Measurement of void frequency distributions and void profiles in nucleate pool boiling using neutron beams

NUCLEAR INSTRUMENTS

AND METHODS

167 (1979) 2 5 5 - 2 5 9 ;

(~) N O R T H - H O L L A N D

P U B L I S H I N G CO.

MEASUREMENT OF VOID FREQUENCY DISTRIBUTIONS AND VOID PROFILES IN NUCLEATE POOL BOILING USING NEUTRON BEAMS J. A. OYEDELE* and A. A. HARMS

McMaster University, Hamilton, Ontario, Canada Received 13 July 1979 The results of neutron experiments designed to provide accurate measurements of the frequency distribution of void fractions and the mean-void profiles in nucleate pool boiling are presented. It is found that the void distributions and the void profiles are distinctly determined by both the source heat flux and the distance from the heat source. These results are suggestive of the complex void formation-coalescing processes which occur in pool boiling.

1. Introduction The study of void dynamics and the role of voids in transport processes in pool boiling and two-phase flow has long constituted an important field in theoretical and applied research1). The fundamental role of the void fraction under pool boiling conditions represents a particularly tractable case which is vital not only in its relevance to traditional hydrodynamic analysis but also to problems of current technical interest 2'3). The accurate measurement of the void fractions is generally problematic for two fundamental reasons: one is the obvious requirement to avoid disturbing the liquid by the insertion of diagnostic probes 1) while the other - though less obvious but equally significant - is the requirement to minimize the experimental bias attributable to bubble dynamics4). The measurements of void frequency distributions and void profiles which we report here are for pool boiling using the neutron transmission technique in its gated - or discrete time - measurement modeS); since the neutrons in their passage through the fluid do not effect the fluidic characterstics and since the gated mode of operation provides essentially instantaneous measurements of the void fraction along a traverse, both the above mentioned experimental errors are avoided. Our specific experiment here has several objectives. Restricting ourselves to simple pool boiling we wish to determine how the void frequency distribution along a given traverse through a boiling channel varies with distance from the heat source and with the heat flux. As used here, the term void frequency distribution refers to the stable probabili* Permanent address: University of lfe, lie-Ire, Nigeria.

ty density function (pdf) of the void fractions; this form of void fraction information has recently been used by a number of researchers 5-7) and is clearly an improved characterization of two-phase fluids. With the frequency distribution of the void fraction thus measured we then determined void distribution averages also as a function of both distance from the heat source and the magnitude of the heat flux; these distributions were then used to determine the mean-void profiles for this case of pool boiling. Additional determinations include distribution comparison, considering the effect of time, and comparison to other results where possible.

2. Analytical-experimental formulation In fig. 1 we illustrate in cross-sectional representation the experimental set-up used here. The open chamber containing the boiling liquid was constructed of aluminum to yield a pool surface area of 8.0 × 0.95 cm 2. An expander overflow container was located at a height of 24 cm from the base of the chamber. The heat source consisted of a calibrated flat surface laboratory hot-plate mounted on a vertically adjustable jack allowing smooth and quick position changes of the chamber; this pool boiling apparatus was then mounted at a neutron beam port so that the neutrons would penetrate the 0.95 cm ID distance of the chamber. The neutrons used for these experiments were highly thermalized in order to provide the necessary neutron-hydrogen scattering interaction density for good void fraction sensitivity. The neutrons are available in the normal course of operation of the McMaster University Nuclear Reactor; as a result of previous similar requirements, the beam port had been designed to provide a well collimated beam. However, in order to attain good spatial sensitivity

256

Y.A.

