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Spectral proper orthogonal decomposition (SPOD) is applied to direct numerical simulation datasets of a lean and a stoichiometric methane–air turbulent premixed jet flame. SPOD is used to extract the coherent structures that correlate with the radiated sound by using an inner product based on a linearized disturbance energy. Two types of structures are prominent in the data. The first type arises in the jet’s shear layer and is linked to the Kelvin–Helmholtz instability, which is an important mechanism of sound generation in nonreacting jets. These structures produce sound through deformation of the flame front in the shear layer. They contain most of the acoustic energy and are dominant at Strouhal numbers (defined based on the jet’s diameter and the inlet mean velocity) less than unity. The second type of structures is found near the jet centerline, where large fluctuations of the flame surface are observed. The structures are linked to small nonlinear flame dynamics and to the Orr mechanism. They travel at a speed close to the inlet mean velocity and are important at higher Strouhal numbers. Regardless of their energy content, both types of structures have important contributions to the broadband nature of combustion noise.

Jet noise reduction remains an important long-range goal in commercial and military aviation. Compared with their early counterparts, modern, ultrahigh-bypass-ratio turbofans on commercial aircraft are very quiet, but ever more stringent noise regulations dictate further reductions. In addition, hearing loss by personnel and community noise issues are prompting the military to seek noise reduction on future tactical aircraft. Further increase in bypass ratio not being a practical option, military applications in particular call for nuanced approaches to noise reduction including mixing devices like chevrons or even active noise control approaches using unsteady air injection. In this paper, we briefly review some recent developments in theoretical, experimental and computational approaches to understanding the sound radiated by largescale, coherent structures in jet turbulence that might guide these noise reduction efforts.

We use data from a new, carefully validated, Large Eddy Simulation (LES) to investigate and model subsonic, turbulent, jet noise. Motivated by the observation that sound-source dynamics are dominated by instability waves (wavepackets), we examine mechanisms by which their intermittency can amplify their noise radiation. Two scenarios, both involving wavepacket evolution on time-dependent base flows, are investigated. In the first, we consider that the main effect of the changing base flow consists in different wavepacket ensembles seeing different steady mean fields, and having, accordingly, different acoustic efficiencies. In the second, the details of the base-flow time dependence also play a role in wavepacket sound production. Both short-time-averaged and slowly varying base flows are extracted from the LES data and used in conjunction with linearized wavepacket models, namely, the Parabolized Stability Equations (PSE), the One-Way Euler Equations (OWE), and the Linearized Euler Equations (LEE). All results support the hypothesized mechanism: wavepackets on time-varying base flows produce sound radiation that is enhanced by as much as 20dB in comparison to their long-time-averaged counterparts, and ensembles of wavepackets based on short-time-averaged base flows display similar amplification. This is not, however, sufficient to explain the sound levels observed in the LES and experiments. Further work is therefore necessary to incorporate two additional factors in the linear models, body forcing by turbulence and realistic inflow forcing, both of which have been identified as potentially important in producing the observed radiation efficiency.

We present diagnostic experiments and reduced-order models aimed at understanding and mitigating supersonic jet noise from coherent wavepackets in the turbulent shear layer, generally accepted to be the source of peak aft-angle mixing noise. The work builds on a successful Caltech/UTRC modeling approach that predicts the evolution of the wavepackets as instability waves of the turbulent mean flow, as well as the noise radiated from their near field. The models are experimentally assessed for unforced and forced supersonic isothermal and heated Mach 1.5 jets from ideal expansion nozzles. A spinning valve device is used to inject air near the nozzle lip at frequencies up to a Strouhal number of about 0.25. Results indicate a 2-3 dB benefit near peak frequencies of the spectrum and a 2 dB OASPL reduction at a mass flow percentage of 3.2. For the same injection plenum pressure, steady blowing yields more noise benefit than the unsteady actuation schemes explored until now. However, this may be explained by the slight decrease in injection velocity incurred in going from steady to unsteady operation. The reduced-order models, based on parabolized stability equations (PSE), are found to be in good agreement, in terms of envelope and phase, with those educed from the experimental data of the unforced jet. For the actuation schemes we have considered to date, the model and experimental data support a tentative explanation for the observed noise reduction in terms of attenuation of the wavepacket amplitudes by the thickened shear layer. Wavepackets induced by the harmonic component of the actuation are linearly superposed on those produced by broadband turbulence, without significant interaction, such that they lead to the addition of tones to the far-field noise that are counterproductive as far as noise reduction is concerned.

