Performance of two kT-kL-? models in a separation-induced transition test case C. Turner and R. Prosser [e-mail]

1
Performance of two kT-kL-? models in a
separation-induced transition test caseC.
Turner and R. Prosserclare.turner_at_postgrad.manch
ester.ac.uk
Introduction
Results
Laminar-turbulent transition is a common
occurrence for many industrial applications. RANS
models, which are generally preferred in industry
because of their efficiency, often give poor
predictions of transition position and duration.
Transition models have been developed to give
sufficiently accurate predictions whilst keeping
costs to a minimum.
Transition Modelling

• Two examples of transition models are those of
  Walters Leylek 1 and Walters Cokljat 2.
  Both use laminar kinetic energy to replicate
  physical phenomena that cannot be captured by
  standard RANS models.
• Laminar kinetic energy (kL) describes
  stream-wise fluctuations in a transitional
  boundary layer, caused by large length scales
  being deflected by a wall.
• The turbulent length scale (?T) is sufficiently
  large when it is greater than ?eff MIN(C? d,
  ?T), where C? is a constant and d is distance
  from the wall.
• The transport equations for both models are
  summarised by equations 1-3.

Figure 2 Pressure coefficient profile for models
tested in Code_Saturne
Figure 3 Visualisation of leading edge
separation using velocity vectors
The Test Case

• The Walters-Cokljat model performs well for flat
  plate bypass transition test cases.
• To be of industrial use it must perform on more
  realistic geometries and for different transition
  types.
• A test case which is transferrable to many
  industrial applications, including rotating
  machinery and wings, is separation-induced
  transitional flow over a Valeo-CD aerofoil.
• Moreau et al. 3 took measurements around the
  Valeo-CD aerofoil and its wake in an open jet
  wind tunnel. The geometric angle of attack is 8
  and the Reynolds number is 1.6 x 105. These
  conditions are sufficient for separation at the
  leading edge.

Conclusions

• All of the models tested, with the exception of
  the Walters-Cokljat model, capture the
  separation-induced transition and compare well
  with the experimental data.
• The Walters-Cokljat model predicts a larger
  separation bubble and no subsequent turbulent
  transition. The laminar boundary layer then
  separates again. This is the cause of the
  relatively large wake predicted in Figure 5.
• Analysis shows there is excessive damping of kT
  in the Walters-Cokljat model due to a function
  which is intended to suppress production in the
  pre-transitional boundary layer however it is
  also affecting the separation bubble.
• Possible measures to avoid this problem are to
  employ a method of thresholding or adopt a
  definition of effective length scale that better
  describes the boundary layer a suggestion is
  using strain-rate rather than wall distance.

Figure 1 Domain and mesh for Valeo aerofoil
simulations
References
1 D.K. Walters and J.H. Leylek. Computational
Fluid Dynamics Study of Wake-Induced Transition
on a Compressor-Like Flat Plate. Journal of
Turbomachinery, 1275263, 2005. 2 D.K. Walters
and D. Cokljat. A Three-Equation Eddy-Viscosity
Model for Reynolds-Averaged Navier-Stokes
Simulations of Transitional Flow. Journal of
Fluids Engineering, 130114, 2008. 3 S.
Moreau, D. Neal, and J. J. Foss. Hot-Wire
Measurements Around a Controlled Diffusion
Airfoil in an Open-Jet Anechoic Wind Tunnel.
Journal of Fluids Engineering, 128 699-706,
2006.

• Inlet conditions are taken from results from
  RANS calculations using a larger domain which
  includes the jet geometry from the wind tunnel.
  The mesh shown in Figure 1 is refined to give a
  y 1.1.