AIAA 95-0797 Effect of Correlated Precision Errors on the Uncertainty of a Subsonic Venturi Calibration

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AIAA 95-0797

Effect of Correlated Precision Errorson the Uncertainty of aSubsonic Venturi Calibration

A;E R I L I : P t Y ! e , _

: £ t ~/?

S.T. Hudson and WJ.Bordelon, Jr.

NASAJMarshaII Space Flight CenterHuntsville, AL

H.W. ColemanPropulsion Research CenterUniversity of Alabama.in Huntsville .---- ---.-.--------.-._Huntsville, AL

33rd Aerospace Sciences

~eeting .andExhibit

January 9-12,1995 I.Reno, NV

For permission to copy or republish, contact the American Instftuts 01Aeronautics and Astronautics

310 L'Entant Promenade, S.W., Washington, D.C. 20024



EFFECT OF CORRELATED PRECISION ERRORS ON THE

UNCERTAINTY OF A SUBSONIC VL"ITURI CALIBRATION

S.T. Hudson- and W.J. Bordelon. Jr."

NASA lM a rs ha ll S pac e Flight Center

Structures and Dynamics LabHuntsville. AL 35812

H.W. Coleman*

Propulsion Research Center

Mechanical and Aerospace Engineering Department

University of Alabama inHuntsville

Hun~lle. AL 35899

Abstract

An uncertainty analysis performed in conjunctionwith the calibration of a subsonic venturi for us e in a

turbine test facility produced some unanticipated results

which can have an extensive impact on a variety of test

siruations. Precision uncertainty estimates using the

preferred propagation techniques in the applicable

ANSI! ASME standards were an order of magnitude

larger than precision uncertainty estimates calculated

directly from a sample of results (discharge coefficient)

obtained at the same experimental set point. -An

analysis explaining this phenomenon forms the basis of

this paper.

Nomenclature

B: Bias limit estimate

C~: Discharge coefficient

d: Diameter

J: Number of measurement variables

Mn: Mach number

M: Number of tests- (measurement sets)

'N: Number of readings

P: Precision limit estimate

p: Pressure

r: Result

Re: Reynolds numberS: Sample standard deviation

"Aerospace Engineer, Member AIAA

tAerospace Engineer

*Eminent Scholar in Propulsion and Professor,

Senior Member AIAA

Copyright \I 1995 by th" American Institute of Aeronautics and /

Astronautics. Inc. No copyright is asserted in the United Sta~s

under Title 17, U.S. Code. The U.S. Government haa a royalty-

free license to exercise all rights under the copyright claimed 1herein for Governmental purposes. All other' rights are reserved

by the copyright owner.

T: Temperature

U: Uncertainty estimate

W: Mass flow rate

X: Measurement reading

~: Bias component of error

5: Total error

E: Precision component of error

6: Sensitivity coefficient

u: Population mean

p: Correlation coefficient __,

a: Population standard deviation

Subscripts

0: Total

1: Venturi inlet

2: Venturi throat

Introduction

Mass flow venturis are U s e d in a variety of test

situations to determine the mass flow rate of gases or

liquids. Inorder to accurately determine the mass flow

rate using a venturi. the discharge coefficient must be

known. The discharge coefficient is defined as the ratio

of the actual mass flow passing through the venturi to

the ideal one-dimensional inviscid mass flow rate.

Critical flow venturis are often used since Cli is well

known for standard designs such as the Smith-Matz'and the ASMEI.z nozzles. However, a critical flow

venturi is not always the most desirable optimr. When

subsonic flow meters must be used, determination of

the discharge coefficient is crucial to meter accuracy.

