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2007
An Improved Model of Cryogenic Propellant Stratification in a Rotating, Reduced Gravity Environment
TFAWS Conference NASA Glenn Research Center
Florida Institute of Technology NASA Kennedy Space Center
Department of Mechanical and Aerospace Engineering
Expendable Launch Vehicle / Mission Analysis Branch
2007 TFAWS
Paul A. Schallhorn
Jorge L. Piquero
Mike Campbell
Sukhdeep Chase
Justin Oliveira
Daniel R. Kirk
https://ntrs.nasa.gov/search.jsp?R=20120003253 2019-08-30T19:21:14+00:00Z
CONTENTS
Project Overview
Analytical Modeling
Current Work
Concluding Remarks
Future Work
2007 TFAWS
. - I PL
- LH2
• Avionics
Interstage
Port strap-on
LH2 tank L02 tank booster
First-stage RS-68 Y
engines
OVERVIEW: UPPER STAGE MODELING
Lockheed Martin Atlas V 401
t
- -p'.
Boeing Delta IV Heavy
Second-stage DemoSat Starboard strap-on RL1OB-2 engine and Nanosat-2
booster payload LO tank
Payload attach fitting
Core booster Second stage
http://www.boeing.comIdefensespace/space/de1taJde1ta4/d4hdemo,1jooko41
2007 TFAWS 3
OVERVIEW: WHAT CAN HAPPEN INSIDE TANKS?
>Second-stage ignition-2 = 1.229,5 sec
vA.
Sec on cl-stage ignition-3
= 20,233 sec '
SECO-3 = 20,427.3 sec
- --
SECO-2 t 1711.6 sec
Transfer orbit 514hr coast
DemoSat payload separation = 20,977.5 sec
Orbit = 19,622 x 19,623 nmi at lO-deg Inc
Parking orbit 7.7 mm coast
• Stage exposed to solar heating
• Propellants (LH2 and LOX) may thermally strati f'y
• Propellants may boil
• Slosh events during maneuvers
• Upper stage must re-start at conclusion of coast phase for insertion
http://www.boeing.comIdefense-space/space/delta/delta4/d4Idernoo0 1 4.html XSS-l() iew of Delta H rocket: An Air Force Research Laboratory XSS-10 micro-satellite uses its onboard camera system to view the second stage of the
Hoeing Delta II rocket during mission operations Jan. 30. (Photo courtesy of Boeing.), http://www.globalsecurity.org/space/systems/xss.htm
2007 TFAWS 4
Stait Box
( h-S :a ( ) e1ation
t)
0
H
V
5
EIl1lne Inlet Pressqiie
2007 TFAWS
.pratt-whitney.comiprodspacerl I O.asp
OVERVIEW: WHAT CAN HAPPEN INSIDE TANKS?
Propellant T&P must be within specified range for turbomachinery operation
- If propellants outside specified T&P box engine may not restart
- Orbit cannot be circularized
MOTIVATION
• Rotation present during missions to evenly heat spacecraft • Effect rotation has on propellant thermal properties unknown • Upgrade current analytical/numerical stratification models to include rotation
4\ Paraboloid of revolution liquid flee sace,(c'
/'
Elliptical end-caps
¶c) _
2007 TFAWS
MISSION PARAMETER RANGES
Tank Dimensions: - Square 3 m diameter tanks
• Cryogenics: LH2, LOX
- TbUlk LH2 : 16 K, 28.8 °R, -430.9 °F
- TbUlk LOX: 91 K, 163.8 °R, -295.9 °F • Tank Pressure (All Cryogenics): 30 psi • Initial Fill Levels: 10, 20, 30%
Heating Conditions:
- Constant wall temperature: 0 = Twaii - TbUlk : AT = 0.1, 0.5, 1.0 K - Heat flux to fluid: 5-100 W/m2
• Reduced Gravity Environment: g/g 0 = 10, 10, 10-2 , 10 1 , 1 Rotation rates: w = 0.1, 1, 5 °/sec
• Orbital Transfer Time (Simulation Time): 2 —4 HR
2007 TFAWS 7
MASTER MODEL: BASIC FRONT END OPTIONS
1. Tank geometry - Tank diameter, height - Square bottom
2. Boundary layer nature and heat transfer coefficient selection - Free convection
Laminar/Turbulent (w/ & w/out switching)
3. Wall temperature settings - Constant inner wall temperature - Constant inner wall heat flux
