Connected in Various Ways and Pressure Environment

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X-327-69-524 PREPRI NT

INTERNAL PRESSURES OF A SPACECRAFT OR OTHER SYSTEM OF COMPARTMENTS, CONNECTED IN VARIOUS WAYS AND INCLUDING OUTGASSING MATERIALS, IN A TIME-VARYING 1 PRESSURE ENVIRONMENT

J. I. SCIALDONE

/ INTERNAL PRESSURES OF A SPACECRAFT OR OTHER SYSTEM OF COMPARmMENTS, CONNECTED IN VARIOUS WAYS &W INCLUDING OUTGASSING MATERIALS, IN A TLME-VARYING PRESSURE ENVIRONMENT

John 3. Scialdone Test and Evaluation Division Systems Reliability Directorate

August 1969

Goddard Space Flight t errter Greenbelt, Mary1ar.d. INTERNAL PRESSURES OF A SPACECMFT OR QTHER SYSTEM OF COMPARTMENTS, CONNECTED IN VARIOUS WAYS AND INCLUDING OUTGASSING MATERIALS, IN A TIME-VARYING PRESSURE E1'IRONMENT

Prepared by: fohn Vcialdone Research and Technology Office

Approved by hn H. Boeckel eputy Chief, Test and Evaluation Division PROJECT STATUS

This report describes a method for calculating the pressure versus time inside each of a system of volumes containing outgassing materials.

Authorization

Test and Evaluation Charge No. 327-124-12-06-01

iii PRECEDlNG PAGE BLANK NOT FILMED.

INTERNAL PRESSURES OF A SPACECRAFT OR OTFIER SYSTEM OF CBMPAR?%lEN'I'S, CONNECTED IN VARIOUS WAYS AND INCLUDING OUTGASSING MATERIAIS, IN A TIME-VARYING PRESSURE ENVIRONMENT

John J. Scidd~ne Test and Evaluatim Division

SUMMARY

A method od calculating the pressure profile for eac:h compartment of a multi-compartment system such as a spacecraft is presented. Thc method is applicable to volumes connected in series or in parallel or bothby passages of various sizes and geometries, where each volume may include several materials outgassing ac- cox~dingto known or assumed characteristics. The enthe system is exposed to a time-varying pressure environment.

.An appropriate set of differe~tialequations with variable coefficients is derived, which may be solved by computer to provide pressure profiles for each compartment. The profiles obtained zre the result of viscous, intermediate, and molecular flow regimes experienced under appropriate conditions in the system of volumes and passages. Severd computations which have been made are presented and co~nparedto experimental results. Pressure profiles for volumes with various outgassing materials and various orifice sizes have been calculated and are grouped according to the mole~cularflow regime time constants and the outgassing characteristics of the material. From these parametric plots, the quasi-steady pressure in a volume containing outgassing materials can be estimated. PAGE BLANK NOT FILMU), -‘-CEDINGi i'\C

CONTENTS

INTRODUCTION ...... 1 ANALYTICAL MODEL...... 3 Pressure-Time History Equations ...... 4 CO~~UC~~S~.C~S...... 7 Initial Conditions - Boundary Conditions ...... 13 Outgassing Functions ...... ', ...... 15 External Pressure ...... 24 Heat Transfer Considerations ...... 25

METHOD OF SOLUTION - COMPUTER PROGRAM a 31 COMPARISON OF EXPERIMENTAL AND COMPUTED RESULTS. .... 33 APPLICATIONS AND PAHAMETFUC PRESENTATIONS...... 35 CONCLUSIONS ...... 45 RECOMMENDATIONS ...... 47

REFERENCES ..eee..ae.eaeeemee.e.aeeeeoeeee.eeemmaee 47

APPENDICES

A. Typical Computer Input Data and Corresponding Solution (E Chamber) A-1 B. Typical Computer Input Data and Corresponding Solution (3 Chambers) B-1 C. Computer Documentation ...... C -4.

vii ILLUSTRATIONS --Figure 1 Arrangement of Volumes and Passages [Jsed as Model for the Derivation of the Flow Equations ...... , ...... 2 Degassing Rates Per Unit Surface Area Versus Time for Some Materials ...... 3 Evacuation of Clean, Dry, Empty 8' x 8' Vacuum Chambe?: for Vacuum Testing of Small Spacecraft...... 4 Pressure-Time Test Setup ...... 5 Comparison of Experimental & Computed Recu1ts for a 1-Liter Compartment with Orifice Diameter -437 in., 7 =0.1 sec., Am- bient Temperature ...... * ...... = 6 Comparison of Experimental & Computed Results for a 1-Liter Compartment with Orifice Diameter -137 in., 7 =1.0 sec., Ambient Temperature ...... 7 Comparison of Experimental & Computed Results for a 1-Liter Compartment with Orifice Diameter -040 iu., r =10 sec., Ambient Temperature ...... 8 Parametric Curves for a Gne-Compartment Thin Orifice Pres- sure Simulation (7= 0-1 see) at Ambient Temperature. . . . . 9 Parametric Curves for a One-Compartment Thin Orifice Pres- sure Simulation (r = 1.0 sec) at Ambient Temperature . . . . 10 Parametric Curves for a One-Compartment Thin Orifice Pres- sure Simulation (7 = 10 sec) at Ambient Temperature . . . . . 11 Parametric Curves for a Three-Compartment System Having Thin Orifices, 80 cm2 l1PTFEMOutgassing Material in each Compartment, T = 270°K ......

TABLES

Table

1 Coefficients for Conductances ...... 2 Outgassing Hates Constants for Metallic Materials ...... 3 Outgassing Rates Constants for Non-Metallic Materials . . . . . 4 Coefficients for the Outgassing Equations ...... 5 Pressure Profile Equations for an 8' x 8' Chamber ...... 6 ~olurne/Orifice ate rial Combin:dions and Calculated

viii SYMBOLS

Ai - Surface area in volume i or passage (cm2) area

A, - Surface ares of outgassing material (cm2) Conductance through passage irom (1 C i j - sec-') chamber i to chamber j

D - Diameter (cm)

E - Total internal energy (call

Outgassing flow rate in volume i (torr 1 sec-l) Gi = - zQoni (From all materials n contained in Volume i)

H - Total enthalpy (cal)

J - Tabular value for iwrmediate flow

K - Tabular value of moiecular flow in annular section

Knudsen's number (dimensionless) K n -

L - Length (cm)

Leakage conductance between (1 sec'l) Li j - chambers i and j

M - hlolecular weight of gas

Po - External pressure P - Absolute pressure in volume i i=l,2,3, 0.0 n

PI. - Quasi-static pressure - P - Average pressure Flow rate through passage from (torr 1 sec-' ) Qi j - chamber i to chamber j

Leakage flow rate into chamber i (torr 1 sec-') QLi j - from chamber j

- 1 Q, - Outgassing rate of surface material (torr 1 oec crn -") after 1 hour vacuum exposure

R - Gas const,ant (62.36 torr - 1 gram-' mole OK-') D R - Reynold's nu .hbe r (_UF )

S - Pumping Speed

T - Temperature

U - Velocity of gas (cm sec-I )

Vi - Volume of chamber i Y - Tabular value for viscous flow in rectangular ducts

a - Passage dimension (cm)

b - Passage dimension (cm)

h - Heat tsmlsport coefficient (cal sec-I cm-2 "K'l)

k - Thermal conductivity (cal cm sec-' ~rn-~

OK-~)

m. . Mass flow rate through passage (grm sec -I) 11 - from chamber i to chamber j

Initial outgassing rate per unit area -I) %io - (torr - 1 ~rn-~sec from surface material n in chamber i

Final outgassing rate per unit area -2* %i f - (torr 1 cm sec-' ) from surface material n in volume i pi u = ,s 1 - Pressure ratio across an aperture Pi

a - Tabular value for nlolecular flow in rectangular ducts C YZF - Specific heat ratio (dimensionless) v 77 - Ratio of viscosity of air @ 15°C to that of a given gas at the same temperature

A - Mean free path - Viscosity of gas

p - Density of gas

7 - Time constant

- Time constant for surface material n in volume i INTERNAL PRESSURES OF A SPACECRAFT OR OTHER SYSTEM OF COMPARTMENTS, CONNECTED IN VARJOUS WAYS AND INCLUDING OUTGASSING MATERIALS, IN A TIME-VARYING PRESSURE ENVIRONMENT

INTRODUCTION

Many spacecraft failures have been attributed by inference, to improper pressure conditions (Refs. 1 and 2). For example, electrical voltage breakdown has occurred many times during spacecraft testjig or during flight. In some cases it has occurred only during flight with systems which under testing ap- peared to be frc: of this type of problem (Refs. 2 and 3). This breakdown occurs when the ambient gas attains its critical pressure, which is a function of the nature of the gas species, the type of electrodes used and the distance between them, number of charged particles present, and the magnitude of the electric fields. In addition to this difficult problem, some of the other malfunctions and problems dependent on pressure conditions are: * Loss of pressure in sealed components.