A subsonic Herschel-type venturi is used in the

Turbine Test Equipment (TIE) at the Marshall Space

Flight Center (MSFC)3. The subsonic venturi was

American Institute of Aeronautics and Astronautics



chosen over a critical flow venturi to minimize flow matrix. ASE estimated a bias error and a precision

noise. The TIE is used to test liquid rocket engine error for each measurement at each test point. These

turbines in air at scaled conditions. A technology estimates were then propagated through the data

demonstrator gas generator oxidizer turbine is currently reduction equation for Cd to estimate an uncertainty in

being tested in the TIE·. The test data from this the discharge coefficient. Based on these estimates. it

technology turbine is to be used for code validation as a pp ea re d th at the calibration goal of ±0.15 % could be

well as performance evaluation; therefore, absolute achieved at Mach numbers of 0.5 and 0.7 with very

accuracy is very important. The mass flow rate careful calibration. However, the low Mach number

measurement is used to calculate the turbine efficiency (0.2) points seemed to be a problem. Large precision

and to calculate the turbine flow parameter. The goal errors were predicted at these points due to the low

of the technology turbine testing is to determine these pressure differential between the venturi inlet and throat dtwo performance parameters within ± 1s. This means at these conditions. ·Based.:O~·:past .. : ~ ~ _ p e ; t ~ · ·~ _ ~ : ' ; a ~ ;that an accuracy of ±O.S % is needed for the mass flow ~,~~W~':.~#'l~~._~!elt~~L,t1:t,~i::~~.s.,~~lli~ ..

measurement. The accuracy of the mass flow -precision With their test system. thiiii*:f:lat

measurement in the TIE depends on the accuracy of .- - was decided to proceed with the"catibfa,tio to

the venturi inlet pressure, throat pressure, and inlet determine the precision limit in the discharge coefficient

temperature measured during the test; the venturi inlet directly from the test data. Precision limits determined

and throat diameter measured during inspection; and the from the test data would then be combined with the bias

venturi discharge coefficient determined during estimates to determine an overall uncertainty for each

calibration. In order to meet the ±0.5% goal for the test point. These uncertainties would be compared withTIE mass flow measurement, the discharge coefficient the pretest predictions and calibration requirement.

from calibration needs to be determined within When the test data was obtained, two methods of

approximately ::0.15 %. estimating the precision limits in the calibration data

The TIE venturi had been calibrated, but the were used: (1) calculating the standard deviations for

more strict requirements for the technology turbine the pressure and temperature measurements and

testing prompted a review of the original calibration. propagating these through the data reduction equation

This review revealed several concerns. First, the while assuming uncorrelated precision errors; (2)

technology turbine would be operating outside of the calculating the standard deviations directly from

calibration range for the majority of the test matrix. multiple Cd results. The actual test data was used in -

Also, the uncertainty of the standard nozzle used to both cases so that a direct comparison could be made.

determine the calibration mass flow rate was ±O.S %. Method 2 gave precision limits that were an order of

This uncertainty value for the standard mass flow rate magnitude less than those predicted by method 1. The

must be combined with the uncertainty of the venturi calibration approach, calibration results, and an

measurements (inlet pressure and diameter, throat uncertainty analysis explaining the differences between

pressure and diameter, and inlet temperature) to obtain the two methods of determining the precision limits will

the uncertainty of the discharge coefficient for each be presented in this paper.

calibration test point. A curve-fit of test data must then

be used to apply the calibration; therefore, the

uncertainty of the curve-fit must be considered' to

determine the overall uncertainty in Cd' Obviously, this

discharge coefficient uncertainty would have been

greater than the required ±0.15%.

Based on the above findings, it was decided that a

new calibration of the TIE venturi was needed. The

question was whether or not the venturi could becalibrated to the required ±0.15%. A nine point test

matrix consisting of three venturi throat Mach numbers

(0.2, 0.5, and 0.7) and three venturi throat Reynolds

numbers (1, 3, and 6 million) was decided upon.

