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NASA NTRS2016

Wind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics

Experimental techniques to measure rotorcraft aerodynamic performance are widely used. However, most of them are either unable to capture interference effects from bodies, or require an extremely large computational budget. The objective of the present research is to develop an XV-15 Tiltrotor Research Aircraft rotor model for investigation of wind tunnel wall interference using a novel Computational Fluid Dynamics (CFD) solver for rotorcraft, RotCFD. In RotCFD, a mid-fidelity Unsteady Reynolds Averaged Navier-Stokes (URANS) solver is used with an incompressible flow model and a realizable k-ε turbulence model. The rotor is, however, not modeled using a computationally expensive, unsteady viscous body-fitted grid, but is instead modeled using a blade-element model (BEM) with a momentum source approach. Various flight modes of the XV-15 isolated rotor, including hover, tilt, and airplane mode, have been simulated and correlated to existing experimental and theoretical data. The rotor model is subsequently used for wind tunnel wall interference simulations in the National Full-Scale Aerodynamics Complex (NFAC) at Ames Research Center in California. The results from the validation of the isolated rotor performance showed good correlation with experimental and theoretical data. The results were on par with known theoretical analyses. In RotCFD the setup, grid generation, and running of cases is faster than many CFD codes, which makes it a useful engineering tool. Performance predictions need not be as accurate as high-fidelity CFD codes, as long as wall effects can be properly simulated. For both test sections of the NFAC wall, interference was examined by simulating the XV-15 rotor in the test section of the wind tunnel and with an identical grid but extended boundaries in free field. Both cases were also examined with an isolated rotor or with the rotor mounted on the modeled geometry of the Tiltrotor Test Rig (TTR). A "quasi linear trim" was used to trim the thrust for the rotor to compare the power as a unique variable. Power differences between free field and wind tunnel cases were found from -7 to 0 percent in the 80- by 120-Foot Wind Tunnel and -1.6 to 4.8 percent in the 40- by 80-Foot Wind Tunnel, depending on the TTR orientation, tunnel velocity, and blade setting. The TTR will be used in 2016 to test the Bell 609 rotor in a similar fashion to the research in this report.

CFD↗

NASA NTRS2019

Experimental Forward Flight Rotor Performance Testing from Terrestrial to Martian Atmospheric Densities

With the recent interest in Martian exploration using Unmanned Aerial Vehicles (UAV), an experimental study was conducted to investigate rotor performance at Martian atmospheric conditions. Both simulation and testing of rotors is vital for the evaluation of performance and behavior of rotor, especially for operations at Martian atmospheric densities and pressures. Testing and measuring rotor forward flight performance at Martian atmospheric conditions is a relatively unexplored area. Therefore, an experimental study was performed in a wind tunnel to investigate helicopter forward flight performance and to demonstrate successful rotor operation at Martian atmospheric densities. This work was a continuation of the first ever wind tunnel test of a simulated rotorcraft in forward flight at Martian atmospheric densities. A test was conducted in a facility, which could be evacuated to the atmospheric pressure and density of Mars. A 40-in diameter rotor, roughly approximating the scale of the proposed Mars Helicopter design by the NASA Jet Propulsion Laboratory (JPL), was tested in forward flight at Mars atmospheric pressure at the NASA Ames Planetary Aeolian Laboratory (PAL). In this forward flight testing, the drive system of the Martian Surface Wind Tunnel (MARSWIT) was never turned on. The goal of this experiment was to collect rotor thrust, rotational speed, power, torque, and wind speed measurements. Subsequently, these results can be used for correlation with simulated cases using a mid-fidelity Computational Fluid Dynamics (CFD) simulation. Rotor thrust and power seem to decrease approximately proportional to the decrease in density. However, the Reynolds number has an effect on rotor performance that might also be contributing to the change in thrust and power. This effect plays a vital role in rotor performance at reduced pressure that cannot be neglected in the simulation. Despite the challenges involved in testing at a large difference of atmospheric densities between Earth and Mars, repeatable data is obtained in all the measurements at Martian atmospheric conditions.

