February 17, 2006

1

• February 17, 2006
• TO Analex Corporation
• OC Room 2041
• Mail Stop Analex-1
• Kennedy Space Center, Florida 32899
• FROM Daniel Kirk, PI
• Olin Engineering Building, 215
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• Melbourne, Florida 32901
• SUBJECT Midterm Status Briefing for AGREEMENT
  NO. 06-001 Refined Liquid Propellant
  Stratification Model for Cryogenic Upper Stages
• Please find attached a copy of the midterm
  briefing presented at NASA Kennedy Space Center
  on February 17, 2006. This set of slides
  constitutes the deliverable Midterm Status
  Briefing, as per contract 06-001 agreement (page
  8). The slides are available online at
  my.fit.edu/dkirk
• As always, any questions, concerns or comments
  are welcome.
• Respectfully submitted,

2
MODELING OF UPPER STAGE CRYOGENIC PROPELLANT
STRATIFICATION IN A ROTATING REDUCED GRAVITY
ENVIRONMENT Florida Institute of
TechnologyDepartment of Mechanical and Aerospace
Engineering NASA Kennedy Space
CenterExpendable Launch Vehicle / Mission
Analysis Branch

• Daniel R. Kirk
• Mark D. Ratner
• Adam T. Linsenbardt
• Dr. Paul A. Schallhorn, NASA KSC Technical
  Advisor
• Jorge L. Piquero, Analex Technical Advisor
• February 17, 2006

3
CONTENTS

• Project Overview and Scope
• Motivation, Objectives and Approach
• Contract 2 Analytical Modeling
• Completed work and results
• Work in progress
• Future work
• Contract 2 Computational Modeling
• Work in progress
• Future work
• Supplemental Work Analytical and CFD
• Concluding Remarks

4
CONTRACT 2 OVERVIEW AND PROGRESS

• Agreement No. 06-001 Refined Liquid Propellant
  Stratification Model
• Contract Start Date November 28, 2005
• Contract End Date May 31, 2006
• Contract Funding 17,796
• FIT Matching Contribution (Tuition) 3,500
• Key Areas of Focus and Deliverables
• Mass diffusion and evaporation
• Analytical model completed
• Still to be incorporated into master code
• Addition of aluminum tank wall and insulation
• CFD and analytical studies underway
• Thermal conduction within propellant
• Parametric studies

5
OVERVIEW WHAT CAN HAPPEN INSIDE TANKS?

• Stage exposed to solar heating
• Propellants (LH2 and LOX) may thermally stratify
• Propellants may boil
• Slosh events during maneuvers
• If propellants outside specified TP box engine
  may not restart

http//www.boeing.com/defense-space/space/delta/de
lta4/d4h_demo/book14.html XSS-10 view of Delta II
rocket An Air Force Research Laboratory XSS-10
micro-satellite uses its onboard camera system to
view the second stage of the Boeing Delta II
rocket during mission operations Jan. 30. (Photo
courtesy of Boeing.), http//www.globalsecurity.or
g/space/systems/xss.htm
6
INTRODUCTION TO THE PROBLEM

• Analytical and computational thermal modeling of
  cryogenic rocket propellants
• Examine effects parametrically

Tank wall and insulation
LH2 Tank
LOX Tank
7
CONTENTS

• Project Overview and Scope
• Motivation, Objectives and Approach
• Analytical Modeling
• Diffusion and evaporation, rotation,
  stratification and boiling, tank wall
• Completed work and results
• Work in progress
• Current and Future work
• Computational Modeling
• Completed work and results
• Work in progress
• Future work
• Concluding Remarks

8
EVAPORATION CALCULATION REFERENCE GEOMETRY

• Tank geometry
• Nominal 4 m square cylinder tank
• LOX fill levels 10, 20, 30 percent
• Minimum cross-sectional area available for
  evaporation 4p 12.566 m2
• Cross-sectional area increased based on free
  surface area due to rotation

http//www.spaceflightnow.com/delta/d313/050609del
ta4.html
9
BASELINE DIFFUSION / EVAPORATION MODEL

