Noise and flow characteristics of a howling internally mixed jet

Abstract

The noise emitted by axisymmetric, dual-stream, internally mixed jets was studied. At a jet Mach number of 0.90, the jet howled loudly (i.e., acoustic tones dominated over the broadband jet noise) for multiple mixing-duct lengths and for both unheated and heated core flows. Particle-image velocimetry data revealed that the jet’s potential core was substantially shortened when the howling occurred and there were intense velocity fluctuations in the jet’s shear layer. Using schlieren images, it was shown the jet’s instability waves were excited at the frequency of the fundamental acoustic tone, suggesting a flow/acoustic interaction was responsible for these observations.

Keywords

jet noise resonance flow/acoustic interactions

Introduction

Internally mixed exhaust systems (see Figure 1(a)) are receiving increased attention for their prospective use on supersonic civilian aircraft (e.g., see Clemens and Gavin¹). Relative to separate-flow systems (see Figure 1(b)), internally mixed jets can offer thrust-specific noise reductions (e.g., see^2–4 for noise studies and^5–7 for thrust considerations). Internal mixing is most effective and practical when features such as corrugations to the core-nozzle lip (i.e., a so-called ‘lobed mixer’) are used to promote mixing inside the nozzle. This paper focuses on an axisymmetric internally mixed system (which we refer to as a confluent nozzle). This nozzle did not possess any mixing-enhancement features, and it was intended as a baseline for future studies. The nozzle system represents a notional exhaust system intended for a future supersonic business jet, with design inputs as described in reference 8.

Jet-noise measurements using confluent nozzles other than the one studied here have been reported in several prior works (e.g., see references^2–4,9–17 listed in reverse chronological order). The reader may wish to note the varied terminology used to refer to confluent nozzles in these references (e.g., Bridges and Wernet⁴ used the term ‘axisymmetric splitter’). Of these references, only Bridges et al.⁹ reported a resonance. This resonance occurred when an external ‘plug’ centerbody was present, the core stream was heated, and both streams were operated at the same total pressure. The resonance was identified as a howling (i.e., acoustic tones were observed above the broadband jet noise) that persisted at all of sub-critical, critical, and super-critical pressure ratios. With both streams operational and total-temperature- and total-pressure-matched (i.e., the flow into the mixing duct was approximately a single stream), the resonance did not occur. Bridges et al.⁹ noted that the resonance was perhaps due to a feedback phenomenon involving the core jet impinging on the final-nozzle lip.

This paper presents extensive noise and corresponding flow measurements of internally mixed jets, with particular emphasis on a set of operating conditions at which tonal acoustic emissions (or howling) and flow oscillations at the same frequency were observed. There are very few experimental data available in the published literature for such phenomena involving internally mixed jets. As will be discussed in this paper’s conclusions, these data were the building block for a recently developed understanding of the underlying aeroacoustic resonance responsible for the phenomena observed here. Computational researchers may view these data as a set of test cases for aeroacoustic resonances of internally mixed jets, which they may attempt to resolve.

The test nozzle

The confluent nozzle used is shown in Figure 2(a), and it comprised two, coaxial flow paths routing two streams of air into a round, 52.58-mm-diameter mixing duct. The area ratio between the upstream plenum chambers and the mixing-duct inlets were in excess of 30:1 for the core stream and 200:1 for the bypass stream. The core nozzle had 40.64-mm exit diameter. The composite flow was expanded through a final, convergent-straight nozzle with a further 1.48:1 area contraction. Figure 2(b) shows a close-up view of the far-downstream portion of the nozzle, along with important nozzle dimensions and coordinate conventions. In this paper, the Cartesian $x - y$ coordinates appear alongside flow measurements and polar $R - θ$ coordinates alongside acoustic measurements. The nozzle’s mixing-duct length is presented in normalized form, $L_{e} / D_{e}$ (where $D_{e} = 43.18$ mm). Data acquired using several different mixing-duct lengths are presented in this paper, with the mixing-duct length adjusted by adding round spacer ducts. One such extension of the nozzle is seen by comparing the shortest ( $L_{e} / D_{e}$ = 0.7) and longest ( $L_{e} / D_{e}$ = 3.0) mixing-duct lengths tested in Figure 2(b) and (c).

