K.B.M.Q. Zaman

Glenn Research Center, Cleveland, Ohio

Flow-Field Surveys For Rectangular Nozzles

NASA/TM—2012-217410

April 2012

AIAA–2012–0069
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K.B.M.Q. Zaman

Glenn Research Center, Cleveland, Ohio

Flow-Field Surveys For Rectangular Nozzles

NASA/TM—2012-217410

April 2012

AIAA–2012–0069

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

50th Aerospace Science Conference

sponsored by the American Institute of Aeronautics and Astronautics

Nashville, Tennessee, January 9–12, 2012
Acknowledgments

Support from the Supersonics Project of the Fundamental Aeronautics Program is gratefully acknowledged. The author would 

like to thank James Bridges, Franco Frate, Stewart Leib, and Abbas Khavaran for various inputs during this study.

Available from

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7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Available electronically at http://www.sti.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217410 1

Flow-Field Surveys For Rectangular Nozzles 

K.B.M.Q. Zaman 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Flow field survey results for three rectangular nozzles are presented for a low subsonic condition 

obtained primarily by hot-wire anemometry. The three nozzles have aspect ratios of 2:1, 4:1 and 8:1. A 

fourth case included has 2:1 aspect ratio with chevrons added to the long edges. Data on mean velocity, 

turbulent normal and shear stresses as well as streamwise vorticity are presented covering a streamwise 

distance up to sixteen equivalent diameters from the nozzle exit. These detailed flow properties, including 

initial boundary layer characteristics, are usually difficult to measure in high speed flows and the primary 

objective of the study is to aid ongoing and future computational and noise modeling efforts. 

Introduction 

This report documents flow-field survey results for three rectangular nozzles of aspect ratios 2:1, 4:1 

and 8:1 as well as for a fourth 2:1 aspect ratio case with chevrons added to the long edges. The motivation 

for investigating the rectangular nozzles comes from potential noise benefits, as outlined in Reference 1, 

(see also Refs. 2 and 3). Several rectangular nozzles with and without chevrons and other potential noise 

reduction features have been designed and fabricated for flow-field and noise tests. The design 

considerations and details of these nozzles have been discussed in Reference 4. Four of the nozzles were 

adopted for the present flow-field surveys at low-speeds. The primary motivation was to provide detailed 

flow-field and initial boundary layer properties, usually difficult to measure at higher speeds, in order to 

aid computational fluid dynamics (CFD) investigations leading to noise modeling efforts. 

All four nozzles have the equivalent diameter (D) of 2.12 in. Data are also taken with a 2 in. diameter 

convergent round nozzle for comparison. The surveys are conducted primarily by hot-wire anemometry at 

a low jet Mach number of 0.226. Centerline velocity profiles at higher jet Mach numbers are also 

obtained using a Pitot-static probe. Highlights of the results were summarized in a conference paper 

(Ref. 5). In this technical memorandum, the overall summary for the distribution of various flow 

properties, comparing the four rectangular nozzle cases, is discussed first. This is followed by a 

documentation of detailed contours of the properties on cross-sectional planes at various downstream 

locations. The data files can be found on a supplemental CD (not published on the Web) which may be 

requested from the NASA Center for AeroSpace Information (CASI) at http://www.sti.nasa.gov, or 

443–757–5802. The raw data sets are given in a folder on the supplemental CD entitled 

“Rectangular_noz_data_files_April_2011”. Also included are the coordinates for the four nozzles in a 

separate folder on the CD; questions or clarification may be directed to any of the authors of Reference 4 

(Mr. Franco C. Frate and Dr. James E. Bridges of the NASA Glenn Research Center). All data files are 

further described in the Appendix at the end of this report. 

Experimental Procedure 

The experiments were conducted in an open jet facility housed in the Test Cell CW17 of NASA 

Glenn Research Center; an interested reader may find further description of the facility in Reference 6. As 

already stated, the four nozzles included an aspect ratio 2:1 (referred to as ‘NA2Z’ in the earlier design 

and test plan documents, and referred herein simply as ‘R2’), a 2:1 case with chevrons (‘NA2C3’, 

referred as ‘R2C’), a 4:1 case (‘NA4Z’, referred as ‘R4’) and a 8:1 case (‘NA8Z’, referred as ‘R8’). A 
NASA/TM—2012-217410 2

picture of the flow facility fitted with the R4 nozzle is shown in Figure 1(a) while the four nozzles are 

shown in Figure 1(b). The coordinate origin is at the nozzle exit center with y and z denoting lateral 

coordinates in the horizontal and vertical directions, respectively. A single (TSI 1260A-10) hot-wire, 

aligned with the nozzle wall, was used for boundary layer surveys approximately 0.04 in. downstream of 

the nozzle lip. For surveys on cross-sectional (y-z) planes, two (TSI 1241-20) X-wires, one in the ‘u-v’

and the other in ‘u-w’ configuration, were used to obtain all three components of velocity and turbulent 

stresses. The turbulent shear stresses uv and uwas well as mean streamwise vorticity x were also 

obtained in the surveys. 

The hot-wire probes were calibrated at the exit of the round nozzle and the X-wire data were reduced 

using simple ‘cosine law’. For calculation of x, gradient correction was applied for V and W data to 

account for the errors introduced by separation of the sensors in each X-wire. For further details of the 

measurement procedures, see Reference 6. The x data close to the nozzle exit (x/D=0.05) were read to be 

very large in amplitude and thought to be erroneous due to inadequate gradient correction and thus are not 

shown for that station. On the other hand, the x amplitudes for most cases at the farthest downstream 

station (x/D=16) were too small and within measurement noise level and thus are also not shown. The 

averaging time for the measurements at each point is varied from 4 to 10 sec depending on the streamwise 

location, the longest time being allowed for the farthest downstream location. 

