Heat Transfer And Critical Heat Flux In Transient Boiling I.pdf

Journal of Nuclear Science and Technology

ISSN: 0022-3131 (Print) 1881-1248 (Online) Journal homepage: https://www.tandfonline.com/loi/tnst20

Heat Transfer and Critical Heat Flux in Transient Boiling, (I) Fujio TACHIBANA , Mamoru AKIYAMA & Hiroshi KAWAMURA To cite this article: Fujio TACHIBANA , Mamoru AKIYAMA & Hiroshi KAWAMURA (1968) Heat Transfer and Critical Heat Flux in Transient Boiling, (I), Journal of Nuclear Science and Technology, 5:3, 117-126, DOI: 10.1080/18811248.1968.9732415 To link to this article: https://doi.org/10.1080/18811248.1968.9732415

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Journal of NUCLEAR SCIENCE and TECHNOLOGY, 5 (3), p. 117~126 (March 1968)

117'

Heat Transfer and Critical Heat Flux in Transient Boiling, CD An Experimental Study in Saturated Pool Boiling Received September 27, 1967

Fujio TACHIBANA*, Mamoru AKIYAMA* and Hiroshi KAWAMURA* Heat transfer and critical heat flux in saturated pool boiling were experimentally studied under transient power condition. The heating elements were flat plates of nickel submerged facing vertically in sta,unant water. The heat generation rate in the test section was increased linearly in time, upon which, under certain conditions the heat flux was found to reach a maximum point located in the nucleate boiling regime. The hea~ flux of this critical point increased with mounting sharpness of the transient, and the mechanism that occurs such a high critical heat flux may be the rapid formation and evaporation of thin liquid film at the bases of vapor bubbles. Examination of high speed motion pictures reveals that all bubbles on the heating surface are still in the phase of the first generation until the critical condition is reached. Compared to the case of steady boiling, the effect of differences in the heat capacity of the test section upon the critical heat flux was found to be less marked under the present experimental conditions.

I.

INTRODUCTION

A liquid-cooled reactor inherently involves the problem of boiling, since even in a nonboiling type of reactor, boiling of the coolant will take place under anomalous conditions such as a serious power excursion. Through a series of power excursion tests such as SPERT and BORAX, it has been revealed that the boiling of coolant plays a major role in the transient process of power excursion: the void formation and resulting attenuation of neutron moderation is one of the dominant factors for reactivity compensation in a metallic-fuel reactor: the sudden formation of steam, probably due to spontaneous break down of a thermodynamically unstable state as well as to dispersion of molten materials, generates an intense pressure pulse which can disintegrate the reactor core in an extremely rapid transient; and the formation of a vapor blanketing over the fuel cladding can cause the fuel to melt. Related out-of-pile studies, i.e., studies in transient boiling, have been carried out in parallel. Earlier, Cole 0 J and Grahamc'J made step-wise transient experiments with thin ribbon test sections. Cole found that in the

non-boiling region the temperature of ribbon could well be estimated by calculating the pure conduction from the ribbon to the stagnant water, while Graham found free convection to be significant in his experimental arrangement. The exponential transient experiment was first undertaken by Rosenthal & Millerc3J with a ribbon test section submerged in stagnant water. These authors observed temperature overshoot and delay time occurring in the process of incipient boiling, and they studied the effects of the excursion period and subcooling upon the transient characteristics. Johnson, et a/.c•xsJ extended the experimental conditions, and introduced new variables such as coolant flow and system pressure. They further examined void delay time, void overshoot and other void behaviors by measuring the void optically as well as by X-ray attenuation method. In the course of their experiments, extensive data were obtained on transient boiling, covering a wide range of experimental conditions. Subsequently, Martensonc6J undertook a transient experiment under high pressure, followed

*

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Department of Nuclear Engineering, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo.

J. Nucl. Sci. Techno!.,

118

more recently by Hall & Harrisonc'J who investigated the extremely rapid transient region. While experimental data begin to be accumulated through such works, these appears to be little correlation among them, and the information available is still meager compared to the case of steady state boiling. More particularly concerning the critical heat flux in transient boiling, research is still only in its earliest stage. RosenthaJC'l concluded from his experiment that the transient critical heat flux does not differ very much from the corresponding stea::ly flux. More lately, however, Hallm has found that, even in the lowest period tested, film boiling was always preceeded by a short burst of nucleate boiling, and that during this burst the heat flux exceeded burnout heat flux for steady boiling under the same conditions by a factor of between 5 and 10. Hayashi, eta!. csJ have analyzed the SPERT data and pointed out that a very high heat flux is attained in the transient nucleate boiling region. It would appear, however, that the definition of critical heat flux in transient boiling has not yet been well established, and the terms "critical heat flux" and "physical burnout" are sometimes used confusingly.

n.

in distilled water at saturation temperature (see Fig.I). A small mirror was placed beneath the test section to facilitate observation along the surface.

