role 0% the surface in the measurement of the lei den fr os% tem

role 0% the surface in the measurement of the lei den fr os% tem

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https://ntrs.nasa.gov/search.jsp?R=19700024900 2018-04-09T09:45:24+00:00Z

NAS

TECHNICAL M E M O R A N D U M

NASA TM X- 52866

?

ROLE 0%THE SURFACE IN THE MEASUREMENT OF THE LEIDENFROS% TEM PERAPURE by Kenneth J. Baumeister, Robert E. Henry, and Frederick F. Simon Lewis Research Center Cleveland, Ohio

*

''

TECHNICAL PAPER proposed for presentation at the Special session on Augmentation of Convective Heat and Mass Transfer of the American Society of Mechanical Engineers Winter Annual Meeting New York, New York, November 29 -December 3, 1970

€IDLE OF THE SURFACE IN THE MEASUREMENT OF THE LEIDENFROST TEMPERATURE by Kenneth J. Baumeister, Robert E. Henry, * and Frederick F. Simon National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio

ABSTRACT

2 In

Aluminum, brass, stainless steel, gold plated copper, and pyrex glass surfaces were used to investigate the effect of surface properties on the Leidenfrost temperature. The initial drop radius, heater surface characteristics, and liquid subcooling were related by a conduction model to the hidenfrost point. The model indicated the important parameters effecting the Leidenfrost point. Using this model, most of the variation of Leidenfrost temperature reported in the literature could be delineated. Also, for practical purposes, experimental evidence indicates a possible equivalence between the hidenfrost and the minimum temperature in a pool boiling system. Surface roughness and contamination, particularly for water, a r e sb~wnto have extremely large effects on the Leidenfrost and minimum temperatures. The Leidenfrost point, thus, is not a unique property of the fluid: Consequently, the nature of the surface must be considered when estimating the efficiency of boiling heat transfer in quenching operations or in spray cooled systems.

TLeid

Leidenfrost temperature

TLeid, iso

ideal isothermal value of TUid

TUid, meas measured value of Thid point B’ in Fig. 2

SYMBOLS

associated with

Tmin

surface temperature associated with point B in Fig. 1

Tmin, iso

ideal isothermal value of Tmin

TO

initial plate temperature

TP

surface temperature of plate

Tsat

saturation temperature

t

time

t*

dimensionless time

tevap

time for a liquid drop to completely evaporate

t

characteristic time

V

velocity of drop normal to surface just before impact

C

specific heat of heater plate

ii

time average heat transfer coefficient

k

thermal conductivity of beater surface

We

Weber number (We = pLv 2Ro/u

NT

dimensionless group, 6etoo/kpC

Z

axial direction perpendicular to plate

9

heat flu

Z*

dimensionless z, Kz/k

%

critical heat flu

ff

thermal diffusivity, ( k / C p )

qmin

heat 5u at Tmin

P

@Ck)-l

RO

radiusof drop, see Fig. 3

rl

dimensionless radius, k / k

r

radius

T

plate temperature

0

(T - TL)/(To

TL

liquid temperature

P

plate density

‘IO

’Argonne National Laboratory, Argonne, Illinois

1

dimensionless surface radius, &%/k

- TL)

