Two-Point Descriptions of Wake Turbulence with Application to Noise Prediction

Abstract

Measurements of the four-dimensional two-point correlation tensor of a fully developed airfoil wake are presented. These data allow examination of the characteristic eddies of the turbulence through proper orthogonal decomposition and linear stochastic estimation. A simple generic technique has been developed to extrapolate the correlation tensor function from the Reynolds stress eld based on the hypothesis that its form is largely determined by the constraints imposed by inhomogeneity and continuity. Estimates for the plane wake compare favorably with measurements, and, interestingly, proper orthogonal modes and characteristic eddy structures inferred from the estimates are similar to those obtained from measurements. This implies that these measures of the correlation function are largely determined by fairly basic physical information, suggesting some simpli cation of the turbulence-modeling problem for applications such as aeroacoustics.

Using RANS Calculations of Turbulent Kinetic Energy to Provide Two Point Flow Velocity Correlations and Surface Pressure Spectra

“…This approach has been used to analyze the turbulent flow in a blade wake based on the measurements of Devenport et al (2001). These give the details of all three velocity components, their two point statistics and spectra as a function of y and x for the wake behind a NACA 0012 airfoil at zero angle of attack at a Reynolds number of 3.28x10 5 .…”

“…We can then proceed to analyze the oblique blade wake interaction problem in exactly the same way as was done by Glegg and Devenport (2001(a)), defining the upwash from the mode velocity and the cutting angle of the wake, and calculating the unsteady load and the acoustic radiation for each mode independently to give the acoustic pressure at an observer located at x as p'"' (\,(o). Since each mode is uncorrelated the spectral density of the acoustic pressure is…”

“…Wake flows are more challenging than two dimensional boundary layers because the flow is continuously evolving in the downstream direction in a self similar manner. The theory was modified to allow for self similarity and the results were compared to experimental data of the two point velocity correlation functions in turbulent wakes (Devenport et al, 2001) with some success.This approach is then used to predict rotor stator interaction noise that is caused by the wakes from upstream blades impinging on downstream stator vanes. The turbulence modeling developed in Part la is used in Part lb to specify the turbulence in the inflow to the stators.…”

“…Wake flows are more challenging than two dimensional boundary layers because the flow is continuously evolving in the downstream direction in a self similar manner. The theoretical approach was modified to allow for self similarity and the results were compared to experimental data of the two point velocity correlation functions in turbulent wakes (Devenport et al, 2001) with some success. …”

On the wake flow of asymmetrically beveled trailing edges

“…Brooks and Hodgson [1981] conducted extensive surface pressure and acoustic measurements and described an experimental methodology for noise prediction from the statistics of the measured unsteady surface pressure. Later, Devenport et al [2001] measured two-point correlations of the velocity field in the near wake of a NACA 0012 airfoil employing hot-wire anemometry. Although the data provided valuable information regarding the spatial and temporal scales of the wake flow, the correlation approach does not facilitate a detailed understanding of the noise generation mechanism and underlying flow dynamics.…”