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NASA Technical Paper 1188 


msA 

TP 

1188 

C.1 


loan copYi nert, s 

’TECHiyiQAL i ^5 

Experimental and Analytical ^ wrtland afb, i 
Investigation of a Nonaxisymmetric 
Wedge Nozzle at Static Conditions 


George T. Carson, Jr., and Mary L. Mason 


JULY 1978 



■ -' 7 ' / - 



1 




TECH LIBRARY KAFB, NM 


NASA Technical Paper 1188 


TECH LIBRARY KAFB, NM 


□13MSMS 


Experimental and Analytical 
Investigation of a Nonaxisymmetric 
Wedge Nozzle at Static Conditions 


George T. Carson, Jr., and Mary L. Mason 
Langley Research Center 
Hampton, Virginia 


(WNSA 

National Aeronautics 
and Space Administration 

Scientific and Technical 
Information Office 


1978 




SUMMARY 


An experimental investigation of a nonaxisymmetric wedge nozzle has been con- 
ducted at static conditions. The resulting data, in the form of detailed pressure distribu- 
tions and oil flow photographs, expand the current nonaxisymmetric nozzle database. For 
the range of nozzle pressure ratios in this experiment, the nozzle exhaust flow exhibits 
regions of predominately two-dimensional flow and regions of highly three-dimensional 
flow, characterized by shock waves and vortex flow. 

An analytical investigation has been conducted to evaluate a two-dimensional, 
inviscid, time -dependent theory as a nonaxisymmetric nozzle performance predictor. 
Results indicate good agreement between theory and experiment in regions of predomi- 
nately two-dimensional flow for all nozzle pressure ratios considered. Agreement is con- 
siderably weaker in the regions of three-dimensional flow, especially at the higher nozzle 
pressure ratios. When three-dimensional effects are minimized by the flow character- 
istics, the agreement between theory and experiment improves; agreement remains opti- 
mal at the lower nozzle pressure ratios. Such results indicate that, for the wedge nozzle 
and related nozzle configurations, the two-dimensional, inviscid theory may be applied 
as a limited performance predictor. 


INTRODUCTION 

Multimission jet aircraft must operate effectively over a wide range of Mach num- 
bers and power settings. Such aircraft require high-performance propulsion exhaust 
nozzles. Conventional axisymmetric nozzles are lightweight and use a variable geometry 
for high internal performance. As a result, the axisymmetric nozzle has generally been 
implemented in the multiengine jet aircraft design. However, the integration of multiple 
nozzles with the airframe results in a complex aft-end flow field, which can produce an 
aft-end drag problem. (See ref. 1.) In addition, the multiengine jet aircraft design gen- 
erally requires a large boattail "gutter” interfairing between the engines or the nozzles. 
This interfairing increases the drag problem, especially in the case of separated flow near 
the nozzle exit (refs. 2 and 3). 

The effects of such adverse interference may be minimized by the use of nonaxisym- 
metric wedge nozzle designs. Proper integration of a nonaxisymmetric design can elim- 
inate the boattail "gutter" interfairing and, thus, reduce the adverse drag effects. (See 
ref. 4.) This nozzle also has the advantage of efficient in-flight thrust -reversirg or 



thrust-vectoring capabilities, unavailable in the conventional axisymmetric nozzle. (See 
ref. 5.) Preliminary research has indicated that the isolated aeropropulsive performance 
of the wedge nozzle compares favorably with that of axisymmetric nozzles at transonic 
and supersonic speeds. (See refs. 6 and 7.) 

The available data base for nonaxisymmetric nozzle research is drawn from analy- 
sis of isolated and integrated nozzle designs (refs. 6 to 10). A small part of the data base 
includes pressure measurements and internal flow properties. (See ref. 11.) However, 
the data consist primarily of force measurements, which represent the nozzle aeropro- 
pulsive performance in terms of thrust and drag. The objective of this experiment is the 
addition of pressure measurements and internal flow field characteristics to the present 
data base. In this investigation, an isolated, nonaxisymmetric wedge nozzle has been 
tested extensively at static conditions. The resulting data consist of detailed pressure 
measurements for the internal flow field and the exhaust jet. Oil flow photographs provide 
additional flow field characteristics. Such data types are necessary for expanding the 
currently limited data base. An increased understanding of the flow phenomena is essen- 
tial in the development of adequate prediction techniques. 

In addition to this experimental investigation, an analysis has been performed to 
evaluate the use of a two-dimensional, time-dependent, inviscid theory as a nonaxisym- 
metric nozzle performance predictor. (See ref. 12.) A general, accurate prediction 
theory is essential for the development of high-performance nonaxisymmetric nozzles at 
minimum cost. Comparison of the experimental data and the analytical results evaluates 
the application of the theory as a predictor model under static conditions. 

