Hover performance and acoustics of a 35% scale notional electric vertical take-off and landing rotor operating at moderate Reynolds numbers and Mach tip speeds below 0.4 is presented. Changes to blade count (2-bladed up to 5-bladed) are evaluated for the same blade shape and for a range of rotor collective pitch angles and rotor speeds. Increasing blade count generates substantial changes in thrust and torque at higher rotor collectives, whereas the 5-bladed rotor is only slightly more efficient than the 2-bladed rotor for the same changes in rotor collective. Changes to torque loads are also greater than changes to thrust gains as blade count increases. As for the sound field, all traditional source of noise (thickness-, loading-, and broadband-noise) are observed. When the sound field is scaled and then weighted (dBA) for human perception, the spatial topography reveals dipole-like behavior for all rotor operating conditions. A separation between tonal and broadband sources of perceived noise reveals how broadband noise is the dominant source of perceived noise for all blade number combinations at low rotor collective pitch angles. At higher rotor collectives, both tonal and broadband noise contribute equally to total perceived noise with the tonal noise contributing more for the 5-bladed rotor.

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The trade-space between hover performance and acoustics for different blade loading conditions of a 35% scale notional eVTOL rotor is characterized. The database comprises systematic changes to rotor collective, Mach tip speed, and rotor solidity using identically shaped blades. Thrust and torque levels are shown to follow a log-linear relationship over the range of Mach tip speeds tested while blade loading coefficient and rotor figure of merit appear unaffected by Reynolds numbers at this scale. The sound field is evaluated separately for changes to rotor solidity and Mach tip speed with an emphasis on observers located below the rotor disk plane. The trends demonstrate that higher rotor solidity configurations may be capable of generating less total noise than lower solidity configurations for the same thrust setting. Human perception effects are then considered using the D-weighting function while non-linear metrics like skewness and kurtosis are used as annoyance indicators. The D-weighted trends provide evidence that, above a certain thrust threshold, the rotor collective and Mach tip speed required to achieve a desired thrust will generate the same perceived noise regardless of rotor solidity. However the higher-order metrics reveal how, for the same rotor figure of merit at high disk loading conditions, significant reductions in both metrics are achieved by increasing rotor solidity.

Formulations for the gappy-proper orthogonal decomposition (gappy-POD) comprising both homogeneous and heterogeneous forms are developed and exercised using a large eddy simulation of the unsteady ship airwake. The homogeneous form is derived by simply replacing the full sensor set with a gappy sensor set when computing the POD expansion coefficients and is the least accurate of all available forms. As for the heterogeneous forms, these leverage an error minimization method in order to generate a collection of transfer functions to estimate the full sensor set from the gappy sensor set; this follows the stochastic estimation technique proposed by Adrian (Phys. Fluids, Vol. 22, 1979). Unlike the original heterogeneous form of the gappy-POD derived by Everson and Sirovich, (J. Opt. Soc. America, Vol. 12, 1995), two alternative forms are derived for instances where both the gappy sensor set and the POD covariance matrix share the same vector space. Different sensor selection methods are evaluated using a greedy algorithm in order to reduce the computational expense involved in configuring the gappy sensor set. An evaluation of all available gappy-POD forms in combination with the different sensor selection methods reveal how the alternative heterogeneous forms produce more accurate reconstructions of the unsteady ship airwake with fewer sensors, for a given combination of POD modes. It is also shown that a gappy sensor that provides relatively uniform coverage of the sensor field produces more accurate estimates than one that is localized by a region of space, even when the region of space is concentrated on locations where the most significant changes to the flow dynamic reside. A computer program is provided in the Appendix for computing all homogeneous and heterogeneous forms of the gappy-POD using conventional kernels.