Martian↗

NASA NTRSDate not supplied

Overview of Rotor Hover Performance Capabilities at Low Reynolds Number for Mars Exploration

The Evolutionary aLgorithm for Iterative Studies of Aeromechanics (ELISA) software was developed in support of the Rotorcraft Optimization for the Advancement of Mars eXploration (ROAMX) project. ELISA was developed to enable aerodynamic rotor hover optimization for low Reynolds number flows in the Mars atmosphere. ELISA comprises two modules. The first module is dedicated to airfoil optimization and allows for the creation of multi-objective Pareto optimal (PO) airfoil sets with the airfoil performance evaluation performed using OVERFLOW. The second module is dedicated to rotor hover performance optimization and generates multi-objective PO rotor sets with the rotor performance evaluation performed using the comprehensive analysis code CAMRAD II. This paper presents recent updates to the ELISA optimization toolset. The airfoil module now includes variation in section Reynolds number, alongside simultaneous maximization of section lift and minimization of section drag. Consequently, the rotor optimization module can query PO airfoil sets (as a function of section lift, drag, and Reynolds number) and generate PO C81 decks tailored to specific Reynolds numbers, eliminating the need for adequate initial chord guesses and allowing for arbitrary rotor solidities to be studied. Furthermore, the rotor optimization has been extended to incorporate a third dimension, alongside maximization of blade loading and minimization of rotor power. This enables optimization across a relevant density range on Mars, presenting the lowest power rotor hover geometry, for each attainable blade loading, for each density. The goal of this work is to present the relevance of recent updates to the ELISA optimization toolset, by showing full rotor hover optimization using unconventional airfoils across a practical Mars density range, and by presenting various optimizations for changing blade numbers with unconstrained solidity in the Mars atmosphere.

Rotor↗

NASA NTRS1973

Nonlinear transient analysis of multi-mass flexible rotors - theory and applications

The equations of motion necessary to compute the transient response of multi-mass flexible rotors are formulated to include unbalance, rotor acceleration, and flexible damped nonlinear bearing stations. A method of calculating the unbalance response of flexible rotors from a modified Myklestad-Prohl technique is discussed in connection with the method of solution for the transient response. Several special cases of simplified rotor-bearing systems are presented and analyzed for steady-state response, stability, and transient behavior. These simplified rotor models produce extensive design information necessary to insure stable performance to elastic mounted rotor-bearing systems under varying levels and forms of excitation. The nonlinear journal bearing force expressions derived from the short bearing approximation are utilized in the study of the stability and transient response of the floating bush squeeze damper support system. Both rigid and flexible rotor models are studied, and results indicate that the stability of flexible rotors supported by journal bearings can be greatly improved by the use of squeeze damper supports. Results from linearized stability studies of flexible rotors indicate that a tuned support system can greatly improve the performance of the units from the standpoint of unbalanced response and impact loading. Extensive stability and design charts may be readily produced for given rotor specifications by the computer codes presented in this analysis.

Kirk, R. G.↗

NASA NTRS1982

Stall induced instability of a teetered rotor

Recent tests on the 38m Mod-0 horizontal experimental wind turbine yielded quantitative information on stall induced instability of a teetered rotor. Tests were conducted on rotor blades with NACA 230 series and NACA 643-618 airfoils at low rotor speeds to produce high angles of attack at relatively low wind speeds and power levels. The behavior of the rotor shows good agreement with predicted rotor response based on blade angle of attack calculations and airfoil section properties. The untwisted blades with the 64 series airfoil sections had a slower rate of onset of rotor instability when compared with the twisted 230 series blades, but high teeter angles and teeter stop impacts were experienced with both rotors as wind speeds increased to produce high angles of attack on the outboard portion of the blade. The relative importance of blade twist and airfoil section stall characteristics on the rate of onset of rotor unstability with increasing wind speed was not established however. Blade pitch was shown to be effective in eliminating rotor instability at the expense of some loss in rotor performance near rated wind speed.

Glasgow, J. C.↗

NASA NTRS1984

Hover test of a full-scale hingeless helicopter rotor: Aeroelastic stability, performance and loads data

A hover test of a full-scale, hingeless rotor system was conducted in the NASA Ames 40- by 80-foot wind tunnel. The rotor was tested on the Ames rotor test apparatus. Rotor aeroelastic stability, performance, and loads at various rotational speeds and thrust coefficients were investigated. The primary objective was to determine the inplane stability characteristics of the rotor system. Rotor inplane damping data were obtained for operation between 350 and 425 rpm (design speed), and for thurst coefficients between 0.0 and 0.12. The rotor was stable for all conditions tested. At constant rotor rotational speed, a minimum inplane dampling level was obtained at a thrust coefficient approximately = 0.02. At constant rotor lift, a minimum in rotor inplane damping was measured at 400 rpm.