Fig. I

The dimension of the vessel was about 20 x 20 x 20 em, and provided with two 300 kW

electric heaters to warm the water and keep it close to saturation temperature. The power transient generator consists of four parts, i.e., pulse generator, arbitrary function generator, power amplifier and batteries. The desired function is generated by photo-forming, amplified by a transistor regulated power amplifier, and supplied to the test section. Figure 2 shows the schematic diagram of the experimental arrangement.

ExPERIMENTAL

A series of pool boiling experiments was carried out under transient power condition, in which the test section was directly heated by transient electric current supplied from a power transient generator. Information on exponential power transients may be desired for direct application of experimental results to reactor technology, but in the present experiment, the power was increased linearly for simplicity, since the present study is aimed more at gaining a clearer basic understanding of the phenomena than at direct applications. I.

Te3t piece and s·.1pport

Experimental Apparatus

The test pieces were flat strips of nickel about 50 mm long and 6 mm wide, and of different thicknesses to examine the effect of heat capacity upon transient boiling (0.01, 0.05, The test section was suspended 0.1 mm). with its length horizontal and width vertical

Fig. 2 Diagram of transient boiling experiment

A dual beam oscilloscope was used to measure the voltage drop across the test section and the voltage difference created by the resistance bridge. A small amount of drift in the vertical DC amplifier was found, and it was compensated in the process of data reduction. In several runs, motion

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Vol. 5, No.3 (Mar. 1968) 1 Qa(t) =qa,o10 '

pictures were taken with a 16 mm HIMAC camera operating at about 5,000 frames/sec. 2.

Experimental Procedure

The test piece was placed in the vessel after cleaning with acetone. Before starting the experiment, the water in the vessel was boiled for about half an hour by passing electric current both to the test section and to the immersed heaters. The balance of the resistance bridge was always checked prior to each experimental run, and then transient power was supplied to the test section. So long as the transient period was short the test section did not sustain physical burnout, the total energy having been insufficient to bring the test section temperature up to melting point. Experiments with one test section were carried out beginning with the shortest run and followed by runs of increasing periods, until the test section became colored or suffered physical burnout and had to be replaced. 3.

Data Reduction

The average temperature of the test section was calculated from the change of electrical resistance, and a resistance double bridge was devised to measure the increment of the resistance. The voltage drop across the test section was also measured, which gave the heat generation per unit surface area of test section (qa). The heat flux from the test section to water (q,) was calcu!ated from the equation q,(t) =qo(t)- H~},

where Qa.o=1X10 6 kcal/m 2 ·hr. The procedure for the calculations described above was coded in a source program TRAB- using HARP 5020, and all of data were processed by a HIT AC 5020 digital computer.

m.

Figures 3 and 4 are examples of experimental data on transient boiling, where the mean temperature of the test section (T), heat generation rate per unit surface area (qa), net heat flux (q.,) and heat transfer coefficient (a) are plotted as functions of time. The zero point of time has been determined so as to optimize the linear fitting of the qa(t) line that passes through that point at zero value. Photos. 1 ~ 4 are typical examples of motion pictures of transient boiling, where corresponding heat transfer data are also noted in. The time scale of pictures and figures are well synchronized; the discontinuity between

(1)

(

RESULTS AND DISCUSSIONS

1. Experimental Results

where the heat ca.l'acity per unit surface area of test section is denoted by H. The heat transfer coefficient is defined by a=qn(t)/(T,-T80 ,),

(3)

2)

where T, is the average surface temperature, obtained by solving the thermal conduction equation in the test section using the net heat flux (Eq.( 1 )) and the given heat generation (q 0 ) . The rate of power increase is specified by the "ramp-period" (to), which is the time interval in which the heat generation (q0 ) reaches 1 x 106 kcal/m 2 • hr starting from zero. Then, -27-

160

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150

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140

130

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Fig. 3 Results of transient boiling experiment

120

J. Nucl, Sci. Techno!.,

and the net heat flux from test section to water

150 1.4

140

Ni 0.01 mm to=16.lmsee

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propertie3 of metal and water a: Thermal diffusivity of water k: Thermal conductivity of water .

