. I I

c

. c

; - research and advanced development division

I 201 Lowell Street Wilmington, Mass. 01887

T E L E P H O N E A R E A 617 E X C H A N G E 1 6 5 8 - 8 9 A A

24 August 1965

National Aeronautics and Space Administration Office of Advanced Research and Technology Washington, D. C. 20546

Attention: I

Chief, Physics of Fluids Branch/Code REU?

Gentlemen :

Subject : Quarterly Progress Report Contract 1 % s ~ - ~ 8 8

I Transmitted herewith in accordance with the provisions of Article III

to the Contract are two (2) copies of Avco's First &uasterly Progress, Report under Contract - -~88- cqvering the period 29 April 1965 through 281 July 1965.

Very truly yours,

AVCO COFPORATION Research and Advanced Development Division

Contract Admini s t rdt or

m:mS

Attachments (2)

cc: NASA/Washington, D. C. (1) Office of Technology Utilization Att'n: New Technology Representative/Code ATU

NASA/Post Office Box 5700, Bethesda, Maryland ( 2 ) Att'n: Representative/Contract ~~sw-1.188 . .

EVALUATION Of H IGH-TEMPERATURE GAS TRANSPORT PROPERTIES

First Quarterly Progress Report 29 April 1965 through 28 July 1965

Prepared by

RESEARCH A N D ADVANCED DEVELOPhkENT DIVISION AVCO CORPORA TION

Wilmington, Massachusetts

RAD-SR-65-190 Contract IyASw-1188

Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION RESEARCH DIVISION

Washington, D. C. OFFICE O F ADVANCED RESEARCH AND TECHNOLOGY

I ,

. This document consists of 42 poges 50 copies, Series A

EVALUATION OF HIGH-TEMPERATURE GAS TRANSPORT PROPERTIES

First Quarterly Progress Report 29 April 1965 through 28 July 1965

Prepared by

RESEARCH A N D ADVAXCED DEVELOPMENT DIVISION A VCO CORPORA TION

Wilmington , Massachusetts

RAD-SR- 65- 190 Contract NASw-1188

16 August 1965

Prepared for

NATIONAL AEROXAUTICS AXD SPACE ADLIIYISTR-ATION RESEARCH E A‘ IS10 N

OFFICE OF ,-ZD’i7-X<CED XESEARCFi XSD TF CXS@ZOGY Washington, D. C.

.

CON T E ?; TS

1. IrLrroclucrion.. . . . . . . . . . ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 1

-4. Program Objectives . . . .. . . .. ...... ............. ... .... 1 B. Program Organization . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . 1 C. Technical Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

IL Experimental Investigation of the Thermal Conductivity of Xitrogen ............................................... 4

-4. Experimen'al Apparatus.. . . . . . . . . . . . . . . . -. . . . . .. . . . . . . . 4 B. Spectroscopic Techniques .............................. 5 C. Experimental 0bsery;atior.s . .. . . .. .. . . .. .. .. .... . .... .. 6 3. - k d x - s is of E>-:perimrn*al Obser-.-ations . . . . . . . . . . . . . . . . . 10

111. Program DirecTion . . . . .. . . . . . . . . . . . . . . . . . . . . . . I. .. . . . . . .. 31

IV. References ............................................... 32

8

ABSTRACT

Arc c.iia>r- texi>era:zre dis:r’>.-zaons and voltage gra- dier;s have bee, dc?ern?ined tr, r-iirogen for various arc czrrenrs at pressares of 0 . 5 , 1. and 2 atmospheres. These data have been analyzed to determine thermal conciuctivity as a function of temperature by integrating the Elenbrias -Heller equaiion. The thermal conduc- tivities were found to ‘nave an anomalous dependence upon the ambient pressure of the a r c column and upon the arc current. It is postulated that these effects may be attributed to radiative losses, particularly in the far ultraviolet. Significantly better agreement is obtained between the experimental and theoretical thermal conducti;*itie s when :?e se radiati1.e 10s se s a r e included in the er,erg.: balance.

8

ILLUSTR4TIOlc’S

F i g u r e 1 Absolute Intensity of the Nitrogen Atom Line XI 4 9 3 5 a5 a Function of Temperature at a Pressure of 0 .5 Atmosphere ........................................ 7

2 Absolute Intensity of the Nitrogen Atom Line NI 4935 as a Function of Temperature at a Pressure of 1 Atmosphere .......................................... 8

3 Absolute Intensity of the Nitrogen Atom Line XI 4935 as a Function of Temperature a t a Pressure of 2 Atmospheres ......................................... 9

4 Xadial TernperatGre Distributions for 50- and 80-Ampere Xitroger. -4rcs a i a Pressure of 0 . 5 Atmosphere ........................................ 11

5 Radial. Temperature DistriSarions for 60- and 100-Ampere Nitrogen A r c s a t a Pressure of 0 . 5 Atmosphere ........................................ 1 2

6 Radial Temperature Distributions for 40-, 60-, and 100-Ampere Nitrogen 4 r c s at a Pressure of 1 -4tmosphere ........................................ 13

7 Radial Temperature Distribotions for 50-, 83-, and . - - 130-Ampere S i t r o g e n 3 r c s a t a Pressure of 1-4txosphere ........................................ 14

- - 8 Radia l Teniperature 3 l s t r l 5 , : ~ i c n s for 4 2 - , 33-, and - 17-Ampere Xitrogen Arcs a t a Pressure of 2Atmospheres ....................................... 1 5

9 Circuit for Measuring the Voltage Gradients in the Nitrogen Arc Column,. .................................. 16

10 Theoretical Electrical Conductivity of Nitrogen at 0. 5 , 1, and 2 Atmospheres ............................... 17

1 1 Thermal Conductivity of Nitrogen at 0 . 5 Atmosphere from the Calculated-Current Method without the Inclusion of Radiative Losses ............................ 19

?

