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FLUIDYNE ENGIffflpRTNG CORPORATION

AD-A956 154 •1

&

DETERMINATION OF DISCHARGE

AND THRUST COEFFICIENTS OF A

CHOKED ASME NOZZLE FROM

EXIT FLOW SURVEYS

(ADDITIONAL TESTS)

DTIC ELECTE FEB1 6 1993

C

/

by

James S. Holdhusen Donald Perusse

Conducted for

General Electric Company C i nc i nnat i, Oh i o

CM

(VI

am

9 :-

G. E. Purchase Order No. 200G230285 FluiDyne Project 0470

September 1965

Approved by: lames L. Grunnet Project Engineer

' 55•^!555 STATEMENT A j Appxor*- to? p^cuc fitzMm

Program Planner

10« -<M^

. Lamb Program Manager

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FLUIDYNE ENGINEERING CORPORATION

TABLE OF CONTENTS

Page

DEFINITION OF SYMBOLS ii

LIST OF TABLES AND FIGURES iv

INTRODUCTION 1

CONCLUSIONS 2

DISCUSSION 3

TABLES

FIGURES

DATA SHEETS

DTir QUALITY INSPECTED 3

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FLUIDYNE ENGINEERING CORPORATION

DEFINITION OF SYMBOLS

A Local Area square feet

A Nozzle Exit Area square feet

a Local Speed of Sound feet/second

Cr, Discharge Coefficient

C Stream Thrust Coefficient

Cy Thrust Coefficient Calculated Using p at Nozzle Exi t

F Nozzle Exit Stream Thrust

G Exhaust Thrust (F - p A ) a e

M Mach Number

m Mass Flow

p Static Pressure in Plenum Around a No zJe Exit

p Static Pressure Inside Nozzle s at the Ex i t.

p Total Pressure Ko

p Static Pressure

P Prandtl Number

R Gas Constant for Air

T Static Temperature

T Adiabatic Wall Temperature aw

T Total Temperature

V Ve loc i ty

ß Ratio of Exit to Entrance Diameter of Nozzle

pounds

pounds

slugs/second

psfa

psfa

psfa

psfa

53.35 feet/°R

°R

°R

°R

feet/second

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FLUIDYNB ENGINEERING CORPORATION

Y Ratio of Specific Heats [C /Cy)

X Pressure Ratio IpVp^l O a

p Mass Density slugs/feet

SUBSCRIPTS

act Actual

I idea) Based on Ambient Conditions

i Ideal Based on Exit Static Conditions

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LIST OF TABLES AND FIGURES

TABLE

TABLE

Tabulated Test Results

Dimension less Static Pressure Distributions

FIGURE

1.

2.

3.

4.

5.

6.

7.

9.-42.

DESCRIPTION

ASME Flow Nozzle Installation

Static Pressure Distributions

Ratio of Nozzle Static to Ambient Pressure

Ratio of Nozzle Static to Ambient Pressure - Expanded Scale

Discharge Coefficient Versus Nozzle Pressure Ratio

Discharge Coefficient Versus Throat Reynolds Number

Thrust Coefficient Versus Nozzle Pressure Ratio

Thrust Coefficient Versus Throat Reynolds Number

Integrand Calculations and Plots

i »

FLUIDYNZ ENGINEERING CORPORATION

I. INTRODUCTION

This study, sponsored by the General Electric Company

under their Purchase Order Number 200G230085, determined

the discharge and velocity coefficients of an ASME long

radius metering nozzle. Previous tests of this nozzle

(Reference 1) had been conducted with an exhauster sys-

tem which permitted operation at variable pressure ratio

while keeping the Reynolds number constant. These ad-

ditional tests were conducted to determine:

A. Whether the presence of the exhauster duct or

the survey rake significantly affected the in-

tegrated data.

B. The effect of further changes of operating

pressure ratio in the lower ranges of pres-

sure rat i o.

C. The effect of decreasing the Reynolds number.

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I. CONCLUSIONS

A. These tests confirmed the observation made in

the preceding test program (0431, Reference 1)

that the core survey rake caused a consistent

and appreciable increase in the measured static

pressure, p , inside the nozzle near the exit.

!t may be concluded that this effect is present

whether or not the exit plenum is installed.

The effect is probably a manifestation of the

sensitivity of transonic flow to small amounts

of blockage, since the measured increase in

pressure became greater as the pressure ratio

approached the critical (choking) value.