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~~

0.2

,~~2--4~+6~8~1~0~1~2-+14~16~~18~2~· Time

Fig. 4 Results of transient boiling experiment

one frame and the next corresponds to a maximum error of about ±0.2 msec. Each frame of the motion picture includes both plan and elevation views. 2. Non-boiling Region

Once the power transient generator is set -off, there first occurs non-boiling heat transfer, in which the dominant part is considered to be the heat conduction to stagnant water. Time dependent heat conduction equations for a system composed of metal and stagnant water were solved in one dimension with a linearly increasing heat source in the test ·section. The assumptions adopted in the calculation were that: (1) the test section has a finite heat capacity but no thermal resistance; (2) the liquid is treated as a semiinfinite solid fixed to the test section surface, without thermal resistance; (3) the temperature distribution in the water is one dimensional and symmetrical for both sides of the test section. The temperature rise of the test section is given by T(t)= qa.ot; [~ 7 3/2_ 7 +~ 7 112 H to 3-V r. .V r. -l+e 7 erfcv"T],

(4)

The calculated results of Eq. ( 4 ) are plotted with broken lines in Figs. 3 and 4. These figures reveal that, in the nonboiling region, the calculated temperature curves agree with measured values within the accuracy of experimental measurement and of the paremeters used in calculation. It can be concluded, therefore, that conduction is the main heat transfer mechanism in this region especially in the case of short period transient. 3.

Nucleate Boiling Region

As the power input is increased and the surface temperature rises to a certain level, bubbles begin to appear on the heating surface as seen in the photographs. Then, the temperature begins to deviate from the curve derived from the equation based on pure conduction, implying that there has occurred a transition from non-boiling to boiling heat transfer. Though the clearly discernible inflection seen in the temperature curve for the 0.01 mm thick test section might appear to suggest abrupt nucleation over the whole surface, photographic records reveal that the first bubble has actually appeared appreciably earlier than this inflection point, and that this was followed by a gradual increase of the number of bubbling sites until they covered the whole surface. In this boiling region, the temperature curve for the 0.01 mm test section possesses a level stretch, indicating inst;:~ntaneous transfer of most of the generated heat to the coolant water, which is not the case with the

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121

Vol. 5, No. 3 (Mar. 1968)

Time (msec)

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J. Nucl. Sci. Techno/.,

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123

Vol. 5, No. 3 (Mar. 1%8)

thicker test section providing an uninterrupted decrease in the rate of temperature rise with increasing net heat flux. Such a high capability for cooling, together with the boiling pattern observed, indicates that the boiling in this region is analogous to the nucleate boiling encountered in steady state boiling. In Fig. 5 the data from runs with the 0.05 mm thick test section are re-plotted in the form of what is generally known as the boiling curve, and are compared with that of steady state boiling. This latter curve is based on a steady boiling experiment conducted with the same experimental arrangement and temperature measurement technique as in the transient experiment. From this figure it is seen that the boiling ~urve for short period transient is appreciably different from the steady curve, whereas in the boiling region the curve for long period transient falls close to that of the steady boiling curve, showing that this rate of power rise Cta=183 msec) is gradual enough for boiling heat transfer. The non-boiling part of this long period curve, however, deviates markedly from the steady curve, indicating that, for non-boiling heat transfer, the above rate is still too fast to be considered approximately steady.

net heat flux, as well as the boiling curves, suggest the existence of a certain critical The rate of temperature rise, condition: after decreasing in the nucleate boiling region, again increases sharply, while the heat transfer coefficient rises to a maximum and then begins to decrease. The net heat flux possesses a maximum with thick test section in short period transient, while no clear maximum appears when the test section is thin and the period is long. Even in the latter case, however, the boiling curve clearly deviates from the normal behavior of nucleate boiling, again indicating the existence of a certain critical condition. The heat flux at this critical point is plotted against ramp-period in Fig. 6. It is seen that the critical heat flux under transient power increases with decrease of r~mp-period (to) i.e., with increasingly sharp transient. In the other direction of declining transient, the critical heat flux decreases and asymptotically approaches a fixed critical heat flux level for steady boiling. The steady burnout data has been taken from an experiment also made in the course of the present study; this particular experiment has been the subject of a previous papercs).

