A Comparative Study of Scarfed Nozzle for Jet-Installation Noise Reduction

Abstract

The experimental investigation of the effects of scarfed nozzles on jet-installation noise was conducted using unheated subsonic jets in an anechoic jet noise facility. Four different types of scarfed nozzles with increasing nozzle lip angles were examined to study the installation effects at various plate distances away from the jet. Mach numbers ranging from 0.3 to 0.8 were investigated in the experiments. The use of scarfed nozzles is known to result in the deflection of flow away from the centre axis, inducing asymmetry in the jet shears, leading to azimuthal variation in the spectra, and ultimately, noise reduction. This study aims to explore the possibility of reducing jet-installation noise using scarfed nozzles at subsonic flow conditions. The characteristics of jet hydrodynamic pressure fluctuations were investigated in the axial direction using far-field measurements. The near-field flow features were studied using surface pressure transducers installed on the flat plate for the installed configurations. Detailed spectral, coherence, and correlation analyses were carried out to determine the noise reduction mechanisms associated with scarfed nozzles in the proximity of a flat plate. The results of the study showed that the use of scarfed nozzles significantly reduced the jet-installation noise. The reduction was attributed to the generation of an asymmetric flow field induced by the nozzle geometry. The reduction in noise levels was also observed to increase with increasing nozzle lip angle. The detailed analyses revealed that the noise reduction mechanism was associated with a decrease in the acoustic power generated by the jet. Overall, the results suggest that scarfed nozzles can be an effective means of reducing jet-installation noise in subsonic flow conditions.

1 Introduction

Jet noise has been a topic of significant concern since the advent of high-bypass engines in the 1960s. Increased jet interaction with wings and trailing edges of the aircraft has led to noise amplification in the low and mid-frequency ranges particularly during take-off and landing. Various noise reduction mechanisms through the alteration of hydrodynamic field via nozzle modifications have been employed to mitigate this jet-installation noise. However, a clear understanding of the underlying physical mechanisms resulting in noise reduction is yet to be identified.

Jet-installation noise refers to the noise generated by the interaction between the exhaust flow of a jet and an airframe surface at close proximity, and has been extensively studied since the early works of Bushell (1975) and Head and Fisher (1976), and more recent publications (Lawrence et al. 2011; Brown 2012). In addition to the presence of turbulence-mixing noise in installed subsonic jets, additional noise sources have been identified at the surface of the trailing-edge, especially at low and mid-frequencies in the direction upstream to the jet (Williams and Hall 1970; Head and Fisher 1976; Belyaev et al. 2015; Semiletov and Karabasov 2017; Rego et al. 2020). In some cases, these additional sources can also lead to the generation of tones (Jordan et al. 2018; Tam and Chandramouli 2020).

The hydrodynamic pressure waves generated in the mixing layer of an isolated jet are evanescent in comparison to the acoustic waves propagating to the far-field. However, the deployment of high-lift devices reduces the distance to the jet plume, which causes the hydrodynamic pressure to be scattered by the wing trailing-edge to the far-field noise, thereby intensifying JIN (Lyu and Dowling 2019). High-fidelity eddy-resolving computational approaches have shown that installation effects can amount to approximately 4 EPNdB of the acoustic footprint of the jet (Casalino and Hazir 2014). With the introduction of ultra-high bypass ratio engines, these additional noise sources are set to become even more important as the distance between the jet and airframe progressively decreases (Hughes 2011).

Detailed studies have been conducted to understand the mechanisms behind this phenomenon in order to mitigate the additional noise, which depends on the distance between the jet and the scattering surface. For instance, Mengle et al. attempted to reduce the installation effects of the jet using tailored chevron nozzles; however, the application of chevrons was insufficient to completely mitigate the jet noise due to interaction with the trailing-edge (Mengle et al. 2006).

It was observed that changes to nozzle geometries provided faster plume velocity decay leading to lower noise generation as opposed to plain circular jets. Several studies have been carried out to identify the noise reduction capabilities of various nozzle geometries. One of the most popular attempts was the introduction of Chevron nozzles by Bridges and Brown that showed promising noise reduction capabilities (Bridges and Brown 2004). The serrations along the nozzle lip were observed to induce streamwise vorticity in the shear layer resulting in increased mixing and decreased jet plume length thereby reducing noise levels.

Several efforts have been made to mitigate the noise associated with turbulent mixing by employing bevel nozzles, alternatively referred to as scarfed nozzles (Bridges and Wernet 2015; Tide and Srinivasan 2009; Sandhya and Tide 2018; Guo et al. 2014; Viswanathan et al. 2012). These types of nozzles have a distinctive design where the ends are cut at a sloping or slanted edge instead of a conventional 90$^\circ$ angle, resulting in one side of the nozzle lip being longer than the other. Bridges conducted pivotal research demonstrating that such bevels can significantly influence turbulence levels, consequently leading to a noticeable reduction in noise (Bridges 2012). The primary purpose of bevelling the nozzle was to induce alterations in the noise generation mechanism within the inner shear layer, a modification aimed at reducing the overall noise produced (Viswanathan 2006). Bevel nozzles were shown to cause azimuthal variations in the spectra resulting in considerable noise reduction below the longer lip of the bevel nozzle by Viswanathan (2005). It was demonstrated that noise reduction occurred due to the modification of turbulent structures caused by the bevel nozzle. Significant noise reduction was achieved in the azimuthal directions over the low-frequency range without any increase in the high frequency at the polar angular range of $110^\circ$ to $145^\circ$ at all frequencies (Viswanathan et al. 2008). Noise from large-scale structures was observed to radiate towards the lower polar angles of the bevel nozzle leading to less acoustic energy being available for radiation to the aft angles (Viswanathan 2008). It was further concluded that noise reduction in the bevel nozzle was directly proportional to the jet velocity, with higher reductions at higher jet velocities. Specifically, Viswanathan et al. (2012) reported a decrease in noise as the primary jet velocity increased, but an increase in noise as the flight stream Mach number increased. They conducted a joint computational and experimental program to design dual-stream nozzle geometries that could offer jet noise reduction while allowing for control of the orientation of the jet plumes, minimizing the thrust degradation often associated with low-noise designs. The nozzles tested included round primary and secondary nozzles, bevel primary nozzles, and modified secondary nozzles. It was found that the bevel nozzle design deflected plumes towards the short lip, while the secondary nozzle design deflected in the opposite direction.