B. The nozzle discharge coefficient showed an in-

creasing trend with Reynolds number, varying

from 0.989 at Re « 106 to 0.992 at Re = 107.

The nozzle pressure ratio showed no consistent,

independent effect on the discharge coefficient

C. The nozzle thrust coefficient (at pressure

ratios less than critical) also showed an in-

creasing trend with Reynolds number, varying

from 0.992 at Re - 106 to 0.995 at Re - 6 x 106

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III. DISCUSSION

In the previous study conducted by FluiDyne, dis-

charge and thrust coefficients were determined for a

7.715 inch diameter ASME long radius nozzle. The noz-

zle for these tests discharged into a cylindrical plenum

in which pressure could be controlled by ejectors to

vary the pressure ratio. The total pressure was held

constant for most of the runs, giving a fairly constant

throat Reynolds number.

For this test program, the metering nozzle dis-

charged to atmosphere to eliminate any effects that

might have been caused by the plenum on the first test

series. Discharging to atmosphere meant that the noz-

zle pressure ratio and throat Reynolds number were con-

trolled by the nozzle total pressure. Discharge and

thrust coefficients were obtained over a pressure ratio

range of 1.03 to 3.93 which corresponds to a Reynolds

number variation of 0.95 x 10 to 12.0 x 10 .

The nozzle instrumentation was the same as for the

previous test program except that the total pressure

cross-rake, used to survey the core flow at the exit

of the nozzle, was only installed on four runs. These

four runs were made to determine the effect of the cross-

rake on the static pressure near the nozzle exit. Mer-

cury ana water manometers were used for all pressure

measurement s.

The data reduction procedures used for these data

were the same as described in the report for Project

0431. The calculations and plots of the integrands of

the discharge and thrust coefficient equations are

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FLUIDYNZ ENGINEERING CORPORATION

shown in Figures 9 to 42. The tabulated test results

af. presented as Table I.

A plot of typical static pressure distributions

through the nozzle is presented as Figure 2. A tabu-

lation of these same typical static pressures is pre-

sented as Table II. The ratio of nozzle static to

ambient pressure (Ps/p ) is plotted versus nozzle pres-

sure ratio for each data point of the two test programs

and presented in Figure 3. Both sets of data closely

follow the ideal curve for pressure ratios greater than

two. For pressure ratios less than two, the data points

taken on the 0431 program and the data points with the

exit cross-rake installed on the 0470 program have a

Ps/p ratio slightly higher than the ideal curve. The

ratio of Ps/p in this lower pressure ratio range is

presented as an expanded portion of the curve as Fig-

ure 4.

The nozzle discharge coefficients plotted versus

nozzle pressure ratio and Reynolds number are presented

as Figures 5 and 6, respectively. The discharge coef-

ficients obtained in the previous study are also pre-

sented in these plots. The discharge coefficients

obtained in the two test programs agree when compared

on a throat Reynolds number basis, as would be expected

from similitude considerations.

The two sets of thrust coefficient data, plotted

versus nozzle pressure ratio, are presented as Figure

7. The same thrust coefficient data, obtained at pres-

sure ratios equal to or less than two, are plotted

-4-

FLUIDYNE ENGINEERING CORPORATION

versus Reynolds number and presented as Figure 8. Good

agreement is obtained between these two sets of data

when compared at like pressure ratios. Good agreement

is also obtained when compared on a Reynolds number basis

Reference 1. "Determination of Discharge and Thrust Coefficients of a Choked ASME Nozzle from Exit Flow Surveys," James b. Holdhusen and Charles L. Landgraf, FluiDyne Project 0431, February 1965.

-5-

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TABLE 1 TABULATED TEST RESULTS

Data Press. Po Ps Pa Ps/ M [T7 dA (!L . Point Ratio (psia) (psia) (psia) j ?a JW,

1 1.209 17.23 14.29

1

14.25 j 1.0031 .9902 2 2.408 35.20 18.21 14.25 1 1.2779 .9923 3 1.418 20.14 14.28 14.21 1.0052 .9905 4 1.643 23.34 14.32 14.21 | 1.0079 .9905 5 1.857 26.37 14.45 14,21 1.017O .9915 6 2.059 29.25 15.41 14.21 1.0843 .9921 8 2.276 32.23 16.79 14.42 1.186C | .9924 9 2.487 35.21 18.35 14.42 1.2959 .9925