ILLUS T U TiONS (C oncl 'd j

F i g u r e 12 Thermal Conductivity of Nitrogen a t 1 Atmosphere from the Calculated-Current Method without the Inclusion of Radiative Losses ...........................

13 Thermal Conductivity of Nitrogen a t 2 Atmospheres from the Calculated-Current Method without the Inclusion of Radiative Losses ...........................

14 Estimated Atomic Line Plus Continuum Radiation for Nitrogen as a Function of Temperature at 0.5, 1 , and 2 Atmospheres ( A > 2000A) ............................................

15 Estimated Atomic Line Plus Continuum Radiation far Nitrogen a s a Function of Temperature at 3. 5 , 1 , and 2 Atmospheres (A ' 0 . OA) ............................

16 Thermal Conductivity of Nitrogen at 0. 5 Atmosphere from the Calculated-Current Method Using the Radiation Data of Morris, e t al, for A > 2000 A to Estimate the Ultraviolet Radiation ..............................................

--

17 Thermal Conductivity of Nitrogen at 1 Atmosphere from the Calculated-Current Method Using the Radiation Data of Morris, et al, for A > 2000 A to Estimate the Ultraviolet Radiation ................................... --

18 Thermal Conducrivity of Nitrogen a t 2 Atmospheres from the Calculated-Current Llethod Using the Radiation Data of Morris, et al, for A > 2000A to Estimate the Ultraviolet Radiation ................................... --

19 Measured and Measured-Plus-Calculated Values of the Total Radiation of Nitrogen at Atmospheric Pressure .............................................

20 Thermal Conductivity of Nitrogen at 1 Atmosphere from the Calculated-Current Method with the Inclusion of Cilccrlated and Measured Radititive Losses ...............................................

20

21

23

24

26

27

28

29

30

... -Vlll-

c

t

I. I??TRODUCTION

A. PROGRAM OBJECTIVES

The objectives of this program -- Evaluation of High Temperature Gas Transport Properties -- are:

1, values of the thermal conductivity of nitrogen a t high temperature and when, o r i f , the discrepancy is resolved.. .

To investigate the discrepancy between theoretical and experimental

2. functions of temperature for air and oxygen a t several pressures in the temperature range of 8000 the range of transport property determination to 2 0 , 000 O K . 1

To determine the electrical and thermal conductivity coefficients as

to 15,000 "K. (Efforts wi l l be made to extend

B. PROGRAM ORGANIZATION

This program is being carr ied out finder the sponsorship of the Research Division, Office of Advanced Research and Technology, National Aeronautics and Space Administration, under the technical supervision of Mr. Alfred Gessow, Chief of the Physics of Fluids Program. Dr. Stewart Bennett, and Dr. C. F. Knopp is Project Engineer.

The Avco RAD Project Director is

Theoretical calculations for the thermal and electrical conductivity of nitrogen at various pressures were performed by D r . J. M. YOS. Mr. R. W. Liebermann carr ied out the theoretical predictions for the radiation, based upon experimental data supplied by A h . J. M. Morris.

During the previous {first) year of this program, major effort was devoted to establishing the wall-stabilized a r c as a standard tool for experimental determin- ation of transport properties of high-temperature gases, and to the development of analytical techniques for the calculation of the transport properties , particu- lar ly thermal conductivity of gases a t high temperature. were examined during this initial year. determined thermal conductivity for argon agreed to within approximately 40 percent with analytical predictions. tion losses were not included in the energy balance for the argon column, the agreement is considered to be satisfactory. wall-stabilized arc is a suitable experimental tool for the determination of the thermal conductivity of high-temperature gases.

Both argon and nitrogen It was found that the experimentally

In view of the fact that ultraviolet radia-

As a consequence, it is felt that a

-1-

The experimental results reported for nitrogen in the previous year's effort agree substantially with results reported by other investigators. These results, which do not include the effect of ultraviolet radiative losses, lead to a value for thermal conductivity an order of magnitude larger than theoretical predictions in the neighborhood of 14,000 "K. between theory and experiment should be resolved prior to proceeding with experimental measurements in nitrogen at higher temperatures. In an effort to explain this discrepancy, the bes t available analytical estimates for ultraviolet radiation were included in the energy balance for the nitrogen a r c colurnn. It was demonstrated that inclusion of this estimated ultraviolet radiation as a mechanism for energy transport produced satisfactory agreement between experiment and theory, indicating the strong possibility that radiative heat transfer is a major factor.

