Using the concept of laminar kinetic energy to predict transitional flow
Researcher:
Clare Turner
Supervisor(s): Dr. R. Prosser
Sponsor: CDadapco
Start Date: January 2007 End Date: January 2010
Keywords: RANS, transition, flatplate
Overall Research Aim
Laminarturbulent transition is a phenomenon that occurs in many industrial flows. The initiation and length of transition is important since the state of the boundary layer affects values such as skin friction and the stability of the flow. The use of "laminar kinetic energy" in a RANS turbulence model is a relatively new concept, the work here takes steps to determine whether it is appropriate for the case of a Formula 1 rear wing undergoing separation induced transition. However simpler cases are reviewed for initial development.
Research Progress
Transition prediction with popular RANS models
The type of transition we are concerned with here is bypass transition (induced by external flow turbulence), which RANS models are capable of predicting. However, traditionally, the predictions have been very poor. This can be attributed to the models controlling the transition with only diffusion, while other physical processes contribute. A standard set of test cases used to compare transition prediction capability are the ERCOFTAC T3 test cases. The T3A test case represents a flat plate, with zero pressure gradient and a moderate incoming turbulence intensity (3%). A common method of comparison is the prediction of skinfriction coefficient.

Fig 1: T3A test case using STARCD

Laminar kinetic energy models
It has been shown that nonlinear models give improved predictions in many cases, however the problem that certain physical phenomena are not being taken into account still remains. In 2004 Walters and Leylek developed a model incorporating laminar kinetic energy into a %$k\epsilon$% model. In 2005 they developed the model further and created a %$k_{T}k_{L}\omega$% model.
Initial results
Using the T3A test case as an example; in comparison with other models using %$\omega$% as a scale determining variable, the WaltersLeylek implementation gives an improved prediction. However the transition onset is still predicted to early. The WaltersCokljat model implemented in
Code_Saturne with the equations presented in their paper, "A ThreeEquation EddyViscosity Model for ReynoldsAveraged NavierStokes Simulations of Transitional Flow", shows a very good prediction of transition onset but there appears to be a problem with predictions in the fully turbulent region. The same situation is shown here in the T3B test case.
Fig 2: Code_Saturne implementation for the T3A test case

Fig 3: Code_Saturne implementation for the T3B test case

Current work
It is important to note that in their paper, for the T3A and T3B test cases, Walters and Cokljat obtained the same results for transition onset however they did not experience the same low skinfriction coefficient in the fully turbulent region. The reason for the difference has not been determined. Theoretically when transition is completed the production term should tend to that of the WaltersLeylek model, the shearsheltering damping function, defined as %$f_{SS}=\left[\left(\frac{C_{SS}\nu \Omega}{k_{T}}\right)^{2}\right]$%,, prevents this. %$C_{SS}$% is a constant and %$ \Omega$% is the magnitude of the mean rotations rate tensor. The phenomena is referred to in Jacobs and Durbin's "Shear Sheltering and the Continuous Spectrum of the OrrSommerfeld Equation" but the extent of the effect and whether this function will have an appropriate representation of the effect for the final application is unknown. As with many of the functions, descriptions of these physical phenomena are determined from a combination of dimensional and physical reasoning. Hence the development of %$k_{T}k_{L}\omega$% models is in the form of more accurate representation of the physical phenomena. To understand more thoroughly the influence of laminar kinetic for more practical applications further test cases are required. As an intermediate step before the 3D rear wing, a 2D mesh of an aerofoil is to be simulated using
Code_Saturne. Results have already been obtained for the Durbin %$\overbar{v^{2}}f$% model from STARCD; the same case is currently being set up for the SST, WaltersLeylek and WaltersCokljat models in
Code_Saturne.
Fig 7: Mesh generated for 2D aerofoil undergoing laminar separation

Fig 8: Geometry of the final test case

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