Peterson, R. L.↗

NASA NTRS1986

Aeroelastic considerations for torsionally soft rotors

A research study was initiated to systematically determine the impact of selected blade tip geometric parameters on conformable rotor performance and loads characteristics. The model articulated rotors included baseline and torsionally soft blades with interchangeable tips. Seven blade tip designs were evaluated on the baseline rotor and six tip designs were tested on the torsionally soft blades. The designs incorporated a systemmatic variation in geometric parameters including sweep, taper, and anhedral. The rotors were evaluated in the NASA Langley Transonic Dynamics Tunnel at several advance ratios, lift and propulsive force values, and tip Mach numbers. A track sensitivity study was also conducted at several advance ratios for both rotors. Based on the test results, tip parameter variations generated significant rotor performance and loads differences for both baseline and torsionally soft blades. Azimuthal variation of elastic twist generated by variations in the tip parameters strongly correlated with rotor performance and loads, but the magnitude of advancing blade elastic twist did not. In addition, fixed system vibratory loads and rotor track for potential conformable rotor candidates appears very sensitive to parametric rotor changes.

Mantay, W. R.↗

NASA NTRS1984

Aeroelastic considerations for torsionally soft rotors

Mantay, W. R.↗

NASA NTRS1993

Aeroelastic response and stability of tiltrotors with elastically-coupled composite rotor blades

There is a potential for improving the performance and aeroelastic stability of tiltrotors through the use of elastically-coupled composite rotor blades. To study the characteristics of tiltrotors with these types of rotor blades it is necessary to formulate a new analysis which has the capabilities of modeling both a tiltrotor configuration and an anisotropic rotor blade. Background for these formulations is established in two preliminary investigations. In the first, the influence of several system design parameters on tiltrotor aeroelastic stability is examined for the high-speed axial flight mode using a newly-developed rigid-blade analysis with an elastic wing finite element model. The second preliminary investigation addresses the accuracy of using a one-dimensional beam analysis to predict frequencies of elastically-coupled highly-twisted rotor blades. Important aspects of the new aeroelastic formulations are the inclusion of a large steady pylon angle which controls tilt of the rotor system with respect to the airflow, the inclusion of elastic pitch-lag coupling terms related to rotor precone, the inclusion of hub-related degrees of freedom which enable modeling of a gimballed rotor system and engine drive-train dynamics, and additional elastic coupling terms which enable modeling of the anisotropic features for both the rotor blades and the tiltrotor wing. Accuracy of the new tiltrotor analysis is demonstrated by a comparison of the results produced for a baseline case with analytical and experimental results reported in the open literature. Two investigations of elastically tailored blades on a baseline tiltrotor are then conducted. One investigation shows that elastic bending-twist coupling of the rotor blade is a very effective means for increasing the flutter velocity of a tiltrotor, and the magnitude of coupling required does not have an adverse effect on performance or blade loads. The second investigation shows that passive blade twist control via elastic extension-twist coupling of the rotor blade has the capability of significantly improving tiltrotor aerodynamic performance. This concept, however, is shown to have, in general, a negative impact on stability characteristics.

Nixon, Mark W.↗

NASA NTRS1994

Higher harmonic control analysis for vibration reduction of helicopter rotor systems