PL

drop density

U

drop surface tension

7-

dimensionless time, @t/kpCp

The purpose of the present paper is to explain why there a r e large variations in the Leidenfrost measurements and to delineate the important parameters involved in the measurement of the Leidenfrost temperature. Also, the present paper will consider under what conditions the minimum temperature Tmin might be deduced from measurements of TLeid. For if it is desired to measure the minimum temperature of a new fluid, the Leidenfrost technique would be preferred because of its simplicity. There a r e a number of experimental factors that could account for the large variations in the measured values of the Leidenfrost temperature reported in Table I. For example: 1. How does the placement of the drop on the surface affect the Leidenfrost temperature? 2. How does the extremely short but very important temperature reduction beneath drop affect the Leidenfrost temperature? Here, the properties of the supporting plate a s well a s liquid properties and subcooling Wvern the magnitude of the temperature transient. 3. What effect will surface roughness, contamination (fouling) and chemical reactions have on t h e Leidenfrost temperature 7 4. For a given heated surface, how does wettability liquid contact angle - effect the Leidenfrost temperature? This report will deal with item 2 and 3 above. First, an analytical conduction model will be constructed which will indicate the important dimensionless groups which affect the transient plate temperature beneath a liquid drop in a Leidenfrost boiling experiment. From consideration of these dimensionless groups, the cffect of changes in surface properties, liquid subcooling and liquid volume on the Leidenfrost temperature can be seen. Second, experiments will be presented to verify the predicted trends and to ascertain the effects of surface rougimess and contamination on the Leidenfmt and minimum temperature.

INTRODUCTION In recent years, the familiar pool boiling curve shown in Fig. 1, and the droplet evaporation curve(i-ll) shown in Fig. 2, have been the object of intensive study. In particular, the prediction and experimental determination of the minimum temperature T m h , and the Leidenfrost temperature TLeid, have received much attention. A knowledge of these temperatures is important for a basic understanding of boiling, a s well a s for quenching studies, cool down of cryogenic pumps, spray cooling, liquid droplet removal in mist section of boilers, and in the transition from nucleate to film boiling. The latter example is important in nuclear reactor safety considerations. For spray cooling, the heat removal efficiency depends on whether the surface against which the drops impinge has a temperature above or below the Leidenfrost temperature. If the wall temperature is below the Leidenfrost temperature, high heat transfer rates associated with nucleate boiling occur, while if the surface temperature is above the Leidenfrost temperature,. lower heat transfer rates associated with film boiling occur. It will be shown herein that the Leidenfrost point i s not a unique property of the fluid. Consequently, the surface-fluid combination establishes the type of boiling (film or nucleate) which will occur. Thus, the heat transfer coefficient in these systems can be enhanced (or reduced) by an order of magnitude simply by changing the properties of the surface so a s to increase or decrease the Leidenfrost temperature. The Leidenfrost temperature is also important in constant q systems. In a constant q (heat flux) system, a question of stability must be considered if a small vapor patch of film boiling should occur. Will the vapor patch grow and engulf the whole coolant channel or w i l l it collapse and disappear? Semeria and Martinet(") predicted that stability would depend on the value of the minimum temperature squared. Simon et al(l3? 14) pointed out that any e r r o r in the prediction of the minimum temperature will be greatly magnified in the squaring process. Thus, all the parameters which affect the minimum o r the Leidenfrost temperature should be clearly delineated. At the present time, however. there seems to be considerable uncertainty in the literature a s to what is the Leidenfmt temperature or minimum temperature for a given fluid. Table I displays a variety of Leidenfrost and minimum point data for a given fluid. Water, for example, gives evidence of wide scatter in the reported data. Bell(l) states that at the present time there i s no unique value of the Leidenfrost temperature for a given fluid, and that there i s insufficient information available to predict the Leidenfrost temperature. He further states, "One must either guess from the most similar experimental cases available, or better still yet, test one's own case experimentally. 'I

SURFACE TEMPERATURE CRlTERIA Physical Situation Consider a surface whose temperature i s above the Leidenfrost temperature TLeid. When a drop approaches and touches(2o) this surface, a vapor layer will begin to form under the drop. The exact mechanism by which the heat is transferred to the drop to generate the vapor layer i s unknown; however, a comprehensive discussion of the possible heat transfer mechanisms i s given by Harvey. (20) Thus, upon impact of the drop, the surface temperature begins to decrease, because of the heat transferred to the drop. If the surface temperature falls sufficiently, transition o r nucleate boiling will occur and the drop will seemingly explode. On the other hand, if the initial plate temperature i s greater than T h i d , and if the fall in surface temperature i s not too severe, thc rapor generated beneath the drop will coalesce and form an insulating film. Iierc, the liquid no longer touches (wets) the surfacc, esccpt possibly for small liquid spikcs which can penetrate the vapor Layer. (21) The drop will now evaporate slowly in thc Leidenfrost boiling state where the vapor film supports the drop.

