The major goal of this project is to develop mathematical models of heat pipes which can be used to predict transient behavior under normal and adverse conditions. The models and solution techniques are to be formulated so that they can be incorporated into existing NASA structural design codes. The major parameters of interest are heat flux distribution, temperature distribution, working fluid pressure distribution, fluid and containment thermal and mechanical properties and geometry. Normal transient operation is taken to be operating conditions where the capillary structure remains fully wetted. Adverse transient operation occurs when drying, re-wetting, choking, non-continuum flow, thawing, freezing, etc., occur in the internal heat pipe working fluid

Colwell, G. T.

Hartley, J. G.

English

NASA Technical Reports Server

SEMIANNUAL STATUS REPORT 
MODELING OF TRANSIENT HEAT PIPE OPERATION 
Gum T. Colwsll 
James 0. Hartley 
Repared for 
NATIONAL AERONAUTICS AND SPACE ADMlNiSTRATlON 
LANGLEY RESEARCH CENTER 
HAMPTON, VIRGINIA 23665 
Under 
NASA Grant NAG-1 -392 
February 1984 
GEORGIA INSTITUTE OF TECHRIOLOGY 
A UNIT OF THE UMIVRRSITY SYSTEM OF QlOWQlA 
https://ntrs.nasa.gov/search.jsp?R=19840010507 2020-03-20T23:23:02+00:00Z
Gene T. Colwell and James G. Hartley 
School of Mechanical Engineering 
Georgia Institute of Technology 
Atlanta, Georgia 30332 
National Aeronautics and Space Administration 
Langley *search Center 
H q t o n ,  Virginia 23655 
NASA Technical Officer 
James C. Robinson 
Mail Stop 243 
February 18, 1984 
llamum'Irn 
?he major goal of this project is to develop mathematical models of heat 
pipes which can be used to predict transient behavior under normal and adverse 
conditions. Ihe models and solution techniques are to be formulated so that 
they can be incorporated into existing NASA structural design codes. The 
major parameters of interest arz heat flux distribution, temperature 
distribution, mrking fluid pressure distribution, fluid and containment 
thermal and mechanical properties and geanet~y . Normal transient operation is 
taken to be -rating conditions where the capillary structure remains fully 
wetted. Adverse transient operation occurs when drying, re-wetting, choking, 
non-continuun flow, thawing, freezing, etc., occur in the internal heat pipe 
working f:~lid. 
The mdels and solution techniques developed under this grant will be 
directed primarily towards the types of heat pipes which may be used in the 
"Space Station" for mving large quanities of thermal energy and for heating 
and cooling of instruments. However, with sonre mcdifications, the resulting 
models could be used for designing and predicting performance of high 
temperature heat pipes of the type proposed for cooling airframe and engi~z 
components in hypersonic applications such as the "Scramjet" 2nd the 
"Shuttle". 
Another goal of this project is to supply to NASA cm a contin~ing basis 
throughout the grant period, infonnation needed to determine sizes and weights 
of various types of heat pipes that m y  be proposed by others for "Space 
Station" use. 
RO[amW3RI[- 
The program will require about three years to conplete. Ihe following 
steps will be taken to accarplish the work. 
i. Carpile governing transient equations for nonnal heat pipe 
operation. 
ii. Model adverse conditions and select non-dimensional groups 
which can be used to define reghres where adverse operation 
occurs. 
iii. Incorporate Ilpdels for adverse aperations into solution 
techniques. his will involve using thennal property 
subroutines to predict properties for use in conduction 
equations. 
iv. Assess adequacy of existing finite element computational 
schemes to handle the models developed. 
V. Develop finite element representation of heat pipe for normal 
operat ion. 
vi. Include non-dimensional groups which define adverse operating 
regimes in conputational scheme. 
vii. Select test case to demonstrate techniques. 
viii. Corrpute operating parameters for test case. 
ix. Test v u t e d  values against experimental results for test 
case. 
x. Perform parametric studies for systems to the extent 
possible. 
xi. Develop, to the extent possible with given time and 
resources, simplified correlation equations or design 
procedures. 
xii. Integrate the ~sults of the above steps into existing finite 
element stress amputation programs. 
It is anticipated that the wrk included in tasks i, ii and iii and part 
of the work in task iv will be completed during the currently funded grant. 
The second year,of wrk will be needed to carry cut tasks v through viii and 
the third year should allw completion of the remaining tasks. 
HXaESSmDCITe 
Ihe work to date has been mainly directed twards defining the program, 
planning the steps required to achieve the desired final result and in 
formulating very general governing equations for n o w 1  heat pipe operation. 
This activity falls under task i of the program mrk statement. The follwing 
brief sumtry gives the current approach to the modeling. 
Under n o m l  transient operation a heat pipe easily acccmnodates external 
changes in the heat loads at the evaporator or condenser sections. While the 
internal tenperatures and pressures vary as the heat pipe reacts to the 
external changes, the capillary structure remains fully wetted and the 
teqxrature and pressure i~ the vapor region are nearly uniform across any 
cross-section at an instant of time. 'Ihus, for rlonnal transient -ration, 
the follwing assumptions [I1 are usually made: 
1. Heat is transferred through the shell of the heat pipe ancl 
through the liquid-saturated circumferential capillary 
