Artificial noise systems for parametric studies of turbo-machinery aero-acoustics

Abstract

The study of turbo-machinery aero-acoustics encompasses source generation, duct propagation, and radiation to the far field for the purposes of physical understanding, evaluation, and noise reduction. Further, the acoustics subset can be divided into overall, broadband, or tone emphasis. Ultimately, assessments on full-scale turbofans are required. However, for isolating specific effects, or for costs reasons, it is useful to test models. These models may be scaled versions of turbofan components depending on the physical process of interest. The advantage of using models is the lower cost allows for a wider range of conditions to be studied. Even so, the cost of manufacturing and testing scale model fans in mid-technology readiness level can be limiting. A potentially useful supplement to turbo-machinery aero-acoustics studies is the use of artificial sources to generate acoustic signatures. The advantage is that a wide range of signatures can be quickly and efficiently studied, particularly useful for noise reduction concepts, or validating prediction methodologies that are sensitive to variations in geometry or acoustic signature. A disadvantage is the lack of the ability to study source generation. This trade-off must be considered carefully when deciding on the usefulness of utilizing fan artificial noise sources for the study of turbo-machinery aero-acoustics. This paper presents two test articles that have contributed to turbo-machinery aero-acoustics studies. One is a 48 in. diameter duct (nominally full-scale) generating acoustic signatures in the audible range; the second is a 6 in. diameter duct (nominally scaled) generating acoustic signatures in the ultrasonic range.

Keywords

Turbo-machinery aero-acoustics duct propagation far-field acoustics artificial sources

Introduction

The NASA Glenn Research Center has been involved in several programs (Advanced Subsonic Technology, Quiet Aircraft Technology, and the Fundamental Aeronautics Subsonic Fixed Wing) whose goals were the reduction in transport aircraft noise attributed to the turbofan engine. A significant component of turbofan noise is the noise caused by rotor–stator, and other interactions, coupled to duct propagation and radiating to the far field.

It is self-evident that in order to make effective progress in turbofan engine noise reduction, a thorough understanding of turbo-machinery aero-acoustics is essential. Turbo-machinery aero-acoustics encompasses,¹ but is not limited to:

generation of noise sources due to aerodynamic interactions (e.g. rotor–stator interaction);

propagation of the acoustic field (e.g. duct);

radiation to the near field (e.g. fuselage);

radiation to the far field (e.g. community noise)

and the overall acoustic characteristics of these particular examples can be subdivided into tone and/or broadband components for study.

Particular research areas lend themselves well toward the use of relevant experimental models. Computational aero-acoustic codes and unique measurement tools are required to enable the development of noise reduction technologies. In order to validate these codes and tools, it is necessary to have a diverse acoustic database. Evaluating novel liner concepts and nontraditional locations requires the determination of insertion losses. Shielding of engine noise by airframe components is a significant consideration in the design of next-generation transport aircraft. Modeling the impact of aircraft noise on the community accurately will depend partially on knowledge of the effect of nearby barriers on radiation patterns.

Traditional methodologies for studying turbo-machinery aero-acoustics in order of decreasing complexity/technology readiness level (TRL) are as follows: static engine testing,² mid-TRL,^3,4 and low-TRL⁵ scale model testing. These paradigms use rotor–stator combinations to generate and study Tyler–Sofrin⁶-type interactions and duct propagation. These examples have the advantage of representing source generation, duct propagation, and possibly the radiation to the exterior fields. Typically, due to manufacturing and operational costs, these models will be limited to a single point design, or relatively few. The fidelity of these representations depends upon the complexity, scale, and the parameters being investigated.

Alternate paradigms are to generate acoustic signatures based on known or desired characteristics using artificial sources.⁷ The curved duct test rig (CDTR)^8,9 at the NASA Langley Research Center is an operational open circuit wind tunnel that uses a fan to generate airflow up to M = 0.5 through a rectangular duct cross-section. The purpose of this rig is to validate analytical models and to evaluate novel duct acoustic liner concepts. The dimensions of the experimental rig test section are such that the scale to aft bypass ducts of most modern engines is between 25 and 50%. The acoustic signature in the duct is generated by an array of 16 high-intensity acoustic drivers. The operating frequency range of the CDTR is approximately 300–2400 Hz and rectangular duct mode corresponding to circumferential mode to m ≤ 5 and radial mode to n ≤ 2.

While eliminating the ability to investigate source generation mechanism this paradigm allows for a multitude of acoustic parameter variations and representative signatures limited only by the character of the artificial sources and signature generation methods employed.

Two recently developed test rigs have been used for a number of studies of acoustic propagation and radiation. The first rig is in the sonic range, the configurable fan artificial noise system (CFANS) with a frequency range of ∼500 to ∼1500 Hz, a circumferential mode range of m = ±7, and the ability to control four radials. The second is in the ultrasonic range, the ultrasonic configurable fan artificial noise system (UCFANS) with a frequency range of ∼5 to ∼35 kHz, a circumferential mode range of m = ±8, and the ability to control two radials. These rigs bring the spinning mode synthesis, improved mode measurement (for verification), far-field measurement capabilities, and geometry effects, to use in the study of turbo-machinery aero-acoustics.

Generating and sensing circumferential and radial modes

A detailed discussion of the generation of circular duct modes, summarized here, is presented in an earlier paper.¹⁰ Microphone and actuator arrays for addressing circumferential modes of order m consist generally of N individual transducers, arranged in a coplanar, equally spaced circular array mounted flush in the duct wall. The phasing of the g^th transducer around the circle is 2πmg/N. In other words, the transducer signals follow the circumferential trace of the targeted mode. In theory only the target mode is excited or sensed. In practice, extraneous modes are excited and/or sensed owing to transducer imperfections and aliasing. With perfect actuators, it is possible to avoid circumferential mode radiation aliasing by selecting an adequate number of actuators

N_{min} > | m_{target} | + | m_{max} |

(1)

where m_max is the highest circumferential order mode that will propagate. Note that N equally spaced actuators or microphones phased to generate or respond to circumferential order mode m will alias to modes m_target + qN, where q is any integer. The criterion expressed in equation (1) assures that |m_target + qN| exceeds m_max for all q except q = 0.