O Y E D E L E A N D A. A. H A R M S

.q---.-- X0------t~

~----8

NEUTRON BEAM, No

N (q,y,t)

\

p--/~

W' I 8F3

REACTOR BEAM PORT

DETECTOR

COLLIMATOR

Y

T TT\

HEAT FLUX,

Fig. 1. Schematic diagram of the vapour-liquid radiation interrogation apparatus.

for the void fraction traverse measurements, we installed a stepped collimator over the neutron BF 3 detector to define a sufficiently small acceptance angle providing good spatial sensitivity. The attendant electronic equipment possessed a fast gating capability and was equipped with a magnetic tape data accumulation system. The analytical formulation of the void frequency distribution from the experimental procedures can be established by the following. For an arbitrary distance y from the heat source generating a heat flux q we define the void fraction along the radiation path at time t by ~z(q,y, t) which, in terms of the experimental arrangement, fig. 1, is given by

N(q,y,t)

= N Oexp(-2rp6)B[x(q,y,t)]

×

× exp{-rLXo [1 - ~ ( q , y , t ) ] ) .

(3)

Here d x ~ ( q , y , t ) is the instantaneous radiation traverse through a bubble and Xo is the channel thickness; the summation is implicitly taken over the total number of bubbles found in the radiation path at distance y. The associated length of liquid through which the neutron beam passes is

Here, No is the unattenuated incident neutron beam, Z'p and 6 are the neutron macroscopic cross section and thickness of the containment plates, AL is the macroscopic cross section of the liquid and B[x(q, y, t)] is the build-up function which accounts for the departure from the thin-medium radiation transmission model. The determination of these various functions and parameters are straightforward and have been previously described4"5'8); the only unknown is the void fraction a~(q,y. t). Equation (3) applies at any time t; however, if the transmitted neutron beam is counted over a time interval 3ti, which is sufficiently shorter than the time required for a bubble to pass through the neutron beam, then an essentially instantaneous void fraction ~z:(q,y) is measured. Hence, the void fraction a~(q, y) for this ith time interval At, is fully defined by Eq. (3); for our purposes here, we determined ~zi(q, y) simply by iteration in which eq. (3) is written as

x(q,y,t)

[Ni(q,y) - N O exp(-2ZpcS)B[xi(q,y)]

(q, y, t) = ~' Axi(q, y, t) i

(1)

XO

= x o - ~ Axi(q,y,t) i

= x o [1 -

c~(q,y,t)].

(2)

The corresponding instantaneously transmitted neutron beam measured by the neutron detector is therefore given by

x

x exp{--ZLXo [1 -- c~;(q,y)]}[ < e,

(4)

where e is a sufficiently small sensitive parameter. The appropriate frequency distribution of the void fraction - that is the pdf for the case of heat flux q

NUCLEATE

POOL

and at position y - is n o w determined by sequentially gating the transmitted neutron beam for i = 1,2, ... I time intervals each o f which yields one instantaneous void fraction ~zj(q,y) for a given heat flux, q, and the specified distance from the heat source, y. We represent this void frequency distribution function by f~,(q,y). The mean-void along the beam traverse at y for a heat flux q is therefore given by

oq(q, y) f~i (q, y) A:q ~(q,y)

=

i

257

BOILING

source for q = 0.7 cal cm 2. The void spectrum at the smaller distance is slightly skewed with a mean void fraction ~z(q, y ) = 0.55 and a variance of a 2 = 0.013. At the larger distance, the spectrum is 4o =.22 Or= = 022

q = 0.50Col/era 2 y =30era

3o

~0 ,

(5)

Z Li (q, y) A~

,z

=

o

LtJ

where Lkzi is the void interval selected. The variance, and higher m o m e n t s , can be similarly calculated, 3. Results and discussion For the experimental system illustrated in fig. 1, we collected 200 neutron transmission measurements (i.e., I = 200) each of duration o f 0.1 s (i.e., Ati = 0.1 s). These m e a s u r e m e n t s were obtained for different heat fluxes q and at different distances y from the heat source. The discussion of the results is thus most clearly presented by grouping the results according to the variations of q and y.

