Speaker
Description
In aerodynamic flows, viscous effects are concentrated in thin boundary layers along solid surfaces. Numerical simulation at high Reynolds numbers requires the turbulent boundary layer to be correctly described, and the modeling of turbulence is still an indispensable prerequisite. Modern turbulence modeling involves one to seven additional equations with deliberately formulated source terms. As a consequence, the resulting stiff system of flow and turbulence equations leads to severe challenges with respect to an efficient integration towards steady state.
Despite decades-long efforts, up to now no “universal” turbulence model has evolved which can be applied with reasonable reliability to various types of flows, with respect to numerical robustness and efficieny as well as to predictive quality. However, concerning zero-equation or algebraic turbulence models, since about the 1990s there is unanimous consensus that such models are not sufficiently accurate, and these models are not in use anymore. On the other hand, algebraic turbulence models are very efficient, since no additional equations with source terms are introduced. Thus, the objective of the present contribution is to make the predictive capabilities of algebraic models comparable to modern equation-based models.
Algebraic turbulence models mainly rely on the “Mixing Length” hypothesis, which Ludwig Prandtl first proposed 100 years ago at the 1925 GAMM conference in Dresden. Based on this Mixing Length hypothesis and further modifications, algebraic turbulence models like the Cebeci-Smith and the Baldwin-Lomax model were derived, and extensively used in the aircraft industry until the 1990s. Algebraic turbulence models were numerically robust, but for more complex airfoil and wing flows with shock-boundary layer interaction and/or flows being close to separation, these turbulence models proved to be inadequate by predicting shock locations too far downstream and/or too large regions of attached flow.
In the present contribution, an algebraic turbulence model is derived with a predictive quality comparable to contemporary one- and two-equation turbulence models. Here, the classical Baldwin-Lomax model is revised with a formulation very close to the original approach of Ludwig Prandtl. Experimental evidence and a shear stress sensor function are used to enhance the prediction of flows with shocks and close to separation. Flow computations around airfoils and wings show that the resulting model provides predictive properties similar to the most advanced modern one- and two-equation turbulence models. This convincingly confirms that the now 100 years old Mixing Length hypothesis of Ludwig Prandtl is still of high relevance for today’s aerodynamic problems.
