Journal of Undergraduate Research
Volume 9, Issue 2 - November / December 2007

Design and Fabrication of a Phased Acoustic Array to Analyze Noise Generation of Aircraft Components

Nikolas Zawodny 

ABSTRACT

This paper presents an overview of the development of a microphone array for testing within the University of Florida Aeroacoustic Wind Tunnel Facility.  Acoustic measurements are to be taken from a scaled model of a NACA 63-215 airfoil.  The array design contains a total of 33 electret microphones – each of which is 6.0 mm (0.236 inches) in diameter – distributed on an 8.5-inch diameter circular plate.  The microphones are distributed into four concentric circles, eight per circle, with an additional microphone located at the center of the array.  The primary purpose of this array is to obtain directivity and spectral content information of aerodynamic noise emanating from regions of interest on the airfoil model under different flow conditions.  This is accomplished by a process known as beamforming, in which the focus of the array is electronically steered to points in space.  The secondary objective of this research is to perform a benchmark comparison to directional array data obtained by the NASA Langley Quiet Flow Facility (QFF). 

INTRODUCTION

In recent years, increasingly strict regulations on aircraft noise have imposed large economic penalties on aircraft companies and airlines that fail to comply.  As engine technology leads to quieter engines, airframe noise – defined as the "…non-propulsive component of aircraft noise which is due to unsteady flow about the airframe components…." 1 – has become a major contributor to the overall aircraft noise levels.  The physics behind airframe noise generation is still not fully understood and must be characterized before reduction techniques can be implemented 2.

Early techniques of airframe noise analysis involved the concept of an "acoustic mirror," which consisted of a single microphone positioned in the acoustic far field of a large concave elliptical mirror.  The origin of acoustic mirrors can be traced back to the north and southeast coasts of England in the early 1920s, where they were used to provide early warning of incoming enemy aircraft planning to attack coastal towns 3.  These coastal "listening ears" were eventually rendered obsolete with the development of faster aircraft and the invention of radar. 

Such mirrors have been proven to accurately locate individual sound sources, but are limited in that they require physical adjustments in order to determine the distributions of these noise sources around models.  This prevents wide-scale use of such mirrors, although they are still applicable in some larger-scale research facilities.  Other methods of airframe noise characterization have involved independent distributions of microphones, which have proven to be useful in the analysis of airfoil self-noise generation 4.  These microphone distributions are considered independent due to the fact that the microphone outputs remain individualized and are not combined.  These microphone arrangements are considered to be precursors to modern microphone directional arrays, based on their use of amplitude and phase relationships between microphone clusters 1.

Phased or directional arrays capitalize on the amplitude and phase variations sensed by a spatially assorted collection of microphones in the acoustic far-field of a noise source 5.  The primary benefit of utilizing such an array is its ability to extract a desired noise source location and information regarding relative source strengths, even when located in a reverberant, noisy environment.  Another important benefit is having the ability to electronically "steer" its focus in a region in space, requiring no physical movement.  This concept is a vast improvement from an acoustic mirror, which relies on mechanical movement to alter its focus.  This electronic steering is done via a process known as beamforming, or the appropriate weighting and time-delays of the individually measured signals 5.

DIRECTIONAL ARRAY THEORY

Principle of Operation

The primary objective of a microphone directional array is to have the capability of focusing on a noise source of interest.  In order to do this, the outputs of the individual microphones must be phase-shifted by an amount corresponding to their modeled propagation delay from the point of interest and summed together.  The basic principle of such an array is presented in 5 and is summarized as follows.

