Dave Sree

Tuskegee University, Tuskegee, Alabama

Near-Field Acoustic Power Level Analysis of

F31/A31 Open Rotor Model at Simulated

Cruise Conditions

Technical Report II

NASA/CR—2015-218845

July 2015
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Dave Sree

Tuskegee University, Tuskegee, Alabama

Near-Field Acoustic Power Level Analysis of

F31/A31 Open Rotor Model at Simulated

Cruise Conditions

Technical Report II

NASA/CR—2015-218845

July 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNC13BA10B
Acknowledgments

The present work was sponsored by the NASA Environmentally Responsible Aviation Project Propulsion subtask, with Ken Suder 

as Project Monitor. This work was performed under the Universities Space Research Association (USRA)’s Advanced Research 

and Technology Support Task Order, IDIQ Subcontract Number 04555-014 (Prime Contract Number NNC13BA10B) for NASA 

Glenn Research Center. The support from USRA and Acoustics Branch at NASA GRC is greatly appreciated. The author would 

like to thank Dr. David B. Stephens of the Acoustics Branch for all his help, suggestions, and fruitful discussions.

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This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
NASA/CR—2015-218845 iii 

Preface 

The second part of the task under this Universities Space Research Association (USRA) subcontract 

number 04555-014 involved performing and documenting the near-field acoustic power level analysis of 

open rotor model F31/A31 at simulated cruise conditions based on data obtained from high-speed wind 

tunnel (SWT) tests at NASA Glenn Research Center (NASA GRC). The nonproprietary portions of the 

test data were provided by NASA GRC to perform the task. This subcontractor’s report on the second part 

of the task is provided in the form of Technical Report II which consists of relevant sound power level 

results from the analysis and their detailed discussions. The technical report is included as an attachment 

to this summary. The deliverables, namely, revised technical report, data analysis codes, spreadsheets of 

results, tables, figures, etc. will be shipped to the technical monitor at NASA GRC in electronic form at 

the end of the contract period. 

NASA/CR—2015-218845 1 

Near-Field Acoustic Power Level Analysis of F31/A31 Open Rotor 

Model at Simulated Cruise Conditions 

Technical Report II 

Dave Sree 

Tuskegee University 

Tuskegee, Alabama 36088 

Summary 

Near-field acoustic power level analysis of F31/A31 open rotor model has been performed to 

determine its noise characteristics at simulated cruise flight conditions. The nonproprietary parts of the 

test data obtained from experiments in the 8- by 6-Foot Supersonic Wind Tunnel (86 SWT) were 

provided by NASA Glenn Research Center. The tone and broadband components of total noise have been 

separated from raw test data by using a new data analysis tool. Results in terms of sound pressure levels, 

acoustic power levels, and their variations with rotor speed, freestream Mach number, and input shaft 

power, with different blade-pitch setting angles at simulated cruise flight conditions, are presented and 

discussed. Empirical equations relating model’s acoustic power level and input shaft power have been 

developed. The near-field acoustic efficiency of the model at simulated cruise conditions is also 

determined. It is hoped that the results presented in this work will serve as a database for comparison and 

improvement of other open rotor blade designs and also for validating open rotor noise prediction codes. 

Nomenclature 

AOA Angle of attack 

BSA Blade-pitch setting angles 

H Sensor proximity height 

M, M0 Freestream Mach number 

OAPWL Overall power watt level 

OASPL Overall sound pressure level 

Pac Measured acoustic power 

Pref Reference acoustic power 

Pspb Input shaft power per blade 

PWL Power watt level 

R2 Goodness-of-fit parameter 

Raft Aft rotor radius 

SPL Sound pressure level 

1.0 Introduction 

In this case, the term “open rotor” refers to an unducted counter-rotating twin rotor model which is 

being considered as a propulsion device for future aircraft (Refs. 1 and 2). Open rotors are also known as 

