Kaufman, Samuel J

Sparrow, Ephraim M

English

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.t'(IVl 1i5L14a 
NACA 
RESEARCH MEMORANDUM 
VISUAL STUDY OF FREE CONVECTION IN A NARROW

VERTICAL ENCLOSURE
By Ephraim M. Sparrow and Samuel J. Kaufman 
Lewis Flight Propulsion Laboratory

Cleveland, Ohio 
NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
WASHINGTON 
February 16, 1956
https://ntrs.nasa.gov/search.jsp?R=19930089006 2020-06-17T08:23:00+00:00Z
NACA RM E551,14a
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
RESEARCH MEMORANDUM 
VISUAL STUDY OF FREE CONVECTION IN A NARROW VERTICAL ENCLOSURE
By Ephraim M. Sparrow and Samuel J. Kaufman 
SUMMARY 
The free-convection flow of water in a narrow vertical enclosure, 
cooled at the top through a copper surface and open at the bottom to a 
heated reservoir, has been studied by means of a shadowgraph. It was 
found that there is no flow pattern which is steady with time, that is, 
no region of the enclosure is permanently a region of upflow or of down-
flow. Because of variations in the size of the various upflow and down-
flow regions arranged along the length of the enclosure at a given time, 
and because of changes with time, neither upflow regions nor downflow 
regions could be characterized by a definite size. The number of up-
flow and downflow regions varied with time. 
The dominating characteristics of the flow patterns were instability 
and change.
INTRODUCTION 
An experiment on free convection of liquid sodium in a thin annu-
lus of large mean diameter has been reported in reference 1. The annu-
lus, which was oriented with its axis vertical, was closed at the top 
by a surface through which heat was extracted. The bottom of the annu-
lus was open to a reservoir of heated liquid sodium. Temperature meas-
urements were taken around the periphery of the annulus. From these 
data the existence of alternate regions of "upflow" and downflow, ar-
ranged in a regular way around the circumference, was inferred. Not 
only could it be inferred that the alternate upflow and downflow regions 
were uniform in size, but also that the flow pattern, once established, 
did not change. That is, downf low regions always remained as downflow 
regions and upflow regions always remained as upflow regions. 
The present investigation was undertaken to determine by visual ob-
servation-the details of the flow in a system similar to the one de-
scribed above. In order to obtain an apparatus suited for flow visuali-
zation by optical techniques, a number of departures from the system of 
reference . 1 were required. A rectangular enclosure was used instead of
NACA RN E55L14a 
2 
an annulus. However, the basic situation of heat extraction through a 
surface at the top and free exchange with a heated reservoir at the bot-
tom was maintained. Distilled water was used as the working fluid rather 
than liquid sodium. 
The extraction-of heat at the top surface of the enclosure (or .annu-
lus) gives rise to a layer of fluid, in the region of the top, which is 
relatively heavier than the warmer fluid below. The heavier fluid, when 
accumulated in sufficient quantity near the top, will push its way down-
ward through the enclosure. The warmer, lighter fluid will rise to take 
the place of the descending cool fluid.. So, regions of upflow and down-
flow are established. The details of the flow to be determined from a 
visual inspection are (1) the steadiness of the flow patterns with time, 
(2) the size and uniformity of the various . upflow and downflow regions, 
and (3) the direction of flow velocities with particular attention to 
nonvertical components. Further, the visual observation provides an in- 
sight into both the initiation and the breakdown of a particular flow 
pattern.	 -	 - 
APPARATUS 
• The description of the experimental apparatus will be augmented by 
the photographs-of figure 1. An oblique view showing an over-all view 
of the experimental apparatus is shown in figure 1(a). A front view of 
the test section on which the important components have been labeled is 
shown in figure 1(b).	 - 
The vertical enclosure, in which free-convection flow patterns were 
observed, had front and rear walls made of sheets of Plexiglas. The top 
wall of the -enclosure was a solid strip of copper; the end walls were 
made of Plexiglas strips. The enclosure, which was open at the bottom, 
was joined to a reservoir of heated fluid. The vertical enclosure was 
9. inches-high, 44 inches long, and . 3/16 inch thick. The ratio of 
height to thickness was therefore about 50 to 1. 	 - -	 -	 - - 
Heatwas extracted from the -fluid at the top of the enclosure 
through the copper-wall that was soldered to a duct through which cool-
ing -water was passed. The fluid in the reservoir at the bottom was 
heated by three tubes that ran the length of the reservoir through which 
hot water was passed. During the operation of the apparatus, both the 
- reservoir and the enclosure were completely filled with distilled water. 