0 Loss of lubrication due to evaporation or sublimation.

~eteriorationof adhesives such as loss of plasticizer due to evaporation or sublimation.

a Loss of convective heat transfer with resultant development of hot spots or cold spots.

Loss of dielectric resistance followed by corona discharge or arcing.

Fouling of terminals fc-llowing condensation of outgassed material.

~ossof system calibrat: ;n resulting from unavailability of convective heat transfer at the existin; pressure.

a Humidity, aerodynamic performance, radiation and ionization effects, electronic bombardment, etc.

a Pressure difference across surfaces sufficient tc cause mechanical failure. Many of the problems listed above can be eliminated or mi.nimized by the use of pressurized containers, coatings, selective insulation, encapsulation, shielding, etc, (Refs. 3 and 4). Also, in many cases possible difficulties can be avoided expediently by employing selective commands for the experiment; e.g., operation of the system at a limited voltage can be commanded for unfavorable pressure conditions, with full voltage operation at favorable pressure. Of course, it is hoped that those problems related to pressure conditions, as well as any other malfunction, will be discovered and eliminated during the thermal-vacuum testing of the spacecraft. These tests attempt to simulate the temperature and pressure encountered during launch and orbit flight. Chamber pressures below lom6torr are produced to establish the appropriate mode of heat transfer and hence provide simulation of the thermal environment. In testing, it is assumed that after long term vacuum exposure the pressure at any point in the spacecraft will be comparable to that produced and measured in the chamber itself. But this cannot generally be verified, due to the absence of pressur 2 instrumen- tation at inaccessible internal locations and due to the fact that many materials in the pressure range to loe9 torr expel adsorbed and absorbed gases. The latter as well as other gases nroduced by evaporation, distillation and decomposition, affect the pressure donsiderably. These "outgassing" conditions are likely to exist for a long time and set up, ht certain locations of the spacecraft, pressures higher than the chamber pressure (unbeknown to the experimenter). In addition, the transient pressures at the launch phase of the flight may produce . pressure differentials depending on flow conductance, which cannot be reproduced during testing. Such differentials could establish conditions conducive to failures cr temporary malfunctions.

In view of the above, it is the intent of this report to provide an analytical tool which can be used to estimate the variation with time of pressures in a spacecraft or other system of interconnected volumes. Knowledge of these pressures, which will permit undesirable pressure conditions to be identified, should he useful not only in connection with the qualification and ixliability testing of the spacecraft, but also in determining the appropriate time f~rcertain spacecraft operations. It is expected that the accuracy of the mathtmatical results wlll depend on the extent of knowledge of geometric leakage paths, container volumes, and material behavior. Many uses of this analytical tool will be indicated later.

In general, the analytic?! tool must provide a description of the internal Sressure vs time for each compartment of a system of compartments arranged in a most general way, and connected by passages of different types. The following data must be given or assumed in c.vder to carry out the calculation:

0 External pressure vs time under flight conditions, or the chamber pressure during testing.

Type of ambient gas contained in the system. Temperatures of ambient gas and of internal surfaces.

Volume of compartments. /" Surface areas of compartments and of components within the compartments.

Characteristics of the surface areas, i.e. the initial and final outgassing rates, and the outgassing time constant for each outgas sing material.

.Areas, dimensions and types of passages and leakage paths between compartments.

ANALYTICAL MODEL Figure 1 shows a model of volumes and connecting passages chosen so as to represent the general case of a system of interconnected compartments. The

Figure 1-Arrangement of Volumes and Passages Used as a Model for the Derivation of Flow Equations flow equations derived for the model are intended to provide a flow description for any system. The model is ar -anged so as to provide both series and parallel flow thraugh main passages, lwkages between cha mbers, and outgassing from different surfaces. The prrows in the figure show the reference flow directions, corres,wnding to the relative magnitudes assumed for the chamber pressures. The acfval flow directio:~dl be dictated by the actual pressure in each chamber, which will be a functior. oi the system parameters. Outgassing from surfaces is shown by arrows originatir :at the separation walls.

Prasure-Time History Equations

Equating the change of mass of a gas stored in a volume V to the difference of the masses of gas entcring and leaving that volume in time dt gives

Since the change in density, according to the equation of state, is

substitution yields

The flnw rate, Q, may he defined in terms of a conductance, C, and the pressure differential, AP , as

so that the above isothermal equation of mass balance becomes: 9 One can add to the right side of this aquaxon the sources Gi , representing the outgaming from the surfaces within volume i. This outgassing, as will be dis- cussed later, is independent of pressure but depends on temperature and on the nature of the outgassing materials in the chamber, The basic equation for the pressure history in a volume then becomes

Applying this equation co each of the volume of Figure 1 in turn, for an assumed monotonic sequence of pressures

one obtains: - For a given (t), the above equations can be generalized as follows to describe the rate of pressure change in the i th chamber of an N chamber arrangement:

'V (Cij+ Lij)(P. I -Pi) , j =o I where

L, i=l,2, 3 ,...., N;Gi = QGni;Ci , = C, and Li , = - Cn

(The sum in is over all the different outgassing materials n contained in volume i.) The symmet,q conditions for the conductances are valid in the molecular flow regime but not always in the viscous flow regime (Refs. b and 6).

The sign of (P. - I? ) determines the direction of flow between chamber i J 1 and chamber j. For the fictitious chamber arrangement shown in Figure 1, matrices could be used to provide the passage and leakage conductances. Any other chamber arrangement could also be described by equatiollp (2) and the appropriate conductance matrices.

A solution of equations (2), given the initial chamber pressures, the conductances, the environment pressure as a function of time, and the outgassing data, will provide the pressure-time history in each chamber of such an arrangement. The functional fdrms of the conductances, outgassing functions, and external pressure forcing functions will be described next.

Conduct an c es

The conductance of a passage is defined as the rate of flow of gas through the passage per unit of pressure difference producing the flow:

The conductance is a function of the geomstry of the passages, the temperature, and the molecular weight of the gas flowing. It is also a function of the pressure and viscosity of the gas depending on the flow regime.

The characteristics thatgovern the flow regime of the fluid ars the Reynolds number, Re = UpD/p, which relates the inertial force to the viscous force, and the Knudsen number, K, = h/D,which relates the mean free path of the gas to a characteristic dimension of the container (Refs. 5-7).

For Re > 2300, the hertial force prevails over the viscaus force, except for a narrow region adjacent to the walls, and the flow is turbulent. During evacuation, turbulent flow can occur near atmospheric pressure for a very short period. It is experienced when high capacity displacement pumps evacuate the system through improperly sized, long, small diameter passages (Refs. 6-9). This type of flow will not be included here because of its short duration, and (mainly) because of the difficulties it entails. For Re < 2300, the viscous force prevails and the flow is viscous or laminar.

The conductances employed here are appropriate for the three types of flow which occur at low pressure: viscous, slip-intermediate, and free molecular flow. The parameter which differentiates these regimes is the Knudsen number. This number, which can be also expressed as the ratio of the Mach number to the Reynold's number (Ref. lo), compares the mean free path of the molecules to a characteristic dimension of the container. It indicates whether the molecules are colliding with each other 'or with the wall of the ccntainer. The following criteria can be used to distinguish the flow regimes (Ref. 11):

For K, < the flow is governed by collisions of the molecules with each other and is viscous.

For 10'2 < K < n 10, the flow is an intermediate type characterized by collisions of the molecules with each other and also with the container wall.

a For K > 10, the molecules are colliding with the confining wall and the flob is of the free molecular type.

From the formulae for the conductances given below, it will be seen that the molecular conductances are independent of pressure. This is because the flow is a random motion of the ~nolecules. The intermediate flow is a combination of the viscous and the molecular types of flow. The flow changes from completely viscnrrs at high pressure, where a zero relative velocity between fluid and wall exists, to a transition flow with a relative velocity at the wall. At lower pressures, the flow becomes a free molecular flow. Conductances for free molecular flow are modified by an experimental coefficient to account for the transition flow region.

Formulae for conductance of several geometrical arrangements are found in the literature (Refs. 5-3, 11-13). The list which follows includes the most com- mon conductances, taken, for convenience of presentation, fiom Ref. 8. These conductances, which are normally given for air at ambient temperature,, have been modified to make them applicable to other gases and temperatures. For geometric passages not listed, one can make use of the analogy between vacuum circuits and electrical circuits to obtain effective total conductances by c3mbin- ing simple conductances in series or parallel, as follows :

Series combination arrangement: = C- e a Parallel combination arrangement: c = e C cij*

1, Thin small. aperture (Orifice)

flow < a. Viscous i.e.. K n 10'~

For 1 2 u 2 .52,

For .52 2 u 2 .l,

For .l 2 u L 0,

b. Molecular flow i.e. K- > 10

c. Intermediate Flow i.e. lo-' < K, < 10

(Cij) mol t (Ci .) vi sc Cij = 2 a. Viscows flow

The conductance is inversely proportional to the viscesity, which in turn varies directly with the square root of the temperature (Refs. 11 and 14). The conductance of the air at 20°C has been modifled by tnultiplying its coefficient by the ratio of the viscosities and by a temperature function, so that

where 7) , the ratio of the viscosities, is given in Table 1.

b. Molecular flow

c. Intermediate flow

where the intermediate flow coefficient J is shown in Table 1.

