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THERMAL EMITTANCE BEHAVIOR OF SMALL CAVITIES LOCATED ON REFRACTORY METAL SURFACES

by J. Robert Branstetter and Robert D.

Lewis Research Center Cleveland, Ohio Hard copy (HC) ./ '

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Microfiche (MF) '-53 ff 663 July 66

San Diego, California,

NATIONAL AERONAUTICS

TECHNICAL PAPER prepared for Thermionic Conversion Specialists Conference sponsored by the Institute of Electrical and Electronics Engineers

October 25-27, 1965

AND SPACE ADMINISTRATION WASHINGTON, D.C. 1965 \v

3

THERMAL EMITTANCE BEHAVIOR OF SMALL CAVITIES

LOCATED ON REFRACTORY METAL SURFACES

by J. Robert Branstetter and Robert D. Schaal

Lewis Research Center Cleveland, Ohio

TECHNICAL PAPER prepared for

Thermionic Conversion Specialists Conference sponsored by the Institute of Electrical and Electronics Engineers

San Diego, California, October 25-27, 1965

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

THERMAL EMITTANCE BEHAVIOR OF SWILL CAVITSES LOCATED

ON REFRACTORY METAL SURFACES

by J. Robert Branstet ter and Robert D. Schaal

Lewis Research Center National Aeronautics and Space Administration

Cleveland, Ohio

ABSTRACT

The emittance of small c a v i t i e s e l e c t r i c a l l y dis integrated i n tungsten and molybdenum is If proper measured with a disappearing-filament pyraneter.

safeguards are taken, c a v i t i e s such as these a r e r e l i a b l e t a r g e t s on which t o s igh t pyrometers when metal surface temperature is desired. to ry reproducibi l i ty . The emittance r e s u l t s a r e compared with a n a l y t i c a l expressions and the l a t t e r a r e shown t o be of very l imited value except f o r deep, isothermal cavi t ies .

Cones and cyl inders a r e studied.

The fabricat ion method yields cavi t ies of sa t i s fac-

INTRODUCTION

The performance of thermionic converters is strongly dependent on emit ter temperature. An accurate determination of emitter surface temperature by o p t i c a l pyrometry requires a t a r g e t of known emittance value. s t r a y rad ia t ion from other hot sources and incident on the t a r g e t i s absorbed ra ther than re f lec ted in to the pyrometer. l e s s than 0.5; however, deep holes d r i l l e d i n any opaque mater ia l can provide emittance values near unity. Cavity design i s a f a i r l y simple task as long as t h e mater ia l is isothermal; f r e - quently, however, t h i s i s not the case because refractory metals a r e poor thermal conductors, p a r t i c u l a r l y a t elevated temperatures where large thermal flows of ten e x i s t . The r e s u l t i n g nonuniformity of temperature along the walls introduces uncertainty i n t o the t a r g e t emittance value and, hence, i n t o the surface temperature evaluation. Therefore, cavi ty depth must be kept within cer ta in bounds.

The emittance, and hence the absorptance, must be near uni ty , so that

Refractory metals yield surface emittancesL,z t h a t a r e usual ly

Since the r e a r walls of a cavi ty usual ly possess the la rges t and most uniform emittance values, this study is confined t o pyrameter sightings that are along or close t o t h e cavi ty ax is . I n t e r e s t is f u r t h e r r e s t r i c t e d t o spectral emission, since wide band (hea t ) detect ion apparatus is normally not selected for highly accurate temperature measurement of mall objects .

Cavity emittance requires a f u l l e r description i f confusion is t o be avoided. By current convention, surface emittance surface t o the rad ian t energy emitted by a blackbody when both sources a re a t the same tempera- tu re . Cavity emittance eC is a similar r a t i o for an imaginary plane s t re tched across the opening of the cavi ty; the energy beamed towards t h e pyrometer i s canposed of both emitted and r e f l e c t e d l ight f r o m the surface being viewed. energy streaming from the w a l l t o the pyrometer is not uniform f r o m one surface-area increment t o the next, although the surfaces themselves may be isothermal. cav i ty emittance ea, which has been expressed a n a l y t i c a l 1 9 for cy l indr ica l cav i t ies possess- ing d i f f u s e l y (Lambert) emitt ing and r e f l e c t i n g surfaces. y ie ld an overa l l cavi ty emittance

E is t h e r a t i o of the radiant energy emitted by an a r b i t r a r y

For other than r e l a t i v e l y deep cavi t ies , the

This gives r i s e t o a l o c a l

Most a n a l y t i c a l approaches4,5,6,7 E ~ .

