Transient boiling from inclined and downward-facing surfaces in a saturated pool

Transient boiling from inclined and downward-facing surfaces in a saturated pool M o h a m e d S. EI-Genk and Z h a n x i o n g Guo Institute for Space Nuclear Power Studies, Department of Chemical and Nuclear Engineering, The University of New Mexico, Albuquerque, New Mexico 87131, USA Received 17 February 1992; rev&ed 4 June 1992

Quenching experiments investigating transient pool boiling from the underside of inclined and downwardfacing flat surfaces in saturated water were performed. Inclination angles investigated are 00 (downward facing), 5°, 10°, 15°, 30°, 45 ° and 90o (vertical). While transition boiling heat flux and both qcHv and qmin,and the corresponding wall superheats increased as the inclination angle was increased, nucleate boiling heat flux decreased. The values of qcHv and qminand the corresponding wall superheats are correlated as functions of the inclination angle. In addition, the steady-state qcHvdata of other investigators for saturated helium and nitrogen are correlated as a function of inclination angle. These correlations are compared with that for water to determine the effects of the type of the boiling liquid and heating method on qc~F. (Keywords:heat transfer;pool boiling;nucleateboiling;melting; planesurface)

t bullition transitoire/t partir de surfaces inclin6es et tourn6es vers le bas dans un bain satur6 On a effectu~ des expdriences de trempe pour dtudier l'dbullition libre transitoire ~ partir du dessous de surfaces plates inclindes et tourndes vers le bas dans de l'eau saturde. Les angles d'inclinaison dtudids sont 0 ° (face vers le has), 5 °, 10 °, 15 °, 30 °, 45 ° et 90 ° (vertical). Alors que le flux thermique en dbullition transitoire, qcHFet qmi,, et les surchauffes des parois correspondantes ont augmentd h mesure que l'angle d'inclinaison a augmentd, le flux thermique en kbullition nuclkde a diminud. Les valeurs de qcHr et qm~,et les surchauffes des parois correspondantes sont corrdl~es en fonction de l'angle d'inclinaison. En outre, les donndes de qCh'F en r@ime stable obtenues par d'autres chercheurs pour l'hdlium et l'azote saturds sont corrdldes en fonetion de l'angle d'inclinaison. On compare ces corrblations avec celle de l'eau pour ddterminer les effets du type du liquide en dbullition et de la mdthode de chauffage sur qc,p.

(Mots cl6s: transfert de chaleur; ebullition libre; ebullition nucl6~e; fusion; surface plane)

Nomenclature C

g H hfg q qcuv

qctfVo t T

Coefficients in Equations (3), (4), (5), (10) and (11) Specific heat of the disc material (J kg -x K - l ) Gravitational acceleration ( m s -2) Thickness of the disc (m) Latent heat of vaporization (J kg l) Average surface heat flux (W m -2) Critical heat flux (W m -2) Critical heat flux for upward-facing surfaces 16J7 (W m -z) Time (s) Temperature (K)

Although pool boiling from the underside of inclined and downward-facing flat surfaces has many engineering applications in chemical and nuclear industries and in cooling superconductivity coils 1-6, it has received little attention. Only a few experimental studies involving saturated liquids have been reported in the literature; none, except that of Guo and E1-GenkS, 6, has investi0140-7007/93/060414-09 © 1993 Butterworth-HeinemannLtd and IIR 414 Int. J. Refrig. 1993 Vol 16 No 6

Greek letters

cr 0 ATsat P

Zd

Surface tension (N m-1) Surface inclination angle (degrees) Wall superheat (Tw - Ts,t) (K) Density (kg m s) Most dangerous Taylor wavelength (m)