3. Shori; tubes

a. Viscaus flow

One can use the seri;.:s combination of orifice and pipe, i.e., Table 1 Coefficients for Corlductarrces (from Reference 8)

1 I E,

I I H e

NH3 H 0 2 N 2 Air 0 2 A con

Rectangular met Flow htermedikte Flow Factor J I I Coefficients Y, a

Coaxial Tube Factor K

-50 .707 .86/ 1.072 1.154 1.254 1.430 /I 1.675 b. Molecular flow

c . Intern1 ediate flow

4. Rectangular Duct

a. Viscous flow

The conductance of air at 20°C, modified 1n the same manner as for the long pipe, yields the following:

where the values of 7 and Y , a flow coefficient, arc listed in Table 1.

b. Molecular fl2w

a2 b2 Cij = 9.68 (a) i.

~nerethe value of coefficient a is listed in Tabla 1.

c. Iritermediate flow 5. Long annular -tube a. Viscous flow

b. Molecular flow-

where the value of the coefficient K is indicated as a function of the ratio of the diameters in Table 1.

c. Intermediate flow

Initial Conditions - Boundary Conditions

In addition to the geometric description of the system, one must specify the type of gas and the pressure and temperature conditions which exist at the start of evacuation of the system. It is also necessary to establish the pressures at which the different types of flow regimes exist (namely the viscous, intermediate, and molecular flow regimes). At these pressures, which are established by the passage dimensions and the mean free paths of the molecules, the conductances appropriate for each flow must be used for the integration of the flow equation. As indicated previously ,the Knudsen number provides a criteria for the changeover (Ref. 11;: For Kn < 10 -2 the flow is viscous; For K, > 1.0 the flow is molecular.

The Knudsen number, with the substitution of the expression for the mean free path of the gas in terms of the pressure, temperature, and size of the mole- cule, becomes where a is the molecular diameter of the gas (0= 3.74 x lo-* cm for air), n is the number of molecules per unit volume, and B is the Boltzmann Constant.

The flow regimes can now be established in terms of the pressure P and a dimension D as follows:

8 Molecular flow: K n > l,O,

which for air at 25°C becomes

DP < 5 x (torr - cm).

Viscous flow:

which for air at 25°C is

DP2 .5(torr - cm). (25)

In the above, P is an average pressure and D a characteristic dirnensj.cn of the container. This dimension is, for example, the internal diameter of a pipe. In * general, it can be taken as being the smallest dimension in a passage or as an equivalent diameter for a passage of area A, i.e., The pressure of the pipe flow P, is taken to be the average of the inlet and exit pressures.

-Outgas sing I -unctions Also affecting the ambient gas in the container, are gases which evolve from the container surfaces and the equipment inside the container under vacuum conditions. These gases are those which were physically and chemically sorbed by the surfaces, those which were in solution in the material, and those arising from evaporation and decomposition products. The exact mechanism of outgassing is still a matter of controversy, but theoretical and experimental de- terminations of outgassing rates have been reported in the literature (Refs. 15 and 16).

It is found from experience that the outgpssing of materials may be characterized, in general, by the following statements :

The cutgassiag depends on the nature of the materials; for a given material it is a function of the material's surface treatment and of the atmospheric composition to which the material was exposed prior to exposure tcj vacuum.

The outgassing is proportional to the surface area and increases rapidly with the temperature. It decreases slowly with time and apparently never becomes zero at ambient temperature.

At pressures lower than loe3 torr, the outgassing rate is independent of the pressure; i.e., the number of molecules expelled by the surface per unit time does not depend on the pressure above the outgassing surface. This behavior has not been established with complete certainty, but is valid as a first approximation.

Outgassing rates of various materials at ambient temperature have been plotted as a function of tin-e. Figure 2 shows degassing rates for some materials. These outgassing fluxes have been obtained by exposing the materials to vacuum and comparing the rates with those provided by known conductances, or by reading the rates of pressure increase.

Tabulation of outgassing pmperties of many materials is indicated in Tables 2 and 3. These tables, reproduced from Ref. la for metallic, elastomeric, plastics, and ceramic materials at 2S0C, list the outgassing rates and their slopes at 1, 4, and 10 hours of exposure to vacuum. A knowledge of the outgassing rates of the materials at each instant is required for the solution of the yessure NEOPRENE

I ALUMINUM

-TEFLON

5 TIME (hr)

Figure 2-Degassing Rate Per Unit Surface Area Versus Time for Some Materials Table 2 Outgassing Rate Constants for Metallic Materials (From Reference 15) Am- amof ounple (an?; So - pumpin8 opted for dr at 25 % (I/=); Kh- air equivalent outgmaina mts after h hr of pumpin# (T~fr-l-rcc'~-an'~; ah - akdutr dueof dope of 19-log mph of ou- mta *r. tiam after I hr of pumping.

1. Strinlerr rtttl EN SOB (polished, np# dcqnusd) 2. Strinlnr rtnl 3. Stainlcu steel 4. Mild rtctl 5. 1\411d #eel (rlightly NOW) 6. Steel, rusty 7. lron 8. Nickel plated mild rtccl (polirhed, vapor dem) '). Nickel plated ateel 10. Chrome plated mild rtttl (polished, vapor de 11. Aluminum, anodized 12. Aluminum, bright mlled (cleaned in Stergaw) 13. Aluminum 14. Duralun~inum 15. Aluminum spray coated mild rteel 16. Aluminum spray coated mild rteel (wted) 17. Copper (24 hr at 95 per cent humidity) 18. Copper 19. Dasr (24 hr at 95 per cent hivnidi~) 20. Srass, cast 21. Brass, wave-guide oation 22. Nickel 23. Nickel 24. Molybdenum 25. Tantalum 26. Zirconium. 27. Tungot? 79. Silvq

history equation, Equations for the outgassing as a function of time, G(t), have therefore been fitted to the data in the tables. Techniques described below were used to calculate the parameters of these c .pations for several materials.

For ~ut&assingrates at temperatures other than 25OC, an estimate of the increase ai the outgassing rates with the temperature can be obtained from the empirical relation proposed by Arrhenius for the increase of the rate of chemi- cal reaction with the temperature:

where Q is the rate at temperature T, Qo a constant (determined from Q at 25OC), AH a constant representing the energy of the activation of the material, R the gas Table 3 Outgassing Rate Constants for Non-Metallic Materials (From reference 15)

Am= arca of sample.(cml); S. = pumping speed for air at 25 OC (Ilsrc); - air cquivnlcnt eutgnring rato after 1 hr of pumping (Torr-l-scs-~-~n~-~); K, = outgassing rate after 4 hr of pumping; a, = absolute value of slope of log-log graph of outgassing nte vr. time rftcr 1 hr of pumping; a, = absolute value of elope of log-log- -- graph - rftcr 4 hr; tn = time at which a begin$ to increase rapidly above a, for given sample (hr); w: = square of sample thickness, wn (mm).

Material

A. Ehtomrrs 1. Natural gum rubber (32 Durometer) Natural gum rubbcr (32 Duromcter) 2. Natural white rubbcr J.!260 totd outgassing 3. Katural white rubber 1.1 260 non-condensable in liquid . air 4. Natural crcpc rubber (vulcanized with S 20 min) 5. Natural crcpe rubber (vulcanized with To 20 min) 6. Ncoprene F-905 7. i\;eoprenc 60' Shore 8. Neoprene 9. Ncoprene (24 hr at 95 per cent humidity) 10. Neoprene (outgas~d+24hr dry N,) 11. Neoprene GNA (V-4-2) (.) hr 50 per cent n). humidity) 12. Neoprene (bcll jar gasket, 50 Durometer) 13. Neoprene 1157 (suliur free) 14. Rcd vacuum hose (24 hr at 95 per cent humidity) 15. Red vacuum hose (outgassed +24 hr d y NJ 16. Yerbunan 17. Pcrbunan PD 651 (vulcanized 30 min) 18. Pcrbunan DR-39 (low acrylonitrilc) 19. Pcrbunan (Bayer) 20. Pcrbunan (Bayer) (tempered) 21. Duty1 GRI (V-3) (4 hr 50 per cent relative humidity) 22. Duty1 (VR-41) (40% C black; vulcanized 12 min) 23. Ilutyl (IIIJ. 1200) 24. Ilutyl (lr U. 12000) (non-condcnaabla liquid air) 25. Convnscnl 26. Convascal (atruGed # in. aquare) 27. Convaseal 28. Polyirocyanate rubber D-43 29. rtygon 30. Iiycar 13-50 (ASTM spec. SB-510) 31. IIycar H-50 (ASTM spec. SB-510) 32. Silicone rubber (Wacker R 60) 33. Silicone rubber (Wacker R 80) 34. Silicone tubber (24 hr 95 per cent humidity) 35. Silicone tubber (outg~ued+24hr dry NJ 36. Siiastic 37. Silicone rubber 38. Silastic X-6145-C 39. Silastic 8-1 64 (red, 62 Durometer) 40; Silo~tirF.0 (white, cured 24 hr at 480 OF, 74 Durometer) 41. Silostic 50 (white, 53 Uurorneter) 42. Silktic 67-163 (red, 61 Durometer) Table 3 (continued)

