Application of Embedded Thermophones Toward Tonal Noise Cancelation in Small-Scale Ducted Fan

Aircraft noise is the most significant cause of adverse community reactions related to the operation and expansion of airports [1,2]. Therefore, limiting or reducing the number of people affected by significant aircraft noise is one of the most important tasks of modern civil aviation. Among different contributors to noise, the tonal content has a greater contribution due to regulatory definitions associated with perceived noise level and its attenuation characteristics, with the largest contributor being the aero-acoustics of rotor–stator interaction at the engine fan [3], as depicted in Fig. 1. In the last 40 years, aircraft noise has decreased by 20 dB, and the perceived noise was diminished by a factor of four. This achievement is owing to the technological shift from turbojets to high bypass turbofans, in addition to clear-sighted efficient regulatory framework at national and international levels.

Nevertheless, noise is still among the potential environmental concerns for airports, and it will likely remain to be an obstacle for their future expansion capability (e.g., new airport development, new runways construction, and increase of incoming and departing traffic) [5]. To illustrate it, Elliff et al. [6] highlighted a petition concerning Berlin Tegel Airport, wherein residents living directly near the airport have voiced grievances about the escalating number of flights over recent years. Subsequent studies have disclosed that residential areas in close proximity to the airport are impacted by aircraft-generated noise surpassing 55 dB. Baliles [7] highlighted noise concerns as a prominent factor contributing to the limited approval of new airport and runway projects in the United States over the past two decades. Additionally, the author observes that in Europe, similar concerns have resulted in the postponement or cancelation of several significant aviation projects, such as the construction of a new runway at Frankfurt. In Ref. [8], the authors emphasized the importance of mitigating aircraft noise as a pivotal component of sustainable development policies within the aviation sector. Beyond these issues, aircraft noise significantly disrupts both the sleep patterns and quality of rest for passengers and residents in the vicinity of airports, which could potentially lead to health deterioration [9]. Along these lines, Advisory Council for Aeronautics Research in Europe (ACARE) has quantified the objectives in its strategic regulatory agenda. The goals are to reduce perceived levels by 50% (10 dB reduction for each new aircraft generation) and to reach 65 $LDEN$ (day/evening/night average sound level) on the outer limit of airports [10]. These ambitious objectives provide a clear motivation toward revolutionary noise reduction research.

Most of the fan noise mechanisms are well-established and they include interactions of rotor fan blade-tip with the inlet-duct turbulent boundary layer [11], of the eddies along the airfoil surface with the shear layer in the trailing edge [12], and of rotor wake with downstream outlet guide vanes [13]. A typical fan noise consists of a broadband spectrum, with a superimposed succession of high-pitched discrete frequency components and their harmonics. Rather than broadband noise reduction, minimization of the low-frequency tonal content from the fan is more impactful considering that it travels greater distances un-attenuated compared to other frequencies from different sources in a dry environment [14]. Moreover, this is exactly why the noise reduction regulations are written in terms of effective perceived noise level, which further penalizes tonal peaks.

Among the early features used to reduce fan noise, lined porous surfaces with resonant cavities are implemented to absorb a part of the generated noise spectrum through dissipation mechanisms. In addition, some of the contemporary design methods toward noise reduction include lowering the tip speed or modifying the blade shape to reduce shock strength, wake management to avoid strong turbulent mixing, increasing rotor–stator axial gap to promote natural decay of wakes, and installation of inversely scarfed inlet to reflect most of the sound away from the ground [15]. However, modern passive technologies alone are either insufficient or induce too large of an aerodynamic penalty in order to satisfy the increasing regulatory demands.