Because of the free-convection motion, -there was a continual exchange of 
fluid between -the reservoir and the enclosure.	 --
The apparatus was operated for several hours before observations 
were made in order to insure the disappearance of initial transients.
NACA RN E55L14a
	 3 
Flow patterns were studied for temperature differences between the res-
ervoir and the copper strip at the top Of the enclosure in the range 
from 5Q0 to 85° F.
INSTRUMENTATION 
The motion of the fluid was viewed by means of a shadowgraph. A 
point source of light was placed in front of the enclosure as shown in 
figure 1. Light rays passed through the front wall, the 3/16-inch gap 
thickness, and the rear wall of the enclosure. The shadow-pattern was 
viewed on a screen behind the apparatus. The shadowgraph picture was, 
therefore, a two-dimensional picture, which provided information on flow 
patterns in a plane parallel to the front (or rear) wall. No informa-
tion could be obtained about flow normal to front and rear walls. 
The strongest delineation of the shadow lines occurs where the den-
sity gradients change most rapidly. The temperature and density of the 
hot fluid rising from the reservoir is fairly uniform. Hence, little 
evidence of the rising stream is seen except where it contacts the 
cooler, denser fluid. On the Other hand, the cooling at the top of the 
enclosure creates nonuniformities in temperature and, hence, variations 
in density gradient are induced. The moving shadow lines, which are ob-
served in the shadowgraph picture are associated with density gradients 
which are carried along-with-the movement of the cooled, heavier fluid. 
A photograph of a shadowgraph will not show the motion of the shadow 
lines, only their instantaneous location. In interpreting the photo-
graphs of shadbwgraphs (section • Shadowgraph Photographs), the presence 
of the shadow lines in a region of a photograph should be taken as in-
ferring motion of cooled, heavier fluid in the region. 
Thermocouples were installed in the front and rear walls of the en-
closure to provide supplementary information about the flow pattern. 
The thermocouple tips were 1/32 inch from the surface of the enclosure. 
This was the minimum distance at which thermocouples could be installed 
without giving rise to bumps on the wall of the enclosure. 
Shadowgraph Photographs 
Photographs of some shadowgraphs are shown in figure 2. The dy-
namics of the flow, which cannot be learned from photographs, will be 
discussed in the Flow Dynamics section using the information obtained 
from long-time - observation of the flow.	 - 
The eight photographs shown in figure 3(a) cover an area 6 inches 
high by 5 inches wide located about one-half the length of the enclosure.
4	 NACA RN E551,14a 
These photographs were taken over a period of several minutes. The cool-
ing surface at the top of the enclosure appears at the top of each photo-
graph. A rather wide variety of flows are in evidence from these photo-
graphs. For example, one photograph shows a well-developed downflow, 
another shows an upflow (i.e., no downflow). Others show downf lows in 
various stages of development (i.e., downflows penetrating into upflow 
regions and vice versa). Also, upflows and downflows existing side by 
side are apparent. 
The eight photographs shown in figure 2(b) were taken about 1/4 the 
length of the enclosure from the left end (as viewed from the front). 
These pictures show the same variety of flow as has already been noted 
in figure 2(a). 
The conclusion that can be drawn from the photographs and from the 
more revealing long-time observation of the flow, is that there is no 
flow pattern which is steady with time. That is, no region of the appa-
ratus is permanently a region of upflow or of downf low. 