SYMBOLS 


p 

A|. nozzle throat area, cm 

b width of trailing edge of nozzle wedge, cm 

C,p thrust coefficient, t/A^P^ j 

<t center line 

c crown (keel) line, cm (see fig. 3) 

D maximum nozzle diameter, cm 

d half -breadth line, cm (see fig. 3) 


2 


I length of wedge from throat to trailing edge, cm 

p local static pressure, Pa 

p^ atmospheric pressure, Pa 

p^ j jet total pressure. Pa 

r nozzle internal radius, cm 

T thrust, N 

X distance along model center line from nozzle throat, positive downstream, cm 

y vertical distance from plane passing throv^h nozzle throat and center line, cm 

z lateral distance from plane passing through nozzle throat and center line, cm 

77 order of superellipse equation 

6 angular component of (r, 0) polar coordinate system, rad (see fig. 3) 

Abbreviations: 

NAP computer program for computation of two-dimensional, time -dependent, 

inviscid nozzle flow 

SAE Society of Automotive Engineers, Inc. 

MODEL 

The experiment was conducted using the base line, dry power configuration of the 
nonaxisymmetric wedge nozzle discussed in reference 6. Figure 1 contains a photograph 
of the model installed for static testing. The main features of this nozzle are the wec^e- 
centerbody geometry and the nozzle internal area distribution. 

Figure 2 gives the nozzle assembly dimensions and the wedge geometry. Duct- 
wedge cross sections of the internal flow area are given in the figure for the regions 
upstream of the leading edge of the wedge, at the leading edge, and at the geometric throat 
of the nozzle. The internal flow geometry is characterized by a transition from a circle 


3 



upstream of the wedge to a superellipse, a rectangular geometry, at the nozzle throat. 

The transition section is illustrated in figure 3. A detailed discussion of the transition 
and superellipse geometry is given in the appendix. 

APPARATUS 

The experimental investigation was conducted in the static test stand of the Langley 
16-foot transonic tunnel. The air supply system is the same as that of the transonic 
tunnel. Reference 13 describes this facility in detail. The air control system is similar; 
it includes valving, filters, and heat exchange facilities. The data acquisition system, 
also similar to that of the 16-foot transonic tunnel, is based on a 100-channel magnetic 
tape system. 

Figure 4 contains a photograph of the static test simulation system in the static 
test stand. An external high-pressure air system provided the air supply. Dry, heated 
air at a controlled stagnation temperature of 300 K entered a high-pressure chamber 
through six supply lines in the nozzle support. The flow of high-pressure air ran perpen- 
dicular to the model axis. From the high-pressure chamber, the flow entered the low- 
pressure plenum. Air passed from the low-pressure plenum to the nozzle tailpipe to 
simulate jet exhaust flow from the nozzle exit. 

Instrumentation 

This investigation included measurements of surface static pressure, jet total pres- 
sure, jet total temperature, and air mass-flow rate. The pressure values were recorded 
by seven multiple pressure scanning transducer units. A thermocouple was used to mea- 
sure the jet total temperature in the low-pressure plenum. An electronic turbine flow- 
meter was used to record the mass flow of the high-pressure air. The pressure and 
temperature in each air supply line were also measured before the flow discharged into 
the low-pressure plenum. 

The original model (ref. 6) was modified to include 286 pressure orifices, each 
0.1016 cm in internal diameter. Rows of orifices were placed along the surface of the 
wedge, along the inner right sidewall of the cowl, and inside the top of the cowl. Each of 
these areas held three orifice rows. Most of the row positions can be seen in figure 1. 
Specific Cartesian coordinates of the pressure orifices, as well as diagrams of their loca- 
tion on the model, are given in table I. 

On the nozzle wedge, all three orifice rows ran in the axial direction, with 0.635 cm 
between the successive orifices. One row was placed along the center line on the bottom 
of the wedge. The second row was placed along the left quarter span on top of the wedge. 


4 



II 


The third row, also on top of the wedge, was located along the extreme right edge of the 
wedge sidewall. 

Internal pressure orifices were placed along the top inside of the cowl. The rows 
ran in the axial direction, with 0.635-cm spacing between the orifices, as on the wedge. 
One row was placed along the axial center line; another ran along the left quarter span. 
The third row was placed along the inside of the upper left sidewall corner, with an incli- 
nation of approximately 45° from the center of the plane of the wedge. 

Internal pressure orifices were placed horizontally along the right sidewall of the 
cowl up to the leading edge of the wedge. One row ran along the sidewall center line; the 
spacing between orifices in this row was 0.635 cm. The remaining two rows were placed 
2.45 cm above the center line and 2.45 cm below the center line, respectively. Spacing in 
these rows was 1.27 cm between orifices. 


Tests 

Two types of experimental data were obtained: pressure distributions and oil flow 

photographs. The nozzle pressure distributions were determined for a range of nozzle 
pressure ratios from 1.5 to 6.0, at 0.5 increments. For the oil flow data, the orifices on 
the wedge were sealed, and the top of the wedge was painted black. For each nozzle pres- 
sure ratio, the wedge was covered with a thin coat of SAE 140 oil, and a high-speed photo- 
graph of the oil flow pattern was taken. As a secondary oil flow data system, a video tape 
of the developing and final flow field was made at each nozzle pressure ratio. 