The gappy-POD proposed by Everson and Sirovich (J. Opt. Soc. America, Vol. 12, 1995) is derived to include higher-order terms not previously considered in the error minimization problem. The mathematical framework is provided for all available heterogeneous forms of the technique. The first of these forms applies the gappy sensor set to the eigenvectors and is referred to as the XX-topos form, whereas the second form uses the POD expansion coefficients and is referred to as the XX-chronos form; the naming convention follows the language proposed by Aubry (Theor. Comp. Fluid Dyn., Vol. 12, 1991). A third form, the YX form, is also evaluated and is shown to correspond to the original gappy-POD framework proposed by Everson and Sirovich. The quadratic gappy-POD forms are then scrutinized using spatially and temporally resolved schlieren images of sound waves emanating from the near-field of a Mach 3 jet; these sound waves are Mach waves generating by turbulence in the shear layer being convected at supersonic speeds relative to the ambient field. It is shown that quadratic terms are needed when an extremely limited number of sensors are available and performs best with the XX-chronos form of the technique. A computer program is provided in the Appendix that computes the heterogeneous XX-chronos form of the gappy-POD using conventional kernels to include quadratic terms.

A first principles understanding of the hover performance and acoustics of a 35% scale notional eVTOL rotor is presented. Measurements are acquired in a large acoustically treated enclosure with rotor speeds corresponding to blade tipMach numbers and Reynolds numbers around 0.3 and 5 x 10(5), respectively. Rotor thrust and torque are measured alongside a line array of microphones traversed between 1.0 and 3.5 rotor diameters from the rotor hub; this captures a two-dimensional map of the pressure field generated by this rotor. Blade collectives are varied from 0 deg to 15 deg in 3 deg increments. Different blade number combinations are studied and comprise a 5-blade, 4-blade, and 3-blade setup. Hover performance measurements at different rotor speeds demonstrate Reynolds number independence with a peak figure of merit of 0.75 at 15 deg collective. Acoustic data are projected to a common distance using spherical decay and a hub centered source. The projection demonstrates that the measurements are, for the most part, being captured in the acoustic regions and that the enclosure and sound treatment are adequate for studying rotors of this scale.

Several higher-order statistical metrics are used to evaluate the significance of waveform nonlinearities in the sound field of a laboratory-scale coaxial, corotating rotor in hover. These comprise the magnitude-squared coherence, skewness, and kurtosis of the pressure waveform and its time derivative, number of zero crossings per rotation, a wave steepening factor, and the quadrature spectral density and its integral. A unique feature of this rotor setup is the constructive and destructive interference of sound waves produced by neighboring blades, which are incubators for signal distortion effects. Waveform distortions are evaluated for changes to rotor index angle, the separation distance between the upper and lower rotors, as well as changes to rotor speed for different observer positions. Significant sensitivities in the kurtosis of the pressure waveform and its time derivative, the number of zero crossings, and the integral of the quadrature spectral density are shown for changes in rotor index angle, observer position, and rotor speed; stacking distance appears less important at affecting changes to these metrics. The trade space between these metrics and rotor figure of merit demonstrates how changes to the rotor index angle can invoke relatively small changes in rotor performance while generating large changes in acoustic waveform nonlinearities.

This paper describes a mathematical framework for determining the optimal sensor set location for adequately capturing the sound generated by rotors. The approach leverages the gappy-POD method proposed by Everson and Sirovich [J. Opt. Soc. Am., Vol. 12, 1995, pp. 1657-1664], which first identifies the various mode constituents that make up the first few rotor blade-pass frequency harmonics of the sound-field. The algorithm is developed using a covariance matrix for the POD problem comprising auto- and cross-spectral densities of spatially and temporally resolved sound waves captured by an array of microphones oriented parallel to the axis of a laboratory-scale hovering rotor. Three different forms of the technique are developed and compared. These comprise a homogeneous form and two heterogeneous forms; the heterogeneous forms are referred to as XX-topos and XX-chronos and depends on which term in the error minimization equation is assigned the gappy sensor set. A greedy algorithm is then employed to determine the optimal location of the limited sensor set. The findings are analyzed for different combinations of POD modes and blade-pass frequency harmonics of the sound generated by the hovering rotor.