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Fig. 6 Critical heat flux in transient boiling vs. ramp-period 10'

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Fig. 5 Boiling curves under transient power condition, showing the dependency upon ramp-period to

4. Critical Heat Flux

The variations in time of temperature and

The interesting point to be noted is that under transient heat con1itions a heat flux appreciably higher than in steady state boiling can be attained. The mechanism that causes such a high heat flux may be the rapid formation and evaporation of thin liquid film at the base of vapor bubbles, provoking

-31-

J. Nucl. Sci. Techno!.,

124

the extremely high heat transfer rate, as it has been reported in the pastc' 0 l<''l. The rapid evaporation of liquid film, however, gives rise to the appearance of dryout areas, where the cooling ability sharply drops below the level of the wetted area. Thereupon, it is considered that the dryout area rapidly increases and makes the heat flux decline again after a peak point, bringing about a rapid rise of temperature, when the dryout area grows to cover a certain part of the surface. Examination of the motion pictures reveals that all the bubbles on the surface are still in the phase of the first generation when the critical condition is reached. This is the case when the transient critical heat flux is very close to the steady rate (Photo. 2). In ordinary steady boiling bubbles repeat growth and departure at random over the whole surface, which is in sharp contrast to the afore-mentioned behavior in transient boiling. Hence, it may be said that the process of heat transfer in transient boiling is strongly associated with the nucleation and growth of vapor bubbles. The reason for the increase of the critical heat flux with shortening ramp-period can be explained qualitatively as follows. For simplicity, the first bubble is postulated to appear when the surface temperature reaches a certain given leveL (This as3umption is not very far from actuality.) Since the surface temperature rises at a higher rate in the shorter period transient, more bubbling sites can be expected to come into being before one bubble grows and extends over the surrounding nucleation sites. In this manner, the short period transient allows more bubbles to exist on the heating surface at higher superheat. This is what provides for a higher heat flux in the nucleate boiling region, including the case of the critical flux condition. More detailed analysis of this problem will require further fundamental studies on nucleation and growth of vapor bubbles. In Fig. 6 it is seen that the heat capacity of the test section does not affect the critical heat flux in transient boiling s:> markedly as in steady state boiling. Under the present experimental conditions a test section of 0.05 mm

thick is seen to be already ample to avoid the effect of small heat capacity, while in saturated pool boiling under steady power condition, a thickness of more than 0.8 mm is known to have been needed for a stainless steel plate to be free of the effect of heat capacity upon the critical heat flux< 9l. In the same paper< 9l, it was analyzed that, with a surface of small heat capacity, the critical heat flux in steady boiling depends upon sudden local temperature rise and the resulting Leidenfrost phenomena. In transient boiling, on the other hand, the critical condition occurs as already stated when certain parts of the wetted area are replaced by dryout areas. Hence, it is considered natural that the critical heat fluxes in steady and transient boiling - with different mechanisms playing their part- should be affected differently by variations in test section heat capacity. The data from the transient experiment on the 0.01 mm test section would seem to provide some indication of the mechanism that produces the low critical heat flux brought by a small heat capacity. As seen from the conduction calculations, the heat generation rate (qo) of the 0.01 mm test section is smaller than that of the thick test section when compared at the point in time where the surface temperature reaches the level of incipient boiling in transients of the same period. Moreover, the experimental data show that, at the critical point, the q 0 of the 0.01 mm test section is smaller even than the net heat flux of the thick test section, and that all of the generated heat is instantaneously transferred to the coolant. Thus, if a net heat flux equal to that of the thicker test section is to be attained, the temperature of the thin test section must decrease, which is none other than the set-back phenomenon observed in subcooled transient. The phenomenon, however, has never been found in saturated condition<3J<•l, the reason of which has yet to be clarified. 5. Boiling in Post·critical Region

In steady state boiling, the critical condition means physical burnout of the heating section since power is constantly being generated, while in transient boiling the critical

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125

Vol. 5. No.3 (Mar. 1968)

condition is not necessarily associated with physical burnout directly. Under transient power conditions, physical burnout is governed by transient power behavior as well as heat transfer rate in the post-critical region, since a fuel will be saved from physical burnout if the transient power declines due to the selflimiting characteristic of power excursion. Figure 7 is an example of results from transient boiling experiment, and covers also the post-critical domain. In this example, the power was increased monotonously also beyond the critical point, while the heat flux decreased and stayed at a fairly low level. The large scattering of data in the postcritical region is attributed to deterioration of accuracy in electrical measurements and in the interpretation of the recorded curves. Inaccuracies in the time derivatives of the temperature should also be partly responsible for the scattering, while the actual temperature itself were obtained with sufficient accuracy. The scattering should be greatly reduced if the range of measurement is localized to the post-critical region. 2.0

