Flow and acoustics in a model rocket flame deflector and deflector cover

Abstract

The design of a rocket launch environment is a complex process with many different aspects that are highly interconnected. Acoustics, which is one of these, should be investigated in detail due to possible devastating effects on the launch vehicle, crew, and launch environment. This study uses a numerical method to consider a passive noise reduction method applied to a supersonic jet impinging on an inclined flame deflector to decrease the acoustic loads on the launch vehicle and noise levels in the far-field. In a supersonic jet impinging on an inclined flat plate configuration, acoustic waves that travel upstream originate from the impingement and wall jet regions. These upstream traveling waves are a combination of the acoustic waves that are produced by the high speed jet flows in the wall jet region and acoustic waves that reflect from the impingement wall. Due to the inclination of the impingement plate, these waves either travel to the far-field in the upstream direction or travel towards the free-jet region interacting with the high speed flow near the nozzle lip. This interaction can create a self sustaining feedback loop, which can cause acoustic tones to appear in the near- and far-field spectra. It is the aim of the present study to block the upstream traveling waves by introducing a second inclined wall with a circular cut-out between the nozzle exit and the impingement plate. Different configurations with different wall locations and cut-out sizes are investigated using a Detached Eddy Simulation CFD solver and an acoustic solver that is based on the Ffowcs Williams and Hawkings analogy. The mechanisms for the establishment of the feedback loops are examined.

Introduction

One of the most important elements in the design of a launch environment is acoustics. Due to the risks to the health of the crew, the integrity of the rocket payload, electronics and launch vehicle, and the high noise pollution levels around the launch site, NASA included acoustics as one of the top five highest risk categories in their last three major rocket programs. ¹

It is important to obtain a good understanding of the noise generation mechanisms during a rocket launch to effectively decrease the impacts of the acoustic loads. Empirical methods are described in Ref.2. Compared to free-jet configurations, the existence of the deflector in a launch environment, hence the impingement of the high speed jet plume, creates new acoustic sources. There are three distinct regions in a normal impingement configuration:^3–5 the free-jet region, the impingement region, and the wall jet region. The free-jet region is located between the nozzle exit and approximately a nozzle diameter upstream of the impingement plate. In this region, the flow shows similar characteristics to a free-jet. The impingement region is where the flow impinges on the plate and changes direction to follow the plate. Finally, the wall jet region is where the flow follows the impingement plate while still being supersonic. The same regions are observed in inclined impingement cases; however the impingement and wall jet regions are asymmetric due to the plate’s inclination.

Several research efforts have been dedicated to the investigation of the acoustic waves that originate from the flow regions that exist in an impingement case.^5–11 Three different acoustic wave sets were defined by Nonomura et al. ¹² The first two sets of acoustic waves correspond to Mach wave generation. One of them is produced by the main jet and one by the supersonic flow in the wall jet region. Nonomura et al. also detected another set of waves they called “acoustic waves,” the source of which they couldn’t determine. ¹² They suggested possible sources as shock-shear layer interaction, separation, and re-attachment. Further research by Honda et al. ¹³ explained the source of these acoustic waves as plate shock waves and bubble-induced shock waves.

The reflections from the impingement plate and upstream traveling acoustic waves that originate in the wall jet-region cause feedback loops that disturb the flow in the free-jet region. Powell ¹⁴ proposed that the impingement of the large-scale structures originating from the nozzle lip, produce pressure disturbance waves in the impingement region. These waves then travel back upstream to the nozzle lip and create a feedback loop. The downstream parts of this feedback mechanism is explained by the growing flow disturbances that are convected downstream by the jet. However, the upstream parts of the feedback mechanism have not been identified clearly. Ho & Nosseir^15,16 suggested in their classical feedback model that these upstream traveling waves that contribute to the feedback loop lie outside of the flow. Tam & Ahuja ¹⁷ and Tam & Norum ¹⁸ on the other hand, suggested that these waves are a part of the upstream-propagating subsonic acoustic wave modes of the jet, where the feedback waves propagate inside the jet column. They analyzed these modes using the dispersion relations of the upstream-propagating acoustic waves, which were derived using a vortex-sheet jet model. ¹⁷ Gojon et al. ¹⁹ combined the classical feedback model by Ho & Nosseir^15,16 and the wave analysis of Tam & Ahuja ¹⁷ by assuming that the acoustic wavenumber in the feedback loop is equal to the opposite of the wavenumber of the upstream-propagating acoustic waves. Bogey & Gojon ²⁰ used this new feedback loop model to investigate a design Mach number M _d = 1.5, Reynolds number Re = 6 × 10⁴, ideally expanded round jet impinging on a flat plate located at various distances to the nozzle exit, ranging from 3D to 6D, where D is the nozzle diameter. They concluded that the feedback loop is closed by upstream traveling acoustic waves both inside and outside of the supersonic jet.