stntcture by mnduct ion only; 
2. Thermal resistances associated with vaporization and 
condensation along the interface between the vapor region and 
the capillary structure are negligible; and 
3. me tanperature in the vapor space may change with time and 
position (along the length of the heat pipe) but is uniform 
acmes any cross-section troml to the axial direction 
The mathematical description of the heat transfer in a cylindrical heat 
pipe for these conditions can be written as follows: 
where the subscripts 1 and 2 denote the heat pipe shell and the liquid- 
saturated circumferential capillary, respectively. The effective thermal 
condutivity of the liquid filled circumferential structure may be conputed 
fran expressions such as that develcped by William [21. 
'Ihe volunetric specific heat of the capillary (s) , is a mass-averaged 
value to account for the presence of liquid. For t;ie vapor regions, subscript 
3, the energy equation is written as 
In order to satisfy assmption ( 3 )  above, the thermal amductivity in the 
radial direction, kr , can be chosen such that 
3 
The effective thermal conductivity in the axial directicn, k is evaluated 
23' 
by solving manentun and energy equations in the vapor region. Plesset and 
ORIGINAL PAGE IS 
OF POOR QUALITY 
P o p e r s t t i  [31 discuss conditions i n  t h i s  region in  a very general manner. 
lb bandary conditions fo r  t h i s  formulation consist of the M l w i n p t  
1. A t  each i ~ t r r f a c e  between the three regions, the  t q m r a t u r e  
and the heat f lux are c o n t i n m s .  Thus, i n  the evaporator and 
condenser sect ions 
kl ar 
aT2 
= k 2 a r  a t r - r  ( in ter face  
and and 0 < z < Le between shell 
=1 = T2 L LC z < L and cap i l l a ry )  
( in ter face  
and and 0 < z C Le between 
=2 = T3 Lr LC < Z < L cap i l l a ry  and 
vapor reg ion 
and i n  the adiabatic  sect ion 
and 
=1 = T3 
In a ,  r e l a t ive ly  long heat pipe with energy added and removed 
rad ia l ly  along the length energy t ransfer  through the ends my 
be neglected. In those cases where end e f f e c t s  a r e  s ign i f i can t  
they my be e a s i l y  included in  the -1. 
ORIGINAL PAGE 
OF POOR QUALIW 
2. For the cylindrical heat pipe under consideration there is 
radial symnetry about the axis of the pipe, 
3. No hetat transfer occurs external to the shell at the adiabatic 
section, 
ml 
- = 0 at r = ro (auter radius of shell) itr 
4. The external surface of the shell at the evaporator and 
condenser sections can be exposed to a unifonn heat flux, 
conduction, convection, or radiation. Thus, 
5 
kl ar 
n2 
= k2 L at r = ro and 0 6 z < Le 
L - L < z < L  
C .  
where ks is the conductivity of the surrounding material 
ars andF is the gradient in that mterial at ro. TIW initial 
condition for the analysis of normal transient operation m y  be 
taken to b the steady-state solution at design conditions or 
axm other pmscribed state. 
Existing finite elemnt cujer which haw the capability of solving 
tramient condition problem can be modified so that normal transient heat 
pipe -ration, 8 ~ 3  formulated above, can be treated. The finite element 
formlation mrst all- for element gmperty variations with the as mll ae 
from elenrent to element, Furthermore, provision mrst be rmde for treating 
anisotropic elements since the them1 conductivity of elements in the vapor 
region is different in the radial and axial directions. 
Property subroutines rmst be developed in order to evaluate the thermal 
properties as a function of tarperature for elements which represent the heat 
pipe cangbnents and the working fluid. lhese subroutines are presently being 
developed at Georgia IWh and will be incorporated into an existing finite 
element code. 'Ihe n o m l  transient heat pipe model in finite element form 
will be incorporated initially into a finite element codes developed in the 
School of Mechanical Engineering at Georgia T k h  ir: 1978. This is a two- 
dimensional, transient program which is capable of treating three-dimensional 
problem having radial symnetry such as exists in the present heat pipe 
fomlation. Stmple, three- triangular elements are used in this aode, 
krt the pragmed fnplementation is not limited to l w ~ r d e r  interpolation 
ft:wtions. The property subroutines described above will he &led to this 
existing finite element code to demonstrate the validity of the finite element 
inplementation. Validation will consist of catparing r#merical solutions with 
available experimental data fran normal transient heat pipe tests. 
For other than mrmal transient *ration, additional capabilities met 
be added to existing codes in order to model phenanena such as dryaut and 
rewetting of the capillary wick structure as well ars mlting ar freezing of 
the wrking fluid. At present, we believe that these phenanem can adequately 
be treated by mans of mdification and additions to the thermal property 
submutines. Ihe major efforts associated with thebe task consist 02 
devedoping accurate analytical nuckle of the phenomena and nunsrical 
algorithm suitable for finite element solutiom. 
1, Colwbll, G, T, and Clung, We S, , wMPasurmentB of the Transient Behavior 
of R Capillary Structure Ulder Wavy l b r m a l  Loading," Accepted for 
publication in  International Journal of Heat and Mass Transfer. 
2. William, C, , 'Oorrelation of Heat Pi  Parmtem," PhmD. lhesiu, 
mi. rmti t~ tc  ot -logy, m ~ h ,  197r 
3m Plesset, Ma S. and A, Proeperetti, "Flw of Vrrpaur in a Uwid hlosurerU 
J. Fluid b h , ,  78, 4330444 (1976) 


Modeling of Transient Heat Pipe Operation

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