Material

- B. Plas!ics 1. Teflon. Dupont 2. Tcflon, high temperature (24 hr at 95 per cent humidity) 3. Teflon, high temperature (outjpsed+24 hr dry NI) 4. Tcflon, Ccroc (24 hr at 95 per cent humidity) 5. Tcflor~,Dupont 6. PTFE 7. Kel-F (Oak Ridge National Laboratory) 8. Kcl-F 270 (Reairtoflex Corp.) 9. Aralditc D 10. Araldite D 11. Araldite B 12. Araldite F 13. Araldite, Typc 1 (Ciba, cured 15 hr 266 'F) 14. Epoxy resin 200 (24 hr 95 per cent humidity) 15. Epoxy rcsin 200 (outgassed+24 hr dry NJ 16. Eppon, Shcll Oil Co. 17. Plcxiglns (Alsthom) 18. Plcxiglas 31222 (Rohm and Haos) 19. Plcxiglas (24 hr at 95 pcr cent humidity) 20. Plcxiglns (outgasscd + 24 hr dry NI) 21. Xlylar (24 hr at 95 pcr cent humidity) 22. AIplar V-200 (24 hr at 95 per cent humidity) 23. hlylar V-200 (outgasscd+24 hr dry NJ 24. High tcmpcrature Thermalon (24 hr at 95 per cent humidity) 25. Polyvinylchloridc (24 hr at 95 per cent humidity) 26. Polyvinylchloridc (outgasscd + 24 hr dry N3 27. Polycthylcnc (RASF) 2s. Polycthylcnc (Dynamit-AGj 29. Polynm~d(I!sycr) 30. Ultmtnid (IlhSF) 31. I'olyvinylcnrhnrol (BASF) 32. Polystyrol (IlASF) 33. Polystyrol (Dynnmit-AG) 34. Polyurcthnne (Baycr) 35. Tcxtolite 11564 (24 hr at 95 per cent humidity) 36. Tcxtolitc 11564 (outgassed + 24 hr dry NJ 37. Sylon 38. Pcramfil (General Electric Co.) 39. Polycstcr (Zcnith Plastic Co., fiber gbluninqte) 40. Polyester (Plastone, fiber glur !ambate) 41. Polycster (Perault) 42. Polycstcr, Norsodyne 43. Cclluloid 44. Polythene 45. Methylmethrcryhtt 46. Epicote

T C. Ccramiu 1. Porcelain, glued 2. Steatite constant, and T the absolute temperature, The rates of many organic reactions are doubled for each 10% rise in temperature. A rule of thumb frequently sug- gested is that a 10% change in absolute temperature will cause a 10:l change in outgassing rate (Ref. 7).

From the plots of Figure 2, the outgassing rates are seen to be represen- table by the following functions:

and

In these expressions qo is the initial outgassing rate, q , is the final outgassing rate, a is the slope of the outgassing curve (27) and r is a time constant which represe!~ts, for the curve (28), the time required for the outgassing rate to drop to a valm

It should be pointed out that an expression such as the above could be obtained experimentally for an entire pazkage containing various materials. The equivalent outgassing so obtained could then be used in calculations involving the interaction of this package with others. The outgasing can be programmed as a mathematicd function or provided in tabular or graphiqal form for the use to be made of it here.

With the outgassing rates at 1 hour, 4 hours and 10 hours provided by the tables, the parameters of the exponential equation (28) representing the outgassing can be obtained as follows. Using the system of equations where the Qi are the known rates, and A, B, C are the parameters to be found, the following ratio is obtained:

Letting x-' = e -3/c and x-~= e-6/c ,this may be rewritten

which when solved for the positive root yields

from which the parameter 1/C is found: With C known, the pa.;:ameter A can then be obtained as

and finally

The tables provide outgassing rates at only two different times for some materials. However, the slopea of the outgassing, a, are provided at these points. In these caszs, to fit the data to the exponential equation, one ca~use the average of the slopes to establish

The parameters A and, B are then obtained as above, by using equations like (31) and (32).

Table 4 presents the values of A, B, and C calculated for some of the materials listed in Ta.'bles 2 and 3.

If the tables provide only one rate of outgassing and a corresponding slope, the outgassing equation to be used is Q = At -a. The coefficient A can be obtained directly by substitution of the given values, i.e.,

In general then Table 4 Coefficients for the Outgassing Equatihs

--r -t- ..ZLe~~-P4E~-L9943.b UP7k 0 0 . STAINLESS A -. CHECK 1.75000000E-07 1.)5COOOOOE-07 CHFCK 4-4QllWonF-00 ~.990..9DQ?E'~O~6,. .-- , - .....- --- CHECK 2.101100000E-08 2,lOOOOOOQE-08

_I_L~&Y3%lmlkU -- i! = 4*WE!ibE:LI_L- .~_L?BnibB918E99 - . q1~u.sI Ea. CHECK 3.40000GOOE-07 5.40000000E-01 1,40U(L~OOE-07 -_LL4000~'~-QI - __-_.I_._.__.__I ._____- CHECK 5.0000000OE-08 5,00000000E-08

4.w-07 4..9M9 0UOErJ.?.. ... - - - -. -.---.- CHECK 1.~100~000~-07 1.0100000n~-01

L * 2.wk-Ob i! = 9*v&5k9wQ E. -=-2.7~66~~3C)t'01 YiCfili~pQL. .- .- CHECK 5.00000000E-07 ~.0000000~~-01 ~.bOGOnOOO€-o9 36_0CO.OQUIE--OV . .- - CHECK 1.0000fl000E-09 1.00000001E-09

r = 1.64347917F-Ub El = 1*0bL??1LS622~.'0'-. - C -.Iq64124488E 00 ad~>s - ---- CHECK 1.00000000E-06 1. OOOO.O~O~~E-O~

--- A 4.56447441F-Ub 0 2.h7370208 -~ Y 7 A- .La CHECK ~.OOU~~OOO~-O~1.0 L~F~.L(-~-~~DP~PPOF-O~ A@ A = 4.412439b5F-118 U * 4.89773118 u 7-UilLUML-OA 9rD CHECK 2.17b37641E-09 2.1 - 5.a -39 A = 5.31418bblE-07 0 * 1.4993B401 7 -.- 5.0 CHECK 2.50000000E-07 2.5 -- - 1 -2.~3~- 0 7 - .- 1.5 = 1.28652981E-Ob 0 * 2.42698515 Y d.--nh -4.4 CHECK 7.57850283E-07 7.5 I:YCfK 2 --07 3. t) = ~.1~~5120~~-07R = 8.99630405 -- cu~w~.auaa-nns-...a. a cn. :K ~.~~OOO~OOE-O~1.5 rurr 9 4-01F-01 -9,.4 A = 1.2019897ME-05 0 8 5.45fl0105S f'UEPY 7.nnnnnbnag-nA - ,.-LO CHECK 1.54473024E-06 1.5 K 5--07 -- . --%A = 2.527946916-117 w a 5.87401012 WY I --n7 4 CHECM 2.05685441E-U8 2.3 L:YCPK f~-nAU%04F-u9-,d where (3, , tn and a are the values given in the tables. In particclar, if the given value of Q is A = Q n that corresponding to one hour, then n . External Pressure R (t)

Th,e pressure of the environment must be known as a function of time in order to solve ihe system of differential equations. Two vacuum environment profiles will be oncountered by a spacecraft - the prcssure versus altitude during launch and orbiting, and the pressure produced by pumping devices in a test chamber.

The launch and o~bitingpressure versus time profile for a spacecraft can be obtained by combining the pressures versus altitude as f0ur.d in tables with the altitude versus time of the spacecraft (Ref. 17). For example. an equation for the external pressure can be written usir-g simplifying assumptions, for a satellite having a perid T, in an elliptical geocentric orbit. Let Pma, and Pmi,, be the environmental pressures at perigee and apogee respectively, Pa" the average pressure during orbiting and to the time from launch to reach orbit altitude. Then one may write simply: For

while for

max f Pmin 'max - '.in P>tO, Po= t I. sin o) t, 2 2 where

w = 277/Ts, and Pa,, = atmospheric pressiire at launch .

