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Produced by the NASA Center for Aerospace Information (CASI) (SUA—TE-82s12) ATTIt002 COOTS" ate as" 543-22315 CONPINSAIXON 1110t9molt SISTIN Tot 4"Im FiOHZ—E St1ISCBAFT (li fS S) 38 P 8C 103/51 S01 CSCL -223 tlsclas 03/18 03"1 - NASA TECHNICAL MEMORANDUM
NASA TM-82S17
ATTITUDE CONTROL AND DRAG COMPENSATION PROPULSION SYSTEM FOR THE GRAVITY PROBE-13 SPACECRAFT
By D. H. Blount 4 ^ Structures and Propulsion Laboratory Science and Engineering Directorate ^^^E1 V EO
January 1983
NASA
George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama
n I - WFC - Form 3190 (Rr Jnr 1071) rriwi7- LV A&MAM VIVA a SAMN ' i. RKIPM NO. !. WIMP MUSIC* NE a. "cWtIR•a CAT NASA TM-82517 4. TITLE AND SUSTiTIJ :. RE*ORT DATa Attitude Control and Drag Compenastion Propulsion Jarnma .--.,.19 .._•.^ = PUPORM1NS ORGANIZATION 00E System for the Gravity Probe-B Spacecraft
7. AUTNO!(S1 G.PeRRORM"Is OROWIATI N( REOIIRT it D. H. Blount s. PERFORMING ORGANIZATION NAME AND AODMU to. WORK UNIT N0.
Gea jr C. Marshall Space Flight Center 11. CONTRACT OR GRANT NO. Maralmll Space Flight Center, Alabama 35812 1 3. TYPE Of REPORT PERIOD COVERED 12. SPONSORING AGENCY NAME AND ADOIESS Technical Memorandum National Aeronautics and Space Administration Washington, D.C. 20546 14. SPONSORING AGENCY COOK is. SUPPLEMENTARY NOTES Prepared by Structures and Propulsion Laboratory, Science and Engineering Directorate.
16. ABSTRACT
An on-board propulsion system for attitude control and drag compensation is presented which uses helium boiloff gas from an experiment package dewar as propellant. This boniloff gas would normally be vented non-propulsively. Use of a small allowable temperature range in the dewar is exploited to store helium and accommodate incompatibilities in dewar heat leak and thruster demand flow over periods of more than one orbit A relatively detailed thermodynamics analysis of the two- phase helium dewar and simulation of pressure loss through the helium distribution system is included.
17. KEY WOROS 16. OISTRISUTION STATEMENT
Unclassified — Unlimited
Is. SECURITY CLASSIF. ( t fe"R) 20. SECURITY CLAtSIF. (M tue 21. NO. OF PAGES 22. PRICE Unclassified Unclassified 37 NTIS
VC - gr*rn 53141 (MY 19M For Wo b r 11600W Took* of UJIM"NUM 80-Vi o. SPelata" v"2" aslsl TABLE OF CONTENTS
Pop
I. INTRODUCTION ...... 1 i H. SYSTEM REQUIREMENTS AND DESIGN FACTORS ...... 1
III. HELIUM THRUSTER PERFORMANCE ...... 3
IV. PROPULSION SYSTEM DESCRIPTION ...... 5
V. SYSTEM ANALYSIS AND SIMULATION ...... 7
CONCLUSIONS ...... 8 REFERENCES ...... 10
APPENDIX A - HELIUM DEWAR THERMODYNAMIC DERIVATION ...... 11
APPENDIX B - HELIUM DELIVERY PRESSURE LOSS DERIVATION ...... 17
APPENDIX C - HELIUM DELIVERY PRESSURE LOSS RESISTANCE FACTORS DETERMINATION ...... 20
APPENDIX D - COMPUTER SIMULATION ...... 26
PRECEDING PAGE BLANK NOT
iii LIST OF 1LLUSTRATUM
Figure Title Page
1. Gravity Probe-B Spacecraft attitude control system ...... 2
2. Orbital variation of required total thrust ...... 3
3. Helium propulsion system schematic ...... 6
4. Helium distribution system...... 7
S. Porous plug flow versus pressure drop ...... 21
6. Cooling rings schematic ...... 22
7. Distribution lines schematic ...... 24
hr DIFINITION Of =VUBM
Q Hat W Work
V Volume
P
M Mass
W Mass now rate
4 Heat transfer per unit time
U Internal energy
u Specific internal energy
h Specific enthalpy
t Time
v Specific volume
P Density
T Temperature
A ) Function of (given variable)
R Gas constant; flow resistance
C Constants in curve fits
W. Cp Specific heat at constant pressure
D Constant in cum fit; hydraulic diameter W. c Constants in curve fits
CONY 1 Conversion constant
L Length
A Area
gc Dimensional constant
v
NRe Reynold's number
k viscosity
X Flow resistance factor
Subscripts
V Saturated vapor
L Saturated liquid
fg DitTeremce between property of saturated liquid and saturated vapor at the some temperature and pressure
D Total dewar
i Initial state
T Total
B Base or starting point
P Thruster supply delivery point; porous plug
CR1T Porous plug critical flow rate point
O Nominal reference point
C Contraction
E Expansion
X Cross sectional
h Hydraulic
R Cooling ring
L Line
SR Support Ring IL
aoawu. PACK r OF Poae puurtr TECHNICAL. MEMORANDUM
ATTITUDE CONTROL AND DR" COMPENSATION PRWULSION SYSTEM FOR THE GRAVITY PROBE-B SPACECRAFT
1. INTRODUCTION
The on-board propulsion system for the Gravity Probe-B waft must provide attitude control plus thrust to effectively cancel the atmospheric drag encountered at the relatively low orbit dictated by current shuttle capability. A propulsion system was desired which would utilize the boiloff of helium gas from the experiment package dewar as propellant. This helium bclloff would normally be vented non-propulsively and, thus, in a sense be "wasted." A system was devised which could r ye tt^e thrust requirements and the available helium boiloff to provide 100 percent drag free coal of the vehicle. Derivation of the necessary thermodynamic equations is shown and a computer code for a rela- tively rigorous simulation of the two-phase helium dewar is provided along with details of the delivery line pressure loss calculation. These mathematical models were used to estimate the dewar pressure and temperature as a function of time during the predicted extremes of thruster demand and dewar heat absorption.