It was determined that the disagreement

*

While the dtraviolet radiation f r o m high-temperature nitrogen was calculated using the best available analytical prediction, the resrrlts a r e not felt to be quantitatively correct. There is at present a parallel experimental investigation being conducted a t this laboratory to make quantitative measurements of this radiation. Q Pending the results of this investigation, an alternate method of evaluating the effect of ultraviolet radiation upon the measurement of thermal conductivity has been followed. thermal and electrical conductivities of high-temperature nitrogen are insensitive to pressure. while radiation is a strong function of pressure. tivity measurements have been made in nitrogen at 0 .5 and 2 atmospheres, in addition to the data at 1 atmosphere reported previously. For the 0. 5 and 1 atmosphere cases, data were obtained in the temperature range of 8500 to approximately 14,000 9(, while the upper temperature for the 2-atmosphere data was limited to about 13 ,000 X. irom the Elenbaas-Heller equation assuming no radiative losses. ass urnption, it was found that the experimentally measured thermal conductivity decreased approximately as the particle density over the factor of 4 change in the ambient pressure. Conversely, theory predicts that, for the temperature range where disagreement exists between experiment and theory, the thermal conductivity should increase slightly as the particle density decreases.

This approach relies upon the fact that both the

Thermal conduc-

Thermal conductivity values were deduced Under this

Solutions of the Elenbaas- Heller equation were also obtained using the radiation data of Morris, e t al , radiation, are felt to be the most reliable now available. equation was solved under the assumption that all of the a r c column is transparent to radiation of all wavelengths. is not valid, particularly for the ultraviolet, it is felt that such an approach has the advantage of providing trends in a straightforward manner.

These data, which include estimates of the ultraviolet The Elenbaas-Heller

Although it is recognized that this assumption

This work is reing performed under contract AF33 (615) - 296- for t h e .?erospace Research Laborarories. Office of .?erospace Research, U n i t e d States A i r Force

-2-

For the pressures investigated, the inclusion of radiative energy transfer has the effect of bringing the experimental data into much better agreement with theory. s ach as radiation, which is temperature-dependent as well as prgssure-depen- dent, to remove the discrepancy between theory and experiment, as well as the apparent dependence of the thermal conductivity upon a rc current.

Further, it demonstrates that is is necessary to postulate a phenomenon,

-3-

II. EXPERIMENTAL INVESTIGATION OF THE THERMAL CONDUCTIVITY O F NITRGGEN

A. EXPERIMENTAL APPARATUS

The constricted a r c facility used in obtaining a nitrogen a r c column at 0. 5 and 2 atmospheres is the same as that used in the previous investigation of atmos- pheric pressure nitrogen. 1. atmospheres. This instability w a s traced to several small leaks in the system, the a r c operating in a very stable mode when the leaks were eliminated. Little difficulty was encountered in operating subsequently a t 0. 5 atmosphere. At each pressure, the cathode and anode of the a r c a r e blanketed in argon to pre- vent the electrode erosion characteristic of high-current nitrogen arcs . Pr ior to each se t of measurements, the f l o w ra tes of argon and nitrogen a r e adjusted such that there is no argon observed spectroscopically in the portion of the a r c column used for the measurements.

This facility was described in detail in reference Initially, some difficulty was experienced in obtaining a stable a r c at 2

The correct pressure in the a r c column is maintained with a needle valve lo- cated upstream of a mechanical vacuum pump in the case of the 0.5-atmosphere runs, and by a needle valve exhausting to atmosphere for the 2-atmosphere tests. The pressure is monitored on a differential manometer which can be read to 1 mm Hg. This gives an accuracy of approximately f 3 percent for the 0.5-atmosphere case and f 1. 5 percent for the 2-atmosphere case. cases, ambient atmospheric pressure was very close to the nominal value. fluctuations in pressure were discernible during any of the runs a t either pressure . A 0.75-rneter, f /10 grating monochromator, employing a Czerny-Turner mount- ing, is used to obtain the spectroscopic measurements necessary for the de- termination of the radial temperature distribution within the a r c column. The radiation detector is a= EMI type 625SB photomultiplier. column is focussed upon the entrance sli t of the monochromator by a n imaging lens which is apertured to alleviate distortion and to provide a large depth of field. depth of field sufficient to ensure that both the front and back of the a r c column a r e in focus. This is a necessary criterion, since the monochromator must measure accurately the radiation enclosed within a n optical path through the c o l m to obtain meaningful radial intensity distributions f rom the measured intensity distributions. axis of the column and approximately 0 .05 mm perpendicular to the a x i s . This resolution is sufficiently fine to measure the large gradients i n intensity across the diameter of the a r c column.

In all No

The image of the a r c

The f-number of the optical system is approximately f /70, providing a

Spatial resolution is approximately 0.2 mm along the

Calibration of the detection, recording, and optical system is provided by a n NBS tungsten standard lamp located at the same position relative to the op- tical system as that normally occupied by the a r c facility.

-4-

3. SPECTROSCOPIC TECHNQUES

The basic variable determ-ined experirnentalll- in this stt idy is the temperature of the plasma column.

