Publications by Type: Journal Article

C. E. Tinney, Panickar, P., and Vogel, P., “Aeroacoustics of a Planar Multistream Supersonic Nozzle with Aft Deck and Sidewalls,” AIAA Journal, pp. 1-12, 2018.Abstract
The exhaust plume produced by a planar, multistream supersonic nozzle is studied with and without the effect of an aft deck and sidewalls. Measurements encompass static wall pressure of the internal flow, shadowgraphy images of the exhaust plume, and far-field acoustics for a range of pressure ratios. An experimentally validated Reynolds averaged Navier–Stokes model of the internal flow is then used to reveal how the aft deck and sidewalls allow the expanding gas to persist longer, thereby extending the location of the separation shock. Where the far-field sound is concerned, the aft deck and sidewall attachments cause a noticeable reduction in overall sound pressure levels by as much as 5 dB at shallow angles and sideline observer positions. Many of the tones associated with screech and broadband shock associated noise are also absent with the addition of the aft deck and sidewalls.
C. E. Tinney and Sirohi, J., “Multirotor Drone Noise at Static Thrust,” AIAA Journal, vol. 56, no. 7, pp. 2816-2826, 2018.Abstract
A first principles understanding of the sound field produced by multirotor drones in hover is presented. Propeller diameters ranging from 8 to 12 in. are examined and with configurations comprising an isolated rotor, quadcopter, and hexacopter configuration. The drone pitch, defined as the ratio of drone diameter to rotor diameter, is the same for all multirotor configurations and is valued at 2.25. A six-degree-of-freedom load cell is used to assess the aerodynamic performance of each configuration, whereas an azimuthal array of 1∕2 in. microphones, placed between two and three hub-center diameters from the drone center, is used to assess the acoustic near field. The analysis is performed using standard statistical metrics such as sound pressure level and overall sound pressure level and is presented to demonstrate the relationship between the number of rotors, the drone rotor size, and its aerodynamic performance (thrust) relative to the near-field acoustics.
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J. H. Stephenson and Tinney, C. E., “Extracting Blade-Vortex Interactions Using Continuous Wavelet Transforms,” Journal of the American Helicopter Society, vol. 62, no. 022001, pp. 1-10, 2017.Abstract
A framework for using continuous wavelet transforms to isolate and extract blade–vortex interaction noise from helicopter acoustic signals is described. The extraction method allows for the investigation of blade–vortex interactions independent of other sound sources. Experimentally acquired acoustic data from full-scale helicopter flyover tests are first transformed into time-frequency space through the wavelet transformation, with blade–vortex interactions identified and filtered by their high-amplitude, high-frequency impulsive content. The filtered wavelet coefficients are then used to create a pressure signal solely related to blade–vortex interactions. Analysis of a synthetic data set is conducted and shows that blade–vortex interactions can be accurately extracted so long as the blade–vortex interaction wavelet energy is comparable to the wavelet energy in the main rotor harmonic.
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R. Rojo, Tinney, C. E., and Ruf, J., “Effect of stagger on the vibroacoustic loads from clustered rockets,” AIAA Journal, vol. 54, no. 11, pp. 3588-3597, 2016.Abstract
The effect of stagger startup on the vibroacoustic loads that form during the end-effects regime of clustered rockets is studied using both full-scale (hot-gas) and laboratory-scale (cold-gas) data with vehicle geometry. Both configurations comprise three nozzles with thrust-optimized parabolic contours that undergo free-shock separated flow and restricted-shock separated flow as well as an end-effects regime before flowing full. Acoustic pressure waveforms recorded at the base of the nozzle cluster are analyzed using various statistical metrics as well as time-frequency analysis. The findings reveal a significant reduction in end-effects regime loads when engine startups are staggered. However, regardless of stagger, both the skewness and kurtosis of the acoustic pressure time derivative elevate to the same levels, thereby demonstrating the intermittence and impulsiveness of the acoustic waveforms during the end effects regime.
W. J. Baars, Tinney, C. E., and Hamilton, M. F., “A piecewise spreading regime model for calculating effective Gol'dberg numbers for supersonic jet noise.,” AIAA Journal, vol. 54, no. 9, pp. 2833-2842, 2016.Abstract
A method for calculating the effective Gol’dberg number for diverging waveforms is presented, which leveragesknown features of a high-speed jet and its associated sound field. The approach employs a ray tube situated along the Mach wave angle where the sound field is not only most intense, but advances from undergoing cylindrical decay to spherical decay. Unlike other efforts, a “piecewise-spreading regime” model is employed, which yields, separately, effective Gol’dberg numbers for the cylindrically and spherically spreading regions in the far field. The new approach is applied to a plethora of experimental databases, encompassing both laboratory- and full-scale jet noise studies. The findings demonstrate how cumulative nonlinear distortion is expected to form in the acoustic near field of laboratory scale round jets where pressure amplitudes decay cylindrically; waveform distortion is not expected in the acoustic far field where waveform amplitudes diverge spherically. On the other hand, where full-scale jet studies are concerned, effective Gol’dberg number calculations demonstrate how cumulative waveform distortion is significant in both the cylindrical- and spherical-spreading regimes. The laboratory-scale studies also reveal a pronounced sensitivity to humidity conditions, relative to the full-scale counterpart.
