Session EK: Acoustics I: Shear Flows

Investigation of the Near-Field Acoustic Properties of Supersonic Jets with Fluidic Enhanced Chevrons using Large-Eddy Simulations

Since it has been found that chevrons reduce noise more effectively in the underexpanded operating range, but fluidic injection with constant injection mass flow rate is more effective in the overexpanded range, fluidic enhanced chevrons (a combination of chevrons and fluidic injection) are investigated numerically based on a MILES (Monotonically Integrated Large Eddy Simulations) approach. Both overexpanded and underexpanded jet conditions are tested and results are compared with experimental data. The mean flow field and the near-field noise spectra are also compared with those from the case with fluidic injection alone and the case with chevrons alone. It is found that fluidic enhanced chevrons have a larger impact in the overexpanded operating range than that in the underexpanded range.   

Non-linear parabolized stability equation (NPSE) models for predicting large-scale mixing noise of turbulent round jets

We study sound generation from lower-frequency, large-scale wavepacket structures of turbulent round jets using PSE models. The computations use a set of subsonic and supersonic mean flows for which databases from PIV measurements and LES simulations, respectively, are available. Linear PSE models have previously shown good agreements with the amplitude and phase of microphone array data measured just outside the jet shear layer. Non-linear effects are likely to be important for the lower-order modes, near and beyond the closing of the jet potential core, where the wave amplitudes reach their maximum values. Unlike the LPSE evolution, which is independent of the initial amplitudes, an accurate estimate of the near-nozzle disturbance spectrum is necessary as the initial condition for NPSE, which is obtained from precomputed LPSE modal amplitudes, but can also be obtained from experimental data or high-fidelity simulations. Studies show the non-linear evolution to be sensitive not only to the initial modal amplitudes but also to their phases, the number of modes retained in the solution, and also any spurious noise that might be present in the mean flow measurements.   

Adjoint-based minimization of the sound radiated by a Mach 1.3 turbulent jet

A control optimization using the adjoint of the perturbed and linearized Navier--Stokes equations is applied to a simulation of a Mach 1.3 turbulent jet to reduce its radiated sound. The solution of the adjoint system provides gradient information for a minimization algorithm to circumvent the flow complexity and reduce the sound directly. Comparisons between the loud and the perturbed-but-quiet versions of the same jet are examined to identify sound mechanisms. The overall algorithm is designed such that the control can be optimized with degrees of freedom comparable to that of the numerical discretization or with constraints on its spatial or temporal profiles to reflect hardware limitations. The large-eddy simulation of the uncontrolled, baseline jet is carried out in curvilinear coordinates using a non-dissipative high-order finite-difference. The far-field sound is computed using a Ffowcs Williams and Hawkings surface. Turbulence and far-field sound statistics agree with experimental data. An unconstrained optimal control reduces the sound cost functional by 17\%. The far-field sound is reduced at all angles with a maximum reduction of 2.7dB in the peak radiation direction. Constraining the control in actuator-like zones shows a similar result. Optimizations are ongoing.   

Effect of roughness shape on rough-wall boundary-layer noise

Turbulent boundary-layer noise induced by arrays of $10 \times 4$ sparsely distributed roughness elements is investigated using Lighthill's theory with acoustic sources obtained from large-eddy simulation. Two types of roughness elements, hemispheres and cuboids with the same height $h=0.124 \delta$ ($h^+=168$), are considered. The acoustic formulation shows that each roughness element acts as compact in-plane dipole sources strengthened by their images in the wall. The acoustic characteristics are found to be strongly dependent on the roughness shape. For the hemispherical array, the dipole sources are mainly generated by the interaction of hemispheres with incoming turbulent eddies, spanwise dipoles are stronger than streamwise dipoles, and the leading row of hemispheres produces the weakest sound. In contrast, for cuboid elements, unsteady separation and reattachment around the front edges are important acoustic sources, the spanwise dipoles are slightly weaker than the streamwise dipoles, and the leading row produces the strongest radiation. Correlations and coherence between dipole sources associated with neighboring roughness elements are found to be weak, particularly for cuboids and in the spanwise direction.   

Identifying Lighthill source term with large-eddy simulation of subsonic turbulent jet

An acoustic analogy analysis based on the decomposition of the Lighthill source term into subterms is discussed in light of a high-fidelity large-eddy simulation of a subsonic turbulent jet from a baseline nozzle. These subterms consist of density, velocity, vorticity and dilatation fields, representing their reciprocal nonlinear interactions. To understand the aerodynamic noise generation mechanism, intrinsic links between turbulence and emitted sound waves, such as cross-correlation functions, are required. This causality method is directly adopted to the LES data to identify the fundamental noise sources. The cross-correlation between each spatial subterm in the near field and acoustic pressure fluctuation at a far field position is calculated, showing its contribution to noise generation. Three principal noise production terms, related to turbulence kinetic energy and Lamb vector, are witnessed and interpreted. The results show encouraging agreement with previous predictions. Future work will extend the observation to chevron nozzle jet. A comparison of the correlation profiles will possibly lead us to characterize the distinct structures of the chevron nozzle and baseline round nozzle jets. Furthermore, this study is expected to help in better understanding and assessing of noise control devices.   