This phenomenon is also effective in a jet impinging on an inclined plate configuration. Gojon and Bogey ²¹ investigated the effects of the angle of impact on the aeroacoustic feedback mechanism. They investigated a planar jet impinging on a flat plate normally, and with angles of impact of 60° and 75°. They observed that for an angle of impact of 75°, the feedback mechanisms establish mainly along the lip that is farther away from the plate. They also observed that for an angle of impact of 60°, none of the modes of the feedback persists in time, but several modes randomly establish during short periods of time.

There are many different noise reduction methods that have been investigated and applied to decrease the noise levels in the close proximity of the launch vehicle and in the far-field, ranging from the use of water injection,^22–25 to design alterations of the flame deflector and the launch pad.^{6,12,13,26–28} The water injection induces momentum transfer between the water and the main jet, which reduces the broadband shock-associated noise and mixing noise by disturbing the phase relation between the shock cells and the convected turbulence. ²⁹ Most flame deflector design changes focus on using an oblique plate to guide the high intensity flow away from the launch vehicle.^{6,12,13,26–28} Use of curved deflectors is also common, since the jet flow impinges more smoothly on the deflector.^30–32 Eliminating the sharp turns of the high speed jet flow decreases the chances of creating shocks in the impingement region, which are prominent sources of upstream traveling acoustic waves. A detailed investigation was performed by Tatsukawa et al., ³² where the authors aimed to minimize the spatial average of the OASPL(Overall Sound Pressure Level) near the payload fairing, to minimize the maximum time-averaged pressure on the deflector surface, and to minimize the geometry change of the inclined flat plate. Tsutsumi et al., ³³ attempted to block the acoustic waves that are created in the free-jet region reaching the impingement plate, reflecting towards the launch vehicle, by introducing a deflector cover to the upper part of the deflector. Yenigelen and Morris, ³⁴ based on the idea of blocking the acoustic waves by a physical barrier, investigated the effects of introducing a wall with a cut-out between the nozzle exit and an impingement plate. This method proved to be effective in decreasing the noise levels in the near and far-fields. Similar studies by Kawai et al., ³⁵ Troyes et al., ³⁶ and Varé and Bogey ³⁷ examined the effect of a hole in a plate between the jet and the deflector, but they did not consider reflections from the impingement plate itself. Prasad et al. ³⁸ used Doak’s Momentum Potential Theory (MPT) to segregate the flow field into its hydrodynamic and acoustic components to investigate the effects of a wall with a circular cut-out placed between the nozzle exit and the impingement plate. Yenigelen and Morris^39,40 applied the same passive noise reduction method to an inclined impinging jet configuration to investigate the effects of the cut-out size and the wall location on the flow field and acoustic spectra in the near- and far-fields.

The present study investigates the effects of introducing a wall with a circular cut-out (deflector cover) between the nozzle exit of a design Mach number 1.5 nozzle, operated at design conditions producing an unheated jet, and an inclined impingement plate (deflector) located at 6D away from the nozzle exit with an inclination angle of 50°. Five configurations with different wall locations and cut-out sizes are investigated by comparing the flow and acoustic results to a baseline configuration that does not have the noise reduction method applied. The goal is to obtain a better understanding of the noise sources that exist in an inclined impinging jet case and possible new noise sources that are created by the introduction of the wall with a circular cut-out, while trying to find a configuration with a good noise attenuation performance. Although both the Mach number and temperature values are much lower than rocket plumes, they are high enough to provide results for a qualitative discussion of noise sources and suggest a noise reduction method. Nonomura et al. ⁴¹ reference their previous work, Nonomura et al. ¹² to claim that the source locations and noise generation mechanisms, are the same for hot and cold jets.

As with the majority of the previous investigations of this topic, the geometry of the launch pad, deflector cover, and flame deflector is very simplified. For example, in the present study, the noise generated by the flame exhaust from the deflector duct is not considered. This simplification permits individual aspects of a more realistic configuration to be examined separately, without the use of excessive computational resources.

The numerical methods and computational setups used in this research are described in the next section. This is followed by an investigation of the flow and acoustic results for both the baseline configuration and the configurations with the noise reduction method. Finally, the mechanisms associated with the feedback loops are investigated and conclusions from this research and suggestions for future work are provided in a final section.

Numerical methods and computational setup

Flow solver

In this research, a contoured convergent divergent nozzle with a design Mach number of 1.5 is operated under design conditions, where the total temperature ratio is kept as TTR = 1.0 with ambient temperature of 289 K and ambient pressure of 101,326 Pa. The nozzle diameter is D = 0.0362 m and the impingement plate is located at 6D away from the nozzle exit with an inclination angle of 50°.