While i n t e r e s t here is confined t o viewing along or close t o the cavi ty ax is , the direc- t i o n a l r a d i a t i o n charac te r i s t ics of the surface i t s e l f can have a pronounced e f f e c t on the value of cavi ty emittance. 4 ~ 5 consider the surfaces t o be perfect diffusers . of severa l a n a l y t i c a l methods t h a t are popular. a reviewg of the various general methods t h a t have been employed f o r deriving equations f o r cavi ty emittance. good fit t o t h e i r experimental data , which were confined t o length-to-diameter r a t i o s of 0.25 t o 1.0. being t h e i r concern f o r d i f fuse ly r e f l e c t i n g walls.

However, nearly a l l a n a l y t i c a l expressions f o r cavi ty emittance

More recent ly , Kelly and Moore have presented

For c y l i n d r i c a l cav i t ies , they show severa l expressions3~7 t h a t provide a

W i l l i a m s e describes the meri ts and weaknesses

The purpose of t h e i r work was similar t o the present paper, the s ign i f icant difference

The aforementioned information is he lpfu l , but it provides quant i ta t ive values of ea and cC f o r spec ia l cases only. t he experimental r e s u l t s obtairled from e l e c t r i c a l l y d is in tegra ted cav i t i e s i n tungsten and molybdenum.

Herein, severa l of the ana ly t i ca l formulations a r e compared with

DESIGN CONCEPTS

following fea tures a re des i rab le fo r a cav i ty d r i l l e d i n t o a surface so t h a t i t s %em- can be measured by pyrometry:

Target-area emittance near un i ty Isothermal walls Target area of uniform radiance Target area of ample s i ze Emittance constant with time Reproducible i n manufacture

The aforementioned items a r e i n many ways contradictory. i s f r e e l y r ad ia t ing t o space and heat flow within the metal is unid i rec t iona l , temperature gradients ranging from ZOO t o 80' C/cm can occur. surface; the four-fold range i n values i s , r e l a t e d t o t h e surface roughness and, hence, t o t a l emittance. present. small; however, if the t a r g e t diameter ( f i g . 1) is too small, accurate pyrometer s igh t ings cannot be obtained.

If the surface containing t h e cavi ty

These f igu res a r e f o r a 20W0 K tungsten

Gradients can be l a rge r o r smaller when mass t r anspor t (e. g., e lec t ron cooling) i s I n order t o concurrently s a t i s f y items (l), (2), and ( 3 ) , t h e cavi ty entrance m u s t be

The d r i l l i n g process produces two separate e f f e c t s : t h e surface i s roughened, and the ma te r i a l is subjected t o l a t t i c e d i s to r t ions . Bennettg shows that both have a pronounced e f - f e c t on the magnitude of surface emittance and on t h e specular i ty of t h e r e f l ec t ed r ad ia t ion . With proper annealing t h e r ad ia t ion cha rac t e r i s t i c s of t he surfaces undergo change and f i n a l l y become f a i r l y stable.

Cavities must be reproducible i n manufacture i f cC general u t i l i t y . Reproducibil i ty requi res t h a t to le rances of t h e gross-cavity dimensions a r e s m a l l and t h a t surface roughness and damage do not vary from one surface element t o t h e next.

da t a f o r a given cav i ty a re t o be of

APPARATUS

Holes were d r i l l e d i n t o the ends of 3/8-inch-diameter tungsten and molybdenum rods ( f ig s . 2, 3, and 4) . lower. and cavi ty temperature readings w re obtained with a disappearing-filament pyrometer having an e f f ec t ive wavelength h of 6530 !. The view was along the cav i ty ax i s and t h o u g h a window t h a t had a remotely operated shu t t e r which kept contaminants from reaching t h e window. M u l t i - p le r e f l ec t ions between window and rod end were minimized by loca t ing t h e window normal s l i g h t l y off-angle t o t h e ax i s of t he rod ( f i g . 3) . near ly a l l s t r a y r ad ia t ion by chamber walls and induction c o i l .