• 1-D Stefan Problem
• Baseline scenario
• Bulk LOX at 90 K
• Ullage 100 helium
• 30 fill level
• Initial Conditions (Concentrations)
• Y mass fraction
• YGOX(y gt 0.3L, t 0) 0
• YHe(y gt 0.3L, t 0) 1
• YLOX(y lt 0.3L, t 0) 1
• YHe(y lt 0.3L, t 0) 0
• Concentrations are time dependent
• YGOX(y gt 0.3L, t)
• Changes as GOX is introduced
• YGOX(y 0.3L, t)
• Changes as TLOX ? evaporation
• Both are exceptionally small during 4 hour coast

Helium/GOX
L
Interface, i
LOX
10
BASELINE DIFFUSION / EVAPORATION MODEL
Mass flux per unit area due to molecular
diffusion All parameters are time
dependent Partial pressure of oxygen on gas
side of interface must equal saturation pressure
associated with temperature of liquid Definitions
in terms of mole and mass fractions
11
BASELINE DIFFUSION/EVAPORATION MODEL
In crossing liquid-vapor boundary, maintain
continuity of temperature Energy is conserved
at interface Heat is transfer from gas to liquid
surface (g-i) Some of energy goes into heating
liquid, while remainder causes phase
change Calculate net heat transferred across
interface once evaporation rate is known
12
EVAPORATION CALCULATION BASELINE CASE

• Input variables Baseline case
• Ullage pressure 30 psi
• LOX bulk temperature 91 K (163.8 R)
• LOX density 1,140 kg/m3
• Initial LOX mass for 30 fill 17,200 kg
• Partial pressure of GOX on gas side of interface,
  i, must equal saturation pressure associated with
  temperature of LOX
• PO2,i Psat(Tliq,i)
• This provides Psat,LOX(Tliq,i) PGOX,i 16.06
  psi
• Using data, but Clausius-Clapeyron also close
  (2)
• Mole fraction cGOX,i Psat(Tliq,i)/Pullage
  16.06/30 0.53533
• Mass fraction YGOX,i Psat(Tliq,i)/Pullage(MWGOX
  /MWmix,i)
• MWmix,i cGOX(MWGOX) (1 cGOX)(MWHe)
• MWmix,i 0.53533(32) (1 0.53533)(4) 18.989
  kg/kmol
• Mass fraction YGOX,i (0.53533)(32/18.989)
  0.902

13
PARAMETRIC INVESTIGATION OF DIFFUSION
COEFFICIENT, DAB

• Diffusion of A Oxygen into B Helium
• Reference point T 91 K, P 30 psi, DAB
  4.76x10-6 m2/s
• Investigated over wide range 80 lt T lt 100 K, 1 lt
  P lt 3 atm

14
BASELINE CASE LOX/He RESULTS 4 HOUR COAST
Cumulative LOX Mass Diffused, kg
Time, hrs

• Cumulative mass diffused vs. time ( linear for 4
  hours, but not for long times)
• Mass diffusion per unit area 1.13x10-5 kg/s m2
• Mass diffusion 1.68x10-4 kg/s
• At 4 hour coast, 2.4 kg of LOX diffused in
  He/GOX, Dh 0.17 mm
• Change in LOX temperature after 4 hours -0.018 K

15
DIFFUSION CONCLUDING REMARKS

• Diffusion sub-model completed
• Not incorporated into full code
• Rotation and diffusion model coupled
• Parametrics completed
• 80 K lt TLOX lt Tboil (144 R lt TLOX lt Tboil)
• 1 lt PLOX lt 3 atm (14.7 psi lt PLOX lt 44 psi)
• Fill level
• Coast time
• Mass diffusion changes by /- 10 over baseline
  model shown
• Bulk temperature changes less than 0.05 K for all
  cases
• Agreement with Analex / KSC diffusion predictions
• No detailed one to one comparison because exact
  geometry not compared
• Comparison of mass flux per unit area trends
  agree
• No CFD implementation at this point

16
ROTATION UPDATE

• 7 test cases for CFD and analytical modeling
• Square Bottom Tank
• Does not bottom out
• Bottoms out
• Elliptical Bottom Tank Fill level gt ellipse /
  cylinder tangency point
• Bottom of parabola above tangency point
• Bottom of parabola below tangency point, but
  above tank bottom
• Bottoms out
• Elliptical Bottom Tank Fill level lt ellipse /
  cylinder tangency point
• Does not bottom out
• Bottoms out

17
ROTATION PROGRESS 7 TEST CASES COMPLETED
Square Tank Fill Level 30 g/g0 1, w 3
rad/sec
Spherical Tank Fill Level 30 g/g0 1, w 3
rad/sec
Elliptical Tank Fill Level 10 g/g0 1, w 3
rad/sec

