The application of laminar kinetic energy to laminarturbulent transition prediction
C. Turner* and R. Prosser
Results
Abstract
This research is aimed towards determining the most effective
method of transition prediction for an F1 vehicle. After a review of
the literature and analysis of results from the T3 flat plate tests,
laminar kinetic energy modelling shows to be a promising alternative to intermittency modelling.
Transition modelling
One common method of transition prediction is RANS modelling:
 Advantages: single point; low computational cost
 Disadvantages: can only predict bypass transition; have been
shown to give poor predictions (for examples, see figures 1 and 2)
Figure 1: Skin friction coefficient for the
T3A test case (STAR-CD)
Figure 2: Skin friction coefficient for the
T3B test case (STAR-CD)
Another method is to incorporate intermittency modelling:
 Advantages: will predict all transition modes; have been shown to
give accurate results on many test cases
 Disadvantages: non local variables are required (although Menter
et al. [1] have developed a single-point model); have been shown
to be less numerically stable
Figure 3: Skin friction coefficient for the
T3A test case (Code_Saturne)
Figure 4: Skin friction coefficient for the
T3B test case (Code_Saturne)
Figure 5: Velocity profiles for the T3A test
case
Figure 6: u+ profiles for a fully developed
turbulent boundary layer
 Figures 3 and 4 show that the Walters-Cokljat model is a vast improvement on the Walters-Leylek model for transition prediction
 However, the velocity and Cf profiles in the turbulent boundary
layer are under-predicted in comparison with the experimental
values and the results from Fluent [3].
 This anomaly appears to come from the shear-sheltering function
having an excessive effect on the turbulent boundary layer
 Further information on the models’ strengths and weaknesses are
to be determined through the test cases shown in figures 7 and 8
Laminar kinetic energy
 A compromise between CPU requirements, stability and accuracy
is required
 It is proposed that modelling of ―laminar kinetic energy‖ can incorporate the additional physics required
 Walters and Leylek [2] developed a RANS based model incorporating laminar kinetic energy in 2004
 This model has since been developed, the most recent being the
Walters-Cokljat model [3] (see equations 1-3)
Figure 7: Mesh for an aerofoil undergoing laminar
separation (current test case)
Figure 8: Rear wing geometry
(final test case)
Conclusions
 The Walters-Cokljat model implementation gives excellent predictions for both transition onset and length.
 Modelling of laminar kinetic energy is in its early stages, however
the phenomenological functions have been shown to give a good
representation of a transitional boundary layer
 The later test cases will give more data on any required refinements in the modelling for the final application
 The results from the implementation of the Walters-Leylek [4]
and Walters-Cokljat [3] models into an industrial finite volume
code (Code_Saturne) are shown in figures 3-6
 Figure 3 also includes the T3A result from the original Fluent implementation
References
[1] F. R. Menter, R. B. Langtry, S. R. Likki, Y. B. Suzen, P. G. Huang, and S. Volker. ―A correlation-based transition model
using local variables—part i: Model formulation‖. Journal of Turbomachinery, 128(3):413–422, 2006.
[2] D.K. Walters and J.H. Leylek. ―A New Model for Boundary Layer Transition Using a Single-Point RANS Approach‖.
Journal of Turbomachinery, 126:193–202, 2004.
[3] 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, 130:1–14, 2008.
[4] D.K. Walters and J.H. Leylek. ―Computational Fluid Dynamics Study of Wake-Induced Transition on a CompressorLike Flat Plate‖. Journal of Turbomachinery, 127:52–63, 2005.
*Corresponding author: [email protected]