While actuator array requirements depend upon the target modes and all possible modes, microphone array requirements depend only upon modes that are present in the duct. If only a single circumferential mode is present, then in principle only a single microphone at each axial station would be necessary. In practice, flow noise at the duct wall needs to be suppressed relative to the mode signal, and spurious modes, from the fan and/or from the actuator array, need to be filtered out of the control system. This dictates use of a multimicrophone array at each axial station. The “safe” count selection criterion is

N_{mics} > | m_{target} | + | m_{max} |

(2)

where m_max is the highest circumferential order mode that could be cut on in the duct and the critical count criterion is

N_{mics} \neq | m_{target} - m_{interfering} |

(3)

where m_interfering is a nontarget mode known to exist in the duct.

Even in a static duct environment, isolation of radial mode orders is a nontrivial operation. Although the modes are orthogonal to each other, radial eigen functions taken alone are not. Thus, a microphone rake is required that can gather an adequate number of radial and circumferential pressure points to perform a 2D decomposition. The circumferential decomposition must be performed first to recover mode orthogonality. Then, for each circumferential order, the radial modes are orthogonal and may be isolated by conventional means. In a duct with flow, introducing a microphone rake may be problematical. First, flow noise complicates measurements. Second, wake shedding by the rake increases noise and could interfere with the flow. In a fan inlet, microphone rake wakes would interact with the fan rotor and produce a full series of blade passing frequency (BPF) harmonic modes. The modal dependence on propagation angle can be exploited using axially spaced microphones or actuator rows as “antennae” that isolate the radial order modes. Joseph et al.¹¹ and Smith and Burdisso¹² provide a more exhaustive background on this concept.

Test articles

Two distinct test rigs are used for synthesizing turbo-machinery acoustics: (i) for nominally full-scale investigations in the audible acoustic range, the CFANS can be utilized, (ii) for scaled investigations, the UCFANS is applicable.

CFANS

The 48 in. diameter CFANS is based on the advanced noise control fan (ANCF)⁵ and can be operated with the fan running (to provide duct flow) or with the fan at 0 r/min, or even removed (to provide a no-flow environment). The CFANS is utilized to generate and control circumferential modes (m) in the audible (un-scaled) regime. The system consists of four axially distributed rows, each with 16 circumferentially distributed sets of electromagnetic drivers flush mounted on the inner wall. There are two nominally 12 in. long spool pieces, each having two driver rows (see Figure 1). A Labview™ program is used to generate the waveforms sent to each driver independently, in the proper phase relationship to generate the desired circumferential mode. The signals to each row can be adjusted relative to one another to affect the radial distribution, if desired. The practical limits of the system are |m-order| < 7 and frequency < 1500 Hz.

Figure 1.

Schematic of CFANS.

Table 1 provides typical individual circumferential modes that can be generated and the corresponding radial modes cut-on for hub-to-tip ratios (σ) inside the duct, for studies referenced in this paper. The maximum circumferential mode (m) that could be cut-on is presented also. For each frequency, the m-orders (0,…, 6) are generated individually, though circumferential modes can be superimposed.

Table 1.

Typical modes generated for parametric studies using CFANS.

		Cut off	Ratios (σ,*** hub-to-tip ratio)
Freq (Hz)	Modes	inlet (σ = 0.0)	R/S (σ = .375)	EXHAUST (σ = 0.5)
480	±(2,0)	1.77	1.89	2.01
	±(4,0)	1.02	1.03	1.04
580	+(2,0)	2.14
600	+(2,0)/(2,1)	2.21/1.01
700	+(2,0)/(2,1)	2.58/1.17
880	+(2,0)/(2,1)/(2,2)	3.24/1.48/0.99
960	±(2,0)/(2,1)/(2,2)	3.54/1.61/1.08	3.79/1.72/1.02	4.03/1.53/−
	±(4,0)/(4,1)	2.03/1.16	2.06/1.22	2.09/1.22
	±(6,0)	1.44	1.45	1.45

The modes were measured by the rotating rake mode measurement system.¹³ The rotating rake system was developed and implemented by the NASA Glenn Research Center in the 1990s to measure turbofan acoustic duct modes. The system is a continuously rotating radial microphone rake that is inserted into the duct. It provides a complete map of acoustic duct modes present in a duct.

Horizontal orientation

The standard ANCF configuration (see Figure 2) is mounted horizontally on a stanchion and cantilevered support pylon. The fan has a standard r/min range of 1400–2000. An extended spool piece can be installed in the aft converging section where the hub-to-tip ratio transitions from 0.375 to 0.5. Rotating rake measurements at the inlet entrance, or exhaust exit planes, (or between any two spool pieces), and far-field directivity measurements can be acquired in this configuration.

Figure 2.

Horizontal orientation.

Figure 3 shows the typical high quality output from the CFANS for a sample case where mode m = 2 was the target mode generated in the inlet. Along the x-axis is the m-order, along the y-axis is the n-order, and the z-axis is the Power Level (PWL) in mode (m, n). Mode PWL is computed analytically from the measured pressure. Along the “back-wall” is the sum of the radial mode PWL in a given circumferential mode. The bar graph above and to the right of the tombstone provides a quantitative assessment of the modal content by providing the total PWL, the PWL in the mode generated, and the PWL in the extraneous or spillover modes (i.e. modes not desired). This could be considered the signal-to-noise ratio. The upper row of 3D “tombstone” plots is at 480 Hz (equivalent to BPF on ANCF) and the lower row is for 960 Hz (equivalent to 2BPF). The two columns represent data from two different builds (limited teardown and reassembly, about one month apart) for a limited repeatability demonstration. The target mode is at least 20 dB above any other individual mode, and mostly 10 dB above the sum of all other extraneous modes. This is shown in the small bar graph above and to the right of the 3D plot. The repeatability (admittedly limited) is within 1 dB.

