N A S A TECHNICAL

M EMORANDUM

X

wo<C

NASA TM X-2945

FIGURE-OF-MERIT CALCULATION METHODS

FOR ORGANIC HEAT-PIPE FLUIDS

by James F. Morris

Lewis Research Center

Cleveland, Ohio 44135

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • NOVEMBER 1973

1. Report No.

NASA TM X-29452. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

FIGURE-OF-MERIT CALCULATION METHODS FORORGANIC HEAT-PIPE FLUIDS

5. Report DateNovember 1973

6. Performing Organization Code

7. Author(s)

James F. Morris8. Performing Organization Report No.

E-7632

9. Performing Organization Name and Address

Lewis Research CenterNational Aeronautics and Space AdministrationCleveland, Ohio 44135

10. Work Unit No.

503-2511. Contract or Grant No.

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D. C, 20546

13. Type of Report and Period Covered

Technical Memorandum14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

With only chemical formulas and operating temperatures specified, selected correlating equa-tions and tables of chemistry-effect functions allow estimates of figures of merit for organicheat- pipe - fluids.

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

Heat pipesHeat transferHeat-pipe fluids

18. Distribution Statement

Unclassified - unlimited

19. Security Classif. (of this report)

Unclassified20. Security Classif. (of this page)

Unclassified21. No. of Pages

12

22. Price*Domestic, $2.75Foreign, $5.25

*For sale by the National Technical Information Service, Springfield, Virginia 22151

FIGURE-OF-MERIT CALCULATION METHODS FOR ORGANIC HEAT-PIPE FLUIDS

by James F. Morris

Lewis Research Center

SUMMARY

With only chemical formulas and operating temperatures specified, selected corre-lating equations and tables of chemistry-effect functions allow estimates of figures ofmerit for organic heat-pipe fluids.

INTRODUCTION: SELECTING ORGANIC HEAT-PIPE FLUIDS

Some organic chemicals perform adequately as heat-pipe fluids and offer specialapplication advantages (refs. 1 to 3). The heat-pipe potentialities of such compoundsdepend on their properties as indicated by the simple figures of merit described in

reference 4:

"zero-g figure of merit" or "liquid transport factor":

L = VVZ (1)

"g-field figure of merit":

G=^i (2)pl

"nucleation tolerance factor":

k,a ;-=—- (3)Vv

where CT, is surface tension, p, is density, X, is latent heat of vaporization, M? isviscosity, k, is thermal conductivity - all of the liquid; and p is saturated-vapordensity.

Equations (1) to (3) are convenient for screening heat-pipe fluids. However, tabu-lations of the properties necessary to compute these figures of merit over wide temper-ature variations are often unavailable for less common organic compounds. Fortunatelyreferences 5 and 6 provide correlations collected from numerous sources to predictphysical characteristics of various chemicals as functions of molecular formulas andoperating temperatures only. So this minimal information allows estimations and com-parisons of heat-pipe figures of merit for organic fluids. The present report comprisesselections of appropriate equations, conversions, and chemistry-effect functions to en-able such screening,,

CALCULATION METHODS: PHYSICAL PROPERTIES AND FIGURES OF MERIT

Unless otherwise indicated input variables and results of the following equationsbear international units (SI, mksa). Using this system required numerous conversionsin the physical- property correlations, which come from long- established chemical-engineering references (refs. 5 and 6). And because these expressions relate to chem-istry and thermodynamics, the concept of the mol naturally arises: the cgs gram-mol,the British pound- mol, but the mksa gram-mol (ref. 7) not the mksa kilogram-mol. Sothe molecular weight M appears here as grams per gram-mol. This detail is, ofcourse, very important in preventing thousandfold errors during kilogram transforma-tions of the many mol- based characteristics.

Except M and the gas constant R (8.314 (J)(K~ )(mol~ )), though, the dimensionsof the physical properties in this report involve only the usual mksa units (C , (J)(kg~ )(KT1); k, (JXm^Xsec^XK-1); P, (NXm'2); T, K; X, (JXkg'1); M, (NXsecXm'2); P,

_O _ 1

(kg)(m~ ); and a, (N)(m~ )). The appendix defines the symbols, and reference 5 givesunconverted versions of equations (4) to (23).