The Pitot-static probe had a diameter of 0.065 in. The Pitot port was located at the center of the 

hemispherical tip and four equally-spaced static ports were located 0.375 in. from the tip. In the 

calculation of velocities, the measured static pressure was assumed to apply at the tip location. The jet 

velocity (Uj) was determined from the ratio of the plenum tank pressure and the ambient pressure in the 

test chamber using one-dimensional isentropic equations. Unless indicated otherwise, the velocities are 

normalized by the jet velocity Uj and the distances are normalized by the equivalent diameter D. All data 

pertain to cold flows (i.e., with total temperature the same everywhere as in the ambient of the test 

chamber). 

Results 

In the following the exit boundary layer data are presented first. This is followed by profiles of 

properties along the jet centerline obtained by the single hot-wire as well as the Pitot-static probe. Since 

the X-wire survey results involve many plots for various properties at various x-stations, the overall trends 

of these data are discussed next. Trends based on line graphs for the streamwise variation of ‘field 

maxima’ are compared for the four nozzles. The detailed survey results on cross-sectional planes at 

various streamwise locations are shown in Figures A1 to A22 in the Appendix. The data folder, 

“Rectangular_noz_data_files_April_2011”, contains all data files structured for easy use by ‘Tecplot’ and 

the plotting routines are also included. Time traces of hot-wire velocity are also included for the three 

baseline rectangular cases (without chevrons) in the ‘BL data’ sub folder. These data are taken 

approximately at 95% velocity point in the boundary layer on the middle of the long edges. To conserve 

space, the velocity data (in ft/s) are multiplied by 100 and saved as integers. Each trace has 400,000 data 

points taken at the rate of 100 kHz (i.e., for 4 seconds). 

In Figure 2, sample boundary layer profiles are compared for the R2 and R2C nozzles. The mean 

velocity and turbulence intensity data are shown in Figures 2(a) and 2(b), respectively. The 10% jet 

velocity point (y0.1), as measured, is assumed to be the wall location (recall that the measurement location 

is slightly downstream and thus the measured velocity does not drop to zero near the wall). While there 

are some differences in the mean velocity profiles, the turbulence intensity profiles vary significantly 

between the long and short edges. In either figure it can be seen that the addition of the chevrons (on the 

long edges) has not made a difference in the profiles measured on the short edge. The measurement 

locations are indicated in the legend; these are in the middle of the short or long edges except for the ‘long 

edge off-center’ case where the measurement is done halfway between the center and the end of the long 
NASA/TM—2012-217410 3

edge. The boundary layer characteristics are calculated by integration of the mean velocities between the 

98% to 10% velocity points. These are listed in Table 1 and discussed in the following. 

Figure 3 shows boundary layer momentum thickness for several values of Reynolds number for the 

R2 nozzle. Only on the low end of the ReD range does the data roughly resemble a C/sqrt(ReD) 

relationship that would indicate a laminar or ‘nominally laminar’ state; (C = 0.59 is used to approximately 

fit the data on the low ReD range.) From the trends of the data, the boundary layer appears to be 

‘nominally turbulent’ on the higher end of the ReD range since the thickness does not follow the ‘laminar 

prediction’. However, the shape factors (H12), listed in Table 1, are found to be large that are typical of 

‘Blassius-type’ laminar profiles. Thus, a highly disturbed ‘nominally laminar’ state is inferred for the 

boundary layer of the R2 nozzle. Note that the C/sqrt(ReD) law applies to round nozzles and the behavior 

at different points of the periphery of a rectangular nozzle may vary. On the other hand, from a 

consideration of the nature of the velocity fluctuation in the boundary layer, the corresponding states for 

the R4 and R8 nozzles are inferred to be ‘nominally turbulent’ (see Refs. 5 and 7). It is also noted that the 

time traces of the velocity signal do not appear to indicate any dominant periodicity; four such time traces 

are included in the electronic data folder. 

In Figure 4, centerline profiles of mean velocity (U) and streamwise turbulence intensity (u’) are 

compared for the four rectangular cases with data for the round nozzle (denoted as ‘Rnd’ in the legend). 

During data acquisition at each measurement point, all quantities were normalized by the current value of 

jet velocity measured simultaneously. The normalized mean velocity at the nozzle exit often deviated 

slightly from unity due to calibration drifts. All data were subsequently renormalized by the exit mean 

velocity so that U/Uj = 1. One notes a significant ‘vena-contracta’ effect with the rectangular cases, i.e., a 

significant increase in the mean velocity downstream of the nozzle exit. This is more so with the chevron 

nozzle. The turbulence intensity profiles are shown in Figure 4(b). Unfortunately, even 10 sec averaging 

was not enough to obtain convergent data and some scatter marks the profiles at the downstream 

locations. Nevertheless, the relative trends are amply clear. For all rectangular nozzles the peak in the 

streamwise turbulence intensity profile occurs farther upstream relative to the round nozzle case. The shift 

in the location of the peak is the most for the highest aspect ratio case of 8:1. The peak intensity increases 

with decreasing aspect ratio. Note also that the chevrons (R2C) have resulted in a lower amplitude of the 

peak pushing it farther downstream relative to the baseline 2:1 case (R2). (There was some residual 

electronic noise in the hot-wire circuitry affecting the measurements at low intensities. The turbulence 

intensity at the nozzle exit center is thought to be less than 0.5%. However, this has not been looked at 

rigorously.) 