Experimental Data and Discussion 

The pressure distributions and the oil flow photographs for the complete range of 
experimental data are given in figure 5. Pressure data are plotted as the ratio of local 
pressure to jet total pressure against the nozzle length, nondimensionalized by the distance 
from the throat to the end of the wedge. The oil flow photographs are scaled to the hori- 
zontal axis of the data plots. 

The pressure distributions and oil flow photographs describe internal flow character- 
istics at each experimental nozzle pressure ratio. The results are discussed for each of 
the three data acquisition regions on the nozzle: along the internal cowl top, along the 
internal right sidewall, and along the wedge. 

Cowl top.- Along the top of the cowl, the internal pressure distribution is essentially 
the same for the range of nozzle pressure ratios investigated. The flow chokes even at 
the lowest nozzle pressure ratio of 1.5. The critical pressure ratio of 0.528 occurs 
slightly downstream of the geometric throat, but ahead of the nozzle exit. A lack of sig- 
nificant spanwise variation indicates that the flow is essentially two-dimensional in this 
region. 


5 


Cowl right side.- Along the right side of the cowl, the pressure distribution far 
upstream lies in the stagnation chamber of the nozzle. The downstream measurements 
in this region are in the vicinity of the leading edge of the wedge. On the center orifice 
row, the pressures increase slightly as the wedge is approached. This increase in pres- 
sure results from the reduction in velocity which occurs as the flow approaches the stag- 
nation region of the wedge. Along the top and bottom rows, the pressures decrease 
slightly, reflecting an increase in the subsonic velocity as the flow moves into the con- 
verging area of the nozzle. These flow patterns remain similar for the full range of 
experimental nozzle pressure ratios. 

Wedge.- Along the surface of the wedge, the pressure distributions upstream of the 
nozzle exit are similar for all 10 nozzle pressure ratios investigated. The ratio of local 
pressure to jet pressure begins near imity upstream and decreases to the critical pres- 
sure ratio of 0.528 at the throat. In the upstream region and in the throat area, the flow 
is quasi two-dimensional, as has been discussed earlier. However, downstream of the 
throat and nozzle exit, the flow becomes three-dimensional, particularly for nozzle pres- 
sure ratios greater than 2.0. Three-dimensional flow patterns are illustrated by the 
data plots and oil flow photographs for the higher nozzle pressure ratios in figure 5. The 
pressure distributions, oil flow photographs, and video tape data were analyzed to deter- 
mine the basic three-dimensional flow characteristics. A diagram of the dominant flow 
characteristics apparent at a nozzle pressure ratio of 6.0 is given in figure 6. The single 
flow characteristic which is evident at nozzle pressure ratios above 2.0 is a strong shock 
wave just downstream of the nozzle exit. The flow field observations indicate that turbu- 
lence effects due to the shock result in counterrotating vortex flow on either side of the 
wedge center line, slightly downstream of the shock. At the higher nozzle pressure 
ratios, apparent flow disturbance downstream indicates that a weaker secondary shock 
may occur downstream, in the vicinity of the trailing edge of the wedge. The pressure 
distribution near the wedge sidewall is essentially the atmospheric pressure, indicating a 
possible layer separation in this region. 

The shock waves and vortex flow define three-dimensional flow along the wedge, 
downstream of the nozzle exit. Three-dimensional effects are dominant along the wedge 
center line for the higher nozzle pressure ratios. Viscous effects tend to decrease the 
magnitude of the pressure gradient along the center line in the vicinity of shock waves. 

As a result, the pressure variation is minimal along the center line. However, away 
from the center line, the viscous effects become weaker and exert limited influence on 
the magnitude of the pressure gradients. As a result, larger changes in pressure occur 
away from the center line, as illustrated by the variation in the wedge data at the higher 
nozzle pressure ratios. (See fig. 5.) 


6 


In summary, the flow through the nonaxisymmetric wedge nozzle may be divided 
into two regions, one of essentially two-dimensional flow and one of three-dimensional 
flow. Flow through the nozzle cowl is quasi two-dimensional until it passes the throat. 
For all experimental nozzle pressure ratios, the flow choked at this point. Downstream 
of the cowl, the jet flow along the wedge becomes highly three-dimensional. The domi- 
nant characteristics of the flow in this region include a strong shock wave and counter- 
rotating vortex flow. 


ANALYTICAL INVESTIGATION 

A two-dimensional, inviscid, time -dependent theory was applied to the nonaxisym- 
metric wedge nozzle as a potential predictor of the nozzle performance. This theory has 
been incorporated in the development of a computer program (NAP) which calculates inter- 
nal nozzle flow and jet exhaust plume for steady converging, converging-diverging, and 
plug nozzle configurations (ref. 12). The external flow velocity is zero. Internal flow 
may be specified as either axisymmetric or two-dimensional. 