Assume there is a simple acoustic monopole source located a distance r0 from the origin of a circular array of N microphones.  The origin, or phase center, of the array Equation is defined as

Equation,

where Equation is the location of the nth microphone.  The acoustic signal can be denoted as a pressure wave propagating spherically in all directions as:

Equation(1)

where C is a constant, r is the radial distance from the origin of the noise source, ω is the wave frequency, and k is the corresponding wavenumber.  Note that the wavenumber is defined as k = ω/c where c is the speed of sound.  For an array of N microphones located a finite distance from the noise source, each microphone detects a slightly different phase-shifted waveform depending on its distance.  The measured pressure at the nth microphone, pn(t), is represented as:

Equation(2)

where Equation is the distance from the location of the noise source to the nth microphone, c is the speed of sound, and Equation represents the delayed time from the noise source to the microphone.  A positive time delay is used for the microphones closer to the noise source, whereas a negative time delay is used for those located farther from the source.  This scenario is illustrated below in Figure 1.

Figure 1. Acoustic point source located a distance from the origin of a microphone array. (Adapted from [5].)

Figure 1.  Acoustic point source located a distance Equation from the origin of a microphone array. (Adapted from 5.)

Beamforming

Beamforming provides a microphone array with the ability to effectively amplify sound in a region of interest while diminishing sound from other regions.  This process is useful in its ability to adapt the performance of a directional array to the conditions associated with aeroacoustic testing of a model in a reverberant environment, such as a wind tunnel.  The two most general classifications of beamforming are time- and frequency-domain delay-and-sum beamforming 5.

Time-Domain Beamforming

Considering the previously presented scenario of an acoustic source located a distance r0 from the origin of a circular array of N microphones, the general form of the continuous-time beamforming equation can be presented:

Equation(3)

where wn and ?n are the weighting factor and time delay for the nth microphone, respectively.  These terms can be further expanded into the following:

Equation(4)

Inserting Equations (2) and (4) into Equation (3) yields the following expression for array response:

Equation(5)

Thus, the output of the array is reduced to the pressure signal received at the center of the array multiplied by the total number of microphones in the array.  Note that this simplification only applies to the situation when the array's focus is directed at the source of the noise and it represents the maximum possible output of the array for the given system configuration.  Otherwise, considering an arbitrary location in space whose parameters are r, rn, and wn, instead of r0, r0n, and w0n, the response of the array is:

Equation(6)

Equation (6) represents the response of a directional array using basic weighting and time-delays indicative of conventional beamforming to focus the array on an arbitrary location in space.  In practice, the output signal of the array z(t) is monitored while its focus is scanned over a pre-defined spatial region (see Figure 2).

Figure 2. Illustration of directional array steering.

Figure 2. Illustration of directional array steering. (Adapted from 1.)

Frequency-Domain Beamforming

In signal processing, a time-delay for a signal corresponds to a phase shift in the frequency (Fourier) domain.  Applying this concept to beamforming yields the following general correlation:

Equation 7 (7)

Furthermore, this transformation can be applied to Equation (3) to yield the beamformed array response in the frequency domain:

Equation 8(8)

For this transformation to be implemented for experimentation purposes, the Fast Fourier Transform (FFT) must be applied.  For a set of data collected at regular intervals by a data acquisition system p[m], at a sampling frequency fs, the FFT used to obtain a discrete representation of M points is given by

Equation 9(9)

where Pk is the kth FFT coefficient.  Thus, the expression for the array response in the frequency domain from Equation (8) can be redefined as

Equation 10(10)

where ωk = 2πkfs/M is the radial frequency.

In addition to delay-and-sum beamforming in which each individual microphone output is multiplied by a single complex weight factor, another method exists in which the microphone outputs are multiplied by a vector of complex weightings6.  This method, known as matrix weighting, will theoretically yield a better spatial resolution.  It will also be considered during the data analysis phase of this project.

Array Calibration

Since beamforming to a point in space is dependent on the vectors from this point to the microphone locations, any difference between the desired and actual microphone locations will result in errors.  One of the primary causes of such differences in microphone locations is offset errors made during the manufacturing process.  In order to ensure that the computed weight vectors for each of the microphones match the experimentally-measured data, a calibration of the array must be performed. A common method of directional array calibration is with the use of a small speaker used to simulate a point source7. It is advantageous to place the speaker near the location of the model to be analyzed, with it and the array acoustically insulated from the walls and other reflective surfaces present in the testing facility. Array data is then collected and adjusted for a range of analysis frequencies using calibration guidelines similar to the following7.