Centerline mean velocity profiles measured by the hot-wire and the Pitot-static probe are compared 

for the round nozzle in Figure 5 in order to gain some confidence in the consistency of the results. The 

overall agreement is good; the hot-wire data are also found to repeat well relative to earlier measurements 

(Ref. 8). Centerline mean velocity profiles obtained by the Pitot-static probe are shown in Figure 6 for the 

round nozzle for several jet Mach numbers Mj. A lengthening of the potential core with increasing Mj is 

obvious. The ‘asymptotic’ slopes of the inverse of the velocities are found to be less (about 0.125) relative 

to values (about 0.15) reported in Reference 9. This is due to the fact that the measurements did not 

extend far enough downstream in the present study. 

In Figure 7 centerline velocity profiles for the four rectangular cases are compared with the round 

case at two high subsonic jet Mach numbers. For each rectangular case, by plotting the profiles for the 

two values of Mj together with the corresponding hot-wire profile from Figure 4(a), a similar downstream 

shift of the velocity profile may be noted with increasing Mj. This is shown in Figure 8 for the R8 case as 

an example. It is also apparent from Figure 7 that the ‘vena-contracta’ effect practically disappears at 

higher Mj except with the chevron case. 

The variation of the maxima of some of the flow properties from the cross-sectional surveys (detailed 

contours appended in the following), as a function of the streamwise distance, is compared to assess the 

overall trends. Figure 9 shows such data for the mean streamwise vorticity peak. Streamwise vorticity has 

negative and positive regions and the maxima here represent that of the absolute values. The vorticity 

magnitude drops off exponentially with streamwise distance (note the logarithmic ordinate scale). Similar 
NASA/TM—2012-217410 4

results were noted earlier in Reference 5. The magnitude is significantly higher for the chevron case. The 

peak value of streamwise turbulence intensity is similarly compared in Figure 10. Comparison of data for 

the R2 and R2C cases shows that, except for the upstream-most locations, the peak turbulence has been 

reduced by the chevrons. 

For each of the four rectangular nozzles, the maxima of u’, v’ and w’ intensities are compared in the 

four segments of Figure 11. The “anisotropy” in the normal stresses, obvious for all four nozzles, persists 

to the last measurement station. While the v’ and w’ amplitudes are nearly equal the u’ amplitude is larger 

at all streamwise locations. 

Detailed contours of flow properties are documented in the following figures. These are briefly 

discussed below. As stated at the end of the Introduction, the raw data can be found in a folder on the 

supplemental CD entitled “Rectangular_noz_data_files_April_2011”. 

Figures A1 to A5 

Contour plots of the survey results for the R8 nozzle are shown for various downstream locations 

(x/D); the location is indicated in the captions. For each station, the mean velocity (U) and three 

components of turbulence intensity are shown on the left column while the mean streamwise vorticity x

and the Reynolds shear stresses are shown on the right column (recall that x is not shown for the first 

and the last station for most of the cases). Note that on the side of each contour plot the value of the 

maxima in the field is indicated in parentheses in order to provide an idea about the overall levels. In 

Figure A2 at x/D = 1, concentration of streamwise vorticity into two pairs at the end of the major axis 

may be noted. Farther downstream only one pair dominates the flow-field as evident from the subsequent 

figures. At the farthest downstream location of x/D = 16 (Fig. A5), the jet cross-section based on the mean 

velocity as well as the turbulence intensity distributions has become almost round. 

Figures A6 to A10 

Corresponding contour plots for the R4 nozzle are shown. Similar observations as with the R8 case 

can be made. 

Figures A11 to A16 

Corresponding data for the R2 nozzle are shown. Here, for a better assessment of the effect of the 

chevrons an additional data set is provided for x/D = 2 (Fig. A13). Also, while all data are taken covering 

approximately half of the flow domain, here the full domain is covered at x/D = 4 (Fig. A14). 

Figures A17 to A22 

Results for the chevron (R2C) case are shown similarly in these figures, as done with the baseline 

(R2) case in Figures A11 to A16. Here, the first axial station is just downstream of the tips of the 

chevrons. At x/D = 1, pairs of streamwise vortices originating from each chevron can be seen. By x/D = 4, 

however, these vortices have merged into two pairs at the ends of the major axis, similar to that in the 

baseline R2 case (Fig. A14). However, the peak magnitudes are considerably higher in the chevron case. 

An inspection reveals that the overall turbulence intensities are reduced by the chevrons relative to the R2 

case. Compare, for example, the data in Figure A21 with Figure A15 for x/D = 8; (see also Fig. 4(b)). 

However, the amplitudes are higher at upstream locations and the distributions are complex (compare 

Fig. A18 with A12 for x/D = 1). 

The reduction in the intensities at the downstream locations has taken place with all three components 

of turbulence. The overall reduction in turbulence suggests a noise reduction by the chevrons. 
NASA/TM—2012-217410 5

Concluding Remarks 

Flow field properties for rectangular nozzles of three aspect ratios, including one case with chevrons, 

are documented in this paper. The data trends are compared with corresponding results from a round 

nozzle. For the rectangular cases, the peak in the streamwise turbulence intensity profile, measured along 

the centerline, occurs farther upstream relative to the round case. The shift in the location of the peak is 

the most for the highest aspect ratio case of 8:1 covered in the experiment. With decreasing aspect ratio 

the peak intensity is seen to increase. The chevrons result in lower amplitude of the peak pushing it 

farther downstream relative to the corresponding baseline case. From the flow field surveys, it is noted 

that, except for locations closest to the nozzle, the turbulence intensities are generally reduced by the 

chevrons. For all cases, the field maxima of the streamwise component of turbulence intensity is found to 

be significantly larger than the lateral components; the ‘anisotropy’ persists to the farthest measurement 

station of x/D = 16. It is hoped that these detailed flow field results may be useful in computational and 

noise prediction efforts and also advance the understanding of the noise mechanisms for the rectangular 

jets as well as for the effect of the chevrons. 
NASA/TM—2012-217410 6

Appendix—Data Files 

The following is a description of the data files accompanying this TM. The data files can be found on 

a supplemental CD (not published on the Web) which may be requested from the NASA Center for 

AeroSpace Information (CASI) at http://www.sti.nasa.gov, or 443–757–5802. 