11. SYSTEM REQUIREMENTS AND DESIGN FACTORS
The requirements for the propulsion system were established by the need to provide precise attitude control and to provide an additional thrust vector to effectively cancel the vehicle drag incurred by the spacecraft. The thrusters are paired back-to-back with clusters of two pairs located at the ends of the four solar array spars for a total of 16 individual thrusters. Their location relative to the vehicle is illustrated in Figure 1. Each of the thrusters consists of a flow control valve and nozzle and is required to produce a maximum thrust of 650 dynes with a thrust tolerance of t2 percent of the open loop commanded value. The desired transient response of the thruster to a step input thrust command is that of an underdamped second-order system
n e -aw t F/FCOM - 1 + sin (wn t [1 - t2 - a) 71-7-7 where a = cos 1 (4) in radians t = time in sec F - delivered thrust OFMNAL PAGE 19 OF POOR QUALM g W {^ {JG ^
F Im g^
F
8
a
oa
^ J J Z
Z 7V
Fcom a command thrust .0-44"k PP.QV is Of P00,q guftrij W n - undamped natural frequency radieWsec
r - damping fwtw with the values of natural frequency, w n ,and damping fWtOf- t, Oct at 10 Hz (62-8 RAD/860 And &707 respectively.
The thruster flow control valve is requirod to reqmd to thrust command changes a small as 0.1 dynes in the closed loop mode. This very small thrust tolerance is necessary to maintain the Vehicle within the acceleration limit of 10'I0 s (this assume& two thrusters are operating together for drag makeup). this The maximum total thrust required at any one time is set at 1300 dynes. Although thrust happen to be equal to twice the maximum thrust of two nozzles, as many as eight duuftn could be operating simultaneously at lea than their maximum values. This maximum thrust is set by the maxi- mum atmospheric density expected during a 90 min orbit. The required thrust will statistically vary as shown in Figure 2.
100
90•
80.
70-
1;w
so.
L-4i I I I Soo 700 900 1100 1300 MWIMO TOTAL THWT — OMS
Figure 2. Orbital variation of required total thrust
3 The constraints widdn which the helium boftoff duuster system and operate are set by experiment paduve dowar dam, the 1 year Ufa ngvk maot, and the soke but pkkw Copmblity of the helium delivery lines. The beat leak into the dswar (which as lad 300 ks Ioad of Whim In a saturated liquid form) is expected to wo fmm a low of 0.1849 to a high of 0.2326 W. A naimbd dewar temperature of 1.6°K with an allowable tolennoe of t1.I'K was conddned qty to pro- vide the supedluid helium II condition required by the expo invent package. The aolsr heat picked up by the boiloff helium as it cook the dower thermal shields and Uww m the lines leadingto the modules at de ends of the solar array spars raises its temperature to between 300' and 37M Ffady, the vehicle solar array and power supply system indicate a power/w ht penalty of I.S kg/W. Thsaa requirements are summarized in Table 1.
TABLE 1. SYSTEM REQUIREMENTS AND DESIGN FAM)RS
Satellite Life (minimum) I 1 year
Orbit Period ! 90 min
Dewar Initial Helium Load 1 300 ks
Maximum Thrust per Nozzle 1 650 dynes
Thrust Tolerance Open Loop 1 12 percent of commanded value
Transient Response Parameters Damping Factor - 0.707 1 Natural Frequency =10 Hz Sensitivity (minimum thrust increment) Closed Loop 0.1 dynes 10 Allowable Unbalanced Drag Acceleration 1 10 S
Maximum Total Thrust Required 1 1300 dynes
Helium Dewar Heat Leak Range i 0.2326 to 0.1849 W
Nominal Dewar Temperature I 1.6°K
Allowable Dewar Temperature Range 1 1.5 to 1.7°K
Boiloff Delivered Temperature Range ( 300° to 375°K
Power Penalty (system man per W) 1.5 kg/W ik
111. HELIUM THRUSTER PERFORMANCE
helium The ideal (one-dimensional, frictionless) vacuum qpecific Impute of a nozzle at an area ratio of four was calculated using the ODE computer program (1 I for a cumber temperature and characteristic of 3WK and 3 torr, respectively. This ylekled a velocity of 3566 ft*c sad a vacuum specific impulse of 168.9 lbf sec/lbm. However, at the lbw dumber pressures and small Most dame- ten, the throat Reynolds' number will be quite low (approximately 100) and there will be uvnide able friction loss. Testy conducted at Stanford University (2) on a 20 deg half angb conical node with a 1.37 mm (0.054 in.) diameter throat, and area ratio and chamber conditions as above, gave vacuum specific impulse figures of approximately 130 lbf sec/lbm. This specific impulse efficiency of maul- mately 0.77 has been substantiated in wyet unpublished testa at MSFC with a nozzle of simile geometry but a larger throat diameter of 5.01 mm (0.196 in.). It therefore appeeva that a specific impulse of 130 lbf sec/Ibm, or possibly larger, is attainable for the planned prom system. However, for the system developed in this report, a value of 11 S lbf sec/1bm was used for the specific impube to provide some contingency. Even this conservative value is very good in comparison with alternative propellants, particularly when it is available as a waste gas from the dewar boiloff.