With advancements in manufacturing technologies for electrodynamic and piezo-electric actuators, there have been significant efforts undertaken to actively reduce the tonal noise component of fan acoustics. In the realm of developing active noise cancelation (ANC) technology for turbofan engines, NASA has consistently been at the forefront, conducting numerous experimental campaigns in the renowned Advanced Noise Control Fan (ANCF) testbed at NASA Glenn Research Center [16–18]. Notably, the work of Curtis [16] stands out as it marks the first demonstration of active noise cancelation utilizing vane-mounted actuators. The findings of this study indicate a significant reduction in tonal noise in the far field, diminishing the total tone levels by over 6 dB with far-field sound pressure level reductions of up to 17 dB. Another intriguing approach is documented by Sutliff et al. [18], where the authors explore rotor trailing edge blowing to counteract the periodic velocity fluctuations, a primary source of tonal noise generation. While this study yielded reductions in tonal noise, it also resulted in a notable increase in broadband noise. In addition to active control algorithms, NASA ANCF also spearheaded passive control technologies for overall turbofan noise reduction [19]. Observations revealed a decrement of approximately 4 dB in effective perceived noise levels at certain angles, and acoustic results scaled up to a future twin-engine aircraft configuration indicate a potential reduction of 3 EPNdB—a significant milestone in line with NASA Aerospace Technology (AST) initiative goals. Similarly, pioneering EU-funded RANTAC and RESOUND programs, and associated integration efforts in SILENCE(R) and OPENAIR [20,21], have demonstrated noise reduction levels of up to 10 dB at specific far field angles. Gee and Sommerfeldt demonstrated active noise cancelation at multiple harmonics of a compact cooling fan using acoustically compact co-planar sources [22]. Modeling study demonstrated that additional reduction in sound pressure levels was possible by symmetrically placing more than three acoustically compact sources. Although this is an important study, the placement of the anti-noise sources and the form factor associated with them renders this approach unsuitable for on-source powered noise cancelation. Further studies were conducted by Monson et al. in order to make the system more compact and improve its efficiency [23]. However, the issue with the footprint remained prominent.

These innovative works have solved the majority of the control-related issues associated with the application of distributed ANC systems in turbomachines. Considering that rotor wake–stator interaction is the dominant fan noise source [17,24,25], this approach may hold the key toward eliminating tonal turbomachinery noise. The tonal noise is mainly the rotor–stator interaction noise that is generated due to the velocity deficit which is caused by the viscous wakes of the rotor blades [24]. Tonal noises are a major part of the overall noise spectra and a source of great annoyance [25], owing to the significant amplitude difference between tonal and broadband noise spectra. Thus, reduction in the harmonic content of the wake will result in lower amplitudes in fan noise tonal components, thereby reducing overall perceived noise level. However, the major issue that prevents large-scale implementation of ANC is associated with the speaker technology itself. The existence of moving parts in conventional vibro-mechanical speakers, along with their miniaturization, presents significant challenges, and their design is inherently fragile, requires clearance gaps around diaphragm boundaries, and is not suitable for the aero-engine environment at the present time.

In contrast to the vibro-acoustic transducers, the concept of a truly static sound emitter would address all these potential issues. The enabling technology is a surface-deposited motionless thermo-acoustic transducer, comprising of a periodically Joule-heated electrically conductive thin layer, deposited directly on the noise source itself. Pressure field stimulation and sound production via Joule heating has been studied since the late nineteenth century [26]. The term “thermophone” was introduced a few decades later to describe a device that transforms the frequency-dependent thermal oscillations into acoustic waves [27–29]. Thermophones behave as electrical resistors, where an alternating electrical current is converted to produce surface heat flux fluctuations and, consequently, pressure waves in the surrounding fluid, absent of mechanical motion [30]. Potential advantages of these heat-flux transducers include ease of manufacturing, flexibility, broad range of frequency response, and absence of resonances. During the turn of the twenty-first century, there has been a renewed interest in thermophones within the scientific community. Advanced designs, including suspended arrays of aluminum wires, carbon nanotubes, and graphene, are developed to explore the efficiency and performance capabilities of these heat flux-based sound sources [31,32]. These recent advancements have facilitated the evolution of contemporary thermophone designs, making it more feasible to utilize thermo-acoustic transducers in powered noise control systems for turbofan engines.

In the pursuit of innovative solutions for active noise cancelation, thermophones have emerged as a compelling alternative to traditional vibro-mechanical transducers. Recent contributions have advanced the development of high-power carbon nanotube thin-film thermophones [33,34], showcasing their potential for active noise control in exhaust ducts [35] with compact designs and exceptional acoustic performance. The importance of thermophone and substrate thermodynamic properties has been highlighted [36], in particular for high-power sound generation and scalability considerations [37]. Among others, these studies highlight the potential of thermophones in noise mitigation applications, particularly in environments where conventional actuators are impractical.