The noise generated by a jet with different nozzle geometries, flow rates, and temperature conditions has been the subject of multiple computational and experimental studies. Specifically, rectangular turbulent jets have been the subject of more extensive investigation than other non-circular jets due to their superior jet mixing and velocity decay rates. For instance,  Sandhya and Tide (2018) conducted numerical simulations of a compressible subsonic jet from rectangular nozzles with different aspect ratios and bevel nozzles of various lengths. The results showed that increasing the aspect ratio caused a decrease in the potential core length and an increase in the turbulence and mixing. Additionally, beveling the nozzle led to significant changes in flow patterns and turbulence structures in the jet. Keeping the useful characteristics of rectangular nozzles in mind, Frate and Bridges (2011) introduced a novel design called the Extensible Rectangular Nozzle (ERN) with varying aspect ratios. These nozzles were designed with the concept that the bevel and sidewall-cutback designs may offer a solution to reduce noise pollution for observers by incorporating an extended lower edge, which can also provide additional surface area for implementing acoustic wall treatment.

Several studies were conducted by Bridges on rectangular nozzles that included acoustic measurements for nozzles with and without bevels. For instance, Bridges (2012) performed acoustic measurements on rectangular nozzles and showed that rectangular jets produced a greater level of noise in the direction away from their wider sides than their narrow sides. Furthermore, bevel nozzles generated noise that increased in all directions with an increase in bevel length. In another experiment, Bridges and Wernet (2015) investigated the acoustic performance of a family of rectangular nozzles both with and without bevels. Changes made to the nozzle had little effect on noise levels, except for an extended lip on the wide side of the bevel nozzle and extending the lip on the narrow side which produced up to 3 dB and 2 dB more noise, respectively. Non-intrusive chevrons had no significant effect on noise, but inverted chevrons produced up to a 2 dB increase. Adding internal walls within the base nozzle resulted in noise reduction at low frequencies. Bridges and Wernet (2015) tested rectangular nozzles of different aspect ratios and bevels for sound and turbulence in subsonic flow and found that higher aspect ratios resulted in more high-frequency noise, despite uniform exit velocity.

Bridges conducted extensive research on rectangular nozzles, particularly focusing on the acoustic measurements of nozzles with and without bevels. Bridges (2012) undertook acoustic measurements on rectangular nozzles, demonstrating that rectangular jets generated a higher level of noise away from their wider sides compared to their narrow sides. Interestingly, bevel nozzles were found to produce noise that increased uniformly in all directions as the bevel length increased. Further investigations by Bridges and Wernet (2015) into the acoustic performance of a variety of rectangular nozzles, both bevelled and unbevelled, revealed surprising insights. Generally, bevel modifications to the nozzle had minimal impact on noise levels. However, exceptions were observed when the bevel nozzle lip extension was added to the wide side of the rectangular nozzle than the narrow side. These modifications resulted in a noise increase of up to 3 dB and 2 dB respectively. Additionally, while non-intrusive chevrons did not significantly affect the noise levels, inverted chevrons led to a noise increase of up to 2 dB. Interestingly, the introduction of internal walls within the baseline nozzle resulted in a reduction of noise at lower frequencies. In a subsequent experiment, Bridges and Wernet (2015) examined rectangular nozzles of various aspect ratios and bevels for understanding the noise and turbulence mechanisms in subsonic flow. They demonstrated that nozzles with higher aspect ratios generated more high-frequency noise, despite having a uniform exit velocity.

Bridges went beyond the study of isolated jet acoustics to explore the impacts of installation effects on rectangular nozzle (Bridges 2014). By comparing acoustic measurements across various configurations, noise sources were identified emanating from the larger flat side of the rectangular nozzle. The intensity of this noise was found to be dependent upon the size of the nozzle’s flat surface. Moreover, an elevation in noise was noted for bevel nozzle configurations with higher aspect ratios. It’s crucial to acknowledge that numerous studies have been carried out on bevel nozzles, particularly concerning supersonic jets (Wu and New 2017; Aikens et al. 2015; Powers et al. 2011; Powers and McLaughlin 2012; Tam et al. 1997; Viswanathan and Czech 2011; Norum 1983; Rice and Raman 1993; Petitjean et al. 2007). These investigations have shown that bevel nozzles can significantly diminish the amplitude of screech tones, achieving reductions of up to 4 dB at low frequencies. They have also been proven effective in reducing noise below the extended side of the bevel nozzle. However, the amplitude of these screech tones is highly sensitive to the specific configuration of the nozzle used. Importantly, in terms of performance, bevel nozzles were found to produce a total thrust that was either equal to or greater than that of a round nozzle. In a recent study, Kamliya Jawahar and Azarpeyvand (2022a) explored the impact of varying scarf angles in nozzles on jet installation noise in subsonic jets. Utilizing four distinct nozzle designs with incrementally increased scarf angles, they found a direct correlation between the scarf angle and the reduction of low-frequency amplification due to the jet installation effect. Christophe et al. (2023) also investigated scarfed nozzles, but with a focus on their potential to reduce plate interaction tones for installed configuration at low Mach numbers. Particularly, the study focused on small plate heights using both rectangular and scarfed nozzles. This comparative analysis highlights the possibility of jet installation noise reduction using scarfed nozzles. Although studies on isolated jets with scarfed nozzles are available, the properties of scarfed nozzles with jet-installation effects for realistic conditions are yet to be fully characterised. This paper aims to further the existing efforts to identify the impact of scarfed nozzles on noise propagation of isolated jets as well as installed jets. Experimental results are presented in terms of sound pressure level, overall sound pressure level, surface pressure fluctuations, and coherence studies.