10 2.710 33.37 20.02 14.42 1.4141 i .9925 . 11 2.904 41.05 21.27 i 14.14 j 1.5052 1 .9923 . 12 3.120 44.09 22.83 14.13 1.6195 ! .9925 13 3.355 47.20 24.57 14.05 ! 1.7491 .9925 14 3.568 50.10 26.11 | 14.04 1.8602 .9924 15 3.773 52.96 27.60 14.04 1.9662 ,9926 16a 3.985 55.93 29.27 14.03 2.0354 .9930 16b 3.929 55.13 ! 23.79 14.03 2.0513 .9924 • 17 1.219 17-12 14.07 j 14.04 1.0021 1 .9903 _ 18 1.431 20.09 i 14.10 : 14.04 1.0045 .9911 19 1.647 23.13 ! 14.13 14.04 1.0066 .9912 20 1.613 23.14 14.13 14.04 1.0063 .9903 21 1.859 2c.10 i 14.25 14.04 1.0171 Q017 , 22 2.066 29.00 ! 15.25 ; 14.04 1.0361 .9922 !

23 2.073 29.ll i 15.27 14.04 1.0375 .9923 24 1.213 17.1C j 14.14 14.09 1.0035 .9903 1

25 1.647 23.21 ! 14.43 14.09 1.0273 .9913 i 1

26 2.498 35.20 18.85 • 14.09 1.3373 .9923 1

27 2.433 35.0': ; 13.31 14.09 1.3346 .9925 !

28 3.123 44.13 i 22.94 14.11 1.6260 '992' 29 3.136 44.24 23.02 : 14.11 11.6319 .9920 2-1 1.032 14.005 1^.22.3 14.227 jl.OOCC7

.9093 | 2-2 1.053 1-.93C 14.229 14.227 j1.00010 .9900 1

2-3 1.106 15.733 1 14.229 14.227 i1.00012 .9893

2-4 1.152 lc.397 14.231 1 14.227 1.00027 .9397 \

2-5 1.202 17.099 14.232 j 14.227 11.00033 ! .9900

bEST RESULTS

' dA AE

/?M \ 2 dA J\Mi; AE

CD cv Cs Thrt. Re

x 10-6

)2 .9829 .9902 .9927 1.1541 2.54 23 .9874 .9923 .9952 1.2689 7.47 » .9840 .9905 .9953 1.2248 3.62 35 .9851 .9905 .9943 1.2592 4.66 15 .9865 .9915 .9952 1.2683 5.60 21 .9869 .9921 .9953 1.2682 6.19 24 .9879 .9924 .9963 1.2704 6.83 25 .9880 .9925 .9953 1.2680 7.47 25 .9876 .9925 . .9941 1.2683 8.15 23 .9^73 .9923 .9918 1.2633 ^TTO 25 .9880 .9925 .9833 1.2704 9.44 25 .9883 .9925 .9830 1.2686 10.0 24 .9880 .9924 .9875 1.2673 10.6 26 ,9880 .9926 .9338 1.2631 11.2 3C .9385 .9930 .9819 I.2683 12.0 24 .9373 .9924 .9829 I.2683 11.9 03 .9836 .9903 .9929 1.1593 2.52 11 .9353 .9911 .9933 1.2233 3.62 12 .9855 .9912 • 9939 1.2592 4.60 03 .9840 .9903 .9936 1.2587 4.60 17 .9370 .9917 .9954 1.2684 5.5^ 22 .9376 .9922 .9937 I.2683 6.15 23 .9876 .9923 .9957 1.2711 6.17 03 .9843 .9903 • 9939 1.1554 2.53 13 .9364 .9913 • 995C 1.2557 4.62 23 .9879 .9923 .9953 1.2631 7.4? 2- .9373 .9925 GC-~ 1.2634 7.43 2~ .9332 .9927 .9355 1.2631 4.51 23 .9332 .9923 .GQC-, 1,2c7^ 5.72 93 .931? .9393 ,9C21 1.0402 O.oli 100 .9818 .99OC QQi •

• s > — • 1.0571 1.25 93 .9313 .9393 GG1 G

• .» S — s 1.C963 1.73 197 .9327 .9397 . 9921 1.1261 2.11 fco .9835 .9900 GGÄil "> ^ ^ 2.42

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