The basis of all spectroscopic determination of temperature is that the meas- ured quantity (radiation intensity) is determined by two variables of state of the gas (temperature and number density of the radiating species):

I. = I; (n- TI 1 ’

where Ii is the radiativ-e intensity emanating from the number density ni of particles of type i at a temperature T. pressure, the species number densities a r e related to temperature by the laws c! statistical thermodynamics. ~ ; c ’ E , eqaaTion (1) reduces to:

F o r a g a s in equilibrium a t a given

%’hen This relationship is taken into considera-

’

and a measurement of I i then determines the value of the temperature T for a known pressure.

The absolute radiant intensity of a spectral line which is emitted spontaneously per unit solid angle by a unit volume of the plasma is given by:

m vihere kn is the spontaneous transition proSability for a transition from the upper exergy state III to the lower energy state n, re the total numSer of atomsn,; to the enc^rEv o f tce light qilanta h7,,(’mn= frequency of emitted lightj; t~ the stat;stical weight of the upper state grn having an energy E,; and to the partition function of the atom, Q, . is optically thin and t h e number of exciEing collisions IS large compared with the number of emissions. These conditions a r e well satisfied in the visible region of the nitrogen spectrum for the operating conditions employed in the experiments reported here.

Equatlon ( 3 ) may be applied when the radiating volume

Transition probabilities for nitrogen have been determined experimentally by several investigators. reported data. Following a suggestion of Solarski and Wiese, trrznsithn probabilities calcdzted by Bates and Damgaard‘ have been employed. These calculated transition probabilities a r e quite close to the mean of the available experimental data.

Unfortunately, there is a great deal of scatter in the the nitrogen

Energy levels for numerous gases, including nitrogen, have been tabulated by Moore, 7

- 5 -

Partition functions and number densities of the various camponents of high- temperature nitrogen were taken from the tables of Drellishak, e t al. 8 -

Figures 1, 2, and 3 show the dependence of the intensity of the 4935-A h2 line on temperature a t pressures of 0.5, 1, and 2 atmospheres, respectively. Because of the strong dependence of the intensity upon temperature, the temperature determined by absolute intensity measurements of a spectral line is very insensitive to e r ro r s in intensity measurement. for an argon spectral line given in reference 1 is representative of the e r r o r s to be expected when using the intensity versus temperature relationships given in figures l through 3.

The e r r o r analysis

~ C. EXPERIrvLENTAL OBSERVATIONS

The objective of the experimental measurements has been to determine the thermodynamic state of the gas as a firnction of the radial coordinate of the arc column, and to use this measured state to determine the tbermal conductivity as a function of temperature. The general approach has been to determine the temperature from absolute line intensity measurements for a known pressure in the a rc column.

The a r c

The

governing equation for the energy transport in a cylindrically symmetric column is given by the Elenbaas-Heller equation:

1 d ,E2 t - -

r d r (4)

remaining information necessary for the determination of the thermal - conductivity K strength in the column electrical conductivity CJ ,

is obtained from measurements of the applied electric field E, the volumetric radiation losses Prad, and the

The integrated intensity distribution of the a r c column is obtained by translating the image of the column across the entrance slit of the monochromator. centerline of the column is determined by taking intensity measurements across the entire a r c diameter and then "folding" the Signals obtained so that the curves to the right and left of the center a r e mirror images.

The

The integrated distribution is converted to a radial intensity distribution by an inversion of the Abel integral equation in a manner similar to the numerical technique employed by Barr . 9 The accuracy of the inversion technique has been checked by inverting mraerically a function which could be inverted analytically. It was found that the numerical technique gives excellent results with the exception of the f i rs t three inverted points. periphery of the a rc column, a r e not included in the analysis of the temperature profile for thermal conductivity.

These points, which lie a t the

-6 -

. . . . . ~ . . . - - . . . -.-. I.

. . .-.- ~.

Flgwe 1 ABSOLUTE INTENSITY OF THE NITROGEN ATOM LINE NI 4935 AS A FUNCTION OF TEMPERATURE AT A PRESSURE OF

0.5 ATMOSPHERE

-7-

Figure 2 ABSOLUTE INTENSITY OF THE NITROGEN ATOM LINE NI 4935 AS A FUNCTION OF TEMPERATURE AT A PRESSURE OF

1 ATMOSPHERE

-8 -

IU '

I 0 3

4

t /

2

10-4

figure 3 ABSOLUTE INTENSITY OF THE NITROGEN ATOM LINE NI 4935 AS A FUNCTION OF TEMPERATURE AT A PRESSURE OF

2 ATMOSPHERES

I - 9 -

Temperatures in the a r c column were determined on the basis of absolute inten- sity measurements of continuum radiation for the 1-atmosphere runs, the con- tinuum having been previously calibrated against absolute line radiation, and on the basis of absolute line intensity of the 4935-A M line for the 0. 5- and 2-atmos- phere runs. Radial temperature profiles a r e shown in figures 4 and 5 for a r c currents of 50, 60, 80, and 100 amperes a t an ambient pressure of 0.5 atmosphere. Figures 6 and 7 depict the radial temperature distribution for the atmospheric pressure a r c at 40, 50, 60, 80, 100, and 150 amperes. The atmospheric pres- sure data have been previously reported and a r e included here for the purpose of comparison. Figure 8 gives the radial temperature distribution a t 2 atmos- pheres for 42, 55, and 72 amperes.