Along these lines, expanding on recent studies of the coauthors that showcased the potential of thermophones to create non-localized destructive interference on sound emitted by vibro-acoustic sources [38,39], the current effort focuses on experimental demonstration of a thermo-acoustic transducer that is embedded on the outlet guide vane of a small-scale electric ducted fan toward utilizing it in an aero-acoustic tonal-noise cancelation scenario.

To demonstrate feasibility of ANC in an aero-acoustic scenario, a dedicated test facility is constructed using an off-the-shelf small-scale electrically powered ducted single-stage fan, which has a diameter of 120 mm, rotor with 12 blades, and is driven by a motor with power rating of 6300 W. For the sake of simplicity, only a single stator vane has a thermophone transducer deposited on it and is mounted in the fan to demonstrate cancelation of rotor–stator interaction acoustics, Fig. 2. Mounting of a single stator blade forces the planar mode to dominate aero-acoustics of the setup [40], thereby simplifying the experimental procedure. Moreover, the actual source of the noise is identified via cross-correlation beamforming technique ( Appendix).

Then, the fan's speed is controlled by an electronic speed controller (ESC), which is powered via an external DC power supply (Keysight 6032A). The rpm is measured by a laser tachometer (TTI LT-880) that is fixed in a vertical position with respect to the rotor hub. An encoder with 12 equidistant reflective spots is placed on the rotor's hub and is aligned such that each reflective spot represents the location of an individual blade in the fan rotor. The acoustic signature of the fan is measured by two pre-amplified microphones (GRAS 40BE and GRAS 26CB-HT, connected to ENDEVCO Model 133 signal conditioner), one of which is fixed in front of the fan as a reference microphone and the other one samples pressure variations at different locations around the fan in order to measure azimuthal directivity. After completing directivity measurements, the positions of both sensors are fixed at 0 rad and $5π/6$ rad, respectively. A function generator (Tektronix AFG 3102) creates the necessary thermophone input signals, which are amplified by a 10 kW amplifier (PKN XE-10000). The function generator outputs are sinusoidal waves with frequencies and phases tuned based on experimental campaign requirements. To maintain repeatability, the incidence point of the tachometer's laser is kept constant throughout the experimental campaign and the tachometer is used as a reference for triggering the function generator. The current through the thermo-acoustic transducer is measured via RIEDON SSA0100 sensor and all relevant signals are sampled and recorded by a National Instruments data acquisition system (NI cDAQ-9189 equipped with NI-9223 high-speed voltage input modules). The average thermophone input power is determined by multiplying the root mean square values of the measured input current and voltage. Note that this approach is valid only because the tested thermophone is shown to be predominantly resistive by observing that the current and voltage are consistently in phase within 1.5 deg, yielding a power cosine factor of 0.9997. An in-house labview code is used for monitoring and controlling the experimental setup, as well as for acquiring data. The detailed specifications of the experimental setup are summarized in Table 1 and depicted schematically in Fig. 3.

The thermo-acoustic coating used in the scope of the present effort is manufactured based on the guidelines outlined in Ref. [36]. Since efficient thermophones require the bulk of the energy to remain within the active layer, electrical insulation must be maintained between the transducer and the stator vane. For the sake of simplicity, the original stator of the electric ducted fan installed on the test bench is reproduced from glass mica ceramic. When manufacturing the active layer, it is important that thermal effusivity (⁠$ρCpk$⁠, where $ρ,Cp$⁠, and k are the density, the volumetric heat capacity, and the thermal conductivity, respectively) remains low and that it does not oxidize during the heating process. Numerous materials are evaluated in the scope of assessing thermo-acoustic transducer performance [36,38,39]. As a compromise between electro-thermo-acoustic conversion efficiency and durability, a 100 nm thick leaf of platinum (⁠$ρ=24.45g/cm3$⁠, $Cp≅.250J/g⋅K$⁠, [42], and $k≅25W/m⋅K$ [43]) is used to form the thermophone on top of the stator vane. To promote its adhesion to the base layer, a high-temperature silicone paste (Wurth Super RTV Silicon with thermal properties from specification sheet: $ρ=1.25g/cm3$⁠, $Cp≅1.46J/g⋅K$⁠, and $k=0.2W/m⋅K$⁠) is applied on the vane and cured at 100 °C for two hours. Then, after applying the conductive platinum film, the curing process is repeated.

