NASA Contractor 'Report 172523

RESPONSE TIME CORRELATIONS FOR

PLATINUH RESISTANCE THERMOMETERS

I N FLOWING FLUIDS

Dhirendra K. Pandey and Robert L. Ash

OLD DOMINION UNIVERSITY RESEARCH FOUNDATION Norfol k, V i r g i n i a

Contract NAS1-17099 February 1985

National Aeronautics and Space Administration

( g ~ S ~ - C ~ - 1 7 2 5 2 3 ) ggSEG1Ss T ~ l g C O B B ~ A T I O I S 185-2 1606 POB PLATIPUR EBSf STAICB T EBERGHETBRS Il PLOYING PLUIDS F i n a l Beport (Old Domfnion Univ., Borfolk.. Va,) 54 p BC AO4/?lP A01 Uacla s

CSCL 1YB 63/35 14621

https://ntrs.nasa.gov/search.jsp?R=19850013296 2018-05-28T00:46:41+00:00Z

FOREWORD

This word was supported by the NASAILangley Research Center through the

Master Contract Agreement NAS-1-17099, Task Authorization 39, and monitored

by Mr. L. A. Dillon-Tomes o f the IRD-Thermal Instrumentation Section,

NASA/Langley Research Center, Mail Stop 234, Hampton, VA 23665.

TABLE OF CONTENTS

FOREWORD ......................................................... LIST OF TABLES. ..................................................

.................................................. LIST OF FIGURES

LIST OF SYMBOLS .................................................. SUWRY ...............................................*.........

............................................... 1. INTRODUCTION..

....................................... 2. RESPONSE TIWE CONSTANT

3. HEAT TRANSFER COEFFICIENT. ................................... .......... 3.1 Heat Transfer Coeff ic ient i n Flowing Liquids..

.............. 3.2 Heat Transfer Coeff icient i n Flowing A i r . .

4. DESCRIPTION OF THE SENSORS. .................................. 5. EXPERIMENTAL APPARTUS .......................................

....... 5.1 Response Time Testing for PRT i n Flowing Liquids.

.......... 5.2 Response Time Testing f o r PRT i n Flowing A i r . .

6. RESULTS AND DISCUSSION.. ..................................... ..... 6.1 Response Time f o r Hy-Cal Sensor i n Flowing Liquid..

6.2 Response Time f o r Hy-Cal Sensor i n Flowing Air . . ........ ..... 6.3 Response Time f o r Rosemount Sensor i n Flowing O i l . .

... 6.4 Response Time f o r Rosemount Sensor i n Flowing Water..

..... 6.5 Response Time f o r Rosemount Sensor i n Flowing A i r . .

7. PREDICTIONS OF TIME CONSTANTS AT CRYOGENIC CONDITIONS.. ...... 8.. CONCLUSIONS AND RECOMMENDATIONS. ........ .... ................

PRJ!CEDING PAGE B W NOT REMED

i i i

Page

i

i v

i v

v i

v i i

1

2

5

5

6

7

7

7

17

19

19

a4

28

28

32

37

43

Table - .. .................... 1 Specifications o f the PRT's Tested .....

............... 2 Themphysical Properties o f Reference Fluids..

3 Time Constant (T) f o r Hy-Cal i n Flowing Water.. ............... 4 Time Constant (T) f o r Hy-Ca1 i n Flowing O i l . . .................

.... 5 Predict ion o f Time Constant (r) for Hy-Cal i n Flawing A i r .

6 S m r y o f Response Time Correlations f o r Hy-Cal (100 ohm PRT) .................................................

.............. 7 Time Constant ( r ) f o r Rosemount i n Flowing Oi l . .

............ 8 Time Constant (T) f o r Rosemount i n Flowing Water..

9 Predict ion o f T i m Constant (T) f o r Rosemount i n Flcuing Air. ..........................................................

10 Sumnary o f Re~paiise Time Correlotions f o r Rosenr%nt (1000 ohm PRT) ................ ... ....................-........

LIST OF FIGURES

F i qure

1 A Typicai Response t o a Step Change i n Temperature Sensor ............. .........................................

2 Nominal Differences i n Rosemount and Hy-Cal PRT's.. ........... 3 Mechanical schematic o f Plunge Appartus.. .....................

........... . 4 Response Time Testing f o r PRT i n Flow Liquids.. ... ..................... .................... 5 Plunge Mechanism.. ...

.... .......... 6 Electronic Schematic o f Plunge Appartus.. .... ... .................... .................. 7 Electronics Package.. ..

................ 8 Response Time Testing f o r PRT i n F lowing A i r . .

............. 9 T VS l / h f o r Hy-Cal i n Flowing Wdter and O i 1..