IV. PROPULSION SYSTEM DESCRIPTION
The main problem to be overcome on the supply side of the propulsion system is in accom- modating (with minimum waste) the inequality between the boiloff produced by an arbitrarily varying heat leak into the dewar and the on-demand varying flow rate required by the thrusters. Comers of the maximum dewar boiloff due to heat leak (0.2326 W) and the maximum required thrust (1300 dynes at 115 lbf sec/lbm specific impulse) into helium flow rates gives values of 9.75 and 11.S3 mg/sec, respec- tively, and there is no guarantee that the maximum heat leak would occur at the same time as the maxi- mum thruster requirement. Obviously, at other times the thruster demand would be lea than the avail- able boiloff and a surplus of propellant would be available.
A system which could save or store the excess flow to be used to cover the periods of deficiency is most desirable, especially if it can be accomplished without a weight or power penalty. Such a Wstem is made possible by exploiting the small, but significant temperature range allowable for the dewar. The large specific heat capacity, low heat of vaporization, low heat leak, and large helium mass relative to the thruster demand flow rate all combine to cause even extremes in the thruster demand and heat leak to result in very small dewar temperature changes over long periods of time. This allows variations in flow rate and heat leak to average out, thus minimizing any dewar vetting or hating. Averaging the heat leak extremes gives an average boiloff of 8.75 mg/sec and using Figure 2 gives an orbit avenge demand of approximately 4.44 mg/sec (500 dynes weighted average thrust at 115 lbf see/lbm specific impulse). Therefore on a per orbit basis there should be ample propellant boiled off. A schematic of the system capable of accomplishing this is shown in Figure 3. The dewar temperature would be con- trolled within the allowable range of 1.5° to 1.7°K by activation of a heater on the tank at the low temperature limit and venting non•propulsively at the high temperature limit. The heater would require negligible power due to the very small mass flow rates required and the low latent heat of vaposizaticn of helium. The non-propulsive vent logic would be combined with the attitude control/din makeup system. When the high temperature limit is approached and venting needed, the controller would select a thruster which was not at full thrust and increase its thrust and that of the opposite one of the back- to-bad pair an equal amount. This would effectively vent the extra helium boiloff without the cost
5 RNWRMMM
O POROUS PLUM P AiE SEPARATOR HEAT ADDITION TEMP FROM PICKUP NaELDE HELIUM Tw 0 CONTROLLER 14 < T < 1.ft HKAT ADDITION MOM LpIRS;
HELIUM___w DEWAR VENT SIGNALY! @PAR a MM FOLD VOLUME T • l9^It f0.1 WATT 9 l THRUST S.0
TYPICAL THRUST CLUSTER 0 Of 4)
SEO DYNES O-FULL THRUST MAX THRUST PROPORTIONAL EACH NOZZLE CONTROL VALVES
Figure 3. Helium propulsion system schematic. and complexity of an additional non-propulsive vent valve and lines. Although temperature is indicated as the control variable, pressure could be substituted as the measured variable since it is related to the temperature by the two-phase conditions existing inside the dewar.
A sketch of the distribution system from the dewar to the thrusters is shown in Figure 4. The helium exits the dewar through a porous plug which acts as a phase separator, keeping the liquid helium inside the dewar and allowing the vapor to escape. After the helimum leaves the porous plus, it cools the dewar heat shields wing the four cooling rings located around the neck tube and exits the dewar into a 1.75 in. OD supply line. This line carries it doam the side of the dewar to the support ring (with both sides coupled by the cross braces) which is used as a manifold to distribute the helium to the insid of the four solar array spars. A cluster of four thrusters is fed from the end of each spar. Solar heating of the dewar heat shields, lines and spars raise s the helium temperature to at last 300° K by the time it reaches the thrusters. Use of the support ring and solar array spars to deliver the helium Sava the weight of additional lines and the large size both reduces pressure lost and provides volume (approximately 117 liters) to reduce pressure transient fluctuations.
6 DIAL PANE 19 OF POOR QUNM MEAT SMIE COOLING RINGS
POROU SUPPORT RING MANIFOLD
SOLAR ARRAY PAR
THRUSTERS
Figure 4. Helium distribution system.
V. SYSTEM ANALYSIS AND SIMULATION
To properly evaluate the flow averaging effect of allowing the dewar temperature to vary to effec- tively store liquid helium along with enerrj to convert it to vapor on demand, a relatively rigorous thermodynamic analyses of two-phase helium storage was completed. This analysis included heat addition to the dewar; vapor remoc-a `ar thruster demand; changes in the temperature, pressure, and deco ty of the stored helium; and transition from one phase to the other. Details of the derivation of the equations and representation of the thermodynamic properties are covered in Appendix A.