In the above equations, it has been assumed that the drop in pressure is linear with altitude during launch (which is approximately true for altitudes up to 125 km). For computing purposes, however, it will only be necessary to have pressure versus time in tabular form. > The evacuation of a test cbsmber is a functim of its volume adthe pumping speed of the system. It is dependent on the temperature, hbmidity, and surface conditions of the chamber, its material, the gases present and many otiler factors. It is thus quite possible that the results of one test will be somewhat different than another. The pressure versus time data for a particular chamber can be dsscribed analytically and used for the eolution of the chamber-spacecraft system. As an example of this, Table 5 shows the pumpdowl equations for an 8' x 8' chamber, in part derived from the data shown ir, 2'igure 3. The data at the 55°C and -10°C test chamber temperatures shown in this figure cover only pressures below 10-3 torr. The evacuation time from 760 torr down to 10'3 torr is a small fraction of the total evacuation time and was not shown on this graph. The pressure for this interval was assumed to decay exponentially from time zero to .9 hr., followed by a straight line decay to 1 hour. This is in ac- cord with other experimental evidence. For the same time range, a straight line pressure drop can also be assumed. Calculations to fit these data and the above assumptions have provided the equations sho~min Table 5 hr the empty 8' x 8' test chamber at the two different chamber wall temperatures.

Equations for chamber pressure profiles like these indicated here can be derived for other chambers. However, test data on the evacuation of any chamber can also he used directly in tabular form for the solation of the pressure equations. The latter method will generally be used here to calculate pressure profiles.

Heat Transfer Considerations

The pressure relation equation (2) has been derived under the assumption of isothermal flow conditions. This presupposes an average speed of evacuation and sufficient heat transfer from the c~ntainerto the &as to maintain a constant temperature. This condition is .a fact approached dcriug evacuation of a test chamber or in actual flight, with the exception oi the very start of evacuation. At the start, there is a very rapid evacuation to represent the pressure drop experienced during rocket ascent. The flow is turbulent atid viscous, and is provided by the rapid chmgirg environment ar by large capacity displacement pumps. The rapid evacuation produced a sudden drop in tempcmture, 4-5°C for a large vacuwn chamber, followed by z tempershlre recoveF k c1; to the ambient wall temperature. During this very short and rapid exhn~?.s+,%. :: beat transfer from the wall is not sufficient ta maintain the gas terrgdramre constant and adiabatic expansion of the gas is approached. When the rate of expansion of the gas becomes moderate, and the rate of pressure drop is reduced, the heat input from the wall is sufficient to compensate for the heat loss caused by the expansion. An estimate of the temperature effect can be carried out as follows.

The heat gain of the gas i+itime dt is

TIME - HRS. Figure 3-Evacuation of Clean, Dry, Empty 8' x 8' Vacuum Chamber for Vacuum Testing of Small Spacecraft where A is the wall surface, Tw and Tg are respectively the wall and gas S temperatures, and h is a heat transfer coefficient covering conductive, convective and r adiative heat transfer and dependent on many variables such as flow regime, gas type, and initial temperature.

The heat gain of the wall in the same period is

where C is the thermal capacitame of the container and TW1is the container T Setting dQ =- dQ the heating or cooling temperature before it changes to . W , rate of the wall due to gain or lossif theat to the kas is found to be

From this ewation, the gas temperature can be obtained provided ,the coefficient h, the initial conditions, aud the way in which the wail temperature varies with time are known. The solution would have to take into account heat gained or lost by the walls, including the gains due to solar radiation, aerodynamic heating, albedo and IR radiation, and power sources in the system together with the losses due to reradiation, conduction and convection from the walls.

One of the difficulties resides with the heat transfer coefficient. This coefficient chaages radically from the viscous to the molecular flow regime and is related to the gas pressure by an '5"shaped curve. As shown in the kinetic theory of gases, the coefficient of heat conduction in the viscous flow regime is directly related to the gas viscosity and to the coefficient of heat capacity at constant volume (Refs. 10, 11, 14):

Consequently, it varies directly with the temperature and is not affected by the pressure. Making appropriate substitutions in this equation and including the variation of specific heat with temperature leads to the Sutherland relation for the coefficient of heat conductivity for various gases (Ref. 11). One could use this coefficient of heat transfer at pressures in which viscous flow occurs. In this range, heat transfer by radiation is a negligible part of the total heat transfer because the emissivity of the internal surfaces is low, the temperatures ill- volved are low, and the coefficient of conductivity is sufficiently high. For pre- sure corresponding to the molecular flow regime, Lea, when K > 1, the heat transfer becomes orders of magnitude smaller than the viscoui coefficient (Refs. 18 and 19). The heat transfer is then provided by radiation, and conduction and convection are almost inexistent. Depending on the dimension of the contxiner, the changeover from high to low conduction heat transfer occurs between 1 torr and 10-5 or 10'6 torr.

From the above, it appears that as first approximation one could assume a coefficient of heat transfer varying inversely a~ the gas density,

and that the heat balance equation would be

In order to get the ratio of densities appearing in (44), one must estimate the gas temperature, which will change with the pressure. From the energy equation, assuming no inflow and the absence of external heat or work, the change in the total internal energy of the gas is equal to minus the enthalpy carried out by the gas, Lee,

E'-E= AH, Rearranging, dividing by m' , T and C and making the substitution C /C = y , e v P v

Assuming the perfect gas law and that the process is isochoric,

PV I P'V m= - and m = - T RT ' BR B ' one has

which substituted into (46) gives

The ratio of masses in terms of pressure is

and because p = m/V and p' = m' /V the following is obtained for the density ratio in terms of pressure ratio: This expression allown one to estimate the heat transfer coefficient as a function of the pressure ratio and the tjme, tilnd hence to estimate the heat flow from the wall to the gas or vice versa. By arkiterative procedure, one couid therefore obtain a simultaneous solution of the pressure equations (2) and the heat transfer equation (44). The appropriate iterative procedure is as follo vs:

1. Assume, as a start, a constant gas temperature Tg ; calculate the conductance and outgassing; and upon integration of (2) obtain the pressure P', and the density p' from (49) and temperature Tg1from (47).

2. Calculate the coefficient of heat transfer h from (43), and, from (44), knowing the wall temperature, evaluate the new gas temperature T . g

3. Calculate as in step one the conductance for ti:.2 next time interval and repeat the procedure.

The following points concerning the temperature and the isothermal flow conditions employed here should be kept in mind:

1. The temperature is approxiciately constant during the entire evacuation process with the exception of a very brief period at the start of evacuation.

2. A complete heat transfer analysis requires the inclusion of all forms of heat transfer and of heat flow from all directions. It would have to include radiation from space and from other radiating surfaces, conduction from adjacent walls, heat sources and other detailed properties of the walls.

3. Techniques for performing complex heat transfer calculations with a certain degree of confidence are being devised for spakcraft. Such calculations could provide temperature versus time for the surfaces which could then be used to estimate the gas temperature.

4. If the temperatures of the walls are known as a function of time, the-r effects can be utilized to establish the outgassiug rates of surface materials and the gas temperature can be estimated and incordorated in the gas conductances.

METHOD OF SOLUTION - COMPUTER PROGR4M

The program for the solution of equations (2) was coded in Fortran langu- age for the CDC 3100 computer. The numerical integration scheme used was of the fourth order Runge-Kutta type, which requires no starting values other than the initial conditions (Xo, Yo ) and which permits one to change the interval of integration, h, at any time without redoing the previous computati

+ =Y, +1/6(k, t2kl t2k2 tkj) tO(hS), where the k, are calculated fro=

and 0 (h is a trun~itionerror on the order of hS.

The integration time interval is increased exponentially from its initial value, h, to a final value of 2 h in order to speed up the computati.on and reflect the exponential behavior of the pressure time function. To prevent instability of the solution, however, the time interval iu also modified in the process of integration as follows:

At each integration step, the program evaluates the parameter

where the k are the Runge-Kutta variables and E is their average. If CT < 1, the time interval used for the integration has provided a value not too differeqt from the previous value. The time interval i~ acceptable and the computation continues,

If O- > 1, the change from one value to the next has been too great and hence the interval is unacceptable. As a first step, the interval is reduced by 20%, the Runge-Kutta variables are reevalwted and the criteria above is rechecked. If the criteria that GI be less than one Is still unsatisfied, the interval is reduced to 1/2 the previous time interval.

Examples of typical program inputs for the me- and three-volume cases, together with the corresponding solutions, ar,: contained in Appendices A and B respectively; the program itself is documented in Appendix C.

COMPARISON OF EXPERIMENTAL AND COMPUTED RESULTS

In the process of developing the computer solution to the above system of equations with variable coefficients, several combinations of volumes, connecting passages, and outgassing materials were investigated. Some of the profiles computed will be presented in the next section together with an explanation of the parameters chosen to characterize these curves. In this section a comparison of the calculated profiles with experiment will be made.

