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Performance of two kT-kL-ω models in a separation-induced
transition test case
C. Turner and R. Prosser
[email protected]
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
0
• Two examples of transition models are those of Walters &
Figure 2: Pressure coefficient
profile for models tested in
Code_Saturne
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 (λT) is sufficiently large when it
is greater than λeff ≡ MIN(Cλ d, λT), where Cλ is a constant
and d is distance from the wall.
The transport equations for both models are summarised
by equations 1-3.
x/C
0.2
Figure 3: Visualisation of
leading edge separation using
velocity vectors
•
•
•
Figure 4: Turbulent kinetic energy contours for the Walters-Leylek
model (top) and the Walters-Cokljat model (bottom)
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.
•
Figure 5: Stream-wise velocity profiles downstream of the aerofoil
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 k T 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
• 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.
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, 127:52–63, 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, 130:1–14, 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.
School of Mechanical, Aerospace & Civil Engineering
Postgraduate Research Conference, PGR-MACE10