A pressure loss equation for the helium gas delivery system Is derived in Appendix B and includes use of an average density through each individual flow _resistance. A constant temperature is assumed to exist across each resistance element although the temperature can vary from element to element. Chet-king the Knudsen number, N Kn , inside the 1 in. OD (0.02 in. wall) dewar tube which is the most stringent point in the delivery system; (Le., where the highest Knudsen number+~ would b , expected); -•'
AMIGMMI PAN 13 NKa = K T - 2.85 x 10'3 QIJM ti'1f P+rl;2r
when
K - Boltzmann constant - 1.38 x 10.16 nrK
T - temperature = 213°K
P = pressure = 3.0 torr
d - molecular diameter (helium) = 2.18 x 10 cm
r = tube inside radius = 1.22 cm
verifies the use o the eont4nuum equations since the transition range from continuum to free molecular flow is usually ao;epted as
0.01 The resistance factors for use iii the delivery system pressure ion calculation are determined in Appendix C. Details on line sizes and lengths can also be found in that section along with flow curves for the ►orous ph ig at the dewar exit. A computer simulation bated on the equations and factors developed in the three appendices is presenter in Appendix D, along witA% a sample case. THe code was used to evaluate the temperature changes at the extreme (worst case) conditions and the results are shown in Table 2. The first two cam explore tie extremes of heat leak and thruster demand for the full dewar with owes three and four the same, but with only 5 percent of the helium remaining. Case five was used as the sample case in Appendix D to get larger, more obvious changes and has a very small amount of helium and an unreal- istica:ly low (Le.' 0.0) heat leak coupled with maximum demand. All of these cases show ghat 150 min of extreme conditions can be tolerated before a temperature limit condition is even approached (starting from a nominal 1.6°K condition). This means that temperature fluctuations during more than one 90 min orbit can be averaged out. Pressure loss through the distribut;an system at the maximum thruster demsnd rate of 0.01153 g/sec, and at a low dewar pressure of 4.20 toff (1.533°K saturation temperature) was found to be 0.385 toff which is considered satisfactory. CONCLUSIONS A propulsion system utilizing the boiloff helium gas from the experiment package dewar can be made fearible by exploiting the small allowable temperature range of the two-phase helium dewar. S'hh ► small temperature fluctuation allows liquid helium and sufficient heat to vaporize it to be stored in the dewar for later use when a high thruster demand flownte is required. r !empesat rye limits of 1.5° to 1.7°K allow a sufficient range to average the expacted variations in ht.at leak and thruster demand over more than one 90 min orbit even under worst case conditions. 8 F TABLE 2. COMPUTER SIMULATION RESULTS FOR EXTREME CONDITIONS Initial Temperature 1.6°K Saturation Pressure 5.689 toff Conditions Results @ 150 min Initial Helium Saturation Mass Demand Flow Heat Leak Temperature Pressure Case (grams) (B/sec) (w) (OK) (ton) 1 300,000 0.0 115 3 (Max) 0.1849 (Min) 1.598 5.650 2 300,000 0.00 (Min) 0.2326 (Max, 1.605 5.800 3 15,000 0.01153 (Max) 0.1849 (Min) 1.588 5.388 4 15,000 0.0 (Min) 0.2326 (Max) 1.634 6.561 5 550 0.01153 (Max) 0.0 (Below 1.533 4.204 Min.) ORIGINAL PAGE 19 OF POOR QUALITY 9 REFERENCES 1. Gordon, S. and McBride, B. J.: Computer Program for Calculation of Complex Equilibrium Com- positions, Rocket Performance. Incident and Reflected Shocks, and Chapmat0ouquet Detonations. NASA SP-273, 1971. 2. Bull, John S.: Precise Attitude Control of the Stanford Relativity Satellite. SUDDAR No. 452, Stanford University, Stanford, California, November 1971. 3. Hendricks, J. B.: Characterization of Superftuid Porous Plug Performance. Proceedinp of the 9th International Engineering Conference, Butterworth and Co., London, England, 1982, pp. 190-193. 