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