INPUT VARIABLES

Computing figures of merit for an organic heat-pipe fluid begins with specificationof the chemical formula (CF) and the operating temperature T, of the liquid. Usuallythe normal boiling point T, is also available through the literature or simple testing.And because correlations leading to k^, X,, ju^, a,, p,, and py depend strongly onTfe a well-deter mined value of this variable is desirable. But if such a T, is lacking,the first equation of the next section yields a reasonable estimate.

NORMAL-BOILING AND CRITICAL POINTS

Equations for normal-boiling and critical points are given in this section.

Normal boiling temperature:

B- (4)

The parachor [p] and molar refraction fRpTI are sums of CF effects taken directlyfrom table 3-285 of reference 5 (or table 3-287 for [P]). And B is a chemistry-dependent constant from table 3-286.

Critical- point temperature and pressure:

T c =— 2- (5)

100

p = 1.013X1Q9 MC t

Here again SA™ and SAp result from summations of CF contributions listed intables 3-288 and 3-289 of reference 5.

Normal-boiling-point latent heat of vaporization:

RTcTbln

1.013xlOD

(Tc-

Critical-point compressibility factor and density:

z"= 5 (8)/ AT.IVI

3.43 + 0.006714. 184xl06)

cp = - S^-MXIO"*3 (9)

Z RTc c

Normal-boiling-point liquid density:

p, h = P_ 1. 981 + 0. 422 log £ (10)L, D C \ r I

1.013xlOa/

Having these normal-boiling and critical characteristics enables the following eval-uations of physical properties necessary to compute the heat-pipe figures of merit.

SATURATED- FLUID PROPERTIES AT LIQUID OPERATING TEMPERATURE

Saturated-fluid properties at liquid operating temperatures are given in this section.

Saturated- vapor pressure and density:

P . p / x 10(0. 137-0. 0364a')B'

where

\6TB' =36-^- 35 -[— I + 42 In—l- (12)

Tc/ Tc

and

log

a' =0.878+ 2.11 1.013X1CT (13)

The compressibility factor Z is now required to obtain the saturated-vapor den-sity p from the corresponding pressure P and temperature T,. Table I worked up

V V if

from data presented in reference 6 allows interpolations of Z as a function of ZV trf

TZ,r=VTc ' a n d Pv,r= Then

Liquid density:

PVM x 10-3

(14)

(15)

The saturated-vapor density at the normal boiling point py b results from equation (14)and the preceding paragraph used with Tb and P ^ = 101 325 newtons per squaremeter.

Surface tension:

-'v>M

x 10-15 (16)

For this equation a summation of CF effects taken from table 3-294 of reference 5 pro-duces the parachor [p].

Latent heat of vaporization:

RT^TVIn

XT,- xO.38

MxlO" 3 \ 1. 013x107 (T

(17)

Constant-pressure specific heat and thermal conductivity:

(18)

Summing CF contributions from table 3-291 of reference 5 and multiplying by 4184/Mgive the liquid specific heat at 20° C to be used in equation (18). With the resultingCP,Z

k, =4'27C

x 10-8ti (19)

where

T - 303.15 or-^c \ 2

x 8. 8 x 10

T, - 303.15 or-^1

T - 303.15 or -^

- 303.15 or-^

(20)

unless this value is less than unity; then a = 1.0 is used. And

Tb x 8. 8 x 10

according to reference 5, which indicates that this constant applies "at 30° C for mostliquids or at TY2 for low boilers such as methane, N0, and ethylene . . . . Calculated

ovalues of a < 1 should be taken as unity, and at temperatures other than 30 C (orTc/2), a may be assumed to vary linearly between values given by the Eq. [(21)] at30° Cand 1. 0 at T . "

C

Liquid viscosity:

= 1.167pJ/2 x 10 x " / (22)

where B" is another sum of CF effects from table 3-297 of reference 5.

FIGURES OF MERIT

Substituting fluid- property values from the equations of the preceding section intoequations (1) to (3) yields figures of merit for organic heat-pipe fluids:

L = VV^ = 06X15X17) (

M (22)

(15)(2')

(gf)

DISCUSSION: USE OF CALCULATED FLUID PROPERTIES AND FIGURES OF MERIT

The selected correlations for physical properties involve generally modest averageerrors, which references 5 and 6 discuss. But the question of accuracy is a moot one

since these expressions are of value only in the absence of the necessary compilationsof experimental data.