“propfans.” Open-rotor propulsion technology is now being developed as a viable alternative to modern 

day turbofan engines mainly because of predicted fuel economy benefits and improved performance 

(Ref. 3). However, high noise levels associated with open rotors pose both environmental and 

technological challenges. These include community noise around airports, passenger discomfort, aircraft 

structural integrity, and meeting stringent federal noise regulations. 
NASA/CR—2015-218845 2 

NASA Glenn Research Center (NASA GRC), in collaboration with the U.S. aircraft industry, has 

been conducting both analytical and experimental research studies to address this noise issue and to 

develop improved open rotor systems (Ref. 4). Tests on scale-model systems have been conducted in lowand high-speed wind tunnels at NASA GRC to understand the noise mechanisms and evaluate the 

acoustic performance of open rotors. Large amounts of both far-field and near-field acoustic data have 

been collected during an extensive test campaign from 2009 to 2012 to determine the noise levels under 

various simulated flight conditions (Refs. 5 to 7). The open rotor model used for testing was a one-fifth 

scale model having a so-called “historical” baseline blade set made of carbon fiber composite with a 

metal spar. This blade set is designated as “F31/A31” and serves as a nonproprietary baseline design for 

comparison with other blade designs (Refs. 5 to 7). 

Near-field acoustic tests on the model were carried out in the 8- by 6-Foot (high-speed) or Supersonic 

Wind Tunnel (SWT) at NASA GRC to study the model noise characteristics at simulated cruise flight 

conditions. Tests were conducted at various rotor speeds and freestream Mach numbers (M) with different 

blade-pitch setting angles (BSA) to conduct a parametric study of the model noise levels. 

Initial investigations of the test data of F31/A31 model have been reported by Stephens (Refs. 6 and 

7) in terms of narrowband noise spectra, sound pressure levels (SPL), and overall sound pressure levels 

(OASPL) for simulated cruise condition at M = 0.78 with BSA = 64.4/61.8 forward/aft rotor case. 

These investigations were based on the overall noise levels only. No attempts were made to separate the 

tone and broadband noise components from raw test data. No proper data processing tools were available 

at the time to separate tone and broadband noise. It is reported by Stephens (Refs. 6 and 7) that the 

measured unsteady pressure data at simulated cruise conditions in the 8- by 6-Foot Supersonic Wind 

Tunnel were mostly tone-dominated. Based on comparisons of overall noise spectra with extensive 

database on tare (or background) noise spectra, he found that the broadband components were interfered 

by the background noise for frequencies below about 3,200 Hz. It is also believed that the broadband 

components in the measured data were swamped by the tunnel flow over the sensors, particularly at close 

proximities to the rotors. Thus, determination of the tone component of the noise became very important. 

It is known that the open rotor total or overall noise consists of both tonal and broadband components. 

(The terms ‘total’ and ‘overall,’ and ‘tonal’ and ‘tone,’ will be used interchangeably in this report.) The 

determination of tonal and broadband noise components from raw acoustic test data is very important for 

properly assessing the noise control parameters and also for validating the open rotor noise prediction 

codes (Refs. 8 to 10). A new data processing method developed by Sree (Ref. 11) is now available to 

separate the tonal and broadband noise components from raw experimental data of open rotors. This 

method will be applied to examine the tone and broadband noise levels of the F31/A31 model. Because 

the model noise, as mentioned above, is mostly tone-dominated, much focus will be placed on presenting 

the tone noise characteristics in this report. 

The main purpose of the present work is to analyze the near-field experimental data available on 

F31/A31 and report the tone noise results together with total noise in a few selected cases. Some portions 

of the test data are declared nonproprietary and are provided by NASA GRC to perform the task. The 

noise levels will be expressed in terms of SPL and power watt level (PWL) at simulated cruise conditions. 