The characteristics of the systems chosen for comparison, such as the volume dimensions, the pas sage dimensions, the type and amount of outgassing materials, and the external pressure profile were determined by the experimental investigation. The tests were also used to establish the pressures at .which corona discharge between electrodes in the container would be initiated and extinguished and the corresponding times,

Figure 4 is a schematic of the pressure-time test setup and the orifice construction. The one-liter volume was fitted with one of three different orifices, ,437 in diameter, .I37 in diameter, and ,040 in diameter, connecting the compartment to the simulated space environment of the 12-inch diameter by 18-inch height bell jar. The evacuation was provided by a 140-cfm mechanical roughing pump and 2-1500 litjsec oil-diffusion pumps baffled with liquid nitrogen. The bell-jar pressure profile simulates the preesure profile encountered by a Thor-Agena B rocket carrying a 1000-pound payload into a 160-mile orbit. A Hastings thermocouple pressure gage and a nude ionization gage were used to record the pressure in the compartment. The pressure in the bell jar was recorded by a Hastings thermocouple gage and an ionization gage. The polymeric materials included in the compartment, selected as being typical of the encapsu- lants used in flight systems, were: Eccofoam FPH, with a density of 4 lb./cu.ft.; \ ORIFICE

THERMOCOUPLE . PRESSURE GAGE rlONlZATlON I GAGE INDICATOR INDICATOR

- NUDE IONIZATION CAGE - SIMULATED SPACECRAFT COMPARTMENT, 1 LITER POLYMER SAMPLE

2-1500 LSEC-I DIFFUSION

PUMPS LN2 BAFFLED.

CFM MECHANICAL PUMP. VACUUM BELL JAR 12" DIA. x 18"

Figure 4-Pressure-Time Test Setup silicone rubber, RTV 11; and epoxy, Biggs 823 resin. The test specimens of these mateeals were produced in the laboratory in accordance with accepted spacecraft application tecbiques. The Eccofoam and RTV samples had a surface area of 140 cm2, while the epoxy sample consisted of a conformal coating about 0.015 inch thick over an aluminum tube with a lrurface area of 120 cm2. The coating was vacuum-processed while curing. The RTV samples were outgassed for 24 hours before the test. Non-outgassed RTV caused fluctuating ionization-pressure gage readings ' $n the 10 -4 torr region. This was attribtited to contamination of the gage elements, which rendered the gage useless for pressure measurements. The *+hour outgassing phve is, however, typical of space hardware exposure in environment-chamber tesi3. The pressure versus time in the bell jar did not follow the same profile in each test but showed a variation of about one-Calf decade because of the influence of thc variable gas load aud orifice sizes. The temperature in these tests was bout 21.1°C (70°F). Figures 5, 6, and 7 show both experimental and computed results for various combinations of orifice size and outgassing material. The pressure profiles for each combination were obtained mparately and superposed in these figures for convenience.

Comparing these profiles, it is seen that the computed results agree very well with the experimental results. The difference (values in the sane decade) may be attributed to:

a The difficulty of reproducing exactly the same pressure profile in the vacuum jar in the different rum.

Gage errors auil errors in gage-reading.

Diiferences between actual material properties those rwsurned in computation.

For the computation, a mathematical descl?ptim of the outgassing material is used. The clda for. this representation are obtalned from the lizerature and, unless data are available on the specific materid bdng tested, divergence may be expected between test and analytical results.

It is expected that better definition of the materials shou.1d prodwe closer results, if needed, Ah:improvements in computed results can be expected when temperature gradients bek:een compartments are included.

APPLICATIONS AND PARAMETRIC PRESENTATIONS

Additional pressure profiles for .- mgle volumes containing various different outgassing materials were obtained. These are shown in Figures 8, 9, and 10, where they are labeled according to several parametric attributes, Profiles for the more complicated three-volume system were also computed, and these results are shown in Figure 11, parameterized in the same way.

Thc data obtained in the computation of these profiles can be used to estimate the iength of time that should be allowed before certain electrical functions which are affected by preasure can be safely performed. They may also be used to estimate the size flow passages appropriate, for a given volume or set of volumes and given outgassing materials, to insure that suitable pressures are reached inside thesevolumcr within a specified period of time. It would therefore be very useful to generalize ;he results of these computations for application *

LEGEND ., .,EXPERIMENT IMPUTED.

1 ( EPOXL, 0*20~D. )ELL JAR ENVIRONMENT USED It4 CWnUTArION. c 120 cm2) I 'AKEN AS THE AVERAGE OF EXPERIMENTAL. )ELL JAR PRESSURES WHICH VARIED AS MU..: 6 112 DECADE FROM ONE TEST TO ANOTHER

Do = .437 IN. 7 = 0.1 SEC.

T lME (HOURS)

Figure 5,-Comparison of Experimerrtal and Computed Results for a 1-Liter Comportment with Orifice Diameter .437 in., r = 0.1 roc, Ambient temperature (Outgassing material types and surface areas ore indiccted; data ort Outgassing ratoa used in the Com~uia- tion were from ref. 15) LEGEND -- - - EXPERIMEtd' ---COMPUTED

/ 1 SILICONE RUBBER I L-.--,- ] RTV 11 i 140 cm?\ '. -- C----. ---.- - 1 ! ,.. \ ----_ - ----.___ . . I ' '\., r------. '. / ' t FOXY SlXS 823 -- . -;3--.--....- EPOXY "133" --..._ t 120 cm2)

-6.00 t- ! ,*' I i i f L-- 'BELL JAR ENVIRONMEF4T &ED 'N CO?,dPL'?.IT !?I j TAKEN AS THE AVERAGE 9F €YPER:VtNTAL i 8tLL JAR PRFSSURE WttiLtI VARIED A3 MUL! i AS 1.Q DECADE FROM ONE TEST TO THt CTFER -0L ,,,,,-

7 = 1 SEE. ,134 IN.

-8.00 -LL~ 00 .do .80 1.20 1.60 2.0Q 2.40 2.

TIME (HOURS)

Figure 6-Comparison of E.:perimental and Con.puted Results for a l-Liter Compartment wrth Orifice Diameter ,134 in., r = 1.0 sac, Ambient temperature (Outgassing matsrial types and surface areas are indicated; data on Outgassing rates used in the Computa- tion were from r~f.15) I'"""I """'I "'1'"'"'

LEGEND: ---EXPERIMENT. COMPUTED.

SILICONE RUBBER, RTI \ (140 cm2)

-. /SILICONE(80.5 RUBBER cm2) ! I @ f

" - POLYURETHANE (140 cm2)

TAKENASTHE AVERAGEOF EXPERIMENTAL BELL JAR PRESSURE WHICH VARIED AS MUCH AS 1 /2 DECADE FROM CINE TEST TC ONE TTHER.

00 .40 .80 1.20 ' .& 2.00 2.40 2.80 TIME (HOURS)

Figure 7-Comparison of Experimental and Computed Results for a I-Liter Compartment with Orifice Diameter .040 in., r=10 sec, Ambient Tempera- ture (Outgassing material types end surface areas are indicated; data on Outgassing rates used in the computation were from ref. 15) 38

Figure Y-Pcmmetric Cuwes for o One- Comportment Thin-Or if ice Pressure Simulation (7= I .0 sec) a? Ambient Temperature

QL =QGAG IS THE GAS LOAD CORRESPONDING TO 'THE OUTGASSING RATE AFTER ONE HOUR, QG, FROM THE MATERIAL AREA AG.

SEC

COMPARTMENT

I \ \ T - 1.77 SEC \ -5 toir 1 \ QL = 2.42 x 10 ,z I r = 0.905 SEC \ -5 torr 1 QL = 2.42 x 10 5 I

.80 1.20 1.60 2.00 2.40 2.80 T1ME (HOURS)

Figdie 11 -Parametric Curves for Q Three-Compwtment System having Thin Orifices, 80 cm2 "PTFEn Outgassing Matar:al in each Comport- ment, and T =270° K. to other cases (Ref. 20). This can be done through the use of certain parameters, namely those which have been used to label the various curves shown in the figures. The choice of' these parameters is based on the following considerations.

The profiles show that within a very short period of time the pressure drops to a quasi-steady value. This sharp drop occurs in a region of viscous and transitional flow. In this region, the relations expressing the passage conductance are nonlinear and dependent on prewure and viscosity. Beyond this region, the flow is molecular and the conductance depends only on passage geometry. The quasi-steady pressure reached and the corresponding evacuation time for a given sys :-em are thus mainly a function of those parameters which characterize the flow in the free molecular regime. In view of this, the profile curves have been grouped in accordance with certain parameters in the molecular region of tbe curves which are amenable to generalization, namely the molecular time constant, 7 ,the outgassing material gas load at 1 hour vacuum exposure, Q,, and the quasi-steady pressure, Y .