4. Krause, Helmut G.: Orbital Aerodynamics for the Gravity Probe B, Configuration No. 27B, September 18, 1981. MSFC Internal Memo/ED33, December 11,1981. 10 i E I OMOM PAGE 0 APPENDIX A OF POOR QUALITY HELIUM DEWAR THERMODYNAMIC DERIVATION P Vv NV ur hr i V q ML UL First law energy balance (neglecting potential and kinetic energy): SQ - S W +(u+Pv)in 6Mjn-(u+Pv)Out8MOut=dU or in time rate of change with S W and S Min equal to 0. qdt - hv dt=dU out q - hv d (1) The dewar internal energy, U, is the sum of the vapor and liquid portions U=Mvuv+MLuL Substituting the following equalities M=pV u = h Pv p=1/v VV =VD - VL by = hL + hfg 11 z MM and roanwqft Ova an expression for the internal wmV in properties dependant on the satmt ka, T, and a time dependent variable, the liquid volume, VL. U-VI,, OL+hfg)"P)`VL (P (PV V (hL +W -PLhL) Functionally then, U depends only on dower temperature and time U = RT,t) OFORMO POOR L. QUALITY PAGE N in differential form dU = at dt + aT dT IT t and the time derivative of the internal energy is dU _ aU + BUdT (2) dt at IT aT t dt Evaluating the time partial using the expression for internal energy above gives av au = - (p v (hL + hfg) - PL hL) at T An expression for the liquid volume was found as follows (assuming the mass in the tank exceeds P V VD). The total mass is the sum of the mass of the vapor and liquid MT =P V VV+PLVL=PV (VD -VL)+PLVL and solving for liquid volume V _ MT - PV VD L (PL - PV) 12 If the thruster demand, W, is constant, the existing man in the dewar at any time is the initial lolled mar less the flow rate times the elapsed time MT=Mi-Wt 4RiGUW1L PAGE 63 Substitution gives the desired liquid volume relationship OF POOR QUALITY VL = Mi - Wt - P V VD (°L - pV) and the time partial derivative of the liquid volume is aVL W at (PL - pV) giving the time partial derivativg for internal energy below aU p V hfg (3) l W at IT (PL - PV) _ h The temperature partial derivative for the internal energy was found similarly 8U aP V aVL VD - V pV aT taT= ( L) (hL + hfg) aT + I(PL - PV) hL - hfg] V D - VL D + [PV VD + (P L - PV) VLI aThLLP + PV (V ) OT - V 8T and, from the expression for liquid volume, the temperature partial derivative for liquid volume is aVL Mi - Wt - P V VD VD aPV aT(p l _ PV)2 ( - pV) aT 13 ... 3 After substitution and simplifying, the temperature pwdd derivative for internd eater is iii below aul aP V [ I + )2] + pY !h%1 + . P V . l _ 8P COW 1 D TT t hfg aT p L- p V aT (P L - PV)J aT + ahL g _ hfg IpV 1 - PV ahf 11 + ^PV (Mi - Wt)• (4) aT (PL - VP ) aT (PL - VP ) aT L VJ Rearranging equation (2) to get the dewar saturation temperature time derivative (p LPV T [q - (hL + hfg) W] hfg - hL W dT a a _ l V) dt au I au TT— t Wit ORIGINAL PAGE N' abbreviating equation (4) into OF p00R QUALITY au a. = Ifl(T)l I VD + I f2J)I 2 (Mi - Wt) t and substituting, gives an expression to be solved for the dewar saturation temperature as a function of time with given initial condition and constant thruster demand, W. • PV dT q -gW [1+(PL-PV) (S) at Ifl(T)] I VD + If2(T)l2 (Mi - Wo Since the variables could not be separated, a numerical integration was required. The properties were defined by curve fits over the range of 1.4 to ! .8°K. Methods and constants follow: q = Const = input — heat leak, I/sec (W) W - Const - input -- demand flow rate, g/sec Ti = Const - Input — initial dewar temperature, °K 14 Omm . Ras W. OF QUAUIY Mi = Coen = input - initial helium ma k 8 Yp = Cant = input - dewar voltune, L pL = Coat = 145.1 g/L - halium liquid deneity, WL Helium vapor is assumed to obey the perfect gas lap a TR Pv g/L M, torr; rK) (6) R = 15,5938 I K OPv . P + 1 aP ^— BT RT2 YT aT L K (P. torn; T. °K: 8TaP . r)K (7) P = e(Co + CIO/T) + C2 T2) tar (r, K) (8) Co = 7.5959 Cl = 9.9416 °K C2 = 0.13913 OK-2 aP = i- C + CIO/T) + l(1/T2) + 2 C2Tj e(CO C2 T2) torrrK (T°K) (9) aT Using the Claushm Clapeyron relationship to get hfg C InPd = g =- 1 +2C2T dT WT-2 T2 hf, _ (- Cl R + 2 C2 