Each rod was induction-heated i n a vacuum environment of t o r r O r

The e n t i r e polished rod end containing t h e c a v i t i e s r ad ia t ed t o "space." FrOnt-SurfaCe

Care was taken t o ensure the capture of

Dr i l l ing by e l e c t r i c a l d i s in t eg ra t ion yielded holes of near ly uniform sur face teXture f o r a l l surfaces. i t s neighbors. RoughnPss depth w a s about 0.001 cm. s t en a r e shown along with dimensions i n f igu re 4. The c a v i t i e s were out-of-round by approxi- mately 0.002 cm. corners of the cylinders. d r i l l i n g process were required t o a t t a i n these to le rances .

The d r i l l i n g technique produced shallow pocks with t h e rim of each pock touching The cones and cy l inders fabr ica ted i n tung-

The rad ius of curvature was about 0.005 cm f o r t he cone apexes and f o r t h e Frequent dress ing and replacement of t h e e lec t rodes used i n the

The pyrometer was a manually operated and commercially ava i l ab le instrument. Temperature readings when viewing la rge uniformly br ight t a r g e t s contained e r r o r s of approximately 5 de- grees. Reproducibility of brightness matches w a s about 2 degrees for l a rge t a r g e t s . Unpub- l ished work a t t h i s laboratory has shown t h a t e r r o r s i n measurement can be an t i c ipa t ed when t h e tar@ diameter becomes smaller than f i v e times t h e filament diameter. To achieve t h i s minimum er ror - f ree t a rge t diameter e t e r

W a t t h e bottom-center of a cy l ind r i ca l cav i ty , t he cav i ty diam- D must be su f f i c i en t ly la rge so t h a t outermost r ays emanating from t h e t a r g e t and i n c i -

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dent on the pyrometer entrance a r e not blocked by the cavi ty l i p ( f ig . 1). diameter r a t i o of 6 and a distance d of 40 cm, D must be 25 percent l a rge r than W for the subject pyrometer.

For a length-to-

PROCEDURE

Computation of cavi ty emittance eC assumes t h a t t he normal emittance el of t he polished face of t h e rod is known.1° be obtained from t h e Wien equation

The t r u e temperature T of t he f ron t face of t he rod can

where %,1 is the pyrometer-indicated temperature of t he surface and T is t h e window t r ans - mission. Likewise, t he t r u e temperature of t h e front-face of t h e rod is

where S, 2 is the pyrometer-indicated temperature of t he cav i ty after subs t rac t ion of A!?, t he e s t d t e d temperature difference between the backwall of cavi ty and t h e f ront - face of t h e rod. Wherever d i f fe rences i n t h e emittance of various surfaces of a given cavi ty were being examined, cC of equation ( 2 ) was replaced by ca, t h e l o c a l cav i ty emittance.

1 T Equating t h e two expressions for - yie lds

RESULTS AND DISCUSSION

The estimated temperature difference between f ron t and back surfaces of the c a v i t i e s ranged between 0 and 15 degrees. c a v i t i e s f o r tungsten operated near 2200' K. sponds t o a change of about 0.06

The l a rges t values were associzted with the l a rge conica l A t t h i s temperature, a M of 15 degrees corre-

un i t s (eq. ( 3 ) ) .