The molecular time comtant, which relates the size of the volume to the pumping speed in the molecular flow region of the passage, represents the time needm far the pressure to drop to l/e = k3C8 of the initial pressure and is

v r = - ( sec) , S wherc V (liters) is the volume of the container to be evacuated and S (1i4/sec) is the pumping speed of the passage. The pumping speed for an orifice bf area A (cm 2) in the molecular flow region (corresponding to a pressur2 of 10'2 to 10-3 torr for the present orifice diameters and for air at 20°C), is a constant:

The time constant, which presupposes molecula;. flow with constant conductance and no source of gas in the volume being evacuated, is ~btairiedfrom the solution of the linear differential equation expressing the flow balance; i. e., in the molecular region and can be visualized as the slope of the log of the pressure profile at time zero.

If a constant i.e., independent of pressure and time, source of gas B, (torr- l/sec) exists, such as that provided by a leak into the volume, the differential equation will be

the solution of which is

Thm equation shows that as t -. ,the first term becomes very small, so that the second term controls the purrpdown. For Q, constant, an equilibrium pressure,

is thus obtained. This pressure representsi the condition for equilik rium between the inflow leakage, Q,, and the outflow through the orifice, SPL . But when the in-leakage is caused by material outgassing, the rate of inflow is not constant, but is a decreasiug function ef time. Consequently, after the initial rapid decay, the pressure contimes to decay dowly, rather than stabilizing at an equilibrium value. However, one can define a quasi-steady-state ovtgassing rate QL as the mtflow rate from the material after 1 hour of outgassing in vacuum, and then use the corresponding quasi-steady-state equilibrium pressure as one of the parameters des cribing the system. This equilibrium pressure will be: whpr~ (cm2) the surface area of the outgassing material; .: t: is

is the material rate of gas output after 1 hour of vacuum exposure, as given in Tables 2 and 3; and S (lit/sec) is the pumping speed for the orifice, as given by equation (53). This passure is not the ultimate pressure obtained in the volume but is representative of the slowly decaying pressure. Table 6 lists for various systems the geometric data, the outgassing material, the chancteristic rate Q, , the corresponding load rate Q, ,the calculated pumping speed S, and, finally, the resulting parameters 7 and P, .

CONCLUSIONS

An analytical tocl which provides internal pressure profiles for volumes exposed to vacuum has been developed. Comparison between calculated and experimentally cbtained pressure profiles has shown sufficient agreement between the two. The computer program developed to provide this information by solving a system of differential equations is general and can be applied to a system having many volumes, interconnected with various types of passages and containing materials outgassing in a known manner, such as is the case in a spacecraft. The computer results, obtained in both numer' :a1 and graphical form, can be used to provide the following information:

The long term pressure conditions in a compartment.

a The time required to reach the quasi-steady state pressure.

e The pressure differential asross surfaces.

The effects of variation of chamber volume and passage size on attain- able pressures.

The results for an assembly of experiment packages, given the results of tests of the individual packages.

The equivalent conductance of an experimental package tested in a vacuum chamber, including the outgassing effect of materials and surfaces in the packgge. OOUOOOO...... ,4dd4ddd

ff"O". ..a. 2zzz2zz XXXXXXX q'mhl'c) hl CDNITOwOm. 4C;hiACjt-rn. c The behavior of a system in any other envirmment, given the results obtained in a vacuum chamber.

Many pressure profiles have been calculated both for a single volume and for multi-volume arrangements; some of the8 e profiles have been included here. Parameters b-ve been introduced to generalize the results of these particular test runs EO that they may be used to estimate conditions for other similar systems.

RECOMM ENDATIONS

Calculation of pressure prc)files should be carried out in caajunction with a thermal analysis of the system, which provides the transient temperatures of the system walls. By the method delineated here, these tnn~neraturescan t~2 used to estimate the gas temperature and cwsequentiy provick improved valueq of the flow passage conductances. The data from tbthermal analysis can also be used to establish the temperatures of the compartment surface more accu- rately. This better knov~ledgeof the outgassing surface temperatures should then, in turn, provide a better definition of th:; naterial outgasskg rates. This requires, however, a better knowledge of the variation of matwal outgassing rates with temperature than is available at present.

As an additional improvement in the calculation of the pressule profiles, the computer program should be made more efficient to provide faster computation for very large systems.

REFERENCES

1. "Survey and Analvis of Volt.tge ~reakdown/~oronaProblems," K. Mercy, March 1968, Quarterly Progress 'Hepoact,Goddard Space Flight Center.

2. "High Voltage Breakdown Problems in Scientific satellites," X-300-41-66. February 1966, Goddard Space Flight Center.

3. C. Lundeman, 'Corona and High Voltage Bre~kdownof Electr'cal Cmductors in Vacuum," Failure Analysis Heport 347-001, January 1965, Q.raUiy Assur- ance Branch, Goddad Sgace Flight Center.

4- 'manual fc: the Prevention of Electrical Ureakdawn in Spac~craft,'~F. W. Paul and D. Burrowbridge, May 1368, Goddard Space Flight Center, NASA SP-208. 5, Pirani, Memd Yarwd, J., -Principle of Vacuum-- Eugineering,- Chapman and Hall, London, I. 96 1. 6. llrxnbull, A. H., Barton, R. S., and Riviere, J. C., ----An Lntro&?ctionto Vacuum Technilwe,- Jo Wiley, New York, 1963. 7. Vacilum Technology and Space Simulation," D. Santeler, et al., NASA SP- 105, ,660 8. DeLaFosse, J. and Mongodin, G., Le Calcul De -La ~echnique Du Vide, Le Vide #92, Mars -Avril, 1961.

9. Steinherz, He A., Handbook of High Vaca~r:Engineering, Reinhold Publiwh- - --* ing Corp., Few York, 1963.

13. Eckert, E. R., Drake M. D., Heat and Mass Transfer, McGraw Hill Book Co., 1959. -- -

11. Dushman, S., Scientific: I mdations of Vacuum ''echnicp:?s, (To M, Lafferty, .. Editor, J. wiGy and Sons, Nee* York, 1462. 12. Guthrie, A, and Wakerling, R. K., -Vacuum Equipment an,: Tee-hniques,- McGraw Hill Book Co., Inc., 1949.

13. Barringtcn, A. E., High Vacuum Erspjneerin& Prentlce ??.I, Inc., Englewood Cliffs, New Jersey, 1963. 14. Lee, J, F., Sears, I?. W., and Z'urcotte, D. I,., StLLtbtical Thermodynamics,- Addison-Wesley Publishing Co., Reading, ~asi;1963.

15. Daytan, B. B., "Reiaticrm Betwaen Size of Vacuum Chamber, Outgassing Rate. and Required Pumping Speed," 6th National Sympdum on Vacuum Technolcgy Trails ., Pergamon Press, 1959.

16. Daytcn, B. B., 'lOutgassing Rate of Contamina+ed Metal 8th National Vacuum Sjmpoeium and 2nd International Congress on Vacuum Science, Pergamon Prese, !.Qql.

17. Neff,, W. J., Montes de Oca, R A., "Launzfi Environment Profiles for Saunding Rockets and Space~raft,~~NASA TN D-1016,

18. "Advances in Cryogenic Engineering,ll K, D. Timmerkl~s,Editor, Vol. 5, Prmeading~;of Cryogenic "snginaexbg Conference, I S..mm Prese, New Yorlr. 1960, 19. "Thermal Insulation system^,^' A Survey, NASA SP 5027, 1967.

20, Scialdone, J. J', ~~~~ient Pressure in a Volume with Various Orificea and Outgassing Materials," Joint AIAA, ASTM, IES, Space Simulation Confer- ence Transaction, Seattle, Wash., Sept,, 1968. APPENDIX A

TYPICAL COMPUTER INPUT DATA AND C(,RRESRlNDING SOLUTION FOR THE SINGLE CHAMBER CASE APPENDIX A

TYPICAL COMPUTE 3 INPUT DATA AND CORRESPONDING SOLUTION FO 3 THE SINGLE CEAMBER CASE

0 INPUT DATA .o*.*...... *.*o..*ooooooo~oooo**e*oo**oo~e*o*~~o*o*oooo

rjrF VFRSUS DRESS,ME ENV 1ROY qEYT vicnros - 760.0nnooonon~ TORR s6cnUDS .nnninnat~no TORI SECoYD5 .OnnO5n~onP TnRR FtCOWDS .O~~F?~PP~OTORI <€corns - .nnnninnonu TORR SECONDS .nnnFy45cnO TnRQ SEcnrOS - .nnnoi~nrn~TORI SECOVDS .nnnotofirno TORR SCCokDS - .onn11n8snno TORI SECnrnF .nnlIUQ72EnO TORI s€CnrDS .oonoo~~~~oTrim SECOUDS .nqnon5rcn0 TORI SFcorvDS - .onnnn5rnoo rnaa SFCONUS .OE00~46l?OU rORQ SkiQNDS .nnnnn4wno TORI SF:OYDS .nnnon4ncno rnfiR SFCnYDS .n~nno~73notnna SkCIINDS .nl~rnv*noroRa SECONDS . ,090On34qnO TORR SFCnYDS .nnsno~rano TORR SECONDS .oononm5no T~RR SECONDS .onlon??~n~TnRI StCOkDS .nnnnn?w~nu tnnR SECnNDS .onnnnwinn rnRn 5ECOhD5 - .onncnloono TORI PFCONDS - .no~nni~snoTORR SECONDS - .nnqoni%~no TORI SFCIINDS .oo~nnl*~.aaTORR SECCUDF .o~)roniinno TORI SFCOFIDS .oonnnionno TORR SfCONDS - .nnno~~o?nnnTORI