20

u. io

40

=39 0.~ =.018

30

F

; :o?ooo,,orn,

>(J Z LU

= (1;:

~ 20

3.1. VOID DISTRIBUTIONS(q = constant, y = variable) In fig. 2 we illustrate the void frequency distributions at distances o f 3.0 cm and 10.5 cm from the

q_

I0

50

0 40

r.-i

40

i f

I

I

I

I

I

I

I

I

I

I

t

t

L

I I t l

t

t

>. 5 0 C,

eJ

U--'~l ~

Ud

~ :055 0.017col Icm ~ q0.2==0.70

>(~ Z hi

~=. 0,3

',

z

3C

y=3.Oem

~=.55

0

I I r

~J

rC )

y =30cm

u. 2 0 y = 10.5 cm :.55 ,¢=.o3

io

I ~ ) l

r-

j_j

Io

'

a

L_..~ 0

0.2

0.4 0.6 VOID FRACTION, (z

0.8

0

1.0

Fig. 2. Void fraction distributions obtained at distances of 3.0 cm and 10.5cm from the heat source for a heat flux of 0.70 cal cm - 2.

,

0

r--[

,

t

0.2

,

J ,

,

I

0.4

,

,

,

~

0.6

08

I0

VOiD FRACTION, a

Fig. 3. Void fraction distribution at a distance of 3 cm from a heat source of (a) 0 . 5 c a l c m 2 (b) 0 . 6 c a l c m - 2 a n d (c) 0.7 cal cm - 2.

258

Y.A.

O Y E D E L E A N D A. A. H A R M S

distinctly broadened; though the mean is the same, a'(q. y) = 0.55, the variance is now ~72 = 0.03. Due to this broadening, most of the void fractions at the larger distance are between 0.28 and 0.84 while most of those at the smaller distance are only between 0.36 and 0.72. It is therefore apparent that a prediction of void frequency distribution cannot be made from a measurement of only the mean void fraction. 3.2. VOID DISTRIBUTIONS (q = variable, y = constant) The void spectra obtained at y = 3.0 cm and for various q = 0.50, 0.60 and 0.70 cal c m - 2 are shown in fig. 3. At low heat flux (q = 0.50 cal cm-2), the void spectrum is essentially composed of low void fractions and is bimodal while at higher heat fluxes (q = 0.60, 0 . 7 0 c a l c m 2) the spectra consist of correspondingly higher void fractions. Also the mean void fraction calculated from the spectrum increases with increasing heat flux. Thus the void spectrum reflects the amount of heat transferred into the system and also characterizes the flow pattern in the system; the void spectrum at low heat flux could be identified with the bubble flow regime observed in two phase flow, while that at high heat flux is similar to a slug flow regime9). Although the mean void fraction increased with heat flux, the spread in the spectra, as indicated by the variance, does not show a corresponding increase. In fact, the variance decreases with increasing heat flux or mean void fraction. 3.3. VOID PROFILES (q = variable, y = variable) Figure 4 shows the variation of mean void fraction with distance for different heat fluxes. In the figure, we have used the weighted averages of two sets of mean void fractions obtained from two separate experiments in which the distance from the source was respectively increasing and decreasing such that the first position to be diagnosed in the first experiment becomes the last in the second experiment and vice versa. This was done in order to minimize the effect of any variation of mean void fraction with time during the time required to take a set of measurements at a given heat flux. At low heat flux, the mean void fraction increases with distance up to about 6.5 cm before it starts to decrease with further increases. This positive inflection seems surprising since one would expect the mean void fraction at low heat flux to be largest very close to the heat source and to decrease

06-

llcm

O.5

i 0 I-~ 0.4

~

I

/

m = .

c

2

0 > Z 03

O.2

O0

i

I

i

5.0 DISTANCE,

I

I0.0

i

I

15.0

cm

Fig. 4. The variation of mean void fraction with distance from heat source for different heat fluxes.