FluiDyne Aerotest Groupof Aero Systems Engineering"~\,

. (ASE). Inc.,was asked to·evatuate'the-uncertam~'m~C"":.• • ~ ''' ':''''~ __ • . •• • t-: ", •.;;.~." .. . ty - d··

_;,hat'they:ci>uld'obtaiIi 'in"'illI~ir t e s t -facility for this test~'.-.- - .. :..:--

Calibration Approach

The venturi calibration runs were conducted in a ir

in the Channel .1 .test facility at Aero Systems

Engineering' (ASE) Medicine Lake Aerodynamic

Laboratory. The calibration test runs were conducted

between January 21 and February 1, 1994. This

section describes the experimental setup, m easurem ents, ..and test procedure as well as details of the test venturi

itself. For more information, refer to the ASE

calibration report'.

The venturi (Fig. 1) used in the MSFC TIE is a

Herschel type venturi as defined by Bean", The

nominal inlet diameter is 7.980 inches, and the nominal

2




throat diameter is 3.396 inches. This venturi was sized

to operate at subsonic conditions to minimize flownoise

or pressure fluctuations caused by a normal shock. The

venturi is made of stainless steel and contains two

instrumentation planes. as shown in Fig. 1. The

venturi inlet plane contains two gas temperature probes

and four static pressure taps. The venturi throat

contains four static pressure measurements. The overall

length of the venturi is S9 inches.

The facility used for the venturi calibration was

Channel 7 at ASE modified as shown in Fig. 2. The

facility consisted of a SOOpsi air storage source, heater,

inlet control valve, ASME metering nozzle, settling

chamber, test venturi, and back pressure control valve.

The air supply, heater, control valve, metering nozzle,

and settling chamber were part of the existing facility

setup. An adapter was fabricated to attach the venturi

to the settling chamber discharge. Downstream of the

venturi a 16 inch t06 inch reducer was made fromstandard pipe reducers to install the 6 inch back

pressure control valve. The flow was exhausted to

atmospheric conditions downstream of the back pressure

control valve. Two ASME long radius metering

nozzles were used as the calibration standards to cover

the range of calibration conditions. The ASME nozzle

nominal throat diameters were 1.47 inches and 1.7S

inches. Both nozzles were operated at choked

conditions for all test runs.

Pressure and gas temperature measurements were

recorded for both the metering nozzle (calibration

standard) and test venturi. The inlet total pressure, twoinlet gas temperatures, and a static pressure just

downstream of the throat were measured on the

metering nozzle. Measurements taken on the test

venturi included four inlet static pressures, four throat

static pressures, and two inlet. gas temperatures.

Atmospheric pressure was also measured for each run.

The pressure measurements were made with a PI'eSSUI'e

Systems Inc. (PSI) pressure scanning system. The

metering nozzle gas temperatures were measured with

shielded type J thermocouples, and the venturi gas

temperatures were measured with type K

thermocouples. The voltage outputs from the

thermocouples were measured using an electronicdigital data acquisition system.

The venturi was calibrated over the range of throat

Mach numbers and throat Reynolds numbers by setting

the metering nozzle upstream pressure (mass flow for

choke condition) with the upstream control valve and

the test venturi back pressure with the back pressure

control valve. With the metering nozzle choked. the

test mass flow and venturi Reynolds number were fixed

for a constant metering nozzle inlet total pressure and

temperature. The venturi back pressure was then

adjusted to set the venturi Mach number. All test runs

were conducted with the air at room temperature. Once

the test conditions were established, the pressure and

temperature measurements were scanned ten times with

about six seconds between each scan.

Calibration Results

The venturi was calibrated over a nine point test

matrix. The nominal throat Mach numbers for this

matrix were 0.2. 0.5, and 0.7. The nominal throat

Reynolds numbers for this matrix were 1, 3, and 6

million. Ten data scans were taken at each set point.

The venturi pressures and temperatures were recorded

and used to calculate Mn, Re, and Cd for each scan.

The equations for these calculations are closed form and

are given in Appendix A6..7. The ten scans were then

averaged to obtain mean values of Mn, Re, and Cd '

Three runs were made (10 scans each. except run 808

which had 9 scans) for the 'worst case" data point

(Mn=0.2, Re= lxl()6). This was the point where the

uncertainty was expected to be the highest. These

repeat runs were made to provide more data for

understanding the precision behavior associated with

this point. The average values of Mn, Re, and Cd for

each run are given in Table 1. A curve fit was then

applied to this data and interpolation is used to apply

the calibration data in the TIEs. (Note: At Mn=0.7,

Rehad to be increased to 1. 5 million to achieve the testpoint.)