Jet operating conditions

A jet Mach number will be reported as $M_{j} = U_{j} / a_{j}$ , where $U_{j}$ and $a_{j}$ are the velocity and speed of sound in the jet. The two streams were operated at the same $M_{j} \leq 1.00$ due to interest in the present work in the noise produced by internally mixed jets at conditions relevant to take-off and landing. When the two streams were unheated, the total temperature ratio between either of the two streams and the ambient was approximately unity. When the core stream was heated, its total temperature was set to a nominal $T_{t 1} \approx 533$ K and the bypass stream was left unheated. This yielded core-to-ambient total temperature ratios in the range of 1.75 to 1.81 and bypass-to-ambient total temperature ratios of approximately unity.

The measured $M_{j}$ (obtained from the measured nozzle pressure ratio via isentropic-flow equations¹⁸) was set to within $\pm 0.005$ of the desired $M_{j}$ . If the measured $M_{j}$ fell outside this range for either stream, the test was terminated by the operator. The estimated uncertainty in $M_{j}$ was typically $\pm 0.005$ because uncertainties in $M_{j}$ due to uncertainties in the measured pressures were relatively small. When heated, the measured total temperature of the core stream was ensured to fall within $\pm 8.33$ K of a nominal 533 K, otherwise the measurements were terminated by the operator. With thermocouple and data acquisition system uncertainties taken into account, the uncertainties in $T_{t 1}$ were less than $\pm 4$ K in the worst case presented in this paper.

A look at the observed phenomena

Figure 3 previews the results to be presented later in this paper, with the measurement systems described below. In Figure 3(a), acoustic spectra measured in the jet’s farfield at $θ = 90 °$ from the jet axis are shown. The core and bypass streams were operated unheated. Thus, the final jet was approximately a single, round, unheated jet. At $M_{j} = 0.80$ , a typical, broadband jet-noise spectrum was measured. By using well-established jet-noise scaling relations for round jets,^19,20 this measured spectrum was scaled to $M_{j} = 0.90$ , establishing an expected noise level for this higher $M_{j}$ (see the spectrum without data markers). However, the spectrum measured at $M_{j} = 0.90$ reflected a much higher noise level, containing discrete tones and a ‘broadband amplification’ of jet noise (e.g., see^21,22 for further details) that is emphasized with cross-hatching in the figure.

The schlieren flow visualization in Figure 3(b) acquired at $M_{j} = 0.80$ shows a typical, turbulent jet. While, at $M_{j} = 0.90$ , Figure 3(b) shows that the jet’s instability waves were excited as indicated by upward-facing arrows. The goal of this paper is to characterize the noise produced and flow features present at $M_{j} = 0.90$ as a function of operating condition and mixing-duct length.

Layout of this paper

The Background section provides a discussion of flow/acoustic interactions and excited jets. In the Methodology section, the facilities and measurement systems used are described. In the Results section, the findings are reported and discussed. Concluding remarks are given in the Conclusions section.

Background

The following subsections briefly discuss two topics of relevance to this paper. First, flow/acoustic interactions which have been found in prior works to give rise to powerful resonances are described. Then, the concept of an excited jet is discussed. These topics form a foundation for interpreting the results to follow.

Flow/acoustic interactions

Flow/acoustic interactions can occur when unsteady flow features couple with the acoustics of a duct or enclosure, and this coupling can produce powerful flow oscillations and acoustic tones at the same frequency. The well-known Parker resonance²³ associated with air flowing through a cascade of parallel, flat plates offers a classical example of this. This configuration leads to powerful pressure oscillations when vortex shedding from the plates couples to natural acoustic modes of the plate arrangement. The oscillation frequencies were equal to or just less than the frequency of vortex shedding from a single, isolated plate. The “lock-on”²⁴ of the vortex-shedding frequency to the frequency of the acoustic modes is a resonant flow/acoustic interaction, and both the flow and acoustic field influence one another. A more-recent paper by Zaman et al.²⁵ dealt with a co-annular nozzle system that emitted powerful tones due to a coupling between vortex shedding from centerbody struts with the acoustics of the nozzle interior. Vortex shedding is just one type of unsteady flow feature that can lead to a flow/acoustic interaction. The instability waves of a jet are another.