gradually with distance from the source. However, it could be explained as local boiling in which the voids start to coalesce very close to the heat source and the voids therefore become larger as they move upwards from the source. Then, as the voids move into cooler regime, they transfer heat to the pool and get smaller and condense and finally collapse in the pool. The variation of the mean fraction with distance at a higher heat flux q -- 0.60 cal cm 2 is similar to that at low heat flux but the corresponding change with distance is much reduced. At a high heat flux, q = 0 . 7 0 = c a l c m -2, the variation of the mean void fraction with distance undergoes a negative inflection. It decreases slightly with distance up to about 8.0 cm and then increases sharply with further increase in distance. This increase at large distances is evidently due to void coalescence. Obviously, at this high heat flux, the whole pool is at a sufficiently high temperature so that the voids do not collapse. These results indicate that, as the heat flux is increased, there is a transition from a state in which the lower part of the pool contains the largest void fraction to a state in which the top of the pool

N U C L E A T E POOL B O I L I N G y = 13.0 cm

/y=3Oom

0.6

/ / y = 8 . 0 cm

7

o I-

0.4

t~

6 z

03

0.2

further increase in distance. Although these observations were made in an internally heated boiling pool, a qualitative comparison with our results is not inappropriate. 4. Conclusion A discrete-time neutron attenuation technique has been used to investigate the frequency distribution of void fractions and the mean-void profile in nucleate pool boiling. It was observed that both the frequency distribution and void profile are determined by the heat flux and the distance from the heat source and display complex distribution characteristics; the observation of spatially dependent positive and negative inflection of the mean voids appears particularly significant. A comparison of the frequency distributions indicate that a prediction of the distributions cannot be made from a simple measurement of the mean void fraction; distributions having the same mean value may have significantly different distributions.

0.5

CE

259

/ I 0.5

0.6

0.7

HEAT FLUX, q (c01/cm 2)

Fig. 5. The variation of mean void fraction with heat flux at different distances from the heat source.

attains this state. This transition may be further illustrated by considering the variation of mean void fraction with heat flux at different distances from the heat source. Fig. 5 shows such a variation at three different distances. At a large heat flux, the largest mean void fraction is at large distances from the heat sources while at low heat flux the largest fraction is found at smaller distances. In the intermediate heat flux region, at about q = 0.63 calcm 2, the mean void fraction at the three different distances are almost equal; this is the transition region. One similar observation of a void profile inflection had been previously reported for internally heated boiling pools1°; the authors observed that the local void fraction, deduced from temperature fluctuation measurements in natural and forced circulating boiling pools of water, increases slightly with distance from the heated wall up to a point but above this point the fraction decreases with

The authors wish to thank Mr. M. H. Younis and Dr. R.L. Judd for useful comments. One of us (JAO) is grateful for a fellowship from the University of Ife, Nigeria. Financial support for this work has been provided by the Natural Science and Engineering Research Council of Canada. References 1) y . y . Hsu and R. W. Graham, Transport processes m bolting and two-phase systems (McGraw-Hill, New York, 1976). 2) M.S. Kaximi and J.C. Chen, Nucl. Sci. Eng. 65 (1978) 17. 3) H.C. Unal, Frans. Am. Soc. Mech. Eng. 100 (1978) 268. 4) A.A. Harms and C.F. Forrest, Nucl. Sci. Eng. 46 t1971) 408. 5) W.T. Hancox, C. F. Forrest and A. A. Harms, AiE71E-ASME Heat Trans/i,r Carl~i, Denver, Col. 6 - 9 August 1972, 72HT-2 (1972). 6) O. C. Jones Jr. and N. Zuber, Proc. Fifth Int. Heat Transl~'r E'ot!l~, Japan (1974) paper B-5-4. 7) M.H. Younis, PhD Dissertation (in preparation), private communication. 8) A.A. Harms, S. Lo and W.T. Hancox, J. Appl. Phys. 42 (1971) 4080. ~) W.T. Hancox and A. A. Harms, Trans. Am. Nucl. Soc. 14 (1971) 699. 10) M. Stefanovic, N. Afgan, V. Pislar and Lj-Jovanovic, Proc. Fourth Int. Heat Transl~,r Cot#., Vol. 5 Versailles, France (1970), Paper B. 12.