Session D4: Acoustics II: Aeroacoustics (Jets)

Sensitivity analysis for the control of supersonic impinging jet noise

The dynamics of a supersonic jet that impinges perpendicularly on a flat plate depend on complex interactions between fluid turbulence, shock waves, and acoustics. Strongly organized oscillations emerge, however, and they induce loud, often damaging, tones. We investigate this phenomenon using unstructured, high-fidelity Large Eddy Simulation (LES) and global stability analysis. Our flow configurations precisely match laboratory experiments with nozzle-to-wall distances of 4 and 4.5 jet diameters. We use multi-block shift-and-invert Arnoldi iteration to extract both direct and adjoint global modes that extend upstream into the nozzle. The frequency of the most unstable global mode agrees well with that of the emergent oscillations in the LES. We compute the ``wavemaker'' associated with this mode by multiplying it by its corresponding adjoint mode. The wavemaker shows that this instability is most sensitive to changes in the base flow slightly downstream of the nozzle exit. By modifying the base flow in this region, we then demonstrate that the flow can indeed be stabilized. This explains the success of microjets as an effective noise control measure when they are positioned around the nozzle lip.   

Linear frequency response analysis of a high subsonic and a supersonic jet

A linear frequency response, or resolvent analysis of two turbulent jet mean flows is conducted. The mean flows are obtained from two high-fidelity large eddy simulations of a Mach 0.9 and a Mach 1.5 turbulent jet at Reynolds numbers of $1\times10^6$ and $3\times10^5$, respectively. For both cases, curves of the optimal and sub-optimal output gains are calculated as a function of frequency for different azimuthal wavenumbers. The gain curves bring to light pseudo-resonances associated with different linear instability mechanisms. The same mechanisms are recovered in global stability analyses, and the results are compared. In the case of the Mach 0.9 jet, the resolvent analysis allows for a detailed study of trapped acoustic modes inside the potential core that were subject to previous stability studies. The structure of the resolvent and global modes are compared to POD mode estimates of the LES data. Additionally, the projection of the LES data onto the modes allows for quantitative assessment of how well the modal structures represent the coherent structures in the jet.   

Asymptotic structure of low frequency supersonic heated jet noise using LES data to re-construct a turbulence model

The Goldstein-Sescu-Afsar (2012, vol. 695, pp. 199- 234) asymptotic theory postulated that the appropriate distinguished limit in which non-parallel mean flow effects introduces a leading order change in the ‘propagator’ (which is related adjoint linearized Euler Green’s function) within Goldstein's acoustic analogy must be when the jet spread rate is the same order as Strouhal number. We analyze the low frequency structure of the acoustic spectrum using Large-eddy simulations of two axi-symmetric jets (heated & unheated) at constant supersonic jet Mach number to obtain the mean flow for the asymptotic theory. This approach provides excellent quantitative agreement for the peak jet noise when the coefficients of the turbulence model are tuned for good agreement with the far-field acoustic data. Our aim in this talk, however, is to show the predictive capability of the asymptotics when the turbulence model in the acoustic analogy is ‘exactly’ re-constructed by numerically matching the length scale coefficients of an algebraic-exponential model for the 1212-component of the Reynolds stress auto-covariance tensor (1 is streamwise & 2 is radial direction) with LES data at any spatial location and temporal frequency. In this way, all information is obtained from local unsteady flow.   

Impact of surface proximity on flow and acoustics of a rectangular supersonic jet.

Advances in jet technology have pushed towards faster aircraft, leading to more streamlined designs and configurations, pushing engines closer to the aircraft frame. This creates additional noise sources stemming from interactions between the jet flow and surfaces on the aircraft body, and interaction between the jet and the ground during takeoff and landing. The paper studies the impact of the presence of a flat plate on the flow structures and acoustics in an M$=$1.5 (NPR$=$3.67) supersonic jet exhausting from a rectangular C-D nozzle. Comparisons are drawn between baseline cases without a plate and varying nozzle-plate distance at NPRs from 2.5 to 4.5, and temperature ratios of up to 3.0. At the shielded side and sideline of the plate noise is mitigated only when the plate is at the nozzle lip (h$=$0). Low frequency mixing noise is increased in the downstream direction only for h$=$0. Screech tones that exist only for low NTR are fully suppressed by the plate at h$=$0. However, for h\textgreater 0 the reflection enhances screech at both reflected side and sideline. Low frequency mixing noise is enhanced by the plate at the reflected side at all plate distances, while broad band shock associated noise is reduced only at the sideline for h$=$0. Increased temperature mitigates the screech tones across all test conditions. The results are compared to a circular nozzle of equivalent diameter with an adjacent plate.   

Toward forced-wavepacket jet-noise models

Large-scale hydrodynamic wavepackets have been identified by numerous studies as an important source of turbulent jet noise. Linear models have proven capable of predicting the average statistics of these wavepackets but severely under-predict the associated acoustic radiation in subsonic jets in particular. Further studies have suggested that this under-prediction can be attributed to the sensitivity of the far-field noise to second order statistics of the wavepackets that are not properly reproduced by fully linear models. One approach to incorporating nonlinear effects is the computation of so-called resolvent modes, which represent the linear response of the flow to a nonlinear forcing that is presumed to be temporally and spatially uncorrelated, i.e., white noise. This approach has delivered promising results (see for example Jeun et al., \textit{Phys. Fluids} 2016), but its quantitative accuracy is limited by its implicit white-noise assumption. In this talk, we will show how correlated forcing can be systematically incorporated into a resolvent-based model and demonstrate the effect of applying modeled forcing that is designed to mimic the actual nonlinear terms present in a Mach 0.9 turbulent jet.   