Finally, to establish electrical contact with the thermophone layer, thin nickel strips are used as leads. The strips are attached to the substrate using small screws, and are supported by graphite gaskets, which protect the thermophone layer from wear and tear. The leads are then connected to electrical wires and to the amplifier that completes the circuit and provides current flow. The overall structure of the thermo-acoustic transducer attached to the stator vane is illustrated in Fig. 5.

A typical acoustic signature of fan rotor–stator interaction consists of fundamental blade pass frequency (BPF) and its harmonics, superimposed on a broadband noise. Since these tonal peaks have major influence on perceived noise levels, the present aim is to demonstrate the feasibility of global noise reduction via attenuation of maximal peak level. Furthermore, the generality of the cancelation is verified by placing two microphones in differing locations, which are maintained during the entirety of the measurements. The pre-amplified microphones are individually calibrated using GRAS 42AB sound calibrator; and after completing directivity measurements they are placed 420 mm directly upstream of the rotor along the central axis, and 420 mm radially away at $5π/6$ rad position. The positions are chosen after studying the directivity of tonal noises in both the excited and un-excited cases using the setup described in Fig. 4. The microphones are considered to be placed in the acoustic far-field as the measurement distance to the source is longer than two wavelengths, based on the fundamental BPF. From here on, the two microphones are denoted as “Mic 1” and “Mic 2,” respectively. The measured voltage signals are converted to pressure through the calibration and represented in logarithmic scale according to $SPL(dB)=20log10P/Po$⁠, where $Po=20μPa$⁠.

During the experiments, the thermo-acoustic emitter is supplied with sinusoidal signals created by the function generator, which are synchronized with the fan's rotation via reference tachometer pulses. These sinusoidal voltage inputs induce periodic thermal oscillations in the thermophone layer. Due to the quadratic relationship between power dissipation and voltage in a predominantly resistive system (where reactive components are negligible), the thermal power oscillates at twice the input frequency. This frequency doubling is leveraged to align the thermo-acoustic output with the fan noise. Then, the function generator produces a series of sine pulses, when its burst mode is triggered by the movement of the fan. In the meanwhile, the thermophone and fan input signals, the tachometer readings, and the acoustic signature are measured by the two microphones are recorded. Before conducting the ANC experiments, the baseline fan noise at differing speed levels and thermophone sound pressure levels at a range of power and frequency inputs are recorded. Then, at each fan rpm setting, the thermophone is powered by a sine waveform with a constant peak-to-peak voltage and frequency equivalent to the first harmonic of BPF, while varying the relative phase with steps of $π/18$ in the range of –2π to 2π. The data are sampled at each phase increment, resulting in 73 datasets for each constant speed.

After microphone data are acquired in the time domain, it undergoes processing, which includes data truncation, ensemble averaging, and fast Fourier transformation (FFT) to frequency domain. All microphone data obtained for a unique combination of fan speed and thermophone input phase are divided into individual fan revolutions using the tachometer output. However, due to small fluctuations in ESC output, the fan speed varies, and at fixed acquisition frequency, each revolution has a different number of sampled points. Then, all subsets are interpolated to include the same number of points, according to guidelines in Ref. [44]. In the following, the data are ensemble averaged over the revolution, the resultant signal is repeatedly stacked end-to-end in a periodic manner to form the length of the original dataset. Lastly, FFT algorithm is applied to the time-series data to convert it into the frequency domain and the amplitude response at the frequency of interest is noted down to be charted against the thermophone input phase angle. The overall data processing methodology is summarized graphically in Fig. 6.

The nominal sampled sound pressure level is $∼75dB$⁠, which corresponds to acoustic pressure of $0.1Pa$⁠. The microphone system sensitivity is $0.91(V/Pa)$ and has an accuracy of 0.5%. Although the microphone noise floor dominates the acoustic pressure uncertainty, the analog acquisition module introduces additional uncertainty, which is related both to sampled value (error of up to 0.02%) and the full-scale range of the device (error of up to 0.01%, which also accounts for quantization effects). Thus, in accordance with equipment accuracy, the uncertainty estimate of acoustic pressure is $0.01Pa$⁠.

