Mohammed Afsar

Jet Noise: Acoustic Analogy informed by Large Eddy Simulation

A novel approach to the development of a hybrid prediction methodology for jet noise is described. Modeling details and numerical techniques are optimized for each of the three components of the model. Far-field propagation is modeled by solution of a system of adjoint linear Euler equations, capturing convective and refraction effects using a spatially developing jet mean flow provided by a Reynolds-averaged Navier―Stokes computational fluid dynamics solution. Sound generation is modeled following Goldsteins acoustic analogy, including a Gaussian function model for the two-point cross correlation of the fourth-order velocity fluctuations in the acoustic source. Parameters in this model describing turbulent length and time scales are assumed to be proportional to turbulence information also taken from the Reynolds-averaged Navier―Stokes computational fluid dynamics prediction. The constants of proportionality are, however, not determined empirically, but extracted by comparison with turbulence length and time scales obtained from a large eddy simulation prediction. The large eddy simulation results are shown to be in good agreement with experimental data for the fourth-order two-point cross-correlation functions. The large eddy simulation solution is then used to determine the amplitude parameter and also to examine which components of the cross correlation are largest, enabling inclusion of all identified dominant terms in the Gaussian source model. The acoustic source description in the present approach is therefore determined with no direct input from experimental data. This model is applied to the prediction of sound to the experimental configuration of the European Union JEAN project, and gives encouraging agreement with experimental data across a wide spectral range and for both sideline and peak noise angles. This paper also examines the accuracy of various commonly made simplifications, for example: a locally parallel mean flow approximation rather than consideration of the spatially evolving mean jet flow and scattering from the nozzle; the assumption of small radial variation in Green function over the turbulence correlation length; the application of the far-field approximation in the Green function; and the impact of isotropic assumptions made in previous acoustic source models.

Comparison of jet noise models

Acoustic analogy theories for jet noise prediction are formulated from the Navier Stokes equations using Green functions, describing wave propagation, and semi-empirical modeling of the turbulent statistics that act as noise sources. In a departure from this standpoint the Tam and Aurialt use an ad-hoc kinetic theory type argument that has been successful in predicting the 90 degree acoustic spectrum. In this paper we reassess the underlying assumptions of the Tam and Aurialt model. It is shown, while the Tam and Aurialt model can be interpreted as the integration of a source with a derivative of a Green function; the particular derivative is discontinuous across a thin shear layer, resulting in a sound power spectrum that is sensitive to the position of the discontinuity even when the acoustic wavelength is large. This is a disadvantage because there is some arbitrariness in the radial position of maximum shear, if a parallel shear flow is used to represent a developing jet. Comparison is made between predictions of the far-field sound from acoustic analogies and from the Tam and Aurialt model. I. Introduction

Iterative control of Görtler vortices via local wall deformations

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.

Towards the prediction of supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green's function

In this paper we continue efforts aimed at modeling jet noise using self-consistent analytical approaches within the generalized acoustic analogy (GAA) formulation. The GAA equations show that the far-field pressure fluctuation is given by a convolution product between a propagator tensor that depends on the (true) non-parallel jet mean flow and a generalized fluctuating stress tensor that is a stationary random function of time and includes the usual fluctuating Reynolds’ stress tensor as well as enthalpy fluctuation components. Here, we focus on approximating the propagator tensor by determining an appropriate asymptotic solution to the adjoint vector Green’s function that it depends on by using an asymptotic approach at all frequencies of interest for jet noise prediction. The Green’s function is then rationally approximated by a composite formula in which the GSA (Goldstein-Sescu-Afsar, J. Fluid Mech., vol. 695, pp. 199-234, 2012) non-parallel flow Green’s function asymptotic solution is used at low frequencies and the O(1) frequency parallel flow Green’s function is used for all frequencies thereafter. The former solution uses the fact that non-parallelism will have a leading order effect on the Green’s function everywhere in the jet under a distinguished scaling in which the jet spread rate is of the same order as the Strouhal number for a slowly-diverging mean flow expansion. Since this solution, however, is expected to apply up to the peak frequency, the latter O(1) frequency Green’s function in a parallel flow must be used at frequencies thereafter. We investigate the predictive capability of the composite Green’s function for the prediction of supersonic axi-symmetric round jets at fixed jet Mach number of 1.5 and two different temperature ratios (isothermal & heated) using Large-eddy simulation data. Our results show that, in the first instance, excellent jet noise predictions are obtained using the non-parallel flow asymptotic approach, remarkably, up to a Strouhal number of 0.5. This is true for both heated and un-heated jets. Furthermore, we develop the analytical approach required to extend this solution by appropriate asymptotic approximation to O(1) frequencies.

Reduced‐order models for jet noise

The research reported here leads to a simple prediction methodology based on a reduced‐order model for jet noise. The approach is a hybrid one made up of three components. Each component uses modeling and numerical techniques optimised to suit a particular purpose. The propagation of noise to the far field is captured via a new method for solution of the adjoint linearised Euler equations, describing how sound emitted by the jet is modified by propagation through the time‐averaged but spatially varying jet flowfield. The directivity of the quadrupole sources is more general than is usually assumed and their statistical properties are modeled based on a RANS solution for the jet: the cross‐correlation of the turbulent quadrupoles is modelled as Gaussian with length and time parameters proportional to the local length and timescales from the RANS solution, The constants of proportionality are determined through comparison with correlations from LES and from experimental data. Hence the source model is determined entirely from near field data and the far‐field sound is then predicted with no empirical constants. Comparison between this predicted noise and experimental data is very good, across a wide spectral range and even at angles close to the jet axis.