RT3) Conv l J/g (T°K) (10) bhfg = (6 C2 RT2) Conv, VeK (TO K) 01) IS T ORIGMAL PAGIE IS hL m hLbm + f dhL OF POOR QUALITY TB dhL = cp dT - [T (!a—vTL ) - vL] Corw I dP P Since PL gg COnst, avL/aT a 0 PW and vL dP is negligiblenegli b ^B T hL - h Cp dT Lbaw + B with p = C co +c l T+C2T2 Let hLbase = 0. @ Tbase - 1.60K, then C' 2 + 3 h COT + 2 T C2 T + D J/g (T,*K) (12) L 3 Co 8.1071 i1eK c, -13.2199 J/g *K2 C2 5.7071 J/g *K3 D -3.842 J/g ML i T+ C2 T2 J/g OK aT ' co+c (TIOK) (13) J/L Cony I - 0.13331 torn 16 ORRWM PAGE 13 OF POOR QUALITY APPENDIX S HELIUM DELIVERY PRESSURE LOSS DERIVATION AP i It R2 R3 P4 The pressure losses are a combination of frictional lows and expanson /contraction type losses and the loss for each section can be expressed as the sum of these two, W2 W2 AP= fL +K D A2 p 2gc A2 p 2gc Since the flow is laminar, the friction factor, f, may be expressed as _ 64. 64 f NRe D^A µµ and the average density, p, can be related to a nominal density, p o, at a nominal pressure, Po, and the average pressure, P, by assuming it obeys the perfect gas law P - p RT, and the temperature is constant across the resistance element. p—poPo Combining and rearranging 64 g L Po K Po PAP =W+ W2 A 2gc D2 po A2 2gc Po Applying this equation to a line represented by four sections as an example 17 P1 API = K11 ' K21 W2 V POOR QUALITY P2 AP2 =KIZW+K22W2 P3 AP3 =K13W+K23W2 P4 AP4=K14W+K24*2 Summing API+P2 (Fl AP2 +P3 AP3 +P4 AP4)=(K11+K12+K13+K14)W+(K21+K22 + K23 + K24) W2 = KIT W + K2T yy2 The average pressure at each section is the upstream pressure at that section leas half the pressure on for that section P1 = (PD -API/2) P2 = (PD - API - AP2/2) P3 = (PD - API - AP2 - AP3/2) P4 s (PD - API - AP2 - AP3 - AP4/2) and substitution into the above equation gives APl 2 Ap 2 K D API - + P 1T W + K2T W2 ' P 2 D AP2 - AP I AP2 - 22 + PD AP3 - API AP3 AP3 2 Ap 2 - AP2 AP3 - 2 + PD AP4 - AP I AP4 -AP3 AP4 - 18 f ORKWM PAGE M f , Reanmnging and factoring OF PQ4R quAL"y KIT W + K2T W = PD (API + AP2 + AP3 + Ap4) - 2 (API + AP2 + AP3 + AP4) (API + AP2 + AP3 + AP4) Recognizing that the bracketed ternna are the overall loan, AP T, the expo aimpHfin to KIT W + K2T W2=PDAPT-2APT2 Salving the quadratic in W gives + -KIT K IT2 -4K2T(ZAPT2 -PD APT) W= 2 K2T or alternately for APT D APT =P - D2-2 (K IT W +K2TW2) . 19 OMWNAL PAGE 19 APPENDIX f OF POOR QUALITY HELIUM DELIVERY PRESSURE LOSS RESISTANCE FACTORS DETERMINATION Raistance Factors for Porous Plug Flow characteristics (Fig. S) for the porous plug were obtained from Reference 3. The dwrp change of dope of these saves was referred to as the "critical mass flow rate" point and bemm of it the curve required two resistance representations. The unit area of the tested pW& Ap, was the sanw as that to be wed on the GPB dewar. Temperature range for than equations is 1.6 Wit - [ 0 + 10 (T - 1.65)l x 10-3 g/sac (T, °K) The premmfiow relationship for flow below critical, i.e., low resistance, was AP - 0.5769 W torn * g/sec) FAP-0.5769FW . IfP'wPD P oP - 0.5769 PD 'V (1^V, g/sec; PD, tort) with K 1 i - 0.5769 PD . Above critical flow, i.e., high resistance, 3.65 W - 1.65 + 2-0 [T - 1.651 + A x 10.3 g/sec (T, °K; DP, torn) 0.2 x'.50 x 10"3 0 - 1.233 W - 1.233 [1.6S x 1(T 3 (1 + 9.S (T/ 1.65 - 1))[ 20 DIAL PAQE_W elelle LISK To • LIGK n To a IJK To m LOOK AP ftx Figure S. Porous plug flow venm prenure drop. FAP - 1.2337 1.233 F 11.65 x I(r3 (I + 9.5 (T/1.63 - 1))l If PD 1 P AP - 1.233 PD iV - 1.233 PD 11.65 x 0-3 (1 + 9.5 (T/1.65 - 1))] tor,2 a K I I W + c (PD,tom TOK) where K I I - 1.233 PD 10 C - -1.233 PD (1.65 x *3 (1 + 9.5 (T/1.65 - 1))l 21 0 o • - $x k N ^ Al O Av. W. • i!! JJ ppJ ^O 1 s O m _a s — 1^ n s • x G0 1 N!! — ^ r 0 X s gyp. ;^^; —^ IA ^ N r p Il') s OD 1 C4 I! •R q an U ^o o_ m' w s ^ Q Ff Q ^ w \_N O n !r1 • it! q N ^ s \O F- LLIV %0 fin .Q PC - . x ;Q Ln J O1J81 n s (N fir ^ SAM ^M • ► S(KRM o a ^^ 4 22 J Equation for Helium Delivery System Pressure Lou Simulati:xn for