C. E. Tinney, Canchero, A., Rojo, R., Mack, G., Murray, N. E., and Ruf, J. H., “The Sound-field Produced by Clustered Rockets During Startup,” Whither Turbulence and Dig Data for the 21st Century. Symposium held at the Institute dEtudes Scientifques de Cargese, Corsica, France, April 20-24, (Springer Hardbound Volume, DOI: 10.1007/978-3-319-41217-7), 2015.Abstract
The vibroacoustic loads produced by a cluster of two large area-ratio thrust optimized parabolic contour nozzles are studied over a range of pressure ratios encompassing free-shock separated flow, restricted shock separated flow and the end-effects-regime. The rocket plume is visualized using a retroreflective shadowgraphy system while an experimentally validated RANS model provides insight into the internal flow and shock structure patterns. Pressure loads that form on the base of the vehicle (behind the nozzles) are then measured using a eighth-inch microphone, as most of these loads are caused by high intensity sound waves produced by the rocket nozzle flow. The objective of the study is to provide a direct link between the sources of most intense vibro-acoustic loads that form during the ignition of high area ratio rocket nozzle clusters.
S. M. Mula and Tinney, C. E., “

A study of the turbulence within a spiraling vortex filament using proper orthogonal decomposition.

,” Journal of Fluid Mechanics, vol. 769, pp. 570-589, 2015. Publisher's VersionAbstract
The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition. The rotor is operated at a tip chord Reynolds number and tip Mach number of 218,000 and 0.23, respectively, and with a blade loading of CT /σ = 0.066. In-plane components of the velocity field (normal to the axis of the vortex filament) are captured by way of 2D particle image velocimetry with corrections for vortex wander being performed using the Γ1 method. The first POD mode alone is found to encompass nearly 75% of the energy for all vortex ages studied and is determined using a grid of sufficient resolution as to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. The spatial eigenfunctions of the first few Fourierazimuthal modes associated with the most energetic POD mode is shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used.
R. Fievet, Tinney, C. E., Baars, W. J., and Hamilton, M. F., “Acoustic waveforms produced by a laboratory scale supersonic jet,” 20th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2014-2906. Atlanta, Georgia. USA, 2014.Abstract
The spatial evolution of acoustic waveforms produced by a Mach 3 jet are investigated using both 1/4 inch and 1/8 inch pressure field microphones located along rays emanating from the post potential core where the peak sound emission is found to occur. The measurements are acquired in a fully anechoic chamber where ground, or other large surface reflections are minimal. The calculation of the OASPL along an arc located at 95 jet diameters using 120 planar grid measurements are shown to collapse remarkably well when the arc array is centered on the post potential core region. Various statistical metrics, including the quadrature spectral density, number of zero crossings, the skewness of the pressure time derivative and the integral of the negative part of the quadrature spectral density, are exercised along the peak emission path. These metrics are shown to undergo rapid changes within 2 meters from the source regions of this laboratory scale jet. The sensitivity of these findings to both transducer size and humidity effects are discussed. A visual extrapolation of these nonlinear metrics toward the jet shear layer suggests that these waveforms are initially skewed at the source. An experimentally validated wave packet model is used to confirm the location where the pressure decay law transition from cylindrical to spherical. It is then used to estimate the source intensity which is required to predict the effective Gol’dberg number. 1
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S. M. Mula and Tinney, C. E., “Classical and snapshot forms of the POD technique applied to a helical vortex filament,” 44th AIAA Fluid Dynamics Conference, AIAA Paper 2014-3257. Atlanta, Georgia. USA, 2014.Abstract
Low-dimensional characteristics of a helical vortex filament from a reduced-scale rotor are investigated using proper orthogonal decomposition (POD). Measurements are captured by way of particle image velocimetry. Experiments are performed on a 1.0 m diameter, single-bladed rotor in hover. The rotor is operated at 1500 RPM, which corresponds to a blade tip chord Reynolds number of 218,000 and a tip Mach number of 0.23. The blade is set to a collective pitch angle of 7.3◦, which resulted in a blade loading (CT /s) of 0.066. Classical and snapshot techniques of POD are applied to a helical vortex filament, both of which revealed similar characteristics of the dominant modes. Two different techniques (G1 and geometric center methods) of wander correction are applied to test the sensitivity of the low-dimensional characteristics using POD. Using the G1 method, POD revealed that an elliptic instability dominated the energy spectrum of the velocity fluctuations within the tip vortex. However, at early vortex ages an axisymmetric mode, which is found to perform vortex roll-up, is found to be equally dominant. Further, the spatial structures of the most energetic modes derived from POD are found to be sensitive to the choice of the centering technique used.
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A. Canchero, Tinney, C. E., Murray, N. E., and Ruf, J. H., “