The temperature profiles in the region from 1000 to 5000°K were calculated from the conductive energy flux to the wall and the thermal conductivity given by Yos. The dotted portion of the temperature profiles represents interpolation between the calculated and measured portion of the profile. the interpolated portions were used to obtain thermal conductivity. a t atmospheric pressure, it is expected that the uncertainties in the standard lamp, detection and recording system, and in the transition probability could result in an e r r o r of approximately f 15 percent in the absolute line intensity. This corresponds to a f 1.5 percent uncertainty in the temperature at 12, 000°K. To date, the investigation of nitrogen at 0.5 and 2 atmospheres has not been so exhaustive a s that at 1 atmosphere. In view of this, the temnerature profiles for the 0.5- and 2 - atmosphere runs are estimated to be accurate to f 3 percent.

10

Neither the calculated nor For the data

Voltage gradients i n &e nitrogen a rc column were measured using the circuit shown in figure 9- portion of the column serve as probes. to these constrictors to negate the effect of contact resistance between the con- strictor and the a r c column. i s minimized by measuring the voltage between several pairs of constrictors separated by a known diatance.

The efectric field associated with each of the a rc currents is given in the tem- perature-profile plots (figures 4, 5, 6, 7, and 8) .

D. ANALYSIS OF EXPERIMENTAL OBSERVATION

In this circuit, the constrictors a t each end of the nitrogen A small amount of current i s supplied

The effect of random e r ro r s on the measurement

phase of the investigation. ing analytical values for the electrical conductivity in an attempt to explain the gross discrepancy between theoretical and experimental values of the thermal conductivity. Figure 10 shows the electrical conductivity as a function of tem- perature for nitrogen a t pressures of 0.5, 1, and 2 atmospheres. lo

Rather, emphasis has been placed upon using exist-

-10-

1

* l400C

12000

IO000

a n 5 W t

w

4 occ

I 2000

_f

. . ... <

- - - ~

/ / '-f - /

2 80 AMPERES, E = 19.8 v/cm

\ \

ARC RAD!US, crn

65-1 1610

Figure 4 RADIAL TEMPERATURE OlSTRlBUTlONS FOR 50- AND 80- AMPERE NlTROGEN ARCS AT A PRESSERE OF 0.5 ATMOSPHERE

- 1 1 -

12,000

10,000

Booc Y . w a

a a

3

w 0

E t

60OC

400C

200c

loo( 0 .2 0. I 0 0. I

ARC RADIUS. em

.- . . " ." .

~.

0.2

65-1161 I Figure 5 RADIAL TEMPERATURE DISTRIBUTIONS FOR 60- and 100- AMPERE

NITROGEN ARCS AT A PRESSURE OF 0.5 ATMOSPHERE

-12-

i4.0Dt

I2 PO0

IO.000

Y

W a

a a 2 BOO0

3 W 0

4-

6000

4000

I

1 I

I I / I /

I/

I

I

I 40 AMPERES, E= 228 V/CM

2. 60 AMPERES, E.22.5 V/CM

1 I I

I

0. i O AD1 U

Figure 6 RADIAL TEIlPERATURE DJSTRJBUTIONS FOR 40-, 60-, AND 100-ArvIPERE 4ITRBGEN ARCS AT A PRESSURE OF

1 AT'I'OSPHERE

-1 3 -

a

14.001

12.00c

ropoc .

6000

4 0 0 C

2000

- IO00 - .I . _ _ .- .

I ' 1. 50 AMPERES. E.22.6 VlcM - 2 BO AUPERES. E a 2 2 5 VlcM

3.150 AMPERES E a 2 3 8 VlCM

Qt 0

ARC RADIUS. crn

- . . -__ - , . . . , . . . . . - , . . ~- .

Figure 7 RADIAL TEMPERATURE DfSTRlBUTlONS FOR 50-, 80-, AND 150-AMPERE NITROGEN ARCS AT A PRESSURE OF

1 ATMOSPHERE

- 14-

4 14,000

IO00

12.000

10,000

8000 2 W

3 c a

a L w 0. 0 W t-

6000

4000

2000

/ J i

4

i 0.2

GS - I1612

I 42 AMPERES, E = 26.1 v /cm 2 59 AMPERES. E = 25.4 v/cm

, . . ... ... . . . ~~

~- 0 . I 0 0. I

ARC RADIUS, cm

---I 1

0 .2

--

Figure 8 RADIAL EMPERATURE DISTRIBUTIONS FOR 42-, 55-, AND

2 ATMOSPHERES 72-AMPERE NITROGEN ARCS AT A PRESSURE OF

-15-

- 16-

toe

E 0 \

0 .e E b >

f

2

1 I I 1

65-4 I 6 13

I I I I

I 1. 0.5 ATMOSPHERES 2. 1.0 ATMOSPHERES I 3.2.0 ATMOSPHERES

4 I I I bo It

TEMPERAME, OK

d

Figure 10 THEORETICAL ELECTRICAL CONDUCTIVITY OF NITROGEN AT 0.5, 1, AND 2 ATMOSPHERES

-17-

The radial temperature gradient appearing in equation (4) is determined by graphical differentiation of the radial temperature profiles. accuracy of this technique has been obtained by comparing the analytically and graphically evaluated slopes of a parabola. It was found that the e r ro r s of the graphical technique were approximately 2 percent for slopes in the neighborhood of one. rising to 7 percent for larger and smaller slopes. random errors , a smooth curve passing through the origin at zero radius is fitted by eye to graphidly determined slopes of the temperature distribution.