Page

9

20

22

23

25

LIST OF FIGURES - Concluded

Figure Page

...................... 10 T VS 1 f o r Hy-Gal i n Floriisg A i r ... 26

......... 11 T VS l / h for Hy-Cal i n Flowing Water, O i l and A i r . 27

.................... 12 T VS l /h fo r Rosemount i n Flowing Oi 1.. 30

13 T VS l / h fo r Rosemunt i n Flowing Water.. .................. 34

.................... 14 T VS l /h f o r Rosemount i n Flowing Air.. 36

............ 15 T VS l /h fo r Rosemount fn Flowing Oi 1 and Air.. 38

LIST OF S'fHBOLS

Dsh Sheath diameter, m

h Heat transfer coefficient based on sheath diameter

ash. w a t t / d k.

k Thermal conductivity, watt/m k

MPE Maximum Percentage Error defined as = 100 x ('E - Tpredfctefi T~

P r Prandtl n&r, r Cp/k

Reynolds number, Dsh . " D

IJ

T Temperature, Oc

V Flow velocity, mlsec

X1'X2 Gap between the sheath and the sensing element

P Dynamic v i scosi t y , kg/m. sec

P Density, kg/m 3

T Time Constant, second

Subscripts

a

E

ti K

0

0 A

W

WO

WOA

A i r

Experimental

Hashemi an and Kerl i n

O i 1

O i 1 and A i r

Water

Water and O i l

Water, O i l and A i r

RESPONSE TIHE CORRELATIONS FOR PLATINUM RESISTANCE THERMOMETERS IN FLOWING FLUIDS

BY 1 Dhirendra Kunar Pandey , Co-Princi pal Investigator

Robert L. Ash,? Principal Investigator

SUmARY

The thermal response o f two types of Plat inun Resistance Thermcnneters

(PRT's), which are being considered f o r use i n the National Transonic Wind

Tunnel Fac i l i ty , were studied. Response time correlat ions f o r each PRT, i n

flowing water, o i l and a i r , were established separately.

1264.9 A universal correlat ion, T y 0 ~ = 2.0 + -7 f o r a Hy-Cal Sensor

(wi th a reference resistance of 100 ohm) w i th in an e r ro r o f 20% was estab-

l ished while the universal correlat ion for the Rosemount Sensor (with a

1105 6 reference resistance o f 1000 ohm), rOA = 0.122 + --, was found wi th a

maximum percentage e r ro r o f 30%. The cor re la t ion f o r the Rosemount Sensor

was based on a i r and o i l d ~ t a only which i s cer ta in ly not su f f i c i en t t o

make a correlat ion applicable t o every condition. Therefore, the corre-

l a t i o n needs more data t o be gathered i n d i f f e ren t f lu ids . Also, i t i s

necessary t o state tha t the calculat ion o f the parameter, h, was based on

the avai lable heat transfer correlations, whose accuracies are already

reported i n 1 i terature uncertain w i th in 20-30%. Therefore, the universal

response constant correlat ions established here f o r the Hy-Cal and

Rosemount sensors are consistent w i th the uncertainty i n the input data

and are recomnended f o r future use i n flowing l iqu ids and gases.

'~esearch Assistant Professor, Department of Mechanical Engineering and Mechanics, Old Dominion University, Norfolk, V i rg in ia 23508.

2 ~ h a i man, Department o f Mechanical Engineering, Old Dominion University, Norfolk, V i rg in ia 23508.

1. INTRODUCTION

Transducer response charac ter is t i cs are a c r i t i c a l element i n the de-

s ign and operation of cont ro l led mechanical systems. Temperature transduc-

e rs (thermometers) are an important c lass of instrunents used i n temperature

control , and the Pl at inun Resistance T h e m e t e r s (PRT) c lass o f thenome-

t e r s i s the subject o f t h i s invest igat ion.

The most systematic e a r l y work on measuring the time constant o f (glass

bulb) thermometers was developed by Harper [I] i n 1912. He observed the

influence o f f l u i d properties, convection and ag i ta t ion on the time constant

o f the thermometer. Subsequently, the denand for accuracy has changed the

design o f tenperature sensors. Goodwin [2] and Hornfeck [3] studied the

response time and thermal l ag o f t h e r m m ~ t e r s when they were placed i n a

wel l , and other more deta i led studies o f time-? ag i n sheathed indus t r i a l

thermometers can be found i n references [4-81.

Aikman e t a l . [5] and Looney [8] suggested the use o f heat t rans fer

c o e f f i c i e n t t o determine the e f f e c t i v e time constant. This idea was used

extensively by Kerl f n e t a l . [I)-13) i n establ ish ing a co r re la t i on o f the

t ime constant f o r several p l at inun resistance thermometers. Hashemi an and

K e r l i n [13] have reported recent ly a cor re la t ion f o r a Rosemount Sensor of

1000 ohm* Rosemount PRT, which was being considered f o r use i n the National

Transonic Wind Tunnel F a c i l i t y (NTF) a t NASA Langley Research Center. How-

ever, they had reservations about the genera l i ty o f the corre lat ion. There-

fore, the object o f t h i s study was t o v e r i f y o r improve the estimates and

character ize the response behavior o f these sensors. The u l t imate nb jec t ive

- *Platinun , ,sistance thermometers are characterized t y p i c a l l y by t h e i r ref - erence temperature resistance value.

i s t o predict the response character'istics o f these sensors i n the wind

tunnel environments o f the National Transonic F a c i l i t y (NTF) a t NASA Langley

Research Center.

The Plunge Method recomnended by ASTM [17] was used i n t h i s study t o

determine the time constant o f a Hy-Cal and Rosemount Sensor. Experimental

data were analyzed and compared wi th previous l i te ra ture . Thus, correla-

t ions t o predict time constants f o r each PRT sensor have been establ ished.

2. RESPONSE TIME CONSTANT

The behavior o f a sensor can be characterized by i t s response t o a

disturbance i n i t s surroundings. Such disturbances are a step change, a

1 inear ramp change, or a sinusoidal osc i l la t ion. A simple and accurate

method used i n t h i s study i s a step change as i l l u s t r a ted i n Figure 1. This

step change may be produced by plunging the sensor from a reference mediun

i n t o a moving f l u i d . Time constant i s then defined as the time required for

the sensor t o register 63.2% o f the temperature change. The time constant

o f a temperature sensor depends on the physical properties o f the sensor,

transport properties o f the f l u i d and the thermal environment. The thermal

environment can include effects due t o convection, conduction and radiat ion.