For an array center microphone with an ideal location at the array origin

Equation

and an actual offset location denoted by Equation, a quantity known as the phase factor denoting the nominal and actual coefficients of propagation can be defined respectively as

Equation (11)

where Equation represents the speaker location in space.  With this information, a corrected weighting factor for a point source location at can be defined:

Equation(12)

Therefore, application of Equation (12) to all microphones in the directional array will yield a corrected weight factor for each microphone.  These weight factors are then summed to yield a single calibrated array response, the formulation of which is outlined in the next section.  A visual representation of the parameters involved in the array calibration process can be seen in Figure 3.

Figure 3. (a) Speaker/array apparatus for calibration of center microphone, and (b) corrected microphone weightings for a noise source after calibration.

Figure 3. (a) Speaker/array apparatus for calibration of center microphone, and (b) corrected microphone weightings for a noise source after calibration.

Array Response

The theoretical response of a directional array is based on the assumption that a noise source seen by the array exhibits monopole, or omnidirectional, behavior.  The actual performance of a directional array with the application of beamforming is almost always different from that predicted by the theoretical model due to the fact that real-world noise sources practically never behave as independent monopole sources.  For the sake of simplicity, however, the ideal response of a directional array to a noise source is considered with the assumption that the source exhibits monopole behavior1:


Equation (13)

where Equation is an arbitrary location in space and Equation is the noise source location.  Another way to express the array response is in decibels (dB) relative to the level obtained at the noise source location:

Equation(14)

In this form, the array response can be plotted as a contour map representing the computation of Equation (14) over a series of steering locations located a specified distance from the array.  This type of plot allows one to examine the spatial selectivity of the array, indicated by a mainlobe and sidelobes.  The mainlobe of the array response pattern is of particular interest since its acoustic energy represents the desired response of the array to a noise source, the width of which is defined as the array beamwidth5.  In addition, the array response may be represented in terms of normalized pressure, in which the peak response of unity represents the origin of the noise source2.  Examples of such plots are provided in the Preliminary Results section of this report.

ARRAY DESIGN

Testing Facility

The experiments to be conducted will be performed with the intent of examining the root causes of sound generation on, for example, a wing configuration.  They will be performed in the University of Florida Aeroacoustic Wind Tunnel Facility.  The wind tunnel is an open-jet, quiet-flow facility designed for anechoic (echo-free) testing of airframe components.  Characterization of the tunnel has shown a maximum attainable test section speed of approximately 250 ft/s.  The test stand, which is the apparatus designed to hold and orient the test model within the test section consists of aluminum rectangular channels manufactured by 80/20 Inc.  This test stand was designed to have a large safety factor for withstanding the forces imposed on it from the air flow through the test section.  Figure 4 is a rendered model of the wind tunnel test section, including the test stand and sample directional array placement.

Figure 4. Digital reproduction of wind tunnel test section with mounted directional array
Figure 4. Digital reproduction of wind tunnel test section with mounted directional array. (Courtesy of J. Sanford and A. Hart.)

Test Model

Airfoils or wing profiles are an important component of airframe noise generation.  The model that will be used to test the response of the array is a ­­­scaled NACA 63-215 Mod B airfoil (Figure 5).  One of the primary acoustic features of interest of the airfoil in this study is the rear, or trailing edge.  Generally, the trailing edge is the section of the airfoil that possesses the greatest amplitude of sound generation and is thus a feature that deserves special attention.  Figure 6 is a scaled profile view of the wind tunnel test section, including the NACA airfoil model as well as a sample array placement.

Figure 5. Plot of the NACA 63-215 airfoil
Figure 5. Plot of the NACA 63-215 airfoil (Courtesy of [8]).

Figure 6. Profile view of wind tunnel test section (units are in inches)
Figure 6. Profile view of wind tunnel test section (units are in inches).