The approach need to determine the thermal conductivity from the Elenbaas- Heller equation (4) donsists of integrating the equation once and ~olving for the thermal conductivity of the gas a t the radial distance r ’ f rom the column axis:

An estimate of the

To reduce the effect of

0 (K),, = -

r ‘(d T/d r)r,

This is referred to a s the calculated-current method in reference 1.

This equation is equivalent to the statement that the heat conducted out across a cylindrical surface of radius r’ i s equal to the heat generated inside the surface by Joule heating, less the heat lost from inside the surface by radiation.

Since the radial temperature distribution is know& equation ( 5 ) determines the thermal conductivity a t the temperature associated with r ’ , if the electrical con- ductivity 0 and radiative power loss Pfaa a r e known as functions of temperature.

Figure lls 12, and 13 show the thermal conductivity obtained from the measured temperature profiles and voltage gradients given in figures 4 through 8, using the calculated-current method. The electrical conductivities given in figure 10 were used. 13, the radiative losses were assumed to be zero. the possible effect of radiation upon the thermal conductivity would not be con- fused by the inclusion of only a portion of the radiation, i. e. s the radiation meas- ured in the spectral region between 2000A and 6 microns.

The experimentally determined thermal conductivities a t 0 .5 atmosphere (figure

In determining the thermal conductivities shown in figures 11 through This w a s done in order that

sigriificant is the reduction in the current dependence of the experimental data obtained at 0 . 5 atmosphere a s compared to the 1-atmosphere data. conductivity measured a t a pressure of 2 atmospheres (figure 13) follows the same general trend of appearing to increase with increasing a r c pressure, although the dependence of the &ta upon a r c current is not so pronounced a s that a t 1 atmosphere.

The thermal

-18-

7

'r---r -.

0.09 - THEORETICAL ( YDS) EXPERIMENTAL (ASSUMING NO RADIATIVE LOSS)

0 100 AMPERES 0.08

. .

I

TEMPERATURE, *K 65 -I I614

Figure 11 THERMAL CONDUCTIVITY OF NITROGEN AT 0.5 ATMOSPHERE FROM THE CALCULATED-CURRENT METHOD WITHOUT THE

INCLUSION OF RADIATIVE LOSSES

-19-

7 0.

0

0.0

: cxo

T aa .. c c 0

J om %.

0.a I

65-1 I615

f f 1 1 1 1 ;

L -1HEORET ICAL [ YOSI

EXPERiWENTAL ( ASSUMIN0 NO RAWTIVE LOSS) 1 A150 AMPERES 0 100 AMPERES

80 AMPERES X 6 0 A M P E R E S m 50 AMPERES o 40 AMPERES 1

9

0

d)

A A

A

A 0 A

0

0 A

A 0

0 Ax

A &

O e A x 0

x

- so00 l0,OOo

TEMPERATURE, *&

. . t I 15,000

Figure 12 THERMAL CONDUCTIVITY M NITROGEN AT 1 ATMOSPHERE FROM THE

INCLUSION OF RADIATIVE L3SSES CALCULATED-CURRENT METHOD W ITHOIJT THE

-20-

I

0.09 - THEORETf GAL ( YOS I

0.00

a07

EXPERIMENTAL (ASSUMING NO RADIATIVE LOSS)

- t - e 72 AMPERES + 55 LIMPERES

. [1 42 AMPERES

0.02 L

0

e

+

D e

+

8 +

0 .+

l0,OOO 15,000 100 Tamm, 1(

. 65-11616

Flgure 13 THERMAL CONDUCTlVlTV OF NITROGEN AT 2 ATMOSPHERES FROM THE CALCULATED-CURRENT METHOD WlTHOUT THE

INCLUSION OF RADIATIVE LOSSES

-22 -

. .

Comparing the data presented in figures 11 through 13, i t appears that the dis- crepancy between theory and experiment may be attributed to a phenomenon which is characterized by two effects. First, the increase in the magnitude of the measured thermal conductivity for a constant temperature, but increasing pressure, indicates a pressure-dependent phenomenon. In particular, examim- tion of the data indicates that the thermal conductivity determined from the Elenbaas- Heller equation under the assumption of no radiative losses increases in an ap- proximately linear manner with pressure- Secondly, the dependence of the ex- perimental data upon a r c current, for a given temperature and pressure, suggests that the phenomenon is dependent upon geometrical considerations. Referring to the Elenbaas-Heller equation in i ts integrated form, equation (5). it is seen that the deduced value of the thermal conductivity depends upon the volume over which

Assuming the electrical conductivity to be correct, it is apparent that an er ror in the value of the volume integral of the radiation will produce an e r ro r in the thermal conductivity which is a function of the volume of integration. For different a r c currents, a given temperature will be achieved a t different radii in the arc , identical temperatures occurring a t larger radii for higher a r c currents. conductivity is determined increases faster than does the surface area. Conse- quently, the effect of an e r ro r in the volume integral of radiation, for example, will affect the thermal conductivity at a given temperature in a manner that is a function of the radius at which the temperature occurs. Referring to figure 12 , for example, it will be seen that as arc current increases, the thermal con-

ductivity also increases for constant temperature. found a t increasing radii as a r c current increases weighting the effect of an error in the volume integral more heavily. On the basis of these arguments, it is con- cluded that the current dependence of the data shown in figures 11 through 13 is a direct result of failure to include radiative losses in the solution of the Elenbaas- Heller equation.

