Turbulence Modeling for Rotor Stator Interaction Noise

Abstract

The prediction of broadband rotor stator interaction noise produced by inhomogeneous turbulence is considered. The rigorous characterization of the turbulence, discussed previously by Glegg and Devenport (2001(b)), requires that it be specified in terms of the uncorrelated modes of the fluctuating velocity field. In this paper we demonstrate how these can be predicted from the turbulence kinetic energy and the length-scale information provided by most CFD solutions. The predicted modes can then be used to estimate all the single and two point statistics of the velocity field, and the sound radiated by the interaction of that field with an intersecting blade. Sample calculations are made using a fully developed plane wake. Predicted single and two-point turbulence statistics are shown to be in good agreement with experimental measurements. Sound predictions are presented for a series of blade wake interactions with different cutting angles. I. Introduction Turbomachinery broadband noise is often dominated by the turbulence in the rotor wakes interacting with downstream stator vanes. The accepted approach for analyzing this problem is to model the turbulence incident on the stator vanes by a locally homogeneous turbulent flow whose spectrum can be defined by a von Karman or Liepmann model, with a specified turbulence intensity and length scale. This is a very simplistic model of the complex turbulent flow downstream of a rotor, which is dominated by rotating wake flows, secondary flows and end wall effects. In an earlier paper Glegg and Devenport (2001(b)) proposed a more general approach to turbulence modeling in complex flows based on proper orthogonal decomposition of the unsteady flow incident on the stator. The limitation of this approach was the determination of the proper orthogonal modes. In this paper we will revisit this problem and show how the modes of the flow can be obtained from the solutions to the linearized Navier Stokes equations, or in the case of quasi two dimensional flows, the Orr Sommerfeld equations. We will illustrate the procedure by showing results for a simple idealized model of an oblique blade wake interaction. One of the interesting features of this analysis is that the modes of the flow can also be used to define its turbulent kinetic energy as a function of position, which is given by RANS calculations. We will show that if the turbulent kinetic energy is known as a function of position in the flow then the mode amplitudes can be estimated and this allows for the specification of the two point correlation functions of the turbulent velocities, their spectra and the definition of the acoustic radiation from a blade wake interaction. This is an extension of the concept introduced by Glegg, Morin, Atassi and Reba (2008) that was used successfully to predict trailing edge noise from an isolated airfoil.