Dense compressible multiphase flows exist in variable phase turbines, explosions, and fluidized beds, where the particle volume fraction is in the range 0.001 < α_d < 0.5. A simple model problem that can be used to study modeling issues related to these types of flows is a shock wave impacting a particle cloud. In order to characterize the initial shock-particle interactions when there is little particle movement, a two-dimensional (2-D) model problem is created where the particles are frozen in place. Qualitative comparison with experimental data indicates that the 2-D model captures the essential flow physics. Volume-averaging of the 2-D data is used to reduce the data to one dimension, and x-t diagrams are used to characterize the flow behavior. An equivalent one-dimensional (1-D) model problem is developed for direct comparison with the 2-D model. While the 1-D model characterizes the overall steady-state flow behavior well, it fails to capture aspects of the unsteady behavior. As might be expected, it is found that neglecting the unclosed fluctuation terms inherent in the volume-averaged equations is not appropriate for dense gas-particle flows.

Parabolized stability equation (PSE) models are being developed to predict the evolution of low-frequency, large-scale wavepacket structures and their radiated sound in highspeed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. Here we show they also in very good agreement with hot-wire measurements at the jet centerline in the potential core, for a different set of experiments. When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large-scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative importance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that nonlinearity has a very limited impact on the evolution of the wavepackets for St ≥ 0.3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.

High speed exhaust noise reduction continues to be a research challenge for supersonic cruise business jets as well as for current and future tactical military aircraft. Significant noise reduction may be possible from advanced concepts for controlling instability generated large-scale turbulence structures in the jet shear layer, generally accepted to be the source of aft-angle noise. In response to this opportunity, our team is focused on experimental diagnostic studies and unique instability modeling suited for identifying control strategies to reduce large scale structure noise. The current paper benchmarks the jet noise from supersonic nozzles designed to provide the supporting experimental data and validation of the modeling. Laboratory scale jet noise experiments are presented for a Mach number of Mj = 1.5 with stagnation temperature ratios ranging from Tr = 0.75 to 2. The baseline configuration is represented by a round converging-diverging (CD) ideal expansion nozzle. A round CD nozzle with chevrons is included as the first of several planned non-circular geometries directed at demonstrating the impact on large scale structure noise and validating noise prediction methods for geometries of future technological interest. Overexpanded and underexpanded conditions were tested on both nozzle configurations. The resulting data base provides an opportunity to benchmark the statistical characteristics of round and chevron nozzle data. The current paper examines far field spectra, directivity patterns, and overall sound pressure level dependence comparing observed characteristics with the fine scale turbulence noise and large-scale turbulence structure noise characteristics identified by Tam. In addition, the paper probes the effect of chevrons on the developing flow field and suppression of screech tones. Measurements are also reported from a far-field narrow aperture phased array system used to map the acoustic source distribution on the jet axis. The dominant so

Active flow control is used to modify the lift, drag and pitching moments on a semicircular wing with aspect ratio, AR = 2, and chord Reynolds number is 68,000. The wing is mounted on a pitch/plunge sting mechanism that responds to the instantaneous loads and moments acting on the wing. The leading edge of the airfoil contains 16 spatially localized actuators that can be independently controlled. Smoke wire visualization, surface pressure and six-component force balance measurements are used to characterize the effects of openloop forcing. The lift coefficients on the steady wing are enhanced with the actuation, similar to the effect of dynamic stall vortex lift enhancement that occurs during a pitch up maneuver. Surface pressure measurements are being used to construct a flow model for use in feedback control. Progress toward the goal of designing a feedback controller to stabilize the flight of the model in an oscillatory freestream is discussed.

Current research programs directed at supersonic engine exhaust noise reduction are demonstrating benefits of 3-4 dBA using passive methods to increase jet mixing and break up shock cells in over-expanded flows. While progress is being made, high speed jet noise continues to be a research challenge for small business jets and tactical military aircraft. The current work benchmarks high speed jet noise using laboratory scale jets for the purpose of a) identifying source and propagation mechanisms, and b) providing validation data for simulation/modeling methods. Laboratory scale experiments are presented over a Mach number range of M = 0.68 to 1.5 with static temperature ratio ranging from Tr = 0.68 to 2. A unique near field rotating phased microphone array technique was used to identify the large-scale turbulence structure noise source and Mach waves in supersonic shock-free jets. A companion paper documents the near field pressure statistics and projection of the convected wave packet to the far field. Validation against the directly measured far field levels quantitatively establishes the large scale structure noise contributions. The combined studies underpin a long term effort to develop modeling methods and new concepts for jet noise suppression based on controlling the evolution of the large-scale turbulence structures.

We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity.

