Interacting effect of gravity and size on peak and minimum pool boiling heat fluxe

Lienhard, J. H.

English

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GRAVITY BOILING ST 
(Final report to the NASA Lewis Resear 
on research done under the first one-year 
extension of NASA Grant NGR-18-001-035. 
Sept. 1, 1969 to Dec. 31, 1970) 
by 
John H. Lienhard, Professor of Mechanical Engineering 
Boiling and Phase-Change Laboratory 
Mechanical Engineering Department 
University of Kentucky 
Lexington 
May, 1971 
Project Personnel: Bakhru, N.; Research Assistant 
Bhattacharya, A . ;  Research Assistant 
Davis, E.; Engineering Aide 
Dhir, V.; Research Assistant 
Dogget, W e ;  Engineering Aide 
Lienhard, J.; Principle Investigator 
Reich, R , ;  Engineering Aide 
Singh, J, D.; Teaching Assistant 
https://ntrs.nasa.gov/search.jsp?R=19710016487 2020-03-11T20:09:13+00:00Z
CIRCUMSTANCES AND OBJECTIVES 
The present report accounts for progress under NASA Grant 
NGR-18-001-035, "Interacting Effects of Gravity and Size Upon 
the Peak and Minimum Pool Boiling Heat Fluxes", during its first 
extension following an original two-year grant. The extension 
period was from September I, 1969 to December 31, 1970. 
The primary objectives of the project were three fold: 
1.) The work of the first two years revealed that the 
hydrodynamic mechanisms of the peak and minimum heat fluxes fail 
when the Bond (or Laplace) number becomes small. An objective of 
the extension grant was to learn what mechanisms dictate boiling 
heat fluxes in the near-zero-gravity range, and to develop pre- 
dictive equations. This was to be done for the specific case of 
small cylindrical heaters. 
2 . )  A second matter of some importance that arose during 
the original grant period had to do with the role of viscosity 
in boiling. We showed that heaters could induce side-flows 
through viscous action, and that these flows could in turn increase 
the peak heat flux significantly. We therefore set out in the 
extension period to determine whether there might be significant 
direct effects of viscosity on the extreme boiling heat flux. 
This question was to be attacked from two directions: First, 
a flat plate heater was to be built with vertical side walls to 
prevent the secondary viscous effect of induced convection from 
entering the experiment, This heater was to be effectively increased 
-2- 
in size relative to the Taylor unstable wavelength by operating 
it in the centrifuge facility, 
mination of the influence of viscosity on the peak heat flux on an 
infinite flat plate,for comparison with the existing inviscid 
hydrodynamic theory for flat plates, 
This test was to provide a deter- 
The second line of attack was theoretical, We proposed to 
include viscosity in the conventional stability theory, and then 
to include the viscosity-modified unstable wavelengths in the 
hydrodynamic formulation of the peak and minimum heat fluxes. 
was to provide a quantitative indication of how much direct in- 
fluence of viscosity we might expect in experiments. 
This 
, 
3 . )  The third major objective was that of establishing the 
analogy between boiling and electrolysis. Since these processes 
have much in common we proposed to delineate the analogy between 
them so that information relating to one process might be used to 
explain the bther. This was to be done first for the individual 
bubble growth problem and then f o r  the gross process, 
This work was done under the cognizance of the NASA Lewis 
Research Center with Mr. Thomas H. Cochran acting as Project Man- 
ager. The electrolysis analogy work w a s  done in cooperation with 
a Themis Project entitled "Bubble Dynamics" within Grant DAA B07- 
69-C-0366 under the direction of Prof. James E. Funk. 
PROGRESS 
A.) Carryover: The Appendix lists three papers describing 
work done during the first two yearsp which were completed and 
appeared in print during the extension period, They are Appendix 
-3- 
items le), 2 . )  and 3 - 1 -  
l e )  J, He Lienhard and K. H. Sun, "Effects of Gravity 
and Size upon Film Boiling from Horizontal Cylin- 
ders," Jour. of Heat Transfer, vol. 92 ,  No. 2, 1 9 7 0 ,  
p. 292.  
-
2,) J:H. Lienhard and K. B. Keeling, "An Induced Con- 
vection Effect upon the Peak Heat Flux," Jour. Heat 
Transfer, vol. 92,  No. 1, 1 9 7 0 ,  p. 1. - -