A. Canchero, Tinney, C. E., Murray, N., and Ruf, J. H., “Acoustic imaging of clustered rocket nozzles undergoing end-effects.,” AIAA Journal, vol. 54, no. 12, pp. 3778-3786, 2016.Abstract
A nonintrusive measure of the exhaust plume and immediate sound field produced by a cluster of two thrust optimized parabolic contour nozzles is studied during two steady-state conditions. The first condition is at a nozzle pressure ratio of 25, at which point the flow is in a restricted-shock separated state. The second condition is at a nozzle pressure ratio of 37 and is when the flow and internal shock pattern transition rapidly between free-shock separated flow and the end-effects regime. These end-effects regime pulsations produce significant vibroacoustic loads due to the intermittent breathing of the last trapped annular separation bubble with the ambient. The exhaust plumes and surrounding sound field are first visualized by way of retroreflective shadowgraphy. Radon transforms of the spatially resolved shadowgraphy images are then used to characterize the statistical behavior of the acoustic wave fronts that reside within the hydrodynamic periphery of the nozzle flow. The findings reveal quantitative evidence of the sources of most intense vibroacoustic loads during the end-effects regime of clustered rockets.
A. Canchero, Tinney, C. E., Murray, N., and Ruf, J. H., “Flow and acoustics of clustered rockets during startup,” AIAA Journal, vol. 54, no. 5, pp. 1660-1669, 2016.Abstract
The plume produced by a cluster of two large area-ratio thrust-optimized paraboliccontour nozzles is visualized over a range of nozzle pressure ratios by way of retrore-flective shadowgraphy. Both nozzles exhibit free-shock separated flow, restricted-shockseparated flow and an end-effects regime prior to flowing full. Transient (startup) op-erations of the nozzles are studied with the primary focus being the pulsations thatform during the end-effects regime. This occurs at a pressure ratio of 37 for thesenozzles and is associated with elevated sound levels in the immediate vicinity of thenozzles and vehicle. The shadowgraphy images reveal the formation of turbulent largescale structures, on the order of the nozzle diameter, during the end-effects regime.These large scale structures are driven by the intermittent opening of the last trappedannular separation bubble to the ambient and grow rapidly within the first two nozzlediameters.
R. Fievet, Tinney, C. E., Baars, W. J., and Hamilton, M. F., “Coalescence in the sound field of a laboratory-scale supersonic jet,” AIAA Journal, DOI: 10.2514/1.J054252, vol. 54, no. 1, pp. 254-265, 2016.Abstract
The spatial evolution of acoustic waveforms produced by a laboratory-scale Mach 3 jet are investigated using both 1∕4 in. and 1∕8 in. pressure field microphones located along rays emanating from the postpotential 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. Various statistical metrics are examined along the peak emission path, where they are shown to undergo rapid changes within 2m from the source region. An experimentally validated wave-packet model is then used to confirm the location where the pressure amplitude along the peak emission path transitions from cylindrical to spherical decay. Various source amplitudes, provided by the wave-packet model, are then used to estimate shock formation distance and Gol’dberg numbers for diverging waves. The findings suggest that cumulative nonlinear distortion is likely to occur at laboratory scale near the jet flow, where the waveform amplitude decays cylindrically, but less likely to occur farther from the jet flow, where the waveform amplitude decays spherically. Direct inspection of the raw time series reveals how steepened waveforms are generated by rogue like waves that form from the constructive interference of waves from neighboring sources as opposed to classical cumulative nonlinear distortion.
W. J. Baars, Tinney, C. E., and Ruf, J. H., “Non-stationary shock motion unsteadiness in an axisymmetric geometry with pressure gradient,” Experiments in Fluids, DOI: 10.1007/s00348-015-1958-y, vol. 56, no. 92, pp. 1-18, 2015.Abstract
Shock wave / boundary layer interaction is studied in a large area ratio axisymmetric nozzle comprising a design exit Mach number of 5.58. Shock motion unsteadiness is captured by way of the dynamic wall pressure and is evaluated during overexpanded operations up to a nozzle pressure ratio of 65. Stationary SWBLI is first considered at a nozzle pressure ratio of 28.7 such that the internal flow structure is in a restricted-shock separated state; the mean position of the annular separation shock resides at a fixed position. Conditional averages of the wall pressure fluctuations show how the motion of the incipient separation shock is out of phase with pressure fluctuations measured in the separated region downstream of the shock; pressure decreases when the shock moves downstream and vice versa. This is indicative of a long intermittent region, in terms of the boundary layer thickness, as the observed phenomena can be explained by translating the static wall pressure profile along with the shock motion. Non-stationary SWBLI is then considered by increasing the nozzle pressure ratio over time (transient startup). Under these conditions, the shock pattern varies in strength and structure as it sweeps through the nozzle. A time-frequency analyses of the fluctuating wall pressure during the non-stationary operations, and at the same location that the stationary unsteadiness is analysed, reveals a similar spectral footprint. However, for relatively slower start-ups, the amplitude of the unsteadiness is reduced by a factor of about seven. The findings demonstrate how the rate at which the nozzle pressure ratio increases can have a significant influence on the amplitude of the unsteady shock foot motion.