2 Experimental Setup

The newly commissioned Bristol Jet Aeroacoustic Research Facility (B-JARF) at the University of Bristol was used to conduct the experiments presented here. Previous studies have thoroughly validated the BJARF facility (Kamliya Jawahar et al. 2021a, b; Kamliya Jawahar and Azarpeyvand 2021; Kamliya Jawahar et al. 2021c; Kamliya Jawahar and Azarpeyvand 2022b). The facility uses a pressurized air system capable of reaching up to 7 bars. This pressurized air is distributed to the facility via an intricate system of pneumatic tubes and connections. As shown in Fig. 1, the flow in BJRAF was conditioned and silenced using three custom-built in-line silencers to achieve a clean and quiet air flow with a jet exit Mach number of $M = 0.3$. The first two silencers were installed right after the control valve outside the anechoic chamber, each with a diameter of 0.3 m and a height of 1.5 m. The third larger silencer, which also serves as a plenum is placed within the acoustic chamber. This component has a diameter of 0.457 m and a height of 1.9 m. Perforated tubes were installed in the silencers to allow the flow to pass through, and the remaining space was filled with glass wool. The anechoic chamber had dimensions of 7.9 m in length, 5.0 m in width, and 4.6 m in height, including the surrounding acoustic walls (Mayer et al. 2019). Prior to testing, the silencers, the collector, and the far-field array were covered with foam to minimize acoustic reflection. The acoustic Mach number and flow conditions were determined from the total temperature and pressure measurement devices fitted within the large silencer and the acoustic chamber.

The experiments were conducted on five different nozzles, including a round convergent nozzle SMC000 and four scarfed nozzles (SCF001, SCF002, SCF003, and SCF004), as depicted in Figs. 2 and 3. The SMC000 nozzle was characterized for isolated configurations by Bridges and Brown (2004) and, in this study, a scaled-down version of the nozzle with an exit diameter of $D=38.10$ mm was tested. The scarf angles $\beta$ were SCF001 = $10^\circ$, SCF002 = $20^\circ$, SCF003 = $30^\circ$, and SCF004 = $40^\circ$ relative to the round SMC000 nozzle, as shown in Fig. 3. The design of the scarfed nozzles, as depicted in Fig. 3, incorporates the same throat diameter as the round nozzle, specifically $D=38.10$ mm, in accordance with Viswanathan et al. (2008). For every 10$^\circ$ of scarfing, the scarfed nozzle is designed to yield a plume deflection within the range of 1.6$^\circ$–2.2$^\circ$. This magnitude of plume deflection aligns with observations from previous studies (Viswanathan and Czech 2011; Powers et al. 2011; Aikens et al. 2015; Viswanathan et al. 2008; Petitjean et al. 2007).

While the present study provides valuable insights into the acoustic characteristics of scarfed nozzles, it is crucial to acknowledge its limitations. Given that this study did not perform flow measurements a direct correlation between the scarf level and actual jet deflection remains to be conclusively established. Most importantly, the acoustic behaviour of the presented scarfed nozzle may not be universally applicable as the effect of the scarfed nozzle could involve complex behaviour beyond just flow deflection away from the plate. The acoustic results might be influenced by various factors such as the jet noise facility, nozzle design, upstream flow conditions, and boundary layer states. Nevertheless, it is also important to note that the present study is focused on investigating the potential of scarfed nozzles in mitigating jet-installation noise.

In the present study, a jet-plate configuration was employed to accurately simulate the arrangement of a real aircraft’s main wing and jet exhaust. This approach was aimed to facilitate a deeper understanding of the jet installation effects. It’s crucial to highlight that the plate representing the wing was positioned below the jet (see Fig. 4) to simplify the process of experimental measurements. Consequently, the microphones were positioned above the plate to mirror the configuration of conducting measurements under the wing, thereby ensuring the data collected was most representative of the observer on the ground. The jet-plate arrangement illustrated in Fig. 4, consists of a 5 mm thick aluminium flat plate chamfered with a sharp trailing edge. The plate’s lower side was reinforced with three 10 mm x 10 mm aluminium spars to increase rigidity. The flat plate had a total length of 6D and a total span of 26D to avoid side-edge scattering. It should be noted, for clarity, the sizes of the microphones and nozzles in the schematic in Fig. 4 are not drawn to scale. Tests were carried out for a flat plate length $L=4D$ and a wide range of plate heights, as shown in Fig. 4. An automated traverse system was used to move the plate to various distances axially away from the jet. The effect of plate height was examined through the investigation of various h/D values, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5, 4, 5, and 6. The plate extended 2D upstream from the nozzle exit to avoid scattering effects at the upstream leading edge. The tests were carried out for a wide range of subsonic flows with acoustic Mach numbers ranging from $M=0.3-0.8$.

Far-field noise measurements were performed using a 1/4-inch GRAS-46BE microphone with a corrected flat frequency response between 10 Hz and 40 kHz and a dynamic range of 160 dB. An array of 21 microphones was distributed on an arc centred on the jet exit at a distance of 1.6 m ($R\approx 42D$), covering a polar angular range between $50^\circ$ upstream and $150^\circ$ downstream, with the $90^\circ$ microphone at the sideline position on the reflected side for the installed configuration. An additional far-field microphone was placed at $\theta =270^\circ$ at the sideline position on the shielded side. Surface pressure fluctuations were acquired using Kulite XTEL-190(M) Miniature Ruggedized High-Temperature Pressure Transducers with a KSC-1 compact signal conditioner. Five Kulite sensors were distributed on the plate, as shown in Fig. 5. The data were acquired for $t=24$ s at a sampling frequency of $f = 2^{17}$ Hz using a National Instrument PXle-4499. The power spectral density (PSD) of the collected pressure signals was computed using a Hanning window, and the data is ensemble averaged 256 times to achieve a frequency resolution of $\Delta f=8$ Hz. Subsequently, the Sound Pressure Level (SPL) was computed using the equation (Eq. 1):

$$\begin{aligned} \text {SPL} = 10\text {log}{10}\left( \frac{\text {PSD}(f)\Delta f}{p^2_{\text {ref}}}\right) , \end{aligned}$$

