Hot Jets and Sources of Jet Noise

Abstract

A prediction method based on the generalized acoustic analogy is presented and used to evaluate aerodynamic noise radiated from high-speed hot jets. The set of Euler equations are divided into two sets of equations that govern what may be considered as a non-radiating base flow plus its residual components. Under certain conditions, the residual equations are rearranged to form a wave equation. This equation consists of a third-order wave operator, plus a number of non-linear terms that are regarded as the equivalent sources of sound and their statistical characteristics are modeled. A specialized RANS solver provides the base flow as well as the variance in both velocity and thermal fluctuations that determine the source strength. The main objective here is to evaluate the relative contribution from various source components to the far-field spectra and to show the significance of temperature fluctuations as a potential source of aerodynamic noise in hot jets.

Identifying turbulent jet sound sources

“…If we ignore terms containing pulsation values to the third or higher power and consider only dominant terms that determine the main noise sources of the turbulent flow [10,11,25], then the right hand side of Eq. (2) is represented in the form of two terms and It is possible to estimate the spectral noise charac teristics of a nonisothermal turbulent jet proceeding from Eq.…”

“…Due to the limi tations of the currently available volume of experi mental data on distributions of turbulence characteristics in the jet mixing range, certain difficul ties in calculating the sound field cause difficulties in choosing the form of functions describing the spatial and temporal dependences of the correlation function [41][42][43][44][45]. In estimating noise source intensity, we introduce the assumption, widely used in the practice of theoretically predicting the aeroacoustic character istics of turbulent jets [11,15,25,40,46], that it is pos sible to represent the spatiotemporal correlations of velocity pulsations via the expressions used in the the ory of isotropic turbulence [47,48].…”

“…Bearing in mind that in ten sor R ijkl ( , τ) there are only components changing in time and space [11,15,37] R ik ( )R jl ( ) + R il ( )R jk ( ) and R(τ), we obtain the spectral density in the form (7) where the expression in square brackets, e.g., repre sents the correlation function R 11 ( ) for longitudinal velocity pulsations.…”

“…Using the Millionshchikov hypothesis and taking into account equality to zero of the autocorrelation of product u'H' for isotropic turbulence [11,47], we obtain the expression for the correlation function ( τ) in the following form: where the spatiotemporal correlation describing the change in enthalpy pulsations in the flow, = is represented by analogy with expression (3) using two multipliers describing, respectively, the change of the correlation function in space F 1 ( ) and time F 2 (τ).…”

“…The acoustic field of a nonisother mal turbulent jet is characterized by a large amount of physical quantities and parameters. Intensive studies in recent years have been conducted [5][6][7][8][9][10][11] in devel oping scientifically substantiated methods for simulat ing and predicting noise source characteristics of nonisothermal jets and elaborating efficient noise reduction methods [1,[12][13][14][15].…”