Sensor-based computation of transitional flows using wall-modeled large eddy simulation

To be applicable to complex aerodynamic flows at realistic Reynolds numbers, large eddy simulation (LES) must be combined with a model for the inner part of the boundary layer. Aerodynamic flows are, in general, very sensitive to the location of boundary layer transition. While traditional LES can predict the transition location and process accurately, existing wall-modeled LES approaches can not. Simply put, wall-models are derived assuming a fully developed turbulent boundary layer; hence wall-modeled LES grossly overestimates the friction and momentum losses in locations where the boundary layer is laminar. Aside from leading to erroneously predicted overall friction, it also leads to an artificially thick boundary layer that has a different sensitivity to an adverse pressure gradient. Therefore, wall-modeled LES will only ever be useful in airfoil-type flows once the wall model correctly distinguishes between laminar and turbulent regions and allows for prediction of transition. Moreover, this should be accomplished in a way that can be applied to arbitrary geometries; most notably, any proposed method must not rely on the presence of homogeneous directions. In the present work, the behavior of the wall model is adapted locally by sensing the turbulent kinetic energy in the outer part of the boundary layer that is resolved by the LES. The sensor is defined for arbitrary geometries and does rely on any homogeneous direction. The full proposed method (i.e., the sensor coupled to a wall model in an LES) is tested first in a very controlled setting: transition over a flat plate induced by blowing and suction. It is then applied to compute the flow around the MD 30P/30N multi-element airfoil at the realistic chord Reynolds number of 9 million. It is important to note that the transition on the slat of the MD 30P/30N (at the 19◦ angle of attack that is considered here) occurs immediately after a small laminar separation bubble, which effectively determines the transition location for the airfoil case. In this scenario, existing wall-models can overestimate the skin friction in the laminar region, thus leading to slightly thicker boundary layers. This situation is, obviously, highly dependent on the airfoil, Reynolds number, and angle of attack. The purpose of the first test case (flat plate boundary layer transition) is to directly test the ability of the proposed method to predict the transition location.