Figure 3.

Sample output of CFANS (horizontal orientation—inlet location). GEN: power in generated mode; OTH: power in other modes (non-R/S modes); TOT: total power in harmonic (all modes).

As mentioned, the advantage of implementing the CFANS in the standard horizontal configuration is the ability to run the fan to generate flow in the duct, up to M = 0.12 in the inlet and M = 0.16 in the exhaust section. By synchronizing the rotating rake system to the CFANS signal, the modal structure generated by the fan is rejected by the Doppler-shift analysis technique¹³ and the modal decomposition is based only on the CFANS output. This method allows for the study of the influence of low duct Mach number duct flow. Figure 4 shows the generated positive and negative mode PWLs at M = 0 or −0.12 (negative indicates flow against acoustic propagation as is the convention in the inlet). These modes were individually generated in the inlet duct, forward of the fan, and measured at the inlet exit radiation plane, and the results combined on the figures. At BPF equivalent, little influence of ± mode number, or influence of Mach number is noted (Figure 4(a)), except for m = ±2, which has ∼3 dB drop in mode PWL at the higher Mach number. Likewise, at 2BPF (Figure 4(b)) the influence of these parameters is small except between m = +6 and m = −6. These differences may be due to reflections off the fan face.

Figure 4.

Influence of Mach # on CFANS mode generation—in-duct PWLs (horizontal orientation—inlet location). (a) In-duct mode PWL—1xBPF, (b) In-duct mode PWL—2xBPF.

Figure 5 shows the far-field directivity of the generated mode at ± modes and M = 0 or −0.12. Far-field acoustic directivities¹⁴ were acquired using 30 microphones placed at a 12 ft radius from the duct centerline and 10 ft high. Fifteen of these were in an arc about the inlet exit plane (0°–90° measured from the inlet axis) and 15 were in an arc about the exhaust exit plane (90°–165° with 180° being the exhaust axis). The tone levels were isolated by external sampling (order tracking) to the CFANS input signal. The far-field directivity trends correlate well to the in-duct. In Figure 5(a), the directivity of m = ± 6 is plotted. This mode is cut off at BPF, so the level, nearly 25 dB lower at the directivity peak, shows the effect of noninfinite duct length. (Since the mode is cutoff, the rotating rake algorithm does not compute the mode PWL and is not presented in Figure 4(a)).

Figure 5.

Influence of Mach # on CFANS mode generation—far-field directivity (horizontal orientation—inlet location). (a) Far-field SPL directivity—1xBPF (M# = 0), (b) far-field SPL directivity—1xBPF (M# = −0.12/0.16), (c) far-field SPL directivity—2xBPF (M# = 0), (d) far-field SPL directivity—2xBPF (M# = −0.12/0.16).

In addition, the CFANS can provide a broadband signal. A signal generator outputting a 250–10,000 Hz bandwidth white noise signal to all drivers was utilized. Spectra were computed from the microphones at 0° and 45°, and is compared to the input signal as shown in Figure 6. Compensation for driver response or to generate a modal structure is available through a bank of finite impulse response filters.

Figure 6.

Broadband CFANS at far-field microphones compared to input signal.

Vertical orientation

To provide a clean geometry for simpler experiments the CFANS can be built up off of the stanchion/pylon assembly that normally supports the ANCF fan and duct sections that make up the nacelle. That is, the spool pieces were stacked up in a vertical orientation on the floor (Figure 7). This removes center body, support pylon, and fan from the arrangement, providing a constant area annular duct. Two configurations have been tested in this setup: (i) with a constant 24″ diameter cylindrical tube and (ii) with a constant 36″ diameter cylindrical tube. These provided an equivalent annular duct hub-to-tip ratio of 0.5 and 0.75, respectively. The entire stack rests on the floor, and approximately 6″ of foam material is placed in the bottom of the stack to minimize reflections from the floor. Obviously, in this orientation, there can be no flow.

Figure 7.

CFANS vertical orientation.

Figures 8 to 10 are “tombstone” style plots that provide a detailed breakdown of the modal content at the frequency of interest. Figure 8 presents the frequency at the upper limit (1500 Hz) where the generated mode (m = 2) is aliasing into m = −14, a completely expected phenomenon, with 16 actuators (i.e. 2 – 16 = −14). In spite of the aliasing, the mode generation is still useful as the rotating rake can separate out the desired mode from aliased” mode for in-duct analysis. This would not be the case if explicit far-field directivity separation is required. Figure 9 shows the PWL content at three different hub-to-tip ratios for m = 2 at 500 Hz generated. The target mode is generally 20–25 dB above the extraneous modes, and the overall signal-to-noise ratio is ∼10–15 dB. Figure 10 shows the variation in m-order at 1000 Hz for σ = 0.5. At the higher frequency more m-orders are possibly propagating and as the m-order increases, the number of radials cut-on decrease. This effect (more modes present) causes the signal-to-nose ratio to drop slightly.

Figure 8.

High frequency excited in vertical orientation—CFANS. m = 2, σ = 0·5, 1500 Hz.

Figure 9.

Variation in hub-to-tip ratio (σ) in vertical orientation—CFANS (m = 2 @ 500 Hz). (a) σ = 0.0, (b) σ = 0.50, (c) σ = 0.75.