2

In m e a w i n g the Leidenfrost temperature, the experimenter sets a plate a t an initial temperature To, ejects a liquid drop on to the surface, and measures the time it takes for the liquid drop to evaporate. Next he plots his vaporization time data against To a s shown in Fig. 2 and determines the Leidenfrost temperature, T u i d , meas from this curve. In this type of experiment, however, the experimenter generally does not measure the transient temperature directly beneath the drop at the plate surface, he only measures the initial temperature of the surface. But, a s previously discussed, the initial surface temperature will fall when the liquid comes in contact with it. Thus, the 9rue11 value of the Leidenfrost temperature is the real wall temperature that exists under the drop in the short period after the drop makes contact with the surface. In all cases the surface temperature will decrease; consequently, the actual Leidenfmst temperature will always be less than the initial plate temperature associated with point B in Fig. 2. The Leidenfrat temperature, therefore, measured on a surface which does not experience any temperature drop, TLeid, isO (an isothermal surface) will be somewhat less than the measured Leidenfrost temperature on a real surface which experiences a temperature drop, assuming that both surfaces have the same surfaces finish and wetting characteristics. Thus,

Since the drop is symmetric a b u t the origin, the governing energy equation in the =lid material becomes

with the conditions t=O

t . 0 - k - aT az

T=To

2 2 0

(3)

z=O ra0 (4)

t > O - limit

T = To

z-00

(5)

Introducing the following dimensionless variables

TLeid, is0 < TLeid, meas

e=-

T

- TL - TL -hr

To

since the surface temperature is measured before the liquid is placed on the surface. The parameters which affect a decrease in surface temperature beneath the drop can mw be found by consideration of the transient conduction equation in the heated plate. It must be emphasized that the following considerations apply only to the very short time in which the initial transient has occurred, perhaps 100 msec. The end of this short initial transient is designated by time, t. For times greater than t m , the drop enters a steady state of nucleate, transition, or film boiling. The transient time t m is negligible compared to the evaporation time scale shown in Fig. 2. However, the thermodynamics which occurs during this short transient controls which of the boiling regimes in Fig. 2 the drop will enter.

q=-

k

into Eq. (2) gives Conduction Model Consider a hot semi-infinite solid at initial temperature To, a s shown in Fig. 3. A drop of liquid is now placed gently on the surface. If liquid is injected onto the surface with a sufficient vebcity, mechanical breakup will occur and the present analysis will not apply. This will be discussed later. For simplicity, during the initial but very short transient period, the unlmown time dependent heat transfer coefficient is represented by a time averaged heat transfer coefficient designated 'li. For this simple model, liquid properties and liquid subcooling w-ill affect the surface temperature through the parameter h. At present, a s Harvey(2o) points out, we just dD not understand what is happening during this extremely short complex transient process to be any more specific. W C will, however, consider general effects that would result from a decrease o r increase in E.

where

and t, is a short characteristic time which is of sufficient length s0 either 8tead.v state nucleate or Leidenfrost boiling could be established. The initial conditions and boundary conditions become t*=o

3

z*20

0=1

(13)

the nonisothermal region where the qo curves fan out. However, in the isothermal region the radius of the drop will have little effect, since a drop of infinite radius does not effectively lower the surface temperature. Conduction Criteria Consequently, after the liquid touches the surface, the surface temperature of the plate Tp will be equal to the initial surface temperature To when N, approaches zero, that is, limit Tp = To N7-0 The dimensionless number N, tells us under what conditions the measured value of the Leidenfrost temperature TLeid,meas will be equal to the Leidenfmt temperature on an isothermal surface TLeid, iso. By inspection of Eq. ( l l j , if NT is large, the time dependent temperature gradient will be large and the temperature beneath the drop falls; the surface is nonisothermal. On the other hand, for small NT the change in surface temperature will be very small; the surface is nearly isothermal. We can better comprehend the above ideas and get a better physical feeling for the effect of the dimensionless parameter N, by considering the solution of Eq. (11)for the case of an infinite drop ('lo = m). In this special case, Eq. (11)becomes