For an exemplary microphone acquisition, Fig. 7 provides the variation of phase error for a different number of rotational cycles considered. It can be seen that the minimum in variance is achieved after 300 revolutions at a value around 0.014 rad² which also provides a bound to the relative phase error at ∼0.12 rad. According to the acquisition period, each data set contains more than 600 complete cycles. Then, the number of samples is divided into three bins of 300 revolutions with 50% overlap, and the Fourier transform is conducted on each one, followed by the averaging of the resultant magnitudes.

Without actuating the thermophone transducer, the baseline acoustic signature of the fan rotor with a single stator vane is recorded at three speeds—6250 rpm, 6500 rpm, and 7000 rpm (two runs). Figure 8 charts the pressure amplitude distributed across the various frequencies as measured by Mic 1. The slight frequency shift at first harmonic for 7000 rpm (2793–2800 Hz) in between the runs can be explained by a more stable rotation of the fan in the latter case. The noise generated appears to be mostly tonal, and the blade passing frequency and its harmonics are the highest contributors to power spectra. Moreover, the first harmonic of the BPF appears to have the highest magnitude in the Fourier space for all the cases considered. Additional frequencies appearing in the spectrum are typical of operation of a DC motor, such as the one that powers the fan [45]. The results of this reference measurement are summarized in Table 2 in terms of fan speed, blade passing frequency, its first harmonic, and the sound pressure levels observed by the two microphones. The experimentally measured values are in line with the analytical estimation made based on the theoretical framework established by Kemp and Sears to evaluate the unsteady force distribution in turbomachines [46]. For the sake of completeness, the velocities and volumetric flowrates through the fan are also measured at the three speeds of operation and they are equal to 8.1, 8.3, and 8.7 m/s; and to 0.069, 0.071, and 0.074 m³/s, respectively. The annulus area at the point of measurement is 8.5 × 10⁻³ m².

The phase estimation at the frequencies of interest is conducted via FFT-based phase measurement techniques applied to ensemble-averaged datasets for unexcited conditions. In each fan speed, the phase calculations result in consistent phase values, independent of microphone angular position. The phase calculation at the frequency of 2793 Hz (first BPF harmonic at 7000 rpm) for two microphones placed at different angular positions (0 rad and 5π/6 rad) is charted in Fig. 9. As indicated by Allan variance analysis, after sampling 300 cycles, the phase acquired by the microphones is consistent within 0.58–0.63 rad range, with standard deviation of 0.06 rad.

Then, a preliminary performance test is conducted to evaluate the baseline thermo-acoustic performance of the transducer. Absent of fan rotation, the thermophone is actuated at power levels of 15, 35, 55 W for discrete tonal frequencies spanning 1500–5000 Hz. The acoustic response of the stator-deposited thermophone at the location of the sampling microphones (0 rad and 5π/6 rad) is charted in Fig. 10. In this case, the power levels are constrained in order to preserve the structural integrity of the transducer in the absence of the beneficial convective cooling effect of the fan. Nevertheless, it can be observed that there is a general increase in acoustic response at frequencies above 2000 Hz. Along these lines, in the scope of this experiment, the thermophone is operated at frequencies that target the first harmonic of blade passing, which anyhow contains the highest tonal magnitude. Moreover, the directivity response of the thermophone is measured around the fan at a fixed distance of 420 mm using the approach described in Fig. 4. The directivity for a particular frequency of 2800 Hz is shown in Fig. 11.

In following, the fan is maintained at 7000 rpm and the angular position of Mic 2 is continuously shifted to measure the directivity of the first BPF harmonic. First, the thermophone is disabled and datasets are recorded at each position in unexcited conditions. Then, the datasets are ensemble averaged, and processed via FFT to determine the phases corresponding to the frequency of interest (2793 Hz). Finally, the thermophone is enabled, its input power is adjusted to 60 W, and its phase is tuned to have a difference of $π$ rad with respect to the phase of unexcited case. New datasets are recorded in excited conditions, processed using same data analysis approach and are contrasted with the non-excited case to assess the reduction in amplitude of the first harmonic.