Variations of the noise levels with rotor speed, freestream Mach number, measurement location, bladepitch setting angles, and input shaft power will be studied. Correlation of PWL with input shaft power 

will be developed to study the acoustic performance of the model. It is hoped that the results presented 

here will serve as a valuable database for comparing other open rotor blade designs with F31/A31 and 

also for validating open rotor noise simulation codes. 

2.0 F31/A31 Model and the Test Rig 

A detailed description of the F31/A31 model and the test rig is given by Elliott (Ref. 5) and Stephens 

(Refs. 6 and 7). However, a few salient features of the model will be worth repeating here. The F31/A31 

model has two counter-rotating rotors. The axial distance between their pitch axes is 19.9 cm (7.8 in.). 

The forward rotor is approximately 65.2 cm (25.7 in.) in diameter and has 12 blades whereas the aft rotor 
NASA/CR—2015-218845 3 

Figure 1.—Photograph of F31/A31 model and ORPR test rig installed in 

the 86 SWT; (Courtesy: Acoustics Branch, NASA GRC). 

is approximately 63.0 cm (24.8 in.) in diameter and has 10 blades. The hub diameter of the forward rotor 

is approximately 26.6 cm (10.5 in.) and that of the aft rotor is 24.6 cm (9.7 in.). The pitch of the rotor 

blades could be adjusted to provide different operating conditions at cruise. 

For all the tests conducted in the 8- by 6-Foot Supersonic Wind Tunnel, the F31/A31 model was 

mounted on a test rig called the “Open Rotor Propulsion Rig (ORPR)” in a simulated pusher-type 

arrangement (Refs. 6 and 7). The model was tested in an isolated configuration, without an upstream 

pylon. The turbines within the test rig were fed by high pressure air at about 20 atm (300 psi) to turn the 

rotor blades. All test runs were made at zero angle of attack (AOA) relative to the longitudinal axis of the 

model. A photograph of the model and the test rig installed for test in the 8- by 6-Foot Supersonic Wind 

Tunnel is shown in Figure 1. 

3.0 Near-Field Sideline Acoustic Measurements 

The near-field sideline acoustic measurements in the 8- by 6-Foot Supersonic Wind Tunnel were 

performed at various simulated cruise conditions. The tests were conducted using three different BSA 

with varying freestream Mach numbers and rotor speeds. These details will be given in the next section. 

An aluminum plate with 17 flush-mounted unsteady pressure measuring transducers (Refs. 6 and 7) was 

used to collect data simultaneously at seventeen axial locations parallel to and above the model’s 

(centerline) longitudinal axis (Fig. 2). The plate can be seen in Figure 1. The plate could be remotely 

lowered from the wind tunnel ceiling to achieve various near-field sideline distances or sensor proximity 

heights (H) from the model’s axis of rotation. The height could be varied from 42.65 to 116.08 cm. The 

geometric and acoustic emission directivity angles corresponding to the seventeen axial locations depend 

on H and M (Refs. 6 to 7). For example, their values, relative to aft rotor pitch change axis, for H = 50.85 

cm and 116.08, and M = 0.78 are given in Table 1. Note that the angles are measured from upstream with 

respect to the longitudinal axis of the model. The near-field unsteady pressure data at these locations were 

collected using a sampling frequency of 200 kHz. The data record length for each test run was 15 sec. 

 
NASA/CR—2015-218845 4 

Figure 2.—Illustration showing the seventeen 

measurement locations above the model and 

relative to aft rotor pitch change axis; (Courtesy: 

Acoustics Branch, NASA GRC). 