An advanced higher harmonic control (HHC) analysis has been developed and applied to investigate its effect on vibration reduction levels, blade and control system fatigue loads, rotor performance, and power requirements of servo-actuators. The analysis is based on a finite element method in space and time. A nonlinear time domain unsteady aerodynamic model, based on the indicial response formulation, is used to calculate the airloads. The rotor induced inflow is computed using a free wake model. The vehicle trim controls and blade steady responses are solved as one coupled solution using a modified Newton method. A linear frequency-domain quasi-steady transfer matrix is used to relate the harmonics of the vibratory hub loads to the harmonics of the HHC inputs. Optimal HHC is calculated from the minimization of the vibratory hub loads expressed in term of a quadratic performance index. Predicted vibratory hub shears are correlated with wind tunnel data. The fixed-gain HHC controller suppresses completely the vibratory hub shears for most of steady or quasi-steady flight conditions. HHC actuator amplitudes and power increase significantly at high forward speeds (above 100 knots). Due to the applied HHC, the blade torsional stresses and control loads are increased substantially. For flight conditions where the blades are stalled considerably, the HHC input-output model is quite nonlinear. For such cases, the adaptive-gain controller is effective in suppressing vibratory hub loads, even though HHC may actually increase stall areas on the rotor disk. The fixed-gain controller performs poorly for such flight conditions. Comparison study of different rotor systems indicates that a soft-inplane hingeless rotor requires less actuator power at high speeds (above 130 knots) than an articulated rotor, and a stiff-inplane hingeless rotor generally requires more actuator power than an articulated or a soft-inplane hingeless rotor. Parametric studies for a hingeless rotor operating in a transition flight regime and for an articulated rotor operating at the level-flight boundary (high speed and high thrust conditions) indicate that blade parameters including flap, lag, torsion stiffness distributions, linear pretwist, chordwise offset of center-of-mass from elastic axis and chordwise offset of elastic axis from aerodynamic center can be selected to minimize the actuator power requirements for HHC.

Nguyen, Khanh Q.↗

NASA NTRS1997

Rotor-Fuselage Interaction: Analysis and Validation with Experiment

The problem of rotor-fuselage aerodynamic interaction has to be considered in industry applications from various aspects. First, in order to increase helicopter speed and reduce operational costs, rotorcraft tend to be more and more compact, with a main rotor closer to the fuselage surface. This creates significant perturbations both on the main rotor and on the fuselage, including steady and unsteady effects due to blade and wake passage and perturbed inflow at the rotor disk. Furthermore,the main rotor wake affects the tail boom, empennage and anti-torque system. This has important consequences for helicopter control and vibrations at low speeds and also on tail rotor acoustics (main rotor wake-tail rotor interactions). This report describes the US Army-France MOD cooperative work on this problem from both the theoretical and experimental aspects. Using experimental 3D velocity field and fuselage surface pressure measurements, three codes that model the interactions of a helicopter rotor with a fuselage are compared. These comparisons demonstrate some of the strengths and weaknesses of current models for the combined rotor-fuselage analysis.

Berry, John D.↗

NASA NTRS2002

Psychoacoustic Testing of Modulated Blade Spacing for Main Rotors

Psychoacoustic testing of simulated helicopter main rotor noise is described, and the subjective results are presented. The objective of these tests was to evaluate the potential acoustic benefits of main rotors with modulated (uneven) blade spacing. Sound simulations were prepared for six main rotor configurations. A baseline 4-blade main rotor with regular blade spacing was based on the Bell Model 427 helicopter. A 5-blade main rotor with regular spacing was designed to approximate the performance of the 427, but at reduced tipspeed. Four modulated rotors - one with "optimum" spacing and three alternate configurations - were derived from the 5 bladed regular spacing rotor. The sounds were played to 2 subjects at a time, with care being taken in the speaker selection and placement to ensure that the sounds were identical for each subject. A total of 40 subjects participated. For each rotor configuration, the listeners were asked to evaluate the sounds in terms of noisiness. The test results indicate little to no "annoyance" benefit for the modulated blade spacing. In general, the subjects preferred the sound of the 5-blade regular spaced rotor over any of the modulated ones. A conclusion is that modulated blade spacing is not a promising design feature to reduce the annoyance for helicopter main rotors.

Edwards, Bryan↗

NASA NTRS2008

Rotor Performance at High Advance Ratio: Theory versus Test

Five analytical tools have been used to study rotor performance at high advance ratio. One is representative of autogyro rotor theory in 1934 and four are representative of helicopter rotor theory in 2008. The five theories are measured against three sets of well documented, full-scale, isolated rotor performance experiments. The major finding of this study is that the decades spent by many rotorcraft theoreticians to improve prediction of basic rotor aerodynamic performance has paid off. This payoff, illustrated by comparing the CAMRAD II comprehensive code and Wheatley & Bailey theory to H-34 test data, shows that rational rotor lift to drag ratios are now predictable. The 1934 theory predicted L/D ratios as high as 15. CAMRAD II predictions compared well with H-34 test data having L/D ratios more on the order of 7 to 9. However, the detailed examination of the selected codes compared to H-34 test data indicates that not one of the codes can predict to engineering accuracy above an advance ratio of 0.62 the control positions and shaft angle of attack required for a given lift. There is no full-scale rotor performance data available for advance ratios above 1.0 and extrapolation of currently available data to advance ratios on the order of 2.0 is unreasonable despite the needs of future rotorcraft. Therefore, it is recommended that an overly strong full-scale rotor blade set be obtained and tested in a suitable wind tunnel to at least an advance ratio of 2.5. A tail rotor from a Sikorsky CH-53 or other large single rotor helicopter should be adequate for this exploratory experiment.