Under the condition of small N,, the surface temperature will remain isothermal during the experiment. Therefore, when condition (19) holds, the measured value of the Leidenfrost temperature TLeid meas, will be equal to the isothermal value of the hidenfrost temperature T u i d , iso under the conditions of the particular experiment. That is, limit TLeid, meas - TLeid, iso N,+O

A s will be discussed later, Tuid, iso may not be solely a property of the fluid under consideration. Rather TLeid, iso is a complicated function of other system parameters, for example surface roughness and surface contamination. In correlating the experimental data to be presented later, it is convenient to write N, a s the product ?t and P where

where we have chosen the new dimensionless time T to be of the form The parameter p contains the important surface material properties, while Qt, implicitly contains the effects of liquid properties, subcooling and some surface roUghne66 effects. These effects will be superimposed on the thermal property effects contained in 0. Then a s an approximation to Eq. (19), assume

The solution to Eq. (16)with the conditions (14)and (15) is given in Ref. (22) (p. 71) and i s shown in Fig. 4, a s the curve marked q,. The temperature drop is smaller for finite qo because of radial conduction effects. Assuming the ratio of t/t, is order 1,

limit Tp = To

0-0

t = O(1) t,

For finite value of the product e t , , Eqs. (19)and (22) have the same limiting value. Equation (20)can also be written in the form

that is, sufficient time has occurred for the drop to enter the nucleate or film boiling state, then the abscissa in Fig. 4 is equivalent to N,. As was previously stated, for small N, drop in surface temperature will be quite small, and we label (arbitrarily) this region when N, c 0.01 the '(isothermalfvregion. For N, > 0 . 1 the surface will be v(nonisothermal.v ( The region between these two regions is arbitrarily labeled the Tntermediatervregion in Fig. 4. Any change in the system, therefore, whickdecreases N,, such a s increased k, p , C , or decreased h will make the surface more nearly isothermal. Furthermore, an increase in rjo will increase the temperature drop maklng the surface nonisothermal. However, this only occurs in

limit TLeid, meas = TLeid, iso P O

The key property group kpC has been observed to be an important parameters in drop impingement studies for large Weber number(23) and for Tmin in flow film boiling. (24) Measurement of Tmin In a pool boiling system, consider a hypothetical surface which remains at a fixed temperature even when liquid comes in contact with it. In principle, there should be

4

some minimum temperature T such that if the surface temwrature is below T m nu%?ate or transition h i l i n g will occur On the other hand, if the surface temperature is greater than T m the vapor generated at the surface will coalesce and film boiling will occur. At first glance, no criteria should be required for the steady state constant temperature pool boiling measurement of Tmh, since by definition the surface is held at constant temperature. In reality, however, fluxations in the so-called steady state heat transfer coefficients will cause a time dependent surface temperature variation. For example, in nucleate boiling, sites are alternately active and quiet. (25) In film boiling, vapor domes alternately shift positions a s the liquid-vapor interface adjusts to the unstable body force. (26* 27) . Finally, in transition boiling, extremely large variations in the heat transfer coefficient occur along the surface, due to alternate wetting and dewetting. To reduce the effebt of the temperature fluctuations in the pool boiling experiment, the criteria given by Eqs. (19) and (22) is applicable. The equivalent form of Eqs. (20) and (23)becomes