TABLE 1.—SEVENTEEN SENSOR AXIAL LOCATIONS AND THEIR 

CORRESPONDING GEOMETRIC AND ACOUSTIC EMISSION 

ANGLES RELATIVE TO AFT ROTOR PITCH CHANGE AXIS 

AT H = 50.85 cm AND 116.08 cm, AND M = 0.78 

H=50.85 cm H=50.85 cm H=116.08 cm H=116.08 cm

Sensor

Number

Sensor

Axial

Location

(cm)

Geometric

Angle

(degree)

Acoustic

Emission

Angle

(degree)

Geometric

Angle

(degree)

Acoustic

Emission

Angle

(degree)

1 ‐46.6 132.5 97.4 111.9 65.5

2 ‐39.0 127.5 89.3 108.6 60.9

3 ‐34.1 123.9 83.5 106.4 57.9

4 ‐29.6 120.2 77.8 104.3 55.2

5 ‐23.5 114.8 69.7 101.4 51.6

6 ‐18.9 110.4 63.4 99.2 48.9

7 ‐14.8 106.3 57.8 97.3 46.6

8 ‐7.0 97.8 47.3 93.5 42.3

9 0.0 90.0 38.7 90.0 38.7

10 7.0 82.2 31.6 86.5 35.4

11 14.8 73.7 25.3 82.7 32.0

12 18.9 69.6 22.6 80.8 30.4

13 23.5 65.2 20.1 78.6 28.7

14 29.6 59.8 17.4 75.7 26.6

15 34.1 56.1 15.8 73.6 25.2

16 39.0 52.5 14.3 71.4 23.7

17 46.6 47.5 12.4 68.1 21.7
NASA/CR—2015-218845 5 

TABLE 2.—TEST CONFIGURATIONS FOR F31/A31 MODEL IN THE 86 SWT 

4.0 Test Configurations 

The test configurations for the model at simulated cruise flight conditions are summarized as shown 

in Table 2. Three cases of blade-pitch setting angles (forward/aft) were considered: (1) BSA = 

60.5/59.0, (2) BSA = 62.9/60.5, and (3) BSA = 64.4/61.8. These cases were chosen in order to 

obtain the best aerodynamic performance of the system at a given shaft speed and freestream Mach 

number. The Mach number variations ranged from 0.73 to 0.85 except for case (1) where they ranged 

from 0.67 to 0.85. (Tests conducted at other Mach numbers are not considered in this report.) All tests 

were performed by operating both rotors at the same speed. The rotor speeds were varied differently from 

70 percent to about 110 percent of corrected design speed depending upon BSA, as shown in Table 2. The 

corrected rotor design speed was taken as 7516 rpm. All tests were performed with AOA set to zero. Five 

sensor proximity heights (H) were chosen for data collection and are also given in Table 2. At each 

height, seventeen axial unsteady pressure measurements were made simultaneously. As mentioned earlier, 

data were collected for 15 sec, for each test run, using a sampling frequency of 200 kHz. 

5.0 Results and Discussion 

Special data processing techniques were applied to the near-field acoustic data obtained from 

simulated cruise tests in the high-speed wind tunnel. The new technique developed by Sree (Ref. 11) was 

used to separate the tone and broadband noise components from the raw data. Noise levels of each 

component were computed in terms of SPL and PWL, and as a function of rotor speed, Mach number, 

and measurement location for each BSA case. The main focus will be on presenting the tone noise 

characteristics here. 

Since the test cases and the range of operating conditions were large, and the number of outcomes 

many, only selected results of SPL and PWL will be presented in this report. The results obtained at 

various rotor speeds with BSA = 64.4/61.8 and M = 0.78 were of particular interest. A large number of 

interesting measurements were made at this operating condition. Also, these results are representative of 

similar results obtained in the other two BSA cases. However, some results of PWL variation with rotor 

speed at M = 0.78 will also be presented to compare the differences in PWL among the three BSA cases. 