3 . )  K. H. Sun and J, H, Lienhard, "The Peak Pool Boiiing 
Heat Flux on Horizontal Cylinders," Int. Jour. Heat, 
Mass Transfer, vol. 13, 1 9 7 0 ,  pp. 1425-1439 .  - 
B.) The ranqe of small Bond number: An experimental determina- 
tion of the heat vs.temperature - difference curve for very small 
wires revealed that the peak and minimum heat fluxes no longer 
occur. A description of this behavior, along with a quantitative 
explanation of it are the subject of a report which we list as 
Appendix item 4.) : 
4.) N. Bakhru and J. H. Lienhard, "On the Non-Existence 
of Peak and Minimum Boiling Heat Fluxes at Low Gravi- 
ty," University of Kentucky, TR No. 18-70-ME 5 ,  March, 
1970. 
Subsequent work has been aimed toward expanding our capabil- 
ity for predicting the heat flux as a function of temperature 
difference over the full range of the curve. This involved the 
development of heat transfer predictions: for convection in the 
very small ITusselt number range: for the mixed film-boiling and conv- 
ection mode that was peculiar to this configruation; and for film 
boiling on very small wires. Additional experiments were also made 
to show how this transition of behavior evolves with decreasing 
wire size (or decreasing gravity),, 
This work will be the subject of a Ph.D. thesis which should 
be completed in the summer of 1971. 
-4- 
C,) Peak heat flux on infinite flat plates and the role of vis- 
. cosity: 
Theoretical: The first stage in this effort was to prepare a 
detailed review of the inviscid hydrodynamic theory of boiling and 
some of its background. This was the subject of a report which 
we list as Appendix item 5 , )  : 
r 
5.) V. Dhir, "Some Notes on the Development of the Hy- 
drodynamic Theory of Boiling", University of Ken- 
tucky, TR No. 19-70-ME-6, March 1970. 
The next step was to include viscosity in the prediction of the 
Taylor unstable wavelength. This has been completed and predic- 
tions of the dimensionless wave frequency as a function of a di- 
mensionless wavelength have been computed numerically with the 
Borishanski number as a parameter. The prediction applies to both 
flat plates and cylinders. 
Application of this wavelength information has been made to 
the prediction of the minimum heat flux, and additional work is 
presently being done toward applying it to the prediction of the 
peak heat flux. These efforts are to be the subject of a Ph.D. 
thesis which is scheduled for completion in the early Fall of 1971. 
Experimental: We have measured the Taylor unstable wavelength 
during film boiling in viscous liquids (cool glycol and isopropanol) 
and obtained partial verification of the viscous theory. This line 
of experimentation is about half finished. 
A flat plate apparatus was completed and shake-down testing 
on it has been started. This apparatus posed a particularly knotty 
design problem which led us into some peripheral work described be- 
low, The flat plate experiments and the Taylor wavelength experi- 
ments are to be part of the Ph.D, thesis presently under completion. 
-5- 
Some related work: The design of the flat plate apparatus 
gave rise to the problem of designing a reflux condenser in the 
spatially varying gravity field of the centrifuge apparatus. In 
resolving this problem ~7e saw how to solve three related problems 
of condensation and natural convection in varying gravity fields. 
At the cost of modicum of time from one Research Assistant we wrote 
three papers which are listed as Appendix items 6 . ) ,  7.) , and 8*): 
6.) V. Dhir and J. H. Lienhard, "Laminar Film Condensa- 
tion on Plane and Axi-Svmmetric Bodies in Non- 
4 
Uniform Gravity," Jour. Heat Transfer, vol. - 93, No., 1, 
1971, pp. 97-100. 
7 . )  J. H. Lienhard, R. Eichhorn, V. Dhir, "Laminar Na- 
tural Convection Under Non-Uniform Gravity," under 
review. 
8 . )  J. H. Lienhard and V. Dhir, "A Simple Analysis of 
Laminar Film Condensation with Suction," under re- 
view. 
D.) The boiling-electrolysis analoqv: This work was begun with 
a nondimensionalization of existing buble growth theories. It 
was then possible to compare an electrolysis bubble growth theory 
with bubble growth data and, in so doing, to extend our predictive 
capability. This development was first presented in Appendix item 
9 . )  A .  Bhattacharya and J. H. Lienhard, "The Similar- 
ity of Bubble Growthwin Boiling and Electrolysis," 