A f a i r l y deep cy l ind r i ca l cav i ty ( f ig . 4, hole 14) ws fuund t o be of uniform brightness across t h e back surface. Such a t a r g e t should provide measured eC values independent of d i s - tance and observer; therefore , hole 14 was used t o e s t ab l i sh t h e reproducib i l i ty and accuracy of the data. Figure 5 shows the r e s u l t s of numerous readings by each of two observers. Reproducibil i ty of each observer de te r iora tes badly when the cavity-to-filament-diameter r a t i o becomes smaller than 3.2. values obtained by t h e two observers are shown t o de- crease when t h e pyrometer i s placed too fax f r m t h e cavity. Both observations conform t o the remarks about minimum permissible t a r g e t diameter made i n the APPARATUS sec t ion of t h i s report . Accuracy l a rge ly depends on reproducib i l i ty of readings, observer judgnent , pyrometer ca l ibra- t i o n e r r o r , and uncer ta in ty i n emittance of the f ront face (€1

Also, t he cC

of eq. ( 3 ) ) .

The annealing (aging) process produced in te res t ing developnents. Whisker growth occurred on t h e cav i ty surfaces during the i n i t i a l heat of t he molybdenum rod. The growth was rapid, occurred below 1400° K, and resu l ted i n a very marked lowering of cavi ty emittance. The rod w a s removed, cleaned by gentle scraping, and returned t o the vacuum vessel. ing, whiskers did not develop. cannot always be r ead i ly detected.

On further heat- Whisker diameter was only about 0.001 cm; hence, t h i s nuisance

Enittance data were obtained f o r molybdenum c a v i t i e s during t h e annealing process. While t h e temperature underwent numerous cycles, one heat of 2000' K was maintained f o r a day. cy l ind r i ca l hole had the same dimensions as the tungsten cavi ty used f o r f igure 5; the other two c a v i t i e s were a l s o of 0.04 cm diameter, but they had length-to-diameter values of 3.74 and 2.95, respec t ive ly . As aging progressed, t h e surface s t ruc ture of the shallowest cav i ty could be observed through t h e pyrometer optics. measurements were very d i f f i c u l t t o obtain. The intermediate hole underwent t h e same process,

One

I n i t i a l l y , t he back wall of each hole appeared t o be of uniform brightness.

The a rea of uniformly bright surface became so small t h a t temperature

4

but t h e e f f ec t w a s smaller. By t h e time a s tab le or near-stable surface condition was attained, t h e bottom of the deepest hole had l o s t a l i t t l e of i ts uniformity; however, temperature read- ings had accuracies comparable t o those f o r t h e tungsten cavity. This la t ter molybdenum cavi ty (L/D, 4.85) provided a cavi ty emittance eC of 0.946 a t temperatures from 1300' t o 2200' K.

On removal from the vacuum vesse l , t he molybdenum cavi ty surfaces were found t o be shiny. These surfaces had o r ig ina l ly appeared lu s t e r l e s s . more l o c a l sca le t h e surfaces appeared t o be very smooth when viewed with a microscope. ilar but less noticeable e f f ec t was observed f o r tungsten, which was aged a t about 2350' K for a day. molybdenum rod.Fl,12 However, changes of tungsten values eC with time were not observed for t h e considerable number of hours required t o obta in t h e data presented herein. ened area (no. 15 of f i g . 3) yielded a surface emittance of 0.5. d is in tegra ted molybdenum surface, e was near 0.4.

The pock marks were s t i l l present, but on a A S b -

The t u n s t en rod may not have been as thoroughly annealed and cleaned by hea t ing as t h e

The aged rough- For an aged, e l e c t r i c a l l y

The la rge ly specular behavior of t h e r e f l ec t ions observed for flat, e l e c t r i c a l l y d i s in t e - grated surfaces implies that experimental ies based on d i f fuse ly r e f l e c t i n g surfaces. On t h e basis that eC equals cavi ty absorptance ac, t h e r e f l ec t ion behavior of t h e m e t a l surface i t s e l f can be i l l u s t r a t e d by example. beam of f i n i t e cross-sectional a r ea t r ave l ing p a r a l l e l t o t he axis and i n t o a conical cav i ty s t r i k e s a wall and i s p a r t i a l l y absorbed. i s re f lec ted fu r the r i n t o t h e cav i ty when t h e t o t a l cone angle i s l e s s t h n 90'. face been a d i f fuse r e f l ec to r , a por t ion of t he l i g h t , on i t s f irst contact with the wall, would have been r e f l ec t ed out of t h e cav i ty entrance. In the case of a cy l ind r i ca l cavity, a specular ly r e f l e c t i n g end-disk-surface r e f l e c t s a x i a l l y incident l i g h t back along the p t h it entered. Cavity e f f e c t is minimal.

