Unsteady RANS Simulation of High Reynolds Number Trailing Edge Flow

Unsteady vortex shedding at a trailing edge may cause pressure fluctuations and strong tonal noise which can have important consequences to the performance of marine and aeronautical type lifting surfaces. This paper presents data from unsteady RANS simulation of high Reynolds number trailing edge flow. It aims to identify and quantify dominant features of the trailing edge flow field over a two-dimensional hydrofoil at Reynolds numbers of chord (Re) from 1.4x10 to 8.0x10. The foil section is a NACA0015 profile with a trailing edge cut at 0.2% chord from the trailing edge. It is found that the onset of vortex shedding occurs at a bluntness parameter h/δ* ≥ 0.28 and Reh ≥ 1.9x10, where h is the characteristic length scale of the trailing edge bluntness, δ* is the boundary layer displacement thickness and Reh is the Reynolds number based on h. Introduction The flow of an incompressible viscous fluid over a submerged lifting surface at high Reynolds numbers induces a variety of fluid phenomena. Laminar boundary layers form at the leading edge and depending on the viscosity of the flow, may quickly transition into turbulence which completely envelops both sides of the lifting surface near the trailing edge. Turbulent boundary layers near the trailing edge generate broadband scattering noise as well as surface pressure fluctuations which tend to excite structural vibration and fatigue [1]. Furthermore, separation of the turbulent boundary layer at the trailing edge can cause sustained shedding of vortices into the wake and generate tonal noise. An accurate prediction of trailing edge flows is therefore crucial to estimate the associated noise. The onset of vortex shedding at the trailing edge is closely related to the characteristics of the boundary layer flow near the trailing edge and its bluntness, h/δ* [1]. Thus significant changes in Reynolds number and slight modifications to trailing edge geometry may lead to fundamental changes in the trailing edge boundary layer flow. This, in turn, affects the near wake flow and modifies the shedding of vorticity into the wake [2]. This type of turbulent flow over hydrofoils or aerofoils is of particular interest to designers of propellers, control surfaces and lifting devices seeking quiet high performance components. Examination of the two-dimensional flows over hydrofoils can give insight into how the trailing edge geometry influences performance measures such as lift, drag and pressure loss, as well as the magnitude and nature of damaging structural vibration and the generated noise from surface pressure fluctuations. Numerical simulation provides an avenue for potentially accurate prediction of this damaging phenomenon. However, despite the rapid increase of computer power, analysis of such complex flows by Direct Numerical Simulation (DNS) and the alternative technique, Large-Eddy Simulation (LES), remains computationally expensive. Thus, the modelling of high Reynolds number flows continues to be based on the solution of the Reynolds-averaged Navier-Stokes (RANS) equations despite the claims of experts that the noise generating eddies over a wide range of length scales cannot be adequately represented by RANS equations [3]. This paper presents the development of a numerical prediction method using the commercial computational fluid dynamics (CFD) code of FLUENT based on RANS equations to determine the extent to which RANS modelling can predict trailing edge flow and tonal noise. The following will thus be a close examination of the trailing-edge and near wake flow over a hydrofoil at high Reynolds numbers to verify the relationship between the trailing edge parameter h/δ*, and the occurrence of vortex shedding. The validation of the turbulence model used for high Reynolds number hydrofoil flows has been reported by Mulvany et. al. [4]. The time-averaged results of displacement thickness are compared to semi-empirical data on flat plate boundary layer growth. The computed results are then used to obtain the unsteady turbulent flow field around the trailing edge and the time history of surface pressure fluctuations and velocity changes in the wake. The frequency spectra of the pressure fluctuations can thus be calculated and the resultant Strouhal numbers compared with published data from Blake [1]. The case under study is a two-dimensional hydrofoil with a NACA0015 section and chord length of 540mm. This symmetrical profile represents a generic section shape used on submerged control surfaces for submarines and ships. Limitations on current manufacturing equipment make it impossible to produce a perfectly sharp trailing edge. To accommodate this, the hydrofoil is ‘cut’ at 0.2% chord from the trailing edge resulting in a blunt edge with a vertical height of just over 2mm. The hydrofoil is aligned at zero degrees to the incident uniform stream of 2, 5, 7, and 11.5m/s which correspond to Reynolds numbers of chord based on freestream velocity Uref of 1.4, 3.5, 4.9, and 8.0 x10 respectively. Figure 1 shows the trailing edge geometry under investigation and a close-up on the blunt edge. Stations A, B, C, D and E refer to measurement stations of pressure fluctuations on the upper surface of the hydrofoil. They are located 100mm from the trailing edge xA=438.92, 70mm from the trailing edge xB=468.92, 40mm from the trailing edge xC=498.92, 0.95 chord lengths from the leading edge xD=513 and at the trailing edge xE=538.92 respectively. Station F refers to the horizontal line offset 0.5mm above the chord line which runs from the blunt edge, through the wake and to the rear end of the control region. The time-history of the vertical velocity along this line is recorded to give an assessment of the fluctuating vorticity in the wake. The value of displacement thickness, δ* used to calculate the bluntness parameter, h/δ* is calculated from the boundary layer velocity profile at a distance of 0.2Yf as defined in Blake for the edge geometry under investigation [1].