Similarity Analysis of Jet Wing Interaction Noise

doi:10.21203/rs.3.rs-2332792/v1

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Similarity Analysis of Jet Wing Interaction Noise

https://doi.org/10.21203/rs.3.rs-2332792/v1

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For deeper understanding of the mechanism of the jet wing interaction noise, and improving the current generation of aircraft noise prediction tools. An experimental study of jet installation effects is conducted in this paper by operating a cold jet with a Mach number range of 0.6 to 1.1. The experiment set-up consists of a flat plate placed in proximity to a jet. Installation effects cause low-frequency noise increase with respect to the isolated case, mainly occurring in the direction normal to the plate and upstream of the jet’s exit plane. Based on the similarity analysis of noise spectra, scaling laws are found for the far-field noise produced by different plate lengths and jet exit velocities. The sound intensity of the jet plate interaction noise scales with the third power of the jet velocity and fourth power of the turbulence length scale. And an effective Helmholtz number is proposed to replace Helmholtz number to normalize the jet plate inter action noise spectrum. Finally, a semi-empirical prediction model is proposed based on the similarity analysis. And the verification results show that the prediction model is capable of accurately predicting jet noise in a wide range of jet velocity and plate length.

Jet plate interaction noise

Similarity analysis

Semi-empirical prediction model

Engine noise is a main source of aircraft noise. Even though the introduction of modern high bypass ratio turbofan engine has reduced engine noise greatly, engine noise is still a major noise source. For the under the wing mounted engine, jet noise suffers an installation effect, which makes the jet noise louder than isolated jet. For a modern commercial turbofan aircraft, measurements (Langtry et al, 2014) have shown that the landing gear, the high-lift system as well as the engine-jet/wing interaction effect are the most significant parts of overall airframe noise source. With the ultra-high bypass ratio turbofan, the engine is forced to be positioned closer to the wing, thus some coupling effects, extra installation noises, occur.

Jet noise installation effect had been noticed since 1970s, lots of experiments were carried about this problem. As to reveal the noise generation mechanism and to develop the corresponding control and reduction technologies, laboratory experiments based on reference configuration and numerical tools need to be executed and developed in parallel. Most of the work was based on scaled model of real aircraft or realistic wings. Understanding of the dependence of jet noise on the installation parameters such as the flap setting are very important for installed jet noise control. In the understanding of the engine-jet/wing installation effects, several parametric studies have been carried out. In 1980s, the under-wing installation effect for scale and full-size models have been studied (Way & Turner, 1980; Stevens et al, 1983; Wang, 1980). In the late 1990s, the Boeing Company has launched a series of experiments (Shivashankara & Blackner,1997; Blackner & Bhat,1998) in the Boeing Low Speed Aero-acoustic Facility (LSAF). The elliptic mirror microphone technique and the far-field microphone array technique are used to locate the noise source and to record the far-field noise respectively. These studies have compared the isolated jet and the installed jet, and attention is fixed on the influence of the wing geometry, the effect of the engine pitch angle, the relative position of the engine with respect to the wing and the flap deflection. Based on the data obtained in the experiments, some semi-empirical models for the prediction of installed jet noise of coaxial jets with flight effect have been developed. Recently, with more sophisticated acoustic measurement technology, the jet-flap interaction noise (JFI) and the tonal jet-flap impingement noise are studied for high bypass ratio engine with chevrons and pylons.

Hitherto, there has been little doubt about the mechanism of installation effects on noise at high frequencies: the noise is generated by fine-scale eddies in the jet and reflected off the wing and flap surface; the reflected noise is refracted and attenuated by the presence of the turbulent jet plume. On the other hand, the noise mechanism at low frequencies has not been accepted unanimously. One of the proposed ideas was that the noise is due to the trailing-edge scattering. In Shearin (1983), a jet–surface interaction mechanism is suggested. Pastouchenko & Tam (2007) argued that it is the downwash effect of the wing flap causing more turbulence in the jet that is the principal mechanism. By analyzing the acoustic properties of the low-frequency installed noise and its dependence on the engine position, jet condition and flap position, Lyu et al (2017) concluded that the dominant component of low frequency jet wing interaction noise is trailing-edge noise.