As discussed by Massey and Ahuja,²⁶ a 20-foot-diameter steel duct with six-inch-thick walls was shaken when a supersonic jet was operated inside it. This duct was part of an Arnold Engineering Development Complex (AEDC) engine test cell. They stated that such powerful oscillations must be the result of a coupling between the jet and the natural acoustic modes of the facility. Through model-scale experiments of a system comprising a jet issuing into a test cell equipped with an ejector (similar in principle to the AEDC test cell), Massey and Ahuja²⁶ showed that when the most-preferred frequency of a jet’s instability waves matched closely with a natural frequency of the ejector, there were marked changes in the jet’s flow field and powerful acoustic tones were produced. For more details on this type of phenomenon, see the detailed study of Tam et al.²⁷ and related papers.^28–31

As the howling of the confluent nozzle at $M_{j} = 0.90$ is discussed in this paper, the possibility of a resonant flow/acoustic interaction should be kept in mind.

Excited jets

A jet’s instability waves are generally present regardless of whether it is excited or not; however, they are more powerful and less random in the former case as shown by Ahuja et al.²² for example. Ahuja et al.²² also showed that the potential core of an excited jet tends to be shorter than that of an unexcited jet – a trend which will be important later in this paper. Here, an excited jet is taken to be one whose instability waves have been made more powerful and less random via forcing at particular frequencies and amplitudes which perturb the shear layer of the jet near the nozzle exit. The ‘more powerful’ descriptor is meant to exclude the effect of turbulence suppression via instability-wave excitation that was studied by Zaman and Hussain,³² among others.

Introducing discrete tones of particular amplitudes and frequencies into a jet flow in a controlled manner (e.g., via an acoustic driver upstream of a nozzle) can produce an excited jet and allows for isolated study of the effects of excitation. In this paper, the flow of air through the confluent nozzle led to powerful acoustic tones and an excitation of the resulting jet. This jet may be called self-excited.

Methodology

The following three subsections describe the facilities and measurement systems used to obtain (i) farfield noise, (ii) particle-image velocimetry (PIV), and (iii) time-resolved schlieren data.

Farfield noise

The acoustic data presented were measured in the GTRI Anechoic Jet Facility, with the details of this facility documented in great detail in prior works.^33–37 Figure 4 shows the GTRI Anechoic Jet Facility and the confluent nozzle installed therein. Figure 4(a) shows a view of the anechoic chamber from the facility’s entry. On the right, the co-axial plenum chambers to which the nozzle was mounted are seen. In Figure 4(b), the confluent nozzle ( $L_{e} / D_{e} = 3.0$ configuration) is shown installed for testing. The outer surface of the nozzle was covered with porous foam to help prevent acoustic reflections. Although this foam was found to have negligible effect on the jet-noise spectra during early testing, it was left in place for consistency and out of an abundance of caution.

A single microphone in the farfield of the jet at an angle of $θ$ = $90 °$ relative to the jet axis was used in this paper (B&K 4939 1/4-inch free-field microphone paired with a B&K 2669 pre-amplifier and connected to a B&K Nexus 2960-A-0S4 signal-conditioning amplifier). The signals were sampled at 204.8 kHz for 45 s using NI PXIe-4499 modules. Power spectra were computed using Welch’s method³⁸ with 6400-point, Hanning-windowed data segments and 50% overlap between neighboring segments. These spectra were corrected for the presence of a protective grid cover on the microphone, the microphone’s free-field correction, the microphone-specific actuator response, and the attenuation of sound³⁹ over the distance between the nozzle and the microphone. For example, see Ahuja³⁵ and Karon³⁶ for a more-detailed discussion of these corrections required to render jet-noise spectra lossless and fully corrected. All spectra were projected to a radius of $R = 84.7 D_{e}$ from the center of the final-nozzle exit using the inverse-square law and have a frequency resolution of $Δ f$ = 32 Hz. As shown in the first author’s doctoral dissertation,⁴⁰ the uncertainties in the SPL spectra were less than $\pm 0.70$ dB at the lowest frequencies reported and less than $\pm 1.25$ dB at the highest frequency reported.