A second finding, which can only be hinted at by photographs, and 
which is derived mainly from long-time observation, is that the size of 
an upflow region or of a downflow region is strongly variable. In other 
words, at a given time, the various upflow and downflow regions existing 
within the enclosure all generally covered different lengths of the en-
closure. With the passing of time, as the flow pattern changed, the 
newly emerging upflow and downf low regions were generally different in 
size from their predecessors and also differed in size among themselves. 
So, there was no particular size characterizing either an upflow or a 
downflow region. In accordance with this observation, the number of up-
flow and downflow regions varied considerably with the passage of time. 
From observation of the flow during the period of formation or 
breakdown of the downflow regions, there was considerable nonvertical, 
sidewise- motion throughout most of the height of the region in which 
the flow pattern was changing. When a downflow was well established, 
strong sidewise motions were primarily confined to the top of the re-
gion of the downf low, although even a well-established doimflow often 
did not fall in a directly vertical line. 
Flow Dynamics 
The following description of the flow dynamics is based on long-
time observation of the flow. 
1Sidewise motion means motion in the direction of the length of the 
enclosure.
NACA RN E55L14a	 5 
The cooling of fluid at the top of the enclosure gives rise to a 
continuous generation of relatively heavy fluid. Heavy fluid generated 
above an upflow region which is located near a downflow region may move 
sidewise along the top of the enclosure until it reaches the downflow 
region. When it reaches the downflow region, the sidewise-moving fluid 
is turned in an almost vertical direction. A downflow fed by fluid en-
tering it in this fashion is funnel-shaped in appearance; and the down-
flow region may be regarded as a funnel through which the heavy fluid 
generated in a given region escapes from the top surface. Heavy fluid 
generated above an upflow region that is farther from a downflow region 
may also feed into the nearest downf low region. However, the amount of 
heavy fluid accumulated during the longer path of sidewise flow may often 
be sufficient to push downward. In this circumstance, the sidewise mo-
tion of the heavy fluid to the nearest downflow region takes place in a 
band (several inches in height) below the top of enclosure, as well as 
at the top itself. 01 course, these descriptions are generalizations. 
Sometimes the strength of the upflow is sufficient to confine sidewise 
moving fluid, generated above a region of upflow, to a small layer near 
the top of the enclosure, even though the sidewise movement may be over 
a relatively long path. Alternately, some "chunks" of heavy fluid carry 
out a sidewise movement below the top layer even though their path of 
travel is short. 
On some occasions, heavy fluid, generated above an upflow region, 
does not follow an existing path of descent. (For example, the nearest 
established dowaflow may be too far away.) Under these circumstances, 
the heavy fluid generated continues to accumulate above the upflow re-
gion. Finally, chunks of heavy fluid force downward. There are three 
possible endings to this attempted downward movement. One possibility 
is that the downward-moving chunks of cooled fluid, reinforced by addi-
tional heavy fluid from above and also from adjacent regions, reach the 
reservoir at the bottom. This initial descent is often accomplished 
haltingly and with considerable nonvertical flow. Whether or not the 
downflow path thus established is sustained depends upon the supply of 
additional heavy fluid from adjacent regions near the top of the enclo-
sure. A second possibility is that descending chunks, stopped in any 
downward motion because of the opposition of the rising hot fluid, are 
pushed sidewise and reinforce the efforts of adjacent chunks of cooled 
fluid which are descendingslowly. The third possibility is that de-
sending chunks of cooled fluid are repelled by the rising stream and 
are driven sidewise into an already established downflow. 
A downflow continues only as long as there is sufficient cool, 
heavy fluid to supply it. If the rate of removal of the cooled fluid 
exceeds its rate of production, the downflow may cease. Alternately, 
the downflow may move sidewise into a region . (previously occupied by an 
upflow) in which the supply of cooled fluid (located along the top of 
the enclosure) is sufficient to sustain it.	 ..	 .