Over the past decades, extensive examination of a large database of supersonic laboratory-scale jet data led to the empirical formulation of a similarity spectrum for jet noise. Tam et al. (1996) examined the NASA Langley Research Center’s Jet Noise Laboratory database and investigated the self-similarity of the noise spectra from jets operated at different conditions. Far-field data from a range of cold and heated supersonic laboratory-scale jets were used to develop two similarity spectra that match the primary features of the noise from the fine-scale structures (FSSs) and the large-scale structures (LSSs). The LSS spectrum, which has a relatively narrow peak and power-law decay on both sides, was reported to fit the data for aft angles. On the other hand, the FSS similarity spectrum, with its broader peak and a more gradual roll-off at both high and low frequencies, matched the radiated spectra to the sideline direction. Tam et al. (1996) proposed that jet noise at any radiation angle can be represented as a sum of LSS and FSS similarity spectra. Two review articles by Tam et al. (2007) and Viswanathan (2008) discussed how the similarity spectra have been compared to a wide variety of laboratory-scale jets.

There are far fewer comparisons between jet plate interaction noise and similarity spectra, which motivates the present study. For deeper understanding of the mechanism of the jet wing interaction noise, and improving the current generation of aircraft noise prediction tools. A number of experimental tests have been performed to quantify the effect on jet noise of installing an aeroengine on a plate. The experiment is conducted to supply experimental data covering a wide range jet of jet plate relative positions. And far-field noise measurements were made at various polar angles (from upstream ${\theta =50}^{\text{o}}$ to downstream ${\theta =160}^{\text{o}}$).

A brief introduction to the experimental setup is provided in Section 2. Section 3 presents the analyses the noise spectrum characteristics and far-field directivity of jet plate interaction noise. Section 4 presents the similarity analyses of jet plate interaction noise. And a semi empirical prediction model is provided in Section 5. Finally, Section 6 concludes the paper.

A simplified model of the jet-wing configuration was considered in order to gain insight into the mechanisms generally responsible for the installation noise. Experiments were carried out in the full anechoic chamber of BUAA as shown in Fig. 1 (a). The chamber has a lowest operation frequency of around 100 Hz. The geometry tested during the jet-surface interaction test consisted of a round nozzle and a flat plate using the geometry shown in Fig. 1 (b). The round profiled nozzle has a diameter D = 50.8mm (Fig. 2 gives the geometry of the nozzle plan view). As shown in Fig. 3, the plate was mounted on rails so that it could be moved manually in the axial direction. The plate was made using a 2 mm thick aluminum cut into sections that could be added or removed to change the length of the surface. This allowed testing of 5 different surface lengths ranging from L/${D}_{j}$ =2.5 to L/${D}_{j}$ =6.5.

Far-field noise was measured using 22 GRAS 46BF 1/4” microphones (type 4189, frequency range 4–100K Hz, sensitivity 3.6 mV/Pa), sampled by a data max digital recorder at 100kHz for 5 seconds, simultaneously with all rig parameters. As shown in Fig. 4, the microphones were located on an arc over 60 diameters from the nozzle exit over an angular range of 60° to 160° for both shielded and unshielded sides. Microphone calibrations were maintained according to manufacturer’s strict specifications. Before the measurements, the microphones were calibrated with a B&K pistonphone type 4228.

Measurements were performed for subsonic and supersonic jets. The parameters of the investigated jet operating conditions are presented in Table 1 in the form of Mach numbers ${M}_{j}$, which were calculated from the jet-outflow velocity ${U}_{j}$ and the ambient sound speed c. The Reynolds number for this nozzle model for the minimum jet-outflow regime calculated from the nozzle diameter and the jet velocity is Re ~ 10⁶, which corresponds to the self-similar jet-outflow regime and, if necessary, provides scaling of the relevant noise data.

Table 1

Jet operation condition
Regime	1	2	3	4	5	6
Acoustic Mach number ${M}_{j}$ of jet	0.6	0.7	0.8	0.9	1.0	1.1

Before discussing the experimental results, it is worth comparing the current experimental data with well-known datasets to ensure that the experimental rig is set up properly. It is sufficient to only compare the reference isolated jet noise spectra. Figure 5 shows the narrow band far-field noise spectra of this study against that of NASA SHJAR^[7], respectively. The Strouhal number is defined as $St=f*{D}_{j}$. As can be seen, the far-field sound spectra at ${90}^{\text{o}},$ ${120}^{\text{o}}$and ${150}^{\text{o}}$ agree with each other well in their spectral shapes and absolute magnitudes. There is, however, a small deviation (about 1dB) at peak frequency. This might be due to the different nozzle shapes and inlet flow conditions. Considering the inevitable differences between the two experiments, such an agreement is sufficient to show that the experiment is set up properly and the measurement is reliable.