The flow field is computed numerically by a flow solver called CHOPA (Compressible High Order Parallel Acoustics). The compressible unsteady Reynolds-Averaged Navier-Stokes (URANS) equations, supplemented with a modified version of the Detached Eddy Simulation, ⁴² are solved in a general curvilinear coordinate system with a 4th order Dispersion-Relation-Preserving (DRP) scheme. ⁴³ Sub-Grid Scale (SGS) models are not included, as used in model-free large eddy simulations (LES) computations, ⁴⁴ to avoid excessive dissipation that was observed in previous research. ⁴⁵ The unsteady turbulent jet flow is marched in time by the dual-time stepping method, ⁴⁶ and the Spalart-Allmaras turbulence model ⁴⁷ is used as the turbulence model.

The computational grid for the baseline configuration and configurations with the noise reduction method have approximately 32 million grid points. These grid points are distributed in 16 blocks in the baseline configuration: 5 inside the nozzle, 4 upstream of the nozzle exit around the nozzle shroud surfaces and 7 downstream of the nozzle exit. A center block is created to avoid the singularity at the centerline and this block is surrounded by 4 perfectly cylindrical blocks downstream of the nozzle extending to x/D = 1.24 and r/D = 1.5. The cut-outs of the configurations with the noise reduction methods are located inside these blocks. Since the cut-outs are to be parallel to the nozzle exit, the upstream and downstream surfaces of these cylindrical blocks are constructed to also be parallel to the nozzle exit. The grid sizes used in this study are set to resolve frequencies up to St = 2.0 in the near-field. Grid sizes in the streamwise direction are kept constant, dx/D = 0.015, between the nozzle exit and the impingement plate. In the 4 cylindrical blocks that surround the center block, the grid sizes are set to be dr/D = 5.5 × 10⁻⁴ at the nozzle shroud surfaces and gradually stretch to dr/D = 0.03 at radial edge of the blocks at r/D = 1.5. After r/D = 1.5, grids continue to stretch gradually to the edge of the computational domain where the largest grid size in the radial direction is dr/D ≈ 0.13. The details of the selection of the grid sizes are given in Refs. 34 and 48. The configurations with the noise reduction method are created by removing the grid points where the wall with a cut-out is located, which creates walls with the thickness of dx = 0.17D. The grid sizes and the structure of the grid for configurations with the noise reduction method are kept the same as the baseline configuration to ensure a more reliable comparison.

Acoustic solver

The flow field results are extended to near and far-field observers by a noise prediction code called PSJFWH (Permeable Surface Jet noise prediction with the Ffowcs Williams & Hawkings theory) in this research. The Ffowcs Williams & Hawkings (FWH) theory ⁴⁹ is implemented in this code with a 5 point Gauss–Legendre quadrature integral approximation using a 2-dimensional Lagrange interpolation method.

The permeable FWH surfaces are shown as translucent green surfaces in Figures 1 and 2. Figure 1 shows the surfaces that are used in the baseline configuration and Figure 2 shows an example of the surfaces that are used for the configurations with the noise reduction method. These acoustic data extraction surfaces both have a cone shaped part to enclose the acoustic sources in the free-jet region. This conic part of the surfaces extends until the impingement region for the baseline configuration and is connected to surfaces that are parallel to the impingement wall extending to the wall jet region. These surfaces extend from (x/D, y/D) ≈ (5.5, − 1.05) to (x/D, y/D) ≈ (10, − 4.85) on the negative y-side of the jet centerline and from (x/D, y/D) ≈ (3.4, 1.2) to (x/D, y/D) ≈ (3.23, 1.5) on the positive y-side of the jet centerline. The cone part of the surfaces stops at the wall with a cut-out for the configurations with the noise reduction method. An extensive part of the upstream side of the wall with a cut-out is also included in the acoustic data extraction surfaces to ensure that the acoustic waves that are being reflected from the upstream side of the wall with a cut-out are included in the calculations. On the positive y-side of the nozzle, data extraction surfaces extend to approximately y/D = 4.9 forming a half circular surface due to the grid structure. On the negative y-side a rectangular surface extends to approximately y/D = 6.8, which has a width of z/D ≈ 16. More details about the far-field acoustic spectra calculations can be found in Ref. 34.

Figure 1.

Ffowcs Williams and Hawkings surfaces shown as translucent surfaces on mean Mach number contours for baseline configuration.

Figure 2.

Ffowcs Williams and Hawkings surfaces shown as translucent surfaces on mean Mach number contours for configuration with noise reduction method.

Results and discussions

Baseline configuration

Figure 3 shows the mean Mach number contours of the baseline configuration. Even though the nozzle is operated at the nominal design Mach number, mean Mach number contours show that there are still shocks in the plume.

Figure 3.