Nozzle coordinates.—These are data files for nozzle coordinates. The four files starting with ‘N’ are 

for the four nozzles. The three files starting with ‘D’ are for the transition pieces connecting the aspect 

ratio 2, 4 and 8 nozzles with a common round receptacle. Any CAD program should be able to import 

these files for viewing the different pieces of hardware. These files can also be assembled and with some 

effort used for grid generation for the four nozzle cases for numerical simulations. 

X-wire surveys.—These are X-wire survey data for the nozzles as annotated in the file name. The 

measurement stations are at x/D = 0.05, 1, 4, 8 and 16, except for R2C nozzle where the first 

measurement station is at x/D = 0.38. For R2 and R2C cases, additional data sets at x/D = 2 are provided. 

For each nozzle case, separate folders contain data for each x-station. While examples of U, u’and x data 

are discussed in the TM, each folder also include data files for v’, w’, uv and uw (all nondimensionalized 

by jet velocity (Uj) and nozzle equivalent diameter (D)). [Notes: (1) Plot routines are included for 

convenience; (2) In the data files, U is represented by ‘ubv’, u’ by ‘ur’, v’ by ‘vr’, w’ by ‘wr’ and x by 

‘wx’; (3) the quadrants of survey are indicated in the file title.] 

BL_profiles.—These are single hot-wire data for the exit boundary layer profiles. The measurement 

locations as well as the jet velocity in ft/s are annotated in the names of some of the data files. (Example: 

‘y_survey_R2_long_offcntr_anlzd’ indicate profile at a location midway between the end and the center 

of the long edge of the R2 nozzle). Files not having annotation for measurement location represent 

profiles in the middle of the long edge. [Notes: (1) Plot routines are included for convenience; (2) In the 

data files, y1 (first column) represents the radial location relative to the approximate location of the nozzle 

wall, negative values being towards the axis of the nozzle.] 

Also included are four time series data at 95% velocity points in the boundary layer. The velocity data 

(in ft/s) are multiplied by 100 and recorded as integers. Each trace has 400,000 data points taken at the 

rate of 100 kHz (i.e., for 4 seconds). 

Centerline profiles.—These are centerline profiles measured by hot-wire or Pitot-static probe; the 

measurement method is annotated in the file names. For the Pitot-static data files, the jet velocity in ft/s is 

also annotated with the names. In the hot-wire data files, the three columns of data represent normalized 

axial distance, mean velocity and turbulence intensity. In the Pitot-static data files, the three columns 

represent normalized axial distance, normalized mean velocity and current jet velocity in ft/s. [Note: Plot 

routines are included for convenience]. 

Profiles of max field values.—These are field maxima of various properties as a function of axial 

distance. The five columns of data represent normalized axial distance, u’, v’, w’ and x. [Note: Plot 

routines are included for convenience]. 
NASA/TM—2012-217410 7

TABLE 1.—EXIT BOUNDARY LAYER 

CHARACTERISTICS 

Nozzle Location Uj

(ft/s) 

2 

(in.) 

H12 u’max

R2 Short 

edge 

256 0.0034 2.14 0.090 

R2 Long mid 256 0.0038 2.55 0.130 

R2 Long offcenter 256 0.0033 2.46 0.139 

R2C Short 

edge 

256 0.0033 2.13 0.090 

R4 Short 

edge 

256 0.0040 1.79 0.110 

R4 Long mid 256 0.0030 2.23 0.113 

R4 Long offcenter 256 0.0026 2.33 0.109 

R8 Short 

edge 

256 0.0044 1.91 0.110 

R8 Long mid 256 0.0032 1.97 0.107 

R8 Long offcenter 256 0.0028 2.20 0.101 

 

R2 Long mid 56 0.0045 2.16 0.143 

R2 Long mid 79 0.0041 2.14 0.144 

R2 Long mid 98 0.0038 2.16 0.149 

R2 Long mid 146 0.0036 2.21 0.147 

R2 Long mid 221 0.0037 2.51 0.139 

R2 Long mid 257 0.0040 2.73 0.137 

R2 Long mid 276 0.0042 2.77 0.130 

R2 Long mid 297 0.0042 2.80 0.130 

R2 Long mid 341 0.0043 2.83 0.132 

(a)

(b)

Figure 1.—Experimental facility. (a) Open Jet 

with 4:1 rectangular (R4) nozzle; the x-wires 

probes are in foreground. (b) Four nozzles. 

(a)

(b)

Figure 2.—Exit boundary layer profiles for 2:1 nozzle 

with and without chevrons at Uj  256 ft/s; (a) mean 

velocity, (b) turbulence intensity. 

Figure 3.—Exit boundary layer momentum thickness vs. 

ReD for R2 nozzle. Measurement at middle of long edge.

y-y0.1 (inches)

U/Uj

-0.06 -0.04 -0.02 0 0

0.2

0.4

0.6

0.8

1

R2 long edge mid

R2 long edge off-center

R2 short edge

R2C short edge

(Nozzle rotated by 90o

for long edge measurement)

y-y0.1 (inches)

u'/Uj

-0.06 -0.04 -0.02 0 0

0.05

0.1

0.15

R2 long edge mid

R2 long edge off-center

R2 short edge

R2C short edge

(Nozzle rotated by 90o

for long edge measurement)

ReDx10-3

2 (inches)

50 100 150 200 250 300 350 400 0.003

0.0035

0.004

0.0045

0.005

0.0055

0.006

R2 data

R2 laminar prediction
NASA/TM—2012-217410 8

(a)

(b)

Figure 4.—Comparison of (a) centerline mean velocity 

and (b) turbulence intensity profiles. Hot-wire data at 

Uj  256 ft/s. 