Figure 10.

Variation in mode circumferential excited in vertical orientation—CFANS (σ = 0·5, 1000 Hz). (a) m = 2, (b) m = 4, (c) m = 6.

UCFANS

The UCFANS is an approximately 6% scale model of a typical modern high-bypass ratio turbofan nacelle and fan duct. It was designed, built, and tested for measuring acoustic shielding by prospective airframe components of modal fan tone radiation in an anechoic chamber. Ultrasonic actuators are used in the model to reproduce the noise characteristics of a turbofan engine without the complexity of scaling down a fan. The artificial sources offer control over the mode and frequency to give a larger database for prediction code development and validation. Model fabrication was accomplished using rapid prototype technology at NASA Glenn Research Center.

An array of 36 wide-bandwidth electrostatic actuators is installed in a dual annulus within the fan duct. Three rows of 24 wide-bandwidth microphones are installed in the duct between the actuator array and the configurable inlet/exhaust exit plane to measure the modal tone generation. Modal excitation and analysis at up to nine simultaneous frequencies is accomplished by multiplexing. (This allows for more efficient parametric studies during lengthy traverse sweeps.) Note that this arrangement allows fine control over tone frequency and azimuthal mode but only limited control over radial modes.

Spectral components of the in-duct microphone data corresponding to reference excitation frequencies are spatially filtered to recover complex amplitudes of circumferential mode orders for each of the three rings. For each circumferential mode, radial components are estimated by steering vector matrix inversion for the three rings.

Actuators

Each actuator and in-duct microphone was bench tested for complex frequency response and equalization tables created to minimize the effect of actuator nonuniformity on modal radiation and of microphone nonuniformity on modal analysis. Actuators are driven from a dedicated D/A system using presynthesized 37-channel multifrequency signals (one for each actuator and one reference) WAV file. These actuators have a nominal frequency response of 95 dB SPL @ 10 cm for a 9.9 V_{peak to peak} 5 kHz input signal, ±11 dB from 4 to 110 kHz. Dedicated amplifier/power supply assemblies drive the actuators.

Internal microphones

The acoustic signature was measured in-duct, for modal content verification, by flush-mounted miniature electret condenser microphones. These microphones are typically used in the audible range (20–16,000 Hz) but have been utilized for ultrasonic wildlife studies.¹⁵ These microphones were also evaluated for frequency response and compared to the response of a ¼″ B&K 4939 style microphone. Microphones whose response was relatively inconsistent were not used. In-duct microphone data are recorded on a separate dedicated analog-to-digital (A/D) system, resulting in a 73-channel (one for each microphones and reference) TDMS file (a National Instruments file format).

Assembly

Figure 11 shows CAD drawings of the model. Areas critical to far-field acoustic radiation from the duct, such as inlet lip and duct exit dimensions are held to high fidelity, while areas not so critical to acoustics (e.g. internal flow path) are relaxed. The rapid prototype model is cast in five sections so that any section could be removed, replaced, or redesigned. In particular, the exhaust lip and tail cone can be removed and replaced with the inlet lip and spinner to switch the model from an inlet (Figure 11(a)) to an exhaust radiation model (Figure 11(b)). In these cases, the opposite end of the model is blocked off and sound-absorptive material placed in the cavity to minimize internal reflections. The remainder of the model is unchanged. The cabling for the internal drivers is routed through the center section. While this arrangement means that the complete internal and external lines do not completely match a target nacelle, this area is not primarily relevant to duct/far-field radiation. The flexibility in this arrangement (i.e. no rewiring actuators or moving the model) more than outweighs any minor effect on the radiation.

Figure 11.

(a) Line drawing of UCFANS nacelle in inlet configuration. (b) Line drawing of UCFANS nacelle in exhaust configuration.

The actuators are mounted in an annular ring, whose dimensions match the hub-to-tip ratio of a candidate engine nacelle. The inner path is kept constant to the spinner to minimize mode variation due to area change. Two rows of 18 actuators each are mounted circumferentially, the first row from the hub, and the second row from the “tip.” These rows are offset radially in the same axial plane but interlocking. The actuator count and distribution allow for circumferential modes up to m = 8, and two radial modes to be controlled. Higher modes can be generated but effects such as aliasing and underspecification become factors.

The microphones were flush mounted internally in three axially distributed rows, 24 microphones each, equally spaced in the circumferential direction. This distribution allows for measurement of up to m = 11, and n = 2, without aliasing. In addition to the bench test factors, in situ compensation curves for all microphones were obtained at several junctures during testing. Figure 12 shows the nacelle mounted in the NASA Glenn Acoustic Testing Laboratory.¹⁶

Figure 12.

UCFANS in exhaust configurations installed in ATL.

In-duct signature generation and validation

See Figure 13 for a block diagram of the signature generation and in-duct measurement.

Figure 13.

Block diagram for UCFANS signature generation and measurement. (*Digital Acoustic Data System).

The signature to generate the modal content was precalculated using the desired modes and frequencies, and stored. Each actuator in the array was driven by a composite signal of seven excitation frequencies, equalized for variations in individual actuator amplitude and phase response, and phased to match the circumferential wave numbers of the modes to be radiated. A graphical user interface program was used to create the algorithm to read in the prestored signal. These 36 signatures, plus a reference signal were output by a 200 kS/s sample rate digital-to-analog (D/A) chassis, allowing the full desired frequency range to be well below the Nyquist frequency. In addition to the 36-actuator drive channels, a reference channel consisting of the unity amplitude cosine wave of all excitation frequencies which was output directly to the data recorder. Because the test frequencies were limited to integer values up to 60 kHz, the excitation signals were multiples of 1 s duration.