In a recent article by Tinney, Zhao-Dubuc and Valdez (International Journal of Aeroacoustics, 2023, DOI: 10.1177/1475472X231199186), proper orthogonal decomposition (POD) and the Vold-Kalman order tracking filter (VKF) were combined to evaluate the most energetic signals in the sound field of a coaxial, corotating rotor in hover. The method comprised a covariance matrix for the POD problem that was constructed using auto- and cross-spectral densities of a stationary sensor set. The POD technique isolates structures in space while VKF methods filter structures in time. The current study reconsiders the same unique combination of analysis techniques, but develops the framework using a different form of the covariance matrix for occasions when the stationary sensor set is large, or when a spectral domain representation of the signals is not necessary. As such, this defaults to the conventional form of Lumley’s POD. The combined use of these techniques (conventional POD with Vold-Kalman filters) is then exercised using the same database of the sound-field generated by a coaxial, corotating rotor in hover to study the effect that changes to the rotor index angle has on the sound directed at listeners located below the rotor disk plane. Filtered acoustic waveforms are extracted using the first four spatial POD modes and VKF phasors associated with the first four rotor blade-pass frequency harmonics; these filtered signals are responsible for the impulsive like signatures that drive community annoyance. An assessment of the trade-space between these filtered waveforms and the rotor’s aerodynamic performance demonstrates that an 8% shift in rotor figure of merit is obtainable without changing the sound pressure levels generated by the stacked rotor. Alternatively, 6.3 dB and 4.0 dB reductions in sound pressure levels propagating along the rotor disk plane and below, respectively, can be achieved without any changes to rotor performance.

The design and characterization of a new laboratory-scale rotor test stand for assessing the aerodynamic and acoustic performance of side-by-side synchrophased rotors is described. Each rotor is powered by a dedicated motor that communicates with other motors through a master/slave arrangement. The hardware/software combination is capable of holding angular phase synchronization to within an accuracy of 0.2 deg over sufficiently long periods of time required to capture statistically converged laboratory data. Acoustic measurements using two, side-by-side 18-inch diameter rotor blades (APC model 18x5.5MR-P with two blades per rotor) spinning in a counter-rotating configuration are then captured at four microphone observer locations. This comprises, two observers located at the rotor disk plane perpendicular to- and parallel to the multi-rotor axis, and two located 45 degrees below, also perpendicular to- and parallel to the multi-rotor axis. The findings demonstrate a significant change in the first few rotor harmonics as sound waves progress from causing constructive interference to destructive interference at the different observer locations. Sound pressure levels associated with the first four rotor harmonics are then evaluated during steady operations of the rotors and for all observer positions during systematic changes to the rotor phase over 180 degrees in increments of 10 degrees. The first blade pass frequency harmonic exhibits the most significant change in sound levels with a 30 dB reduction to the rotor disk plane observer when the synchrophased rotors are shifted by 90 degrees, and a 20 dB reduction for the observer located below the rotor disk plane with a 125 degrees phase shift. Albeit, the second and fourth rotor blade pass frequency harmonics are shown to fill in where the first and third rotor harmonics fall off. Thus, the acoustic benefit in the form of an overall noise reduction may not be as great with delayed phase-synchronized rotors. However, the benefit may come more in the form of a broadening of the sound pressure spectrum and an overall flattening of the tonal components that produce impulsive like signatures that are believed to drive community annoyance.

The sound field of hovering rotors has generated tremendous interest in recent years with the prospect of urban air mobility platforms comprising eVTOL type designs. In this presentation, we will review a number of key advancements that have been made with regard to an understanding of the sound field produced by multirotor systems in hover and how it relates to the aerodynamic performance of the rotor. Much of this work is based on laboratory-scale measurements of different configurations starting with multirotor drones comprising quad-copter, hexacopter, and even octocopter arrangements (Tinney and Sirohi, AIAA J., 2018) followed by stacked corotating rotors (Valdez and Tinney, AIAA J., 2022) where the trade-space based on stacking distance, index and angle and rotor speed are evaluated. Of particular interest is the constructive and destructive interference of sound waves from neighboring rotors which augment the first few fundamental rotor harmonics. Methods for characterizing the first few rotor harmonics based on POD-based Vold-Kalman order tracking filters (Tinney etal., Int. J. Aeroacoust., 2023) is presented as well as methods for collapsing the high frequency rotor broadband noise using a moving source model (Tinney et al., AIAA Paper 2023-3222).