Figure 5.—Centerline mean velocity profiles for Round 

jet. Comparison of HW and Pitot-static data. 

Figure 6.—Centerline mean velocity profiles for Round 

jet. Pitot-static data showing Mach number effect. 

(a)

(b)

Figure 7.—Comparison of centerline velocity profiles for 

different nozzles at (a) Mj 0.72 and (b) Mj 0.96. 

x/D

U/Uj

0 4 8 12 16 0.2

0.4

0.6

0.8

1

Rnd Mj

=0.226

R2 Mj

=0.226

R2C Mj

=0.226

R4 Mj

=0.231

R8 Mj

=0.227

x/D

u'/Uj

0 4 8 12 16 0

0.05

0.1

0.15

Rnd Mj

=0.226

R2 Mj

=0.226

R2C Mj

=0.226

R4 Mj

=0.231

R8 Mj

=0.227

x/D

U/Uj

0 5 10 15

0.4

0.6

0.8

1

Rnd Mj=0.259 Pitot-static

Rnd Mj

=0.225 HW

x/D

U/Uj

0 5 10 15

0.4

0.6

0.8

1

Mj = 0.259

Mj = 0.502

Mj = 0.712

Mj = 0.959

Round Jet

x/D

U/Uj

0 5 10 15 0.2

0.4

0.6

0.8

1

Rnd Mj=0.712

R2 Mj

=0.720

R2C Mj

=0.721

R4 Mj

=0.718

R8 Mj

=0.722

x/D

U/Uj

0 5 10 15 0.2

0.4

0.6

0.8

1

Rnd Mj=0.959

R2 Mj

=0.956

R2C Mj

=0.956

R4 Mj

=0.955

R8 Mj

=0.957
NASA/TM—2012-217410 9

Figure 8.—Centerline mean velocity profiles for R8 

case showing Mach number effect. 

Figure 9.—Maximum (absolute) field values of 

streamwise vorticity as a function of axial distance. 

Figure 10.—Maximum field values of turbulence 

intensity (u’) as a function of axial distance. Figure 11.—Maximum field values of three components 

of turbulence intensity as a function of axial distance, 

for the nozzles as indicated. 

x/D

U/Uj

0 5 10 15

0.4

0.6

0.8

1

R8 Mj = 0.227

R8 Mj = 0.722

R8 Mj = 0.957

x/D

 D/U x j maximum

0 5 10 15 10-2

10-1

100

101

R2

R2C

R4

R8

x/D

u'/Uj maximum

0 5 10 15 0.05

0.1

0.15

0.2

R2

R2C

R4

R8

x/D

field maxima of turbulence intensities

0 4 8 12 16 0.05

0.1

0.15

0.2

u'/Uj

v'/Uj

w'/Uj

R2

x/D

field maxima of turbulence intensities

0 4 8 12 16 0.05

0.1

0.15

0.2

u'/Uj

v'/Uj

w'/Uj

R2C

x/D

field maxima of turbulence intensities

0 4 8 12 16 0.05

0.1

0.15

0.2

u'/Uj

v'/Uj

w'/Uj

R4

x/D

field maxima of turbulence intensities

0 4 8 12 16 0.05

0.1

0.15

0.2

u'/Uj

v'/Uj

w'/Uj

R8
NASA/TM—2012-217410 10

Uj

U

(1.03)

2 U j

uv

(0.005)

Uj

u'

(0.078)

2 U j

uw

(0.002)

Uj

v'

(0.072) 

Uj

w'

(0.059)

Figure A1.—For the R8 nozzle, contours of various flow properties on y-z plane at x/D = 0.05. 

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.05 0.21 0.37 0.54 0.70 0.86 1.02

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

-0.005 -0.003 -0.002 0.000 0.002 0.003 0.005

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.01 0.02 0.03 0.04 0.05 0.06 0.07

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.01 0.02 0.03 0.04 0.05 0.06 0.07

y/D

z/D

0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.01 0.02 0.03 0.03 0.04 0.05 0.06
NASA/TM—2012-217410 11

Uj

U

(1.01)

2 U j

uv

(0.0079)

Uj

u'

(0.165)

2 U j

uw

(0.0075)

Uj

v'

(0.122)

j

x

U

 D

(0.70)

Uj

w'

(0.107)

Figure A2.—For the R8 nozzle, contours of various flow properties on y-z plane at x/D = 1. 

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.05 0.22 0.39 0.56 0.72 0.89 1.06

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.007 -0.005 -0.002 0.000 0.002 0.005 0.007

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.01 0.04 0.06 0.08 0.11 0.14 0.16

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.007 -0.005 -0.002 0.000 0.002 0.005 0.007

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.01 0.03 0.05 0.07 0.08 0.10 0.12

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60

y/D

z/D

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 12

Uj

U

(0.807)

2 U j

uv

(0.0061)

Uj

u'

(0.172)

2 U j

uw

(0.0081)

Uj

v'

(0.114)

j

x

U

 D

(0.188)

Uj

w'

(0.110)

Figure A3.—For the R8 nozzle, contours of various flow properties on y-z plane at x/D = 4. 

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

0.05 0.17 0.30 0.42 0.55 0.68 0.80

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

-0.007 -0.005 -0.002 0.000 0.002 0.005 0.007

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

0.01 0.03 0.04 0.06 0.08 0.09 0.11

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

-0.150 -0.107 -0.064 0.021 0.064 0.107 0.150

y/D

z/D

0 0.4 0.8 1.2 1.6 -0.8

-0.4

0

0.4

0.8

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 13

Uj

U

(0.570)

2 U j

uv

(0.0036)

Uj

u'

(0.128)

2 U j

uw

(0.0046)

Uj

v'

(0.086)

j

x

U

 D

(0.053)

Uj

w'

(0.091)

Figure A4.—For the R8 nozzle, contours of various flow properties on y-z plane at x/D = 8. 