The computer code incorporates the two-dimensional equations of motion in noncon- 
servative form. A geometric computational grid spans the entire flow area. The 
interior mesh points are calculated by a MacCormack finite-difference scheme, a two- 
step predictor-corrector. The boundary mesh points, inlet and exit, are computed by a 
second-order reference plane method of characteristics. Shock waves are modeled using 
a "shock smearing" technique which incorporates an explicit artificial viscosity term with 
numerical smoothing. For this analysis the program output was generated as velocity, 
temperature, density, and pressure for grid points spanning the internal and external jet 
flow areas. The exhaust jet plume boundary and thrust values were also calculated. 

To evaluate the two-dimensional theory as a nonaxisymmetric nozzle performance 
predictor, the computer-generated results were compared with the experimental data 
discussed previously. The internal flow characteristics and the jet plume boundary and 
flow characteristics were calculated using the wedge configuration under two-dimensional 
conditions. Since the experiment was conducted at static conditions, no external flow 
specification was necessary. Results are presented for seven cases; these cases range 
from nozzle pressure ratios of 3.0 to 6.0, at 0.5 increments. Analytical flow was not cal- 
culated below the nozzle pressure ratio of 3.0, since limitations in the computer code 
inhibit the flow velocity from returning to subsonic levels once it has become supersonic. 

Several input parameters are important in achieving a stable solution with an accept- 
able level of accuracy. A convergence parameter controls the total number of iterations 
and the stability of the solution. The theory is also sensitive to an input initial estimate of 
the exhaust jet boundary in those cases which require a jet calculation. An inaccurate jet 


7 



plume boundary estimate may cause errors in the initial data surface and may result in a 
trxmcation of the solution process in its early iterative stages. 

The convergence of a solution is based on the amoimt of change in maximum velocity 
between two consecutive time steps. The maximum horizontal velocity over the full com- 
putational region is found at each time step. The percentage difference between the maxi- 
mum velocity at a current time step and the value of maximum velocity at the preceding 
time step is then computed. When the percentage change in velocity falls below the input- 
specified convergence parameter, the solution reaches convergence, and the iterative 
process stops. Thus, the convergence parameter reflects the stability of the calculated 
flow velocity. The convergence parameter, the final number of iterations, and the time 
step size for each case are given in table II. 

Comparison of Theory and Experiment 

Figure 7 compares the NAP analytical results with the experimental data for seven 
nozzle pressure ratios. The analytical results were calculated along the axial center line 
of the wedge and the top inside center line of the cowl. The computer program output is 
compared with the experimental data along the center line and along the quarter span for 
both the wedge and the inside top of the cowl. 

On the cowl top, there is good agreement between the two-dimensional theory and 
the experiment for the full range of nozzle pressure ratios. The NAP center-line results 
agree well with the experimental data along both the quarter span and the center line. 

The experimental data indicate that the flow along the top of the cowl is essentially two- 
dimensional, with no spanwise variation. Viscous effects are negligible in this region. 
Because of the two-dimensional, inviscid nature of the flow, the experimental quarter- 
span data and center-line data are so similar that the NAP predictions agree with both 
data sets. Thus, the two-dimensional inviscid theory is an accurate flow model for the 
internal flow along the top region of the cowl. 

Along the wedge, the theory and experiment agree well in the internal flow regions 
for all seven cases. In the exhaust jet, the comparison between analytical and experi- 
mental results shows rather limited agreement. For the experimental center-line data, 
the agreement with the computed results is only fair for the nozzle pressure ratios 
above 4.5, but improves as the nozzle pressure ratio drops to 3.0. The general lack of 
agreement at the higher pressure ratios resvilts from the complex, three-dimensional 
nature of the exhaust jet flow field, as discussed previously. For these cases, a two- 
dimensional, inviscid theory is inadequate for predicting such highly three-dimensional 
flow characteristics. As the nozzle pressure ratio drops, however, so does the magnitude 
of the flow disturbances along the center line, and the theory-experiment comparison 
improves in the center-line region. 


8 



The analytical results and the quarter- span experimental data for the jet region 
show better agreement than the center-line comparisons, except at the higher nozzle 
pressure ratios. For the higher pressure ratios, the strong three-dimensional effects 
dominate the entire jet region. At the lower nozzle pressure ratios, the viscous effects 
tend to damp out the strong shock effects, so that the three-dimensional flow character- 
istics along the quarter span diminish in magnitude. Since the flow is more two dimen- 
sional in these cases, the results of the two-dimensional, inviscid theory compare 
favorably with the quarter-span data. 

In addition to the pressxrre distributions, analytical gross thrust values were calcu- 
lated for all seven nozzle pressure ratios. These predictions were compared with exper- 
imental data for the wedge nozzle, which are presented in reference 6. The experimental 
and analytical results are given in figure 8 as thrust coefficients at each nozzle pressure 
ratio. The coefficients of the ideal isentropic gross thrust, as calculated in reference 6, 
are also plotted. The predicted thrust coefficients generally lie between the ideal and 
experimental values. However, agreement is rather inconsistent, reflecting the lack of 
agreement in certain experimental and analytical pressure distributions, as discussed 
previously. Thus, for the wedge nozzle, the theoretical thrust prediction is rather 
limited. Results for other types of nozzles indicate an improvement in prediction of 
thrust or discharge coefficient, as is discussed briefly in reference 12. 