(1)

where PSD represents the power spectral density derived from the fluctuating pressure $p'(t)$, defined as $p'(t) = p(t) - p_{\text {mean}}$, and $p_{\text {ref}}=20~\mu$Pa is the reference pressure. The Overall Sound Pressure Level (OASPL) was determined using the following equation (Eq. 2):

$$\begin{aligned} \text {OASPL} = 10\text {log}{10}\left( \frac{\int \text {PSD}(f)\text {d}f}{p^2_{\text {ref}}}\right) , \end{aligned}$$

(2)

In this equation, PSD represents the power spectral density dependent on the unsteady pressure $p'(t)$, defined as $p'(t) = p(t) - p_{\text {mean}}$. The OASPL is calculated over a frequency range of $St=0.01-10$. In the presented study, an extensive analysis of SPL and OASPL for both far-field and near-field results is conducted. The comprehensive experimental dataset of jet installation effects is instrumental for computational validation and mathematical modelling of aeroacoustics, including nozzle shape optimization studies. The focus is placed on bevel nozzles ranging from 10$^\circ$ to 40$^\circ$, offering a solid foundation for developing low-noise jet installation configurations. High-fidelity measurements from both far-field and near-field microphones are utilized, shedding light on the interactions between surface pressure fluctuations close to the jet and the transmission of noise to distant areas. Coherence analysis is also included to provide further insight into the frequency characteristics of noise transmission. With this work, a better understanding of jet noise and jet installation effects is made available, which is expected to impact the design and performance optimization of more efficient and environmentally acceptable aviation technologies.

Fig. 1

Side view of the aeroacoustic facility including the silencers: (A) First and second silencer, (B) Connecting underground pipe, (C) Third large silencer, (D) Contraction for the jet nozzle, (E) Collector, and (F) Far-field microphone array

Fig. 2

Schematic of the various nozzle configurations used in the present study

Fig. 3

Schematic of the scarfed nozzle profiles (SCF001-004) compared to the round nozzle (SMC000) used in the present study

Fig. 4

Schematic of the experimental setup with the position of the far-field microphones used in the present study for the isolated and installed jet. For representational clarity, the microphones and nozzles depicted in the schematic are not drawn to scale

Fig. 5

Schematic of the Kulite pressure transducers used in the present study at the vicinity of the trailing edge for the installed jet configuration

3 Results and Discussion

3.1 Far-Field Noise Validation

Obtaining accurate spectral measurements from low-velocity jets is often considered a challenging task, as noted in previous works (Viswanathan 2003, 2006). To establish the accuracy of the current experimental setup, comparisons were made with previous studies in the literature, including those conducted by Bastos et al. (2018) and Brown and Bridges (2006). The results of the previous studies (Bastos et al. 2018; Brown and Bridges 2006) were compared with far-field measurements obtained at various inlet angles ($\theta$) for a round nozzle SMC000, with an exit diameter of $D = 38.10$ mm, at a Mach number of $M=0.5$, corresponding to a Reynolds number of $Re=441,000$. The far-field measurements from the current experimental setup were found to conform with the results from the literature after correcting for distance and diameter, as shown in Fig. 6. It was observed that the experimental setup used in this study is capable of obtaining accurate spectral measurements from low and high-velocity jets.

Fig. 6

Comparison of SPL for isolated round convergent nozzle (dashed line) with experimental data available in the literature Brown and Bridges (2006) (solid lines) for select polar angles ($\theta = 60^\circ , 90^\circ , 120^\circ$ and $150^\circ$) obtained at acoustic Mach number M = 0.5

3.2 Far-Field Spectra

The following far-field spectra were measured in the anechoic facility for a wide range of Mach numbers. The sound pressure level (SPL) in terms of jet diameter-based Strouhal numbers ($St=fD/U_j$) for isolated and installed jet configurations measured at $\theta =90^{\circ }$ above the nozzle is shown in Fig. 7. The spectra exhibit a monotonic increase in level for the isolated round jet (SMC000) presented in Fig. 7a as the acoustic Mach number is progressively increased from $M=0.3$ to 0.8, as expected. The difference between the SPL reduces as the Mach number is increased. With respect to the scaling laws of jet acoustic Mach number, there is an inversely proportional relationship between the spectral SPL differential and the Mach number. Specifically, as the Mach number increases, the SPL differential between subsequent Mach numbers diminishes. It is noteworthy that this difference is particularly substantial at lower Mach numbers, and progressively declines in magnitude as the Mach number advances. In jet studies, SPL is well known to scale at $U^8$. These results are consistent with this trend, which was previously illustrated by the authors in a study on the SMC000 nozzle (Jawahar et al. 2023).

The results for the installed configuration with a plate height of $h/D=1$ are presented in Fig. 7b. The characteristic low-frequency amplification associated with jet-surface-interaction noise is well captured at low Mach numbers. Evidently, the spectral hump reduces as the Mach number is progressively increased, demonstrating that the installation effect is prominent at low Mach numbers and less significant at higher Mach numbers. Overall, the results presented in Fig. 7 highlight the ability of the facility to accurately capture the acoustic characteristics of turbulent jet flow over a wide range of Mach numbers.

Fig. 7

Sound pressure level comparison for SMC000 nozzle measured at $\theta =90^\circ$ and R=42D above the nozzle exit for a range of acoustic Mach numbers comparison for the isolated and installed configuration

Fig. 8

Sound pressure level comparison for round and scarfed nozzles measured at various polar angles $\theta =70^\circ ,90^\circ ,120^\circ$ and $150^\circ$ for the isolated and installed configurations at acoustic Mach number of M=0.5, with a plate height of $h/D=1.5$

Fig. 9

Sound pressure level at far-field location for various plate heights for the installed configuration at $M=0.5$ at $\theta =90^\circ$

Figure 8 presents the far-field results for all the tested nozzles for both isolated and installed configurations. The left and right columns of the figure show the spectra for the isolated and installed configurations, respectively. The far-field spectra for the isolated configuration are indifferent amongst the tested nozzles at all the polar angles. However, SCF004 exhibits a mild increase in the spectra of approximately 1–2 dB at $St=0.015-1$ for angles closer to the jet axis ($\theta >120^\circ$). Moreover, all the scarfed configurations exhibit noise reduction of up to 5 dB in the high-frequency range ($St=1-10$) at $\theta =150^\circ$.