cC da ta w i l l cor re la te poorly with ana ly t i ca l stud-

A l i g h t

For a pe r fec t ly specular surface the remaining l i g h t Had t h e sur-

As expected from the preceding discussion, t h e experimental data for cones co r re l a t e poorly with ana ly t i ca l r e su l t s6 based on d i f fuse surfaces ( f i g . 6 ) . possible area f o r a fi lament-target brightness match, one des i r e s t o s igh t t h e pyrometer on the center of the cavity. This presents problems i n t h e case of cones because of t h e d i f f i c u l t y i n f ab r i ca t ing a pointed bottam. a reas of reduced brightness a t and near t he apex. a brightness match. t h e inner periphery of t he cone. c a l l y d is in tegra ted tungsten, f ab r i ca t ion of small deep cones requi res considerable s k i l l .

data are compared with an ana ly t i ca l expression by Sparrow e t al .3 f o r pe r fec t d i f fuse r s . a given value of L/D, t h e ana ly t i ca l expression y i e lds center and l a rges t near t h e periphery. mental da ta l i e below the ana ly t i ca l values. t i o n of t he tungsten surfaces. Figure 7 a l s o shows t h e change of measured emittance as t h e r a t i o of cavity diameter t o fi lament diameter is varied. Since these cav i t i e s are of the same diameter, a dua l absc issa i s provided on the f igu re . The deepest cav i ty (L/D, 3.1) exh ib i t s a uniformly bright t a rge t area and measured emittance is independent of distance and observer. These r e s u l t s compare favorably with those of f igure 5 f o r cavity-to-fi lament diameter r a t i o s of 3.2 and la rger . A t length-to-diameter values less than 3, br ightness nonuniformity of t h e end d isk was e a s i l y detected; however, at s m a l l values of d t h e minimum e r ro r - f r ee t a r g e t diameter W included only a s m a l l f r a c t i o n of a rea a t t h e center of t h e disk. This a rea w a s of near ly uniform brightness, hence t h e eC values a t small values of d were independent of distance d. A s d was gradually increased from a value of 50 cm, br ightness matching became progressively more d i f f i c u l t because the outer region of t he minimum e r ro r - f r ee t a r g e t a rea be- came brighter. These r e s u l t s show t h a t brightness nonuniformity of t h e end d isk is objectionably la rge f o r these shallow cav i t i e s .

To u t i l i z e t h e l a r g e s t

Cones having a cone angle l a rge r t han 30° were observed t o have This a rea had t o be avoided when conducting

Furthermore, these two cones produced a low-intensity annular surface on While a cone angle of l e s s t han 25' i s prefer red f o r e l e c t r i -

Local cav i ty emittance da t a f o r tungsten cylinders a r e shown on f igu re 7. Experimental For

values t h a t a r e smallest near t he ea For any given length-to-diameter r a t i o , a l l t h e experi-

This i s explained by t h e specu la r i ty of r e f l ec -

The r e su l t i ng measured emittance increases and t h e r ep roduc ib i l i t y decreases.

Experimental values of loca l cav i ty emittance obtained for t h e center of the end-disk are summarized in f igu re 8. The values a r e f o r a t a r g e t diameter W t h a t is small campared t o the cylinder diameter I). Results by D. F. E d ~ a r d s , ~ using t h e &v0s4 ana lys is f o r a non- d i f fuse surface, a r e included. These ana ly t i ca l results a r e suspect a t low values of length- to-diameter r a t i o where the experimental data show t h e end disk t o be of nonuniform brightness. Also, t h e DeVos canputations a re Only f o r a surface emittance of 0.4; however, fou r d i f f e r - e n t surfaces were examined. One was a per fec t d i f f u s e r , and t h e o ther t h ree sur faces had vary-