6	 NACA RN E551,14a 
The nature of the observed flow patterns did not change as the tem-
perature difference between the heated reservoir and the cooling.surface 
at the top of the enclosure was varied. The notable effect was a lessen-
ing of the flow velocities as the temperature difference was diminished. 
There was evidence of end effects associated with both left- and 
right-hand end walls of the enclosure. An almost continuous downflow 
took place ma 3/4-inch band adjacent to both of these walls. However, 
at a distance of 4 inches from either end wall, the flow patterns ob-
served were similar to those that were seen very far from these walls. 
Wall-Temperature Data 
Thermocouples were installed in the front and rear walls of the en-
closure to detect the presence of a spatial temperature pattern which 
would correspond to a permanent group of upflow and downflow regions. 
A representative plot of the temperature on the front wall is shown 
in figure 3. (The rear-wall temperatures give .a similar plot.) There 
was little difference in the temperature at all locations. This lack of 
evidence of a permanent flow pattern is in accord with the visual obser-
vations. The thermal inertia of the Plexiglas wall appeared sufficient 
to smooth any temperature variations with time which might have arisen 
because of the changing flow pattern. 
DISCUSSION 
As has - been already mentioned, the experiment reported in reference 
1 on free convection in a thin annulus using liquid sodium as the work- 
ing fluid gave a wall-temperature pattern from which the existence of 
permanent upflow and downflow regions could be inferred. These results 
differ from the findings of the present study. There are many differ-
ences between the two investigations the influences of whichcannot be 
clearly evaluated. The most obvious differences are in working fluid 
and in geometry. An annulus, as thin as that of reference 1, might, at 
first, be expected to act in a fashion similar to that of a narrow rec-
tangularenclosureof the sort used in the present study. However, the 
lack or presence of end walls may have some not-yet-understood effect 
on flow stability. The definition of the variables comprising dimen-
sionless groups needed to insure dynamic similarity of flows of the type 
considered here is not at all clear.	 . 
Aside from the unevaluated factors already noted, there is a par-
ticular difference between. the apparatus of the two experirments which 
might explain the apparent contradiction in the findings. The heat sink 
at the top of the enclosure in-the present investigation was a smooth
NACA RM E55L14a	 7 
copper surface. In reference 1, the cooling surface at the top of the 
annulus was sodiun itself., which had "frozen out" during the initial 
stages of the operation of the system. It seems plausible to expect 
that the surface thus formed wouldnot .be smooth, but would have hills 
and valleys corresponding to the. upflow-.downflow pattern which developed 
during the initial stages of operation.. Such a wavy surface, once de-
veloped, would tend to perpetuate permanent upflow-downfloW patterns. 
A single photograph of a glass-walled annulus with water as the 
working fluid in which dye is used to define the streaming of the flow 
is included in reference 1. Sufficient information can not be obtained 
from this single photograph toérmit comparison with results of the 
present investigation.
CONCLUSIONS 
The free-convection flow of water in a narrow vertical' enclosure, 
cooled at the top through a copper surface and open at the bottom to a 
heated reservoir, has been studied by. means of a shadowgraph. No flow 
pattern was
-
-found to be steady with time, that is, no region of the en-
closure is permanently a region of upflow or of downflow. Because of 
variations in the size of the various üpflow and downflow regions ar-
ranged along the length of the enclosure at a. given time and because of 
changes with time, neither upflow regions nor -downflow regions could be 
characterized by a definite size. The number of upflow and downflow re-
gions varied with time. 
The dominating characteristics of the flow patterns were instabil-
ity and change. 
Lewis Flight Propulsion Laboratory 
National Advisory Committee for Aeronautics 
Cleveland, Ohio, December 15, 1955 
REFERENCE 
1. Timo, D. P.: Free Convection in Narrow Vertical Sodium Annuli. 
KAPL-1082,-Knolls Atomic Power Lab., Geheral Electric Co., Mar. 5, 
19.54.(Contract No W-31-109 Eng -52 )
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Visual study of free convection in a narrow vertical enclosure

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