For the installed configuration, the round nozzle shows a characteristic low-frequency spectral hump between $St=0.015-0.5$ and a noticeable smaller second hump at $St=0.4-0.5$. Interestingly, scarfed nozzles at upstream location $\theta =70^\circ$ and sideline location $\theta =90^\circ$ show substantial noise reduction of approximately 5 dB over the characteristic low-frequency spectral hump ($St=0.015-0.5$) compared to the round nozzle. The results also indicate a mild increase in noise reduction with increasing scarf angle. When considering the second spectral hump at $St=0.4-0.6$, the scarfed nozzles show a minimal reduction of 2–3 dB compared to the round nozzle. Moreover, the second spectral hump emerges to be stronger at $\theta =90^\circ$ and $120^\circ$ than at $\theta =70^\circ$, suggesting that the acoustic scattering at the trailing edge may be responsible for this hump. Finally, it is worth noting that the noise levels for scarfed nozzles in installed configurations are similar to their respective isolated configurations at $\theta =150^\circ$.

To better understand the effect of plate height on scarfed nozzles, SPL spectra are presented in Fig. 9 for a range of plate heights from $h/D=1$ to 6. For the sake of brevity, the spectra are shown only at $\theta =90^\circ$ and $M=0.5$, with scarf angles of SMC000, SCF001, SCF002, and SCF004. The general trend of the spectra demonstrates that the low-frequency broadband hump associated with jet-installation effects is significantly reduced as the plate height increases. This reduction is consistent with previous studies that have reported a decrease in the amplitude of the broadband hump as the plate height increased (Lawrence 2014; Brown 2013).

Interestingly, for the SCM000 case, the second peak in the broadband hump disappears when the plate height exceeds $h/D=1$, suggesting that this peak may be due to flow scrubbing on the trailing edge. This finding aligns with similar observations from previous studies (Jawahar et al. 2023) that attributed the second peak to flow scrubbing. Moreover, the effect of plate height on the spectra is significantly reduced beyond $h/D=2$. This reduction is expected, as the linear hydrodynamic field has been shown by Suzuki and Colonius (2006) to extend in the radial range of $1<R/D<2$ at $St =0.25 - 0.50$, particularly in each azimuthal mode ($m =0$, $\pm 1$, and $\pm 2$). At plate heights of $h/D=5$, the spectra follow the same trend as that of the isolated jet, indicating that the effect of the jet-installation is minimal beyond this height. Most importantly, the effect of plate height on the spectra decreases as the scarf angle increases with SCF004 having the most minimal effect. Overall, the SPL spectra presented in Fig. 9 demonstrate that scarfed nozzles have a significant effect on jet-installation noise, and this effect remains substantial even as plate height increases.

3.3 Overall Sound Pressure Level Trends

Fig. 10

OASPL comparison for the various tested nozzles for the isolated and installed configurations with a plate height of $h/D=1.5$

Fig. 11

A-weighted overall sound pressure level comparison for the various tested nozzles for the isolated and installed configurations with a plate height of $h/D=1.5$

Figure 10 presents the Overall Sound Pressure Level (OASPL) over a frequency range of $St=0.01-10$, measured at the polar angular microphones for both isolated and installed configurations at acoustic Mach numbers of $M=0.5$ and 0.7. The results are displayed in the left and right columns for isolated and installed configurations, respectively. The abscissa indicates the polar angular range, and the ordinate represents OASPL. The OASPL for the scarfed nozzles in the isolated configuration follows the same trend as the round nozzle for both $M = 0.5$ and 0.7. However, SCF004 with the largest scarf angle $\beta =40^\circ$, exhibits increased noise levels downstream close to the jet axis, particularly at higher jet exit velocity with an acoustic Mach number of $M = 0.7$ (see Fig. 10c).

For the installed configurations, the OASPL results display different trends for $M = 0.5$ and 0.7. At $M = 0.5$, the installed configuration exhibits substantial noise reduction for the scarfed configuration, with about 3 dB compared to the round jet at upstream angles $\theta <90^\circ$ and 1–2 dB between $\theta =90^\circ$–$120^\circ$. At polar angles closer to the jet axis ($\theta >130^\circ$), a considerable noise increase of about 4 dB can be observed with high levels of noise from SCF004. The noise levels dominated by turbulent mixing noise have increased due to the deflection of the jet flow closer to the microphones. As the jet exit velocity increased to $M = 0.7$, the polar angles at which noise reduction is observed expanded to the polar angular range $\theta <120^\circ$, with noise reduction up to 1–2 dB. Interestingly, the noise increase observed at large polar angles due to jet deflection is only in the range of 1–2 dB at $\theta >130^\circ$. Overall, these observations indicated moderate noise reduction in jet-installation noise $\theta <120^\circ$ due to scattering, and a slight increase at large polar angles in noise, possibly due to flow deflection.