• 7 test cases completed on square, spherical, and
  elliptical tanks
• Agreement between CFD and analytical models

18
ROTATION SUMMARY ELLIPTICAL TANK
No bottoming
Tangency
Bottoms Out

• Plot shows fill level (as of vertical height)
  versus w2/g for elliptical bottom tank
• Agreement between CFD and analytical models for
  bottoming vs. no bottoming
• No surface tension included
• Current work, reference Liquid Sloshing
  Dynamics, Raouf A. Ibrahim)

19
LITERATURE REVIEW THERMAL STRATIFICATION

• From Bailey et al., 2
• Analysis for uniform wall temperature
• Heat input to tank to boundary layer
• Flow in boundary layer goes into a warm upper
  layer and remains there
• Stratification defined by mass flow through
  thermal boundary layer
• No mixing between warm stratum and bulk
• No conduction through tank walls
• No energy exchange between stratum and ullage
• No molecular diffusion
• No boiling heat transfer
• From Tellup et al., 3
• Analysis for constant heat flux case
• No mass exchange to ullage
• Energy exchange with ullage gas
• From Reynolds et al., 4
• Criteria for stability of a rotating axisymmetric
  meniscus
• Expressions for growth of stratum with time for
  turbulent and laminar cases

20
STRATIFICATION BASELINE MODEL

• Parameter Space
• Tank Dimensions
• 3 m square cylinder
• Cryogenics LH2, LOX
• Tbulk LH2 16 K, 28.8 ºR, -430.9 ºF
• Tbulk LOX 91 K, 163.8 ºR, -295.9 ºF
• Initial Fill Level 1/3
• Heating Condition Twall - Tbulk DT 0.1, 0.5,
  1.0 K
• Tank Pressure (All Cryogenics) 1.9 bar
• Reduced Gravity Environment g/g0 10-5, 10-4,
  10-3, 10-2, 10-1, 1
• Orbital Transfer Time (Simulation Time) 3 HR
• Rotation w 0.1, 1, 5, 10 º/sec
• Outputs
• Thickness of stratification layer, D, with time
• Temperature of stratification layer with time
• Mass flow into stratification layer with time

21
RESULTS LH2 LEVEL OF STRATIFICATION VS. TIME
100
Faster Stratification
DT0.1 K, g/g010-4
10
DT1 K, g/g010-4
Bulk Remaining
As DT ?, Stratification ? As g/g0 ?,
Stratification ?
DT0.1 K, g/g010-2
1
DT1 K, g/g010-2
0.1
3 hours
Time
22
COMPARISON OF CRYOGENSTIME TO STRATIFY LH2 VS.
LOX, DT1 K
LOX, g/g010-4
LH2, g/g010-4
Bulk Remaining
LOX, g/g010-2
LH2, g/g010-2
Time

• For all cases LH2 thermally stratifies more
  rapidly than LOX

23
BOUNDARY LAYER ESTABLISHMENT TIME SCALE LH2

• Analytical models are fully developed at t0,
  entire boundary layer is present
• How long to establish boundary layer?
• Make estimate based on convective time scale

For g/g0 10-4 and DT0.1 K B.L. established in
30 min
DT0.1 K
Time
DT0.5 K
DT1.0 K
For g/g0 gt 10-3 B.L. established in lt 6 min
g/g0
24
BASELINE ROTATION/STRATIFICATION COMBINED MODEL

• Key Question How does rotation impact results?
• Assume liquid is in solid body rotation
• Uses baseline stratification model
• 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

Spin Rate, w1º/sec
Tank Height
g/g010-4
g/g0 gt10-3
g/g010-5 Note Parabola bottoms out
Tank Width
25
COMBINED ROTATION AND STRATIFICATION RESULTS LH2
g/g010-3 DT1 K
w0