University of Kentucky, TR 23-70-NE-7, May, 1970. 
and then streamlined and extended a little, and submitted for pub- 
lication in the form of Appendix item LO.): 
3.0.) A .  Bhattacharya and J, H e  Lienhard, "Similarity 
The second phase of this work began with the development of 
of Vapor and Gas Bubble Growth," under review. 
current vs. - applied voltage curves for horizontal wires, These 
-6 -  
curves exhibited a peak similar to that shown by the boil.ing curve. 
Close scrutiny showed that this transition occurred not at the 
point at which escaping gas jets became Helmholtz unstable, but 
rather at the point where such jets first form. The transition 
from the region of isolated bubbles to the region of jets and 
columns is known in boiling and is predictable for the flat plate 
geometry e 
A master's thesis scheduled for completion in the early 
summer will report all of this work. It will conclude the de- 
scription of the electrolysis transition a.) by showing why the 
electrolysis curve peaks at the first transition instead of the 
second; b.) by deriving a prediction of the first transition point 
for cylindrical geometry; and c.) by adapting this prediction to 
the electrolysis process, and rationalizing both boiling and 
electrolysis data with it, 
E.) Some additional items: A major in-project service effort, 
developed in conjunction with the other work, was a large computer 
program which contains thermal properties of the fluids we have 
been using, and will present our experimental data in any scheme 
of correlation we might arbitrarily choose, This program has 
been immensely helpful and we have written it up in the form of a 
report which we present as Appendix item 11-1: 
11.) R. A .  Reich and J. H. Lienhard, "A Computer Program 
for Correlating Peak and Minimum Heat Fluxes," Uni- 
versity of Kentucky report in press. 
During the Grant period, another research effort has been 
supported to the extent of expendable supplies and project exper- 
tise, This is a study of the peak heat flux on spheres, It will 
-7- 
be reported in a master's thesis to be completed this smmer. The 
thesis will present a successful hydrodynamic theory of the peak 
heat flux supported by original measurements. 
A final spinoff item is listed as Appendix item 12.): 
12.) J. H. Lienhard and J. E. Funk, "Deisgn of a Per- 
fectly 'Effective Boiling Fin," Jour. of Basic 
Eng., in press. 
-
This was a brief note relating to the design of boilir,g fins. 
APPENDIX 
Papers and. Reports from Grant Period: 9/'1/69 to 12/31/70 
J, H. Lienhard and K, H. Sun, "Effects of Gravity 
and Size upon Film Boiling from llorizontal Cylin- 
ders," Jour. of Heat Transfer, vol. 92, No. 2, 19'70, 
p. 292, 
- 
J. H. Lienhard and X. B .  Reeling, "An Induced Con- 
vection Effect upon the Peak Heat Flux," Jour. Heat 
Transfer, vol. _I 92, No. 1, 1970, p. 1. 
K. H. Sun and J. H. Lienhard, "The Peak Pool Boiling 
Heat Flux on Horizontal Cylinders," Int, Jour, Heat, 
Mass Transfer, vol. - 13, 1970, pp. 1425-1439. 
N. Bakhru and J. II. Lienhard, "On the Non-Existence 
of Peak and Minimum Boiling Heat Fluxes at Low 
Gravity," University of Kentucky, TR No. 18-70-ME-5, 
March, 1970. 
V. Dhir, "Some Notes on the Development of the Hy- 
drodynamic Theory of Boiling," University of Kentucky, 
TR No. 19-70-ME-6, March 1970. 
V. Dhir and J. H. Lienhard, "Laminar Film Condensa- 
tion on Plane and Axi-Symmetric Bodies in Non-Uniform 
Gravity," Jour. Heat Transfer, vol. - 93, No. 1, 1971, 
pp. 97-100. 
J. H. Lienhard, R e  Eichhorn, V. Dhir, "Laminar Na- 
tural Convection Under Non-Uniform Gravity," under 
review. 
J. H. Lienhard and V. Dhir, "A Simple Analysis of 
Laminar Film Condensation with Suction," under review. 
A .  Bhattacharya and J. H. Lienhard, "The Similarity 
of Bubble Growth inaBoiling and Electrolysis, " 
University of Kentucky, TR 23-70-ME-7, May, 1970, 
A .  Bhattacharya and J. H. Lienhard, "Similarity of 
Vapor and Gas Bubble Growth," under review. 
R. A, Reich and J, H. Lienhard, "A Computer Program 
fo r  Correlating Peak and Minimum Heat Fluxes," Uni- 
versity of Kentucky report in press, 
J. H. Lienhard and J, E. Funk, "Deisgn of a Fer- 
fectly 'Effective Boiling Fin," Jour. of Basic 
Enger in press. 


Gravity boiling studies Final report, 1 Sep. 1969 - 31 Dec. 1970

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