Particle-image velocimetry (PIV)

Velocity-field measurements were acquired in the GTRI Flow-Diagnostics Facility using a double-pulsed, two-dimensional, two-component PIV system. The GTRI Flow-Diagnostics Facility is a companion facility to the GTRI Anechoic Jet Facility and was outlined by Burrin and Tanna.³⁴ Although this facility was separate from the GTRI Anechoic Jet Facility, the plenum-to-nozzle contraction ratios were approximately equal and the same compressed and dried air supply serviced this facility as well. The GTRI Flow Diagnostics Facility was not anechoic, although the side walls and the ceiling have been treated with polyurethane foam to reduce reverberation effects of hard walls.

Detailed information about the PIV system was provided by Ramsey.⁴⁰ Only key details are provided here. Two PIVTech fluidized bed seeders introduced ${TiO}_{2}$ seeding particles into the two streams in the plenum chambers upstream of the nozzle. A LaVision Imager Intense camera (1376-by-1040 resolution) equipped with a variable-focal-length Nikon Nikkor lens, a double-pulsed Nd:YAG laser (New Wave Research Solo III) equipped with sheet-forming optics, and a flat turning mirror were located on a traversing table. These elements were moved along the axis of the jet by translating the table, with data collected at various stations and stitched together as shown in Figure 5. Data in the region of overlap was discarded from one station or the other.

LaVision DaVis (version 8.4) was used to acquire and process raw particle images. Before processing, sliding background subtraction and intensity normalization filters were applied. Then, a processing routine was completed using the settings in Table 1. Spurious vectors were rejected using a median-filter-based algorithm and Chauvenet’s criterion (e.g., see Taylor,⁴¹ Bridges and Wernet,⁴² and Bridges et al.⁴³). The data-processing routine yielded a typical spatial resolution of approximately 0.35 mm, resulting in more than 100 velocity vectors per jet diameter.

Table 1.

PIV processing parameters.

Parameter	Setting
Algorithm	Adaptive, FFT-based⁴⁴
Number of interrogation window sizes	2
Number of passes per interrogation window size	2
First interrogation window size/overlap	32 x 32/75% overlap
Second interrogation window size/overlap	16 x 16/75% overlap
Rejecting spurious vectors within single fields	Median filter
Rejecting spurious vectors within ensemble averages	Chauvenet’s criterion

The axial and radial turbulence intensities appearing later are defined as

{TI}_{x} \equiv σ_{x} / U_{j} {TI}_{y} \equiv σ_{y} / U_{j}

(1)

where

σ_{x}

and

σ_{y}

are the sample standard deviations of the axial and radial velocity fluctuations, which converge to root-mean-square fluctuations in the large-sample limit.

Agreement between data obtained using this system and historical data was demonstrated by Ramsey,⁴⁰ along with a detailed explanation of how uncertainty estimates were obtained.

Time-resolved schlieren

A Z-type schlieren setup in the GTRI Flow-Diagnostics Facility was also used. Images of the system, and a detailed description can be found in Breen’s PhD dissertation.⁴⁵ An arc lamp emitted light that followed a Z-shaped path along a series of mirrors and lenses. A knife-edge cutoff was positioned in one of two orientations: normal to the jet axis (showing axial density gradients) or parallel to the jet axis (showing transverse density gradients). The light was then passed through a pair of refocusing lenses and the schlieren images were captured on a Vision Research Phantom v2512 at 25 kHz at a 1280-by-800 resolution with a 1 µs exposure time.

Results

The following subsections are dedicated to discussing (i) farfield acoustic measurements, (ii) velocity-field measurements obtained via PIV, and (iii) time-resolved schlieren flow visualizations, each of which characterize the noise and flow field produced at jet operating conditions that produced the howling.

Farfield noise

Figure 6(a) shows several acoustic spectra measured for $L_{e} / D_{e}$ = 0.7 with unheated flow. These same spectra were discussed briefly in the Introduction section, and in greater detail here. The spectrum measured at $M_{j} = 0.80$ was a typical, broadband jet-noise spectrum. However, at $M_{j} = 0.90$ , the measured spectrum contained many tones. A powerful fundamental tone was present at 6112 Hz, and its harmonic at 12256 Hz. From simple resolution considerations, the uncertainty in all reported tone frequencies can be no less than half the frequency resolution of the power spectra reported – that is, $\pm Δ f / 2 = 16$ Hz. The frequency of the harmonic was not exactly twice the frequency of the powerful fundamental tone, likely due to the finite bandwidth of the frequency analysis. At 8800 Hz, a relatively low-amplitude tone is visible, which was not a harmonic of the 6112 Hz fundamental. This low-amplitude tone is not discussed further. Any remaining tones whose frequencies were not labelled were also harmonics of the fundamental tone.