Computer Program * g/sec AP and PD toff aP=PD - V PD2-2(KITW+K2T W2 +C) W above Wait C = - 1.233 PD (1.65 x 10-3 (1 + 9.5 (TD/ 1.65 - 1))] K IT = 121.97 + 1.233 PD K2T =605.6 W below *crit C=0.0 K IT = 121.97 + 0.577 PD K2T = 605.6 where Wait = (1.5 + 10 (T - 1.65)) x 10-3 g/sec 23 j -96d ORIGINAL PAGE 13 OF POOR QUALITY ^o 0 '^ an M ^, oc m ac J ^ a ~ 24 K ELE - h i _2 C IE11T ELENEMT CONTR- EXPAN- - ^• IN IN I ACTION SION SE PLUG BELOW GRIT - - - 0.5769PI - 0. RP 1 PLUG ABOVE CRIT - - - - - 1.233 P - A RL1 2 POROUS PLUG CONNECTOR 6 .335 .0881 - .66 0.862 60.8 2* RR1 3 COOLING RING #1 27.3 .500 - - 6.861 - RL2 4 RING CONNECTOR 8 .460 .1662 .29 ,63 7.146 139.9 R R2 5 COOLING RING #2 27.5 .625 3906 - - 16.881 - RL3 6 RING CONNECTOR 3.5 .585. .40 .66 7.127 185.0 R R3 7 COOLING RING #3 27.9 .875 2*7656 - - 11.633 - R14 8 RING CONNECTOR 2.6 .710-3959 .55 ,65 6.368 174.4 RM 9 28.1 COOLING RING #4 1.000 000 - - 10.722 - 10 .96 .724 .28 .47 11.437 42.6 RL5 10 SUPPLY LINE 95 1.71 2.297 - .29 19.143 2.3 RSR 11 SUPPORT RING 132 1.25 2**7 - .33 23.29 .6 R16 12 SPAR - - .503 - 135 13.9 11295 BELOW CRITICAL FLOW .576 605.6 0 ABOVE CRITICAL FLOW 1.233P 605.6 25 ORIGINAL PAGE 13 APPENDIX D OF POOR QUAI-try COMPUTER SIMULATION The results of the derivations and constants from Appendices A, B, and C were coded into the computer program shown in this section. Input NT Total number of time increments — NP Number of time increments between printouts — DTM Time increment for integration step Sec WI Initial helium mass in dewar (liquid t vapor) gram WDT Demand flow leaving dewar gram/sec Q Heat leak into dewar watts VD Dewar volume liters TK Upper temperature limit of helium in dewar °K TL Lower temperature limit of helium in dewar °K TI Initial temperature of helium in dewar °K output Line 1 Input DTM WI WCT Q VD TH TL TI Time Initial Demand Heat Dewar Hi Temp Lo Temp Initial Increment Mass Flow Leak Vol Limit Limit Temp sec I gnus G/sec Watts Liters °K °K °K Line 2 Initial Property Values PD RG PP PRV DH PDH H PHL Sat Sat. Vap. aP/ aT a pV/aT Latent ahfg/aT Liq. ahL/aT Press. Density Heat Enthalpy P PV hg h ton G/L ton/°K G/L °K Jft J/G °K J^G J/G °K Line 3 Initial Pressure Loss DELP Delivery system pressure loss at initial conditions torr 26 Line 4 Initial Thruster Pressure OINOM PAW IN PV (W PON QUAUI'fY Pressure delivered to thruster at initial conditions torr Line S Current Property Values As line 2 without PD Property values at (current time - 1 time increment) Line 6 Current Dewar Conditions TM PD T DTDTM W Elapsed Sat. Dewar Temp. Rate Helium Mass Time Press. Temp. of Change (Liq + Vap) t P T dT/dt sec torr °K °K/sec gram Successive Line Pairs Lines 5 & 6 Repeated Next to Last Same as Line 3 for Final Conditions Last Same as Line 4 for Final Conditions 27 A 0111NWM PAGE 19 C DEFINE PROPERTY FUNCTIONS OF POOR QUALITY P(T) = EXP(CO + Cl/T + C2*T**2) RV(T) . P(I)/.(R*T) PPNT(T) _ (2.*C2*T —•CVT**2)*P(T) PRVPT(T) = ( —P(T)/T + PPPTIT))/(R*T) UHFO(T) _ (2.*C2*R*I**3 — CI*R)*CVI PDHPT(T) = CVi*6.*C2*R*T**2 HLtT) = D + SCO*T + (SCI/2.)*T**2 + (SC2/3.)*T**3 PHLPT(T) a SCO + SCI*T + SC2*T**2 C READ(7912) NT READ.(3 9 12) NP READ(3 9 11) DTM READ17 9 11) MI READ.( 39 11) MDT READ(.7, I 1 ) 0 READ(3 9 11) VD READ (7.11) TH READ(7. 11) TL READ(7 9 11) TI WRITE(2.10) DTM.MII.wDT.O.VD.TH.TL.TI C SET UP CONSTANTS CV 1 a-0.13331 R = 15.594 CO •.7.5959 Cl = —9.9416 C2 a-0.13913 SCO = 8.1Q71 SCI = -J3.2199 SC2_ = 5.7071 D = -3.842 C N=NT/NP C RL * 145.1 C INITIALIZE TM = 0.0 T = TI C PRINT INITIAL PROPERTY VALUES PD .= P(T) RG = RV(T) PP .= PPPT(T) PRV = PRVPT(T) DH = DHFG(T) PDH = PDHPT(T) H s HL(T) PHL = PHLPT(T) VIRITE.(2 9 10) PD.RG.PP.PRV.DH.PDH,H.PHL C CALC. PRESS. LOSS TO THRUSTER PLENUM PD = P(T) _ CALL PLOSS(wDT.PD.T) M C INTEGRATE TEMP. RATE. OF CHANGE FUNCTION OF '`RwA UOl I= I .N POOR QUALln DU 1 Ja i ow DH = DHFG(T) PRY =.PRVN.T(T) PDH = PDHPI(T) RG = RV(T) NHL = PHLPT(T) RR = RG/(RL - RG) M =41 - MDT*TM IF(RG*VD.GE.M) 00 TO 4 BI = VD*-(DH*PRV*(1. * RR**2) + R0*PDH*(i. + RR) - CVI*PPPT(T)) 02 = PHL - RR*POH - DH*PRY*(1. + R R)/(RL - RG) DTDTM = (0 - DH*(1. + RR)*NDT)/(Bi + 82*M ) T i T DTDTM*DTM PD • P(T) TM TM + DTM IF (T -TH) 39394 3 IF. (TL - T) i p l p4 1 CONTINUE MRITE12..10) RG•PP.NRY.DHgPDH.H.PHL 2 MRITE.