For some time now it has been theorized that spatially evolving instability waves in the irrotational near-field of jet flows couple both linearly and nonlinearly to generate far-field sound [Sandham and Salgado, Philos. Trans. R. Soc. Am. 366 (2008); Suponitsky, J. Fluid Mech. 658 (2010)]. An exhaustive effort at The University of Texas of Austin was initiated in 2008 to better understand this phenomenon, which included the development of a unique analysis technique for quantifying their coherence [Baars et al., AIAA Paper 2010–1292 (2010); Baars and Tinney, Phys. Fluids 26, 055112 (2014)]. Simulated data have shown this technique to be effective, albeit, insurmountable failures arise when exercised on real laboratory measurements. The question that we seek to address is how might jet flows manifest nonlinearities? Both subsonic and supersonic jet flows are considered with simulated and measured data sets encompassing near-field and far-field pressure signals. The focus then turns to considering nonlinearities in the form of cumulative distortions, and the conditions required for them to be realized in a laboratory scale facility [Baars, et al., J. Fluid Mech. 749 (2014)].
Several years of research at The University of Texas at Austin concerning the sound field produced by large area-ratio rocket nozzles is presented [Baars et al., AIAA J. 50(1), (2012); Baars and Tinney, Exp. Fluids, 54 (1468), (2013); Donald et al., AIAA J. 52(7), (2013)]. The focus of these studies is on developing an in-depth understanding of the various acoustic mechanisms that form during start-up of rocket engines and how they may be rendered less efficient in the generation of sound. The test articles comprise geometrically scaled replicas of large area ratio nozzles and are tested in a fully anechoic chamber under various operating conditions. A framework for scaling laboratory-scale nozzles is presented by combining established methods with new methodologies [Mayes, NASA TN D-21 (1959); Gust, NASA TN-D-1999 (1964); Eldred, NASA SP-8072 (1972); Sutherland AIAA Paper 1993–4383 (1993); Varnier, AIAA J. 39:10 (2001); James et al. Proc. Acoust. Soc. Amer. 18(3aNS), (2012)]. In particular, both hot and cold flow tests are reported which comprise single, three and four nozzle clusters. An effort to correct for geometric scaling is also presented.
Discrepancies between linear predictions and direct measurements of the far-field sound produced by high speed jet flows are typically ascribed to nonlinear distortion. Here we employ an effective Gol’dberg number to investigate the likelihood of nonlinear distortion in the noise fields of supersonic jets. This simplified approach relies on an isolated view of a ray tube along the Mach wave angle. It is known that the acoustic pressure obeys by cylindrical spreading in close vicinity to the jet before advancing to a spherical decay in the far-field. Therefore, a ‘piecewise-spreading regime’ model is employed in order to compute effective Gol’dberg numbers for these jet flows. Our first-principal approach suggests that cumulative nonlinear distortion can only be present within 20 jet exit diameters along the Mach wave angle when laboratory-scale jets are being considered. Effective Gol’dberg numbers for full-scale jet noise scenarios reveal that a high-degree of cumulative distortion can likewise be present in the spherical decay regime. Hence, full-scale jet noise fields are more affected by cumulative distortion.
Analysis of the acoustic signature produced by truncated ideal contour and thrust-optimized parabolic nozzles is conducted during both fixed and transient (startup) operations. The truncated ideal contour nozzle experiences freeshock separation flow, whereas the thrust-optimized parabolic nozzle experiences both free-shock separation and restricted-shock separation flow states during startup. This study provides a direct comparison of the acoustic signature produced during free-shock separation and restricted-shock separation flow states while operating under identical nozzle pressure ratios. During a transient episode, the continuous wavelet transform is used to compare the acoustic signatures produced by the nozzles. The truncated ideal contour nozzle demonstrates a gradual increase in broadband frequency energy with increasing nozzle pressure ratio and with broadband shock noise appearing at higher nozzle pressure ratios. The thrust-optimized parabolic nozzle, however, displays a much larger sensitivity to the nozzle pressure ratio. In particular, the free-shock separation to restricted-shock separation transition, which occurs around nozzle pressure ratio 24.4, is weakly revealed in the acoustic signature along sideline angles to the nozzle. At nozzle pressure ratio 13, the acoustic signal observed at shallow angles to the nozzle decreases abruptly across a broad range of frequencies. The latter phenomenon is attributed to the formation of an open-ended subsonic core surrounded by a supersonic annular flow in the thrust-optimized parabolic nozzle during free-shock separation operations of the nozzle, which does not occur in the truncated ideal contour nozzle.