Simulated

Flight Condition

Blade‐pitch

Setting Angles

(BSA)

Freestream

Mach Number

(M)

% Rotor Design

Speed Range

Measurement Height

(H) from Model's

Longitudinal Axis, cm

60.5o

/59.0o

0.67

0.73

0.78

0.80

0.85

81.6

to

110.2

42.65

50.85

69.11

87.38

116.08

Cruise

(AOA = 0

o

)

(No Pylon)

62.9o/60.5o

0.73

0.78

0.80

0.85

77.5

to

100.1

42.65

50.85

69.11

87.38

116.08

64.4o

/61.8o

0.73

0.78

0.80

0.85

70.0

to

100.0

42.65

50.85

69.11

87.38

116.08
NASA/CR—2015-218845 6 

Figure 3.—Narrowband noise spectra of overall and the corresponding tonal and broadband 

components at simulated cruise condition (sensor #9); BSA = 64.4/61.8, 91.1 percent design 

rotor speed, M = 0.78, H/Raft = 1.61. 

5.1 Narrowband Noise Power Spectra 

As stated earlier, the total, tonal, and broadband narrowband noise spectra were first determined using 

the method developed by Sree (Ref. 11). The spectral analysis was performed using a sample size of 

3 million and a frequency resolution of 12.2 Hz. In order to avoid the interference of wind tunnel 

background noise, particularly at low rotor speeds, the raw data was pre-processed using a 500 Hz to 

50 kHz band-pass filter before the spectral analysis was carried out. The background noise in the 8- by 

6-Foot Supersonic Wind Tunnel has already been addressed by Stephens (Refs. 6 and 7), and Sree and 

Stephens (Ref. 12). 

An example of the narrowband spectra of the overall (blue), tonal (red), and broadband (green) noise 

components is shown in Figure 3. These spectra were computed from the data measured by sensor #9 at 

H = 50.85 cm (or H/Raft = 1.61 where Raft is aft rotor radius) under simulated cruise condition at M = 0.78 

and 91.1 percent rotor design speed. Sensor #9 is in line with the aft rotor pitch change axis, i.e., at 90

geometric (or 38.7 acoustic emission) angle from aft rotor center (see Table 1). The spectral values are 

given in terms of SPL, in dB (referenced to 20 Pa), as a function of frequency, in Hz. The results show 

the rotor alone and other interaction tones from the two rotors at respective blade passing frequencies. 

They also reveal that the data is very much tone-dominated, as has been previously evidenced by 

Stephens (Refs. 6 and 7) also. 

It is also seen from this example that the tone noise is dominant in the 1 to 11 kHz range. The tone 

and broadband components are reasonably well separated except for a few spikes in the broadband 

spectrum. Notice that these spike levels are well below their corresponding (major) tonal levels. The 

spikes are attributed to random phase shifts and modulations in narrow tonal frequencies in the measured 

signal due to unsteadiness or jitter in rotor speeds, particularly at higher shaft speeds. Measured signals 

also get distorted by other extraneous effects. The new data processing technique by Sree is not able to 

eliminate the spikes completely. This is one of the limitations of the new technique, particularly at higher 

shaft speeds with jitter (Ref. 12). 

5.2 Integrated Sound Pressure Levels Versus Rotor Speed 

The sound pressure levels were computed by integrating the spectral results from 500 Hz to 50 kHz. 

Results from selected test data only will be presented here. As mentioned before, only the tone noise 

results will be presented here. (The broadband SPL generally varied between 150 and 155 dB). 
NASA/CR—2015-218845 7 

Figure 4.—Integrated SPL of tone noise as a function of geometric 

directivity angle for various rotor design speeds; BSA = 

64.4/61.8, M = 0.78, H/Raft = 1.61. 

Figure 5.—Integrated SPL of tone noise as a function of geometric 

directivity angle for different sensor proximity heights; BSA = 

64.4/61.8, M = 0.78, 91.1 percent rotor design speed. 