The far-field Power Spectral Density (PSD) for the isolated and installed jets (L = 3.5${D}_{j}$ and h = 0.8${D}_{j}$) are plotted versus the Strouhal number in Fig. 6. The spectra are obtained for a constant frequency band of 32 Hz, and at polar angles $\theta =\pm 60^\circ ,\theta =\pm 90^\circ ,\theta =\pm 120^\circ ,$ and $\theta =\pm 150^\circ$. Against the noise background of an isolated jet for the regime with ${M}_{j}$ = 0.6, jet plate interaction noise prevailed for nearly all values of the polar angle θ. For $\theta =\pm 60^\circ$, installation effects result in the strongest low-frequency noise amplification, up to St = 1.0. The maximum increase, relative to the isolated case, is 17 dB at St = 0.28. In the sideline direction ($\theta =\pm 90^\circ$), there is a difference of 14 dB between installed and isolated noise levels. For $\theta =\pm 150^\circ$, installation effects result in a lower amplification with respect to the isolated case at the spectral peak (3 dB in the frequency range 0.07 < St < 0.5).

From the results shown in Fig. 6, it is clear that the interaction noise extracted in the low-frequency region has a symmetric character (coincidence of the spectra for opposite microphones). This confirms that, for this frequency range, the dominant noise generation mechanism is the scattering of the near-field hydrodynamic waves at the trailing edge of the flat plate. While the observed difference in the spectra for higher frequencies can be explained by the effect of reflection of jet radiated noise from the plate surface. For St > 1, the spectra for the installed cases are dominated by fine scale turbulent jet noise sources. At the reflected side, noise levels are approximately 3 dB higher than those of the isolated case, as expected from the reflection on a half-plane.

The far-field PSD of the installed jet (L = 3.5${D}_{j}$ and h = 0.8${D}_{j}$) for the high Mach number case ( ${M}_{j}$= 0.9) are plotted with the respective isolated configuration spectra in Fig. 7 for polar angles θ = ±60◦, θ = ±90◦, θ = ±120◦ and θ = ±150◦. For the high-Mach-number case (${M}_{j}$= 0.9), installation effects result in a lower amplification with respect to the isolated case at the spectral peak(9dB for θ = ±60◦, 7dB for θ = ±90◦, 4dB for θ = ±120◦ and 0dB for θ = ±150◦). It is worth noting that the contribution of interaction noise to the total noise decreases with an increase in the jet-outflow velocity. For θ = ±150◦, i.e. towards the jet axis, installation effects are no longer visible and the spectra are similar to that of the isolated jet. It shows that, for high-speed jets, jet plate interaction noise could be extracted only in side directions, since the interaction effect hardly manifested itself at all at large polar angles against the jet noise background.

The previous observations are confirmed by the directivity plots of overall sound pressure level (OASPL), integrated in the range of 100Hz to 5000 Hz, shown in Fig. 8 In the polar direction, the maximum noise increase occurs at θ ≈ ±50◦, where the noise levels in the case of plate length L = 3.5${D}_{j}$ and L = 6.5${D}_{j}$ is increased by 3 dB and 5 dB respectively compared with the isolated jet case. Smaller angles could not be obtained due to the presence of the nozzle, which acts as a shielding body. Approaching the jet axis, the curves for the isolated and installed cases collapse, confirming that the large structure turbulent jet noise sources dominate.

In this section, the effects of jet velocity and plate length on the spectral amplitude of an installed jet are addressed. This is performed by finding scaling laws for the far-field spectra for different geometric cases, using only information from the isolated jet. Those scaling laws are deemed to predict the far-field noise independently of the geometric configuration adopted for the plate, reducing the need for testing or computing several cases.