An additional matrix of 36 each, 3 s (600,000 points) Gaussian noise signals was generated and stored in a file and applied to the test fixture actuators as an additional file. Care was taken to ensure that although the signals are statistically independent among the actuators, the radiated signal is coherent from test point to test point, allowing cross correlation and coherence computation between data taken at different traverse stops or even on different test days.

To minimize test time, three unique blocks of the seven frequencies plus one the broadband signature (Gaussian distribution) were generated, sequentially. The two sets of radial drivers could be preset with a desired amplitude and/or phase relation, as a group. To achieve differing radial mode combinations, three consecutive, 2 s signal bursts were applied with differing drive levels to the inner and outer actuators rows. Since the signal is known, parsing the frequency content from each block separately was conceptually straightforward. Effectively, this allowed for 22 separate conditions to be acquired in a short time frame. Figure 14(a) depicts the sequential block concept and Figure 14(b) the Fast Fourier Transform (FFT) of a representative block. It is seen in this figure that the tone penetration is a minimum of ∼10 dB above the background level.

Figure 14.

(a) Illustrative time history, (b) spectral content.

The mode-identification microphone array consists of 72 prepolarized condenser microphones in three rows of 24 each, allowing resolution of circumferential modes up to |m| = 11. The array is located approximately midway between the actuators and the duct termination, at axial positions that were determined to allow identification of radial orders n = 0, 1, and 2 over the BPF, and part of the 2xBPF frequency range 7–30 kHz.

The 72 internal microphones, along with the reference signal, were acquired using an AC-coupled 200 kS/s A/D converter with integrated antialiasing filters. These time histories were streamed to disk for later analysis. The 72 microphone signals and a reference signal were recorded at 200 kHz sampling rate using simultaneous sampling. The cross-power spectrum of each microphone channel was computed against the reference signal and spectral components corresponding to excitation frequencies were isolated into a “compressed spectrum.” The compressed spectrum for each microphone was equalized based on that microphone’s calibration curve and then the 24 spectra from each microphone ring were spatially Fourier transformed to recover the complex amplitude of each circumferential mode order −12 < m < 12, with m = |12| measurable, but the direction indeterminate.

For each circumferential mode m of frequency f, the radial component composition was estimated by computing the modal cutoff ratios and axial wave numbers

k_{z_{mn}} = \frac{2 π f}{c} \sqrt{1 - (\frac{{fco}_{m, n}}{f})^{2}}

(4)

for all radial orders n = 0 to one above the highest cut on.

For each microphone row an axial coordinate z was established relative to the midway point between the extreme rows. The transfer function from this location to each microphone row j and each propagation mode (m, n) is then

p_{j, m} = \sum_{n} p_{0, m, n} \exp (- {ikz}_{m, n} z_{j})

(5)

or, expressed as a transfer matrix function

[p_{j}]_{m} = [H_{j, n}]_{m} [p_{0, n}]_{m}

(6)

Since complex circumferential mode amplitudes p_j are determined from spatial Fourier transform of the mic data, the matrix H is inverted and multiplied with p_j to determine the radial content, p_0, _n relative to the center of the mic array. This inversion was done using Matlab PINV function, which has the properties:

If rows = columns, inversion is exact

If rows > columns, inversion is the minimum norm solution (fewer modes than mic rows)

If rows < columns, inversion is least squares error solution (more modes than mic rows)

Because each test involved hundreds of far-field microphone array traverse stops, with the same excitation signals applied to the simulator drivers, the modal composition of the excitation was computed for a representative subset of the traverse stops. The results were compared for consistency to ensure repeatability of the radiated sound field.

Two methods were employed to separate the duct propagation modes from the 72 microphone signals: (a) A two-step process that separates circumferential modes in each microphone ring and then separates radial modes by inversion of a transfer matrix based on modal axial wavenumber. (b) A simplified “beam-forming” approach that uses the modal transfer functions to each microphone as steering vectors and the cross-spectral matrix of the 72 microphone signals. For the two-step process, only un-aliased circumferential modes (−12 < m < = 12) were considered. In the beam-forming process,¹⁷ the first cycle of aliased modes was also considered (−24 < m < = 24). In either case, only radial orders (0 < = n < = 3) were included.

The full modal analysis process actually consisted of multiple computation steps:

TDMS data files produced by the NI 80-channel acquisition system were converted to MATLAB™ data arrays. Channel 73 was a copy of the zero-phase excitation signal set. The Fourier transform of this reference channel signal was used to phase normalize the Fourier transforms of the 72 microphone channels and to select the spectral components corresponding to the seven-excitation frequencies. The cross-spectral matrix was computed for these seven components only, and the “condensed” phase-normalized spectra and cross-spectral matrices were equalized from tables created during the microphone calibration process and stored for use in the subsequent modal analyses.

Spatial Fourier transforms were computed for each frequency and microphone row. The 24 microphones were equally spaced around each ring, so that complex circumferential mode amplitudes A_fmz were recovered for (−11 < = m < = 12) and plotted.

For each frequency and circumferential mode, the axial wavenumber was computed for each radial order (0 < = n < = 3) based on cutoff ratio (η = f/f_co)

k_{z_{mn}} = \frac{2 π f}{c_{0}} \sqrt{1 - (\frac{1}{η_{mn}})^{2}}

(7)

Transfer matrices were created for each frequency and circumferential mode from the axial center of the three microphone rows where δz is the axial distance to the microphone ring from the center

[A_{fm 1} A_{fm 2} A_{fm 3}]; where A = P * T^{- 1}

(9)

The complex amplitude vector was multiplied by the pseudo-inverse of T_fm to obtain the complex amplitudes of the radial modes. Note, however, that when the number of cut-on radial orders exceeds the number of microphone rows, the inverse of T is actually a least squares approximation (using the MATLAB™ pinv function). For cases where only two or three radial order modes were cut on, the transfer matrix was truncated so that exact inversion was possible.