Uncertainty Analysis Overview

The word accuracy is generally used to indicate

the relative closeness of agreement between an

experimentally-determined value of a quantity and its .

true value. Error (0) is the difference between the

experimentally-determined value and the truth. thus as

error decreases accuracy is said to increase. Only in

rare instances is the true value of a quantity known.

Thus. one is forced to estimate error, and that estimateis called an uncertainty, U. Uncertainty estimates are

made at some confidence level. A 9S % confidence

estimate, for example. means that the true value of the

quantity is expected to be within the ±U interval aboutthe experimentally-determined value 95 times out of

100.

Total error. 5, can be considered to be composed

of two components: a precision (random) component,


3



Table 1. Calibration Results

1.01-1.10 .197 .975 .9899

1.11-1.20 .192 .966 .9917

808.01- .201 1.084 .9866

808.10

4.11-4.20 .199 2.932 .9894

7.01-7.10 .199 5.953 .9933

2.06-2.15 .502 .977 .9885

5.01-5.10 .495 2.971 .9914

8.01-8.10 .493 5.834 .9927

3.11-3.20 .698 1.450 .9907

6.11~.20 .695 2.951 .9914

9.01-9.10 .683 5.894 .9938

e, and a bias (systematic) component, ~. An error is

classified as precision if it contributes to the scatter of

the data; otherwise, it is a bias error. As an estimator

of ~, a systematic uncertainty or bias limit, B, isdefined. A 95 % confidence estimate is interpreted as

the experimenter being 95% confident that the true

value of the bias error, if known. would fall within

±B. As-an estimator of the magnitude of the precision.

errors. a precision uncertainty or precision limit, P, is

defined. A 95% confidence estimate of P is interpreted

to mean that the ±P interval about a single reading of

X, should cover the (biased) parent population mean. /J.

95 times out of 100.

In nearly all experiments. the measured values of

different variables are combined using a data reduction

equation (DRE) to form some desired result. A general

representation of a data reduction equation is .

r = r( X 1• X z . . . . . X)

where r is the experimental result determined from J

measured variables X i. Each of the measured variables

contain bias errors and precision errors. These errors

( 1 )

in the measured values then propagate through tho data

reduction equation. thereby generating the bias and

p re ci si on e rr or s in the expe rimen ta l r es ult , r.

If the -large sample assumption-is made', then

th e 9S % confidence expression for U, becomes

( 2 )

where we define the bias limit (systematic uncertainty)

of the result as

and the precision limit (precision uncertainty) of the

result as

where P b i k is the correlation coefficient appropriate for

the bias errors in X i and X l<' P ,ik is the correlation

coefficient appropriate for the precision errors in XI andXtt and

(5)

The 95% confidence precision limit for a variable ~

can be estimated as

(6)

where the sample standard deviation for X i is

s , = [ _ 1 _ f [(XJt - i ] l ] l I lN-l tel

(7)


4



and the mean value for XI is defined as

( 8 )

Single Test=Single Readings

The precision limits defined in Eq. (6) and used in

Eq. (4) are applicable to a single test with single

readings-that is, at a given test condition, the result is

determined once using Eq. (1). and the ~'s are

considered single measurements. This is the situation

often encountered in large scale engineering tests in

which measurements of the variables are made at a

given set point over a period that is small compared to

the periods of the factors causing variability in the

experiment. A proper precision limit (one indicative of

the dispersion of the variable over several cycles of the

factors causing its variation) cannot be calculated from

readings taken over such a small time interval. For

such data, the measurement(s) of a variable X ; should

be considered a single reading-whether the value of X ,

is the average of 10, l()l or 1()6 readings taken during

the short measurement time. In such a test, the value

for the precision limit to be associated with a single

reading would have to be based on previous information

about that measurement obtained over the appropriate

time inrerval'". If previous readings of a variable over

an appropriate interval are not available, then the

experimenter must estimate a value for Pi using the best

information available at that time9•1l

•

Multiple Tests=Single Readings

.If a test is performed so that M multiple sets of

measurements (XI' X::, ... , Xl)\: at the same test

condition are obtained. then M results can be

determined using Eq. (1), and the best estimate of the

result r would be r where

1 Mr= '"'r

M f : r .I :