Subscripts

1 CHF rain sat v w

Saturated liquid At critical heat flux At minimum film boiling heat flux Saturation Saturated vapour Boiling surface

gated transient boiling. Very few data are available in the film boiling regime and for both the critical heat flux, qCHF, and the minimum film boiling heat flux, qminSeveral experiments have been reported on nucleate boiling from the underside of inclined and downward-facing flat surfaces in saturated pools of R-11, liquid helium, liquid nitrogen, isopropyl alcohol, and water1,7-1s. Ishigai

Transient boiling from inclined and downward-facing surfaces: M. S. EI-Genk and Z Guo et al. 7 have investigated nucleate and film boiling from

downward-facing flat copper discs with diameters of 25 mm and 50mm, Githinji and Sabersky s used a 0.0254 mm thick Chromax flat strip, 3.173 mm wide, to investigate the effect of inclination angle on nucleate boiling; the vertical surface gave the highest nucleate boiling heat flux and qCHF, followed by the upwardfacing surface and then by the downward-facing surface. The recent study of Nishikawa et a l l 4 for saturated water has shown nucleate boiling heat flux to increase as the inclination angle varied from horizontal upward facing (180 °) to inclined downward facing (5°); these results were confirmed by Beduz et al. ~5 for liquid nitrogen. Beduz e t al. have shown qCHF to decrease as the inclination angle changed from horizontal upward facing to inclined downward facing. Neither of these two studies has investigated the horizontal downward-facing position. The results of Vishnev et al.l~ for pool boiling of saturated liquid helium and those reported earlier by Githinji and Sabersky 8 showed the effect of surface inclination on nucleate boiling to be opposite to that reported by Nishio and Chandratilleke 4 for liquid helium, Nishikawa et a l J 4 and Beduz et al. ~5 for liquid nitrogen, and most recently by Guo and E1-Genk 5,6 for water. The transient results of Guo and El-Genk 5,° in the nucleate boiling regime agreed qualitatively with those of Nishikawa et al. 14 and Beduz et al. ~5 and with those of Vishnev et al. H and Beduz et al. 15 for qCHF. Before the most recent work of Guo and E1-Genk 5,6, only one data point each for qcHv and qmm for saturated water at atmospheric pressure had been reported by Ishigai et al. 7 Additional data have been reported by Vishnev et al. H, Nishio and Chandratilleke 4 and Beduz e t al. ~s for saturated pool boiling of liquid helium and liquid nitrogen. Because all investigators, except Guo and E1Genk 5,6, have conducted steady-state experiments, no transition boiling data have been available. Guo and E1Genk used the quenching method to generate the transient pool boiling curves for saturated water at near atmospheric pressure (about 0.086 MPa) for inclination angles of 0 °, 5 °, 10 °, 15 °, 30 °, 45 ° and 90 °. In this paper the critical and minimum film boiling heat flux data from the quenching experiments of Guo and E1-GenM ,6 are correlated as functions of the inclination angle. Also, steady-state qCHFdata of Vishnev et al. H and Beduz et al. ~5 for helium and nitrogen, respectively, are correlated as a function of the inclination angle. These correlations are compared with that developed for saturated water 5,6 to determine the effects of the type of boiling liquid and heating method on qctfF at different inclination angles. The following two sections briefly summarize the setup and conduct as well as the results of Guo and E1-Genk experiments. 5,6

Experimental setup and procedures A Pyrex beaker, 25 cm high by 15 cm in diameter and insulated on the outside, was used to contain the saturated water in the experiments. The instrumented test section is shown in F i g u r e 1. Five Chromel-Alumel (Ktype) thermocouples were used to measure the temperatures of the copper disc at several locations. Three thermocouples (1, 2 and 3 in F i g u r e 1) are placed 1 mm from the boiling surface, and two (4 and 5 in F i g u r e 1) are

(All dimensions are in ram)