Acoustic wavepackets and sound radiation by jets

The three-dimensional spatio-temporal evolution of the acoustic mode in a supersonic jet is analyzed using Doak's Momentum Potential Theory on an LES database. The acoustic mode exhibits a well-defined wavepacket nature in the core and convects at sonic speed. Its spatial coherence is significantly higher than the hydrodynamic component, resulting in an efficient sound radiation mechanism dominated by the axisymmetric and the first helical modes. Enthalpy transport by the acoustic mode yields insight into the sound energy flux emitted by the jet. Intrusion and ejection of coherent vortices into the core and ambient outer fluid respectively are found to be major intermittent sources of acoustic radiation. The scalar potential which defines the acoustic mode is found to satisfy the homogenous wave propagation equation in the nearfield which makes it a suitable variable to predict farfield radiation. The propagated acoustic field closely resembles the corresponding nearfield LES result. The acoustic mode thus provides a physically consistent wavepacket model to predict sound radiation from jets. Ongoing efforts on subsonic jets will discern the influence, if any, of the Mach number on the model.   

Jet crackle: skewness transport budget and a mechanistic source model

The sound from high-speed (supersonic) jets, such as on military aircraft, is distinctly different than that from lower-speed jets, such as on commercial airliners. Atop the already loud noise, a higher speed adds an intense, fricative, and intermittent character. The observed pressure wave patterns have strong peaks which are followed by relatively long shallows; notably, their pressure skewness is $S_k\ge0.4$. Direct numerical simulation of free-shear-flow turbulence show that these skewed pressure waves occur immediately adjacent to the turbulence source for $M\ge2.5$. Additionally, the near-field waves are seen to intersect and nonlinearly merge with other waves. Statistical analysis of terms in a pressure skewness transport equation show that starting just beyond $\delta_{99}$ the nonlinear wave mechanics that add to $S_k$ are balanced by damping molecular effects, consistent with this aspect of the sound arising in the source region. A gas dynamics description is developed that neglects rotational turbulence dynamics and yet reproduces the key crackle features. At its core, this mechanism shows simply that nonlinear compressive effects lead directly to stronger compressions than expansions and thus $S_k>0$.   

A combustion model for studying the effects of ideal gas properties on jet noise.

A theoretical combustion model is developed to simulate the influence of ideal gas effects on various aeroacoustic parameters over a range of equivalence ratios. The motivation is to narrow the gap between laboratory and full-scale jet noise testing. The combustion model is used to model propane combustion in air and kerosene combustion in air. Gas properties from the combustion model are compared to real lab data acquired at the National Center for Physical Acoustics at the University of Mississippi as well as outputs from NASA's Chemical Equilibrium Analysis code. Different jet properties are then studied over a range of equivalence ratios and pressure ratios for propane combustion in air, kerosene combustion in air and heated air. The findings reveal negligible differences between the three constituents where the density and sound speed ratios are concerned. Albeit, the area ratio required for perfectly expanded flow is shown to be more sensitive to gas properties, relative to changes in the temperature ratio.   

Towards the characterization of noise sources in a supersonic three-stream jet using advanced analysis tools

Strict noise regulation set by governing bodies currently make supersonic commercial aviation impractical. One of the many challenges that exist in developing practical supersonic commercial aircraft is the noise produced by the engine's exhaust jet. A promising method of jet noise reduction for supersonic applications is through the addition of extra exhaust streams. Data for an axisymmetric three-stream nozzle were generated using the Naval Research Laboratory's JENRE code. This data will be compared to experimental results obtained by NASA for validation purposes. Once the simulation results show satisfactory agreement to the experiments, advanced analysis tools will be applied to the simulation data to characterize potential noise sources. The tools to be applied include methods that are based on proper orthogonal decomposition, wavelet decomposition, and stochastic estimation. Additionally, techniques such as empirical mode decomposition and momentum potential theorem will be applied to the data as well.   

Understanding sideline jet noise using input-output analysis

We apply input-output analysis to high-speed turbulent jets to obtain the far-field acoustic response at different radiation angles. We consider both axisymmetric and higher azimuthal modes over a range of different frequencies to investigate the resulting noise spectra. At each frequency, singular value decomposition of the resolvent operator distinguishes between the optimal mode and several sub-optimal input-output modes by the magnitude of corresponding singular value. While both types of modes resemble wavepackets, the optimal mode associated with the largest singular value is superdirective in the peak noise radiation angle. Sub-optimal modes, in contrast, appear increasingly omnidirectional, rotating progressively to the sideline direction. Our analysis also recovers a broadening of the far-field acoustic spectra as the radiation angle increases. We show that a significant amount of the entire acoustic field can be captured by a superposition of a small number of coherent input-output modes.