The two-dimensional, inviscid, time -dependent theory is a good performance 
predictor for the wedge nozzle in the internal regions where flow is essentially two- 
dimensional. In regions of three-dimensional flow, the theory gives reasonable approx- 
imations to the flow field characteristics at lower nozzle pressure ratios, where the 
viscous effects are minimized. At higher nozzle pressure ratios, the theory is inade- 
quate for prediction of highly three-dimensional flow. Thus, for the wedge nozzle and 
similar configurations, the two-dimensional, inviscid theory may be applied as a limited 
performance predictor of internal and jet flow characteristics. 

CONCLUSION 

An experimental investigation of a nonaxisymmetric wedge nozzle has been con- 
ducted at static conditions. The resulting detailed pressure distributions and oil flow 
photographs expand the current nonaxisymmetric data base, which consists primarily of 
thrust and drag data. In addition, an analytical investigation has been made to evaluate a 
two-dimensional, inviscid, time -dependent theory as a nonaxisymmetric nozzle perform- 
ance predictor. In the regions of two-dimensional nozzle flow, the analytical results 
agree well with the experimental data for the full rar^e of nozzle pressure ratios under 
investigation. 


9 



In regions of three-dimensional flow, the theory predicts the basic flow character- 
istics of the real data; the agreement of theory with experiment is optimum at the lower 
nozzle pressure ratios, where three-dimensional effects are minimum. Results indicate 
that for the wedge nozzle and similar designs, the two-dimensional, inviscid, time- 
dependent theory may be applied as a limited performance predictor of internal and jet 
flow characteristics. 

Langley Research Center 

National Aeronautics and Space Administration 
Hampton, VA 23665 
May 2, 1958 


10 


APPENDIX 


TRANSITION GEOMETRY 

The internal geometry of the nonaxisymmetric wedge nozzle is characterized by a 
region of transition from a circular flow area to a rectangular area. This transition sec- 
tion is illustrated in figure 3. The section begins upstream of the leading edge of the 
wedge and ends at the nozzle geometric throat. The subsequent equations define the 
superellipse, or rectangular, geometry and the area distribution of the flow region. The 
cross sections are defined by r, 9, c, d, and rj in the form 


r 

0^1 

7 

+ 



The coordinates y and z may then be computed at each x, using 
y = r sin 6 
z = r cos 9 

The duct internal geometry is based on the parameters c, d, and rj, used in the 
superellipse equation. The dimensions shown in the subsequent equations define the 
internal duct geometry of the static test model. All dimensions are in centimeters. 

For -17.600 ^ x g -13.830 
c = 6.286 


d = 6.286 


V = 2.0 

For -13.830 ^x2-6.915 


_ X + 13.830 
6.915 


^2 = 


sin +1.5^ +1 


11 



APPENDIX 


d = 6.287 - (0.095 )x2 


X + 13.830 
3“ 13.830 


Xo = 


X4 - 


sinl^^Xg + 1.5^ + 1.0 
2^0 


X5 = 1.0 + (2048 \/2- l.o)x4 


77 = 


In 2 


In 


/2 


Xr 


The cross-sectional area is fixed in this region. To find ( 


V /^\V 
c I \d 


=1 


At X = -6.915 


c = 6.250 


d = 6.191 
V = 3.559 

For -6.915 ^ X ^ 0 


d = 6.191 


X + 6.915 
6.915 


^2 = 


sin 77 ^Xj + 1 . 5 ) + 1 


, iterate 


12 


APPENDIX 


Xg = 0.75 - 0,5x2 

Cj = c at (x = -6.915) = 6.2504 

c = + ^6.2865 - 

^ ^ X + 13.830 
4 13.830 

sinj^^x^ + 1.5)j + 1.0 
Xg = 1 + (2048^- l.o)x 5 


7 = 


In 2 


IniH 


For 0^x^ 26.505 
c = 6.2865 
d = 6.1913 
77 = 11.0 


13 



REFERENCES 


1. Schmeer, James W.; Lauer, Rodney F., Jr.; and Berrier, Bobby L.: Performance of 

Blow-in -Door Ejector Nozzles Installed on a Twin- Jet Variable -Wing-Sweep 
Fighter Airplane Model. NASA TM X-1383, 1967. 

2. Reubush, David E.; and Mercer, Charles E.: Effects of Nozzle Interfairing Modifica- 

tions on Longitudinal Aerodynamic Characteristics of a Twin-Jet, Variable -Wing - 
Sweep Fighter Model. NASA TN D-7817, 1975. 

3. Maiden, Donald L.; and Berrier, Bobby L.: Effect of Airframe Modifications on 

Longitudinal Aerodynamic Characteristics of a Fixed-Wing, Twin-Jet Fighter 
Airplane Model. NASA TM X-2523, 1972. 