Figure 1 A schematicof the instrumented test section Figure 1 Section du module expkrimental de trempe

placed 3 mm from the insulated back surface. The orientation of the boiling surface was adjusted to the desired angle with the aid of an aluminium support frame. A high speed data acquisition system, controlled with an 80486 personal computer, was used for temperature monitoring and data collection. The distilled water in the Pyrex beaker was degassed by keeping it boiling for about 15 rain before experimenting. Prior to each test, the heat transfer surface of the copper disc was polished, using No. 1200 silicon carbide sandpaper, then cleaned with acetone. A copper disc of the same diameter was placed on top of an electric heater and the test section was placed on top of it and heated by conduction. This method was chosen to avoid burning the Bakelite skull. The maximum temperature of the test copper disc was limited to 533-539 K to avoid surface oxidation in air before quenching. The hot test section was then lowered into the saturated water pool and all thermocouples, including those measuring the pool and the insulation temperatures, were scanned simultaneously once every 100 ms.

Data reduction

Because of the high thermal conductivity of the copper test section, the cooling rate of the surface was not uniform and hence, the local heat fluxes calculated from the local temperature measurements would be difficult. Such high thermal conductivity increases lateral heat Rev. Int. Froid 1993 Vol 16 No 6

415

Transient boiling from inclined and downward-facing surfaces: M. S. EI-Genk and Z. Guo 30

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Figure 2 Comparison of quenching behaviour at different locations on the boiling surface for 45 ° and 90 ° Comparaison du eomportement ~t la trempe, h diffdrentes localisations, sur la surface d'dbullition pour 45 ° et 90 °

Figure 2

conduction in the test section as the quenching front moves from the lowermost position on the surface upward. As Figure 2 shows, quenching always begins at TC No. 1 location (lowermost), where the average wall superheat is the highest, propagating upward to TC No. 2 then TC No. 3, at a progressively lower wall superheat. To avoid the uncertainty associated with determining the heat flux from the local temperatures, an energy storage method is used to determine the average surface heat flux. In the energy storage method, the average surface heat flux at any instant was calculated from the rate of change of the stored energy in the disc as: d

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where the mean temperature of the copper disc, Tl_5, is taken as the average of the five thermocouple readings in the disc. The uncertainties in the temperature measurements and the inclination angles were about 4-0.15 K and :k 0.5 °, respectively. To remove the high-frequency, low-magnitude oscillations in the recorded temperatures, a numerical filtering of the raw temperature measurements in the test section during quenching was performed before calculating the surface heat fluxes. Numerical filtering was implemented by moving a window containing a certain number of data points (3, 5, 7, 9 points, etc.), through each column of the entire data array. The data point in the middle of the window was replaced by the average of the data points in the window. Typical boiling curves of raw and processed data are presented in Figure 3a-3d. The best results were obtained when the raw data were filtered twice using a three-point window (Figure 3c); the temperature oscillations in transition and film boiling regimes were effectively reduced, with minimal effect on the maximum heat flux. When the raw data were filtered once using a wider, five-point window, the boiling curve (Figure 3d) showed a relatively larger reduction in the maximum heat flux (Figure 3a) and the oscillations in the film boiling and transition boiling regimes were not effectively smoothed out. Therefore, the data presented in the paper have been 416

Int. J. Refrig. 1993 Vol 16 No 6

processed using a three-point window twice. It is worth noting that filtered data did not disguise any real oscillations which could significantly affect the calculated surface heat flux or result in misleading conclusions. During quenching the maximum temperature difference among all five thermocouples in the disc at minimum film boiling was about 2.2 K, but decreased as the inclination angle was decreased to about 0.16 K at 0 °. The largest temperature difference occurred near the maximum heat flux; it was as much as 30 K at 90 ° but decreased to about 8 K at 0 °. It should be noted that this temperature difference near the maximum heat flux (see Figure 4) is not indicative of the difference in the cooling rate, which is more important in calculating the transient average surface heat flux by the energy storage method. To quantify the error of the energy storage method, a one-dimensional transient conduction solution is used to calculate the mean temperature of the disc and the corresponding average surface heat flux. In the transient solution, the arithmetic averages of the measured temperatures near the surface and near the back of the disc were used as boundary conditions. The calculated mean temperatures and maximum average surface heat flux at 90 ° inclination were about 3.6 K and 1.4% higher than those determined by the energy storage method. These results confirmed the soundness of the energy storage method for determining the average surface heat flux in the experiments. The results also show that the estimated test section surface temperature, calculated by linear extrapolation of the measured front and back temperatures in the disc, is less than 1 K higher than that from the transient conduction solution.