The computed tonal SPL results from data obtained at M = 0.78 and H/Raft = 1.61 for the BSA = 

64.4/61.8 case are shown in Figure 4. They are plotted as a function of geometric directivity angle, 

relative to aft rotor pitch change axis, for different rotor speeds ranging from 74.7 to 91.1 percent design 

speed. It is seen from these results that the SPL is directly proportional to the rotor speed. The tonal SPL 

rises sharply to about 165 dB around the rotors. Also noticed is a “dip” in the SPL for axial locations in 

between the rotors at this proximity height of H/Raft = 1.61. 

5.3 Integrated Sound Pressure Levels Versus Sensor Proximity Height 

The integrated SPL was also computed for different sensor proximity heights at a given rotor speed. 

Figure 5 shows the tonal SPL variations with H/Raft for the case where both rotors were running at 

91.1 percent design speed. The x-axis shows the geometric sound directivity angles, in degrees. As one 
NASA/CR—2015-218845 8 

would expect, the tonal SPL steadily increases as the sensor translating plate moves closer to the rotors. 

When moved very close to the rotors (i.e., at H/Raft = 1.36 and 1.61), a “dip” in the SPL occurs for axial 

locations in between the rotors, the tonal SPL is in the range of 144 to 167 dB. 

5.4 Acoustic Power Levels 

Sound or acoustic power is sonic energy per unit time and is measured in Watts (W). The sound 

power level, sometimes, is expressed as Power Watt Level (PWL) in dB units. PWL is a logarithmic 

measure of the sound power level in comparison to a reference level of 10–12 W, i.e., PWLdB = 10 log10

(Pac/Pref) where Pac = measured acoustic power in W and Pref = 10–12 W. 

In this work, the acoustic power level, Π (or PWL), was calculated by assuming the measured sideline 

pressures were in the acoustic far-field. Spherical spreading was assumed to map the sideline 

measurement on to a constant radius arc. The following equation, which takes into account the tunnel or 

freestream Mach number effect, was used to compute the PWL (Ref. 13): 

Π ൌ

2πdଶ

ρ଴c଴

න ሺ1െM଴ cos θୣሻଶ p′ തതതଶത൫d, θ୥൯

sin θୣ

dθୣ

஠

଴

where 

d sideline distance from model centerline, 

ρ0 ambient air density, 

c0 speed of sound, 

M0 tunnel or freestream Mach number, 

e sound emission angle, 

g geometric (measurement) angle, and 

p′ തതതଶത(d,g) time-averaged sideline mean-squared pressure at measurement angle, g, 

[Note: e = g – sin–1(M0 sin g)] 

The acoustic intensity at each rotor speed was calculated using the information from corresponding 

narrowband spectra and was integrated over frequencies between 500 Hz and 50 kHz. The intensity was 

assumed to be symmetric about the axis of the model and integrated over the portion of the spherical surface 

spanned by the sideline measurement angles. The upstream and downstream portion beyond the 

measurement angle was excluded from the calculation. The span of the directivity angles, however, is 

limited due to very close proximity of the measurement locations in the 8-by 6-Foot Supersonic Wind 

Tunnel and may not satisfy the far-field and spherical distribution assumptions in PWL calculations. The 

presence of the overhead sensor plate may also have some influence on the final results. The computed 

PWL may be questionable, but, unfortunately, there are no similar data available at present to compare and 

verify them. 

5.4.1 PWL Versus Sensor Proximity Height; Effect of Rotor Speed 

PWL of the model’s noise components was computed as a function of sensor proximity height (H) for 

different rotor speeds at simulated cruise conditions. Here again, the emphasis will be placed on tone 

noise only. (The broadband PWL generally varied between 152 and 156 dB.) The tonal PWL results for 

the case of BSA = 64.4/61.8 and M = 0.78 are given in Figure 6. Similar results were obtained for the 

other two BSA cases. Note on the x-axis in Figure 6, H is normalized with respect to aft rotor radius, Raft. 

It is seen from these results that, for a given rotor speed, the PWL does not change very much with 

proximity heights. However, for a given H, the PWL increases significantly as the rotor speed is increased. 
NASA/CR—2015-218845 9 

Figure 6.—PWL of tone noise as a function of sensor proximity 

height at different rotor design speeds; BSA = 64.4/61.8, 

M = 0.78. 