Figure 12(a) illustrates amplitudes observed at the first harmonic of the BPF at 2793 Hz, depicting both un-excited (represented by dashed lines) and excited (shown as solid lines) conditions across various microphone placements. During the experiments, both the un-excited and excited cases are evaluated twice at each point in order to observe any temporal changes in directivity pattern. [0–2π] and [2π–4π] markers indicate the first and second evaluations for each point, respectively. The points are located equidistantly 420 mm away from the stator blade in a circular pattern. Figure 12(b) displays the corresponding phase calculations at 2793 Hz for the un-excited scenario. The upper and lower error bounds specify the maximum limit of error in phase calculations. These bounds are determined from Allan variance analysis to be ±0.06 rad, with a total uncertainty band of 0.12 rad. Data acquisition involves azimuthal plane measurements, with microphone repositioning at π/6 rad intervals, while maintaining constant fan speed of 7000 rpm and constant microphone distance from the stator blade. Subsequently, sound pressure level amplitudes at the first harmonic of the BPF and associated phase angles under un-excited conditions are derived from the recorded data using in-house matlab code. These computations utilize ensemble averaged FFT techniques, outlined in Fig. 6. The obtained SPL data are charted in Fig. 12(a) and demonstrate the global nature of the cancelation. It is further supported by Fig. 12(b), which showcases the calculated phase angles derived from recorded data. The calculated phase angles across distinct microphone placements fall within a ±0.06 rad uncertainty bounds and are consistent with predictions from Allan variance analysis. This particular measurement confirms the noise source's behavior indeed closely resembles that of a monopole. Although dipole radiation can be expected from thin airfoils of the fan when subjected to harmonic oscillations [47], due to non-zero angle of attack, the tonal noise spectrum is dominated by one of the stator sides, resulting in asymmetric dipole that acts closer to a monopole [48,49].

Based on the findings of the directivity measurements, two measurement locations (0 rad and 5π/6 rad, respectively) are selected and are sufficient to assess the noise cancelation effect, due to their high stability and significant amplitude response. Thus, in the following measurements, both the thermophone and the fan are operated simultaneously, and the findings are presented for the selected microphone locations.

For different experimental datasets, the rotational speed is regulated, while the thermophone frequency is set at the first harmonic of blade passing and the power input is adjusted to 60 W in order to roughly match the aero-acoustic noise generated by the rotor–stator interaction. The aggregate pressure emanating from the fan aero-acoustics and thermophone output is measured, while the thermophone input phase is varied in the range of $[−2π,2π]$ with respect to the tachometer signal. For all the fan speeds, Fig. 13 portrays the sound pressure level at the thermophone excitation frequency as measured by the two microphones in different positions. The notation “PP” corresponds to positive input phase angles in the range of $[0,2π]$ rad. The notation “NP” in the legend relates to negative input phase angles in the range of $[−2π,0]$⁠, which are wrapped around to their equivalent values within the positive range (by adding $2π$⁠); this step ensures the repeatability of the relative phase variation. Lastly, “FF” denotes the free field measurement of the fan acoustic signature, when the thermophone is not operating, and the baseline tonal noise is generated solely by the rotor–stator interactions.

For negative and positive relative phase positions, the data overlay one another within an average accuracy of ∼25 mPa, resulting in deviations of ∼1.4 dB in the chart. Within observed fan speed fluctuations, the tonal noise is periodic in time. For all speeds, at around 0 and 2π phase angles, there is an increase in observed pressure fluctuations of roughly 6 dB, compared to the free field sound pressure level without thermophone actuation. Doubling the acoustic signature, this is clearly indicative of constructive interference. As the relative phase is varied toward the angle of $π$⁠, a consistent decrease of ∼6–13 dB is observed depending on the microphone location and the operating speed. For the speed levels of 6250 rpm, 6500 rpm, and 7000 rpm, the sound pressure levels are reduced by 4.5-, 4.3-, and 2.3-fold, respectively. Based on the logarithmic scaling, this represents an average of ∼3.7-fold reduction in tonal noise. This is particularly visible in the lower fan operating rpm for which the constant power input to the thermophone better matches with the stator aero-acoustic tonal noise level. Lastly, despite the two different angular positions of the reference microphones, the constructive and destructive interferences are picked up by both sensors at the same input phase of the thermophone. This highlights the global nature of constructive and destructive interferences, rather than them being a local phenomenon.