Reduced data

A significant amount of data was acquired for noise shielding prediction code validation. Reported herein will be a selection of the reduced data, encompassing select changes in the parametric study. The data include the in-duct relative modal decomposition and sound pressure level (SPL) contour plots of the resulting radiated far-field planes. The SPL contour planes were also integrated to obtain noise power level PWL – (actually partial power to be used for comparison purposes). A qualitative analysis is provided herein, as the objective is to assess the character of the system. A limited range of mode/frequency combinations is presented to demonstrate the capability of the UCFANS. These are presented in Table 2.

Table 2.

UCFANS code validation modes.

Frequency (kHz)	Modes	Cutoff ratio	Amplitude ratio
7	(6,0)	1.32	(Outer = 1/Inner = 1)
8	(6,0)	1.51	(Outer = 1/Inner = 1)
9	(6,0)/(6,1)	1.70/1.08	(Outer = 1/Inner = 1)
11	(8,0)/(8,1)	1.59/1.12	(Outer = 1/Inner = 1)
12	(8,0)/(8,1)	1.73/1.22	(Outer = 1/Inner = 1)
13	(2,0)/(2,1)/(2,2)	7.17/2.07/1.08	(Outer = 1/Inner = 1)
14	(6,0)/(6,1)/(6,2)	2.64/1.68/1.07	(Outer = 1/Inner = 1)

In-duct modal signatures

The in-duct modal decomposition for the inlet nacelle and for the exhaust nacelle is shown in Figures 15 and 16, respectively, unlike the CFANS, the UCFANS has no flow, and therefore radiation differences would be a result of the differences in lip and center-body configuration. Subplots (a)–(c) show cases where the frequency was held constant at 7 kHz and the single cut-on circumferential mode varied. Subplots (d) and (e) show the cases with frequency held constant at 12 kHz and the circumferential mode m = 8 with two radials cut-on are being generated. The variation is in the driver row actuation (both, inner, or outer)—in order to cause a differentiation in the radial mode mix. The ratio between the outer/inner driver row signals is varied to qualitatively illustrate radial mode effects. While the mode generation system could infinitely vary the relative magnitude or phase between the two rows, this simple on/off was chosen for evaluation purposes. In theory, a desired radial structure could be selected and generated if a significant number of magnitude/phase variations were generated and measured, then a steering vector matrix determined.

Figure 15.

Relative modal decomposition for the UCFANS nacelle in the inlet configuration. (a) 7 kHz—mode (6,0), (b) 7 kHz—mode (8,0), (c) 7 kHz—mode (4,0), (d) 12 kHz—mode (8,0) (8,1) both drivers actuated, (e) 12 kHz—mode (8,0) (8,1) outer drivers actuated, (f) 12 kHz—mode (8,0) (8,1) inner drivers actuated.

Figure 16.

Relative modal decomposition for the UCFANS nacelle in the exhaust configuration. (a) 7 kHz—mode (6,0), (b) 7 kHz—mode (8,0), (c) 7 kHz—mode (4,0), (d) 12 kHz—mode (8,0) (8,1) both drivers actuated, (e) 12 kHz—mode (8,0) (8,1) outer drivers actuated, (f) 12 kHz—mode (8,0) (8,1) inner drivers actuated.

The single mode cases show the dominant mode substantially above the background. The target mode (4,0) was strongly excited with very little spillover. Both the inlet (Figure 15(a) to (c)) and exhaust (Figure 16(a) to (c)) show this clearly. At the higher frequency, 12 kHz, with two-radials propagating (8,0)/(8,1) the results are more mixed. For the exhaust configuration, there is clear aliasing to m = −10, which is expected due to the driver count. (The aliased mode is the target mode minus the number of drivers, e.g. 8-18 = −10). The inlet configuration has generally cleaner modal decomposition. The outer driver (Figure 15(e)) and inner driver (Figure 15(f)) couple nicely to the zeroth and first radials, respectively. The combination of the two rows creates a cancellation that reduces the overall target mode strength, with modest spillover. In the exhaust configuration, the outer drivers (Figure 16(e)) generate a reasonable target mode with moderate spillover, while the inner driver (Figure 16(f)) target mode generation is weak and more spillover.

The two cases presented generally represent the range of clarity of the modal decomposition. The majority tended to be closer to the stronger target mode with modest spillover. Imperfections in the compensation curves may account for spillover and could be corrected in an iterative process.

Nacelle radiation to far-field array contours

Far-field noise data were acquired to provide data for the development of noise propagation codes. Time series data were recorded at a 200 kHz sample rate. A Kaiser window function (2¹⁴ points) was then applied and a Fourier transform used to convert the data to “as measured” spectra. Each spectrum was then corrected on a frequency-by-frequency basis for the individual microphone response and the effect of the grid cap (using calibration curves supplied by the manufacturer). Finally, the data were converted to a lossless condition by correcting for the atmospheric attenuation of propagating sound.^18,19 Note that the data presented are at the measurement location and include the spherical spreading of sound. At this point, the tones of interest may be extracted from the overall spectrum.

The far-field traverses were taken in either horizontal (two) or vertical planes (three). Both horizontal planes were above the model at approximately 7.5 and 10.1 diameters. Two vertical planes were on either side of the model (6 and 12 diameters). The array consisted of 13 microphones, spaced 3 in. apart, spanning 36″, such that the seventh microphone was centered and tracked the centerline of the model and data were acquired with a 3″ resolution between traverse stops. The array was then shifted 33″ or 66″ in either the ±Y directions and another planar sweep acquired, providing a total lateral span of 160″ (due to an overlap of two microphones). The resolution at Y = ±33″ was 6″; at Y = ±66″ it was 12″. Figure 17 depicts the traverse plane locations relative to the model.

