Modified TNO-Blake model for aerofoil surface pressure prediction with canopies

Abstract

The modelling of the surface pressure spectrum beneath a turbulent boundary layer near the trailing edge of an aerofoil with bio-inspired surface treatments, called canopies, is investigated. Canopies are simply a cylindrical rods uniformly spaced along the span of the aerofoil. The velocity measurements indicated that the flow at the trailing edge of an aerofoil treated with canopies is localised and shows periodic behaviour across the span with treatment spacing. As a result, the mean-flow velocity gradient along the span (@U1=@x3) cannot be assumed as zero for x2=h = 4, which is shown in this paper. Therefore, the original surface pressure solution of Poisson’s equation is modified by introducing an additional source term consisting of the mean-shear contribution, given as @U1=@x3 @u3=@x1. Furthermore, the surface pressure attenuation due to the canopies shows a periodic behaviour across the span for treatments with an Open-Area-Ratio (OAR) between 70% and 90 %. This observation is consistent with our previous experimental results; therefore, the primary motivation for proposing a 3D TNO-Blake model, accounting for the interaction between the gradient of the stream-wise mean velocity along the span and span-wise fluctuating component along the stream. The model is built based on the inputs from Large Eddy Simulation results and additional wind tunnel measurements.