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VACUUM CHAMBER HEAT-TRANSMISSION ANALYSIS

by Wulter W. Gay and Wilbert E. Ellis

Manned Sbucecrafi 1 J Center ouston, Texas

T 4

ATIONAL .'ea AERONAUTICS AND SPACE ADMINISTRATION/ . WASHINGTO TO^ c. .I FEBRUARY 1967

https://ntrs.nasa.gov/search.jsp?R=19670008184 2020-04-25T04:40:38+00:00Z

I .

NASA TM X-1355

VACUUM CHAMBER HEAT - TRANSMISSION ANALYSIS

By Wal te r W. Guy and Wilbert E. E l l i s

Manned Spacecraft Cen te r Houston, Texas

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION ’

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - Pr ice $1.00

.

ABSTRACT

An analytical investigation was conducted to study the effect of the test-chamber pressure level on the accuracy of deep-space heat-transfer simu- lation, using as parameters the test vehicle emit- tance and surface temperature. The study reveals that, with the exception of extremely low tempera- ture conditions, a test-chamber pressure of approx- imately lom5 mm Hg provides the best thermal simulation.

ii

VACUUM CHAMBER HEAT-TRANSMISSION ANALYSIS

By Walter W. Guy and Wilbert E. Ellis Manned Spacecraft Center

SUMMARY

An analytical investigation was conducted to study the effect of the test-chamber pressure level on the accuracy of deep-space heat-transfer simulation, using as parameters the vehicle emittance and surface temperature.

The greatest portion of heat transfer would be through gas conduction and free convection in an environmental control chamber with Apollo test capability, at atmos- pheric pressure. This, as well as using a nitrogen cold wall to approximate the

. near-absolute zero of space, introduces inconsistencies into the simulation.

The study reveals that, with the exception of extremely low temperature condi- tions, a test-chamber pressure of approximately thermal simulation.

mm Hg provides the best

INTRODUCTION

The accurate simulation of a deep-space environment is mandatory for valid vehicle and component thermal evaluation and heat-transfer research. Since radiation is the only mode of external thermal transfer in deep space, other means of heat transmission (conduction and convection) introduce e r rors in thermally simulating a deep-space environment. These e r rors are not the only source of erroneous data. Using a nitrogen cold wall to approximate the near-absolute zero of space also intro- duces inconsistencies into the simulation. The purpose of this paper is to present the results of an analytical investigation into the effect of the test-chamber pressure level on the accuracy of deep- space heat-transfer simulation.

SYMBOLS

2 AI vehicle lateral area, f t

2 A2 cold-wall lateral area, f t

I

C P

C V

dl

d2

M

P

q

RM

T1

T2

T

U

1

2

(r

(Y

Y

AT1

€1

€2

Q

specific heat capacity at constant pressure, Btu/lb- OR

specific heat capacity at constant volume, Btu/lb- O R

vehicle diameter, f t

cold-wall diameter, f t

molecular weight of residual gas

2 pressure of residual gas, lb/ft

2 heat flux, Btu/hr-ft

universal gas constant, ft-lb/mole- OR

temperature of residual gas, OR

vehicle surface temperature, OR

cold-wall temperature, "R

heat-transfer coefficient, Btu/hr-ft2- "R

vehicle accommodation coefficient

cold-wall accommodation coefficient

cPlcv

vehicle surface temperature e r ro r

vehicle emittance

cold-wall emittance

Stefan-Boltzmann constant, Btu/hr-ft2-"R 4

$ percent error

2

I .

I 1 . VACUUM CHAMBER HEAT-TRANSFER EQUATIONS

In an environmental control chamber with Apollo test capability, the following = 0. 5, the temperature of the nitrogen cold diameter

the diameter (chamber i were assumed 1 wall = 140" R, the emittance E2 of the cold wall = 0.9, the operating pressure - - I range = through mm Hg.

The greatest portion of heat transfer would be through gas conduction and free convection in an environmental control chamber with Apollo test capability, at atmos-

-3 pheric pressure. A s the pressure is reduced to the operating range, 10 mrn Hg, the gas behaves more like separate molecules than gas masses. This alters the mode of heat conduction from a multicollisional diffusion process to "free-molecule" heat transport, and, thus, significantly changes the magnitude of the heat conduction (ref. 1). Although free convection (the transfer of heat propagated by the buoyant movement of a fluid due to a change in density within a fluid by reason of its close proximity with a body of a different temperature) is practically nonexistent at this reduced pressure, radiation heat transfer is not significantly affected.

The Stefan-Boltzmann equation (ref. 2), as adapted for radiation between concen- tr ic cylinders, was used throughout this analysis.

'chamber = c( A1 E ~ lE2 3": - T:)Btu/hr-ft 2

E +- 1-E2E1 A2

Neither the total pressure nor the surrounding air affects the validity of the Stefan- Boltzmann radiation equation.

The Knudsen equation (ref. 3) is accurate only in the region of "free-molecule" 1 conduction.

The accommodation coefficient for air ranges between 1.0 when it is in contact with a surface at 76 " K and 0.85 at a surface temperature of 300" K (ref. 3). The re- sidual gas temperature can be determined a s the numerical average of the vehicle surface temperature and the chamber wall temperature.

