Flows around aerodynamic bodies, like aircraft wings, helicopter blades, wind turbines and turbomachinery components develop boundary layers that, to a large extent, define their performance. The boundary layers can either be laminar or turbulent depending on numerous factors, like Reynolds number, freestream turbulence levels and surface roughness, to name a few. Understanding which type of boundary layer is present, and the location of the laminar-to-turbulent transition point under varying operating conditions, is essential for accurate predictions of the performance of aerodynamic devices.
For many years, modeling the transition from laminar to turbulent flow was one of the most difficult challenges of computational fluid dynamics (CFD), although many industrial flows have Reynolds numbers in the range of 10^4 to 10^6 — regimes in which significant portions of the boundary layers can be laminar. Our ANSYS team succeeded in solving this problem about 10 years ago with the Local-Correlation-based Transition Modeling (LCTM) approach. LCTM successfully introduced transition effects into general CFD. The first model (called γ-ReΘ) solved two transport equations and incorporated experimental correlations to trigger the transition onset. The model formulation was strictly local and, therefore, fully compatible with modern general-purpose CFD codes.
In a new article recently published in the Springer Journal Flow Turbulence and Combustion, we present a second generation model that simplifies the original γ-ReΘ model of the LCTM concept, reducing the number of equations to be solved from two to one. The new transition model (called the γ-model) is now available in ANSYS CFD solutions.
By reducing the number of transport equations to be solved from two to one, the new γ-model substantially decreases the complexity and solution time of boundary layer simulations. The γ-model is also more robust because an even wider range of flows, both generic and industrial, was considered during model calibration, relative to the γ-ReΘ model.
Comparison of the two models with experimental data reveals the improved accuracy of the γ-model. Figure 1 shows a NACA 0021 airfoil. Such thick airfoils are representative of wind turbine blade sections that require proper simulation of the transition onset location to predict performance.
Figure 2 shows the lift coefficient CL of the airfoil vs. angle of attack. The green curve shows a fully turbulent simulation. The red and the blue curves represent the γ-model and the γ-ReΘ models, respectively. Both models predict a significantly closer agreement than the fully turbulent simulation relative to the experimental data. The γ-model is even more accurate in the prediction of stall onset for this case. In addition, the γ-model is substantially less complex and has enhanced capabilities.
A more complex test case, involving a multistage compressor investigated experimentally at the University of Hannover, is shown in Figure 3. Details are given in the Springer article.
Figure 4 shows the efficiency of the compressor for different mass flow rates. The blue curve represents the fully turbulent simulation without a transition model; the red curve demonstrates the improved simulation accuracy when the γ-model is added. The agreement between simulation and experiment is significantly closer when transition is taken into account.
The γ-model is already in industrial use, and has been applied to a wide range of flows, covering turbomachinery blades, wind turbines and racing cars with good success. The model has recently been extended for inclusion of crossflow instabilities, which will be covered in a separate article.
Together with my collaborators at General Electric, we published these results in a paper, A One-Equation Local Correlation-Based Transition Model.