Figure 17.

Traverses for UCFANS code validation mode configurations. PWL = 71.8 dB, PWL = 71.4 dB.

The SPL contours for the exhaust nacelle configuration, 7 kHz m = (4, 0) are presented in Figure 18. The contours show clear and strong modal structure, spreading out as the radiated distance from the nacelle increases from +44.75″ (a) to +60.45″ (b) above the nacelle. The PWL is essentially conserved, with a small amount of leakage outside the measurement plane at the higher distance sweep. Here PWL is computed from the pressure squared times the area of the measurement plane.

Figure 18.

UCFANS exhaust nacelle horizontal plane views (7 kHz mode (4,0)). (a) Far-field Array Sweep @ +44.75″, (b) Far-field Array Sweep @ +60.45″.

SPL contours for the exhaust nacelle are presented in Figure 19. The frequency is held constant at 7 kHz and the circumferential mode (single radial only) is varied. The results obtained in the horizontal plane at 44.75″ above the model are presented on the left-hand side, the vertical curtain at 36.00″ from the model is presented in the right-hand side. Integrated PWLs are indicated next to each contour. As the plots are reviewed from the top of the page to the bottom, the circumferential mode number increases, or the cutoff ratio decreases. For the well cut-on mode (4,0) with ζ = 1.95, Figure 19(a) and (b) the very distinct lobed pattern of a classic mode is seen. It is seen in Figure 19(a) and (b) that as the cut-on ratio decreases the mode becomes more diffuse, until at just above cut-on (ζ = 1.01—Figure 19(c)) the mode is seen to break down.

Figure 19.

Circumferential mode variation in UCFANS exhaust nacelle alone contour plots. Left column—horizontal plane @ 44.75″ above model; right column—vertical plane @ 72.0″ right of model. (a) 7 kHz—mode (4,0) ζ = 1.95, (b) 7 kHz—mode (6,0) ζ = 1.51, (c) 7 kHz—mode (8,0) ζ = 1.01. (a) 12 kHz—mode (8,0) & (8,1), (b) 12 kHz—mode (8,0) & (8,1), (c) 12 kHz—mode (8,0) & (8,1).

The results obtained for the higher frequency case (12 kHz) (also for the exhaust nacelle) are presented in Figure 20. At this frequency two radials are cut-on: (8,0) and (8,1). The ratio between the outer/inner driver row signals is varied to qualitatively illustrate radial mode effects in the far field. The azimuthal variation at this frequency is evident due to the spillover noted, especially in the horizontal sweeps. There is a marked far-field effect due to radial variation. With some imagination, one can see that Figure 20(c) is a superposition of Figure 20(a) and (b), as one might expect as the sources themselves are superpositions. That is the configuration with both rows driven should be a combination of the outer and inner rows individually driven.

Figure 20.

Radial mode variation in UCFANS exhaust nacelle alone contour plots. Left column horizontal plane @ 44.75″ above model; right column vertical plane @ 72.0″ right of model. (a) 7 kHz—mode (6,0); (b) 7 kHz—mode (8,0); (c) 7 kHz—mode (4,0); (d) 12 kHz—mode (8,0)/(8,1): both driver sets; (e) 12 kHz—mode (8,0)/(8,1): outer driver set; (f) 12 kHz—mode (8,0)/(8,1): inner driver set.

A simple check on repeatability was achieved by repeating the main overhead horizontal sweep. Figure 21 compares the SPL contours taken at the beginning of the day and at the end of the day. The qualitative comparison of the contours is excellent. The computed PWL differences range from −0.3 to −0.8 dB, depending on the tone frequency, and averages −0.5 dB. This systematic shift may be due to output drift as a result of temperature or operating time.

Figure 21.

UCFANS repeatability (left column beginning of day/right column end of day).

Significant results

The CFANS was used to obtain acoustic databases in support of multiple investigations. The unique rotating rake mode measurement tool was extended to incorporate a second, axially offset rake, to measure the effect of modal reflections inside the duct.^20,21 The system provided a set of consistent modes to evaluate several axial spacings of the dual rakes which would not be feasible with a fan source. Parametric sets of insertion loss databases²² were acquired for the purpose of validating a novel liner design and manufacturing methodology.²³ A constant impedance liner and variable impedance liner were evaluated using the CFANS system in the vertical build. Each liner was installed coupled to one of two center bodies (24″ and 36″) with a variety of liner planforms evaluated. Insertion loss for each configuration was measured in-duct using the rotating rake measurement system—the methodology was validated. A series of tests using the CFANS in the horizontal configuration were performed primarily for the use of code validation and tool validation. Rotating rake mode measurements using the CFANS as a source acquired modal characteristic data sets^24,25 of: (i) mode blockage, (ii) liner insertion loss, (iii) short ducts, and (iv) mode reflection.

The UCFANS was used to obtain databases in support of wing-body acoustic shielding investigations. Simple modes were generated suitable for code validation²⁶ that can be used for or fan tone noise for system study purposes. A more complex modal signature based on typical turbofan modes and scaled frequencies was utilized in Sutliff et al.²⁷ for a first-order study of the effect of wing shielding on acoustic radiation from an engine nacelle. This configuration of the UCFANS represented the hybrid wing body²⁸ full 3D 5.8% scale model. Benefits from the shielding of the nacelle by a representative 2D wing planform at several geometric positions were documented and available for input to system studies. Validation of an analytical prediction method using Fresnel knife-edge diffraction coupled with a dense phased array of point sources to compute shielded and unshielded sound pressure distributions for the UCFANS is reported in Sutliff and Walker.²⁹

Conclusion

The CFANS and UCFANS test fixtures are fan-mode simulators for turbo-machinery aero-acoustic research. A sample subset of data was presented for illustrative purposes representing the range performance available. In-duct modal analysis and external radiation patterns confirm that consistent targeted combinations of frequencies and modal structure can be achieved. Qualitatively, the far-field modal characteristics are as would be intuitively expected and thus suitable for code validation, noise reduction technology evaluation, and for first-order approximation shielding benefits of fan tone noise for system study purposes.

