The turbulent structure of the flow field generated by a hydrofoil in stalling condition beneath a water-air interface

In this paper, measurements beneath the interface of the flow past a hydrofoil in water during stalling conditions are used to characterize the flow field and to extract and to analyse the small eddies using an original algorithm based on the wavelet transform. The detected eddies are analysed to evaluate their spatial distribution and their intensity separating the wake of the foil-related from the wake of the breaker-related eddies. The wake of the foil-related eddies have an almost symmetric distribution of circulation with slight dominance of counter clock wise (CCW) eddies, while the breaker-related eddies have an asymmetric distribution of circulation, and clock wise (CW) eddies are dominant. The joint probability density function (PDF) of the turbulent kinetic energy (TKE) and the Reynolds shear stress is computed by referring to the time-averaged values in the area occupied by the eddies. A similar PDF computed using the instantaneous values during eddies presence shows values of TKE and Reynolds shear stress roughly twice the average values, i.e., eddies can be associated to larger fluctuations of the flow field respect to the time average flow field. However, on average, the Reynolds shear stress during eddy presence is less than the Reynolds shear stress of the time-averaged flow at the same location. The sign of the Reynolds shear stress is systematically opposite to the time-averaged value in quadrants Q2-Q4 for CW eddies and in quadrants Q1-Q3 for CCW eddies. Therefore, in the presence of eddies there is a counter-flux of momentum. The conditional analysis of the terms of the TKE balance indicates that, in the wake of the foil and during the presence of eddies, the production is 15% stronger than the time-averaged production at the same location occupied by the eddies. Beneath the free surface the production is 30% weaker than the time average. A similar analysis for the advection indicates that, in the wake of the foil, the advection in the presence of eddies is an order of magnitude greater (in absolute value) than the advection due to the time-averaged flow at the same location. Additionally, beneath the free surface, the advection in the presence of eddies is much greater than the average. A similar behaviour can be observed for the transport term due to turbulence. Therefore, in the presence of eddies, production plus advection plus transport is enhanced with respect to the average flow and is increased approximately by 40% in the wake of the foil and 20% beneath the free surface.