The spectrum without data markers is referred to as the predicted, unexcited jet-noise spectrum for $M_{j} = 0.90$ . To obtain this spectrum, the $U^{7}$ scaling of the narrowband jet-noise spectra²⁰ and Strouhal-number frequency scaling were used to scale the spectrum measured at $M_{j} = 0.80$ up to $M_{j} = 0.90$ . In doing so, an estimate for the jet-noise spectrum at the resonance-producing operating condition had the resonance not occurred was obtained. The extraordinarily high level of broadband noise produced when the resonance occurred is made evident through comparison of the measured spectrum with this predicted spectrum. The broadband noise in the measured spectrum exceeded that of the predicted spectrum by more than 3 dB at all frequencies above 3 kHz, as is emphasized by the cross-hatching pattern between the two spectra called out as ‘Broadband Amplification.’ Again, this is typical of a tone-excited jet (e.g., see²²).

Before continuing, we note that the acoustic spectra presented in this paper are plotted against the dimensional frequency in hertz. It is common to find jet-noise measurements plotted against non-dimensional frequencies in the published literature. These dimensionless frequencies are formed using a length scale, $l$ (i.e., the nozzle’s exit diameter), and a velocity scale, $U$ (i.e., the jet velocity for a Strouhal number or ambient sound speed for a Helmholtz number), characteristic of the jet. Such normalization is not pursued here. The main reason is that there is not a clear, suitable frequency-normalization scheme for the measured acoustic tones, which are of greatest interest to this paper.

Figure 6(b) shows spectra measured using $L_{e} / D_{e}$ = 3.0 with unheated flow. Again, no resonance was observed at $M_{j} = 0.80$ . At $M_{j} = 0.90$ , a fundamental tone was produced with a slightly different frequency (about 400 Hz lower) than with $L_{e} / D_{e}$ = 0.7 and all tones were lower in amplitude or vanished entirely. A significant broadband amplification of jet noise occurred, emphasized with cross-hatching.

Figure 7 shows acoustic spectra measured with $T_{t 1} \approx 533$ K. With $L_{e} / D_{e} = 0.7$ , a howling was observed at $M_{j} = 0.90$ , as shown in Figure 7(a). Relative to unheated flow, the fundamental tone’s frequency increased by about 800 Hz. With the core stream heated, the jet could not be treated as a single, round jet, so no predicted, unexcited jet-noise spectrum is shown. Instead, the jet-noise spectrum measured at $M_{j} = 1.00$ was included. Based on jet-noise scaling relations,¹⁹ one would expect the noise measured at $M_{j} = 0.90$ to fall between the noise measured at $M_{j} = 0.80$ and $M_{j} = 1.00$ . Above about 10 kHz, however, the broadband noise measured at $M_{j} = 0.90$ exceeded that measured at $M_{j} = 1.00$ . This indicates that a substantial broadband amplification of jet noise occurred at $M_{j} = 0.90$ with a heated core stream, too. A notable feature revealed here is that no tones were measured at $M_{j} = 1.00$ . Measurements at this $M_{j}$ with unheated flow were not shown in the previous figure to maintain readability; however, the tones vanished at $M_{j} = 1.00$ with unheated flow as well. Figure 7(b) shows that, with $L_{e} / D_{e}$ = 3.0, there were far fewer tones produced at $M_{j} = 0.90$ than were present with $L_{e} / D_{e}$ = 0.7 in Figure 7(a). Further, a similar broadband amplification was evident due to similarity between the broadband noise levels produced at $M_{j} = 0.90$ and $M_{j} = 1.00$ . In summary, the howling occurred at $M_{j} = 0.90$ , but not at $M_{j} = 0.80$ or $M_{j} = 1.00$ whether the core stream was heated to $T_{t 1} \approx 533$ K or left unheated and for the two mixing-duct lengths shown: $L_{e} / D_{e} = 0.7$ and $L_{e} / D_{e} = 3.0$ . Only minor thermal expansion of the nozzle hardware is expected at these conditions. At yet higher core-stream temperatures ( $T_{t 1} \approx 755$ K), a modest axial thermal expansion of the core nozzle was photographically measured during jet operation at $Δ x \approx 0.025 D_{e}$ . Less thermal expansion is expected here where $T_{t 1} \approx 533$ K, and this thermal expansion is not expected to impact our observations.