br room temperature. Therefore, the liquid drop from the syringe was sometimes placed in a metal ladle heated to about 550' C. The drop immediately went into the Leidenfrat state, consequently the liquid temperature was always very near saturation value. The ladle was immediately (within 1 sec) placed on the bot test surface and rotated. The drop skidded off a feather edge to the test surface. It fell about 0.02 cm, thereby minimizing the possibility of it entering a metastable state. For a 0.02 cm fall from the ladle to the surface, the Weber number (We = pLv2Ro/o) is of the order of 0.1. For large Weber numbers, the drops bounce and break up. Wachters(28) and Harvey(20) have experimentally investigated dynamic effects of falling drops impacting on heated surfaces for Weber numbers much greater than 1. A conventional stop watch accurate to a tenth of a second was used to measure the Vaporization time of the liquid drops on the hot surface. DISCUSSEON OF RESULTS Vaporization Time Curves The vaporization time curves for ethanol and water drops a r e shown in Figs. 5 to 7 for various surface materials, liquid temperatures, and drop volumes a s indicated in the figures. The Leidenfrost point occurs where the curves break sharply downward, corresponding to point B' in Fig. 2. For the pyrex glass surface, shown in Fig. 5, &me of the nucleate boiling and natural convection range is seen. As seen in these figures, the Leidenfrost temperatures for the different surfaces are significantly different, a s also seen in the tabulation of table 11. The additional data in table I1 will be discussed shortly.

and limit Tmin = Tmh, iso P-0

EXPERIMENTAL EQUIPMENT AND PROCEDURE Stainless steel, brass, aluminum, gold plated copper, and pyrex glass heating surfaces approximately 12 cm in diameter and 1.5 cm thick were fabricated and instrumented for use in this study. The metal surfaces were polished to a glass-like finish. After a fine lathe cut, the surfaces were sanded with silicon paper (320, 400, 500, 600) in the order given. Then, the surfaces were hand and wheel buffed with Tripoli 3 X abrasive powder and then (Simichrome) polished. Finally the surface was cleaned with a dry cloth. A roughness indicator gave a 3 to 4 r m s pin. measurement of the surface. The pyrex glass had the same r m s range. An 1100-W hot plate was used to slowly bring each of the surfaces up to an equilibrium temperature. From two to four Chromel-Alumel thermocouples (24 gauge) positioned about 1/32 in. beneath the surface were used to measure the surface temperature. The vaporization times of liquid drops placed on these surfaces were measured and vaporization time curves such a s shown in Fig. 2 were pbtted. The liquid was placed on the heated surface by the use of hypodermic syringes, a small calibrated glass beaker and a small metal ladle. A 0.032 milliliter (ml) distilled water drop and a 0.0125 ml ethanol drop were obtained with a calibrated syringe. A small marked glass beaker, which was used to scoop up boiling water, was calibrated to give a 6 ml drop. It was estimated that the standard deviation for the large drop was 0.5 ml. In using the syringe, however, control of the bulk liquid temperature becomes difficult for runs other than

Surface Fouling or Contamination Before investigating the effects of the surface properties, let's consider the effect of contamination of the surface by the liquids. For water, in Fig. 5, a large scattering of the data is seen in the plate temperature range from 150' to 2 7 9 C. In this range the drop bounces and vibrates on the surface. Godleski and Bell(3) discuss in detail the bouncing and swirling of drops which, we believe, accounts for much of the data scatter. But why do small drops vibrate in this temperature range? Hoffman(2s) suggests that the formation of an oxide layer or perhaps partial wetting of the plate could account for the vibration. A most interesting phenomean occurred when the very first drop was placed on a freshly polished aluminum surface at a plate temperature of 167' C , a s shown in Fig. 5. The drop remained in quiescent film boiling at this temperature. No bouncing or swirling of the drop was seen. This point was always easily reproduced on a freshly polished surface. A freshly polished aluminum (3 to 4 rms pin.) was heated to 167' C and held at this temperature for GO minutes, see Fig. 8. Then a water drop was placed on the surface. It went into quiescent film boiling and reproduced the original first drop data point shown in Fig. 5. Thus, the additional amount of surface oxidation that occurred duringthe GO minute heating did not affect the results.

5

. '

.

.