The wandering motion of tip vortices trailed from a hovering helicopter rotor is described. This aperiodicity is known to cause errors in the determination of vortex properties that are crucial inputs for refined aerodynamic analyses of helicopter rotors. Measurements of blade tip vortices up to 260 deg vortex age using stereo particle-image velocimetry (PIV) indicate that this aperiodicity is anisotropic. We describe an analytical model that captures this anisotropic behavior. The analysis approximates the helical wake as a series of vortex rings that are allowed to interact with each other. The vorticity in the rings is a function of the blade loading. Vortex core growth is modeled by accounting for vortex filament strain and by using an empirical model for viscous diffusion. The sensitivity of the analysis to the choice of initial vortex core radius, viscosity parameter, time step, and number of rings shed is explored. Analytical predictions of the orientation of anisotropy correlated with experimental measurements within 10%. The analysis can be used as a computationally inexpensive method to generate probability distribution functions for vortex core positions that can then be used to correct for aperiodicity in measurements
A model is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jet flows. The model relies on the conventional definition of the acoustic shock formation distance and employs an effective Gol’dberg number for diverging acoustic waves. The latter properly accounts for spherical spreading, whereas the classical Gol’dberg number is restricted to plane wave applications. Scaling laws are then derived to account for the effects imposed by jet exit conditions of practical interest and includes Mach number, temperature ratio, Strouhal number and an absolute observer distance relative to a broadband Gaussian source. Surveys of the acoustic pressure produced by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support findings of the model. Acoustic waveforms are acquired on a two-dimensional grid extending out to 145 nozzle diameters from the jet exit plane. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes a wave steepening factor (WSF), skewness, kurtosis and the normalized quadrature spectral density. The analysed data are shown to collapse reasonably well along rays emanating from the post-potential-core region of the jet. An application of the generalized Burgers equation is used to demonstrate the effect of cumulative nonlinear distortion on an arbitrary acoustic waveform produced by a high-convective-Mach-number supersonic jet. It is advocated that cumulative nonlinear distortion effects during far-field sound propagation are too subtle in this range-restricted environment and over the region covered, which may be true for other laboratory-scale jet noise facilities.
A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system’s input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.
The acoustic signatures produced by a full-scale, Bell 430 helicopter during steady-level-flight and transient roll-right maneuvers are analyzed by way of time–frequency analysis. The roll-right maneuvers comprise both a medium and a fast roll rate. Data are acquired using a single ground based microphone that are analyzed by way of the Morlet wavelet transform to extract the spectral properties and sound pressure levels as functions of time. The findings show that during maneuvering operations of the helicopter, both the overall sound pressure level and the blade–vortex interaction sound pressure level are greatest when the roll rate of the vehicle is at its maximum. The reduced inflow in the region of the rotor disk where blade–vortex interaction noise originates is determined to be the cause of the increase in noise. A local decrease in inflow reduces the miss distance of the tip vortex and thereby increases the BVI noise signature. Blade loading and advance ratios are also investigated as possible mechanisms for increased sound production, but are shown to be fairly constant throughout the maneuvers.
The acoustic waveforms produced by an unheated supersonic and shock free jet operating at a gas dynamic Mach number of 3 and an acoustic Mach number of 1.79 are examined over a large spatial domain in the (x,r)-plane. Under these operating conditions, acoustic waveforms within the Mach cone comprise sawtooth-like structures which cause a crackling sound to occur. The crackling structures produced by our laboratory-scale nozzle are studied in a range-restricted environment, and so, they are not the consequence of cumulative nonlinear waveform distortions, but are rather generated solely by local mechanisms in, or in close vicinity to, the jet plume. Our current work focuses on characterizing the temporal and spectral properties of these shock-structures. A detection algorithm is introduced which isolates the shock-structures in the temporal waveforms based on a pressure rise time and shock strength that satisfy user defined thresholds. The average shapes of the shock-structures are shown to vary along polar angles centered on the post-potential core region of the jet. Spectral characteristics of the crackling structures are then determined using conventional wavelet-based time–frequency analyses. Differences between the global wavelet spectrum and the local wavelet spectrum computed from instances when shocks are detected in the waveform show how shock-structures are more pronounced at shallow angles to the jet axis. The findings from this energy-based metric differ from those obtained using the skewness of the pressure and the pressure derivative.
Dynamical characteristics of tip vortices shed from a 1 m diameter, four-bladed rotor in hover are investigated using various aperiodicity correction techniques. Data are acquired by way of stereo-particle image velocimetry and comprises measurements up to 260 vortex age with 10 offsets. The nominal operating condition of the rotor corresponds to Rec = 248,000 and M = 0.23 at the blade tip. With the collective pitch set to 7.2 and a rotor solidity of 0.147, blade loading (CT/r) is estimated from blade element momentum theory to be 0.042. The findings reveal a noticeable, anisotropic, aperiodic vortex wandering pattern over all vortex ages measured. These findings are in agreement with recent observations of a full-scale, four-bladed rotor in hover operating under realistic blade loading. The principal axis of wander is found to align itself perpendicular to the slipstream boundary. Likewise, tip vortices trailing from different blades show a wandering motion that is in phase instantaneously with respect to one another, in every direction and at every wake age in the measurement envelope.