Turbulence in tens i t y and d is t r ibuted thermal capacities also a f fec t the time

constant.

A ihan e t al. [4] and Looney [8] suggested that a s ingle time constant

approximat ion of the 1 aq o f temperature-sensing devices i s often adequate

f o r determininq the ef fect o f the system lag on the control loop. This

s ingle time constant has been related t o the environmental conditions

through an external heat t ransfer coef f ic ient , h, and the suggested corre-

1 at ion takes the form:

where Cl and C2 are co r re la t i on constants. Recently, K e r l i n e t a?.

[3-131 have used t h i s idea extensively i n t h e i r work. They designated

as the in te rna l component o f the sensor t ime constant and C2 as the s ~ r -

face component of the sensor time constant. Their r e s u l t s were develcyed i n

terms o f a lumped parameter and a d i s t r i bu ted parameter approach f o r e s t i -

matinq C1 and h . For the Lumped Parmeter Approach:

whi le f o r the D is t r ibu ted Parameter Approach:

and

where

P = dens i ty o f the sensor

C~ = spec i f i c heat o f sensor

k = t h e ~ 1 8 1 conduct iv i ty o f sensor

r = outer radius o f sensor 0

r = radius a t which sensing element i s located ins ide the sensor. i

Note tha t 5 and C2 are t o t a l l y dependent on sensor properties.

Process temperature may change t h e i r nunerica'l values (due t o temperature

dependent properties), but, i n any case, C1 and C2 should not be

negative on physical grounds. The resu l ts o f Hashemian and Kerl i n 113)

contradicted t h i s non-negative requirement eor the Rosemount ' they tested i n

tha t a negdtive value f o r C1 was reported. That r esu l t w i l l be discussed

1 atgr.

3. HEAT TRANSFER COEFFICIENT

3.1 Heat Transfer Coeff icient i n Flowing Liquids

The accurate determination o f the time constant using Equation (1)

depends on the accuracy o f the heat t ransfer coef f ic ient estimate f o r the

sensing element. A f i r s t order estimate o f the heat transfer coef f ic ient

can be obtained by t reat ing the sensor as an i n f i n i t e l y long c i r cu la r cy l in -

der i n a cross flow. Numerous investigations on t h i s topic have been re-

ported i n the 1 i terature. McAdams' [14] correlat ion i s used widely by re-

searchers. That correlat ion f o r water was found va l id by Fand [15,16] over

the Reynolds nunber, Re, ranqe o f 0.1 < Re < lo5. McAdams' [14] correla-

t i o n can be expressed as

D h sh where Nu = Nusselt Nunber = -

k

Re = Reynolds Nunber = Dsh "

and

IJ c r Prandtl Nunber = 1

Watt h = heat t rans fer coe f f i c i en t , - m 2 ~

DSh = sheath diameter, m

Watt k = thermal conduct l v i t y o f f l u i d , -

mK m

U = f low veloc i ty , - sec

Kg u = Oynmicv iscos i ty , - m sec

Cp = Speci f ic heat o f f l u i d , Watt Sec

Kg K

McAt?.unsl co r re la t i on i s found t o be excel l e n t i n the Reynolds nunber range

c i t e d f o r Prandtl nunbers between 6.58 and 380. However, the present work

uses o i l w i th a Prandtl nunber on the order o f 9000 where no ca r re la t i on

e x i s t s i n t he l i t e r a t u r e . Engine o i l was selected t o t e s t the response

cha rac te r i s t i c o f the Rosemount because o f i t s d i e l e c t r i c e f f e c t s i n f lowing

water as recommended by the manufacturer. Therefore, equation (6 ) must be

extended t o incorporate t h i s f l u i d fo r est imat ion o f the heat transfer

coe f f i r4ent .

3.2 Heat Transfer Coef f i c ien t I n Flowing A i r

The avai lab le 1 i t e ra tu re on heat t rans fe r between a cy l inder placed

v e r t i c a l l y i n f lowing a i r was revfewed thoroughly. H i l pe r t ' s cor re la t ions

[19] were used i n t h i s work as stated betow:

Here the Prandtl nunber i s 0.71.

4. DESCRIPTION OF THE SENSORS

Two Platinun Resistance Thermometers (PRTis) o f d i f fe ren t designs were

tested i n t h i s study and are shown schematically i n Figure 2. (lne i s a

Hy-Cal Sensor (100 ohm reference resistance) wi th sheath dianeter, Dsh =

0.635 cm (Figure 2a), while the other i s a Rosemount Sensor (1000 o h refer-

ence res is tance) w i t h sheath diameter, DSh = 0. bi34 cm (F igure 2b). It

should also be noted that the PRT's i n t h i s study had d i f fe ren t internal

sensor geometries and the d i f fe ren t element/shrcud dime.~sions resul t i n

d i f fe ren t flows around the sensing element. Both PRT's vere designed for

d i rec t immersion (wet type - no thermal wel l ) with the ,' 2ath o f each ?RT

perforated a t the sensing end t o allow f l u i d f low around the sensor. The

specif icat ions o f these sensors are sunmarized i n Table 1.