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.
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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J. H. Stephenson, Tinney, C. E., Watts, M. E., and Greenwood, E., “Time frequency analysis of sound from a maneuvering rotorcraft,” Journal of Sound and Vibration, vol. 333, no. 21, pp. 5324-5339, 2014.Abstract
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.
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W. J. Baars and Tinney, C. E., “Shock-structures in the acoustic field of a Mach 3 jet with crackle,” Journal of Sound and Vibration, vol. 333, no. 12, pp. 2539-2553, 2014.Abstract
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.
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S. M. Mula and Tinney, C. E., “Dynamical characteristics of the tip vortex from a four bladed rotor in hover,” Experiments in Fluids, vol. 54:1600, 2013.Abstract
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.
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W. J. Baars and Tinney, C. E., “Transient wall pressures in an overexpanded and large area ratio nozzle,” Experiments in Fluids, vol. 54:1468, pp. 1-17, 2013.Abstract
Surveys of the fluctuating wall pressure were conducted on a sub-scale parabolic-contour rocket nozzle to infer an understanding of the flow and shock structure pattern during fixed and transient operations of the nozzle. During start-up, the nozzle is highly overexpanded, which results in unsteady wall pressure signatures driven by shock foot unsteadiness. Wall pressure data are first analyzed using spatial Fourier transformations to extract the azimuthal modes during various operating states. A time-frequency analysis of the temporal azimuthal mode coefficients is then used to characterize the time-dependent spectral behavior of the wall pressure signatures during start-up. For both fixed and transient operations of the nozzle, the axisymmetric breathing mode (m = 0) comprises most of the resolved energy. As for the transient operations alone, slight deviations in ramp rate are shown to considerably influence the amount of unsteadiness that the nozzle wall is exposed to, even though the general spectral and temporal features remain similar. In particular, increased ramp rates result in increased wall pressure intensity. Secondly, three major low-frequency events (f [ 400 Hz) were observed during start-up and are attributed to: (1) FSS to RSS transition, (2) the passing of the reattachment line from the first separation bubble, and (3) the ‘end-effects regime’. The last of these refers to a condition where a trapped separation bubble opens intermittently to ambient at the nozzle lip.
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C. N. Dolder, Haberman, M. R., and Tinney, C. E., “Turbulent wall pressure reduction using suction control,” Experiments in Fluids, vol. 54:1436, pp. 1-37, 2013.Abstract
A study of the fluctuating wall pressure beneath a 2-d turbulent boundary layer was conducted in a water tunnel with Reynolds numbers, based on momentum thickness, ranging between 2,100 and 4,300. The boundary layer was perturbed with steady mild suction to assess the effect of upstream suction on the fluctuating wall pressure measured downstream of the suction slit. Wall pressure signatures were captured using a custom-fabricated piezoceramic array with d? values ranging between 64 and 107. Likewise, the velocity field was measured with a laser Doppler velocimeter with l? values ranging between 4.0 and 6.7 for the lowest and highest Reh investigated. Estimates of the wall pressure spectra revealed a noticeable hydrodynamic peak that scaled reasonably well with outer variables and with an average convective speed of 75% of the free stream velocity (based on unconditionally sampled pressure time series). Two boundary layer suction control cases were studied corresponding to suction rates of less then 30% of the boundary layer momentum. The findings reveal how only modest amounts of suction are needed to reduce upwards 50–60% of the hydrodynamic ridge.
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C. N. Dolder, Haberman, M. R., and Tinney, C. E., “A laboratory scale piezoelectric array for underwater measurements of the fluctuating wall pressure beneath turbulent boundary layers,” Measurement Science Technology, vol. 23, no. 4, pp. 1-11, 2012.Abstract
To capture the full spectrum of the fluctuating wall pressure beneath a turbulent boundary layer (TBL) provides a unique challenge in transducer design. This paper discusses the design, construction and testing of an array of surface-mounted piezoelectric ceramic elements with the goal of having both the spatial resolution and the frequency bandwidth to accurately sense the low-frequency, low-wavenumber events beneath a TBL at moderately low Reynolds numbers. The array is constructed from twenty 1.27 cm tall prismatic rods with 0.18 cm × 0.16 cm cross-section made of Navy type II piezoelectric ceramic material. Calibration was performed by comparing the response of a Navy H56 precision-calibrated hydrophone to the outputs of each element on the array for a given input from a Navy J9 projector. The elements show an average sensitivity of −184 dB (re: 1 V μPa−1) and are assembled with a centre-to-centre spacing of 0.2 cm. Measurements of the fluctuating wall pressure below a 2d TBL with Reynolds numbers (based on momentum thickness) ranging from 2100 to 4300 show that the dimensions of the elements are between 64 and 107 viscous length units, respectively. A spatial and temporal footprint of the fluctuating wall pressure reveals convective speeds averaging 75% of the free stream velocity.
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