( 9 )

If the M (M;::10) sets of measurements were obtained

over an appropriate time period, the precision limit that

should be associated with this averaged result would be

2S,P; =-r I M

(10)

and for a single result would be

(11)

where S, is the standard deviation of the sample of M

results

[

1M ] 1 1 2S, '" -- L (ric - ri-

M-I t o o L

(U)

Single Test-Averaged Readings

Some previous approacheslZ.IJ.14 considered the

general case to be that in which the best estimate of the

result is determined using averages of the XI so that

- - -r = r(X1• x . . : • . . . • X 1)

(13)

and specified that (for large samples) the precision

limits be taken as P/(N)'t: in Eq. (4) (with the

correlation terms neglected). The (P,.J'iPJ terms in

Eq. (4) take into account the possibility of precision

errors in different variables being correlated, and these

terms have traditionally been neglected. However.

precision errors in different variables caused by the

same uncontrolled factor(s) are certainly possible. as

shown in this paper. In such cases, one would need to

a c q u i r e sufficient data to allow a valid· statistical _. -

estimate of the correlation coefficients to be made in

Eq. (4). Note, however. that the approach using Eqs,

(10) through (12) implicitly includes the correlated erroreffect-a substantial advantage over the approach of Eq.

(13) .

Uncertainty Analvsis Results

The uncertainty analysis presented here focuses

only on precision uncertainties. Two methods were

used to evaluate the precision limit associated with the

experimental result. Cd' First. the precision limit of the

result was calculated by propagating the precision of the

averaged measured variables through the data reduction

equation as discussed in the paragraph above whileneglecting correlated precision errors (method 1).

Equations (4)-(8) and Eq. (13) were used for this

approach. Second. the precision limit of the result was

calculated directly from the sample standard deviation

of Cd for each test point (method 2). Equations (9)-

(12) and Eq. (1) were used for this approach. These

two methods will be discussed, and the results will be


5



compared and explained in the following paragraphs.

A Fortran program was written to calculate the

precision limit of Crt by the propagation method

(method 1). It was assumed that only PI' P:. and T,contributed to the precision uncertainty;

(14)

Table 2. c . . Precision Results

.197 .975 .9899 2.00 .12

.192 .966 .9917 4.37 . 1 1

.201 1.084 .9866 2.15 .043

.199 2.932 .9894 2.46 .082

.199 5.953 .9933 1.17 .062

.502 .977 .9885 .37 .050

.495 2.971 .9914 .75 .053

.493 5.834 .9927 .14 .061

.698 1.450 .9907 . 0 9 .047

The precision uncertainties associated with the mass

flow rate of the standard and the test venturi inlet and

throat diameter were assumed to be negligible relative

to the precision errors of the test venturi measurements

of pressure and temperature. The standard deviations,

S, of the three measurements (PI' P:. and T,) were

calculated from the 10 data scans for each test run

(N =10). The precision limit for each of these mean

quantities was then calculated using P=2S/(10)112. The

values of PI' p:. and T Iwere set to the average of the

10 scans for each point. The code used these average

values and precision estimates as inputs for thevariables and propagated these values through the ORE

to obtain an estimate of the precision limit for Crt. A

central difference numerical scheme was used to

approximate the partial derivatives. No correlation of

the precision errors in the measured variables was

considered.

