Far Wake and Its Relation to Aerodynamic Efficiency

Sidaard Gunasekaran,Aaron Altman

doi:10.3390/en14123641

Sidaard Gunasekaran, Aaron Altman

Open Access

https://doi.org/10.3390/en14123641

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Abstract

Correlations were found between the aerodynamic efficiency and the mean and fluctuating quantities in the far wake of a wall-to-wall SD7003 model and an AR 4 flat plate. This correlation was described algebraically by modeling the wake signature as a function of wing geometry and initial conditions. The model was benchmarked against experimental results to elicit the wing performance as a function of angle of attack by interrogating the wake. In these algebraic models, the drag coefficient along with other initial conditions of the turbulent generator (either airfoil or wing) were used to reconstruct the Reynolds Stress distribution and the momentum deficit distribution in the turbulent wake. Experiments were undertaken at the United States Air Force Research Labs Horizontal Free Surface Water Tunnel (AFRL/HFWT). These experiments build on previous results obtained at the University of Dayton Low Speed Wind Tunnel (UD-LSWT) on a cylinder, an AR 7 SD7062 wing, and a small remote control twin motor aircraft. The Reynolds stress and the momentum deficit of the turbulent generators were experimentally determined using Particle Image Velocimetry (PIV) with a minimum of 1000 image pairs averaged at each condition. The variation of an empirical factor (γ) used to match the Reynolds stress and momentum deficit distributions showed striking correlation to the variation of drag and aerodynamic efficiency of the turbulent generator. This correlation suggests that the wing performance information is preserved in the free shear layer 10 chord lengths downstream of the trailing edge (TE) of the wing irrespective of the dimensionality of the flow.

Highlights

IntroductionAccepted: 16 June 2021Early literature on turbulent flows indicates that the wake flows achieve a selfpreserved state (where turbulence production equals turbulence dissipation) where the information about the geometry of the model is lost
Accepted: 16 June 2021Early literature on turbulent flows indicates that the wake flows achieve a selfpreserved state where the information about the geometry of the model is lost
A surprising correlation between the aerodynamic efficiency/on-body flow characteristics and the mean and turbulent characteristics of the wake 10 chord lengths downstream of the wing was found independent of the wing dimensionality

Summary

Introduction

Accepted: 16 June 2021Early literature on turbulent flows indicates that the wake flows achieve a selfpreserved state (where turbulence production equals turbulence dissipation) where the information about the geometry of the model is lost. In 1956, Townsend [2] used a velocity scale U0 and a length scale L0 (wake-half width) to normalize the mean velocity and the Reynolds stress profiles in the free shear layer wake of a turbulent generator. By normalizing in this manner, it was theorized that the mean velocity and Reynolds stress of the free shear layer were independent of the geometry of the turbulent generators and downstream distance. To verify Townsend’s results, Wygnanski, Champagne, and Marasli (mid-1970s) conducted the same experiments and found that the properties in the wake of different turbulent generators are unique, which contradicted. This is because Wygnanski et al used the momentum thickness θ as the normalizing length scale instead of L0 used by Townsend. The momentum thickness of the generator can be estimated directly from the drag coefficient of the turbulent generator through Equation (1)

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