Footnotes

Acknowledgments

The authors world like to acknowledge the efforts of D. Podboy, L. Smith, R. Loew, B. Groening, E. Mysliwiec, and J. Mirecki of TFOME for their support in model assembly and Acoustic Testing Laboratory testing. C. Garcia (also TFOME) wrote the A/D and D/A algorithms used for signature generation and in-duct verification.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the NASA Vehicle Systems Integration program/Environmentally Responsible Aircraft project and the Fundamental Aeronautics/Subsonic Fixed Wing program.

Appendix

References

Hubbard HH (ed). Aeroacoustics of flight vehicles: theory and practice: Volume 1, NASA Reference Publication 1258, Vol 1. WRDC Technical Report 90-3052.

Weir D. Engine validation of noise and emission reduction technology. Honeywell Report No. 21-1384A, NASA/CR–2008-215225.

Hodges RM, Gerhold CH, Balster D, et al. Acoustic testing of very high bypass ratio turbofans using turbine powered scale models. AIAA 94-2552, 20–23 June 1994.

Woodward RP and Hughes CE. Acoustic performance of an advanced model turbofan in three aeroacoustic test facilities. NASA/TM–2012-217608.

Loew RA, Lauer JT, MCAllister J, et al. The advanced noise control fan. NASA/TM–2006-214368, also AIAA 2006-3150.

Tyler

Sofrin

. Axial flow compressor studies. SAE Trans 1962; 70: 309–332.

Seiner JM and Reethof G. Design and development of the spinning mode synthesizer. NASA CR–2260, April 1973.

Gerhold C, Cabell R and Brown M. Development of an experimental rig for investigation of higher order modes in ducts. AIAA 2006-2637, May 2006.

Gerhold CH, Brown MC, Jones MG, et al. Report on recent upgrades to the curved duct test rig at NASA Langley Research Center. AIAA 2011-2896.

10.

Walker B. Sensitivity issues in active control of circular duct modes using axially-spaced actuator arrays. In: Proceedings of Active 99, the 1999 international symposium on active control of sound and vibration, Ft. Lauderdale, Florida, USA, December 1999, pp.91–102.

11.

Joseph, Nelson and Fisher. Active control of turbofan radiation using and in-duct error sensor array. In: Proceedings of Active 97, Budapest Hungary: OPAKFI, August 1997, pp. 273–286.

12.

Smith and Burdisso. Active control of inlet noise from a turbofan engine using inlet wavenumber sensors. AIAA 99-1808.

13.

Sutliff

. Turbofan duct mode measurements using a continuously rotating microphone rake. Int J Aeroacoust 2007; 6: 147–170.

14.

McAllister J, Loew RA, Lauer JT, et al. The advanced noise control fan baseline measurements. NASA/TM–2009-215595, also AIAA 2009-0624, October 2009.

15.

http://www.wildlife-sound.org/equipment/technote/micdesigns/ultrasonic.html (accessed 27 October 2011).

16.

Podboy DM, Mirecki JH, Walker BE, et al. Recent improvements to the acoustical testing laboratory at the NASA Glenn Research Center. NASA/TM—2014-218110 also AIAA 2014-0721.

17.

Dougherty RP, Walker BE and Sutliff DL. Locating broadband sources on a low speed fan using virtual rotating microphone imaging. AIAA 2010-3736.

18.

Method for calculation of the absorption of sound by the atmosphere, ANSI S1.26-1995, ASA 113-1995.

19.

Shields FD and Bass HE. Atmosphere absorption of high frequency noise and application to fractional-octave bands. NASA CR-2760, June 1977.

20.

Dahl MD, Hixon DR and Sutliff DL. Further development of rotating rake mode measurement data analysis, AIAA 2013-2246.

21.

Dahl MD and Sutliff DL. Analysis of dual rotating rake data from the NASA Glenn Advanced Noise Control Fan Duct with Artificial Sources, AIAA 2014-3316.

22.

Sutliff DL, Jones MG and Nark DM. In-duct and farfield experimental measurements from the ANCF for the purpose of improved broadband liner optimization. AIAA 2014-3231.

23.

Nark DM, Jones MG and Sutliff DL. Improved broadband liner optimization applied to the advanced noise control fan, AIAA 2014–3103.

24.

Sutliff DL. A mode propagation database suitable for code validation utilizing the NASA Glenn Advanced Noise Control Fan and Artificial Sources, AIAA 2014-0719.

25.

Hixon DR, Envia E, Dahl MD, et al. Comparison of computational aeroacoustics prediction of acoustic transmission through a three dimensional stator geometry with experiment, AIAA 2014-1405.

26.

Sutliff DL, Brown CA and Walker BE. Hybrid wing body shielding studies using an ultrasonic configurable fan artificial noise source generating simple modes, AIAA 2012-2076.

27.

Sutliff DL, Brown CA and Walker BE. Hybrid wing body shielding studies using an ultrasonic configurable fan artificial noise source generating typical turbofan modes, AIAA 2014-0256.

28.

Czech

Thomas

Elkoby

. Propulsion airframe aeroacoustic integration effects of a hybrid wing body aircraft configuration. Int J Aeroacoust 2012; 11: 369–409.

29.

Sutliff DL and Walker BE. Characteristics using an ultrasonic configurable fan artificial noise source to generate modes–experimental measurements and analytical predictions, AIAA 2014-2346.