As additional b p s ~f liquid W B E ~placed on the warface, however, the vawrization tim? of the drops began to decrease and sputtering and vibration began to occur, see Fig. 8 . The surface was apparently being contaminated. A large 6 ml drop was then vaporized on the surface to accelerate the contamination. After the 6 ml drop vaporized, the vaporization times of the small drop was one order of magnitude shorter than on the clean fresh surface. Figure 9 shows the Leidenfmst temperature of water on freshly polished surfaces to be approximately 1520 C, which is nearly 75' C lower than on the conventional contaminated surface (upper curve in fig. 9 will be discussed later). It should be pointed out, that the contaminated surface looks clean and highly polished to the naked eye. When large 6 ml liquid drops were placed on a freshly polished surface no significant decrease was found from that in Fig. 6 (see table II). Apparently, the surface becomes contaminated upon liquid solid contact. For the small drops, however, the drop can move to an uncontaminated portion of the surface after the initial contact. This is not possible with large 6 ml drop. muble distilled water, a s well a s every possible precaution was used to keep the system clean, in this particyJar case. A t present, the contamination is believed by the authors to be brought on by the reaction of water with the fresh aluminum surface, o r by deposits due to possible hardness in the water, or by deposits fmm dissolved salts. To prevent surface reaction, a relatively inert gold plated copper surface was then used to measure the vaporization times of large double distilled water drops. The first drop was placed on the surface at a plate temperature of 189' C. The large drop went into conventional Leidenfrost film boiling. This point is shown in Fig. 9. The nature of surface changed after the drop evaporated. It would appear that very minute impurities were deposited on the surface. Perhaps, the water more easily wets a contaminated surface and prevent stable film boiling from occurring at the same temperature. The vaporization time curves for ethaml are shown in Fig. 7 for various surface materials and liquid temperatures a s indicated in the figure. The results were not strongly dependent on the surface contamination. Whether the surface w a s freshly polished o r contaminated with water and ethanol drops, the vaporization times were nearly identical. In Fig. 7, the d symbols indicates data taken on a freshly polished surface. As seen in Fig. 7, a small drop and a large 6 ml liquid drop have the same Leidenfrost temperature. From this the authors concluded that the Leidenfrost temperature for small or large drops a r e identical for an isothermal surface provided such factors a s surface fouling Q not enter the problem. The new value of the Leidenfrost temperature of 1520 C in Fig. 9 agrees quite well with the value of 155 reported in table I by Blaszkowska and Zakrzewka. The value In table I was found by merely observing the drops by eye. The authors, no doubt, assumed the drop to be in film boiling when a drop vibrated and bounced on the surface. This crude technique of judging may account for the low value of 142 degrees reported by Bovtingny. (18)