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i ng f r ac t ions of t he r e f l ec t ed energy d i s t r ibu ted between d i f fuse and per fec t ly specular modes. The of Sparrow, e t al. ( f i g . 8 ) t h a t they a re not shown. sen ts a surface somewhat less specularly r e f l ec t ing than a highly polished re f rac tory m e t a l sur- face. The molybodenum and tungsten da ta a re s e l f cons is ten t and both a r e shown t o co r re l a t e well with t h e DeVos surface; it must be s t ressed , however, t h a t t h e properties of t h e referenced surface are very a rb i t r a ry . (The most highly polished DeVos surface yielded much lower values than those shown here.)

values f o r a per fec t d i f fuse r i s i n such c lose agreement with d i f fuse surface r e s u l t s The DeVos curve shown i n f igure 8 repre-

Data obtained f r o m all t h e cav i t i e s of f igure 4 conformed t o the experimental r e s u l t s t h a t have been discussed. Reproducibil i ty of fabr ica t ion of these s m a l l c av i t i e s appears s a t i s f ac - t o ry .

CONCLUDING REMARKS

Small cones and cy l inders e l e c t r i c a l l y d is in tegra ted i n re f rac tory metals provide satis-

a r e of l i t t l e value (except f o r nearly b lack c a v i t i e s ) fac tory t a r g e t s on which t o s igh t pyrometers i f the c a v i t i e s a re selected with considerable care. Analytical expressions for unless t h e d i r ec t iona l d i s t r ibu t ion of t h e re f lec ted energy i s known.

REFEXFX?CES

1. Gubareff, G. G. ; Janssen, J. E.; and Torborg, R. H.: Thermal Radiation Proper t ies Survey. Second ed., Minneapolis Honeywell Regulator Co., 1960.

2. Annon.: Data Book. Thermopbsical Properties Research Center, Purdue Univ., West Lafayette, Ind .

3. Sparrow, E. M.; Albers, L. U.; and Eckert, E. R . G.: Thermal Radiation Charac te r i s t ics of Cylindrical Enclosures. J. Heat Trans., vol. 85, p. 73 (Feb. 1962).

4. DeVos, J. C . : Evaluation of t h e Quality of a Blackbody. Physica, vol. 20, pp. 669-659 (1954).

5. Edwards, David F.: The Emissivity of a Conical Black Body. Univ. of Michigan R e s . I n s t . , Report No. 2144-105-T (Nov. 1956).

6. Polgar, Les l ie G.; and Howel l , John R.: Directional Thermal-Radiative Proper t ies of Conical

7 . Gouffg, Andrk:

Cavities. NASA TN D-2904, 1965.

Corrections d 'ouverture des corpnoirs a r t e f i c i e l s compte tenu des d i f fus ions mul t ip les in te rnes . Rev. d'optique, vo l . 24, no. 1-3, January-March, 1945, pp. 1-10.

8. W i l l i a m s , Charles S.: Discussion of t he Theories of Cavity-Type Sources of Radiant Energy. Applied Optics, vo l . 51, May 1961, pp. 564-571.

9. Katzoff, S . , ed.: ML-TDR 64-159).

10. Brans te t te r , J. Robert:

Symposium on Thermal Radiation of Sol ids . NASA SP-55, 1965 ( A i r Force

Formulas f o r Radiant Heat Transfer Between Nongray P a r a l l e l P l a t e s of Polished Refractory Metals. NASA TN D-2902, 1965.

11. Petrov, V. A.; Chekhovskoi, V. Ya; and Sheinblin, A. E.: Experimental Determination of t h e High Temperature, vo l . 1, In teg ra l Emissivity of Metals and Alloys a t High Temperatures.

no. 1, July-August 1963, pp. 19-23, English Trans.

1 2 . Larrabee, Robert Dean: The Spec t ra l Emissivity and Optical Properties of Tungsten. Tech. Rept. 328, Research Lab of Electronics, M.I.T., May 21, 1957. AD 156602.

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