APPENDIX B

TYPICAL COMPUTER INPUT DATA AND CORRESPONDING SOLUTION FOR THE THREE-CHAMBER CASE APPENDIX B -% TYPICAL COMPUTER INPUT DATA AND CORRESPONDING SOLUTION FOR THE THREE-CHAMBER CASE --- .------~ S-"TTA~ *-A- *-- .-----

------CYII#(I 7 VOLUCE. i.ooooi~tans lllllh~~I)UH ?a((((,tom ------OURtbCE hS4 NO. I . @*.SO@@W.CM.e aAl8atAL 11 @POUT -- outolintw cumctrrrsrm - :I

APPENDIX C

COMPUTER DOCUMENTATION

Input Cards

Program listing

Program Flow Charts CARD NO. CARD COL- SYMBOL IDENTIFICATION

1 1 - 10 R Press Number of Pairs of Entries in the Time Versus Pressure Table, This is the Table dich also Defines the Forcing PunctFon. 11 - 20 Factor Floating Point, Nt;nber which Multiplies all Time Entries of the Forcing Function to Get ~imein Seconds, Tim (i) Time Corresponding to Pressure, Table (i) Pressure in Torr (i = 1,2,3,., .,N Press) (as many cards as N Press). Number of Chambers, Temperature in Degree Kelvin, Molecular Weight of Gas in GRM, Maximum Time in Sec, at wfrich Camputer ia to Stop, Initial Pressure of Chamber 1 ID ID DI W 2 DD Dl - ID 3 I# W ID 4 ## *D I* 5 DD *I bD 6 DD DD ID . 7 u DD n 8 Another Card Shauld be used for More Chambers, i,e,, for more than 8 Chambers, OOOOOOOO dnrrnetn\0wa CARD NO, CUID COL-

Liters of I1 I9

#I *I

I1 11

n I#

I1 ID

I1 n

11 I1

Another Card should be used for More than 8 Volume. NiiREA 1 Number of Surface Areas for Chamber 1 -2 I1 H I1 H I1 #I 2 NARIS 3 I1 I1 I* 11 11 I1 3 HAREA 4 H I1 I1 Dl I# I1 4 NAREA 5 ID II II 18 II n 5 NAREA 6 n n n ID #I ID 6 NAREA 7 n I1 I1 I1 I* n 7 NAREA 8 NAREA 9 Use Another Card as for Card 4 and 5, AREA GAS !I,K) ~ms,(an2) of surface K in chamber I. Gas (LK) Title of Material of Surface K in Chamber I, Initiai Outgassing Rate of Surface K, Final Chtgassing rate of Surface K. Time Constant, Outgassing of Surface Ko .. - - .- - - -- . -. .- -. , C CACT~Rs F1.0l1 1 hU*YR TO IIULTtPLI In€ ~IVLNTIM vws c w MmMwIn se~oros C IlN~Ilm TIRE IN s c rmu;1, CnsstUI-a 'C READ tb#.SIO%I PRESSUR .FACtOR MWESSUR r PRESSUI .S DO 3@17 1 ~.WRESSUR AEAO 160.3910 11 1 1

, 1017 111111 m tI.fACTPR . C -AlAa+uus- C ~OMVEIITAU f10W YOURS 10 SECONDS - -

C li-.Yh 1111) JS@@[email protected]@@I .I II 8 1CDM3llI

c2- . CCl -- CSII.JII) . CCI

DO an12 I a 14~

I 22w to.cr.. ---YZ?Y-*. 11b41.~~3) TAU w .C11.4, IN I YE . ICO*OllI

4rtr roir I ?,@b ::A; r..... C PLOT C - CALL C~I(YORIVaCI.IP0,SI C YET TIWE SCALE C MOURS . .7

-- 'C -. CLLL O~ID~~..O.,IS.~~M.-IO)

.@.*-I) --E------. CALL CLO~~O..~~..S) lrEl 2 00 7110 I 1.1ARRAT

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;*, REPRODUClBlLlTY- - -- OF THE- -, ORIGINAL-- ., - PAG

...... -...-. SOPI: FW AT ( ZbuC- - -.EJOICE ) . STOP -- - -- L 7VPE 1 CIRCULAR APERTURE

C ---- .- -- - .- - -.. - C IVPE 2 - LONU CIRCULAR PlPt C - - .-- - -.- - - 2 IF (OP - -015) 201~200~200 201 IF IDP - ) 202.2PS 2 3 201 CONDUCT a J.~*TM*CI(I:J~II)**~IC~~I~J~I()------'. - . - - - 00 TO 240 -- 201 XJ 1 TA0LEJ(PI) - - 50" XI m-i~@~ta~clii,~;i --CONMII-*Z I,C~I!~J,III ------. -- 501 90 10 9999 -.--- . -- . - - -.- 5Od CONDUCT CONDUCT TAILEJIPII

9998 RETURN -Cno XL..a X .~ 12. ABSF ~FLOA~F~N:)-*-VS V -. .Vl P~ Y.. -.-. . - . CALL PLOT (X-Y.~) - LLL- ----.----. - 4U XZ . IS . . . fihW----. - UU 140 1 *i,MM -- - SALL.PL!L._(& LLZ.) CbLL PLUl (XlrV2.2) . -- i~ xi a2 -----. - RUFF a 11

-Am 8 -@ --.*..-- ..- . - . X2 . X . -..@QJUhlrm- 00 150 J 11.10 CILC PLUT (xI,Y~.~) CILL YLllT ,~1.~2.2) ----RbL€.L' ,JL--- - -.- . . . - . . *I111

_ . .?L ._~.Y - .. . - . UU 355 1 .1.N* . Mule..- . .. CALL CLOl (Xi.Vlr2I CALL PLPl (X2rY1.2) RUFF s 11

. . . t Inl.~si~buOtltU7U 1lELl.1 TrnE OllTtWf~~~ ..-- -. - - .- . --WrwEEN CALLS W~ILAND roc . , -..

--(IOU 5 ssotuuzu 73 n I-,a- * rno 4Zlr.. .-- a#~~6 zoooooo~ 3u o ~0non4u LDA 0-2 I'UO 7 4400UU14 44 U PO0014 .IJ . - . .-. - .. ------. .- .. - sur AU~RE~S- bb0,O 19600001 15 1 06001 ? I NA 1 AUTUCLO. C4ARt LC1 - CMAMDRn UttSWW

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CfiA*UCO 1 will wULJ4c ut CIUMScN 1 NAIcA~II NUUdtO OC &*=A. PUN ;NAUBEU I Ci I.Jl .CJNDUCIAMCL ~iT'riN CC441E* I Ah0

MP*=S~U)-'IWIW. JC PA143 M LI*IYIES CACTOR .FLUAT I* PJIN* NUuCL4 TU WCTIPLV IMP GlWtN 1Ilk VUVLS IN Nbi* 1J CtT Tll* I*HCohOS TIUil' - 11- 1n SCCUN~S IAbLrill .raCsswc Ih lbH9 , ------ICLAD caon MVI I Rb / 64 I ------I VIA C09dA1 I IWAD CnOI MV I I dub1 8 be IINTJ frC LIST I I VIA CO1IAl I 8 a001 8------IOITO TW! LIST I ...... -.. LILT - .V(Vtl).l r ...... 1.*1 .

I I* 1< -----z-- . la ------*-- Ink.0 Clam D.v I LOO? b 1 . I V4A COIlAT I I .... - 3010 :""" '7 IINTO I- LISt I ------j-s

nEm CMUTea cuo *------i Mlf 11 ,------, ,,------I 1. ....LIST * .- . . / WRIT1 10 MV,I ....*....**I *I It VIA COIWT I LOOS ,'.rnm lm! LIST I'

-----"------I 61 I I IUA~ worn ocv I I VIACOIUT I / J I ooae C VIA eOaNA1. / I CIM THE Llsl I 3"** / ------I_------IN10 T*F- LIST I I

*------*I 19 CI(I.J.SI cet cat I. Js.1 cu Cll1t.r.R) CCS ----I------. - I I I 89 ----UIUI-I 0 /'mar re am 0 ,' VIA1a &r ,,* I

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...... I wort rr

I CLOT I

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. m Em0 w w *-- . LC*? . .- w a0 w 00 . a room.. .---

a*. 8-->I 14 .------* 1 4 .XW$ a.IO1 I I IOU. f

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