Given the importance of accounting for human auditory perception in assessing noise impacts, this study incorporates an evaluation of the A-weighted Overall Sound Pressure Level (OASPL-A). This measure serves as a variation of the conventional Overall Sound Pressure Level (OASPL), distinctively tailored to reflect the human ear’s varying sensitivity across different frequencies. The A-weighting scale emulates the frequency response of the human ear, highlighting a pronounced sensitivity to frequencies between 1 and 6 kHz and a diminished sensitivity to extremely low or high frequencies. The A-weighting was determined for full-scale frequencies of a jet with a 2 m diameter. In Fig. 11, the OASPL-A for the various nozzles for both isolated and installed conditions are presented. For the isolated jet at $M = 0.5$ and 0.7, a similar trend is seen across all the tested nozzles, with the SMC004 showing increased levels at $\theta <120^\circ$. A notable increase in OASPL-A of up to 1–2 dB is observed for the scarfed jet when considering installed jets at $M = 0.5$ for $\theta <130^\circ$. At angles $\theta >130^\circ$, the results show a significant decrease in noise levels for larger scarf angles when compared to the baseline configuration. This decrease corresponds to the reduction in SPL for the scarfed nozzles observed at $St=1-10$ for $\theta =150^\circ$ in Fig. 8g, h. This reduction in OASPL-A is contrary to the observation in the OASPL results. At a higher Mach number ($M = 0.7$), no increase in the OASPL-A for the scarfed nozzles is observed for shallow inlet angles, where $\theta <120^\circ$. Conversely, for increased inlet angles where $\theta >120^\circ$, the OASPL-A shows reduced levels for the scarfed nozzles, with SMC004, which has the highest scarf angles, showing the most substantial noise reduction. It is important to note that while significant noise reductions were previously noted for the OASPL in Fig. 10, the OASPL-A results reveal a noise increase in the side-ling angles when accounting for human auditory perception, particularly for conditions such as $M = 0.5$.

Fig. 12

Overall sound pressure level at far-field location for various plate heights for the installed configuration at $M=0.5$

The impact of plate height on OASPL at $M=0.5$ is illustrated in Fig. 12. The results obtained for the round nozzle SMC000 indicate a substantial increase in noise levels at the minimum plate height of $h/D=1$. As the plate height is increased to $h/D=1.25$, a considerable reduction in noise levels can be observed. This reduction is particularly noticeable at the upstream angles, with $\theta =50^\circ$ exhibiting the highest level of reduction of up to 4 dB. In contrast, at polar angles closer to the jet axis, such as $\theta =150^\circ$, this reduction is minimal, only in the order of 1 dB.

The significant OASPL reduction observed at the upstream angles could be attributed to the reduction in scattering effects at the trailing, whereas the reduction in angles closer to the jet stream is minimal due to the noise being dominated by turbulence mixing in that region. With an increase in plate height, the difference in OASPL with the previous plate height decreases. This trend is more pronounced after $h/D=2$ since the plate is no longer present in the linear hydrodynamic region. At a plate height of $h/D=6$, the OASPL trend is very similar to that observed in the isolated configuration shown in Fig. 10.

3.4 Near-Field Spectra

The noise reduction properties of the scarfed nozzle are further characterized in this study by presenting the surface pressure fluctuations measured using Kulite pressure transducers placed on the flat plate, as shown in Fig. 5. The results are presented for three locations K1, K2, and K5 at a plate height of $h/D=1$, and are plotted with Strouhal number on the abscissa and SPL on the ordinate in Fig. 13. It is observed that the SPL spectra obtained using Kulite pressure transducers exhibit a similar trend for both the presented acoustic Mach numbers $M = 0.5$ and 0.7, despite a substantial difference in the OASPL trends.

A noise reduction of about 10 dB is observed in the near-field spectra for the scarfed nozzles, and an increase in scarf angle $\beta$ results in greater noise reduction. This could be expected as the flow deflection increases with increasing scarf angle $\beta$. The highest level of noise reduction for the scarfed nozzles is observed in the low frequencies $St<0.05$. Interestingly, at the furthest surface pressure measurement location K5, a double hump behaviour is observed in the near-field spectra for all tested nozzle configurations at both the tested jet velocities. A hypothesis can be postulated that the occurrence of the double hump behaviour at the furthest spanwise location is possibly caused by the presence of two distinct types of flow fields arising from the potential core and the shear layer.

In order to investigate the effect of plate height, the near-field spectra for K2 and K5 at $M = 0.5$ are presented for a total of eleven plate positions in Fig. 14. The magnitude of the near-field spectra is found to decrease with increasing plate heights in line with previous studies (Kamliya Jawahar and Azarpeyvand 2021; Brown 2012; Lawrence 2014). The low-frequency spectral hump due to the installation effect dominates the spectra at plate heights between $h/D = 1-2.5$. These results are consistent with the dominance of the evanescent hydrodynamic field in this region, as reported in previous research (Suzuki and Colonius 2006; Lawrence 2014). Beyond this region, the jet-installation effect reduces substantially along with the overall magnitude of the spectra, in agreement with previous findings (Kamliya Jawahar and Azarpeyvand 2021; Brown 2012; Lawrence 2014). At the furthest spanwise measurement location K5, the double hump behaviour is only at plate heights between $h/D=1-1.75$. Beyond this region or plate positions, the dual hump characteristics are not observed. It is important to note that despite the difference in nozzle geometry, the differences in the SPL between the different plate heights are the same for all the tested nozzle configurations at both K1 and K5 positions.

The results indicate that the scarfed nozzles cause a significant change in the hydrodynamic field in the vicinity of the jet, leading to far-field noise reduction. In summary, the surface pressure fluctuation measurements demonstrate the effectiveness of the scarfed nozzle in reducing jet noise.

Fig. 13

Sound pressure level comparison for the Kulite surface pressure transducers for installed configuration with a plate height of h/D=1.5h/D=1.5, the positions are depicted in Fig. 5

Fig. 14

Sound pressure level on the plate surface for various plate heights for the installed configuration at M=0.5

3.5 Near to Far-Field Coherence

In order to gain a deeper understanding of the noise intensity that is radiated to the far-field and to isolate the non-propagating hydrodynamic field, coherence analysis was conducted between the surface pressure transducer K2 and the far-field microphone placed at a $90^\circ$ angle above the nozzle exit. The coherence was calculated utilizing the following equation (Eq. 3):

$$\begin{aligned} \gamma _{p_ip_j}^2(f)=\dfrac{\mid \Phi _{p_ip_j}(f)\mid ^2}{\Phi _{p_ip_i}(f)\Phi _{p_jp_j}(f)}~~\text{ for }~p_i=~\text{ K2 }~\text{ and }~p_j={\theta }, \end{aligned}$$

(3)

where K2 represents the reference surface pressure transducer, and polar angular far-field microphones are positioned at $\theta =70^\circ ,90^\circ ,120^\circ ,$ and $150^\circ$ above the nozzle exit. The near-to-far field coherence outcomes are presented in Fig. 15. The presented results indicate polar angles of $\theta =70^\circ ,90^\circ ,120^\circ ,$ and $150^\circ$ at $M = 0.5$ and 0.7.