Low-dimensional acoustic structures in the near-field of clustered rocket nozzles

,” in 168th Meeting of the Acoustical Society of America, 2014, vol. 136:2167. Publisher's VersionAbstract
The plume and acoustic field produced by a cluster of two and four rocket nozzles is visualized by way of retroreflective shadowgraphy. Both steady state and transient operations of the nozzles (start-up and shut-down) were conducted in the fully-anechoic chamber and open jet facility of The University of Texas at Austin. The laboratory scale rocket nozzles comprise thrust-optimized parabolic (TOP) contours, which during start-up, experience free shock separated flow, restricted shock separated flow, and an “end-effects regime” prior to flowing full. Shadowgraphy images are first compared with several RANS simulations during steady operations. A proper orthogonal decomposition (POD) of various regions in the shadowgraphy images is then performed to elucidate the prominent features residing in the supersonic annular flow region, the acoustic near field and the interaction zone that resides between the nozzle plumes. Synchronized surveys of the acoustic loads produced in close vicinity to the rocket clusters are compared to the low-order shadowgraphy images in order to identify the various mechanisms within the near-field that are responsible for generating sound.
C. E. Tinney and Baars, W. J., “

Where are the nonlinearities in jet noise?

,” in 168th Meeting of the Acoustical Society of America, Indianapolis, 2014, vol. 136:2101. Publisher's VersionAbstract
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)].
G. Mack, Tinney, C. E., and Ruf, J., “

Scaling metrics for predicting rocket noise

,” in 168th Meeting of the Acoustical Society of America, 2014, vol. 136:2168. Publisher's VersionAbstract
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.
R. Fievet and Tinney, C. E., “Nonlinear acoustic distortion in supersonic lab-scaled jet vicinity,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-fievet.pdf
W. J. Baars, Tinney, C. E., and Hamilton, M. F., “Challenges associated with studying nonlinear distortion of acoustic waveforms emitted by high-speed jets,” 43rd International Congress on Noise Control Engineering. Australian Acoustical Society, Melbourne, Australia, 2014.Abstract
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.
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G. Mack and Tinney, C. E., “Scaling metrics for accurate prediction of rocket noise,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-mack.pdf
S. M. Mula and Tinney, C. E., “Stability and turbulence characteristics of a spiraling vortex filament using proper orthogonal decomposition,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-mula.pdf
R. Rojo, Tinney, C. E., and Ruf, J. H., “End-effects-regime in full scale and lab scale rocket nozzles,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-rojo.pdf
A. Canchero, Tinney, C. E., and Murray, N. E., “Retroreflective shadowgraphy of clustered rocket nozzles,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-canchero.pdf
J. H. Stephenson and Tinney, C. E., “Extracting blade vortex interactions from helicopter acoustic signals,” 2014 Texas Fluid Dynamics Meeting. 2014.PDF icon a2014tfdm-stephenson.pdf
S. M. Mula, Cameron, C. G., Tinney, C. E., and Sirohi, J., “Low-dimensional characteristics of tip vortices from a coaxial rotor in hover,” American Helicopter Society 70th Annual Forum. Montreal, Canada, 2014.PDF icon c2014ahs-montrealmula.pdf
J. H. Stephenson and Tinney, C. E., “Extracting blade vortex interactions from using continuous wavelet transforms,” American Helicopter Society 70th Annual Forum. Montreal, Canada, 2014.PDF icon c2014ahs-montrealstephenson.pdf
B. W. Donald, Baars, W. J., Tinney, C. E., and Ruf, J. H., “Sound produced by large area ratio rocket nozzles during fixed and transient operations,” AIAA Journal, vol. 52, no. 7, pp. 1474-1485, 2014.Abstract
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.
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A. Karpatne, Sirohi, J., Mula, S., and Tinney, C. E., “Vortex ring model of tip vortex aperiodicity in a hovering helicopter rotor,” Journal of Fluids Engineering, vol. 136, no. 7, 071104, pp. 1-9, 2014.Abstract
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
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W. J. Baars, Tinney, C. E., Wochner, M. S., and Hamilton, M., “On cumulative nonlinear acoustic waveform distortions from high-speed jets,” Journal of Fluid Mechanics, vol. 749, pp. 331-366, 2014.Abstract
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.
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W. J. Baars and Tinney, C. E., “POD-based Spectral Higher-order Stochastic Estimation,” Physics of Fluids, vol. 26:055112, pp. 1-20, 2014.Abstract
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.
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