Directional Array Pattern and Structure

The most important design parameter of a directional array is the microphone layout.  Selecting a microphone layout is heavily dependent on the nature of the noise source distributions to be analyzed.  The general procedure for delay-and-sum beamforming previously mentioned is based on the assumption that any detected noise source is a monopole type, and that a source distribution is comprised of a series of uncorrelated simple monopole sources.  Unfortunately, noise sources from airframe components practically never exhibit such behavior.  Instead, the face of the array sees fluctuations in the phase and amplitude of the noise sources, which may cause array response errors in noise source localization.  Therefore, designing the array to have the microphones placed within close proximity of each other would place them approximately within the same source directivity – yielding a smaller array size [1]. 

The array implemented for this project is a Small Aperture Directional Array (SADA) [1], designed to provide directivity and spectra information from regions of interest on the previously mentioned NACA airfoil model under different flow conditions.  It consists of 33 Panasonic electret microphones, each one having a diameter and height of 6.0 mm and 3.4 mm, respectively (Figure 7).

Figure 7. Panasonic 6.0-mm diameter electret microphone, Model # WM-61A.
Figure 7. Panasonic 6.0-mm diameter electret microphone, Model # WM-61A.

The array pattern is comprised of four concentric circles of eight microphones each, centered around a final microphone located at the array center.  Each circle of microphones has twice the diameter of the circle it encloses.  The pattern is consistent with that chosen by Humphreys [1] that was implemented in the NASA Langley QFF (Figure 8).  Note that each circle in Figure 8 represents one 6.0-mm diameter electret microphone.

Figure 8. SADA microphone pattern
Figure 8. SADA microphone pattern. (Courtesy of T. Yardibi.)

Each microphone signal is to be output via a BNC cable to a National Instruments PXI Data Acquisition module.  Due to a current difference between an input channel of the PXI module and the maximum possible current that can be handled by each microphone, additional circuitry was required to have an effective microphone circuit.  It was decided that the microphone array be based off of a printed circuit board (PCB), which would both hold all the electrical components and provide a stable means of support for the array.  In addition, it was deemed necessary to include a cover, or array faceplate, for the purpose of eliminating the possible occurrence of acoustic scattering by the electrical components.  This faceplate was manufactured out of hard plastic using a rapid prototyping machine.  Figure 9(a) shows the completed array PCB circuitry and Figure 9(b) shows the array with the manufactured faceplate installed.

Figure 9. (a) Printed circuit board SADA circuitry, and (b) array with faceplate installed.
Figure 9. (a) Printed circuit board SADA circuitry, and (b) array with faceplate installed.

PRELIMINARY RESULTS

As was mentioned in the Array Response section, application of beamforming to a simulated response of the SADA to a noise source was performed for frequencies of interest.  Figure 10 is a sample contour plot of the theoretical response of the SADA for a noise source located approximately 4 feet above the array center at a frequency of 10 kHz.  As the figure shows, the sampling grid scanned by the array is a 4-foot by 4-foot square with the peak noise source occurring at the center of the plot, represented by 0 dB.  Note that this contour plot was generated with the implementation of a weighting algorithm by Tarik Yardibi of the University of Florida Spectral Analysis Laboratory.

Figure 10. Theoretical SADA response in dB at a frequency of 10 kHz
Figure 10. Theoretical SADA response in dB at a frequency of 10 kHz. (Courtesy of T. Yardibi.)

Another way to view to the relative response of the array is in terms of normalized pressures.  In other words, the pressure distribution within the sampling area seen by the SADA varies from 0 to 1 with 1 representing the peak pressure and origin of the noise source.  Figures 11(a) and (b) show the array response in terms of normalized pressures to a noise source with the same parameters previously mentioned for Figure 10.  Note that these figures were generated using MATLAB source code implementing beamforming methods presented by Underbrink2.

Figure 11. (a) 3D surface plot and (b) contour plot of theoretical array response in terms of normalized pressure at a frequency of 10 kHz.
Figure 11. (a) 3D surface plot and (b) contour plot of theoretical array response in terms of normalized pressure at a frequency of 10 kHz. (Adapted from [2].)