• Key Points
• For w lt 1º/sec and g/g0 gt 10-3, effect of
  rotation on stratification is small
• For w 5º/sec and g/g0 lt 10-3, effect on
  stratification may be substantial
• Under such conditions tank is likely
  bottomed-out, which should be avoided

w1º/sec
w5º/sec
26
BOILING CONSIDERATIONS

• Boiling Regimes
• Free Convection Boiling ?Te 5 K
• turbulent h (?Te )1/3 q (?Te )4/3
• laminar h (?Te )1/4 q (?Te )5/4
• Nucleate Boiling 5 K ?Te 30 K
• q (?Te )3
• Large heat flux for small temperature difference
• Heat flux also a function of g1/2
• Transition Boiling
• h, q decrease with increasing superheat
• Boiling crisis occurs at max heat flux of
  nucleate boiling marking changeover to a
  transition boiling regime
• Film Boiling ?Te 120 K
• Heat transfer coefficients increase as h ?Te1/4
• Heat flux depends strongly upon vapor and liquid
  properties and radiation may play a significant
  role

27
BOILING HEAT FLUX MAGNITUDE COMPARISION WITH KSC
Theoretical Max q
Heat Flux (W/m2)
?Te (K) -- Superheat

• Max heat flux due to nucleate boiling occurs for
  LH2 at higher pressures
• Max heat flux determined by superheat when
  boiling enters transition boiling regime

28
BOILING CONSIDERATIONS

• Nusselt numbers computed using following general
  form correlated from experimental data
• Nu C(Gr Pr)n
• Laminar n 1/4
• Turbulent n 1/3
• C depends upon boundary layer type
• Different Grashoff and Prandtl numbers used in
  these calculations
• For free convection cases, usual Gr and Pr used
• Boiling cases use a slight variant on these
• Subscripts l, v denote liquid and vapor phase
  respectively
• hfgis sensible heat corrected latent heat of
  vaporization
• F(Ja) 1/2 for Jaltlt1
• F(Ja) 1 for Jagtgt1.
• Free convection and film boiling heat fluxes may
  be linearly superimposed to arrive at total heat
  flux away from wall (Ref Tong)

29
BOILING LH2 NUSSELT NUMBER REGIMES
105
Laminar Film Boiling
Turbulent Film Boiling
103
Laminar Free Convection
Turbulent Free Convection
Distance along heated surface from leading edge
(m)

• Nu for boiling cases approximately order of
  magnitude gt free convection
• Nu turbulent film boiling approximately order of
  magnitude gt laminar film boiling

30
BOILING LH2 HEAT TRANSFER COEFFICIENTS
Total
Turbulent
Laminar

• Total heat transfer coefficient at 1 ft. (0.3 m)
  on same order as boiling curves by KSC

31
COMBINED BOILING AND STRATIFICATION LH2
100
Boiling heat transfer coefficient
Bulk Remaining
Free Convection heat transfer coefficient
50
10
Time

• Enhanced heat transfer due to boiling leads to
  significantly shorter stratification times

32
COMBINED BOILING AND STRATIFICATION LH2
100
Mass loss to boil off
Mass Stratified
Bulk Stratified
Mass Evaporated
Decreasing Gravity
1
1 hour

• Mass evaporated much more slowly than mass
  stratified at g/g01, 0.1, and 0.01
• Stratification affected more strongly by gravity
  than evaporation

33
CONTENTS

• Project Overview and Scope
• Motivation, Objectives and Approach
• Analytical Modeling
• Completed work and results
• Work in progress
• Future work
• Computational Modeling
• Completed Work
• Work in progress
• Future work
• Concluding Remarks

34
WHY CFD AT THIS STAGE?

• Motivation
• Limit of what can be learned with reduced order
  analytical models
• Need to capture details of flow field
• Approach
• Initially treat rotation, free convection,
  boiling, diffusion, etc. separately
• Validate / benchmark CFD results versus
  analytical models, data, and KSC CFD efforts
• Combine various physical phenomena for more
  complex problems
• Computational Tools (in place at FIT)
• GAMBIT (mesh generation)
• FLUENT (CFD solver)

35
FREE CONVECTION CFD

• Uniform grid vs. non-uniform grid trades off
  between computational speed and accuracy
• Numerical schemes
• Unsteady 2D flow
• Coupled solver
• 2nd order implicit formulation
• Flow conditions
• Boussinesq approximation ?
• Gravity is varied parametrically
• Atmospheric pressure
• Laminar and Turbulent cases examined

• Boundary Conditions
• Square channel
• Adiabatic top and bottom caps
• Fixed temperature right at left walls at 285 K
• Make use of GASPAK for cryogenic transport
  properties

36
CFD vs. THEORY BOUNDARY LAYERS
at 10 min

• Theory assumes a flat plate in an infinite
  quiescent medium
• CFD shows this is not the case