Effects of heating and Mach number on global modes of high-speed jets

The noise produced by high-speed jets is analyzed by global mode decomposition over a range of Mach numbers and jet-to-ambient density ratios. A massively parallel shift-and-invert Arnoldi method is used to extract global modes from simulations of the fully compressible linearized Navier--Stokes equations. Both laminar and turbulent mean (satisfying the Reynolds averaged Navier-Stokes equations with the k-epsilon model of Tam and Thies) base flows are considered. The least-stable portions of the global spectra were observed to split into two types of branches, which are shown to be linked to Kelvin-Helmholtz and Tam-Hu instability waves, respectively. Because they are upstream propagating, Tam-Hu waves are neglected by traditional analyses based on the parabolized stability equations. Significant transient growth is recovered through an optimal superposition of the global modes, and it is found that non-normality increases with decreasing density ratio as well as with decreasing Mach number.   

Jet Noise Source Parameterization Based on Far-Field Sound Intensity Distributions

Predictive tools for the interaction of jet noise with airframe surfaces require a model for the jet noise source that is simple yet physically relevant. The model used here consists of the incoherent superposition of a wavepacket and a monopole. Data to parameterize such model are limited primarily to far-field sound pressure level spectra. For a given frequency, the source parameters are determined by matching, in a least-squares sense, the polar intensity distribution in the far field. Even though only a small fraction of the wavepacket spectral content radiates to the far field, it is possible to construct models for the jet noise source that reproduce well the far-field polar intensity distribution and contain reasonable wavepacket parameters. In particular, the directivity pattern of the sound intensity provides strong guidance as to the azimuthal mode content of the wavepacket. The contribution of the monopole is small and typically on the order of 10{\%} of the peak intensity. The model is extended to non-axisymmetric jets and to jets with limited azimuthal coherence.   

Acoustics and Mean Flow of Coaxial Jets with Variable Velocity and Area Ratios

We investigate experimentally the far-field acoustics, noise source distributions, and mean flow structure of coaxial jets with secondary-to-primary velocity ratio $U_{s}$/$U_{p}$ ranging from 0 to 1 and diameter ratios of 1.54, 1.64, and 1.98. The mean velocity field is characterized in terms of the length of the primary core $L_{p}$, defined as the high-speed region of the jet, and the length of the secondary $L_{s}$, defined by the outer inflectional points of the radial velocity profile. The ratio $L_{s}$/$L_{p}$ increases with velocity ratio and with diameter ratio. For velocity ratios between 0.4 and 0.8, the elongation of the secondary core relative to the primary core is accompanied by suppression of high-frequency noise sources near the jet exit. This results in a reduction of far-field sound pressure levels, which is particularly strong when the results are scaled to constant thrust. Given the importance of $L_{s}$/$L_{p}$, models for the core lengths are constructed and preliminary correlations for the reduction of overall sound pressure level versus $L_{s}$/$L_{p}$ and other critical parameters are offered.   

The frequency spectrum of sound generated by turbulent shear flows

The frequency spectrum of sound radiated by turbulent shear flows is analytically calculated from Lighthill's acoustic analogy by evaluating space-time correlations. The turbulent shear flow is a simple model for jet noise, with the assumptions that its large scales are steady shear and its small scales are isotropic. Ribner (J. Fluid Mech. 38 1-24 1969) calculates the noise intensity for this model, which shows the basic directivity of jet noise. Recently, a non-frozen flow model is developed for space-time correlations in turbulent shear flows (Phys. Rev. E. 79 046316 2009) and experimentally verified against the Rayleigh-Benard convection (Phys. Rev. E. 81 065303 2010). We use the non-frozen flow model to calculate the noise spectra for turbulent shear flows. The result obtained is explicitly dependent on the lateral angle. It offers a scaling form of noise spectra at high frequencies, which is consistent with the two noise source model by Tam et. al. (AIAA paper 96-1716). The results obtained are also compared with the experiments and numerical simulations.   

Study of supersonic components in high-speed turbulent jets using wavenumber-frequency domain filtering and POD

Near-field characteristics of supersonic components are investigated using LES database by Bodony and Lele (2005). Three unheated jets with jet Mach number ranging from 0.51 to 1.95, and one heated transonic jet are considered. Supersonic components are decomposed from full flow field using wavenumber-frequency domain filtering. Spatial structure of the fluctuating pressure field is obtained by computing proper orthogonal components (POD modes) of the full and filtered data. POD modes of subsonic jet (M$_{j}$ = 0.51) reveals large scale-disparity between full and supersonic components. For the supersonic jet at M$_{j}$ = 1.95, the energetic structures of the pressure field also contribute significantly to the supersonic components and scale disparity is absent. The subsonic pressure variance can be rescaled by V$_{j}^{4}$ (i. e. $\vert \vert $P$^{2}\vert \vert \sim $V$_{j}^{4})$, which is an expected scaling for turbulence associated pressure fluctuations, whereas supersonic pressure variance can be rescaled with V$_{j}^{8}$, which is consistent with the far-field noise intensity scaling associated with Lighthill's analogy. Filtered velocity components are also rescaled and similar pattern is observed (i. e. supersonic near-field veolocity scales as far-field disturbances).