Effectof 0 Variations The surface with the smallest value of p should give the best approximation for an isothermal surface and consequently the lowest value of the Leidenfrost temperature. Plotting the Leidenfrost points from Figs. 5 to 7 in Figs. 10 and 11, we see the expected decrease in the measured values of the Leidenfrost temperature for decreasing 0. A s seen in Fig. 10, the measured values of the Leidenfrost temperatures are nearly the same for the aluminum and brass surface. Consequently, we could assume that both surfaces are for all practical purposes isothermal. From Fig. 10, for 0 less than &lo-3 (hr F2/btu2), the surface can be assumed to be isothermal. Figure 12 gives further proof of this assumption. The temperature history of stainless steel and aluminum surfaces are illustrated for various initial surface and bulk fluid temperatures after a 6 ml water drop reaches the surface. A s seen in the figure, a large temperature drop occurs in the stainless steel surface while little or no temperature drop occurs in the aluminum surface. The drop in temperature on the stainless steel surface most likely accounts for the shift upward of the stainless steel data to the Qtted line shown in Fig. 6. Notice in Fig. 12, that the actual plate temperature which stainless steel begins to nucleate boil is 250' C. This i s quite near the measured value for the aluminum and brass surface. We believe that the relatively high value of p for stainless steel accounts for the higher values of Leidenfrost temperatures reported from measurements on stainless steel in table I a s well a s in the present data in table II. Effect of qo Variations Notice in Fig. 4, that the effect of the initial liquid radius 'lo has a very small effect on the temperature drop in the isothermal region. Since aluminum and brass fall into this region we might expect very little radius effect on the Leidenfrost point. This is confirmed in Figs. 10 and 11. A s shown in those figures, the measured values of the Leidenftemperature were nearly independent of the initial drop volume. The water data is based on the conventional contaminated surface, while the ethanol data is independent of surface contamination. On the other hand, stainless steel is not an isothermal surface a s shown by the temperature plot in Fig. 12. Consequently, stainless steel falls into the intermediate region designated in Fig. 4 . In this region, the conatant qo lines begin to fan out. A s a result, we can expect the Leidenfrost temperatures to be sensitive to the initial drop radius. Gottfried, Lee, and Bell(4) observed an effect of initial radius on the Leidenfrost temperature. In Ref. (4), for example, on a stainless steel surface, the Leidenfrost temperature for a 0.0154 ml water drop is approximately 25 degrees lower than for a 0.032 ml drop. Both drops were at room temperature. In the present study, a s shown in Fig. 10, the larger drop (6 ml) has a Leidenfmst temperature approximately 20' C higher than the smaller drop. This is a relatively small change, and in fact data in Ref. (5) for water on a stainless steel surface did not show this result. This radius effect, however, should 11c even more pronounced on a surface with high 0.

6

Subcooling Effects

,

T,in under certain conditions. In fact, for large saturated drops with similar surface conditions, the two may be identical.

During the initial experimentation, subcooled and saturated water drops were tested on both the aluminum and brass plates. In general, saturated and subcooled drops had the same Leidenfrost temperature. Consequently, most of the data taken to determine the Leidenfmst point on aluminum and brass were for subcooled conditions, a s this was the easiest to do experimentally. Some early experimental results of BorishanskyW confirm that the Leidenfrost temperature is independent of subcooling. According to Bradfield, (30) however, subcooling has a large affect on Tmin for a pool. The difference between pool and Leidenfrost boiling probably results from the fact that small subcooled liquid drops quickly heat to the saturation temperature. For the highly nonisothermal glass surface, however, a large subcooling effect was seen. The increase in ii for subcooling shifted the value of N7 further into the nonisothermal region. Here, for a fixed qo, a much larger temperature drop would occur. A s verified in Fig. 7, the Leidenfrost temperature for subcooled ethanol on glass is 100' C higher than the value for saturated ethanol. Room temperature water could not be made to Leidenfrost boil on glass, even after heating the upper surface of the glass with a propane torch.

CONCLUSIONS A s seen in the present set of experimental data, surface contamination, k, p , C, drop volume, liquid subcooling, and surface roughness can account for the variations in the Leidenfrost and minimum temperatures reported in the literature.