Results and discussion

The transient boiling heat transfer data for all seven inclination angles are plotted in Figure 5. As this figure shows, the values of qCHF and qmi, for the downwardfacing surface were about 150% and an order of magnitude lower than those for the nearest inclination of 5 °, respectively. While the critical heat flux increased as the

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angles d'inclinaison

inclination is increased, the nucleate boiling heat flux decreased, which is in agreement with the results o f other

investigators 4,14,15. As indicated earlier, v a p o u r film destabilization and collapse occurred at the lowermost Rev. Int. Froid 1993 Vo116 No 6

417

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position (near TC No. 1) then propagated upwards (towards TC No. 3). The quenching time, defined as the time it took for the fully submerged boiling surface to reach the critical heat flux, qCHF, increased as the inclination angle was decreased. As shown in Figure 6, the quenching time increased from about 60 to 105 s as the inclination angle decreased from 90 ° to 30 °, then increased rapidly as the inclination angle decreased below 30 °. The quenching time was more than doubled, from about 105 to 230 s, as the inclination angle decreased from 30 ° to 5 °. The steepest increase in quenching time (more than 600% from approximately 230 to 1300 s), occurred as the inclination angle decreased from 5° to the downward-facing position. Visual observations at an inclination of 90 ° showed that a wavy, but stable vapour film covered the surface at high wall superheat. Vapour was seen escaping from the upper edge of the disc (see Figure 7). As the wall superheat decreased, approaching the minimum film boiling temperature, the surface of the vapour film became less wavy. Eventually, the vapour film collapsed locally generating large vapour volumes. Similar observations were made with other inclined surfaces; however, as the inclination angle decreased, the duration in film boiling increased and the transition boiling became less violent. For the downward-facing surface, the behaviour of vapour film was quite different from that at the other inclinations. At high wall superheat a thick, wavy but stable vapour film formed on the surface with vapour escaping from the edges of the test section. As the wall temperature dropped, the film became more stable and the frequency at which the vapour escaped from the vapour film decreased. When minimum film boiling was approached, the vapour film became so stable that its surface was like a mirror. At this stage, vapour no longer escaped from the film and the surface temperature decreased slowly with time. After several minutes, the film began to swell and shrink periodically while its surface stayed relatively flat. Eventually, the vapour film collapsed as the wall superheat became too low to sustain a stable film boiling.

418

Int. J . R e f r i g . 1 9 9 3

Vol 16 No 6

Figure 7 An illustration of film boiling for (a) inclined downwardfacing and (b) downward-facing positions Figure 7 Illustration de l'dbullition pelliculaire pour les positions (a) "surface inclinde" et (b) "surface tournke vers le bas"

Critical and minimum film boiling heat flux correlations for saturated water The measured values of qCnF and qmin,plotted in Figure 8, are correlated as a function of the inclination angle using the general form suggested by KutateladzO 6,~v, except here the coefficient Ccnv(0) is a function of the inclination angle:

qCHF(O) = Cc,v( O)~vvhrg[~Yg(p,_p~)]025

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Equation (2), which is within + 12% of the experimental data, indicates that qCHFfor the inclination angles of 90 ° and 0 ° is 72% and 23.4% of that for the upward-facing position (0 = 180°), respectively. An important question concerning the potential application of Equation (2) is whether the maximum heat flux

Transient boiling from inclined and downward-facing surfaces: M. S. EI-Genk and Z Guo 108