- the integration is extended.

The volume enclosed within the surface at which the thermal

Further, this temperature is

Turning now to the monatonic increase in thermal conductivity with pressure, i t i s instructive to examine the relationship between pressure and specific radiation. Figure 14 presents the tota3 radiation from nitrogen between 2000A and 6 microns as a function of temperature for the three pressures of interest. 3 .The 1-atmos- phere data were obtained experimentally. The radiation a t 0 . 5 and 2 atmospheres was calculated from the known temperature dependence of continuum radiation, using the radiative cross section determined from the experimental data obtained at 1 atmosphere. of Bates and Damgaard.

The contribution of line radiation was obtained by the method 6

function of temperature for 0.5, 1, and 2 atmospheres. These data were ob- tained by choosing the theory whick most accurately described the continuum radiation measured at 1 atmosphere (2000A < A < 6 microns) and using this theory to predict the ultraviolet continuum radiation. 3 The extension of the data to 0.5 and 2 atmospheres, and the inclusion of contribution of line radiation, was per- formed in the same manner a s outlined above. Comparing figures 14 and 15, it

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w o o 10.000

65-11617

Figure

1 t

0.5 ATMOSPHERES 1.0 ATMOSPHERES

2.0 ATMOSMEAES u

r2.000 14,000

TEMPERATURE .OK

16,000

4 ESTIMATED ATOMIC LINE PLUS CONTINUUM RADIATION FOR N I T R O G E N AS A FUNCTION OF TEMPERATURE AT 0.5,

1, AND 2 ATMOSPHERES ( h > 2000A)

- 2 3 -

3

spoo I

I .O ATMOSPHERES

2.0 ATMOSPHERES

m t6.000 12,000 f4,000

TEYPERATUREPK

i

Figure 15 ESTIMATED ATOMIC LINE PLUS CONTINUUM RADIATION FOR NITROGEN AS A FUNCTION OF TEMPERATURE AT 0.5,

1, AND 2 ATMOSPHERES (A> 0.OA)

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i I

is evident that the inclusion of ultraviolet radiation results in a specific radia- tion approximately five times larger than the radiation which is measured be- tween 2000A and 6 microns.

Figures 16, 17, and 18 show the thermal conductivity determined from the tem- perature profiles of figures 4 through 8 by the calculated-current method using the radiation given in figure 15. The agreement between theory and experiment is substantially better than when the radiative losses a r e assumed to be zero.

atmosphere data which are considered tobe the most reliable. that the dependence of the thermal conductivity upon arc current has not been removed entirely, being most pronounced in the 1-atmosphere data. One of the striking features of the data in figures 16 through 18 is the apparent shift in the minimum of experimentally determined thermal conductivity toward lower tem- peratures with increasing pressure. The theoretical curves indicate that the minimum should shift toward higher temperature for increasing pressure. This anomaly i s not understood a t present, although it is believed to be a result of inaccuracies in the radiative term used in obtaining the data, and possibly to self-absorption of the a r c column, which can become appreciable in the neigh- borhood of 9000'K.

I

The agreement, however, is not entirely satisfactory, particularly for the 1- I I It appears also I

I

.

I

For the purpose of comparison, the specific radiation used to analyze the data in reference 1 is given i n figure 19. atmosphere, assuming the higher radiative losses of figure 19, are shown in figure 20, which was first presented in reference 1. These data exhibit a mark- edly better agreement with theory over the temperature range of 8500 to 14000°K than do the data using the radiation given in figure 15. (It should be noted that one of the reasons for the apparently superior agreement is the difference in the analytical value of the thermal conductivity given in figure 20, and that given in figures 12 and 17. The analytical result shown in figures 12 and 17 i s some- what lower. This is the most recent calculation. ) It is felt that the principal reason that the data of figure 17 do not show and experiment as that of figure 20 lies i n the different functional dependence upon temperature exhibited by the specific radiation at 1 atmosphere, as shown in figures 15 and 19. Apart from the difference in functional dependence, the radiation given in figure 19, which was used to obtain the data of figure 20, is approximately a factor of 2 greater than the radiation used in the analysis of the results presented in figure 12. and experiment that is obtained using the radiation of figure 19, it is felt that

adiation presented in figure 15 is the more reliable.

Thermal conductivities of nitrogen at 1

as good agreement between theory

In spite of the better agreement between theory

n i a r c column was treated as if i t were transparent to radiation at all wavelengths and temperatures. This is almost certainly not the case. Ultraviolet radiation i s strongly absorbed b y nitrogen at temperatures of approximately 10, 000°K and below. It remains to be determined what effect self-absorption has upon the method of radiative energy transport.

