Aerodynamic noise from rigid trailing edges with finite porous extensions
A. V. Kisil, L. J. Ayton
TL;DR
This study analytically examines how finite porous extensions on flat plates influence trailing-edge noise, revealing that partial porosity can reduce noise but less effectively than full porosity, with a new iterative Wiener-Hopf solution method.
Contribution
It introduces a novel iterative Wiener-Hopf method for solving complex acoustic problems involving porous trailing edges and permeable-impermeable junctions.
Findings
Permeable-impermeable junctions affect far-field noise by causing interference.
Partially porous plates are less effective at noise reduction than fully porous plates.
The new iterative method converges rapidly and avoids full matrix factorization.
Abstract
This paper investigates the effects of finite flat porous extensions to semi-infinite impermeable flat plates in an attempt to control trailing-edge noise through bio-inspired adaptations. Specifically the problem of sound generated by a gust convecting in uniform mean steady flow scattering off the trailing edge and permeable-impermeable junction is considered. This setup supposes that any realistic trailing-edge adaptation to a blade would be sufficiently small so that the turbulent boundary layer encapsulates both the porous edge and the permeable-impermeable junction, and therefore the interaction of acoustics generated at these two discontinuous boundaries is important. The acoustic problem is tackled analytically through use of the Wiener-Hopf method. A two-dimensional matrix Wiener-Hopf problem arises due to the two interaction points (the trailing edge and the…
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Analytical and Experimental Investigation into the Effects of Leading-Edge Radius on Gust-Aerofoil Interaction Noise
Lorna J. Ayton \corresp
Paruchuri Chaitanya\aunotePhD Student, ISVR, University of Southampton, UK
Abstract
We are not comparing analytical and experiment results directly… we are comparing the trends and explaining it .. we can add ’trends’ in abstract if required.
1 Introduction
please add why this study is important …
Typical OGV geometries are like flat plates i.e. around 5% thickness relative to aerofoil chord. To reduce the interaction noise, increasing the thickness in an unrealistic solution due to it’s influence on aerodynamic performance. Hence, capturing the small changes in nose radius has seen to have significant changes in far-field radiated noise. etc etc
[This is really important work .. as Rolls Royce is now looking to change the nose radius to reduce the turbulence-aerofoil interaction noise.]
2 Experimental set-up and procedure
2.1 Open jet test facility and instrumentation
Far field noise measurements were carried out at the ISVR’s open-jet wind tunnel facility. Figure 1 shows a photograph of the facility within the anechoic chamber of dimensions 8 m 8 m 8 m. The walls are acoustically treated with glass wool wedges. The cut-off frequency of the chamber is about 80 Hz. A detailed description of the facility is presented by chong08. To maintain two-dimensional flow around the aerofoil, side plates are mounted to the nozzle exit which will also support the aerofoil. The nozzle dimensions are 15 cm x 45 cm. Aerofoils are located 0.15 m downstream of the nozzle to ensure that the entire aerofoil is located well within the jet potential core, whose width is at least 12cm, as shown in figure 11a in chong08. As shown in chong08 the flow is two dimensional (no spanwise variation) to within an deviation of about 4%. The maximum jet speed investigated in this study is 80 m s*-1*.
2.2 Far-field noise measurements
Free-field noise measurements were made using 11, half-inch condenser microphones (BK type 4189) located at a constant radial distance of 1.2 m from the mid span of the aerofoil leading edge. These microphones are placed at emission angles of between and measured relative to the downstream jet axis. Measurements were carried for 10 seconds duration at a sampling frequency of 50 kHz, and the noise spectra were calculated with a window size of 1024 data points corresponding to a frequency resolution of 48.83 Hz and a product of about 500, which is sufficient to ensure negligible variance in the spectral estimate.
The acoustic pressure at the microphones was recorded at the mean flow velocities () of 20, 40, 60 and 80 m s*-1* at the exit of the jet nozzle. Details of the calculation method for deducing the Sound Pressure Level spectra , and the Sound Power Level spectra are presented in sn15.