A summary of the results using the propagation

method (method 1) is given in Table 2. These results

indicate that the goal of achieving an uncertainty in Crt

of =0.25 % cannot be attained. Notice particularly the venturi temperature measurement had very little effect

extremely high precision uncertainties calculated for the on the precision of Crt. The venturi mass flow and,

low Mach number points. therefore. C, are functions of the ratio of the inlet to

The precision limit of the discharge coefficient the throat pressure. This means that variations in the

was then determined directly from the Crt results inlet pressure and the throat pressure will not affect the __

(method 2). Cd was calculated for each data scan. A '-'precision ofW o r ' Cd if the ratio remains constant:' ,----

sample _standard deviation. S. was then computed for The propagation method treated the precision

each test point using the 10 data scans (M= 10). The errors in the two venturi pressures as independent. A

precision was again calculated using P=2S/(10)112. plot of these two pressures normalized to the critical

These results are also given in Table 2. The results flow meter inlet total pressure for a particular run (Fig.

indicate that the goal of an uncertainty in Cd of 3) shows that the variations of the two pressures are not

±0.25 % can be attained. independent, however. This same trend was seen for

The precision limits calculated by method 1 were all of the test conditions. The fact that the throat

much higher than those calculated by method 2. The "pressure varied with the inlet pressure was a function of -

differences were especially large at the low Mach the test facility control. The distance between the

number points. The large errors at the low Mach critical flow meter and the venturi was small; therefore. _..numbers were due to the small difference between the pressure variations in the critical flow meter and in the

venturi inlet and throat pressures at these conditions. venturi were in phase. The variations in the pressure

An examination of the influence coefficients obtained measurements were not truly random; they were

from the propagation method revealed that the Cd correlated. This correlation was not accounted for in

precision limit was extremely sensitive to the venturi the propagation analysis. Method 2 automatically

inlet and throat pressure measurements. This sensitivity accounted for the correlation effect since Cd was

to the static pressure is discussed in reference 2. The calculated for each scan. and this data was used to

.695 2.951 .9914 .23 .028

.07 '.024683 5.894 .9938


6



ISmith, R.E. and Matz, R.J.,·" A Theoretical

Method of Determining Discharge Coefficients for

Yenruris Operating at Critical Flow Conditions."

Transactions of the ASME, Journal of Basic

Engineering. December 1962.

uti, D.J.. "Theory and Experiments on

cal Ited b thod 2 eli ussed . us! Subcritical Compressible Gas Flow Metering." Ph.D.

cu a y me uu as sc previa y. D' . . _U' . . f C" . C" . OHC bini th three M 29 for th rail issertanon, ruversity o mcmnan, incmnan, ,am uung e runs gave = 10r e ove 1990 •

data. This data is summarized. . in.Table 3_ ...The d ata . - '~U~Bt rdelc Ji - . J d

sh that th t ....."'....bility i ood Soon, W.J'~. r., Kauffman~ W.L· r...anows e r un - o -r un rer--u IS g • orne' .' • .. ... . C . ted d t t . t .. . Heaman, J.P., The Marshall-Space Flight Center-.---

vananon m :I IS expec ue 0 se pom vananons.. . . .

Th.. limit f th rail di 1.;,-- Turbine Test Equipment;·· Description 'and .... _

e preclslo~.v~ .."",o e ave average lscwuge . o r . -

ffici t iO:lOtllt.·ruh al l three id red Performance, ASME 93-GT-380. 1993.coe cien IS ; j . ; z . A ! . \ . : ' ' ' en runs are COnSl e •(P=2S/(29)11l). This data set allows 'one 'to be more' ;, . ~udson,. S.T~, Johnso~: P.D., aad.Wooler, ~--.- ..

f th. . f th • ". Baseline Design of the OXIdizer Technology Turbine .:: _

sure 0 e precrsion a e worst case . point. Ri • d ed Earth 0-0 bi P ulsi T hn 1g, A vanc -t r It rop Ion ec oogy

C I' .. Conference, Huntsville. AL. May 1994 , · . '_" r· ' .one USIOns . .---_ '. 5TT --.:.: 'P J .. ' a n d ' ' . . . R ,'." 'r i ' :E . · ~ : .~ .' . : " ': ' ~ " .• ~