4. Rotation rate
5. Gravity level
2007 TFAWS 8
GENERAL MODELING PHILOSOPHY
I + I Elliptical end-caps l'i aboloid of i evoltit ion
Z I liquid trcc ..intacc
H- r1
Elliptical eiicl-capi
Paraboloid of revolution lionid fr ciirf'cii' ffr - -- -
Ullage gas
Liquid surface y
T5
Stratum / bulk interface
Tb
• Stratum growth A(t)
u(y) depends on if heating is constant wall temperature or constant heat flux, q
- u(y) depends on nature of boundary layer
- Provides differential equation for A(t)
• Stratum temperature, T(t)
- Heat entering side wall into boundary layer is used to increase stratum temperature
- Energy exchange with ullage negligible
T assumed uniform
8 dA 1bl = 2rRpf u(y)dy = picR2
dt 0
2RH = pR2Ac
2007 TFAWS 9
RELEVANT NON-DIMENSIONAL NUMBERS Grashof number, Gr, governs heat transfer regime for
3 constant wall temperature
G - ________ - Ratio of buoyancy to viscous forces r - 2 - J3, Volumetric thermal expansion coefficient
V- 0, Wall to Bulk temperature difference
Ra = Gr Pr • Rayleigh number, Ra, is product of Grashof and usual Prandtl number, Pr
Prediction of boundary layer transition
- If Ra < 1 O -* Laminar
- If Ra> 1 O -* Turbulent
Gr* = gflqL4 • Modified Grashoff number, Gr*, governs heat transfer
k v2 regime for uniform heat flux, q
Ra * = Gr* Pr Modified Rayleigh number, Ra*, for uniform heat flux
• Others: Reynolds Number, Re (momentum to viscous) Weber number, We (inertial to capillary), Froude number, Fr (inertial to body), and Bond number Bo (body to capillary)
2007 TFAWS 10
1
1012
III 10
I
Ra and Ra* vs. gig0 MAPS for LH2 and LOX Ra vs. gig (LH2) Ra vs. gig (LOX)
108 L._ii;i_.; d__________ ________________
10 io 10t 100
gIg
Ra vs. g/g 0 (LOX)
10' io 10 101 100
1 Q ______________
10_i io_4 ic 10_i 100
g/g1,
vs. g/g 0 (LH2)
fSIII1II::I'1 1 01 l •.LL_ LLL
io 1o' 102 lot 100
gIg.
lu
10''
.': . 10
1010
1010L
I
I 018
I0v
'U
1012
Maps laminar or turbulent boundary layers possible for typical mission profiles (NIST data) 2007 TFAWS 11
Does 1°/sec matter? S
• Not at g/g0= 1 but in coast phase g/g0 1 O
significant dishing effect
Key Question: How does rotation impact results?
-
4lNP1
WHAT IS IMPACT OF BBQ ROLL ROTATION:
Typical rotation rate, m-1°/sec Shape at g/g0=1, w-85O°/sec
• Assume liquid is in solid body rotation (transients can also be treated)
• Model extra height that liquid gains along wall as a longer interfacial heat transfer length
• Center point in radial direction of tank is taken to be point where percent of bulk remaining is referenced -* worst case scenario
• Trade off between heated area and surface area to distribute warm stratum
2007 TFAWS 12
ROTATION / STRATIFICATION COMBINED MODEL
Spin Rate, w= 1°/sec 3
2.5
2
0 C CD
U)
1.5 CD
1
0.5
0 -1.5 -1 -0.5 0 0.5 1 1.5
Radial Distance
h = (wR)2
2g
2007 TFAWS 13
ROTATIONAL CASES
Re-examine boundary layer / stratum mass balance
__ dA\ __ __ mbl =R PL dtJ parabo/oidPdJ 6h2 [(R
2 +4h 2 )3/2 _R3(d Ldt)
Turbulent
Laminar5
____ ______ _____ A(t) H7rR (Gr0 )1/5
1
A(t)'[182HrR
*2/7 1=1— 1-0.616 0 H
(r0, Pr 21 Hcv
[+ Pr
Pr315
G * - gflq, + - gflq (H )4 =
r - kv2 - kv 2 H
Re-derive energy balance to take into account additional heating area
h dT : • i-I22R [\H+_J = iJ22rRHw =picR 2 Ac -
2 dt 0:1
2007 TFAWS 14
102 iü Time (s)
0 1o 5 101 102 lo' 1o4
Time (s)
0 1 10
o0.8 C
0.6
gO.4
O.2
0.8
C
(0 E 0.6 U)
C 0
'I-, U CO 1
U.. 0.2
n
102 1o3 to5
Time (s)102 io3 1o4 10
Time (s)
16' 10 1
94
93.5
'93..