Open-loop active flow control is used to modify the spanwise distribution of circulation around an NACA 0012 and flat plate wing. The leading edge on both airfoils and tip regions of the NACA airfoil contain spatially localized actuators that can be independently controlled in terms of amplitude and frequency, allowing the spanwise distribution of circulation to be modified. Different orientations of the pulsed-blowing actuators were used to provide upstream, downstream, in-line with the flow, and outward span components of actuation. The actuation effectiveness was documented using force balance measurements of the lift and drag, smoke-wire visualization, surface pressure measurements and PIV velocity field measurements. Actuation with an upstream component is shown to be far more effective in reducing the separated region than actuation in the streamwise direction. Initial measurements of the change in circulation on the suction surface of the airfoil indicate that spatially localized forcing produces global changes over the wing, primarily associated with the reduction in size of the separated flow region.

A wave-packet ansatz is used to model noise generation by organized, large-scale structures. The spectrum of the acoustic field is expressed in terms of two-point space-time correlations of hydrodynamic pressure on a conical surface surrounding the jet plume. The surface is sufficiently near the turbulent flow region to be dominated by hydrodynamic disturbances, yet sufficiently far that the wave equation can be used to project the nearfield pressure to the acoustic field. In the present study, a 78-microphone array was used to measure hydrodynamic pressure on the conical surface at a variety of acoustic Mach numbers and temperature ratios. At each jet cross section, 6 microphones are staggered in the azimuthal direction allowing resolution of pressure up to azimuthal mode number m = 2. We compare recent jet noise measurements using an 80-microphone conical mid-field array with those derived from the near-field hydrodynamic array data, showing reasonably good predictions. Source model parameters are identified for various jet temperature ratios. Results show that changes in jet noise directivity with heating can be attributed to contraction of the wave-packet scale.

We report progress in our ongoing effort to compute and understand the instabilities of open cavity flows from incompressible to supersonic speeds. We consider three-dimensional instabilities of nominally two dimensional (spanwise homogeneous) cavity flows (BiGlobal instabilities). Experiments, DNS/LES computations, and preliminary instability computations have shown that the modes of oscillation are influenced by complex interactions between the shear layer and the recirculating flow within the cavity. We present here a framework for computation of the two-dimensional eigenvalue problem for the compressible open cavity. We validate the numerical scheme by computing several canonical flows: square duct flow, boundary layers at speeds from incompressible to supersonic, and two-dimensional parallel shear layers. We present preliminary results for the three-dimensional modes of the compressible open cavity flow with length-to-depth ratio of two at a Mach number of 0.325.

We present analytical, experimental and computational studies aimed at understanding the role of large-scale, organized structures in noise generation from high-speed, compressible jets. Two-point near-field pressure data from experiments are analyzed and used to identify parameters in a wave-packet based model for noise generation from organized, large-scale structures. The statistical spectrum of far field pressure is expressed in terms of two-point space-time correlations of the near-field pressure on a surface enclosing the jet. The surface is assumed to be sufficiently near the turbulent region tobe dominated by non-propagating hydrodynamic disturbances, yet sufficiently far such that linear behavior can be assumed in extending the near-field pressure to the far field. Validity of such assumptions is investigated by interrogating the jet DNS database of Freund [J. Fluid Mech. 438:277-305 2001]. The DNS data analysis is also used to investigate the impact of limited spatial resolution in the experiments. The analytical model is used to study far field noise generation from organized structures. Results show that, for sufficiently short structure lifetime, aft angle far field pressure spectra tend to exhibit frequency scaling with Helmholtz number, rather than Strouhal number.

The identification of numerical residuals from direct numerical simulations (DNS) with the least-damped BiGlobal eigenmodes of an underlying steady-state permits extraction of both the steady-state and amplitude functions of the BiGlobal eigenmodes from simple algebraic operations. Algorithms for the calculation of the basic state and the spatial structure of the related BiGlobal eigenmodes from transient DNS data have been constructed and presented. Here we extend initial calculations for the (closed) incompressible lid-driven cavity to the related (compressible) open-cavity flow. Order-of-magnitude savings are demonstrated when using of the discussed algorithm for the calculation of the basic state, compared with straightforward time-integration of the equations of motion until convergence in time. Further, employing this algorithm, different classes of instabilities in the open cavity are unified in the framework of BiGlobal instability analysis.

The Rayleigh-Plesset equation has been used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Radial diffusion equations may be solved for a single bubble, but these are too computationally expensive to implement into a continuum model for bubbly cavitating flows since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive reduced-order models that account for thermal and mass diffusion. We present a model that can capture the damping effects of the diffusion processes in two ODE's, and gives better results than previous models.