• _nanson. '. •• -: . eeve •. , '.A .."::·~·~.uo'1!!i

. . .. -Calilirationof'Veiituir~fDbl~;"F1~~~Correlated preciston terms can have a slgruficant_'o " '_'sR~ .·,."._,;1~10T:r.r~e.e; 'f f i~~ ';"; :"_~; ':"·-··-- . .U th .. limi f 1 n-._" -' roup "}I"H . • fiiV ......... J .. •

errect on e precision t 0 a resu t, .t:l.....ision :':'.-'.6n '~H's'·'''··F-I-w··dM te Thei Th rv an d. . . . hni .oean, .., e rs, err eo. Juncertainty es~tes using propagatxon. ~ ques ~ere ..; :Application~ • ASME Report, 6th Edition, 1971. . ':.

an order of magnitude larger than precision uncertamty 'D . M W "Calib t' f T H h I.. aVIS, . ., ....... ra Ion 0 wo ersc eesnmates calculated directly from a sample of results Y ruri C o th' T bi T t E' t "S d, .. en ns 10r e ur me es quipmen , ver rupobtained at the same experimental set point. The . M h 31 1988 .

ia l fti fled . . mak memo, arc , .poteau e ect 0 corre at precision terms es it'

better to use multiple results rather than the propagation

calculate the precision limit. In order to account for the

correlation effect in the propagation analysis, a

correlation coefficient must be estimated. To us e this

method for pretest predictions. one must recognize that

the precisions of the two pressures will be correlated

and include the correlation terms in the analysis.

In order to gain more insight into the precision ofthe "worst case" point of Mn==O.2 and Re== lxl04,

three runs were made at this test condition. Two of the

runs (10 scan s e ach ) were made at different times on

the same day, and the third ru n (9 scans) was made

almost two weeks later. The data for each run was

Table 3. Multiple Test Results

1.01- . .197 .975 .9899 .12

1.10

1.11- .192 .966 .9917 . 1 1

1.20

808.0l- .20l 1.084 .9866 . 0 4 3

808.10

·:ro~.008 .9895verall .197

method to determine a precision limit for a result. The

p ro pa ga tio n m eth od is u se fu l in th e p lan nin g p ha se. but

one must recognize the effect of the correlated precision

terms and include this in the analysis if it is applicable

to their particular test situation. The correlated

precision effect is probably much more prevalent than

considered in the past.

Aeknowled&ements

The venturi calibration test by ASE was conducted

for MSFC through Dynamic Engineering Inc. (DE!).

J.R. Herdy was the DEI technical monitor for the

contract; and W.l. Kauffman. Jr •• was the NASA

employee responsible for the venturi calibration. ~~

Heaman of NASA also provided valuable input...:miJ, ~- , ~J .- ~~~~

-~~~~~~'~}~:Ji~~~~t~,·r=~~"'f:-.",~,,-~",,;;-. ~" - " . - - _ - . " • ~ - .. - ~ •

appreciated: Also, thank you to C.E. Hudson. Jr., forassisting with the raw data tables for the uncertainty

analysis .

References


7



'Heaman, ].P., "lncorporation of the TIE Venturi

CalibratiOD,· NASAlMSFC memo ED36-09-94, June

22, 1994.

9Q ua llty A ssessm ent for Wind T un ne l T es tin g,

AGARD-AR-304, 1994.

u'Steele, W.G., Taylor, R.P., Burrell, R.E., and

Coleman, H.W., "The Use of Data from Previous

Experienco to Estimate the Precision Uncertainty of

Small Sample E xp erim en ts, - A L 4 A Journal, Vol. 31,

No. 10, 1993.IlColeman, H.W. and Steele, W. G.,

ExperimDua tion and Uncerta in ty Ana lysis for

Engineers , Wiley, New York, 1989.

IlAmerican Natioual Standards Institute! American

Society of Mechanical Engineers. Me4furement

Uncmainty , PrC 19.1-1985 Par t I, ASME, 1986.