Then, the spectra of fan noise are considered when the thermophone is generating destructive interference at relative phase angle of π. As observed by Mic 1, the magnitude of pressure fluctuations is charted for the three fan speeds, Fig. 14. When compared to equivalent unexcited reference case depicted in Fig. 8, the main difference in the pressure amplitude distribution is the reduction in peak located at the first harmonic of the blade pass frequency. This is expected considering that the thermophone is only actuated at this tonal frequency.

Comparing Figs. 8 and 14, there is a change in the amplitudes at discrete frequencies between 0 Hz and 250 Hz for the case of 7000 rpm, which prompted a second set of measurements. After resampling the acoustic data, new dataset was acquired for 7000 rpm, and the results of the measurements are charted in Fig. 15. It can be observed that, at around 7000 rpm, the discrete frequency SPL in the 0–250 Hz range is almost the same in both the excited and unexcited cases. Moreover, the deviations in discrete non-tonal frequencies are within the maximum calculated uncertainty limit of 0.03 Pa (at 7000 rpm).

The present research endeavor demonstrates the conceptual feasibility of implementing direct on-source global tonal noise cancelation scheme on ducted fan configurations, where a significant contribution to noise stems from tonal aero-acoustic rotor–stator interactions. Furthermore, the applicability of thermophones as purely stationary and robust noise source is portrayed in the framework of non-localized acoustic destructive interference. An experimental setup is constructed to integrate a small-scale electric ducted fan with thermophone-coated stator vane, and to conduct sound pressure level measurements with particular focus on diminishing the tonal content associated with the highest peak at the first harmonic of blade pass frequency. The sound pressure level of the thermophone is chosen to provide roughly equivalent amplitude to that of the targeted fan frequency. Sweeping across the relative phase across the $[−2π,2π]$ range with respect to the tachometer signal, coherent constructive, and destructive interferences are observed for varying fan speeds. The consistent phase relationship across two microphones at differing locations confirms the global nature of the phenomenon, not being concentrated to a spatial locality.

Toward future growth of this thermo-acoustic active noise cancelation approach to higher technology readiness levels, similar experiments are to be conducted in the presence of multiple stators equipped with thermophones, actuated with polyphonic multi-tone signals with a blade-to-blade lag equivalent to the inter-blade phase angle. Moreover, even when the oscillatory pressure loading subjected to the stationary vanes is matched by the thermo-acoustic transducers, there still exists a rotating unsteady pressure field that arises from the potential effect of the stator inducing a time-variant back pressure condition on the rotor airfoils. Therefore, the complete annihilation of tonal blade pass frequency and its harmonics may also require deposition of similar thermophone transducers in the rotating frame of reference, transferring electrical power through slip-rings. Finally, with expected advancements in thermophone design and manufacturing techniques, it is anticipated that future generations of thermo-acoustic sources will become increasingly efficient, which will make it possible to maintain structural integrity while scaling the sound pressure output to match modern transonic fan levels.

This present research effort has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program (Grant Agreement No. 853096, ThermoTON).

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

The source of the harmonic tonal noise in the fan domain is identified by implementing cross-correlation beamforming technique [52]. This approach relies on obtaining the generalized cross-correlation of the signals, applying spatial weighting functions, and finally, estimating the source location via time difference of arrival. The measurements are recorded via an array of seven microphones. The schematic of the array and its position with respect to the ducted fan appears in Fig. 16. The microphones are placed in a circumference with a radius of 0.1 m at a plane 0.05 m away from the fan's rotor assembly. The beamforming results for this configuration are charted in Fig. 17 for an exemplary frequency of 2800 Hz (first harmonic of the blade passing frequency for fan speed of 7000 rpm). The data from the beamforming experiment indicate that the source of harmonic tonal noise (thick circle in Fig. 17) is indeed situated in close proximity to the stator blade position (thick line in Fig. 17(left)). Hence, it can be concluded that the stator blade is indeed the source of the harmonic tonal noise.