At first glance, it is observed that the coherence levels for upstream polar angles are very high, but they progressively decrease past the sideline position and closer to the jet axis. High coherence levels are observed over a broad frequency range of $St=0.05-1$, with a significant second spectral hump between $St=0.2-0.7$. It is noteworthy that the second spectral hump was also observed in both the near- and far-field measurements in the previous sections. Interestingly, scarfed nozzles exhibit a substantial reduction in the coherence levels for the second hump over the frequency range of $St=0.2-0.7$. Coherence levels for $St=0.02-0.2$ are very similar between the tested nozzles, which could be attributed to the noise caused by the hydrodynamic field interaction with the plate. However, the reduction observed in the scarfed nozzle during the second spectral hump is likely due to changes in the hydrodynamic field, as well as scattering effects. These findings demonstrate that scarfed nozzles not only alter the hydrodynamic field but also substantially modify the scattering effects at the trailing edge. This leads to noise reduction in the far-field regions, particularly in the sideline and upstream polar angles.

Coherence analysis was also used to investigate the effects of plate height on the far-field noise. The near-to-far field coherence between K2 and $\theta =90^\circ$ for eleven plate heights are presented in Fig. 16 at $M = 0.5$ for four tested nozzles SMC000, SCF001, SCF002, and SCF004. The coherence levels for the second spectral hump are found to be high at the closest plate height of $h/D=1$ and 1.25 for the round jet nozzle (SMC000). However, as the plate height is increased, the second hump is no longer predominant, and the coherence levels are marginal for plate heights larger than $h/D=2$. This observation further demonstrates that the interaction of the plate with the evanescent hydrodynamic field around the jet is responsible for the low-frequency amplification. It is also important to note that increasing the scarf angle leads to a decrease in coherence levels for the second hump, even at higher plate heights. This finding suggests that increasing the scarf angle could be an effective strategy to mitigate low-frequency amplification for jet-installation noise.

Fig. 15

Coherence between the Kulite pressure transducer K2 and various far-field microphones at $M=0.5$ and 0.7, with a plate height of $h/D=1.5$

Fig. 16

Coherence between the Kulite pressure transducer K2 and far-field microphone at $\theta =90^\circ$ for various plate heights for the installed configuration at $M=0.5$

Fig. 17

Coherence between the far-field microphones above ($\theta =90^\circ$) and below the nozzle ($\theta =270^\circ$) for the isolated jet and plate for the installed configuration, with a plate height of $h/D=1.5$

To characterize the coherent sound in the far-field and isolate non-propagating hydrodynamic fields, coherence analysis was carried out between two far-field microphones between polar angles $\theta =90^\circ$ and $270^\circ$. The results for the isolated and installed configurations at jet Mach numbers of $M=0.5$ and 0.7 are presented in Fig. 17.

For the isolated configuration, low levels of coherence ($\gamma _{p_ip_j}^2=0.2$) are observed in the low-frequency range for all tested nozzles at $M=0.5$, whereas at $M = 0.7$ lower levels of coherence ($\gamma _{p_ip_j}^2=0.1$) are observed. Brès et al. (2018) demonstrated that noise radiation at the sideline regions ($\theta =90^\circ$) comprises equal contributions from three azimuthal modes. These modes are not necessarily correlated between themselves, and each of them contains individual temporal stochasticity. Therefore two diametrically opposed microphones such as $\theta =90^\circ$ and $270^\circ$ are expected to receive uncorrelated information from the three modes, which would reduce coherence even though noise levels were substantial in Fig. 8. The observed low coherence levels likely arise from the radiation being predominantly influenced by a select set of low-order azimuthal modes.

In contrast, high levels of far-field coherence are observed for both round and scarfed nozzles in the installed configuration. Notably, coherence is higher at $M=0.5$ than at $M=0.7$. These observations suggest the presence of a dipole-type noise source in the low-frequency range between $St=0.015-1$ (Head and Fisher 1976; Yu and Tam 1978). The observed high coherence levels are consistent with prior studies (Cavalieri et al. 2014; Lyu and Dowling 2019), providing support that the observed low-frequency noise amplification is due to the scattering of the near-field hydrodynamic waves by the trailing-edge (Cavalieri et al. 2014; Rego et al. 2020; Mead and Strange 1998). According to this hypothesis, the scattered hydrodynamic pressure waves are significantly more coherent than the noise generated from pure isolated jet mixing due to their deterministic dipole nature. Scarfed nozzles are observed to demonstrate lower coherence levels in comparison to the round nozzle, with the magnitude of coherence reduction directly corresponding to the scarf angle of the nozzle. This reduction is notably more significant for larger scarf angles, with substantial reduction at higher jet exit velocities. Such observations indicate that even a minimal deviation of the jet plume modifies the hydrodynamic field leading to a significant reduction in the scattering effects. However, factors beyond jet deflection could be playing a role in noise reduction for scarfed nozzles. Therefore further investigation of the flow field is required to analyse the the asymmetry and modifications to the hydrodynamic field.