5. EXPERIMENTAL APPARATUS

The purpose o f t h i s experiment i s t o obtain the time constants (T) of

Platinun Resistance Thermometers (PRT1s) by using the Plunge method as de-

scribed i n reference [17]. Subsection 5.1 deta i ls the apparatus f o r the

measurement o f time constants for PRTis i n flowing l i qu ids while Subsection

5.2 explains the instrunents used i n flowing a i r .

5.1 Response Time Testing f o r PRT i n Flowing Liquids

The schematic diagram o f the Plunge Method which was used t o obtain the

time constants f o r the PRTis i s shown i n Fiqure 3. A photograph o f t h i s set

up i s also given i n Figure 4. The experimental apparatus consisted o f a

mechanical system and an electronics system.

'pi * '

88

4 c

m d

iam

(.

348

in. 1

Sens

ing

elem

ent

2a 1

000

$2 P

RT (.

25 in

. di

am

P . 2b

100

R P

RT

Figu

re 2

- No

min

al d

iffer

ence

s in

Ros

emou

nt a

nd H

y-Ca

l PR

T's.

Speci f i c d t i o n

Model

Seri a1

Sensor Type

NO. ~f E l wnen ts/RTI)

NO. o f Ledd Wires/Elenwnt

Sheath Diameter

Table 1

Speci f ications o f the PRT's Tested

134FLA 48

19399

Wet

1OOO ohms

1

4

Wet

ORlGhYAL PAGE !3 OF POOR QUALm

Figure 4. - Response time testing for PRT i n flowing liquids.

A. Mrchanical System

The mechanical system had the fcl lowing components:

I. Tank - A stainles; steel tank wi th a d i e t e r o f 45 cm and height o f

15 cm was employed. This tank was attached t o a ro ta t ing tab le whose rota-

t i o n w z - control led electronical ly . Further, the tank was rotated 3 t a

specif ic speed t o create a moving mediun around the PRT when i t was im-

mersed.

11. Pneunatic Plunge Mechanism - A solenoid-controlled, pneunatic

plunge m c h d n i a held the PRT above the f l u i d mediun and, on cmand, moved

i t f ran one thermal environment t o the other creating the step tenperature

change. This mechanism alsc i n i t i a t e d a d i g i t a l recording, \ ' a a micro-

switch, o f the PRT's output during the step change. The recording was

star ted j u s t before the PRT reached the f l u i d surface. An explanatory view

o f t h i s mechanism i s shown i n Figure 5.

111. Microswitch - The microswitch was used t o i n i t i a t e the oscilloscope

recordings j us t before ihe probe reached the f l u i d surface.

I V . A i r Blower - The step temperature input was produced by heating the

PRT, with control led hot a i r from a blower, t o a steady state temperature

which was nominally 8'C above the f l u i d temperature i n which the sensor was

p 1 unged . 0. Electronics System

The electrcnics system i s based on a constant current source (Figure 6)

t o act ivate the PRT as show i n Figure 7. This system had the fol lowing

components:

V. D ig i ta l Storage Oscilloscope - This was used t o store the PRT's

output h is to ry when i t was subjected t o the temperature step change.

.,' - ' c - OFl"34.5;~ F';.. .: 8 3

OE POGR Qi'kLm

Figure 5. - Plunge mechanism.

Calib

rate

d so

urce

( 1

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lOO

Q St

ep

calib

rate

d re

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or -

inpu

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curr

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Bure

au o

f

Figu

re 6

. - E

lect

roni

c 'h

emat

ic

of p

lung

e ap

para

tus.

Figure 7. - Electronics package.

V I . 'Standard' Constant Current Source

V T T . Current and Voltage Meters

Test Procedure

The tes t procedure consisted o f the fol lowing steps:

(1) F i l l ha l f of the ro ta t ing tank with f l u i d .

(2) Put thermocouples i n t o the moving f l u i d t o measure the temper-

ature.

(3 ) Instal 1 the PRT i n the plunge mechanism.

( 4 ) Set the a i r pressure a t 20 ps i needed f o r the plunqe mechanism t o

dr ive the PRT smoothly i n t o and out o f the ro ta t ing tank.

(5) Set the posi t ion of PRT r a d i a l l y i n t o the ro ta t ing tank where the

ve loc i ty o f f l u i d wi th in 1 mlsecond i s assured.

(6) Heat the sensor by an a i r blower up t o 5 - 8'C above the f l u i d

temperature.

(7) Set speed o f tank with electronic control i n motion wi th agreement

of Step 5.

(8) Put a l l the electronics instrunents on.

( 9 ) Adjust the immersion depth o f the PRT i n t o the flowing f l u i d s t o

avoid conduction error along the length o f the sensing element.

(10) Connect the microswitch t o the scope t o record the response o f the

o f the PRT.

(11) Maintain 1 ma current across the PRT by adjusting 100 ohm working

standard.

(12) Immerse the PRT i n to the ro ta t ing f l u i d using the plunge mechanism

actuation switch.

(13) Wait f o r the voltage across the PRT t o reach a steady state.

(14) Move tho sensor out o f the ro ta t ing tank,

(15) Observe the response behavior o f the PRT on the scope and calcu-

1 ate the time constant .r which i s equal t o the Sime required f o r

a sensor output t o r e g i s t e r 63.2% of a temperature step change.

(16) Take a t least three readings f o r each experimental condi t ion t o

minimize personal and inst runenta l errors.

(17) Change the speed of r o t a t i n g t a b l e t o get the more experimental

data a t d i f f e r e n t condit ions.