An accurate assessment of the vibro-acoustic loads that form during startup of large area ratio rocket nozzles is important for sea-level launch vehicle design and certification. These loads are driven principally by various flow and shock patterns that form inside the nozzle, which are unique to the nozzle contour. This presentation will review a number of laboratory-scale measurements of different nozzle contours and configurations reported by Baars and Tinney, Exp. Fluids, (2013), Donald et al. AIAA Journal (2014), Canchero etal. AIAA Journal (2016), and Rojo et al. AIAA Journal (2016) as it relates to launch platforms of current interest. In particular are the various sources of noise pertaining to transonic resonance, broadband shock associated noise, and the end-effects-regime (EER). The latter of these is unique to the thrust-optimized parabolic contour nozzle as is used on the current Space Launch System vehicle. This EER event occurs when the annular flow structure is in a partial restricted-shock separated (RSS) flow state and is categorized by an onset of relatively low frequency energy driven by intermittent buffeting between RSS flow and partial free shock separated flow at the nozzle lip.

Proper orthogonal decomposition and the Vold-Kalman order tracking filter are combined to evaluate the most energetic components of the sound field produced by a coaxial, co-rotating rotor in hover. The study leverages the database generated by Tinney and Valdez (2020; AIAA J. vol. 58, no. 4) comprising an array of eight stationary microphones oriented to capture the acoustic near-field below the rotor disk plane where ground observers are expected to reside and where concerns over community annoyance are greatest. Changes to rotor conditions focus primarily on rotor speed and index angle (angular separation between the upper and lower rotors), as this has the greatest effect on the sound field produced by stacked rotors by way of the constructive and destructive interference of the sound generated, separately, by the upper and lower rotors. Proper orthogonal decomposition is performed using a kernel constructed from auto and cross-spectral densities of the spatially coherent sound field. The eigenvectors demonstrate the spatial extent of the sound field for discrete frequencies corresponding to the first few blade pass frequency harmonics. In order to improve the clarity and accuracy of the low-order reconstructions, a second generation, Vold-Kalman multi-order tracking filter is employed to isolate discrete frequencies. Relative to conventional spectral filtering methods, the Vold-Kalman filter is performed in the time-domain and is shown to accurately isolate discrete tones while preserving changes to the phase of the signal. Findings from this analysis reveal the effect of index angle on the spatial make-up of the coherent sound field produced by hovering stacked rotors.

High-speed schlieren images of the field surrounding a supersonic jet provide a rich database for testing convolutional neural network (CNN) classification methods due to the presence of many waveform structures of interest. One such structure is waveform coalescence, where waves intersect at small angles, which can lead to increased steepening and nonlinear distortion in the jet near field [Willis et al., AIAA Journal (2023)]. Although waves exhibiting coalescence behavior have been identified in narrow field-of-view (FOV) schlieren images, new methods are needed for large FOV images to improve computational efficiency. This presentation will explore methods to track and classify waves observed in large FOV schlieren images as coalescing or noncoalescing using CNNs. Using transfer learning, pretrained networks can be retrained for this problem, with training data obtained from narrow FOV schlieren or from two-dimensional simulated waveforms using the Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation. The impact of model hyperparameters, choice of pretrained network, image scaling, and other factors on the results of waveform classification by the CNN will be explored. [WAW is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

View Video Presentation: https://doi.org/10.2514/6.2023-0021.vid The coalescence of intersecting Mach waves has been proposed as a significant contributor to acoustic waveform steepening in the near field of a jet, thus providing a potential cause for the observation of more steepened waves in a laboratory-scale jet than predicted by effective Gol'dberg numbers [Baars et al., J. Fluid Mechanics 749 (2014); Fiévet et al., AIAA Journal 54, 254 (2016)]. Recent numerical simulations have demonstrated that the coalescence process can lead to increased steepening [Willis et al., AIAA SciTech Forum (2022)]. Schlieren imaging of a laboratory-scale, Mach 3 jet flow has been used for comparison with simulations based on reduced-order models, but additional examples of coalescing waves were desired that did not depend on turbulence for wave generation. Thus, two experiments have been designed using spark generated waveforms that intersect, either after reflection from a rigid surface or after emanating from a 3D-printed enclosure. Schlieren images and microphone measurements allow for analysis of these waveforms to examine steepening behavior. Additionally, large-eddy simulation (LES) of the same Mach 3 jet flow presents an opportunity to compare behavior of intersecting Mach waves with prior simulations and experimental results. A machine learning algorithm has been trained using transfer learning and then applied to the LES pressure data to identify waveforms of interest for further analysis of coalescence.

