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Title: 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
Technology Department of Mechanical and Aerospace
Engineering NASA Kennedy Space
Center Expendable 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 CRYOGENS TIME 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
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