Colloquia

Summary

As the aviation industry strives to reduce its environmental impact, the design of next-generation low-drag Natural Laminar Flow (NLF) airfoils has become increasingly important. The design of such NLF airfoils using computational fluid dynamics requires accurate prediction of the laminar-turbulent transition process within Reynolds Averaged Navier-Stokes (RANS) solvers to allow for rapid iteration in design cycles.

The current industry consists of Local Correlation-based Transition Models (LCTMs), which rely exclusively on information available at each grid point and, in many cases, introduce additional transport-type partial differential equations, such as the  model. These equations lack a physical basis, are computationally expensive, mathematically stiff, and pose additional challenges for adjoint-based optimization. As a result, new algebraic LCTM solutions are being developed, which use no additional transport-type equations to predict transition.

In this thesis, an existing algebraic model, originally formulated by Baş et al., has been modified to implement the transition criterion of Arnal, Habiballah and, Delcourt (AHD) for Tollmien-Schlichting transition. Two model variants are proposed and imfor cwith theplemented into the DLR TAU code. The first employs a constant dependence on the turbulent viscosity ratio, while the second introduces a parameterized dependence. The latter variant incorporates a new sensor to prevent streamwise decoupling between the transition onset predicted by the criterion and the activation of the turbulence model, thereby extending its applicability to both low- and high-Reynolds-number flows.

The model performance is assessed using the Eppler 387, NLF(1)-0416 and NACA 642A015 airfoils, to validate the model for low-, intermediate-, and high-Reynolds cases respectively. In this analysis, the global results are presented, followed by an evaluation of the transition prediction in the laminar regime and a verification of the turbulent boundary layer behavior. This assessment gives detailed insight into the functioning of the transition model and characterizes its behavior as a result of the underlying design choices.

Overall, the model is shown to closely match experimental results, with the parameterized variant —using the new sensor— performing significantly better for high-Reynolds-number flows. It is also demonstrated that the algebraic formulation is able to recover the correct fully turbulent velocity profile downstream of transition onset, while maintaining the level of accuracy achieved by models that rely on transport equations for this purpose.