Flow field results for the baseline configuration. Mean Mach number contours with the sonic line. Black dots show the locations of the near-field observers with a table showing the exact locations of the observers on the positive y-side of the shroud. The observer locations on the opposite side of the shroud are mirror images of the observers on the positive y-side.

The instantaneous density gradient magnitude and pressure time derivative contours of the baseline configuration are shown in Figure 4. The pressure time derivative contours show the prominent acoustic waves. It is observed that the majority of the acoustic waves that travel to the far-field in the upstream direction are on the negative y-side of the nozzle, because of the inclination angle. These acoustic waves mostly originate from the impingement and wall jet regions. Both the high speed flow in these regions itself and the interaction of the downstream traveling acoustic waves and this high speed flow are the sources of these acoustic waves. On the positive y-side of the nozzle, the acoustic waves originating from the free-jet region are reflected from the impingement plate and travel back towards the free-jet region interacting with the downstream traveling acoustic waves and the high speed flow.

Figure 4.

Density gradient magnitude and pressure time derivative contours for the baseline configuration.

The goal is to block most of these upstream traveling waves by introducing a wall with a circular cut-out between the nozzle exit and the impingement plate to reduce the noise levels in both near- and far-fields, especially around the shroud.

Figures 5 and 6 show a comparison of the acoustic spectra at far-field observers calculated numerically with experimental data taken at the Florida Center for Advanced Aero-Propulsion’s High-Temperature Jet Facility at Florida State University. ⁵⁰ The observers are located at R/D = 13.7, θ = 90° and R/D = 84.8, θ = 270°, where R is the distance of the observer from the center of the nozzle exit and θ is the angle measured from the downstream jet centerline. Both predicted spectra show a good comparison with the experimental results. The differences in the lower frequencies are expected to improve with additional time-steps. Since the aim of this paper is to compare the configurations with the noise reduction method to the baseline configuration, the reasonable accuracy of the results should be sufficient.

Figure 5.

Acoustic spectra comparison of numerical calculations with experimental data ⁵⁰ at far-field observers: R/D = 13.7, θ = 90°.

Figure 6.

Acoustic spectra comparison of numerical calculations with experimental data ⁵⁰ at far-field observers: R/D = 84.8, θ = 270°.

Configurations with the noise reduction method

The locations of the wall and the sizes of the cut-outs for the five configurations with the noise reduction method are shown in Table 1. The first three configurations have the same wall location with decreasing cut-out sizes. x1.r2 and x3.r2 have the same cut-out sizes as x2.r2, but x1.r2 is located closer to the nozzle exit and x3.r2 is located further downstream. The location of the walls and the size of the cut-outs are determined by examining the flow field results of the baseline configuration and the results gathered in previous research focusing on the same nozzle setup, but with a flat impingement plate. ³⁴

Table 1.

Configuration list for the inclined impinging jet with the noise reduction method. x/D: distance of the wall with a cut-out to the nozzle exit, r/D: radius of the cut-out.

Config. name	x/D	r/D
x2.r3	0.87	0.95
x2.r2	0.87	0.88
x2.r1	0.87	0.80
x1.r2	0.67	0.88
x3.r2	1.07	0.88

Acoustic spectra and noise reduction

In this section, the acoustic characteristics of the configurations with the noise reduction method are compared to the baseline configuration at near and far-field observers. The far-field observer locations are the same as for the baseline configuration. The near-field observers are located in close proximity of the nozzle shroud, shown as small dots on the mean Mach number plot that is shown in Figure 4.

Table 2 shows the noise reduction levels achieved for different configurations compared to the baseline noise levels at both near- and far-field observers. The final two rows of the table show the average OASPL levels at near- and far-field observers for the different configurations. While x1.r2, which has the cut-out located closest to the nozzle exit, is observed to have the highest noise reduction average at the far-field observers with −24.4 dB, it can be concluded that the far-field noise reductions for all configurations are very promising with high noise reduction values. The wall with a cut-out is located farthest to the nozzle exit for x3.r2, which has the poorest noise reduction performance in the far-field. Hence, it can be argued that effective blockage of the acoustic waves that are produced in the free-jet region is important in decreasing the noise levels in the far-field observers that are considered in the present study. The noise reduction average at the near-field observers is highest for x3.r2 with −9.2 dB and lowest for x2.r3 with 3.7. It is important to note here that x2.r3, which has the poorest near-field noise attenuation performance, has the largest cut-out size. This is followed by x1.r2 which has the wall with a cut-out located closer to the nozzle exit. Smaller cut-out sizes and locating the wall closer to the nozzle exit both puts the cut-out edges farther to the high speed jet flow. This allows more area for possible upstream traveling flow and acoustic waves, resulting in higher noise levels in the near-field. From the configurations with the best near-field noise attenuation levels, x2.r1 has the smallest cut-out size and x3.r2 is located the farthest from the nozzle exit, which supports this argument.

Table 2.

