NASA Technical Reports Server (NTRS) 19910009864: Multi-dimensional modeling of a thermal energy storage canister. M.S. Thesis - Cleveland State Univ., Dec. 1990

196 Pages·5.5 MB·English

by  NASA Technical Reports Server (NTRS)

lli-,q o
NASA Technical Memorandum 103731
Multi-Dimensional Modeling of a Thermal
Energy Storage Canister
Thomas W. Kerslake
Lewis Research Center
Cleveland, Ohio
, '-- "i7¢
January 1991

MULTI-DIMENS IONAL MODELING
OF A
THERMAL ENERGY STORAGE CANISTER
Thomas W. Kerslake
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
ABSTRACT
The Solar Dynamic Power Module being developed for Space
Station Freedom uses a eutectic mixture of LiF-CaF 2 phase
change material (PCM) contained in toroidal canisters for
thermal energy storage. Presented herein are the results
from heat transfer analyses of a PCM containment canister.
One- and two-dimensional finite-difference computer models
are developed to analyze heat transfer in the canister
walls, PCM, void, and heat engine working fluid coolant.
The modes of heat transfer considered include conduction in
canister walls and solid PCM, conduction and pseudo - free
convection in liquid PCM, conduction and radiation across
PCM vapor filled void regions and forced convection in the
heat engine working fluid. Void shape, location, growth or
shrinkage (due to density difference between the solid and
liquid PCM phases) are prescribed based on engineering
judgement. The PCM phase change process is analyzed using
the enthalpy method. The discussion of results focuses on
how canister thermal performance is affected by free
convection in the liquid PCMand void heat transfer.
Characterizing these effects is important for interpreting
the relationship between ground-based canister performance
(in l-g) and expected on-orbit performance (in micro-g).
Void regions accentuate canister hot spots and temperature
gradients due to their large thermal resistance. Free
convection reduces the extent of PCM superheating and lowers
canister temperatures during a portion of the PCM thermal
charge period. Surprisingly small differences in canister
thermal performance result from operation on the ground and
operation on-orbit. This lack of a strong gravity
dependency is attributed to the large contribution of
container walls in overall canister energy redistribution by
conduction.
ii
TABLE OF CONTENTS
PAGE
ABSTRACT i
vi
NOMENCLATURE
ACKNOWLEDGEMENTS x
CHAPTER
1
I. SUMMARY
5
II. INTRODUCTION
2.1 Attributes of Canister Heat Transfer
2.1.1 Thermal Loading
2.1.2 Role of Conduction Within
Canister Walls
2.1.3 Void Behavior
2.1.4 Void Heat Transfer
2.1.5 PCM Radiant Transmission
Characteristics
2.1.6 Convection in the PCM Melt
2.2 Methods For Solving Phase
Change Problems
2.3 Literature Review
2.4 Thesis Approach
26
III. PROBLEM FORMULATION
3.1 Problem Statement
3.2 Governing Equations
3.2.1PCM Canister Energy Balance
3.2.2 Constitutive Relationships
3.2.3 Mushy Zone Properties
3.2.4 Void Models
3.2.4.1 One-Dimensional Analyses
3._.4.2 Two-Dimensional Analyses
3.2.5 Liquid PCM Free Convection
Models
iii
3.2.6 Canister Cooling Fluid
Heat Transfer
3.3 Boundary and Initial Conditions
3.4 Thermophysical Properties
IV. NUMERICAL APPROACH . 55
4.1 Solution Algorithm
4.2 Stability Requirements
4.3 Grid Selection
4.4 Combined Grid Element Technique
4.5 Computer Resource Requirements
V. RESULTS AND DISCUSSION 63
5.1 Numerical Solution Accuracy
5.2 One-Dimensional Analyses
5.2.1 Semi-infinite PCM
5.2.1.1 Effects of the Void
5.2.1.2 Effects of Boundary Conditions
5.2.1.3 Effects of Free Convection