When such collections of physical properties are unavailable, an initial screeningwith only L (eq. (!')) and G (eq. (2')) estimates seems appropriate for conventionalheat pipes. Then N (eq. (3')) comparisons for the more promising fluids would furtherreduce the field. This is a desirable approach because L is the most widely used fig-ure of merit, because G bolsters the meaning of L and depends only on results neces-sary to compute L, and because k, and p required for N involve time-consumingcalculations.

Neglecting p at the outset simplifies the calculations of p, (eq. (15)) and a,(eq. (16)) and limits the initial screening to heat pipes where p «p7. But this con-

V if

dition generally applies because the liquid pumping potential a , (eq. (16)) decreasesvery rapidly as p — p .

Incidentally, the ratio form for the correlation of density differences

p l - (15t)

is quite similar to that for latent heats of vaporization:

°-88X , T - T 7(23)

This comparison indicates clearly that the heat pipe becomes less effective as the den-sity of the vapor increases toward that of the liquid - because simultaneously the heat ofvaporization approaches zero. So heat pipes, which essentially transport the enthalpyof condensation, should operate with p «p,. Consequently, neglecting p effects inthe suggested initial screening is a justifiable economy.

These simplifications used with the selected physical- property correlations and thefigure- of- merit expressions allow meaningful first- round evaluations of unusual organicheat- pipe fluids.

Lewis Research Center,National Aeronautics and Space Administration,

Cleveland, Ohio, September 18, 1973,503-25.

APPENDIX - SYMBOLS

B CF-dependent constant

B' function of reduced temperature TZ/TC in vapor-pressure equation

B" sum of CF effects in liquid-viscosity equation

C 7 constant-pressure specific heat for liquidP, 6

SD I 20 constant-pressure specific heat for 20° C liquid

G G-field figure of merit

k, thermal conductivity of liquid

L liquid transport factor (zero-g figure of merit)

M molecular weight

N nucleation tolerance factor

[P] parachor, sum of CF effects in normal-boiling-temperature and surface-tension equations

P pressure at critical point\s

Py saturated-vapor pressure at T^

P , saturated-vapor pressure at normal boiling point

R gas constant

RD molar retraction, sum of CF effects in normal-boiling-temperature equation

TV normal-boiling temperature

T critical-point temperature\s

T, liquid operating temperature

Z critical-point compressibility factor

Z compressibility factor of saturated vapor at T,

a functional factor in thermal-conductivity equation

Q!OA functional factor at 30° C (or T /2) in thermal-conductivity equationOx/ * •

a1 functional factor in exponents of vapor-pressure equation

\, latent heat of vaporization at normal boiling point

X, latent heat of vaporization at T,L 6

M7 liquid viscosity at T,£• t-

pc critical-point density

9

pj liquid density at T,

Pj k liquid density at normal boiling point

p saturated- vapor density at T7V ts

p h saturated- vapor density at normal boiling pointv, DSA sum of CF effects in critical-point-pressure equation

sum of CF effects in critical- point- temperature equation

liquid surface tension at T,

REFERENCES

1. Basiulis, A. ; and Filler, M. : Operating Characteristics and Long Life Capabilitiesof Organic Fluid Heat Pipes. Paper 71-408, AIAA, Apr. 1971.

2. Anon. : Study of Applications of Heat Pipes to Temperature Control for EuropeanMeteorological Satellite. Inst. f. Kernenergetik, Tech. Hoch. Stuttgart, Mar. 1971.

3. Holmgren, J. S. : Preliminary Program Plan Heat Pipe Parametric Data. Rep.DWDL-698-008, McDonnell Douglas, Co., Aug 1969.

4. Marcus, B. D. : Theory and Design of Variable Conductance Heat Pipes. NASACR-2018, 1972.

5. Perry, Robert H. ; Chilton, Cecil H. ; and Kirkpatrick, Sidney D. : Perry's ChemicalEngineers' Handbook. Fourth ed. , McGraw-Hill Book Co. , Inc, 1963.

6. Hougen, Olaf A. ; Watson, Kenneth M. ; and Rogatz, Roland A. : Chemical ProcessPrinciples. Seconded., John Wiley and Sons, Inc., 1954.

7. Mechtly, E. A. : The International System of Units. Physical Constants and Conver-sion Factors. NASA SP-7012, 1964.

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NASA-Langley, 1973 33 E-7632 11

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