5.2 Response Time Testing for PRT i n Flowing A i r

I n order t o proper ly i n t e r p r e t the dynanic behavior o f PRT's i n a cryo-

genic gaseous mediun, the next l o g i c a l step was t o observe t h e i r behavior i n

a gaseous mediun ( a i r ) a t room temperatures. Furthermore, i t was desired t o

attempt t o p red i c t PRT gaseous response using the cor re la t ions developed

from the l i q u i d tests.

A low speed, open loop wind tunnel was used t o determine transducer

response over the speed range o f 5 t o 45 mlsec. That tunnel was described

b r i e f l y by Daryabeigi e t al. [20]. The present experimental setup used the

sane mechanical and e lec t ron ics systems as de ta i l ed i n Subsection 5.1. The

wind tunnel conf igurat ion i s shown i n Fiqure 8.

Test Procedure

(1) Switch on the a i r wind tunnel.

(2) Put the P i t o t tube p a r a l l e l t o the a i r f low a t the loca t ion where

the PRT i s supposed t o be.

(3) Read the presure reading across the p i t o t tube using d i f f e r e n t i a l

pressure transducer.

(4) Read t h e temperature o f t h e f l o w i n g a i r us ing a d i g i t a l

thermocoupl e.

( 5 ) P u l l the P i t o t tube close t o t h e wal l of the a i r wind tunnel.

(6) Repeat the procedures of the plunging method as out1 ined i n Sub-

sect ion 5.2 f o r f lawing 1 iqufds.

6. RESULTS AND DISCUSSION

D i s t i l led water, engine o i l and a i r were used as the forced convection

media, and t h e i r t ransport proper t ies are sunmarized i n Tbt le 2.

To minimize the uncer ta int ies involved i n measwing the temperature

dependent f low properties, the f lowing f l u i d was kept a t r r .mperatuze.

Errors associated w i th maintaining the sensor a t constant tt ;ture, un-

c e r t a i n t y i n the f l u i d f low ve loc i ty , in f luence o f temperature dependent

sensor proper t ies and f luc tua t ions o r d r i f t i n the e lec t ron ics could nat be

avoided absolutely which i s the basis f o r the estimated uncer ta inty o f 25%.

The present data are presented i n two ways: one where the time constant i s

considered as a funct ion o f heat t rans fer c o e f f i c i e n t (h) only, which re -

qui res an addi t ional heat t ransfer co r re l ations, wh i le the other way repre-

sents the t ime constant as a func t ion o f the Reynolds nunber (?e) and

Prandtl numbers. I n the fo l low ing sections, :he r e s u l t s o f response time

fo r each PRT are discussed.

6.1 Response Time f o r the Hy-Cal Sensor i n Flowing L iquids

The time constant, T, f o r the Hy-Cal Sensor determined experimental l y

i n water and o i l , i s shown i n Figure 9 a; a funct ion o f the inverse o f heat

t rans fer coe f f i c i en t . Numerical values used i n t h i s f igure are displayed i n

Tables 3 and 4 f o r water and o i l , respect ive ly . Present data fit the curre-

l a t i o n , rWO = 1.597 + 2083*3 (which i s also shown i n Figure 9). t o w i th in h

a maximum e r r o r o f 1.4 percent.

Tabl

e 2

Then

noph

ysic

al P

rop

erti

es o

f R

efer

ence

Flu

ids

[Ref

. 181

I -

Ai r

297

1.19

1

1.95

5 x I$

0.02

60

0.71

- P

rop

erty

. .

Ref

eren

ce T

empe

ratu

re

( K !

Den

sity

' (K

CJ/III

~)

Vis

cosi

ty

(Kg/

m

s)

Ther

mal

Co

nd

uct

ivit

y (w

/m

K)

Pra

nd

tl N

umbe

r *

Sym

bol

T P v k Pr

Wat

er

295.

3

997.

06

9.54

0.60

6

6.58

. .

Eng

ine

Oil

296.

5

' 8'

36.1

0.69

6

0.14

42

. .

9T39

Table 3

Time Constant (t) for Hy-Cal i n Flowinq Hater

Table 4

Time Constant ('t) for By-Cal in Flowing O i l

I n addition, t o avoid the need of'heat t r a n s f ~ r correlations, the pres-

ent data (Tables 2 and 3) can be represented as

t o wi th in a maximum error o f 4.8%.

6.2 Response Time for the Hy-Cal Sensor i n Flowing A i r

Table 5 displays the time constant data p lo t ted i n Figure 10 f o r the

Hy-Cal Sensor (100 ohm PRT) i n flowing air . Experimental data are conpared

w i t h the t ime constant p red ic ted by a correlat ion, rWO = 1.597 + 2083.3

h

(based on water and o i l data) and Hashemian and Ker l in 's 1131 correlation,

'HK = 1.6 + - 4168 . The predicted time constant ruo i s 50% higher than h

t h e experimental data, wh i le rHK [13] p r e d i c t s 18551 h igher than the

experimental data. It i s important t o note tha t the present correlat ion

WO' based on water and o i l data, cannot be t rea ted as universal. The

e r ro r o f 50% i s consistent wi th the errors which occur i n predict ing heat

t ransfer coef f ic ient f o r a i r by using the heat t ransfer correlat ion based on

water data (Equation 6). To establ ish a universal correlation, one has t o

use a1 1 the response time data observed i n every f l u i d and should expect an

appreciable e r ro r o f 20-30%. Recently, Churchil l and Bernstein [21] have

reported a general i zed correl at ion f o r heat transfer from sol i d cy l inders

placed v e r t i c a l l y i n the f low o f l i qu ids and gases wi th in the uncertaint ies

of 20-25%.