Noise reduction comparison of different configurations in OASPLs. Free-jet impinging on an inclined plate case is used as the baseline. FF: Far-field, NF: Near-field, p: Positive y side of the nozzle, n: Negative y side of the nozzle, Obs.: Observer, configuration names: x: distance to nozzle exit, r: hole size. The first column shows the OASPL for the baseline configuration.

(dB)	Obs.	x2.r3	x2.r2	x2.r1	x1.r2	x3.r2
80.7	FF1	-21.1	-24.2	-23.8	-24.7	-22.2
106.7	FF2	-21.2	-22.6	-23.2	-24.0	-19.9
142.8	NF1p	-0.0	-10.6	-3.9	-4.7	-10.8
141.5	NF2p	-0.1	-4.7	-5.0	-0.6	-5.0
139.8	NF3p	-2.9	-6.1	-6.6	-2.6	-6.6
139.2	NF4p	-3.7	-6.8	-7.3	-3.4	-7.4
143.5	NF1n	-3.5	-13.4	-6.7	-8.2	-14.1
142.2	NF2n	-4.6	-7.5	-8.6	-3.6	-8.2
140.6	NF3n	-7.0	-9.7	-10.7	-6.4	-10.3
140.0	NF4n	-7.7	-10.5	-11.4	-7.2	-11.0
	FF Av.	-21.2	-23.4	-23.5	-24.4	-21.1
	NF Av.	-3.7	-8.7	-7.5	-4.6	-9.2

The acoustic spectra comparisons for configurations with the noise reduction method and the baseline configuration at the far-field observers are shown in Figures 7 and 8. These spectra show several new peaks for the configurations with the noise reduction method that do not exist for the baseline configuration. The strongest peaks occur at frequencies St = 0.37, St = 0.54, St = 1.2 and St = 1.75. These peaks are a result of feedback loops that are sustained by acoustic waves that travel upstream as a result of the presence of the wall with a cut-out between the nozzle exit and the impingement wall. Acoustic waves that are created in the free-jet region upstream of the wall with a cut-out are reflected from the upstream surfaces of the wall with a cut-out traveling back towards the nozzle lips. These waves then trigger pressure disturbances with the same frequency, closing the feedback loops that result in spectral peaks.

Figure 7.

Acoustic spectra comparison of configurations with the noise reduction method to the baseline configuration at far-field observers, (a) R/D = 13.7, θ = 90°.

Figure 8.

Acoustic spectra comparison of configurations with the noise reduction method to the baseline configuration at far-field observers, R/D = 84.8, θ = 270°.

The most significant difference in the spectra shown in Figures 7 and 8 is observed at St = 0.37. At both observer locations, this peak is only observed for x2.r1 and x1.r2. As mentioned earlier in this section, these configurations have the cut-out edges located closer to the high speed jet flow. So, it is argued that the acoustic waves that trigger the pressure disturbances around the nozzle lip to sustain the feedback loop that results in the spectral peak at St = 0.37 originate closer to the cut-out edges. On the other hand, the peaks at St = 0.54, 1.2 and 1.75 are observed for all configurations, which requires further investigation to understand the nature of these peaks.

Figures 9 and 10 show the acoustic spectra at the near-field observers on the positive y-side of the nozzle, circled in Figure 4. The peaks that are observed in far-field observer spectra are also present in these spectra. The spectra for x2.r3 have higher levels than the other configurations at most of the frequencies. Since the cut-out size is largest for x2.r3, this suggests that upstream traveling flow disturbances and acoustic waves are blocked less efficiently for this configuration. The peak at St = 0.37 has the highest magnitude for x2.r1 at both observers. This peak is present for x3.r2 at both observers and does not exist for x1.r2. The magnitudes of the peaks are very similar for x2.r1 and x3.r2, except at the observer P1p which is located in the same plane with the nozzle exit. The fact that x2.r1 and x3.r2 have the cut-out edges located closer to the jet flow and x1.r2 has them located farthest, supports the argument that the acoustic waves that close the feedback loop that results in this peak originate closer to the cut-out edges. None of the peaks of interest are present for x1.r2, for which the cut-out is located closest to the nozzle exit. The lack of these peaks for this configuration can be due to the higher magnitude broadband noise levels. It is also observed that x1.r2 has a broadband peak at St ≈ 1.0, which makes the spectra of this configuration closer to the baseline case spectra for higher frequencies. Since the cut-out edges of this configuration are farther from the high speed jet flow, there is a larger area for acoustic waves to travel through. So, it can be argued that this broadband peak is related to acoustic waves that travel upstream through the cut-out. At observer P1p, the peak at St = 0.54 has similar magnitudes for x2.r1 and x3.r2 and the magnitude of this peak for x2.r2 is 8 dB lower than these configurations. At this frequency, there are no significant peaks for x2.r3, but the magnitude of the sound pressure level is close to the peaks for x2.r1 and x3.r2. Since this peak is located in the same plane with the nozzle exit, the reason for this peak not being discernible for x2.r3 is argued to be the high magnitude of the broadband noise. At observer P4p on the other hand, the highest magnitude at St = 0.54 is observed for x2.r3, which is followed by x3.r2 and x2.r2. Interestingly, this peak does not exist for x2.r1 at observer P4p, which is argued to be a result of decreasing magnitude with distance. The peaks at St = 1.2 and St = 1.75 are observed for all configurations except x1.r2 at both observers.

