 percent chord on the pressure side and until approximately 55 percent on the suction side, then transitions to turbulent as it moves further downstream. The onset is caused by small separation bubbles at these locations. The following images show the negative pressure coefficient (-Cp) on the surface of the airfoil. The mean pressure at a reference point upstream of the airfoil is subtracted from the surface pressure and divided by the inlet velocity and air density to arrive at Cp. The Cp computed from AcuSolve is compared with experimental data, as described in Somers, 1997. The image shows black circles representing the experimental data and a solid red line for the AcuSolve results. Additional plots show contours of intermittency that illustrate the transition from laminar to turbulent flow.

Figure 3. Negative pressure coefficient on the airfoil surface showing experimental and simulated results for the SA two equation (γ- Reθ) transition model

Figure 4. Contours of Intermittency Demonstrate the Onset Location from Laminar to Turbulent over the Airfoil

Summary

The AcuSolve solution compares well with experimental data for transitional flow over the S809 airfoil at a low angle of attack. Additional simulations and measurements for the full drag polar have been tested and compare well with considerably better accuracy when transition closure is included into the RANS solution. The good agreement with experimental results for the transition location and magnitude of expected pressure demonstrate that AcuSolve is capable of predicting the transition onset location for flow over surfaces with mild to moderate pressure gradients.

Simulation Settings for Laminar to Turbulent Transition Over an Airfoil

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

Global

• Problem Description
  • Analysis type - Steady State
  • Turbulence equation - Spalart Allmaras
  • Turbulence transition model- Gamma-ReTheta
• Auto Solution Strategy
  • Max time steps - 100
  • Convergence tolerance - 0.0001
  • Relaxation Factor- 0.5
  • Turbulence transition- on
• Material Model
  • Air
    • Type - Constant
    • Density - 1.0 kg/m3
    • Viscosity - 5.0e-7 kg/m*sec

  Model

• Volumes
  • Fluid
    • Element Set
      • Material model - Air
• Surfaces
  • +z slip
    • Simple Boundary Condition
      • Type- Slip
  • -z slip
    • Simple Boundary Condition
      • Type- Slip
  • farfield
    • Simple Boundary Condition
      • Type- Far Field
      • X velocity = 1.0 *cos(α), where α is the angle of attack in radians
      • Y velocity = 1.0 *sin(α), where α is the angle of attack in radians
      • Turbulence input type- Auto
      • Turbulence intensity type- Value
      • Turbulence intensity percent- 0.025
  • airfoil surface
    • Simple Boundary Condition
      • Type- Wall

References

Somers, D., Design and Experimental Results for the S809 Airfoil. NREL/SR-440-6918. 1997