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Figure 9 Effect of surface inclination on the heat flux ratio (qmin/qc~F)

for saturated water Figure 8 Effet de l'angle d'inclinaison de la surface sur le qCHFet qm~. transitoires pour l'eau saturde

for water Figure 9 Effet de l'inclinaison de la surface sur le rapport de flux thermiques (qmin/qcHF)pour l'eau

in the experiments really corresponds to the critical heat flux. When Equation (3) was extrapolated to the upwardfacing position the predicted value of CCHF was about 11% higher than the average value of 0.131 recommended by Kutateladze ~6,17for steady-state heating and 2.3% lower than that recommended by Lienhard and Dhir 1s,~9and Lienhard et al. 2° for large surfaces having a diameter or a width larger than three times the most dangerous Taylor wavelength, Xd. In the present experiments, the diameter of the heated disc (50.8 mm) is less than 3Xd for water (kd = 27.8 ram). Therefore, it could be argued that the maximum heat fluxes in the experiments are representative of quasi-steady-state values. However, it has been established that qCHFfrom quenching experiments is lower than that obtained under steady-state heating conditions. In an attempt to clarify this difference, Peyayopanakul and Westwater 21 have conducted a series of quenching experiments in liquid nitrogen at atmospheric pressure, which investigated the limits of the quenching method. In their experiments, boiling occurred on an upwardfacing surface of a horizontal circular copper block, 5.08 cm in diameter and of variable thicknesses (0.05 to 51 cm). They concluded that a minimum time of 1 s to traverse the upper 10% of the boiling curve is needed to establish quasi-steady-state condition. In the present experiments at 90 °, this time is about 0.7 s, but increases to 1.1 s as the inclination angle is decreased to 5 °. Therefore, the maximum heat fluxes for the largest inclinations are expected to be somewhat lower than the quasisteady-state qcHv values, while those for the lower inclinations should be representative of the quasi-steadystate qCnF. The values of qmi, for saturated waterS, 6 are also correlated as functions of the inclination angle using the same general form of Equation (2) as: qmi,(0) = Cm,n(0)X/~ hrg[O'g(pl -- pv)]°25 where

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Equation (4), which is also within + 12% of the experimental data, indicates that increasing the inclination angle from 0 ° to 5 ° increases qminby 330%, but increasing the inclination angle from 5 ° to 90 ° increases qmin by approximately 170% (see Figure 8). The heat flux ratio (qCuF/qmin) is also correlated as a function of inclination angle as: (qmin/qCHF) = 0.014 + 0.155 0 -0.107 - 0.132 0 -o.195

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As this equation and Figure 9 indicate, qmin increases from about 1.4% of qCHF at 0 ° inclination to 5.5% at 90 ° inclination. The values of the wall superheats corresponding to both qCHF and qmin are correlated as functions of the inclination angle (see Figure 10) as: (ATsat)CH

F

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(ATs,t)min = 33.1 + 44.7 00.197

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Also, the ratios of the wall superheats at qminand qCHFare correlated as a function of the surface inclination angle as:

[(ATsat)minl(ATsat)CHF] = 2.55 + 2.03 0 °.061

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Similar to qcHv and qmin, the corresponding values and ratios of the wall superheats increase with the inclination angle (see Figures 10 and 11). The wall superheat ratio increases rapidly with inclination angle from 0 ° to 15°, then it increases very slowly. As Equation (9) indicates, the wall superheat ratio increases from 2.6 at 0 ° to about 5.0 at 15 ° (a 93% increase), but it is only 5.2 at 90 °. This increase in the wall superheat ratio between 0 ° and 15° should be of interest to nuclear reactor safety, concerning the coolability of the bottom head of a PWR reactor vessel, following a core meltdown accident. Rev. Int. Froid 1993 Vol 16 No 6

419

Transient boifing from incfined and downward-facing surfaces: M. S. EI-Genk and Z Guo 160

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Angle, e (deg)

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Critical heat f l u x correlations f o r saturated liquid nitrogen and liquid helium