4. Maiden, Donald L.; and Petit, John E.: Investigation of Two-Dimensional Wedge 

Exhaust Nozzles for Advanced Aircraft. J. Aircraft, vol. 13, no. 10, Oct. 1976, 
pp. 809-816. 

5. Capone, Francis J.: Supercirculation Effects Induced by Vectoring a Partial-Span 

Rectangular Jet. J. Aircraft, vol. 12, no. 8, Aug. 1975, pp. 633-638. 

6. Maiden, Donald L.; Performance of an Isolated Two-Dimensional Variable -Geometry 

Wedge Nozzle With Translating Shroud and Collapsing Wedge at Speeds Up to 
Mach 2.01. NASA TN D-7906, 1975. 

7. Maiden, Donald L.: Performance of an Isolated Two-Dimensional Wedge Nozzle 

With Fixed Cowl and Variable Wedge Centerbody at Mach Numbers Up to 2.01. 

NASA TN D-8218, 1976. 

8. Martens, Richard E.: F-15 Nozzle/Afterbody Integration. J. Aircraft, vol. 13, no. 5, 

May 1976, pp. 327-333. 

9. Capone, Francis J.; and Maiden, Donald L.: Performance of Twin Two-Dimensional 

Wedge Nozzles Including Thrust Vectoring and Reversing Effects at Speeds Up to 
Mach 2.20. NASA TN D-8449, 1977. 

10. Pendergraft. O. C.: Comparison of Axisymmetric and Nonaxisymmetric Nozzles 

Installed on the F-15 Configuration. AIAA Paper 77-842, July 1977. 

11. Harrington, Douglas E.; Schloemer, James J.; and Skebe, Stanley A.: Thrust 

Performance of Isolated Two-Dimensional Suppressed Plug Nozzles With and 
Without Ejectors at Mach Numbers From 0 to 0.45. NASA TM X-3384, 1976. 


14 



12. Cline, M. C.: NAP: A Computer Program for the Computation of Two-Dimensional, 

Time-Dependent, Inviscid Nozzle Flow. LA-5984 (Contract W-7405-ENG-36), 

Los Alamos Scientific Lab., Jan. 1977. 

13. Corson, Blake W., Jr.; Runckel, Jack F.; and Igoe, William B.: Calibration of the 

Langley 16 -Foot Transonic Timnel With Test Section Air Removal. NASA 
TR R-423, 1974. 


15 



TABLE I.- Pressure ORmcE locations 
( coordinate system is defined in fig. 2] 



Pressure orifice rows are indicated 
by dashed lines. 