Therefore, the present data obtained i n f lowing water, o i l and air, 1264.9 shown i n F igure 11, are co r re l a ted by an equation, rum = 2.0 + -

h

I

n

C U

B = C

u ( 3 - Q ) s y y

h . *

.d

.. - 0 . 0 ;

w

Q) a

3

.

c h . I

O N y

c u w - 2

I E ? y

C

u I.'

W I.'

s

u,

0 .

I n o -

rC:

(3 -

C3 F

b m u ,

e

J

m u ,

=

2

o ~ m

' 0 r h F - N - h

m

W . ( O

m

u,

w m - r c u - IC)-

V ) ' m r 0 u e . q . = " Z r r w m e

% ? I W y * - Q , h U ) W

g r o o h u , ~ r n e m m h o

Q l h r D I C )

- r n e c n r ~ w F + d h r n Q ) , - + N N C U

h-

z z z

C O h V ) -

I

I n o Q '

a ' -

0-

- ? ,

within the maxtun error of 20%. The values o f heat transfer coeff ic ients

based on sheath dianeter were obtained by using Equation (6) f o r water and

o i l and Equation (7) for air. Such correlation can be considered as a uni- r

versa1 correlation fo r the &<a1 Sensor (100 ohn PRT) t o predict the time

constant i n any flowing fluids. Also, the a i r data are f i t t e d by the corre-

1 a t ion T = 1.3 + 1368* within the muimun error o f 2.5%. A1 1 three h

co r re l ations, tA, 'YO, and TrWOAs are compared with the experimental

data and Hashenian and Ker l in8s [13] correlation i n Table 5. tHK [13] pre-

dicts larger errors overal l because i t was based on water data only. There-

fore, tHK [13] cannot be t reated as a universal correlation. Response

time correlations f o r t&-Cal Sensor are sunmarized i n Table 6.

6.3 Response Time fo r the Rosenount Sensor i n flowing Oi 1

Figure 12 shows the response characteristics fo r the Rosenount Sensor

(1000 ohn PRT) i n o i l . A correlation was established using the o i l data

displayed i n Table 7. This correlation, T,, = 0.132 + 12880S predicts the h

response time correctly to within an error of 1.4%. Present resul ts are

canpared with Hashemian and Ker l in 1131 i n Table 7. It i s important t o note

that the Hashenian and Ker l in 1131 correlation predicts negative time con-

stants i n a l l cases. Note that the Hashenian and Ker l in [ I31 correlation

was based on the i r a i r data only. herefore, the appl i c a b i l i t y o f t he i r 1 ; 1 .

correlation i n flowing o i l i s questionable.

6.4 Response Time for the Rosenount Sensor i n Flowing Water

The information reported i n references 113, 223 does not recommend the 1 i testing o f the Rosemount Sensor i n flowing water. The reason i s assocfated 1 1 with the d ie lect r ic properties o f the Rosenount Sensor. Above al l , i t was I ;

Table 6

Sunrnary o f Response Tine Correlations for Hy-Cal (100 u h W

L -.- ..

FLUIDS USED

Water and

o i 1

A i r

water, Oil and Air

.Water

I 11 31 I I r

CORRELATI oris

2083.3 f~ = 1.597 +,r.

.TA" 1.3 + F 1264.9 T m 1 ' 2 . 0 + ,,,

= 1.6 + 4168 'HK . h

MPE

1.4

2.5

20

-

*

Table 7

T i m e Constant ( r ) for Rosemount in Flowinn O i l

decided t o t es t t h i s sensor t o detemiine i t s response behavior i n flowing

water. It was observed that i t has a faster responsive nature i n flowing

water than i n o i l . Keeping these uncertaint ies i n mind, the water data

displayed i n Table 8 i s correlated separately. The data i s p lo t ted i n Fig-

ure 13. Further, the water data i s not used t o establ i sh a universal re-

sponse time correlat ion f o r t h i s sensor. Note tha t from Table 8, again

Hashemian and Ker l i n ' s [13] correlat ion predicts negative time constants i n

i n f 1 owing water. The present correlat ion for the water data, rU = 0.068

i- i s found t o wi th in an e r ro r o f 0.9%. h

6.5 Response Time f o r the Rosemount Sensor i n Flowing A i r

The response time a i r data given i n Table 9 are represented by an equa-

t i o n T A = -1.983 + 309*5 w i t h i n an e r ro r o f 2.5%. Experimental data h

p lo t ted i n Figure 14 are compared with the Hashemi3n and Ker l in 1131

r e s u l t s . The existence o f negative values f o r C1, reported i n the 1 i te ra-

tu re (reference 13) as well as found i n the present correlation, are obvi-

ously inconsistent with the known fac t that response time i s pos i t ive even

as heat transfer coef f ic ient increases without bound. In addition, the

present authors have t r i e d other possible ways t o correlate the experimental

data i n the fol lowing ways:

( A ) TA = 5962 Re -'754 P r '*333 wi th in the maximum error o f 5%.

and

(6) T A = -2.809 + 1393 Re -'554 P r -*333 wi th in the maximum error o f

2.8%.