Harris, Franklin D.↗

NASA NTRS2009

SMART Rotor Development and Wind-Tunnel Test

Boeing and a team from Air Force, NASA, Army, Massachusetts Institute of Technology, University of California at Los Angeles, and University of Maryland have successfully completed a wind-tunnel test of the smart material actuated rotor technology (SMART) rotor in the 40- by 80-foot wind-tunnel of the National Full-Scale Aerodynamic Complex at NASA Ames Research Center, figure 1. The SMART rotor is a full-scale, five-bladed bearingless MD 900 helicopter rotor modified with a piezoelectric-actuated trailing-edge flap on each blade. The development effort included design, fabrication, and component testing of the rotor blades, the trailing-edge flaps, the piezoelectric actuators, the switching power amplifiers, the actuator control system, and the data/power system. Development of the smart rotor culminated in a whirl-tower hover test which demonstrated the functionality, robustness, and required authority of the active flap system. The eleven-week wind tunnel test program evaluated the forward flight characteristics of the active-flap rotor, gathered data to validate state-of-the-art codes for rotor noise analysis, and quantified the effects of open- and closed-loop active-flap control on rotor loads, noise, and performance. The test demonstrated on-blade smart material control of flaps on a full-scale rotor for the first time in a wind tunnel. The effectiveness and the reliability of the flap actuation system were successfully demonstrated in more than 60 hours of wind-tunnel testing. The data acquired and lessons learned will be instrumental in maturing this technology and transitioning it into production. The development effort, test hardware, wind-tunnel test program, and test results will be presented in the full paper.

Lau, Benton H.↗

NASA NTRS2013

Wind Tunnel Measurements of the Wake of a Full-Scale UH-60A Rotor in Forward Flight

A full-scale UH-60A rotor was tested in the National Full-Scale Aerodynamics Complex (NFAC) 40- by 80-Foot Wind Tunnel in May 2010. The test was designed to acquire a suite of measurements to validate state-of-the-art modeling tools. Measurements include blade airloads (from a single pressure-instrumented blade), blade structural loads (strain gages), rotor performance (rotor balance and torque measurements), blade deformation (stereo-photogrammetry), and rotor wake measurements (Particle Image Velocimetry (PIV) and Retro-reflective Backward Oriented Schlieren (RBOS)). During the test, PIV measurements of flow field velocities were acquired in a stationary cross-flow plane located on the advancing side of the rotor disk at approximately 90 deg rotor azimuth. At each test condition, blade position relative to the measurement plane was varied. The region of interest (ROI) was 4-ft high by 14-ft wide and covered the outer half of the blade radius. Although PIV measurements were acquired in only one plane, much information can be gleaned by studying the rotor wake trajectory in this plane, especially when such measurements are augmented by blade airloads and RBOS data. This paper will provide a comparison between PIV and RBOS measurements of tip vortex position and vortex filament orientation for multiple rotor test conditions. Blade displacement measurements over the complete rotor disk will also be presented documenting blade-to-blade differences in tip-path-plane and providing additional information for correlation with PIV and RBOS measurements of tip vortex location. In addition, PIV measurements of tip vortex core diameter and strength will be presented. Vortex strength will be compared with measurements of maximum bound circulation on the rotor blade determined from pressure distributions obtained from 235 pressure sensors distributed over 9 radial stations.