The qcnF correlation developed herein for liquid nitrogen is based on the data of Beduz et al?L They measured the steady-state qcHv as a function of the inclination angle from 180 ~ (upward facing) to 5 ° (inclined downward facing); no data have been reported for 0 °. Results showed that the type of heater material insignificantly affects qCHF,except in the upward-facing position. In this position, qcnv for the aluminium surface was about 11% higher than that for the copper surface. The q c n z data of Beduz e t al. 15 is correlated using the general form of Equation (2), where the coefficient is given as: 42.0

Int. J. Refrig. 1993 Vet 16 No 6

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Figure 12 Critical heat fluxes data and correlations for water, liquid nitrogen, and liquid helium as functions of inclination angle Figure 12 Donndes sur les flux thermiques critiques et corr~lations pour l'eau, l'azote liquide et l'h~lium liquide en fonction de l'angle.d'inclinaison

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120

(lO)

As shown in Figure 12, the predictions of Equations (2) and (10) are in good agreement with the experimental data, within ± 10%. When these equations are extrapolated to the upward-facing position it gives a value of C = 0.1485. This value is about 13% higher than the average value of 0.131 recommended by Kutateladze 16,~7, but about the same as that recommended by Lienhard et ai.ts 2o for large surfaces. In Beduz et al. ~5experiments the heater width (50 ram) is greater than 3kd (Xd for nitrogen at atmospheric pressure is 11.54 ram). Vishnev et al. H have measured qCHV for saturated liquid helium as a function of inclination angle, from 180 ° (upward facing) to 0 ° (downward facing). Lyon 22 has also reported qCHF values for liquid helium at three inclinations, 180 °, 90 ° and 0 °. Most recently, Nishio and Chandratilleke 4 reported qCHFfor helium at 180 °, 90 ° and 5 ° inclinations. The qcHv values of Lyon z2 and Nishio and Chandratilleke 4 are significantly higher than those reported by Vishnev et al. 11 (see Figure 12). For the horizontal upward-facing position, the qCHF values of Lyon 22 and Nishio and Chandratilleke 4 are about 42% and 80%, respectively, higher than that reported by Vishnev et al. 11 At 0 ° inclination, the qCHF of Lyon 22 is about 15 times higher than that of Vishnev et al.lL Because of these large differences between the qCHF values reported by Lyon 22, Nishio and Chandratilleke 4 and those of Vishnev et al. ~1, the qCHF correlation developed herein for saturated liquid helium is based solely on the data of Vishnev et al. H As shown later, these data are in good agreement with the Kutateladze~6, ~7and Lienhard and Dhir~S,~9 correlations for the upward-facing orientation. The developed correlation has the same general form as Equation (2), where the coefficient Ccuv(O) is given as: CCHF(0 ) = 0 . 0 0 2

+ 0.0051 00.633

(11)

Equations (2) and (11) are within 4- 10% of the experi-

Transient boiling from inclined and downward-facing surfaces: M. S. EI-Genk and Z. Guo 1.2

~

-

-

~ 112 1/4 qCHF = C(0)Pv h~[ga(PFPv)]

Kutateladze (1952. 1 9 6 1 )

lO

qcHv values for liquid nitrogen and helium are correlated

~

z

......................................................

as a function of the inclination angle as:

~.--~"

/i;7

.f/Z.//"

~

?=7 . . . . . . . . . . .~-~...... .....