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a o 8 ~ 0 or

I -THEORETICAL (YOS 1

EXPERIMENTAL iMORRlS ,u, INCLUDING LKTRAVIOLET RADIATION 1 0 I 0 0 AMPERES

80 AMPERES

X 60 AMPERES

+ 50 AMPERES

0.01 u 5000 10,Ooo

TEMPERATURE, K

-- I- -

Figure 16 THERMAL CONDUCTlVlTY OF NITROGEN AT 0.5 ATMOSPHERE FROM

MORRIS, ET AL, FORA>2000 A TO ESTIMATE THE ULTRAVIOLET RADIATION

THE CALCULATED-CURRENT METHOD USING THE RADIATION DATA OF

-26-

0 08

1 __ O 07r

T

1 - THEOR ET I C I L EXPERIMENTAL 1 MORRIS ,u I NC,UDIMG ULTRAVIOLET RADIATION )

Y OS

0 150 AMPERES

0 100 AMPERES

80 AMPERES

I 60 AMPERES

I

I I I

I

“4 0 Oxo xo 00 :I

0

Figure 1 7 THERMAL CONDUCTIVITY OF NITROGEN AT 1 ATMOSPHERE FROM THE CALCULATED-CURRENT METHOD USING THE RADIATION DATA OF

f~=lORRIS, ET AL, FORA72000 A TO ESTIMATE THE ULTRAVIOLET RADIATION

-27-

f

01

0 09

0.00

0 07

006

0 0 5

5 004 c: f a Y

> k > 0.03 - i 4 8 -J a I a I w t

0 02

- THEDRETICAL (YOS) EXPERIMENTAL t MORRIS, et 0 1 ,

INCLUDING ULTRAVtOLET RADIATION 1 e 72 dMPERES

+ 55 awmEs 42 AMPERES

0.01 u 65-11621

Figure 18 THERMAL CONDUCTIVITY OF NITROGEN AT 2 ATMOSPHERES FROM THE CALCULATED-CURRENT METHOD USING THE RADIATION DATA OF

MORRIS, ET AL, FORA>2000 A TO ESTIMATE THE ULTRAVIOLET RADIATION

-28-

E

r - 4

- - - - - -

cr) -

- E 0

- - - - - - - - -

- - - - - - - - -

_. - - - - - - - -

I 1 1 I 1 I -

10 I # 42 13 14 TEMPERATURE, io3 OK

65-3108

Figure 19 MEASURED AND MEASURED-PLUS-CALCULATED VALUES OF THE TOTAL RADIATION O F NITROGEN AT ATMOSPHERIC PRESSURE

-29-

t

i f 1 I I I I I p 0, a D . b CD m P cr) (u

9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0

0 s

0 0

-p 9 0

I I 1 I I

" \ 0

a w c

d

3 3

3 Iu

3,

D D 9 9

K W K 3 t U K w n

O h 0

s 2

0 0 0 m

a -30-

IIL PROGRAM DIRECTION

Additional experimental temperature profiles wi l l be obtainedat 0. 5-, 1-, and 2-atmosphere pressures during the next quarter. profiles is to enhance the reliability of the data at hand, the range of temperature will be approxba , tdy ttie same as reported in th is work. and future data wiU continue in an effort to determine, in as quantitative a manner as possible, the continuing discrepancy between theory and experiment. As exper imenw &&a for ultraviolet radiation become available, they will be incorporated into the present system of data analysis, radiation by the a r c column will be included in the data analysis. At this time i t appears that radiation is the principal source of the discrepancy between the measured and calculated thermal conductivity values, and i t is necessary to treat the radiation accurately to obtain reliable values of thermal conductivity, although self-absorption is mathematically cumber some. self-absorption is expected to be pressure-dependent.

Concurrent with further investigation of nitrogen in the temperature interval reported here, initial data will be obtained for nitrogen using a new a r c facility which should be capable of temperatures well in excess of 15,000"K.

Since the purpose of these . I

I Scrutiny of present

i Self-absorption of

The amount of I I

-31-

1.

2.

3.

*

4.

5.

6.

7.

8.

9.

10.

IV. REFERENCES

RAD, Theoretical and Experimental Studies of High-Temperature Gas Transport Properties, Final Report, Avco RAD-TR-65-7, Contract NASW-916 (?May 1965).

Mascker, H., Zeit. Phys, - 157, 1 (1959); - 158, 392 (19601,

RAD Research on Radiation from Arc Heated Plasma, Final Report, Avco RAD-TR-65-17, Contract A.F33(616)-8390, Project 7063, Task 7063-3 (July 1965).

Drallishak, Ki%., Technical Documentary Report No. AEDC-TDR-64-22, Arnold Engineering Development Center, Air Force Syetems Command, U. S. A. !F.+ (January 1964).

Solatski, J.E.', and W . 2 . ' Wiese , Phys. Rev., 135, A1236 (1964). -

Bates, D.R., a d k Damgaard, Phil. Trans. Roy. Soc. (bndon), A242, 101 (i949). - Moore, C. E., editor, Atomic Energy States, Bureau of Standards Circular 467 (1952).

Drelliehak, K., D. A e e c h l m , and A Cambel, Technical Documentary Report No. AEDC-TDR-64-12, Arnold Engineering Development Center, Air Force SyStem6 Command, U. S . A. F. (1964).

Barr, W. L., JOSA 52, 885 (1962).

Yes, J. M., Avco RAD, unpublished calculation.

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i

Addressee

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