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.05 0.14 0.22 0.30 0.39 0.48 0.56

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.004 -0.003 -0.001 0.000 0.001 0.003 0.004

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.029 0.048 0.068 0.087 0.106 0.125

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.004 -0.003 -0.001 0.000 0.001 0.003 0.004

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.023 0.035 0.048 0.060 0.073 0.085

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.045 -0.032 -0.019 0.006 0.019 0.032 0.045

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.023 0.037 0.050 0.063 0.077 0.090
NASA/TM—2012-217410 14

Uj

U

(0.374)

2 U j

uv

(0.0015)

Uj

u'

(0.081)

2 U j

uw

(0.0018)

Uj

v'

(0.056)

Uj

w'

(0.056)

Figure A5.—For the R8 nozzle, contours of various flow properties on y-z plane at x/D = 16. 

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.05 0.10 0.16 0.21 0.26 0.32 0.37

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.022 0.033 0.045 0.057 0.068 0.080

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.018 0.025 0.033 0.040 0.048 0.055

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.018 0.025 0.033 0.040 0.048 0.055
NASA/TM—2012-217410 15

Uj

U

(1.023)

2 U j

uv

(0.0048)

Uj

u'

(0.069)

2 U j

uw

(0.0030)

Uj

v'

(0.071)

Uj

w'

(0.072)

Figure A6.—For the R4 nozzle, contours of various flow properties on y-z plane at x/D = 0.05. 

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

0.05 0.21 0.37 0.53 0.68 0.84 1.00

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

-0.004 -0.003 -0.001 0.000 0.001 0.003 0.004

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

0.01 0.01 0.02 0.03 0.04 0.05 0.06

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

-0.004 -0.003 -0.001 0.000 0.001 0.003 0.004

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

0.01 0.01 0.02 0.03 0.04 0.05 0.06

y/D

z/D

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

-0.1

0

0.1

0.2

0.01 0.01 0.02 0.03 0.04 0.05 0.06
NASA/TM—2012-217410 16

Uj

U

(1.031)

2 U j

uv

(0.0090)

Uj

u'

(0.159)

2 U j

uw

(0.0073)

Uj

v'

(0.118)

j

x

U

 D

(0.65)

Uj

w'

(0.105)

Figure A7.—For the R4 nozzle, contours of various flow properties on y-z plane at x/D = 1. 

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

0.06 0.22 0.39 0.55 0.71 0.88 1.04

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.03 0.05 0.08 0.10 0.13 0.15

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

-0.007 -0.005 -0.002 0.000 0.002 0.005 0.007

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.02 0.04 0.06 0.08 0.10 0.12

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

-0.50 -0.33 -0.17 0.00 0.17 0.33 0.50

y/D

z/D

0 0.2 0.4 0.6 0.8 1

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.02 0.04 0.06 0.07 0.09 0.11
NASA/TM—2012-217410 17

Uj

U

(0.955)

2 U j

uv

(0.0080)

Uj

u'

(0.169)

2 U j

uw

(0.0088)

Uj

v'

(0.123)

j

x

U

 D

(0.250)

Uj

w'

(0.114)

Figure A8.—For the R4 nozzle, contours of various flow properties on y-z plane at x/D = 4. 

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

0.08 0.23 0.37 0.52 0.66 0.81 0.95

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

0.01 0.04 0.06 0.09 0.11 0.14 0.16

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

0.01 0.03 0.05 0.07 0.08 0.10 0.12

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

-0.200 -0.133 -0.067 0.000 0.067 0.133 0.200

y/D

z/D

0 0.4 0.8 1.2 1.6

-0.8

-0.4

0

0.4

0.8

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 18

Uj

U

(0.685)

2 U j

uv

(0.0049)

Uj

u'

(0.148)

2 U j

uw

(0.0066)

Uj

v'

(0.100)

j

x

U

 D

(0.074)

Uj

w'

(0.106)

Figure A9.—For the R4 nozzle, contours of various flow properties on y-z plane at x/D = 8. 

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.05 0.15 0.26 0.36 0.46 0.57 0.67

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.005 -0.003 -0.002 0.000 0.002 0.003 0.005

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.032 0.055 0.077 0.100 0.122 0.145

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.024 0.038 0.053 0.067 0.081 0.095

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.060 -0.043 -0.026 0.009 0.026 0.043 0.060

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.010 0.025 0.040 0.055 0.070 0.085 0.100
NASA/TM—2012-217410 19

Uj

U

(0.409)

2 U j

uv

(0.0021)

Uj

u'

(0.089)

2 U j

uw

(0.0021)

Uj

v'

(0.063)

Uj

w'

(0.63)

Figure A10.—For the R4 nozzle, contours of various flow properties on y-z plane at x/D = 16. 

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.05 0.11 0.17 0.22 0.28 0.34 0.40

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.023 0.035 0.048 0.060 0.073 0.085

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.018 0.027 0.035 0.043 0.052 0.060

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-1.6

-0.8

0

0.8

1.6

0.010 0.018 0.027 0.035 0.043 0.052 0.060
NASA/TM—2012-217410 20

Uj

U

(1.046)

2 U j

uv

(0.0068)

Uj

u'

(0.091)

2 U j

uw

(0.0048)

Uj

v'

(0.088)

Uj

w'

(0.082)

Figure A11.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 0.05.