Wadcock, Alan J.↗

NASA NTRS2013

Open Rotor Aeroacoustic Installation Effects for Conventional and Unconventional Airframes

As extensive experimental campaign was performed to study the aeroacoustic installation effects of an open rotor with respect to both a conventional tube and wing type airframe and an unconventional hybrid wing body airframe. The open rotor rig had two counter rotating rows of blades each with eight blades of a design originally flight tested in the 1980s. The aeroacoustic installation effects measured in an aeroacoustic wind tunnel included those from flow effects due to inflow distortion or wake interaction and acoustic propagation effects such as shielding and reflection. The objective of the test campaign was to quantify the installation effects for a wide range of parameters and configurations derived from the two airframe types. For the conventional airframe, the open rotor was positioned in increments in front of and then over the main wing and then in positions representative of tail mounted aircraft with a conventional tail, a T-tail and a U-tail. The interaction of the wake of the open rotor as well as acoustic scattering results in an increase of about 10 dB when the rotor is positioned in front of the main wing. When positioned over the main wing a substantial amount of noise reduction is obtained and this is also observed for tail-mounted installations with a large U-tail. For the hybrid wing body airframe, the open rotor was positioned over the airframe along the centerline as well as off-center representing a twin engine location. A primary result was the documentation of the noise reduction from shielding as a function of the location of the open rotor upstream of the trailing edge of the hybrid wing body. The effects from vertical surfaces and elevon deflection were also measured. Acoustic lining was specially designed and inserted flush with the elevon and airframe surface, the result was an additional reduction in open rotor noise propagating to the far field microphones. Even with the older blade design used, the experiment provided quantification of the aeroacoustic installation effects for a wide range of open rotor and airframe configurations and can be used with data processing methods to evaluate the aeroacoustic installation effects for open rotors with modern blade designs.

Czech, Michael J.↗

NASA NTRS2018

Tri-Rotor Aircraft Capable of Vertical Takeoff and Landing and Transitioning to Forward Flight

Systems, methods, and devices provide a vehicle, such as an aircraft, with rotors configured to function as a tri-copter for vertical takeoff and landing ("VTOL") and a fixed-wing vehicle for forward flight. One rotor may be mounted at a front of the vehicle fuselage on a hinged structure controlled by an actuator to tilt from horizontal to vertical positions. Two additional rotors may be mounted on the horizontal surface of the vehicle tail structure with rotor axes oriented vertically to the fuselage. For forward flight of the vehicle, the front rotor may be rotated down such that the front rotor axis may be oriented horizontally along the fuselage and the front rotor may act as a propeller. For vertical flight, the front rotor may be rotated up such that the front rotor axis may be oriented vertically to the fuselage, while the tail rotors may be activated.

North, David D.↗

NASA NTRSDate not supplied

Broadband Noise Prediction of Two Small Hovering Rotors using FUN3D-ANOPP2

A computational study was performed on two small hovering rotors, the ideally twisted rotor and the optimum hovering 2-bladed rotor, using FUN3D-ANOPP2. The effects of different inviscid upwinding techniques and temporal resolutions on aerodynamic performance and acoustic prediction were compared against experimental data obtained in the Small Hover Anechoic Chamber facility at the NASA Langley Research Center. Decreasing the numerical dissipation with 𝜅 tuning or by using a higher-order inviscid flux reconstruction scheme was shown to improve aerodynamic performance predictions when compared to measured data for most cases. The effect of dissipation on the vorticity field was also seen to influence the amount of turbulence surrounding the vortex core of the first blade-vortex interaction (BVI), the coherence of the second and higher BVI vortex cores, and the downstream breakdown of the rotor wake for both rotor geometries. Tonal and broadband noise predictions from simulation cases with lower dissipation were seen to agree better with the experiment for the ideally twisted rotor, whereas temporal resolution differences had negligible impact on the broadband noise results. Similar fundamental BPF directivity patterns were obtained by all simulation cases for the optimum hovering 2-bladed rotor, while the most accurate 2*BPF directivity trend, compared to the experiment, was predicted by the lower-dissipation case at the coarse temporal resolution, albeit with an amplitude underprediction. Broadband noise spectral roll-off behavior was seen to occur at a higher frequency when using a finer temporal resolution for the optimum hovering 2-bladed rotor, unlike for the ideally twisted rotor geometry. The broadband noise prediction for the optimum hovering 2-bladed rotor from the higher-dissipation case at the coarse temporal resolution was also seen to predict a tone centered around approximately 8.5 kHz, which was similar in amplitude to the measured tone around 16.5 kHz.

Christopher S. Thurman↗