A similar howling was observed for the intermediate mixing-duct lengths of $L_{e} / D_{e}$ = 1.0 and 2.0. Dedicated views of the fundamental tones in the spectra of all four mixing-duct lengths are shown in Figure 8 to illustrate this. Figure 8(a) shows that, at $M_{j} = 0.90$ with the core flow unheated, the fundamental tone’s frequency decreased monotonically with increased mixing-duct length; however, there was some ambiguity in the effect of the mixing-duct length on the amplitude of the tone. Increasing from $L_{e} / D_{e}$ = 0.7 to any of the longer mixing-duct lengths reduced the tone’s amplitude, but no trend among the three longest mixing-duct lengths was identifiable. Figure 8(b) shows that, when the core flow was heated, increasing $L_{e} / D_{e}$ from 0.7 to any of the longer mixing ducts resulted in a decrease in the tone’s frequency. However, the frequencies produced by the three longest mixing-duct lengths varied little, and only minor changes in amplitude were observed. Overall, the howling appeared at similar frequencies for all four mixing-duct lengths whether the core stream was heated or not, and heating the core stream increased the fundamental tone’s frequency.

As the farfield characteristics of the fundamental tone were roughly similar for all mixing-duct lengths and core-flow total temperatures, the remainder of this paper focuses on the $L_{e} / D_{e}$ = 0.7 mixing-duct length with the core flow unheated. As a reminder, all flow data were collected in the GTRI Flow Diagnostics Facility, which was not anechoic.

Velocity-field measurements

Witze⁴⁶ gave an expression for the centerline axial velocity distribution of a compressible round jet that agreed well with a large body of experimental data. This expression is

\frac{U}{U_{j}} (\frac{x}{D_{e}}) = 1 - exp (\frac{- 1}{2 κ (x / D_{e}) {({\bar{ρ}}_{e})}^{0.5} - X_{c}}),

(2)

where

κ \equiv 0.08 (1 - 0.16 M_{j}) {({\bar{ρ}}_{e})}^{- 0.22},

(3)

${\bar{ρ}}_{e}$ is the jet-to-ambient density ratio, and $X_{C} = 0.7$ . The density ratio, ${\bar{ρ}}_{e}$ , and $U_{j}$ were estimated by using isentropic-flow relations (e.g., see Anderson and Cadou¹⁸) in conjunction with the ideal gas law. A total temperature ratio of unity was assumed in calculating this density ratio.

Figure 9 shows comparisons of measured centerline distributions of mean velocity to Witze’s model. In Figure 9(a), a very good agreement between Witze’s model and the measured data for $M_{j} = 0.80$ . Figure 9(b) shows that, at $M_{j} = 0.90$ , a much shorter potential core was measured than predicted by Witze’s model (approximately $2.5 D_{e}$ shorter). This is emphasized by the arrow on the plot. Finally, Figure 9(c) shows that the measurement and Witze’s model agree well once again for $M_{j} = 1.00$ . Witze’s model’s agreement with the measurements at $M_{j} = 0.80$ and $M_{j} = 1.00$ support its use as a frame of reference for the shortening of the potential core at $M_{j} = 0.90$ . The differences between the two curves in Figure 9(b) therefore provides evidence that the jet was excited when the howling occurred, similar to, for example, observations in the controlled-excitation studies by Ahuja et al.²²