The effect of changing the plate length is shown in Fig. 9. Spectra are obtained for three surface lengths, at fixed radial position h = 0.8${D}_{j}$, for θ = −90◦ and ${M}_{j}$ = 0.9. It is shown that, for longer surfaces, noise increase is higher at low frequencies, with a difference of 9 dB between the curves for L = 6.5${D}_{j}$ and L = 2.5${D}_{j}$, for h = 0.8${D}_{j}$ and St = 0.11. For longer plates, the spectral peak also moves towards lower frequencies: for h = 0.8${D}_{j}$ the spectral peak is at St = 0.15 and 0.11 for the shortest and longest plates, respectively. This is due to the increase of energy content of large-scale structures in the mixing layer in the downstream direction of the jet (Lawrence et al., 2011). Since these structures generate low-frequency hydrodynamic pressure waves, the scattering effects are also amplified in that frequency range. At low Strouhal numbers, the integral length scales of jet shear layer exhibit near constant behavior (Kerherve ́ & Fitzpatrick, 2011). Based on similarity equation for potential core lengths of jet flow (Witze, 1974), the jet length scale near the trailing edge for jet plate interaction noise prediction is given by:

$${l}_{s-i}=3\left(1-0.16{M}_{j}\right)\sqrt{\frac{L}{{D}_{j}}}{D}_{j}$$

where ${M}_{j}$ is jet exit Mach number,${D}_{j}$ is nozzle diameter.

The far-field noise data in Fig. 9 show higher noise levels and a broader frequency range of amplification when the trailing edge is farther away from the nozzle exit. Based on the respective plate length for each case, the fourth power of the length scale for jet plate interaction noise is used to scale the jet plate interaction.

As shown in Fig. 10, where there is a fairly good agreement between the curves for 0.03 < Helmholtz number < 0.3. For Helmholtz number > 0.3, the curves diverge since this region of the spectra is dominated by noise from jet fine scale turbulent noise sources reflected on the surface. As a result, the sound intensity of jet plate interaction noise with the fourth power of the length scale:

$${I}_{i}\propto {l}_{s-I}^{4}$$

The installed far-field noise levels can be scaled with ${M}_{j}^{3}$, based on the respective jet exit velocity for each case. This is shown in Fig. 11, where there is a fairly good agreement between the curves for 0.03 < Helmholtz number < 0.3. As a result,th, sound intensity of jet plate interaction noise with the fourth power of the jet velocity:

$${I}_{i}\propto {M}_{j}^{3}$$

As shown in Fig. 9,it is obvious that the Strouhal number of the spectrum peak decreases with an increase of plate length. And the Helmholtz number of the spectrum peak increases with a increase of jet velocity which is shown in Fig. 11. Neither Strouhal number nor Helmholtz number can perfectly reflect the similar characteristics of jet plate interaction noise spectrum. Based on the length scale near the trailing edge for jet plate interaction noise, as shown in Formula (1), an effective Helmholtz number is given as follow:

$${He}_{eff}=\frac{f*{l}_{s-i}}{{c}_{0}+{U}_{j}}$$

where f is the frequency, ${l}_{s-i}$ is the length scale near the trailing edge for jet plate interaction noise, ${c}_{0}$ is the acoustic velocity and ${U}_{j}$ is the jet exit velocity.

The dimensionless spectrum of jet noise under different experimental conditions is shown in Fig. 12 The horizontal coordinate is the new frequency dimensionless parameter ${He}_{eff}$, and the vertical coordinate is the dimensionless power spectral density (PSD) according to Formula (2) and Formula (3). As shown in Fig. 13, there is a fairly good agreement between the curves in the frequency range 0.025 <${He}_{eff}$< 0.1, where jet plate interaction noise is dominant.

Against the noise background of an isolated low speed jet, interaction noise prevailed for nearly all values of the polar angle θ (up to a 17dB excess in jet upstream direction for a jet with ${M}_{j}$= 0.6). As for high-speed jets, interaction noise could be extracted only in upstream and side directions, since the interaction effect hardly manifested itself at all at large polar angles against the jet noise background. Jet noise and interaction noise were separated under the assumption that these types of noise are mutually uncorrelated:

$${I}_{total}={I}_{j}+{I}_{i}$$

where ${I}_{j}$ and ${I}_{i}$ are the sound intensities of jet noise and jet plate interaction noise, respectively.

According to Tam’s two-source model, there is a similarity spectrum that represents each type of turbulent mixing noise in jets: L for the LSS and F for the FSS. The similarity spectra are functions of the frequency ratio ${f}_{r}=f/{f}_{peak}$, where ${f}_{peak}$ is the spectral peak (or characteristic) frequency. The detailed equations for computing the similarity spectra are found in Ref. 16. The L and F similarity spectra, for the perdition of isolated jet, are illustrated in Fig. 13.