2.3 Turbulence characterization
A bi-planar rectangular grid with overall dimensions of 630 x 690 mm2 located in the contraction section of the nozzle was used to generate turbulence that is closely homogeneous and isotropic. The grid was located 75 cm upstream of the nozzle exit. The streamwise velocity spectrum was measured using a hot wire at a single on-axis position 145 mm downstream from the nozzle exit. It is found to be in close agreement with the von-Karman spectrum for homogeneous and isotropic turbulence with a 2.5% turbulence intensity and a 7.5 mm integral length scale. The turbulence integral length scale was obtained by matching the theoretical spectra to the measured streamwise velocity spectra and dividing by two, assuming perfect isotropic turbulence. A comparison of the two measured streamwise velocity spectra () plotted against together with the theoretical von-Karman spectra are plotted in figure 2, where close agreement is observed.
2.4 3D Aerofoil models
[Can we approximate the leading-edge profiles I=0,I=6 and I=10 to profile in the form , where we can expressed in-terms of m .. I will try to do this if I get it] [we can only say we tested 6 cases as we are showing only these results … ]
In this present study, thirteen NACA symmetric aerofoils are fabricated using 3D printing technology. A systematically varying thickness and nose radius of the aerofoils are chosen, as shown in Figure 3. In the case of the NACA 4-digit aerofoils, the leading edge nose radius is related to maximum thickness by
[TABLE]
where I is a non-dimensional parameter that defines the shape of the leading edge as shown in figure 3gill13. I=0, represents a sharp leading edge, represented as NACA xxxx-03, whereas I=10 represents blunt aerofoils, represented as NACA xxxx-103 and I=6 represents standard NACA profile geometries.
In order to prevent tonal noise generation due to Tollmien-Schlichting waves convecting in the laminar boundary layer, and to ensure complete consistency between the different cases, the flow near the leading edge of the aerofoil was tripped to force transition to turbulence using a rough band of tape of width 1.25 cm located 16.6% of chord from the leading edge, on both suction and pressure sides. The tape has roughness of SS 100, corresponding to a surface roughness of 140 m. Transition is forced by the use of trip tape, which is many orders of magnitude rougher than the aerofoil surface, and is therefore highly unlikely to affect transition. Previous noise measurements in our facility have indicated that self-noise is insensitive to the method of tripping.
3 Influence of Self-Noise
[optional .. you can take few sentences if required]
In this section we show that the total noise radiated by the aerofoil located within a turbulent flow is dominated by leading noise at low frequencies and trailing edge noise at high frequencies. As it is very difficult to measure interaction and self-noise separately, our analysis was limited to the frequency region where the interaction noise dominates self-noise. Figure 4 shows the influence of self-noise on total noise spectra. Sound power levels are plotted against a non-dimensional frequency () for two different thickness aerofoils. It is observed that the thicker aerofoil has lower interaction noise and the self-noise starts dominating the total noise at lower frequency compared to the thinner aerofoil. The non-dimensional frequency () where self-noise starts if the dominant noise source is around for this particular turbulence intensity of about 2.5%. For the case of flat plates, levels of self-noise were observed to be negligible over the frequency range of interest.
As aerofoil thickness was increased, trailing edge noise was found to increase in low frequency range and decrease in the high frequencies range as discussed by chaiTE15, due to a thickening of the boundary layer thickness. For these symmetric aerofoils leung16 has used the panel code XFOIL to demonstrate an almost linear variation of boundary layer thickness with aerofoil thickness. Thicker boundary layers near the trailing edge lead to larger scales of turbulence that contain more energy, and hence the increase in low frequency noise in the trailing edge noise spectra. The decrease in high frequency noise with thickness was attributed by leung16 to a decrease in the coefficient of friction.
4 Conclusion
[you last para also says the similar thing]
Aerofoil thickness remains the main geometric parameter controlling turbulence interaction noise (shown previously). Local leading edge geometry, such as leading noise radius, nevertheless, is an important parameter for thin aerofoils at high frequencies, particularly when the gust wavelength is comparable to noise radius. Therefore attempts to predict interaction noise based on single values of thickness-chord ratio are likely to be inaccurate for thin aerofoils.