~---

rqf

qi(0) = Ci(0)4pv hfg[O-g(,ol -- ,Ov)]02s

/ - ' ~ ' ~ " -~ / ~ ' ~ / " /" e/'~ ~./"

C(0l=0.033+0.00966 °'4~

\

"'~ O-

/

//~"

0(8) -- O'034+(ZOO37e°'~e

..-\

o6

G

0.4

• "

/ / [] ~ '

II0.2

/ // /

0

~0

30

g

a

| /

V A

L

[2 60

i et al., 1963, d- 50 ram) _ _ Nitrogen (Beduz et al., 1988, w-50 turn. Cu) Nitrogen (Beduz et al., 1988. w-50 rnm, AI} Helium(Vishnev et al.. 1976. w-10.4 ram) 90

120

150

180

where the coefficient Ci(O) is a function o f the inclination angle and type o f boiling liquid (Equations (3), (5), (10) and (11)). Results showed the ratio (qcuv/qc~vo) for liquid nitrogen to be the highest, followed by that for water and helium. While the difference in the critical heat flux ratios o f these liquids for the upward-facing position is less than 11%, it increases with decreasing inclination, reaching approximately 73% at 0 °. The wall superheats corresp o n d i n g to qCHFand qmin for water, and their ratio, which also decrease with decreasing surface inclination, are correlated as functions o f the inclination angle.

Inclination Angle, e (degree)

Figure 13 Ratios of measured critical heat flux to that of a horizontal

upward-facing flat surface for water, liquid nitrogen and liquid helium as functions of inclination angle Figure 13 Rapports du flux thermique critique mesurk ~ celui d'une surface plate, horizontale et tourn~e vers le haut, pour l'eau, l'azote liquide et l'hdlium liquide en fonction de l'angle d'inclinaision

Acknowledgements

This research was sponsored by the University o f New Mexico's Institute for Space Nuclear Power Studies

References

mental data. F o r the horizontal upward-facing position, E q u a t i o n (11) gives a value o f 0.1385, which is a b o u t 5.7% higher and 7% lower than those given by Kutateladze 16,17and Lienhard and Dhir 2°, respectively. According to the criteria o f Lienhard e t al. 18-2° the heater used by Vishnev e t al. 11 can be classified as a large surface (10.4 m m wide), since Zd for liquid helium at atmospheric pressure is 3.44 ram. This g o o d agreement justifies using the data o f Vishnev et al. to develop the qcHv correlation. In F i g u r e 13, the ratios o f qcuF, given by E q u a t i o n (2) along with Equations (3), (10) and (11), to that given by Kutateladze correlation 16J7 for upward-facing surfaces, qcHvo, are plotted as functions o f the inclination angle. As shown in this figure, the lowest critical heat flux ratios are those for liquid helium, followed by the transient values o f water; the highest qCHF ratio is that for liquid nitrogen. In all cases, this ratio decreases as the inclination angle o f the surface is decreased. F i g u r e s 12 and 13 also show that the qCHF for water at 0 ° inclination 5,6 is only 1 1.5% lower than the steady-state value reported by Ishigai et al. 7. Such a c o m p a r i s o n confirms the conclusion that the qCHF values in G u o and E1-Genk experiments 5,6 are representative o f the quasi-steady-state values.

1

2 3 4 5

6 7

8 9 10

Summary

Quenching experiments investigating transient pool boiling f r o m the underside o f inclined and downward-facing fiat surfaces in saturated water are conducted to determine the effects o f inclination angle on heat transfer in all boiling regimes. Results showed that while transition boiling heat flux and both qCHV and qmin, as well as the corresponding wall superheats, increased as the inclination angle is increased, nucleate boiling heat flux decreased. The data o f transient qminfor saturated water and the transient qC~F data for water and the steady-state