1

3

This low-conduction region is established at various pressure levels for different gases and separation distances of the heat-transfer surfaces. Gas conduction in the pressure range above the free molecular zone is considerably greater than that indi- cated by the Knudsen equation. No attempt was made to define the point at which the region of "free molecule" conduction was established, since the simulator geometry, the test object geometry, and the exact composition of residual gases are points of conjecture. Therefore, for this analysis the Knudsen equation will be assumed valid at pressures of lom3 mm Hg and below. Any deviation encountered because of this assumption will result in "lower-than-actual" values for gas conduction computed at the upper portion of the to mm Hg range.

EFFECTS OF GAS CONDUCTION IN A VACUUM CHAMBER

The importance of gas conduction in a vacuum chamber can be illustrated with a practical example. To determine a temperature profile for a launch vehicle during the cool-off period after aerodynamic exit heating, a chamber such as the one de- scribed previously would be needed. If the chamber were evacuated to 10 mm Hg and the vehicle surface heated, the heat rejected could be accurately determined by temperature monitoring. To assume that this heat rejection was by radiation (as will be the case in deep space) would be incorrect. In fact, for an aluminum-skin vehicle with a nominal emittance of 0.05 and an effective surface temperature in the 700" R range, the error would be approximately 48 percent (fig. 1). This e r ro r could be

- 3

0

10

20

30

4 0

50

Chamber pressure, mm ng

reduced to approximately 8 percent by a pressure reduction to 10 mm Hg and to almost 0 .2 percent at lom5 mm Hg. Thus, gas-conduction heat transfer appreciably affects test results.

-4

Figure 2 represents the composition of the total heat f l u x to the chamber wall from objects at various surface tempera- tures. The f i r s t curve (0) is radiation; the second curve (A) is gas conduction; and the last ( 0 ) is the total heat flux to the cold wall (that is, a summation of the con- duction and radiation).

Figure 3 plots the total heat flux for a chamber at and mm Hg, and a vehicle emittance of 0. 75. In addition,

Figure 1. - Heat transfer e r ro r in chamber simulation of space.

4

5O'K 1OO'K 1 5 O ' K ZOOo K 2 5 0 " K 3 0 0 9 K 35O'K I I I I I I

100" R 200"R 3 0 0 ' R 400" R 500" R 6OO'R

Vehicle surface temperature, T

Figure 2. - Composition of chamber heat flux.

1 0 0 " K 150" K 200' K 2 5 0 ' K 300" K

I I I 1 I 100" R 200" R 3 0 0 " R 400' R 500" R

T 1 Venlcle rllrlace le!,lpera1L4rel

Figure 3. - Heat transfer for equilibrium condition.

the heat flux that would be radiated from the vehicle in outer space is plotted

(lspace radiation = E 1 uA 1 T 1 ') This information can be utilized to determine simulation-temperature e r rors by cross- plotting the data of a particular problem.

For example, if the test object were a typical manned spacecraft and a realistic deep-space sinfare eqiiilihriiim temperature were desired, the aforementioned cham- ber would again be needed. It is assumed that the spacecraft is divided into zones of different thermal-conduction characteristics and that the overall coefficients of heat

boundary values will be used for illustration. By using a nominal interior temperature of 75" F and by allowing the vehicle outer-surface temperature to vary, a heat- conduction curve fox each of the U values can be plotted

transfer lie within the band U = 0.0136 through 0.191 Btu/hr-ft 2 - R. These two

[9 = UA1 (535 - T$]

5

The intersections of these two curves (0) with the total-heat-flux curves for

space-radiation curve determine vehicle surface equilibrium temperatures.

lo4, ami mm ami the

Vehicle surface equilibrium tempera- tures at the three operating pressures are shown in figure 4. The temperatures y a y more than 18" R for either overall cos- cient of heat transmission.

The vehicle surface temperature- difference error encountered in the simula- tor over the actual deep-space condition is shown in figure 5. This indicates that for the U values considered, there is a cham- ber pressure that results in zero error. That is, the simulated temperature is the actual deep-space surliace equilibrium temperature. Could this combination of pressure and temperature be duplicated, perfect simulation would be achieved. However, this is of more academic interest than practical value, since it requires knowing the deep-space surface equilibrium temperature which in most cases is the reason for conducting the chamber simula- tion. Even if the analytical determination of this temperature is sufficiently accurate to establish the required chamber -pressure level, great difficulty is encountered in obtaining and maintaining a precise pres- sure ambient in a large chamber.

These two examples are not meant to be indicative of every type of problem that will be encountered. Rather than trying to find representative problems to cover the range of test conditions, a better under- standing can be achieved by pursuing a more general line of analysis.

"R I 'K

380

360

4

340

F: P Y, 5 320

% $ 300 5

280

260

220

210

200

190

,180

170

160

150

14C 1 o - ~ 0

Chamber cfessure, mm Hg

Figure 4. - Equilibrium temperature conditions.