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

0.05 0.22 0.38 0.55 0.71 0.88 1.04

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

-0.005 -0.003 -0.002 0.000 0.002 0.003 0.005

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

0.010 0.022 0.035 0.048 0.060 0.072 0.085

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

-0.005 -0.003 -0.002 0.000 0.002 0.003 0.005

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

0.010 0.022 0.035 0.048 0.060 0.072 0.085

y/D

z/D

0.4 0.5 0.6 0.7

-0.3

-0.2

-0.1

0

0.010 0.022 0.033 0.045 0.057 0.068 0.080
NASA/TM—2012-217410 21

Uj

U

(1.057)

2 U j

uv

(0.0090)

Uj

u'

(0.175)

2 U j

uw

(0.0102)

Uj

v'

(0.129)

j

x

U

 D

(0.78)

Uj

w'

(0.115)

Figure A12.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 1. 

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.04 0.21 0.38 0.55 0.71 0.88 1.05

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-0.008 -0.006 -0.003 -0.001 0.003 0.006 0.008

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.03 0.05 0.07 0.08 0.10 0.12

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-0.70 -0.51 -0.32 -0.13 0.12 0.31 0.50

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 22

Uj

U

(1.034) 

2 U j

uv

(0.0091)

Uj

u'

(0.178)

2 U j

uw

(0.0097)

Uj

v'

(0.129)

j

x

U

 D

(0.329)

Uj

w'

(0.120)

Figure A13.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 2. 

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.04 0.21 0.37 0.54 0.70 0.86 1.03

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.008 -0.006 -0.003 -0.001 0.003 0.006 0.008

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.03 0.05 0.07 0.09 0.11 0.13

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.30 -0.21 -0.13 0.04 0.13 0.21 0.30

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12
NASA/TM—2012-217410 23

Uj

U

(1.022)

2 U j

uv

(0.0086)

Uj

u'

(0.173)

2 U j

uw

(0.0107)

Uj

v'

(0.128)

j

x

U

 D

(0.227)

Uj

w'

(0.124)

Figure A14.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 4.

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.04 0.20 0.36 0.52 0.68 0.84 1.00

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.200 -0.143 -0.086 0.029 0.086 0.143 0.200

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12
NASA/TM—2012-217410 24

Uj

U

(0.759)

2 U j

uv

(0.0060)

Uj

u'

(0.166)

2 U j

uw

(0.0079)

Uj

v'

(0.111)

j

x

U

 D

(0.086)

Uj

w'

(0.115)

Figure A15.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 8. 

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.03 0.15 0.27 0.39 0.50 0.62 0.74

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.04 0.06 0.08 0.11 0.14 0.16

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.03 0.04 0.06 0.08 0.09 0.11

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.07 -0.05 -0.02 0.00 0.02 0.05 0.07

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 25

Uj

U

(0.421)

2 U j

uv

(0.0020)

Uj

u'

(0.092)

2 U j

uw

(0.0024)

Uj

v'

(0.066)

Uj

w'

(0.066)

Figure A16.—For the R2 nozzle, contours of various flow properties on y-z plane at x/D = 16. 

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.03 0.10 0.16 0.23 0.29 0.35 0.42

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.01 0.02 0.04 0.05 0.06 0.08 0.09

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.010 0.019 0.028 0.037 0.046 0.055 0.064

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.010 0.019 0.028 0.037 0.046 0.055 0.064
NASA/TM—2012-217410 26

Uj

U

(1.079)

2 U j

uv

(0.0109)

Uj

u'

(0.154)

2 U j

uw

(0.0114)

Uj

v'

(0.139)

j

x

U

 D

(9.0)

Uj

w'

(0.129)

Figure A17.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 0.38. 

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2 0.04 0.21 0.38 0.55 0.71 0.88 1.05

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2

-0.008 -0.006 -0.003 -0.001 0.003 0.006 0.008

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2 0.01 0.03 0.06 0.08 0.10 0.13 0.15

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2 0.01 0.03 0.05 0.07 0.09 0.11 0.13

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2

-5.00 -3.33 -1.67 0.00 1.67 3.33 5.00

y/D

z/D

0 0.2 0.4 0.6

-0.4

-0.2

0

0.2 0.01 0.03 0.05 0.07 0.09 0.11 0.13
NASA/TM—2012-217410 27

Uj

U

(1.074)

2 U j

uv

(0.0127)

Uj

u'

(0.200)

2 U j

uw

(0.0138)

Uj

v'

(0.142)

j

x

U

 D

(1.775)

Uj

w'

(0.140)

Figure A18.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 1. 

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.04 0.21 0.38 0.55 0.71 0.88 1.05

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-0.008 -0.006 -0.003 -0.001 0.003 0.006 0.008

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.04 0.07 0.10 0.13 0.16 0.19

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.03 0.05 0.07 0.10 0.12 0.14

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

-1.50 -1.00 -0.50 0.00 0.50 1.00 1.50

y/D

z/D

0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.01 0.03 0.05 0.07 0.09 0.11 0.13
NASA/TM—2012-217410 28

Uj

U

(1.033)

2 U j

uv

(0.0095)

Uj

u'

(0.166)

2 U j

uw

(0.0087)

Uj

v'

(0.121)

j

x

U

 D

(0.672)

Uj

w'

(0.117)

Figure A19.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 2. 

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.04 0.20 0.37 0.54 0.70 0.86 1.03

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.008 -0.006 -0.003 -0.001 0.003 0.006 0.008

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.009 -0.006 -0.003 0.000 0.003 0.006 0.009

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.03 0.05 0.07 0.09 0.11 0.13

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.65 -0.43 -0.22 0.00 0.22 0.43 0.65

y/D

z/D

0 0.2 0.4 0.6 0.8 1 1.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12
NASA/TM—2012-217410 29

Uj

U

(1.024)

2 U j

uv

(0.0080)

Uj

u'

(0.170)

2 U j

uw

(0.0099)

Uj

v'

(0.115)

j

x

U

 D

(0.369)

Uj

w'

(0.116)

Figure A20.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 4. 

