An Experimental Investigation of the Flow in the Near Wake of a Sharp-edged Strut

This paper describes an experimental investigation of the coherence function of the turbulent velocity, in the near wake of a two-dimensional sharp-edged strut, at zero angle of attack and at Rec = 500,000 , using hot wire anemometry. The paper focuses mainly on the shape of the coherence function as a function of spatial separation. It is found that the spanwise coherence function is well represented by a Gaussian curve, while the wall-normal coherence function is better represented by an exponential curve. For both cases the decay rate is a function of wall-normal distance. Introduction Turbulent boundary layer flow over a sharp edged airfoil generates broadband noise, which can be detrimental in a variety of engineering applications, including aircraft, wind turbines and submarines. Understanding the flow over the trailing edge (TE) is paramount for the development of TE noise prediction methodologies, such as the RANS-based Statistical Noise Method (RSNM) [1]. This method requires a model of the turbulent velocity cross-spectrum near the TE. The cross-specrum can be defined in terms of the auto-spectra at each point and the coherence function between the points. Models for the velocity auto-spectrum in boundary layers are well established [8], but models for cross-spectrum are not. There have been programs to measure two-point statistics in wall bounded flows, including zero pressure gradient (ZPG) turbulent boundary layers [10, 2, 9, 3] and turbulent boundary layers subjected to pressure gradients [5]. However, there have been few attempts to analytically model the turbulent velocity two-point space-time correlation (or its equivalent in the frequency domain, the cross-spectrum) for boundary layers. Phillips [7] developed a model of the velocity cross correlation based on channel flow DNS data of Kim et al. [6]. The model is a function of spatial separation, a length scale, the Reynolds stresses and mean flow velocity. They conclude that the model should be applicable to turbulent boundary layers as well as for channel flow. Gavin [3] proposed another model for ZPG turbulent boundary layers based on hot wire measurements. In this work, the correlation volume was modeled as an ellipsoid inclined at an angle θ to the wall. Values were provided for the inclination angle and stretching ratio between the major and minor axes of the ellipsoid, based on best fit to the experimental data. The model requires a convection velocity and the specification of a correlation length. To the authors’ best knowledge, there are no models of the turbulent velocity cross-spectrum for turbulent boundary layers subject to adverse pressure gradients. The main aim of this paper is to measure the streamwise turbulent velocity coherence function in the near wake of an airfoil, and provide the basis to develop a coherence function model, which coupled with the auto-spectrum model of Pope [8] can provide a model for the turbulent velocity cross-spectrum. Experimental Setup Experiments were performed in an open-jet low-speed wind tunnel at the University of Adelaide. The tunnel has a rectangular contraction outlet of dimensions 690 mm × 360 mm. The jet velocity was set at 6.4 m/s and the measured free stream turbulence intensity was Ti = 0.65%. The model used in the experiment (Figure 1) is a 1.2 m chord strut of 25 mm thickness, with a circular leading edge and a wedge-shaped trailing edge with an apex angle of 12 degrees. The trailing edge thickness is 1 mm. The boundary layer was tripped on both sides by a 0.5 mm thick turbulator strip placed at 10% chord. The model was positioned such that the leading edge coincided with the exit plane of the contraction outlet, and extension plates were fitted to the contraction outlet to ensure the trailing edge of the model was well within the potential core of the jet and measurements were not influenced by the nozzle lip shear layers. A depiction of the experimental setup is shown in Figure 2, with a coordinate system centered at the mid-span of the trailing edge and coinciding with the airfoil chord line. x, y, z are the streamwise, wall-normal and spanwise directions respectively. U is the mean velocity in the streamwise direction and u′ is its fluctuating component. A pitot probe was positioned at x = (−1200,84,0) mm to monitor the free stream velocity. Two TSI 1210-T1.5 single wire probes with wire length of L = 1.27 mm and a wire diameter of d = 3.81 μm (L/d ≈ 400) were used, and were operated using an IFA 100 constant temperature anemometer, with an overheat ratio of 1.8. The reference (“fixed”) hot wire probe was mounted on a manual traverse with an accuracy of 0.01 mm and was positioned at the center span (z = 0) and desired y location before each measurement. The reference probe positions ranged from y/δ = 0 to y/δ = 0.8, where δ is the boundary layer thickness at the TE. The moving hot wire probe was mounted on a TSI 9400 2-axes traverse system, with a positional accuracy of 0.01 mm. The TSI traverse was controlled using the TSI-9400 traverse controller, which was connected to a computer via RS-232 port. When the moving probe was traversed in the wall-normal direction, the reference probe was always the one closer to the wall. All two-point data were taken at 1 mm downstream of the trailing edge (x = 1 mm).