Figure 9.

Acoustic spectra comparison of configurations with noise reduction method to the baseline configuration at near-field observers located on the positive y-side of the nozzle, observer Nf1p.

Figure 10.

Acoustic spectra comparison of configurations with noise reduction method to the baseline configuration at near-field observers located on the positive y-side of the nozzle, observer Nf4p.

The acoustic spectra at the near-field observers on the negative y-side of the nozzle are shown in Figures 11 and 12. Like the acoustic spectra on the positive y-side of the nozzle, it is observed that the spectra for x2.r3 are higher overall than the other configurations. The peak at St = 0.37 is observed only for x2.r1 at observers NF1n and NF4n. The peak at St = 0.54 is only observed at NF1n, which is located in the same plane with the nozzle exit. This observation suggests that these peaks are associated with feedback loops closed by the acoustic waves that are reflected from the wall with a cut-out, since the inclination of the wall with a cut-out is away from the nozzle on the negative y-side of the nozzle. The peak at St = 1.2 is observed for all configurations except x1.r2 at Nf1n and with significantly reduced magnitude at Nf4n. The spectra of x2.r1 at Nf1n is the only configuration that contains the peak at St = 1.75. Finally, it is important to note here that the observers are located very close to the nozzle shroud. So, even though if the feedback loop is closed by the acoustic waves that reflect from the upstream wall surface, the wave-front of the resulting acoustic waves might not cover the location of the near-field observers due to the inclination of the wall with a cut-out on the negative y-side of the nozzle.

Figure 11.

Acoustic spectra comparison of configurations with the noise reduction method to the baseline configuration at near-field observers located on the negative y-side of the nozzle, observer NF1n.

Figure 12.

Acoustic spectra comparison of configurations with the noise reduction method to the baseline configuration at near-field observers located on the negative y-side of the nozzle, observer NF4n.

Since significant spectral peaks are only observed for configurations where the wall with a cut-out is present, it is argued that the feedback loops that result in these peaks are sustained by acoustic waves that are reflected from the upstream surface of the wall with a cut-out. To strengthen this suggestion, acoustic spectra calculated with and without the inclusion of a part of the upstream surface of the wall with a cut-out as a FWH data extraction surface are compared at Nf4p for x2.r3 and x3.r2 in Figures 13 and 14. It is observed that including a part of the wall with a cut-out as a FWH data extraction surface changes the spectra and OASPL significantly at the near-field observer. The OASPL is 3 − 5 dB higher, when the wall is included in the calculations. This suggests that the acoustic waves that are reflected from the wall make a large contribution to the near-field noise levels. It can be seen that, for Strouhal numbers less than 0.4, the difference in SPL ranges from 5 to 8 decibels. So, the reflected acoustic waves contribute to the low frequency components of the near-field acoustic spectra. It is also observed that the peaks are not present in the calculations made without the inclusion of the wall. This supports the idea that these peaks are related to feedback loops that are closed by the acoustic waves that are reflected from the upstream surface of the wall with a cut-out.

Figure 13.

Acoustic spectra comparison of calculations made with and without including a part of the upstream surface of the wall with a cut-out as a FWH data extraction surface at observer Nf4p. Configuration x2.r3.

Figure 14.

Acoustic spectra comparison of calculations made with and without including a part of the upstream surface of the wall with a cut-out as a FWH data extraction surface at observer Nf4p. Configuration x3.r2.

Feedback loop models

For the purpose of making a more quantitative argument about the nature of the acoustic waves that sustain the feedback loops resulting in the spectral peaks, both the classical model ¹⁵ and the model of Gojon et al. ¹⁹ are used.

The classical feedback model developed by Ho & Nosseir ¹⁵ and Nosseir & Ho ¹⁶ is given as:

$\frac{L}{〈u_c〉}+\frac{L}{a_0}=\frac{N}{f}$

(1)

where ⟨u _c ⟩ is the average convection velocity in the shear layers, a₀ is the speed of sound outside of the jet, N is the mode number and L is the impingement wall distance.

Gojon et al. ¹⁹ give a formula for the average convection velocity ⟨u _c ⟩,

$〈u_c〉\left(L/r_0\right)=0.65u_j-\left(0.65u_j-0.5u_j\right)\times \frac{1}{1+0.15{\left(L/r_0\right)}^2}.$

(2)

where r₀ is nozzle radius and u _j is the jet velocity.