5.2.1.4 Observations
5.2.2 PCM Slab Canister
5.2.2.1 Void Thermal Resistance
5.2.2.2 Wall 1 Temperatures
5.2.2.3 Effects of Void Distribution
and Consequences for
One.Dimensional Analyses
5.2.2.4 Effects of Free Convection
5.2.2.5 Ground-Based Testing of
Flight Design Hardware
5.3 Two-Dimensional Analyses
5.3.1 Canister Without Void or
Free Convection Models
5.3.1.1PCM Phase Distributions
5.3.1.2 Temperature Distributions
5.3.1.3 Temperature and Heat
Transfer Variations
5.3.1.4 Side Wall Heat Transfer
Fractions
5.3.1.5 Limiting Effects of a Void
5.3.2 Canister With Void Model
5.3.2.1 Temperature and PCM Phase
Distributions
5.3.2.2 Void Heat Transfer
iv
5.3.3 Canister With Void and
Free Convection Models
5.3.3.1 Temperature and PCM Phase
Distributions
5.3.3.2 Effects of Free Convection
5.3.3.3 Free Convection Model
Assumptions
5.3.3.4 Free Convection Model
With Local Nu Numbers
5.3.4 Performance Comparison
5.3.4.1 Maximum Wall Temperatures
5.3.4.2 Side Wall Heat Transfer
Fractions
5.3.4.3 Relationship Between Void
Characteristics, Side Wall
Fractions, and
Wall Temperatures
VI. CONCLUSIONS 129
6.1 One-Dimensional Analyses
6.2 Two-Dimensional Analyses
6.3 Future Work
BIBLIOGRAPHY . 135
APPENDICES 141
AI. Finite-Difference Equations
A2. FORTRAN Program Description and Listing
A2.1 Two-Dimensional Analysis
Program Listing
A2.2 Program Variable Definitions
A3. Video Animations
NOMENCLATURE
c
= Specific Heat, J/g-K
A
= Void Surface Element Area, cm 2 or constant
B
= Constant
C5 = Constant
D = Cooling Fluid Tube Inner Diameter, cm
div = Divergence Operator
e = Specific Enthalpy, J/g
F = View Factor
g = Gravitational Acceleration, cm/sec 2
h = Film coefficient, W/cm2-K
H = PCM Heat of Fusion, J/g
He-Xe= Helium-Xenon Gas Mixture
i = Grid Element Index
iv = Grid Element Which Contains Xv
iv" = Combined Grid Element
k = Thermal Conductivity, W/cm-K
L = Annular Canister Length, cm
L" = Slab Canister Thickness, cm
LH = Liquid PCM Vertical Layer Height, cm
LiF- = Lithium Fluoride-Calcium Fluoride
CaF 2
= He/Xe Mass Flow Rate, g/sec
MF = Mass Fraction PCM in Element iv
MFL = PCM Mass Fraction Liquid
NRS = Number of Void Radiating Surface Elements
vi
n3 = Constant
Nu = Nusselt Number
PCM = Phase Change Material
Pr = Prandtl Number
q = Heat flux, W/cm 2
Q = Thermal Power, W
r = Radial Coordinate, cm
R = Thermal Resistance, cm2-K/W
Ra = Rayleigh Number
Re = Reynolds number
S = Conduction path length, cm
St = Stefan Number
t = Time, sec
T = Temperature, K
TES = Thermal Energy Storage
U = Velocity of Void-PCM Interface, cm/sec
U = Overall Heat Transfer Coefficient, W/cm 2-K
VVF = Void Volume Fraction
W = Liquid PCM Width, cm
= One-Dimensional Coordinate, cm
X
X = Melt or Void Front Position, cm
XF = Mushy Zone Liquid PCM Mass Fraction
YF = Mushy Zone Liquid PCM Volume Fraction
Z = Axial Coordinate, cm
= Dot Product
V = Gradient Operator
vii
Greek Symbols
= Thermal Diffusivity, cm2/sec
= Volumetric Thermal Expansion Coefficient, I/K
6 = Canister Wall Thickness, cm
A = Kronecker Delta Function
Ar = Radial Grid Spacing, cm
At = Time Step, sec
AT = Temperature Difference, K
Ax
= One-Dimensional Grid Spacing, cm
Az
= Axial Grid Spacing, cm
6 = Emittance
= Pi Constant, 2*sin'1(1)
P = Density, g/cm 3
0 = Stefan-Boltzmann Constant, 5.67051xi0 -12 W/cm2-K 4
v = Kinematic Viscosity, cm2/sec
= Dimensionless Function of Ar and r
Subscripts and Superscripts
E = Enhanced
EFF = Effective
f = He-Xe Fluid
i = Inner Radius or Grid Element Index
J = Void Surface Element
k = Void Surface Element
L = Liquid PCM
m = PCM Melt
n = Current Time Step
n+l = Future Time Step
viii