39 th AIAA Fluid Dynamics Conference, San Antonio, Texas. A selective review of CFD transition models D. Di Pasquale, A. Rona *, S. J. Garrett Marie Curie EST Fellow, Engineering, ddp2@le.ac.uk * Lecturer, Department of Engineering, ar45@le.ac.uk, Lecturer, Department of Mathematics, sjg50@le.ac.uk 23 June 2009
Transition (1) Transition is a complex phenomenon, defined as the whole process of change from laminar to turbulent flow. Schematic of transition process 2
Transition (2) Main features Increased diffusivity in the flow. Skin friction and heat transfer may increase considerably. Complexity: Simultaneous presence of turbulent and laminar flow, and also interaction between the two phases. It involves a wide range of scales and it is very sensitive to physical flow features (Pressure gradient, Tu,Re,etc.). It occurs through different mechanisms in different applications. 3
Eight more widely used approaches have been reviewed: 1.The stability theory approach 2.The low Reynolds number turbulent closure approach 3.The intermittency transport method with integral correlations 4.The intermittency and the vorticity Reynolds number approach 5.The Thelaminar fluctuation energy method 6.The v 2 f model 7.Large Eddy Simulation (LES) for transition 8.Direct Numerical Simulation (DNS) for transition The approaches are compared to one another, highlighting their respective advantages and drawbacks. 4
Stability theory approach (1) Assume a laminar base flow u(x) Superimpose a small disturbance u (x (x,y,t) yt) Unstable if: Stable if: 5
Stability theory approach (2) Advantage: the equations can be linearized, which makes this problem amenable to an analytical approach. Making use of : Continuity equation Momentum equation The single oscillation of disturbances: For 2D, incompressible, unsteady flow and neglecting gquadratic terms in the disturbance velocity components results in the Orr Sommerfield equation: The problem of stability thus reduces to an eigenvalue problem. The stability of each eigenmode is given by eigenvalues. 6
Stability theory approach (3) Disadvantage: The eigenfunctions are non orthogonal Transient growth The experimental critical Reynolds number exceeds its theoretical value. It cannot predict the transition due to non linear effects. 7
Intermittency transport method (1) It uses the concept of intermittency as introduced by Dhawan and Narasimha (1958), to blend together laminar and turbulent flow regimes. as done by : Abu Ghannam (1980) Mayle (1991) Suzen & Huang (2000) based on empirical correlations 0 1 laminar flow fully turbulent any value in between indicates that the flow is transitional By letting the intermittency grow from zero to unity, the start and the evolution of transition can be imposed. Mostly, this is done by multiplying the eddy viscosity in a two equationturbulence model bythe intermittency factor. 8
Intermittency transport method (2) Advantages: Although much more limited in capturing the real physics than DNS or LES, statistical modelling is still the only viable method to compute complex flows with transition phenomena. Statistical RANS models can adequately capture the effects of transition in situations where most of the natural transition development stages are bypassed by some strong external disturbance. These models are relatively easy to calibrate and are often sufficiently accurate to capture the major effects of transition. 9
Intermittency transport method (3) Disadvantages: The approach neglects the interaction between the turbulent and non turbulent regions. The main limitation of the model is thought to be the accuracy of the empirical ii correlations, lti in which h the physics of transition is entirely contained. These models have an inherently non local formulation, that precluded their implementation into general purpose CFD codes. 10
Direct Numerical Simulation A DNS computation is performed by solving the full time dependent NS equations. It is a suitable tool to predict transition, but in order to capture the small scales of turbulence, it requires a very fine grid. Disadvantages: It is too costly for typical engineering application The proper specification of the external disturbance level and structure poses a substantial challenge Advantage: It is an useful tool as research tool and as a substitute for controlled experiments 11
Large Eddy Simulation In LES computations, only the large scale eddies are resolved, the small scale eddies are modelled using an eddy viscosity approach such as that proposed by Smagorinsky The predicted d transition location is very sensitive to the choice of the Smagorinsky constant that is used to calibrate the sub grid eddy viscosity The dynamic sub grid model (Germano 1991) has the advantage that in the laminar BL the sub grid eddy viscosity is automatically reduced to zero This model should be more appropriate for predicting transitional flow 12
List of desirable features for CFD transition models 1. Allow the calibrated prediction of the onset and the length of transition 2. Allow the inclusion of different transition mechanisms 3. Be formulated locally (no search or line integration integration operations) 4. Avoid multiple solutions (same solution for initially laminar or turbulent boundary layer) 5. Not affect the underlying turbulence model in the fully turbulent regime 6. Be formulated independent from the coordinate system 7. Applicable to three dimensional boundary layers 13
Conclusion The review highlighted the difficulty in combining classical CFD to transition models There is clearly a need in industry for an accurate and robust transition model, basedonlocal state variables. Despite its complexity, transition should not be viewed as outside the range of RANS methods: in manyapplications, transition is constrained to a narrow area of the flow due to geometric features, pressure gradients and/or flow separation. Even relatively simple models can capture these effects with sufficient engineering accuracy. The challenge to a proper engineering transition model is therefore mainly in the formulation of a model that can be implemented into a general RANS environment. 14
Thank you for your attention Any questions? 15