Equation (3) relates the wavenumber k _sw of the hydrodynamic-acoustic standing wave due to the feedback mechanism and the acoustic and hydrodynamic wavenumbers k _a and k _p , where N _sw is the whole number of shock cells.

$k_{sw}=k_p+k_a=\frac{2\pi N_{sw}}{L}$

(3)

Gojon et al. ¹⁹ combined the classical feedback model and the wave analysis that uses the dispersion relations (details in section 3.2 of Ref. 19), by assuming that the acoustic wavenumber in the feedback loop is equal to the opposite of the wavenumber k of the upstream-propagating acoustic waves of the wave analysis. Using N _sw = N, k _p = 2πf/⟨u _c ⟩ and k _a = −k, equation (3) yields the following equation.

$f=\frac{N〈u_c〉}{L}+k\frac{〈u_c〉}{2\pi }$

(4)

Both of these models use the characteristic length, L, as the distance between the nozzle exit and the impingement plate. However, in the present study due to the fact that the spectral peaks are only observed when the wall with a cut-out is present between the nozzle exit and the impingement plate and due to the asymmetric geometry of the wall with a cut-out, different L values need to be considered. Through the investigations of the acoustic spectra and configuration geometries, it is argued that the feedback loops resulting in the spectral peaks are closed by acoustic waves that reflect from the upstream surface of the wall with a cut-out. Thus, two different characteristic lengths are considered in the feedback loop models: the distance between the lip and the cut-out edge, l _e , and the normal distance between the lip and the wall with a cut-out, l _n . These lengths are shown in Figure 15. Values of these lengths for configurations that are used in the feedback loop model investigations are provided in Table 3.

Figure 15.

Characteristic lengths to be used in the feedback loop models shown on instantaneous pressure time derivative contours of x2.r1. Yellow: l _e and green: l _n .

Table 3.

Characteristic length values of different configurations. All lengths are non-dimensionalized with the nozzle diameter D.

Lengths	x2.r1	x3.r2
l e	0.93	1.14
l n	1.10	1.23

Since x2.r1 showed the most prominent peaks in the acoustic spectra, this case will be investigated using the feedback loop models. The near-field spectra of x2.r1 at observers P2 and P1 at both positive (p) and negative (n) y-sides of the nozzle are shown in Figure 16. The peaks at St₁ and St₃ are present at both observers, with lower magnitudes at the farther observer. The peak at St₂ is only observed at P2p. Finally, St₄ is only observed at observers located on the positive y side of the nozzle.

Figure 16.

Acoustic spectra for x2.r1 at observers located on the positive and negative y-side of the nozzle with higlighted peak frequencies. p: positive, n: negative.

Figures 17 and 18 show the results of the feedback loop models calculated with the characteristic length values of x2.r1. In this figure, the Gojon et al. ¹⁹ feedback model results are represented by the diagonal grey lines and the classical feedback model results of Ho & Nosseir ¹⁵ are shown as green dots. The different lines and dots represent the solutions of different feedback mode numbers, which are represented by N in equations (1) and (4). The acoustic waves propagating with a group velocity of −a₀, which are defined by k = −ω/a₀, are represented by the dashed diagonal lines. The feedback loops are only sustained when acoustic waves at a specific frequency excite aerodynamic disturbances with the same frequencies close to the nozzle lips. The diamonds show the peak frequencies observed at the near and far-field observers for different configurations with the noise reduction method. Due to computational resource restrictions, the frequency resolution is not very fine. So, there is a chance that the peaks are not estimated to the accuracy that the feedback loop models need. Thus, red arrows are used to show the range St ± 2 × dSt, where dSt = 0.0415 is the Strouhal number resolution.

Figure 17.

Feedback loop models using the characteristic length values of x2.r1, L = l _n . Diamond: Peak frequency, red arrows: Possible peak range, gray —: Gojon et al. model, ¹⁹ green dot: Ho & Nosseir,^15,16 — k = −ω/a₀.

Figure 18.

Feedback loop models using the characteristic length values of x2.r1, L = l _e . Diamond: Peak frequency, red arrows: Possible peak range, gray —: Gojon et al. model, ¹⁹ green dot: Ho & Nosseir,^15,16 — k = −ω/a₀.