1 3American Natioual Standards Institute! American

Society of Mechanical Engineers, Me4furement

Unc er ta in ty fo r FUd d Flow in Closttd Conduits, MFC-

2M-1983, ASME, 1984.

14Abernethy, R.B., Benedict, R.P., and Dowdell,

R.B. , ·ASME Measurement Uncertainty: J. Fluids

Engineering. Vol. 107, 1985.

~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -9 D O - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~

T1 a . P1 On tlc e RIng

t

1----------- 22.56 -------t-----

-" -r _--_ _ _ _ _ - - ; ; . _ " _ - * " . . : n o - : .a:"7

I I 1

FIg. 1. TIE SubsonicVenturi "

8




C:Oftt~l vAlv ••

-\J

Chlnnel7 _

Idlpa!t 2013.002 '\ uJwua 10

1

2

81

8

Upstro:1II1 ASMI! flow IIIcter

jlw dUwll~trCllIll of m ot cr I hro ~1

v Cl ll ur i i nl ct

v en tu ri I hr o~ 1

(Note: The notation is from the calibration test and differs from tha t in the paper.)

Fig.2. Venturi Calibration Schematic -_- .. = = - = 7:':.-- -:...:"_-:_:_..:......

0. .572

0.57

0.. 568

ei 0.. 566O PI

e 0 • .564~

- = 0 • .562. §!. .56

~ 0.. 558

0 . .5 .56

0• .5 .54

0.552 +----+-----+-----+----+----t---+---+---+----i

--a- P2 f Po crit

• PI fP o crit

1 2 3 4 5 6 7 8 9 10

D ata S can

Fig. 3. Normalized Venturi Inlet and Throat Pressures

9




Appendix A

,

The equat io ns used to calculate the venturi M ach num ber, R eynolds num ber, m ass flow rate, and di.scharge

coefficient for this application are included here. The basic equations cam e from ref'ere:ace 6 , and th ey a re a pp lie d

to this s pe cif ic c as e in reference 7. (Note: The equations for M ach num ber and Reynolds number are the same as

those used by ASE in reference 5 . but the equation for mass flow is different.) The equations are written for

English units; therefore. pressure m ust be in psia, area in i nc he s:, a nd t emper atu re in o a . Coasants used include

y-1. 4 and R"" ,5 3 .3 5 f t- lb r1 lb . .o a . T he sym bol p is now used for density (p was th e cor re la tio n coe ff ic ie nt in th etext o f th e p ap er). Also, the symbol M (not Mn) is now used for M ach num ber. The constant 9.9xl04 in Eq. (7)

is the thermal expansion coefficient. .. -- ... .. - .. . -.- .. . . . .

(1) Venturi diameter ratio and pressure ratio

PR '" P1.

Pl

(2) Throat Mac h n um be r

(3) Inlet Mach number

(4) Inlet static temperature

(5) Inlet density

(6) Throat adiabatic wall temperature

[

1 +O.1784MijT .. =T

: . n o . II I 1+ O . 2 M 1 .2

10




(7) Throat diameter corrected due to difference between operating temperature and room temperature

4,•~ [ 1 + 9.9xlO~{T_ -S29.67)]

(8) Throat area based on throat diameter in (7)

(9) Throat Reynolds number per foot per psia

94 '" (181.176.192) M: [ T O l +198.6(1 +O.2M%~l

dpDJ (Tal' (1 +O.2M:~%.j

(10) Throat Reynolds number

(11) Ideal mass flow rate (lb,jsec)

[ p P R I 0 1 7 ( I _ P R 2 I 7 ) ] l f lW. = w : = 1.250605 ( A _ ) . . ; _ t : . . ; _ P . . : , . . l _ _ , ; .

i t iM K 1 - - z r 1 _ D R 4 P R 1 0 1 7P l M . -.I?L \ \

(12) Discharge coefficient

11


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Documents

AIAA 95-0797 Effect of Correlated Precision Errors on the Uncertainty of a Subsonic Venturi Calibration