*R I 'K

21 - 24 -

21 -

18 - 4

c 4

: 15 - E

i 3 3 12 -

u 9 - r"

f 6 - = J

3 -

0 -

-3 -

-6 -

16

14

12

10

8

6

4

2

0

-2

1 0 ' ~ 0 Charnbcr pr~sl ine, rnm HQ

Figure 5. - Simulation temperature error.

6

RESULTS AND DISCUSSION

The duplication of the thermal characteristics of a deep-space environment is the object 6f a chamber test run; the accuracy of the simulation is the measure of success. The deviation from perfect simulation is the difference in heat transfer under deep- space conditions and heat transfer in the chamber. This e r ro r may be positive or negative depending on test conditions. .The three parameters that most affect this er ror are the test vehicle emittance, the surface temperature, and the chamber absolute pressure. By plotting simulation error against chamber pressure at a fixed vehicle surface temperature for various emittance values, a more complete picture is given. The pressure was confined to the to loe5 mm Hg range, while the emit- tance was allowed to vary from 0.05 to 0.95. Separate figures were drawn for vehicle surface temperatures of 720" R (fig. 6), 540" R (fig. 7), 360" R (fig. 8), and180" R (fig. 9).

Figures 6, 7, and 8 indicate that reasonable accuracy was maintained for all

emittances at loe5 mm Hg. With decreasing surface temperature, progressively more e r ror was encountered at 10 mm Hg. -3

This generalization was false when applied to the 180" R test vehicle in figure 9.

The e r ror was considerable at either or loe5 mm Hg. This can be explained by realizing that the nitrogen cold-wall temperature was only 140" R, thus introducing a

e +

t e I

6 0

40

20

0

-20

-40

-60

-80

-100 lo-"

Chamber pesrure, mm Hg

e +

b e t

e

Figure 6. - Simulation error in heat transmission

' 10-4 Chamber pressure, rnm Hg

Figure 7. - Simulation error in heat transmission

7

60

40 e +

-20

-40

e

-60

-80

-100 -5

lo-) 10 Chamber pesrure, mm Hg

Figure 8. - Simulation error in heat transmission

large radiation error at the lower vehicle surface temperature. If work is to be done in this low-temperature region, reasonable accuracy can be obtained by using an 8" R helium cold wall and decreasing the cham- ber pressure by a factor of 10 to

mm Hg (fig. 10).

Figure 11 was included to give a general picture of the maximum error in deep-space heat-transmission simulation encountered at any vehicle surface tempera- ture. At mm Hg, this maximum er ror (for test-vehicle emittances ranging from 0.05 to 0.95 and surface temperatures ranging from 360" R to 720" R) was approx- imately 6 percent. At the higher pressure, 10 mm Hg (for the same ranges of emit- tance and temperature), the mayimum er ror was in excess of 80 percent. In the vehicle surface low-temperature range, 180" R, the maximum error for the emittance range of 0.05 to 0.95 was greater than 50 percent

-3

8

60

40 s +

it : 2l -20

-4 0 e

-60

-8C

-lo(

For ++, qSpace ,ad,ation is greater than qchamber

4' q~pace radiation is less than qchamber

T. . v h i c l e surface ternmalure: 100" K = 180" R

Chamber pressure, rnm Hg

Figure 9. - Simulation error in heat transmission

e +

e

60

4 0

20

- 0

-20

-40

-60

-80

-100

10-6 Chamber persure, mm Hg

Figure 10. - Simulation e r ror in heat transmission (T1 = 180" R, T2 = 8" R).

100

90

80

70

E 60 B

30

20

10

0

for pressures through mm Hg. This error can be reduced to about 6 per- cent by using an 8" R helium cold wall and reducing the chamber pressure to lom6 mm Hg. It should be noted that the helium cold wall does not reduce the error at mm a.

10'~ 10-6 Chamber pressure, mm Hg

Figure 11. - Maximum heat transfer error for vehicle temperatures of 180" R, 320" R, 540" R, 720" R.

CONCLUDING REMARKS

An analytical investigation was conducted to study the effect of the test-chamber pressure level on the accuracy of deep-space heat-transfer simulation, using as parameters the vehicle emittance and surface temperature.

A conclusion stating a definite course of action is impossible with the multitude of variable parameters, but a general statement can be made. With the exception of extremely low-temperature work, a test-chamber pressure of 10 mm Hg gives the hest t!~ermal simulation accuracy for all parameters considered.

-5

Manned Spacecraft Center National Aeronautics and Space Administration

Houston, Texas, July 14, 1966 914 -50-80-02 -72

9

REFERENCES

a

1. Jakob, Max: Heat Transfer, Vol. I. John Wiley and Sons, Inc., Seventh Printing, 1959, p. 71.

2. Jakob, Max; and Hawkins, George A. : Elements of Heat Transfer. Third ed., John Wiley and Sons, Inc., 1957, p. 230.

3. Scott, Russell B. : Cryogenic Engineering. 1962, p. 145.

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3. Scott, Russell B. : Cryogenic Engineering. 1962, p. 145.

10

D. Van Nostrand Co., Inc.,

NASA-Langley, 1967 s-99

sting contribudon tv existing knowledge.

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1

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