11

12

13 14 15

Jung, D.S., Venart, J.E.S. and Sousa, A.C.M. Effects of enhanced surfaces and surface orientation on nucleate and film boiling heat transfer in R-I 1 Int JHeat Mass Transfer (1987) 30 02) 2627-2639 O'Brien, J.E. and Hawkes, G.L. Thermal analysis of a reactor lower head with core relocation and external boiling heat transfer AIChE Syrup Series (1991) 87 (283) 159-168 Park, H. and Dhir, V.K. Steady-state thermal analysis of external cooling of a PWR vessel lower head AIChE Syrup Series (199i) 87 (283) 1-7 Nishio,S. and Chandratilleke, G.R. Steady-state pool boiling heat transfer to saturated liquid helium at atmospheric pressure J S M E Int J Series I (1989) 32 (4) 639-945 Guo, Z. and EI-Genk, M.S. An experimental study of the effect of surface orientation on boiling heat transfer during quenching A S M E Winter Annual Meeting (1991) Atlanta, GA, Paper No. 91-WA-HT-1 Guo, Z. and EI-Genk, M.S. An experimental study of saturated pool boiling from downward facing and inclined surfaces Int J Heat Mass Transfer (1992) 35 2109-2117 Ishigai, S., Inoue, K., Kiwaki, Z. and Inai, T. Boiling heat

transfer from a flat surface facing downward Int Heat Transfer Conf(1961) Paper No. 26, Aug 29-Sept 1 Githinji,P.M. and Sabersky, R.H. Some effects on the orientation of the heating surface in nucleate boiling Trans A S M E J Heat Transfer (1963) 85 379 Marcus,B.D. and Dropkin, D. The effect of surface configuration on nucleate boiling heat transfer Int J Heat Mass Transfer (1963) 6 863-867 Anderson,R.P. and Bova, L. The role of downfacing burnout in post-accident heat removal Trans Am Nuclear Sac (1971) 14 294-304 Vishnev, I.P., Filatov, I.A., Vinokur, Ya. G., Gorokhov, V.V. and Svalov, G.G. Study of heat transfer in boiling of helium on

surfaces with various orientations Heat Transfer-Soviet Res (1976) 8 (4) 104-108 Seki, N., Fukushako, S. and Torikoshi, K. Experimental study on the effect of orientation of heating circular plate on film boiling heat transfer for fluorocarbon refrigerant R-11 Trans A S M E J Heat Transfer (1978) 100 624-628 Chen,L.T. Heat transfer to pool boiling freon from inclined heating plate Heat Mass Transfer (1978) 5 111-120 (letter) Nishikawa, K., Fujita, Y., Uehida, S. and Ohta, H. Effect of heating surface orientation on nucleate boiling heat transfer A S M E - J S M E Thermal Engng Joint Conf(1983) 1 129 136 Beduz, C., Scurlock, R.G. and Sousa, A.J. Angular dependence

Rev. Int. F r o i d 1 9 9 3 V o 1 1 6 N o 6

421

Transient boiling from inclined and downward-facing surfaces: M. S. EI-Genk and 7_. Guo

16 17 18 19

422

of boiling heat transfer mechanisms in iiquid nitrogen Adv Cryogenic Engng (1988) (Ed R.W. Fast) Plenum Press, New York, 33 363-370 Kutateladze, S.S. Heat Transfer in Condensation and Boiling US AEC Report AEC-tr-3770 (1952) Kutateladze, S.S. Boiling heat transfer Int J Heat Mass' Transfer (1961) 4 31-45 Lienhard, &H. and Dhir, V.K. Hydrodynamic prediction of peak pool-boiling heat fluxes from finite bodies Trans A S M E J Heat Transfer (1973) 95 152-158 Lienhard, J.H. and Dhir, V.K. Extended Hydrodynamic Theory

Int. J. Refrig. 1993 Vo116 No 6

20 21 22

of the Peak and Minimum Pool Boiling Heat Flux NASA R-2270 (1973) Lienhard, J.H., Dhir, V.K. and Riherd, D.M. Peak pool boiling heat-flux measurements on finite horizontal fiat plates Trans A S M E J Heat Transfer (1973) 95 477-482 Peyayopanakul, W. and Westwater, J.W. Evaluation of the unsteady-state quenching method for determining boiling curves Int J Heat Mass Transfer (1978) 21 1437-1445 Lyon, D.N. Boiling heat transfer and peak nucleate boiling fluxes in saturated liquid helium between the ,~ and critical temperatures Int Adv Cryogenic Eng (1964) 19 371-378