(2 9 10) TM.PD.T.DTDTM.M 4 CALL PLOSS(MDI•ND.T) 10 FORMAT(JX9y(IX.E12.5)) 11 FORMATM 0.5) 12 FORMAT(I6) _ . STOP END C C SUBROUTINE PLOSS(WDT.PD.T) WDSO = ADT MDCRTs (1.5•+ 10.*(T - 1.65)) *1.0E-3 CK2T s 605.6 IF(MDBO -.MDCRT) 19292 C FLOW RATE BELOW CRITICAL i C s 0.0 CK 1 T = .121.97 + ( 5.77E-1) *PD 00 TO 3 C FLOW RATE ABOVE CRITICAL 2 C : -1 .233*PD*(1.65E-3*(1. + 9.5*dT/1.65 . CK 1 T . m 121.97 + 1 .233*PD 3 .. DELP s PD - SQRT(PD**2 - 2.*(CKI T*MDBO ♦. CK2T*MDBO**2 + 0) PV = PD - DELP MRITE(2 9 4) DELPgPY 4 FORMAT(I1412.5) -RETURN END r 29 PAGE IS OSVLp©ORAL QUA1.11Y OF so ss IM f m ^ ^ •11 X11 M U 111 1t1 ^ f_ ^ _~I^ w ^^ is p'; t 1 1 1 ^ ^ 1^ l ^• 1 F ^ 1 1 ► 1 i o °.:^• 34 o4kc4,4gg0gOC cdc vgo00ci ori;Og00003s c^ {^ {1^^11 W A W W {W,y W W W Y1{i1 W W W ^Uy{ W W yfY^ "1 Q^^^^!ppyy) 1"1+ yo1 OfA'^O O^Nr^111^ W WW W W 1tyit W W W W {t^ {tt 1^ W WW W L>a ► nO01•''ff rl-f-umf^^Mwl^p1f11J^^ppp^sl!^yy ^ ^O► MtiNY1NMryO^^Q^A1Qy1 'O ti^O 'Ohlgfl f•yy O1+^I+ppO^Orl+pp^ 4 N ♦ f ♦ ff+ ♦ •gAI^M^NPI^IN1N N •!fy PIy N e1^ M - MI-19+•'1-IA a MN ^tA 111 f1/1f1t1f111fi11f 111f111f 11 MI*24 v t WinwMfM V'n vi1f1N f1 _WWWWW.YWW {^ W1^ W WWW WW{{^WWW yW^WW {{yyWWWt^t1 i11 rfryN^f0In a^NIll O 0i#'N+-pp-^^ ^0^pp^^ ^ ^'pp11+_AOM1 M 1► 8. O^d s a I + Or f 0 t^0 i^ N 0.1tl O ^ S O• 0^ ^0 0^ COON nt 1'1 nl 1 Al N^N^N^ONON^NONf^NANrf1.1 ? A ON0N0 Sf11+N-fy.^p/rNNfyfyfyNf111 ► N1^NtiNA1V^N^fVNN1► fV! 1 ,1 1 1 1, ^1 1 1 1 1 1 1 1 1 1 1 1 8! $03-080$-0808-08 3+ 8-08'08-08 -ol! 8-8ia8o3o8'o8-o8i t^ WW qy{♦y,^ WWI ♦ WWWWWWILWWWWW^tOWWf ♦ ♦ M M W ^^ 0.1 1N OaDnm•tin ^a nM•9fm• wN^ I^ m^ 0 2 OOF* O^ M ^^^^•'I^^i I* :;ul S1rM - MON1f ^OV1^AN^O ^d^1 ^-^ ^^^ 1110^s ^a^ pNslf ^1 W WWWWWWWWWIVAIWt ^ rye 1 ryAmhwN^ p- N N N f N- f ^fppyy► f^! !^^yy ry !!^^ ^ff^^yy n fe^ I.• O p ^'N •DSO o ^'a^ '^ev ♦♦ oN ♦♦pp ^ ^N N111eY1fINNNN^N1^Nt111ANit1NtV1ff111 • • • • • • • • • • • • • • • • • • • • • • • • • • • • .A111N11111111t•111• • • • • • • • O 80 8 - w^^g 8337I ♦•8888i386838i3838i3838i3838383838388e ♦ • ♦♦♦♦♦•♦♦ ♦ •+• i 1y •f Si J • fj ♦ ^ 13 low ♦1o` ^ •^O^af ^ ^A^pp^^N1Aee^^^N^Nee^^M?f-.,p.^^^^'^^ey 'r—,p— ^See^^/ p O, N ---O OA^ +2rDvNNMf• • N ^ • s • • NONa • • • t•N •— •N+ • •N+N • •Z •N •— •N •r INNNr• • • •y •NNNNN^'1N•'1 • • • • • • • • 1gt`ji^ • • • N s 30 MOM PAGE 18 OF POOR QUALITY 1 ^ ^ 1 1 1 1 ^ I ! i ^ I • I r _ OMIN NNa$ a mann^^ nj j;SgR "mill; ^lnl^{i^^^iw^i^^^•^=i•^nryl^^^ •n{ii•^^^^i^^iet^^^^^^^^^i{^^^^iR^i^1ry1^^+^^+i^^ ••••• • •^• ^O^eON^^^ ••••• • 1 1 1 1 1 1 1 1 1 1 / ^ 1 1 1 1 ^ 8 o^8Q$ ffl: !B 8 8 8 s s ^1i ir_WW_W WWIWW W W W M i — mrm^ —lbrz—l^—lr—lti—-1 -;--on ^ $ 3^$^ -1"•—ss — —lrrl^—^: #susp -1r—A—l ^,am 1••r!^—s —1^=aka=rl ^f^rlrwlr_ a a '• • • • • • • • • • • • • • • ►• • • • • 1 • • • • • • • • • • • • •^ •Z • • • • • • •► • •► • • • • • • b Hul 11VI1111m i^^^ k' 3 ^k3^„ - ^1 V11 ,11 111411 3" $♦ iON3, 3^ 1 N1 3 ,11 1 1 n n " nn n nnl n^^ 11113n 4 • • • • • • • • • • • • • • N• • nit • • • • • • • • • • • • •• • , • • • •• • • ••11 •• • ► ••^ • • • • • v it^a •sa^a^3^as^saaas $asa^aB e^^asas^s B 8^e g_ Irf 01 W Iss I l it *1 Ile ♦ 0 08 ? •ijy7 ^x^ a . a l, ^i^^i^n.n^-^no• ^ ^ ''a^- - -a 31 APPROVAL ATTITUDE CONTROL AND DRAM COMPENISATION PROPULSION SYSTEM FOR THE GRAVITY PROW4 WACECRAFT by D. H. Blount The information In this report has been reviewed for tedudcd content. Review of any informa- tion concerning Department of Defense or nudear energy setivities or programs has been made by the MSFC Security Classification Officer. This repot, in its entirety, has been determined to be unclassified. A A ool Dir, tor, Structures and Propulsion Laboratory z 32 O U.S. GOVERNMENT PAINTING OFFICE: 1991-6/6.0661163