Wedge 


(a) Center line (b) Left quarter span (c) Right edge 


V./1 

y/i 

z/l 

1 x/i 

y/i 

z/l 


x/l 

y/i 

z/l 

I x/l 

y/i 

z/l 


x/l 

y/i 

z/l 

x/l 

y/i 

- 0.263 

- 0.023 

0 

|o .356 

- 0.112 

0 


- 0.263 

; 0.024 

- 0.119 

; 0.352 

0.113 

- 0.119 


- 0.263 

0.024 

0.230 

0.352 

0.114 

-.250 

-.044 

0 

1 .380 

-.107 

0 


-.252 

.042 

-.119 

] .376 

.109 

-.119 


-.251 

.044 

.230 

.376 

.110 

-.234 

-.062 

0 

, .403 

-.103 

0 


-.235 

.061 

-.119 

1 .399 

.105 

1 -.119 


-.236 

.062 

.230 

.400 

.106 

-.218 

-.078 

0 

.427 

-.099 

0 


-.219 

.077 

-.120 

! .423 

.101 

1 -.119 


-.220 

.077 

.230 

.423 

.102 

-.199 

-.092 

0 

.451 

-.095 

0 


-.201 

.092 

-.119 

, .447 

.097 

-.120 


-.199 

.094 

.230 

.447 

.098 

-.179 

-.107 

0 

.475 

-.091 

0 


-.180 

.106 

-.120 

, .470 

.093 

-.119 

1 -.181 

.106 

.230 

.470 

.094 

-.160 

-.118 

0 

.498 

-.087 

0 


-.160 

.119 

-.119 

.494 

.069 

-.119 


-.159 

.120 

,230 

1 .494 

.090 

-.139 

-.130 

0 

.522 

-.083 

0 


-.140 

.130 

-.120 

.518 

.085 

-.119 


-.139 

.130 

.230 

.518 

.086 

-.116 

-.141 

0 

.545 

-.078 

0 


-.117 

.140 

-.120 

.541 

.081 

-.119 


-.117 

.141 

.229 

.541 

.082 

-.093 

-.150 

0 

.569 

-.074 

0 


-.096 

.149 

-.120 

.565 

.077 

-.119 


-.095 

.150 

.229 

.565 

.077 

-.071 

-.158 

0 

.593 

-.070 

0 


-.074 

.157 

-.119 

.589 

.072 

-.119 


-.074 

.158 

.229 

.589 

.073 

-.048 

-.164 

0 

.617 

-.066 

0 


-.051 

.163 

-.120 

.613 

.068 

-.119 


-.052 

.164 

.229 

.612 

.069 

-.024 

-.169 

0 

.640 

-.062 

0 


-.028 

.168 

-.120 

.636 

.064 

-.120 


-.028 

.169 

.229 

.636 

.065 

0 

-.170 

0 

.664 

-.058 

0 


-.005 

.170 

-.120 

.660 

.060 

-.120 


-.005 

.171 

.229 i 

.660 

.061 

.024 

-.169 

0 

' .688 

-.053 

0 


.020 

.169 

-.120 

.684 

.056 

-.120 


.019 

.170 

.229 

.683 

.057 

.048 

-.165 

0 

.712 

-.049 

0 


.044 

.166 

-.120 

.707 

.052 

-.119 


.044 

.167 

.229 

.707 

.053 

.072 

-.161 

0 

.736 

-.045 

0 


.068 

.162 

-.119 

.731 

.050 

-.119 


.068 

.163 

.229 

.731 

.049 

.098 

-.157 

0 

.759 

-.041 

0 


.092 

.158 

-.119 

.755 

.044 

-.119 


.092 

.159 

.230 

.756 

.045 

.121 

-.153 

0 

.783 

-.037 

0 


.116 

.154 

-.119 

.778 

.040 

-.119 


.115 

.155 

.230 

.778 

.041 

.144 

-.149 

0 

.806 

-.033 

0 


.139 

.150 

-.119 

.802 

.036 

-.119 


.139 

.151 

.230 1 

.802 

.036 

.168 

-.145 

0 ' 

.830 

-.029 

0 


.164 

.146 

-.119 

.826 

.032 

-.119 


.163 

.147 

.230 

.826 

.032 

.192 

-.140 

0 ' 

.854 

-.024 

0 


.187 

.141 

-.119 

.849 

.028 

-.119 


.186 

.143 

. 230 , 

.850 

.028 

.215 

-.136 

0 1 

.878 

-.020 

0 


.210 

.138 

-.119 

.874 

.023 

-.120 


.210 

.138 

. 229 ,' 

.874 

.024 

.240 

-.132 

0 1 

.901 

-.016 

0 


.234 

.133 

-.119 

.898 

.019 

-.120 


.234 

.134 

. 229 : 

.897 

.020 

.262 

-.128 

0 : 

.927 

-.012 

0 


.258 

.129 

-.119 

.922 

.015 

-.120 


.257 

.130 

.229' 

.921 

.016 

.285 

-.124 

0 

.949 

-.008 

0 


.283 

.125 

-.119 

.945 

.011 

-.120 


.282 

.126 

.229 

.944 

.012 

.309 

-.120 


.973 

-.004 

0 


.305 

.121 

-.119 

.969 

.008 

-.120 


.305 

.122 

.230 

.968 

.009 

__.333 

-.116 

“1 





.328 

.117 

-.119 





.328 

.118 

. 230 ^ 




z/l 

0.229 

.229 

.229 

.229 

.229 

.230 

.229 

.229 

.229 

.229 

.229 

.229 

.229 

.229 

.229 

.229 

.230 

.229 

.228 

.228 

.228 

.228 

.228 

.228 

.228 

.228 

.228 




TABLE I.- Concluded 



Pressure orifice rows are indicated 
by dashed lines. 