POD-based reduced-order models of vortical structures that form in the unsteady wake behind a simple frigate ship are studied using translating coordinates. Unlike traditional POD-based methods where an Eulerian frame of reference is bounded by surfaces through which the evolving flow passes, the use of translating coordinates offers a unique opportunity to quantify changes to the evolving structures over space and time. The challenge then lies in developing robust and user friendly methods for tracking the evolving vortical structures. Three different approaches are examined. The first assumes that structures convect along lines of constant streamlines and computes the streamline dependent convective speed to estimate where the structures are advecting to next. Jittering motions of the vortex, relative to the mean streamlines, show this to be the least accurate approach. A second method is then developed which tracks vortex centers based on locations where the well known λ2 criterion (a Galilean-invariant of the velocity gradient tensor) is maximum. The last approach correlates the bulk motion of the λ2 field of isolated vortices, and is shown to be the most accurate and effective. The efficacy of these tracking methods are based on convergence of the eigenvalues while their low-order reconstructions reveal the different mode numbers that make up the evolving flow structures.

The intersection of Mach waves in the near field of a jet can lead to a phenomenon referred to as coalescence, which is believed to increase acoustic waveform steepening more than predicted by effective Gol'dberg numbers [Baars et al., J. Fluid Mechanics 749, 331 (2014); Fiévet et al., AIAA Journal 54, 254 (2016)]. Recent studies have constructed algorithms to identify coalescing waveforms in narrow field-of-view (FOV) schlieren images, then compared the detected coalescence events to simulations by using reduced-order models [Willis et al., AIAA Journal 61, 2022 (2023)]. Large-FOV images can capture a larger region of the sound field but require a decrease in the imaging frame rate that decreases the effectiveness of previous coalescence-detection algorithms. A new method for coalescence detection is thus desired. Convolutional neural networks are trained using transfer learning and then applied to large-FOV schlieren intensity data to identify waveforms of interest for further analysis of coalescence. Two approaches are compared for network training, one using pressure data and the other using pressure gradient data, both simulated using the Khokhlov-Zabolotskaya-Kuznetzov (KZK) equation. Interacting waves classified as coalescing are examined both in single image frames and in translating coordinates that follow the waves as they propagate.

Laboratory measurements of the acoustic and aerodynamic performance of a highly twisted eighteen-inch diameter two-bladed rotor are evaluated to understand the mechanisms responsible for generating rotor broadband noise from rotors of this scale. Rotor speeds are varied between 30 and 132 revolutions per second, which equates to blade tip Mach numbers between 0.13 and 0.56, and chord-based Reynolds numbers between 6.6 × 10^4 and 2.6 × 10^5, respectively. Microphones are biased towards locations above the rotor disk plane where Doppler effects and noise from the turbulent wake are less likely to corrupt sound measurements, and where the boundary layer structures on the suction side of the blade are likely to be more mature. Harmonics and subharmonics of the blade pass frequency noise are removed to reveal features attributed to both turbulent boundary layer trailing edge noise and, in some instances, separated flow noise. When the blade tip Mach number is greater than 0.3, peak pressures associated with the turbulent boundary layer noise are shown to scale with $M^{4.4}$, and to scale with peak frequencies by $F^{6.7}$. A moving source model is then proposed for localizing positions on the rotor blade where turbulent boundary trailing edge noise is most prominent. The model is empirical and leverages measurements of the boundary layer properties of static airfoils to estimate characteristic scales that are believed to contribute to rotor broadband noise. The moving source model persistently identifies noise sources near the tip of the rotor that migrate towards the rotor hub with increasing rotor speed.