Figure 10 shows maps of radial turbulence intensities measured near the nozzle exit. The radial turbulence intensity is shown rather than the axial because it revealed the most severe differences between the tone-producing and tone-free $M_{j}$ . Figure 10(a) shows the values for $M_{j} = 0.80$ . For this $M_{j}$ , $N = 200$ snapshots of the velocity field were measured. This is generally considered a low number for producing ensemble-averaged turbulence statistics, so it is cautiously noted that the peak turbulence intensities in the shear layer were around 10%. As shown in the convergence study reported by Ramsey,⁴⁰ a higher sample size would unlikely change this nominal value by much, if at all. At $M_{j} = 0.90$ , where $N = 750$ snapshots were measured, relatively high radial turbulence intensities ( $\geq$ 20%) were measured in many places in the shear layer $(y = \pm 0.5 D_{e})$ , saturating the colorbar which extends up to 20%. Figure 10(c) shows the values for $M_{j} = 1.00$ , which were also obtained from a modest $N = 200$ samples. Like at $M_{j} = 0.80$ , the peak radial turbulence intensities were around 10%. Clearly, at $M_{j} = 0.90$ , there were extremely powerful velocity fluctuations in the jet’s shear layer near the nozzle exit. This is shown more quantitatively by Figure 11, where the 95.4% confidence bounds on the radial turbulence intensity at $x = D_{e}$ are plotted. The shortening of the potential core and the intense velocity fluctuations measured at $M_{j} = 0.90$ suggest that the jet’s instability waves were excited at this operating condition.

Time-resolved schlieren

For reference, Figure 12 shows single frames from high-speed schlieren videos at $M_{j} = 0.80$ , with Figure 12(a) showing transverse density gradients and Figure 12(b) showing axial density gradients. The black strip visible on the left-hand side is the final-nozzle exit, and the jet flowed from left to right. In these images, no instability waves are readily discernible, which is typical of an unexcited jet.

A similar pair of images acquired at $M_{j} = 1.00$ are shown in Figure 13, with qualitative similarity to those in Figure 12. These images do seem to reveal steeper density gradients, but they are qualitatively similar to those obtained at $M_{j} = 0.80$ . Figure 14 shows schlieren images obtained at $M_{j} = 0.90$ , which appear drastically different from the images obtained at $M_{j} = 0.80$ and $M_{j} = 1.00$ . Organized instability waves are clearly visible.

Figure 15 shows further analysis of the time-resolved schlieren corresponding to Figure 14(a). Figure 15(a) shows a map of the sample standard deviation of pixel intensity values calculated using 500 images. The time history of the pixel located at the single, red ‘ × ’ in this figure was extracted from a total of $N = 2048$ time-resolved images. This position was selected because the fluctuations were relatively large there. Then, the power spectral density of this pixel’s fluctuations was estimated using Welch’s method³⁸ and Hanning-windowed data blocks of 256 images ( $Δ f = 97.66$ Hz) with 50% overlap. The power spectral density is shown in Figure 15 (units omitted due to lack of a clear meaning of ‘power’ in such a signal). A fundamental tone was found at 6152.34 $\pm$ 48.83 Hz, which is very close to the measured fundamental acoustic tone for this operating condition and nozzle configuration. Evidently, the fluctuations in the schlieren video were dominated by fluctuations at the frequency of the fundamental acoustic tone. This strongly indicates that a flow/acoustic interaction was responsible for the observed phenomena.

Conclusions

It has been shown that, when operated at $M_{j} = 0.90$ , a model-scale confluent nozzle produced a howling (i.e., acoustic tones measured in the farfield) attended by a broadband amplification of jet noise. This occurred for all mixing-duct lengths tested and with an unheated and a heated core stream, with the fundamental tone’s frequency decreasing a small amount with increased $L_{e} / D_{e}$ and increasing with $T_{t 1}$ .

With the $L_{e} / D_{e} = 0.7$ mixing-duct length, measurements of the velocity field revealed drastic changes to the jet when the howling occurred. The potential core of the jet was substantially shortened (by about $2.5 D_{e}$ ) and extremely high radial turbulence intensities were observed near the nozzle exit (about $20 %$ at $x \approx D_{e}$ ). Spectral analysis of a schlieren recording showed that the jet’s instability waves were excited at the frequency of the fundamental acoustic tone.