Cowl top 


(a) Center line (b) Left quarter span (c) Left corner 


x/i 

y/f 

z/Z 

x/i 

y/i 

z/l 


x/i 

y/i 

z/l 

x/f 

y/i 

z/l 


x/i 

y/l 

z/l 

X ./1 

y/l 

z/l 

- 0.619 

0.239 

0 

- 0.282 

0.211 

0 


- 0.619 

0.209 

- 0.116 

- 0.281 

0.204 

- 0.118 


- 0.619 

0.155 

- 0.182 

- 0.282 

0.171 

- 0.195 

-.594 

.239 

0 

-.258 

.211 

0 


-.595 

.208 

-.116 

-.258 

.206 

-.118 


-.594 

.157 

-.180 

-.256 

.177 

-.197 

-.570 

.239 

0 

-.234 

.214 

0 


-.571 

.208 

-.116 

-.232 

.211 

-.118 


-.573 

.154 

-.183 

-.233 

.182 

-.202 

-.547 

.239 

0 

-.210 

.218 

0 


-.546 

.208 

-.116 

-.210 

.216 

-.118 


-.551 

.152 

-.184 

-.209 

.187 

-.207 

-.522 

.238 

0 

-.186 

.223 

0 


-.522 

.208 

-.116 

-.186 

.221 

-.118 


-.527 

.152 

-.185 

-.185 

.193 

-.212 

-.499 

.237 

0 

-.161 

.227 

0 


-.499 

.208 

-.116 

-.162 

.226 

-.118 


-.502 

.154 

-.185 

-.161 

.198 

-.217 

-.474 

.235 

0 

-.138 

.232 

0 


-.475 

.208 

-.116 

-.137 

.231 

-.118 


-.476 

.155 

-.185 

-.137 

,202 

-.221 

-.450 

.231 

0 

-.114 

.236 

0 


-.450 

.207 

-.117 

-.114 

.235 

-.117 


-.452 

,156 

-.186 

-.113 

.207 

-.225 

-.425 

.228 

0 

-.090 

.238 

0 


-.425 

.206 

-.117 

-.090 

.238 

-.117 


-.428 

.156 

-.189 

-.089 

.209 

-.228 

-.401 

.224 

0 

-.066 

.239 

0 


-.402 

.206 

-.117 

-.066 

.239 

-.117 


-.408 

.160 

-.188 

-.065 

.211 

-.230 

-.377 

.220 

0 

-.042 

.239 

0 


-.378 

.206 

-.117 

-.042 

.239 

-.117 


-.381 

.162 

-.189 

-.041 

.213 

-.230 

-.353 

.217 

0 

-.018 

.239 

0 


-.354 

.205 

-.117 

-.018 

.239 

-.117 


-.355 

.162 

-.192 

-.016 

.213 

-.230 

-.328 

.214 

0 

.006 

.240 

0 


-.329 

.204 

-.117 

.006 

.241 

-.117 


-.332 

.167 

-.191 

.008 

.213 

-.230 

-.306 

.212 

0 





-.303 

.202 

-.117 





-.302 

.169 

-.194 






Pressure orifice rows are indicated 
by dashed lines. 

Cowl right side 


(a) Center line 


(b) Below center line 


V./1 

y/l 

z/l 

x/l 

y/t 

z/l 


x/l 

y/l 

zll 

- 0.614 

0 

0.237 

- 0.445 

0 

0.237 


- 0.469 

- 0.095 

0.220 

-.587 

0 

.237 

-.420 

0 

.237 


-.419 

-.095 

.223 

-.564 

0 

.237 

-.396 

0 

.236 


-.372 

-.095 

.226 

-.539 

0 

.238 

-.370 

0 

.236 


-.323 

-.096 

.228 

-.516 

0 

.238 

-.346 

0 

.236 


-.275 

-.095 

.231 

-.492 

0 

.238 

-.321 

0 

.236 




-.467 

0 

.237 

-.299 

0 

.236 







-.275 

0 

.235 





(c) Above center line 


x/l 

y/l 

z/l 

0.468 

0.096 

0.220 

-.420 

.096 

.223 

-.370 

.096 

.226 

-.324 

.097 

.228 

-.270 

.095 

.231 


17 


I 






TABLE II.- CONVERGENCE CRITERIA 


Pt.iAa 

Convergence 

parameter 

Total 

iterations 

Step size, 
sec 

3 

0.005 

8175 

0.76 X 10-6 

3.5 

.005 

5181 

.79 X 10-6 

4 

.005 

3915 

.79 X 10-6 

4.5 

.005 

3422 

.78 X 10-6 

5 

.006 

3441 

.78 X 10-6 

5.5 

.005 

4034 

.78 X 10-6 

6 

.007 

3671 

.78 X 10-6 






















































































1. Report No. 2. Government Accession No. 

NASA TP-1188 

3. Recipient's Catalog No. 

4. Title and Subtitle 

EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF 
A NONAXISYMMETRIC WEDGE NOZZLE AT STATIC 
CONDITIONS 

5. Report Date 

July 1978 

6. Performing Organization Code 

7. Author(s) 

George T. Carson, Jr., and Mary L. Mason 

8. Performing Organization Report No. 

L-12065 

10. Work Unit No. 

505-11-23-06 

9. Performing Organization Name and Address 

NASA Langley Research Center 
Hampton, VA 23665 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Paper 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 
Washington, DC 20546 

14. Sponsoring Agency Code 

15. Supplementary Notes 


16. Abstract 


An experimental investigation of a nonaxisymmetric wedge nozzle has been conducted 
at static conditions. The resulting data, in the form of detailed pressure distributions and 
oil flow photographs, expand the current nonaxisymmetric nozzle data base. An analytical 
investigation has been conducted to evaluate a two-dimensional, inviscid, time -dependent 
theory as a nonaxisymmetric nozzle performance predictor. For the range of nozzle pres- 
sure ratios investigated, results indicate good agreement between theory and experiment 
in regions of predominately two-dimensional flow and limited agreement in regions of three- 
dimensional flow. For the wedge nozzle and related nozzle configurations, the two- 
dimensional, inviscid theory may be applied as a limited performance predictor. 


17. Key Words (Suggested by Author(s)) 

Propulsion nozzles 
Nonaxisymmetric wedge nozzle 
NAP 


19. Security Classif. (of this report) 

Unclassified 


18. Distribution Statement 

Unclassified — Unlimited 


20. Security Classif. (of this page) 

Unclassified 


21. No. of Pages 

42 


Subject Category 02 

22. Price’ 

$4.50 


For sale by the National Technical Information Service, Springfield, Virginia 22161 


NASA-Langley, 1978 


National Aeronautics and 
Space Administration 

Washington, D.C. 

20546 

Official Business 

Penalty for Private Use, $300 


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