In this study, a similar procedure is carried out to find a scaling law for the noise generated by plates with different lengths and different jet velocity.

The scaling law for sound intensity of jet plate interaction noise is as follow:

$${I}_{i}\left(f\right)={A}_{I}{M}_{j}^{3}{l}_{s-i}^{4}{e}^{-2{\left[{\text{log}}_{10}(f)-{\text{log}}_{10}\left({He}_{eff}\frac{{c}_{0}+{U}_{j}}{2\pi *{l}_{s-i}}\right)\right]}^{2}}$$

Therefore:

$${I}_{total}={I}_{F}+{I}_{L}+{I}_{i}$$

On converting to decibel per Hz, the spectral density of the sound pressure field can be written as:

$$PSD=10{\text{log}}_{10}\left(\frac{{I}_{total}}{{p}_{ref}^{2}}\right)$$

An example of the empirical jet plate interaction noise prediction model is shown in Fig. 14, where the fine scale turbulent noise of isolated jet and jet plate interaction noises are predicted at L = 4.5${D}_{j}$ and h=${0.8D}_{j}$, for the regime with ${M}_{j}$= 1.1. It is shown that, compared to the experimental results, both fine scale turbulent jet noise and jet plate interaction noise are well predicted in the frequency range 100Hz to 2000Hz, where jet plate interaction noise is dominant.

Figure 15a–15d show comparisons of the calculated noise spectra and the experimental measurements for the regime with${M}_{j}$ = 0.7. Figure 16a–16d show comparisons of the calculated noise spectra and the experimental measurements for the regime with ${M}_{j}$ = 0.9. Figure 17a–17d show comparisons of the calculated noise spectra and the experimental measurements for the regime with ${M}_{j}$ = 1.1. As can be seen, there are excellent agreements between the calculated spectra and measurements in the frequency range 100Hz to 3000Hz, where jet plate interaction noise is dominant.

The jet-wing interaction noise experiment is conducted to supply experimental data covering a wide range jet of jet-wing relative positions for improving the current generation of aircraft noise prediction tools. The experiment dataset has been presented to show important features of the jet-surface interaction noise as jet velocity, and surface position change. Installation effects cause low-frequency noise increase with respect to the isolated case, mainly occurring in the direction normal to the plate and upstream of the jet’s exit plane.

The similarity analysis of far-field noise spectra shows that the sound intensity of the jet plate interaction noise scales with the third power of the jet velocity and fourth power of the turbulence length scale. An effective Helmholtz number is proposed to replace Helmholtz number to normalize the jet plate inter action noise spectrum. The comparison shows that the dimensionless parameter can reflect the similar characteristics of jet plate interaction noise spectrum fairly well. Furthermore, a semi-empirical model is proposed for the prediction of jet plate interaction noise. It is demonstrated that the prediction model is capable of accurately predicting jet noise over a wide range of jet velocity and plate length.

Author Contributions Xihai Xu conducted the experiments, processed the data, establish the similarity prediction model, created the plots and diagrams, and wrote the first draft of the manuscript. Junlin Liu contributed to the writing of the paper and created Figs. 9 and 10. Xiaodong Li supervised the research and contributed to the interpretation of the data. All authors commented on previous versions of the manuscript and read and approved the final manuscript.

Fundings The present work is under the support of National Key Research and Development Project (Grant No. 2018YFA0703300), the National Natural Science Foundation of China (No. 91952301), the National Science and Technology Major Project (No. J2019-II-0006-0026) and the Key Laboratory of Aerodynamic Noise Control of China Aerodynamics Research and Development Center (No. ANCL20190101).

We confirm that the material is the authors’ own original work, which has not been previously published or is being considered for publication elsewhere.

Conflict of interest The authors have no conflicts to disclose.

Ethics approval Not applicable.
Consent to participate Not applicable.
Consent for publication Not applicable.

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No competing interests reported.

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Similarity Analysis of Jet Wing Interaction Noise

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Abstract

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1. Introduction

2. Experimental Setup

3. Installation Effects And Trailing-edge Scattering

4. Similarity Analysis

5. A Semi-empirical Prediction Model

6. Conclusion

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References

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