There have been a number of publications on internally mixed nozzles equipped with lobed mixers. We wish to point out several publications^{11–13,47–49} which dealt with an additional, broadband noise produced by such nozzles. This additional noise was ultimately due to a small-radius, convex bend in the nozzle wall and an associated region of over-expanded supersonic flow just upstream of the nozzle exit. A recent paper by Ramsey et al.⁵⁰ showed that the howling studied in this paper is due to a similar transonic flow inside the nozzle. However, unlike the studies referenced above, this region of transonic flow led to shock-induced separation of the boundary layer – giving rise to a periodic flow instability that coupled with a natural acoustic mode of the nozzle interior in a flow/acoustic interaction (or ‘feedback phenomenon’). The physical mechanism at play is a true flow/acoustic interaction involving both a natural acoustic mode (which some may call a ‘duct resonance’) and an unusual flow instability coupled to this natural acoustic mode. The flow instability was a transonic phenomenon, and thus only exists above a certain, subsonic $M_{j}$ (just above $M_{j} = 0.80$ ⁵⁰) and below $M_{j} = 1$ . Ultimately, this resonance can be avoided by carefully avoiding small-radius, convex nozzle-wall curvature¹ or by tripping the final nozzle’s boundary layer just upstream of the final-nozzle exit.⁵⁰ The notable increase in tone frequency with increased $T_{t 1}$ was the result of a modification of the natural acoustic frequency of the nozzle’s mixing duct with increased core-stream temperature. Furthermore, it is most likely that the increased nozzle length influenced the natural frequency via a subtle change to the mean flow, with some evidence put forth by Ramsey et al.⁵⁰ that this could be the streamwise development of the core nozzle’s wake.

For completeness, we note that the Strouhal number (based on the velocity and diameter of the final jet) of the acoustic tones and flow oscillations measured at $M_{j} = 0.90$ with unheated flow was approximately 0.9. As was explained at the beginning of the Results section, the measured frequencies presented in this paper were left in dimensional form rather than in normalized form (e.g., as a Strouhal number based on length and velocity scales characteristic of the final jet as commonly seen in the jet-noise literature). A few, additional thoughts about this are provided here. The recent work of Ramsey et al.⁵⁰ discussed above has clearly shown that the frequency of the measured acoustic tones and flow oscillations were in excellent agreement with an expected natural frequency of the nozzle interior. This makes it clear that length and velocity scales of the nozzle interior are most important for determining the frequency of the tones – not those in the final jet.

This is not to say the Strouhal number (based on, say, the velocity and diameter of the final jet) of the howling and flow oscillations is unimportant. On the contrary, the Strouhal number of the howling would provide rough insight into the coupling between the resonance responsible for the howling and the instability waves of the final jet. This is especially true when the core jet was unheated and the final jet was approximately a single, uniform stream. In this case, the Strouhal number of the howling was about 0.9. This Strouhal number is higher than the expected most-preferred frequency of the instability waves in a round jet (e.g., see the work of Ahuja and Blakney²¹ on axisymmetric instability waves of model-scale jets) and, had the Strouhal number been lower, instability waves in the final jet might have been even higher in amplitude.

To date, no dynamic measurements of the fluctuating flow field inside the nozzle have been conducted. However, these measurements would be of great interest. Though a detailed understanding of the resonance is now available,⁵⁰ in-duct measurements obtained simultaneously with farfield acoustic data could shed light on the contribution of the resonance internal to the nozzle to the farfield noise.

It is noted for the interested reader that more recent work by Ramsey et al.⁵¹ also outlined a different resonance of the exact same nozzle, which was rooted in impingement of the core/bypass shear layer upon the final-nozzle lip under certain conditions. It is emphasized that only certain operating conditions led the nozzle studied here to howl. For example, the paper by Ramsey et al.⁵² dealt only with conditions at which no howling was produced.

Footnotes

Acknowledgements

The authors are grateful to GTRI for allowing the use of their facilities in completing this work. Senior Research Engineer Michael Mayo (GTRI) is thanked for his consultation regarding PIV measurements. The efforts of Callum Gray (LaVision GmbH) to provide technical support and information regarding the DaVis software is gratefully acknowledged.

ORCID iDs

David N Ramsey

Aharon Z Karon

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: As part of his doctoral research, DNR was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-2039655 and much of the work reported here was conducted under this grant. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The building block for this work was the discovery of large-amplitude tones in the acoustic farfield of confluent nozzles during work under FAA ASCENT Project 59B under grant GR00005737 (Program Manager: Sandy Liu) and through a cost-sharing partnership with Gulfstream Aerospace (POC: Brian Cook). The authors are grateful to GTRI for allowing the use of their facilities in completing this work.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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