In addition to these array response simulation tools, a microphone array software (MAS) package provided by the National Instruments Corporation has also been tested.  Once several modifications are made to this software package, it is expected to be the primary method of SADA data analysis.  The functions of the MAS are to test the array with a simulated noise source of a given strength at a given location as well as to apply beamforming algorithms to measured microphone time data.  Figure 12 shows the graphical user interface of the noise simulation portion of the software.

Figure 12. Microphone array software (MAS) user interface for noise source array response simulation.
Figure 12. Microphone array software (MAS) user interface for noise source array response simulation.

As the figure shows, the user inputs a desired scanning range, distance of the noise source from the array, frequency of interest, and other parameters (not displayed).  The result of the noise source simulation (seen at right of Figure 12) is a contour map showing the sound pressure distribution in dB within the scanned spatial region.  A comparison of Figures 10, 11, and 12 show similar SADA response simulations to a centrally-located noise source.  This is beneficial because it shows that there are multiple simulation tools with which the experimentally measured array data can be compared.

CONCLUSIONS

In this paper, an overview of the design and fabrication of a directional microphone array for aeroacoustic testing has been presented.  A Small Aperture Directional Array (SADA) has been successfully constructed and is currently undergoing calibration procedures and ideal placement within the University of Florida Aeroacoustic Wind Tunnel Facility.  To date, experimental wing acoustic data obtained with the fabricated SADA has not yet been collected.  As was mentioned, a series of array response simulations utilizing calibration and beamforming correlations have been obtained and tested to validate the theoretical results with those obtained by the NASA Langley Quiet Flow Facility (QFF).  In addition, the University of Florida Wind Tunnel Facility is currently undergoing acoustic insulation modifications in order to ensure ideal aeroacoustic testing conditions.  Experimentation will begin by mid-June of 2007.

ACKNOWLEDGEMENTS

I would like to express special thanks to my adviser, Dr. Lou Cattafesta, for the invaluable guidance he has provided me during the three years I have worked for the Interdisciplinary Microsystems Group.  The students of IMG also deserve thanks, particularly Christopher Bahr, who has been an excellent source of knowledge and advice for this project, as well as Dylan Alexander for his assistance in the array fabrication process, and, finally, Adam Hart, Jeremy Sanford, and Drew Wetzel for their improved design work on the Aeroacoustic Wind Tunnel Facility.  I would also like to acknowledge Tarik Yardibi of the University of Florida Spectral Analysis Laboratory for his work on the application of beamforming techniques to this study.  Finally, I would like to thank my family and friends for their support of me in all of my endeavors.

REFERENCES

  1. Humphreys Jr., W.M., Brooks, T.F., Hunter, Jr., W.W., and K.R. Meadows, "Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements", AIAA Paper 98-0471, 1998.
  2. J.R. Underbrink, "Practical Considerations in Focused Array Design for Passive Broad-band Source Mapping Applications", Master's Thesis, Pennsylvania State University, 1995.
  3. A. Grantham, "Early Warning Sound Mirrors."  Available online: http://www.ajg41.clara.co.uk/mirrors/index.html
  4. Brooks, T.F., Pope, D.S., and M.A. Marcolini, "Airfoil Self-Noise and Prediction", NASA Reference Publication 1218, July, 1989.
  5. D. P. Arnold, "A MEMS-Based Directional Acoustic Array for Aeroacoustic Measurements", Master's Thesis, University of Florida, 2001
  6. Li Y. Xie, J. Li, X. Zheng, and J. Ward, "Optimal beampattern synthesis via matrix weighting," submitted to IEEE Transaction on Signal Processing, July 2006
  7. R. P. Dougherty, "Beamforming in Acoustic Testing", Aeroacoustic Measurements, p. 62-97, Springer, 2002.
  8. "UIUC Airfoil Coordinates Database".  Available online: http://www.ae.uiuc.edu/m-selig/ads/coord_database.html#N

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