Note that Equations (A) and (8) w i l l reduce t o zero and -2.809, respec-

t i ve ly , as Re approaches t o i n f i n i t y . Again, the predicted resu l ts become

Table 8

Time Constant (r) for Rosemount I n Flowing Water

inconsistent wi th the t rue expected values cif response time. Some other

parameters, 1 i ke Reynolds nunbers b. -4 on sensqr dimeter, gap between the

sheath and sensor, and the r a t i o o f the hole dianeter on sheath t o the gap

were tr ied, but the values o f C1 remained negative.

I t i s necessary t o note tha t the Rosemount Sensor's behavior does not

ljecolne questionable i n flowing l i qu ids i n which the values o f Cl were

never found t o be negative. Therefore, i t i s possible that a universal

correlat ion f o r the Rosemount Sensor ex is ts f o r 1 iquids other than water.

- I n add i t ion, t he o i l and a i r data were co r re l a ted by an equation rOA - 1105.6

0.112 + - within the er ror o f 30%. Note that C1 i s not found t o be h

negative. The a i r data are presented i n Figure 15. The er ror o f 30% i s not

1 arge, once oqe i s 1 wking f o r a generalized correlat ion applicable t o any

situations. Mote that t h i s er ror i s also associated wi th the values o f h

which were determined from the heat transfer correlat ions 114, 191 reported

i n l i t e ra tu re . Heat transfer correlat ions are found wi th in the er ror of 20-

30%.

However, the authors believe that a universal correlat ion f o r t h i s

sensor can be found by having more data i n flowing a i r and l iquids. We also

b e l i e v e t h a t a neqative Cl i n a i r correlat ion rA (Table 10) i s associ-

ated with the experimental data given i n Table 9. There i s a systematic

e r r o r of 2 seconds between experimental data and predicted values by r0 =

0.132 + 1 2 8 8 . 5 l t based on o i l data (Table 7).

7. PREDICTION OF T IME CONSTANTS AT CRYOGENIC CONDITIONS

This section uses the response time correlat ions as establ ished f o r the

PRT's t o predict time constants a t a given cryogenic conditions. Note that

Table 10

A i r 2326

t HK =-= .6+ - h [UI

-

the conditions used here, don't represent the real s i tuat ion occurring i n

National Transonic Facil i t y a t NASA, Langley Research Center.

EXWLE: Estimate the time constants fo r the Hy-Cal and Rosemount Sensors

exposed t o Nitrogen gas flowing at 25 m/second i n cryogenic wind tunnel.

The gas i s maintained at 1 atmospheric presure and temperature o f 200 K.

Thennophysical properties o f Nitrogen Gas [Ref. 181 are given below:

P r = 0.747 (closed t o a i r )

Hy-Cal Sensor

Using Equation 7

Present response time correlation estimates

UOA = 2.0 + = 7.40 seconds 234.2

and

T~ = 1.3 + 1368*5 = 7.14 seconds

234.2

bile Hashemian and Kerl i n's co r re la t i on [13] predicts

'HK = 1.6 + 4168 = 19.40 seconds

C131 234.2

The universal correlat ion, rUOA which i s based on water, o i l and a i r data,

predicts a 3.6% larger e r r o r than a co r re la t i on rA based on a i r data only.

Such an e r ro r must be expected from a universal corre lat ion. It i s neces-

sa ry t o n o t e t h a t Hashemian and Ker l i n ' s correlat ion, rHK 1131 overest i -

mates t h e response t ime by 172%. Such a discrepancy i s j u s t i f i a b l e because

t h e i r c o r r e l a t i o n was based on water data only. Therefore rHK 1131 cannot

be used i n f lowing gases. Thus t h e u n i v e r s a l i t y o f Hashenian and K e r l i n ' s

[13] cor re l at ion i s questionable.

Rosemount Sensor:

Using Equation 7,

Present response time correl at ion estimates

OA = 0.112 + 1105*' = 5.47 seconds 206.4

and T A = -1.983 + 1309*5 = 4.36 seconds 206.4

Using Hashemian and Ker l in 's [13] correlat ion, the time constant i s computed

The correlat ion rOA which i s based on o i l and a i r data gives 5.47 seconds,

wh i l e T~ based on a i r data o n l y p r e d i c t s 4.36 seconds a t the sane con-

d i t ions. The r e l a t i ve e r ro r i s found t o be wi th in 18%. Such er ror one

shoul d expect from a universal cor re la t ion l i k e rOA = 0.112 + 1105.6. It

h

i s important t o note t ha t Hashmian and Ker l in 's cor re la t ion 1131 does not

srjrvive i n such an environnent, although t h e i r cor re la t ion [13J was based on

t h e i r a i r data. Furthennore, rHK [13] also predicts negative time constants

i n fl owi ng water tnd o i l (Tables 8 and 9).

8. CONCLUSIONS AND RECOMENDATIONS

Based upon the experiment a1 measurements developed i n t h i s invest iga-

tion, i t i s possible t o ccnclude t ha t the response time o f ven t i l ated, p l at-

i nun resistance thermometers can be correl ated wi th the reciprocal o f the

heat transfer coef f ic ient i n a given f lu id . The experimental data corre-

lated f o r the m 6 a l and the Cdosemount sensors are given i n Tables 6 and 10,

respectively . Furthermore, a un ive rsa l c o r r e l a t i o n rWOA = 2.0 + 1264*9, f o r the

h

Hy-Cal Sensor w i th in the uncertaint ies o f 20% has been established. A uni-

versal c o r r e l at i o n rOA = 0.112 + 1105*6 , f o r the Rosenount Sensor based h

on o i l and a i r data i s found t o be wi th in the uncertaint ies o f 30%. Such

er ror one should expect f r an a universal cor re la t ion which can be applied t o

any flowing mediun i n which the Frandtl nunber varies frorr, 0.7 t o 10,000.