5.4.2 PWL Versus Rotor Speed; Effect of Freestream Mach Number 

We noticed from the results just presented in Figure 6 that the tonal PWL values do not significantly 

change with H for a given rotor speed. The change is less than about 2 dB. A large number of 

measurements were made at H = 116.08 cm (or H/Raft= 3.69) compared to other H locations. Enough data 

were available at this H location so that meaningful results of PWL versus rotor speed can be presented at 

different Mach numbers. These results of tone noise are shown in Figure 7 for the BSA = 64.4/61.8

case. The results reveal that the PWL steadily increases as the rotor speed is increased. For any given 

rotor speed, there is less than 3 dB change in PWL as M is increased. The PWL seems to level off to 

about 159 dB beyond about 90 percent design speed. It is also seen that, for speeds greater than 

85 percent design speed, PWL at M = 0.85 (purple) is lower than those at other Mach numbers. 

5.4.3 PWL Versus Rotor Speed; Effect of Blade-Pitch Setting Angles 

So far all the results that have been presented are for the BSA = 64.4/61.8 case only. However, it 

was also of interest to compare and study the differences in PWL among the three BSA cases considered 

in the simulated cruise test program (see Table 2). This comparison is done as shown in Figure 8 for a 

given M of 0.78. (The results are similar at other given Mach numbers also.) Figure 8 shows the tonal 

PWL as a function of rotor design speed for the three BSA cases. The data do not overlap and show some 

differences in each case. In general, the PWL increases with increasing speed in each case. The BSA = 

64.4/61.8 case seems to have higher noise levels than the other two. Note that the rotor speed ranges 

tested were different for each case. In the 85 to 90 percent speed range, the maximum difference of the 

tone noise between BSA = 64.4/61.8 and BSA = 60.5/59.0 cases is about 8 dB. 
NASA/CR—2015-218845 10 

Figure 7.—PWL of tone noise as a function of rotor speed at 

different freestream Mach numbers; BSA = 64.4/61.8, 

H/Raft = 3.69. 

Figure 8.—PWL of tone noise as a function of rotor design speed 

at three different BSA; M = 0.78, H/Raft = 3.69. 
NASA/CR—2015-218845 11 

5.5 Overall PWL Versus Input Shaft Power 

Relation between total emitted sound power level and input shaft power is always of interest when 

dealing with aeroacoustics of flying machines. This relation is shown in Figure 9 for the BSA = 

64.4/61.8 case at M = 0.78 and 0.80 only because good correlation was observed at these Mach 

numbers. (The data gets too scattered when all Mach number cases are included in the plot.) Also, the 

results shown in this figure are for the proximity height H/Raft = 3.69. Similar results can be obtained for 

other BSA cases also. Janardan and Gliebe (Ref. 13) found a good correlation between overall PWL 

(OAPWL) and input shaft power for one of the earlier open rotor models they tested. They suggested to 

use a plot of overall PWL as a function of shaft power per blade, or log10 (shaft power per blade), to 

obtain a good indication of blade loading for a given input shaft power. Both types of plots are presented 

in Figure 9 for the F31/A31 model. As seen from these results, a good correlation between OAPWL and 

input shaft power is observed. Using regression analysis, polynomial curve-fits of the form: 

 OAPWL = - 0.00167 Pspb

2 + 0.2653 Pspb + 151.3955 (1) 

with R2 = 0.9613 is found for the results in Figure 9(a), and 

 OAPWL = 7.4407 Pspb

2 - 10.7878 Pspb + 157.4165 (2) 

with R2 = 0.9589 is found for the results in Figure 9(b). In both of these equations, Pspb stands for input 

shaft power per blade, in kW, and OAPWL is in dB. Based on the actual results obtained in this work, the 

maximum error associated with these empirical equations is found to be less than 1 dB. Similar 

correlations can be obtained for tonal and broadband PWL also. 