7001-

;::

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Ni 0.05 mm to=25.7msec

1.5

600~

-

material that served as test piece, and this curve was used in the reduction of experimental data. But the calculations for Fig. 7 further required higher temperature portions of this curve, and the necessary data above 450°C was taken from "International Critical Tables, Vol. 6, p.l35", the two curves being interpolated smoothly between 200° and 450°C. The heat flux data sometimes show negative values, which probably arises from incorrect selection of the p- T curve in the higher temperature ranges, as well as from inaccuracies in measurement and difficulties of curve interpretation. In Fig. 7, the heat flux in the post critical region would appear to be of the same order as the heat flux in usual film boiling, so that boiling in this region is what might be con· sidered a form of transient film boiling. In this example, the power continued to increase monotonously after passage into the postcritical region, and the boiling failed to return to nucleate boiling condition. If instead the power had decreased after the critical point, return to nucleate boiling might quite well have taken place especially in subcooled boiling. The study of this problem is important in reactor technology, and it is now under investigation.

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A critical condition relative to boiling heat transfer has been found under transient power conditions. The net heat flux reaches a clear peak at the critical point, especially in the region of shorter period. (2) The critical heat flux in a power transient increases with rising rate of transient power increase, while with lowering rate, the heat flux asymptotically approaches a critical heat level particular to steady boiling. (3) Even under critical condition, all bubbles on the surface are still in the phase of the first generation. This applies also to cases of long period transients such as in the region of asymptotic approach to steady boiling. (4) In pool boiling at saturation temper-

(1)

~0, ~

1001-

o

I

~ so

Time

Fig. 7 Results of transient boiling, extending over post-critical region

An explicit correlation between resistivity and temperature (P- T curve) is necessary to calculate the temperature of test section from changes of resistance. The P-T curve was obtained experimentally up to 200°C in the course of the present study, using the same -33-

CoNCLUSIONS

126

J Nucl. Sci. Techno!.,

t: Time (hr, msec) t,: Time constant pertinent to physical proper-

ature, the heat capacity of a test section does not affect the critical heat flux so markedly under transient power conditions as under steady power.

ties of metal and water (hr, msec)

to: Ramp-period (msec) a: Heat transfer coefficient (kcal/m 2 • hr) 'Y: Specific weight of test section material (kg/m') P: Resistivity (Om) T: Dimensionless time, t/t,

ACKNOWLEDGMENT

Financial support was furnished by the International Atomic Energy Agency under Contract No. 356/RB/Rl.

CNOMENCLATUREJ

--REFERENCES--

(2)

CoLE,R.: NACA-TN-3885, (1956). GRAHAM,R.W.: NASA-TN D-2507, (1964).

(3)

ROTHENTHAL, M. W., MILLER, R.L.:

(1)

a: Thermal diffusivity of water (m 2 /hr) c: Specific heat of test section material (kcal/kg · o C) d: Thickness of test section (m) H: Test section heat capacity per unit surface area (kcal/m 2 • °C) k: Thermal conductivity of water (kcal/m ·hr·°C) qa: Heat generation rate per unit surface area (kcal/m 2 • hr) 6 2 Qa. 0 constant 1 X 10 kcal/m • hr qn: Net heat flux, heat flux (kcal/m 2 ·hr) T: Temperature, temperature rise COC) 1',: Surface temperature of test section (°C) Tsat: Saturation temperature CC)

ORNL-

2294,(1957). (4)

(5) (6) (7) (8) (9)

(ll] (lU

-34-

JoHNSON, H. A., et al.: SAN-1001, (1961). ibid.: SAN-1007, (1963). MARTENSON,A.J.: WAPD-T-1290, (1963). HALL, W.B., HARRISON, W.G.: Proc. 3rd Int. Heat Transfer Conf., Chicago, No. 99, (1966). HAYASHI, S., et al.: J. At. Energy Soc. Japan, (in Japanese), 6 [7], 399~405 (1964). TACHIBANA, F., et al.: J. Nucl. Sci. Tee/mol., 4 [3), 121~130 (1967). TORIKAI, K., et al.: A/Conf., 28/P/580, (1964). KIRBY, D. B., WESTWATER, ]. W. : CEP Sym., Ser. No. 57, Vol. 61, (1965).