It is observed that when L = l _n , which is the normal distance between the nozzle lip and the inclined upstream surface of the wall with a cut-out is used as the characteristic length in the feedback loop models, the best match between the feedback modes and peak frequency ranges is achieved. With l _n as the characteristic length, the four peak frequencies are observed to be close to the feedback modes N = 1, N = 2, N = 4 and N = 6, respectively. Specifically for St₃, there is a perfect match with the feedback mode number N = 4, when L = l _n . It is also observed that when L = l _e , the distance between the nozzle lip and the cut-out edges, St₁ and St₄ are located very close to the feedback modes N = 1 and N = 4. This observation suggests that the acoustic waves that close the feedback loops related to these peaks originate closer to the cut-out edge. The peak at St₁ exists in the spectra of observers located on the negative y-side of the nozzle, shown in Figure 16. Since the inclined part of the wall with a cut-out is angled away from the nozzle lips, this could suggest that this peak is related to feedback loops that are closed by acoustic waves that reflect from the part of the upstream surface of the wall with a cut-out, where the wall is parallel to the nozzle exit. This part of the wall with a cut-out is located closer to the jet flow, which makes the characteristic length closer to l _e instead of l _n .

Flow field

In order to improve the understanding of the sources of the peaks that are observed in the near- and far-fields, an example of flow field results for configuration x2.r1 is shown in this section. Figure 19 shows the instantaneous pressure time derivative contours, plotted as black and white filled contours, and density gradient magnitude contours, plotted as lines, for configurations with the noise reduction method. The acoustic waves that are trapped between the wall with a cut-out and the impingement plate, reflecting back and forth, are observed through the pressure time derivative contours. The majority of the upstream traveling waves are blocked by the wall with a circular cut-out and reflected downstream towards the impingement plate. However, acoustic waves travelling upstream originating from the close proximity of the cut-out are also observed in the pressure time derivative contours. Two sets of acoustic waves are seen on the negative y-side of the nozzle, where the wall with a cut-out is inclined away from the nozzle. The first set of waves are highlighted with dashed arrows on Figure 19, which travel upstream and away from the nozzle. The second set of acoustic waves, marked as a solid arrow on Figure 19, travel upstream following the shroud surface. On the positive y-side of the nozzle, upstream traveling acoustic waves are observed to travel closer to the shroud, compared to the negative y-side of the nozzle. This is a result of the inclination of the wall with a cut-out on this side of the nozzle. There are also two sets of acoustic waves observed on the positive y-side of the nozzle. The first set of acoustic waves are observed to be traveling upstream following the shroud surface, highlighted by a solid blue arrow in Figure 19. The second set of acoustic waves, highlighted by dashed blue arrows, travel away from the shroud and reflect from the wall with a cut-out and travel towards the shroud. This supports the idea that the peaks that were observed, only on the positive y-side, are related to the feedback loop closed by the acoustic waves that are reflected from the wall with a cut-out. All of these upstream traveling waves are a combination of acoustic waves that originate from the free-jet flow upstream of the cut-out, acoustic waves that reflect from the wall with a cut-out and acoustic waves that are created by the possible interaction of the high speed jet flow with the cut-out edges. This interaction can be observed from the density gradient magnitude contours.

Figure 19.

Instantaneous density gradient magnitude (blue-pink-yellow: 0 to 150) and pressure time derivative contours (grayscale: −1 to 5) with noise reduction method, x2.r1.

Conclusion

Different configurations of a wall with a circular cut-out placed between the nozzle exit of a supersonic jet and an inclined plate, as a passive noise reduction method are investigated, using Detached Eddy Simulation to resolve the flow fields and the Ffowcs Williams-Hawkings analogy to estimate the near- and far-field acoustic spectra. A baseline configuration without the noise reduction method is compared to experimental results. The baseline configuration showed asymmetric acoustic waves that travel upstream. These waves consists of acoustic waves originating from the impingement and wall-jet regions due to high speed flow in these regions, acoustic waves that are produced in the free-jet region reflected by the inclined flame deflector, and acoustic waves that are caused by interactions between the downstream traveling waves and high speed jet flow in the impingement and wall-jet regions.

Five different configurations with different cut-out sizes and wall locations are investigated in this research. The locations of the wall and the sizes of the cut-outs are chosen carefully by evaluating the flow field results of the baseline configuration. The placement of the wall and the size of the cut-out is important, since the introduction of a physical barrier like this in a high speed jet flow field can cause undesirable effects on the flow field creating new higher amplitude noise sources. All configurations decreased the noise levels in both near- and far-fields and the configurations where the cut-outs are closer to the jet flow have better noise attenuation performances. This is related to the blockage of more of the upstream traveling waves and flow which are trapped between the two walls.

The acoustic spectra at near- and far-field observers for the configurations with the noise reduction method, showed new peaks at several frequencies that were not observed in the baseline configuration spectra. These peaks are related to the introduction of the wall with a cut-out between the nozzle exit and the inclined plate. From the comparisons of the acoustic spectra, flow field results and feedback loop model results for the different configurations, these peaks are shown to be a result of feedback loops that are sustained by the acoustic waves that are reflected from the upstream surface of the wall with a circular cut-out.