It i s necessary t o mention tha t the important paraneter, h, i s computed

f ran heat transfer correlat ions [14, 191 h i c h are already reported un-

cer ta in t o wi th in 20.30%.

An exanpl e based on cryogenic conditions was also set up t o t e s t the

present and previous response time correlations. It was found t ha t the

present response time correl ations maintained i t s accuracies w i t h the ex-

per imental data, whl le Rshemian and Ker l in 's correlations, rHK [13] were

determined inappl icable t o every situation. The universal i t i e s of t h e i r

cor re l ations [13] were found h iqh ly quest ionable.

In conclusion, we reconmend our universal response time correl a t ions

fo r each PRT t o predict time constants i n any f lowing medim. We also

reconmend qathering more response time data so that the e r ro r as found i n

establ ishing a universal cor re la t ion could be reduced.

Harper, D.R., 3d, nlhermanetric Lag,' B u l l e t i n BS, Vol. 8, 1912, pp. 659-714.

Goobrin, U.N., Jr., 'Response Time and Lag o f a Thermaneter Element Mounted i n a Protect ing Case,' Trans. E l e c t r i c a l Engineering, Vol. 64, 1945, pp. 665-670.

Hornfeck, A.J., "Response Character ist ics o f lhermorneter El enent," Trans. ASME, Vol. 71, 1349, pp. 121-133.

Aikman, A.R., k M i l l a n , J. and h r r i s o n , MU., "S ta t ic and mnanic Performance o f Sheathed Indust r ia l thermometer^,^ Trans. Society o f Instrunent Technology, Vol. 5, No. 4, 1953, pp. 138-151.

Fi shwick, W., "Time-Lags i n Thennometer hckets,' Trans. Society o f Instrunent Technology, Vol. 4, No. 1, 1952, pp. 29-49.

Ilrl ler-Gi rard, 0. , 'The mnanics of Fi 1 led Temperature Measuring 9 s - tems," Trans. ASME, Vol. 77, 1955, pp. 591-595.

Linahan, T.C., 'The Qynanic Response o f I ndus t r i a l l h e n n m t e r s i n Wells," Trans. ASME, Vol. 78, 1956, pp. 759-763.

Looney, R., I1Method f o r Presenting t t e Response o f Temperature Measur- ing Systems," Trans. ASME, Vol. 79, 1957, pp. 1851-1856.

Kerl in, T. W., Hashmi an, H.M., and Petersen, I(. M., "Time Response o f Temperature Sensors," ISA Transactions, Vol. 20, No. 1, 1981, pp. 65- 77.

10. Kerl in, T.W., "The E f fec t o f F l u i d Conditions on t h e Response o f Temp- era t ure Sensors ," Oak Ridge National Lab. 40X-40472C, 1981.

11. Hashenian, H.M. e t a l . "Resistance lhermmeters Response Time Charac- t e r i z a t ion," presented at 28th Southeastern Conference and Exhibi t , Richnond, Virginia, May 1982.

12. Kerl in, T.W. e t al., llksponse o f Insta! led Temperature Sensors," Temp- erature, I t s Measurement and Control i n Science and Industry, Vol. 5, Part 5, 1982, 1357-1366.

13. Hashenian, H.M. and Kerl in, T.W., H I n - s i t u Response Time Test in o f P I atinun Resistance Thermometers i n Fl owl ng Gases,11 NASA CR-172t50,

4 1984.

14. kWans, W. H., Heat Transnissfon, l h i r d Ed., k ( j r a w H i l 1 , New York, 1954.

15. Fand, R. M., "Heat Transfer by Forced Convection from a Cyl i n d r i c a l t o Water i n Cross-flow," Internationa: Journal o f Heat and Mass Transfer, Vol. 8, 1965, pp. 995-1030.

16. Fand, R.M. and Keswani, K.K., 'The Influence o f Property Variation on Forced Convection Heat Transfer t o L i u i d ~ , ~ International Heat and Mass Transfer, Vol. 15, 1972, pp. 1515-1\36.

17. ANSI/ASME, €644-78, "Standard Methods for Testing Indust r ia l Resistance Thermometers," 1979 Annual Book of ASTM standards, Part 44, pp. 820- 842.

18. Holman, 3. P., Heat Transfer, Fourth edition, McGraw-Hill, New York, 1976.

19. McAdans, W. H., Heat Transmission, Third edition, McGraw-Hill Book Company, New York, 1954, p. 269.

20. Daryabeigi, K., A s C . R. L. and Gertnain, E. F., "Measurement of Convective Heat Transfer t o Sol id Cylinders Inside Ventilated Shrouds," AIAA-84-1725, presented a t AIM 19th. Thermophysics Conference, Snow- mass, Colorado, 1984.

21. Churchill, S.W. and Bernstein, M., 'A Correlat ing Equation f o r Forced Convection from Gases and Liquids t o a Circular Cyl inder i n Cross- fly,'' Journal o f Heat Transfer, Trans., ASME, Series C, Vol. 99, 1977, pp. 300-306.

22. Bul l e t i n 1341, Rosemount Engineering Company, September 1965.