92.5
92
91.5 10 1
21
20
19
U' 18 I-
17
COMBINED ROTATION / STRATIFICATION MODEL: LH 2 and LOX Fraction Remaining vs. Time (LH2, g/g 0 = 1O) Fraction Remaining vs. Time (LOX, g/g 0 = 1O)
T vs. Time (LH2, g/g 0 = 1O) strat T vs. Time (LOX, g/g 0 = 1O) strat
S For q=10 W/m2, L=3, R=1.5, 20% fill level, H/R=O.4 and o=l°/sec at g/g0=104: - Rotation decreases time to stratification time by 15%
- Rotation increases stratification temperature by 1.0 K
2007 TFAWS
15
'Teuti'a1 level
i'aboloid >urtae
H
EFFECTS OF ROTATION AND TRADEOFFS Increased boundary layer running length (H —* H) - more heated area
larger Grashof number • Larger surface area at bulk-stratum interface (S —* Sparaboloid)
- increased mass flow rate into stratum layer - more area to spread mass flow
_'j'j/ 1FPtYV)
0.5 1 1.5 2 2.5
w (degis)
0.0000
0
0.2500
0.2000
0.1500
0.1 000
0.0500
:: ________________
g'g = 1O-
________
;;=:=J:_:---
gigo = le-2, R = 0.75 m _____
-----
gigo = le-2, R = 1.5 m
g/go1e-2,R3m
- -=- --- - -g/gole-3,R0.75m
- -g/gole-3,R1.5m
= 10-2- g/gole-4,R1.5m
g/go1e-4,R3m
3 3.5 4
EFFECTS OF ROTATION . Spinning always increases stratification
Stratum temperature affected by spin rate; especially at low gravity levels . LOX cases shown with heat flux of 5 W/m2 after 2 hour mission
Effect of Rotation on Stratum Temperature
2007 TFAWS 17
EFFECTS OF ROTATION
• 0critica1 -) spin rate to minimize stratum temperature
• 0critica1 needed for large g/g0 impractical
• 0critica1 needed for typical mission profiles very practical (w < 1.5 deg/s) • LOX results discussed previously shown
r4
Wi'
3.5
U)
•D
2
1.5
—g_go = le-3
—g_go = le-4
gig0 =
0+
0
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9
0.5
H/R 2007 TFAWS
SUMMARY! CONCLUDING REMARKS
Thermal stratification impacts T&P at conclusion of coast phase
Rotation (creeping of fluid up side walls) has large effect for w= 1°/s and g/g0 1 O
- 'Classical' literature model upgraded to include rotation effects - Can decrease time to stratify by 30-60 minutes during 4 hour coast - Larger heating area and lower liquid level above sump inlet - For various missions stratum temperature may increases or decrease relative to no-spin
case - Mixed tank temperatures always larger because A increased with rotation
Future work Comparison with CFD studies
2007 TFAWS 19
SELECTED REFERENCES
Literature Review References:
1. Eckert, E.R.G., Jackson, T.W.: Analysis of Turbulent Free-Convection Boundary Layer on a Flat Plate, Lewis Flight Propulsion Laboratory, July 12, 1950.
2. Bailey, T., VandeKoppel, R., Skartvedt,D., Jefferson, T., Cryogenic Propelilant Stratification Analysis and Test Data Correlation. AIAA J. Vol.1, No.7 p 1657-1659,1963.
3. Tellep, D.M., Harper, E.Y., Approximate Analysis of Propellant Stratification. AIAA J. Vol.1, No.8 p 1954-1956, 1963. Schwartz, S.H., Adelberg, M.: Some Thermal Aspects of a Contained Fluid in a Reduced-Gravity Environment, Lockheed Missiles & Space Company, 1965.
4. Reynolds, W.C., Saterlee H.M.,: Liquid Propellant Behavior at Low and Zero g. The Dynamic Behaviour of Liquids, 1965. 5. Ruder, M.J., Little, A.D., Stratification in a Pressurized Container with Sidewall Heating. AIAA J. Vol.2, No.1 p 135-137, 1964. 6. Seebold, J.G.; and Reynolds, W.C.: Shape and Stability of the Liquid-Gas Interface in a Rotating Cylindrical Tank at Low-g. Tech. Rept.
LG-4, Dept. of Mech. Engineering, Stanford University, March 1965. 7. Birikh, R.V.: Thermo-Capillary Convection in a Horizontal Layer of Liquid. Journal of Applied Mechanics and Technical Physics. No.3,
pp.69-72, 1966
8. Ostrach, S.; and Pradhan, A.: Surface-Tension Induced Convection at Reduced Gravity. AIAA Journal. Vol.16, No.5, May 1978. 9. Levich, V.G.: Physiochemical Hydrodynamics.Prentice Hall. 1962 10. Yih, C.S.: Fluid Motion Induced by Surface-Tension Variation. The Physics of Fluids. Vol. 11, No.3, March 1968.
Web-based References for Graphics: • http ://www. skyrocket.de/space/index frame.htm?http ://www. skyrocket.de/space/docsdat/goes-n.htm • http://www.boeing. cornldefense-space/space/deltaldelta4/d4h demo/bookO 1 .html • http://www. spaceflightnow.comlnews/n020 1 /28delta4mate/delta4medium.html
2007 TFAWS 20
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