 (a) OAPWL vs Shaft Power/Blade (b) OAPWL vs log10 (Shaft Power/Blade) 

Figure 9.—Variation of overall PWL with input shaft power for BSA = 64.4o/61.8o case; M = 0.78 and 0.80, 

H/Raft = 3.69. 
NASA/CR—2015-218845 12 

Figure 10.—Acoustic efficiency as a function of input shaft power for 

three BSA cases at simulated cruise condition; M = 0.78 and 0.80. 

5.6 Acoustic Efficiency 

The acoustic efficiency is defined as the ratio of the radiated acoustic power to the input shaft power 

where the radiated acoustic power is taken as the OAPWL (Refs. 14 and 15). Both powers are taken in 

kilowatt units in this work. Based on computed OAPWL values for the three BSA cases with M = 0.78 

and 0.80 in the 8- by 6-Foot Supersonic Wind Tunnel, the near-field acoustic efficiency for the F31/A31 

model is found to be below about 2.7 percent, as shown in Figure 10. However, for the BSA = 64.4/ 

61.8 case (blue symbols) this efficiency is less than 1.4 percent. The validity of these efficiencies has not 

been verified yet. 

6.0 Conclusions 

Analysis of near-field sound pressure levels and acoustic power levels of the open rotor model 

F31/A31 at simulated cruise flight conditions has been presented in this work. The analysis was 

performed on the nonproprietary portions of the test data provided by NASA-GRC. The model’s acoustic 

tests at simulated cruise conditions were conducted in the 8- by 6-Foot Supersonic Wind Tunnel facility at 

NASA-GRC. Test configurations consisted of three blade-pitch settings with varying rotor speeds, 

freestream Mach numbers, and sideline measurement locations. Both rotors were running at the same 

speed and the angle of attack was set to zero in all the test configurations. 

A new data analysis technique has been successfully applied to separate the tone and broadband noise 

components from the measured raw data to understand their level of contribution to the total noise. Since 

much of the measured unsteady pressure signals were dominated by tone noise, emphasis was placed on 

presenting mainly the tone noise characteristics. (The broadband SPL and PWL were found to be 

generally in the range of 150 to 156 dB, but they were believed to be marred by the tunnel flow over the 

sensors.) Computed SPL and PWL and their variations with rotor speed, freestream Mach number, 

measurement location, and input shaft power have been presented and discussed. 
NASA/CR—2015-218845 13

The results show that the near-field tonal SPL is directly proportional to rotor operating speed and 

measurement proximity. They dominate around the rotors. The tonal SPL is in the range of 140 to 

167 dB. The tonal PWL is also directly proportional to the rotor speed. However, no significant changes 

in the tonal PWL are found as the measurement proximity is increased toward the rotors. The tonal PWL 

is in the range of 145 to 161 dB. At any given rotor speed, the freestream Mach number causes only small 

changes in PWL, except for the 85 to 90 percent design speed range where up to 5 dB differences are 

observed. For a given blade-pitch setting and proximity height, the noise results at M = 0.78 and 0.80 

have similar characteristics. At any given Mach number and proximity height, the noise levels resulting 

from higher blade-pitch setting are found to be slightly higher than those from lower settings at all rotor 

speeds, except for the 85 to 90 percent design speed range where the differences are found to be as much 

as 8 dB. 

Based on good correlation, empirical relations between the model’s overall PWL and input shaft 

power have been developed. The SWT test results for the three BSA cases with M = 0.78 and 0.80 show 

that the near-field acoustic efficiency of the model is less than about 2.7 percent. 

Lastly, it is hoped that the results presented in this work will serve as a good database for comparison 

and improvement of other open rotor blade designs as well as for validating open rotor noise prediction codes. 

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