37
CFD vs. THEORY BOUNDARY LAYERS
at 1 min

• Notice much closer agreement in profiles at
  shorter times
• Attribute to lack of stratification and
  recirculation

38
FREE CONVECTION CFD
Temperature Contours
Boundary Layer
Oxygen at 10 minutes

• Notice significant warming of bulk

39
FREE CONVECTION CFD
Velocity Contours
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
Boundary Layer
Oxygen at 10 minutes

• Notice recirculation of oxygen
• Numerical issues still to resolve

40
FREE CONVECTION CFD

• Curves for theoretical and CFD boundary layer
  profiles do not match up. Why?
• Theory is based on boundary layers forming on an
  infinite flat plate in an infinite quiescent
  medium
• Theory does not take time dependent temperature
  gradient into account
• Theory does not take velocity recirculation into
  account
• For small times, CFD temperature boundary layer
  matches with theory
• Not enough time for recirculation and
  stratification to take place
• Velocity boundary layer profile grows and then
  shrinks with time
• Never develops into fully turbulent theoretical
  boundary layer
• Steady-state velocity boundary layer time-scale
  is longer than time fluid takes to develop
  recirculation and stratification

41
CONDUCTION EFFECTS

• Initial CFD and analytical models assume warm
  temperature condition is imposed directly on
  inner wall of tank
• Apply conductive thermal resistance model to
  walls of tank
• Two cases
• ¼ in. Aluminum walls
• Composite walls ¼ in. Aluminum, 2 in. Cryolyte
  insulation
• Thermal transport properties of Aluminum from
  CRYOCOMP
• Full thermal properties down to 4K
• Calculations for constant outer wall temperature
  and for constant wall heat flux
• Can run all metrics on cases with finite wall
  thicknesses without an increase in computational
  time by using thermal resistance instead of
  meshing actual walls

42
FREE CONVECTION CFD LH2 _at_ 1 min.
1 G
No wall
Aluminum - .25
Insulated 2.25
0.1 G
43
FREE CONVECTION CFD LH2 _at_ 2 min.
1 G
No wall
Aluminum - .25
Insulated 2.25
0.1 G
44
FREE CONVECTION CFD LH2 _at_ 5 min.
1 G
No wall
Aluminum - .25
Insulated 2.25
0.1 G
45
BOILING CFD

• Devise two-phase flow model that takes boiling
  modes into account

Time

• Preliminary boiling CFD results with Fluent
  based on tutorial
• Bottom surface is heated, left and right walls
  are planes of symmetry

46
SUMMARY OF CURRENT WORK AND NEXT STEPS

• Use results to create analytical stratification
  model which will allow for a time dependence of
  boundary layer
• Coupling of warming of tank, recirculation, and
  boundary layers
• Simple two-phase flow model of liquid cryogen and
  either He or GH2 as ullage gas
• Two-phase flow with boiling
• Combine two-phase flow model with heat flux/wall
  thickness model
• Apply rotational boundary conditions to this
  model using results from strictly rotational CFD
  study
• Two-phase, rotating, and boiling flow with given
  wall thickness and prescribed external heat flux

47
SELECTED REFERENCES

• Literature Review References
• 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.
• Bailey, T., VandeKoppel, R., Skartvedt,D.,
  Jefferson, T., Cryogenic Propelllant
  Stratification Analysis and Test Data
  Correlation. AIAA J. Vol.1, No.7 p
  1657-1659,1963.
• 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.
• Reynolds, W.C., Saterlee H.M., Liquid Propellant
  Behavior at Low and Zero g. The Dynamic Behaviour
  of Liquids, 1965.
• Ruder, M.J., Little, A.D., Stratification in a
  Pressurized Container with Sidewall Heating. AIAA
  J. Vol.2, No.1 p 135-137, 1964.
• 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.
• 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
• Ostrach, S. and Pradhan, A. Surface-Tension
  Induced Convection at Reduced Gravity. AIAA
  Journal. Vol.16, No.5, May 1978.
• Levich, V.G. Physiochemical Hydrodynamics.Prentic
  e Hall. 1962
• 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/doc_sdat/goes-n.htm
• http//www.boeing.com/defense-space/space/delta/de
  lta4/d4h_demo/book01.html
• http//www.spaceflightnow.com/news/n0201/28delta4m
  ate/delta4medium.html