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.04 0.20 0.36 0.52 0.68 0.84 1.00

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.04 0.06 0.09 0.12 0.14 0.17

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.008 -0.005 -0.003 0.000 0.003 0.005 0.008

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

-0.320 -0.213 -0.107 0.000 0.107 0.213 0.320

y/D

z/D

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0.01 0.03 0.05 0.07 0.08 0.10 0.12
NASA/TM—2012-217410 30

Uj

U

(0.800)

2 U j

uv

(0.0046)

Uj

u'

(0.158)

2 U j

uw

(0.0075)

Uj

v'

(0.103)

j

x

U

 D

(0.124)

Uj

w'

(0.107)

Figure A21.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 8. 

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.03 0.15 0.27 0.39 0.50 0.62 0.74

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.004 -0.003 -0.001 0.000 0.001 0.003 0.004

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.04 0.06 0.09 0.11 0.14 0.16

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.03 0.04 0.06 0.08 0.09 0.11

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-0.10 -0.07 -0.03 0.00 0.03 0.07 0.10

y/D

z/D

0 0.4 0.8 1.2 1.6 2 2.4 2.8

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.01 0.03 0.04 0.06 0.08 0.09 0.11
NASA/TM—2012-217410 31

Uj

U

(0.426)

2 U j

uv

(0.0018)

Uj

u'

(0.092)

2 U j

uw

(0.0027)

Uj

v'

(0.064)

j

x

U

 D

(0.018)

Uj

w'

(0.067)

Figure A22.—For the R2C nozzle, contours of various flow properties on y-z plane at x/D = 16. 

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.03 0.10 0.16 0.23 0.29 0.35 0.42

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.01 0.02 0.04 0.05 0.06 0.08 0.09

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.010 0.019 0.028 0.037 0.046 0.055 0.064

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

-0.016 -0.011 -0.005 0.000 0.005 0.011 0.016

y/D

z/D

0 0.8 1.6 2.4 3.2 4 4.8

-2.4

-1.6

-0.8

0

0.8

1.6

2.4

0.010 0.019 0.028 0.037 0.046 0.055 0.064

NASA/TM—2012-217410 33

References 

1. Bridges, J.E., “Noise of embedded high-aspect ratio nozzles,” presented at the NASA Fundamental 

Aeronautics Program 2011 Technical Conference, Cleveland, OH, March 15-17, 2011. 

2. Balsa, T.F., Gliebe, R.R., Kantola, R.A., Mani, R., Stringas, E.J. and Wang, J.C.F., “High velocity jet 

noise source location and reduction, Task 2—theoretical developments and basic experiments,” 

Report No. FAA-RD-76-79, II, General Electric Co., Aircraft Engine Group, Cincinnati, OH, May, 

1978. 

3. Massey, K.C., Ahuja, K.K. and Gaeta, R., “Noise Scaling for Unheated Low Aspect Ratio 

Rectangular Jets,” AIAA paper 2004-2946, 10th AIAA/CEAS Aeroacoustics Conference, 

Manchester, England 10-12 May 2004. 

4. Frate, F.C. and Bridges, J.E., “Extensible rectangular nozzle model system,” AIAA Paper 2011-975, 

49th Aerospace Sciences Meeting, Orlando, Fl, 4-7 January, 2011. 

5. Zaman, K.B.M.Q., 2012, “Flow field surveys for rectangular nozzles,” AIAA Paper 2012-0069, 50th

AIAA Aerospace Sciences Meeting, January 9-12, Nashville, TN. 

6. Zaman, K.B.M.Q., 1996, “Axis switching and spreading of an asymmetric jet: the role of coherent 

structure dynamics.” 1966, J. Fluid Mech., 316, pp. 1-27. 

7. Zaman, K.B.M.Q., 2011, “Effect of nozzle exit conditions on subsonic jet noise,” AIAA Paper 2011-

2704, 17th AIAA/CEAS Aeroacoustics Conf., 5-8 June, Portland, Oregon. 

8. Morris, P.J. & Zaman, K.B.M.Q., “Velocity measurements in jets with application to noise source 

modeling,” Journal of Sound and Vibration (2009),doi:10.1016/j.jsv.2009.09.024. 

9. Zaman, K.B.M.Q., 1998, “Asymptotic spreading rate of initially compressible jets—experiment and 

analysis,” Physics of Fluids, 10, pp. 2652-2660. 
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1. REPORT DATE (DD-MM-YYYY)

01-04-2012 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Flow-Field Surveys For Rectangular Nozzles 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Zaman, K.B.M.Q. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 984754.02.07.03.17.04 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18082 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

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NASA 

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NASA/TM-2012-217410 

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Unclassified-Unlimited 

Subject Categories: 71 and 34 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

A CD-ROM containing the supplemental data files mentioned in the Introduction section of this report can be requested from the NASA 

Center for AeroSpace Information at http://www.sti.nasa.gov, or 443-757-5802. 

14. ABSTRACT

Flow field survey results for three rectangular nozzles are presented for a low subsonic condition obtained primarily by hot-wire 

anemometry. The three nozzles have aspect ratios of 2:1, 4:1 and 8:1. A fourth case included has 2:1 aspect ratio with chevrons added to the 

long edges. Data on mean velocity, turbulent normal and shear stresses as well as streamwise vorticity are presented covering a streamwise 

distance up to sixteen equivalent diameters from the nozzle exit. These detailed flow properties, including initial boundary layer 

characteristics, are usually difficult to measure in high speed flows and the primary objective of the study is to aid ongoing and future 

computational and noise modeling efforts. 

15. SUBJECT TERMS

Aeroacoustics; Jet noise; Turbulence 

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39 

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