Further analysis of the coherence for different plate heights for two far-field microphones is presented in Fig. 18 at $M=0.5$ for eleven plate heights. As the plate height increases, a decrease in coherence levels is observed. Moreover, there is a significant difference in coherence levels between different plate heights, particularly in regions where the plate height is $h/D<2$. The second hump coherence of the round jet is high, indicating its dipole nature, and is associated with scattering effects. At regions $h/D>2.5$, there is a negligible difference in coherence levels among the tested plate heights. As previously observed, an increase in scarf angle leads to a reduction in coherence levels of the second hump at the closest plate heights. The SCF004, which has the largest scarf angle, exhibits no coherence for the second hump. Overall, this analysis indicates that the scattering effect is most significant when the plate is positioned close to the jet, and the use of scarfed nozzles helps reduce these effects.

Fig. 18

Coherence between the far-field microphones above ($\theta =90^\circ$) and below the nozzle ($\theta =270^\circ$) for various plate heights for the installed configuration, with a plate height of $h/D=1.5$

3.6 Correlation Studies

Cross-correlation analysis is a fundamental tool that is utilized for investigating the dynamics of turbulent jet flow fields and their relationship to radiated noise. The relationship between pressure fluctuations at various points along the jet axis is often quantified using this method, providing insight into the spatial and temporal evolution of the turbulent structures that generate noise. This analysis allows for a better understanding of the underlying mechanisms of jet noise and enables the development of more effective noise reduction strategies.

The current study utilizes unsteady surface pressure to compute cross-correlation using the following equation:

$$\begin{aligned} R_{p_ip_j}(\tau ) =\dfrac{\overline{p_i(t+\tau )p_j(t)}}{p_{i_{RMS}}p_{j_{RMS}}}, \end{aligned}$$

(4)

here $p_i$ and $p_j$ represent consecutive surface pressure transducers K1 and K2, respectively, while $p_{i_{RMS}}$ and $p_{j_{RMS}}$ denote the root mean squared pressure fluctuations. $\tau$ represents the time-delay and the time average is indicated by the overbar. Figure 19 presents the results of the auto-correlation of surface pressure at $M = 0.5$ and 0.7.

The cross-correlation results $R_{p_ip_j}$ at $M = 0.5$ indicate that surface pressure correlations peak at positive time-delays, which suggests the presence of a downstream-moving hydrodynamic field that travels in the direction of the free-stream flow. Results for scarfed nozzles show that the correlation peaks shift rapidly in the positive time-delay direction, which implies the existence of a long-lasting energy field. For the round nozzle, results show that surface pressure fluctuations have a slightly higher correlation, and the correlation peaks shift slowly (larger time-delay) compared to the scarfed nozzle.

Furthermore, based on Taylor’s frozen flow hypothesis, the convection velocity $U_c$ was determined using the distance between the transducers and the maximum value of the cross-correlation time-delay, and these values are presented in Table 1. The normalized convection velocity $U_c/U_j$ at $M = 0.5$ indicates a slow-moving hydrodynamic field for the round nozzle SMC000 and a fast-moving field with high convection velocity for scarfed nozzles. At $M = 0.7$, the hydrodynamic field for all scarfed nozzles shows very similar convection velocity, while the round nozzle exhibits lower convection velocity. Additionally, the value of the maximum correlation coefficient decreases progressively for increasing scarf angle.

Table 1 Convection velocity between K1 and K2

Fig. 19

Cross-correlation between K1 and K2 surface pressure for the installed configuration at acoustic Mach number M = 0.5 and M=0.7, with a plate height of $h/D=1.5$

4 Conclusion

The aim of this study was to investigate the sources and effects of jet-installation noise from scarfed nozzles. Experiments were conducted using four different scarfed nozzles with increasing scarf angles, as well as a round nozzle for reference. The tests were performed on both isolated and installed jets using an instrumented flat plate located at various distances from the jet axis. The far-field noise measurements were obtained using 21 polar angular microphones, which covered a range of 50$^\circ$–150$^\circ$. Additionally, surface pressure fluctuations on the flat plate were examined using Kulite pressure transducers.

To validate the facility, the polar measurements were compared with established studies in the literature (Bastos et al. 2018; Brown and Bridges 2006). The results for the isolated jet showed that, at most polar angles, negligible difference in the far-field noise levels between the round and scarfed jets. However, there was a marginal increase of approximately 1 dB in the low-frequency region and a considerable reduction in the high-frequency region. For the installed configuration, the scarfed nozzles exhibited significant noise reduction in the low-frequency range, with a reduction of about 5 dB compared to the round jet. Closer to the jet exit, the scarfed nozzle exhibited similar noise levels to its respective isolated nozzle, while the round nozzle showed a reduction in spectral levels compared to its isolated case. Overall sound pressure levels (OASPL) showed a substantial reduction in the noise levels for the installed configuration at upstream angles in regions where the jet-installation noise was most dominant. These plots also revealed the noise increase that the scarfed nozzle possessed at downstream angles close to the jet axis.

Investigation of the hydrodynamic field using the Kulite surface pressure transducers revealed a significant reduction in the spectral levels of the hydrodynamic field for the scarfed nozzles, with the reduction directly related to the scarf angle. Near-to-far-field coherence studies showed that the scarfed nozzle not only reduced the hydrodynamic field but also reduced the noise from scattering effects at the trailing edge. This was further confirmed by the coherence of the far-field microphones between $\theta =90^\circ$ and $270^\circ$, where the dipolar nature of jet-installation noise was reduced by the use of scarfed nozzles.

The effect of plate height was investigated and the low-frequency amplification due to jet-installation effects was found to be dominant in the linear hydrodynamic region between $h/D=1-2$ at $St=0.25-0.50$. However, the impact of plate height on the spectra was found to be minimal beyond a height of $h/D=2$. The scarfed nozzle showed superior acoustic performance for all the tested plate heights within the linear hydrodynamic region with a substantial reduction in the second hump.

Cross-correlations were computed for the surface pressure transducers, and the results indicated that the hydrodynamic field for the scarfed nozzle was fast-moving compared to the round nozzle. Interestingly, the scarfed nozzle with fast-moving structures exhibited lower far-field noise levels compared to the round jet with slow-moving structures and high far-field noise. Further investigation of the flow-field is necessary to better understand the noise reduction characteristics of scarfed nozzles.