REFERENCES 1. Bell, K. J., "The Leidenfrost Phenomenon: A Survey,

Chemical Engineering Progress Symposium Series, V O ~ .63, NO. 79, 1967, pp. 73-82. 2. Wachters, L. H. J., Bonne, H . , and van Nouhuis, H. J., "The Heat Transfer from a Hot Horizontal Plate to Sessile Water Drops in the Spheroidal State, Chemical Engineering Science, Vol. 21, Oct. 1966, pp. 923-936. 3. Godliski, E. S. and Bell, K. J . , "The Leidenfrost Phenomenon for Binary Liquid Solutions, Proceedings of the Third International Heat Transfer Conference, Vol. 4, AIChE, New York, 1966, pp. 51-58. 4. Gottfried, B. S., Lee, C. J. , and Bell, K. J. , "The Leidenfbst Phenomenon: Film Boiling of Liquid Droplets on a Flat Plate, International Journal of Heat and Mass Transfer, Vol. 9, Nov. 1966, pp. 11671187. 5. Patel, B. M. and Bell, K. J . , *'The Leidenfrost Phenomenon for Extended Liquid Masses, Chemical Engineering Progress Symposium Series, Vol. 62, NO. 64, 1966, . pp. . 62-71. 6. Borishansky, V. M., "Heat Transfer to a Liquid Freely Flowing Over a Surface Heater to a Temperature Above the Boiling h i n t , Problems of Heat Transfer During a Change of State: A Collection of Articles, AEC-tr-3405, 1953, U. S. Atomic Energy Commission, Washington, D. C. 7. Baumeister, K. J . , Hendricks, R. C . , and Hamill, T. D. , **MetastableLeidenfrost States, I t TN D3226, 1966, NASA, Cleveland, Ohio. 8. Baumeister, K. J., Hamill, T. D . , and Scboesmw, G. J . , "A Generalized Correlation of Vaporization Times of Drops in Film Boiling on a Flat Plate, Proceedings of the Third International Heat Transfer Conference, Vol. 4, AIChE, New York, 1966, pp. 66-73. 9. Schoesmw, G. J . , Jones, D. R . , andBaumeister, K. J . , "Leidenfrost Film Boiling of Drops on a Moving Surface, I t Chemical Engineering Pmgress Symposium Series, Vol. 64, No. 82, 1968, pp. 95101. 10. Tamura, 2. and Tanasawa, Y., "Evaporation and Combustion of a Drop in Contact with a Iiot Surfacc, ' I Seventh Symposium (International) on Combustion, Butterworths, London, 1959, pp. 509-522. 11. Cumo, M . , Farello, G. E:., and Ferrari, G . , "Notes on Droplet Heat Transfer, I f Chemical Engineering Progress Symposium Series, Vol. 65, No. 92, 1969, pi?, 175-187. '

Minimum Temperature B e r e n ~ o n ( ~working l) with a pool boiling apparatus measured the temperature at the minimum point for pentance on inconel, nickel, and copper surfaces under steady state constant temperature boiling conditions. The minimum temperature for his various materials has been replotted a s a function of p in Fig. 13. The minimum temperature decreases a s p decreases, in the similar manner a s in the Leidenfmst experiments. Surface Rouphness and the Minimum Temperature Hosler and Westwater(lg) measured a steady state minimum temperature for water of 258' C on an aluminum surface (see table I) which was polished with " 0 gauge" emery paper. This value was slightly higher than the measured Leidenfrost temperature for a 6 ml water drop on aluminum ( T b i d , meas = 235O c). In the present study, bowever, the surface was highly polished. Therefore, the highly polished surface was roughened with 0 gauge emery paper in order to compare the measured value of T b i d , meas to the experimental value of Tmin by Hosler and Westwater. The experimental results for the roughened surface are shown in Fig. 14. As seen in this figure, the measured value of the Leidenfrost temperature is 265O C, which is, for all practical purposes, the same value a s measured by Hosler and Westwater. A recent paper by Cumo, Farello, and F e r r a r d l l ) shows the same trend for increased surface roughness. A course sandblasted surface has a Leidenfrost temperature 70' C greater than a smooth lapped surface. Because of the agreement with the present experimental results shown in Fig. 14 with those of Hosler and Westwater, we suspect an equivalence between T h i d and

c

12. &meria, R. and Martinet, B., $Talefaction spots on a

13.

14.

15.

16.

17.

18.

19.

Smulders, L. Vermeulen, J. R., and Kleiweg, H. C. , "The Heat Transfer from a Hot Wall to Impinging Mist Droplets in the Spheroidal State,!' Chemical Engineering Science, Vol. 21, Dec. 1966, pp. 1231-1238. Kalinin, E. K., Koshkin, V. K., Yarklo, S. A . , Berlin, I. J., Kostyuk, V. V., and Kochelaev, Yu. S., "Heat Transfer in Tubes with Rod Regime in the Case of Film Boiling of a Subcooled Liquid, I t Proceedings of the International Symposium on Research in Cocurrent Gas-Liquid Flow, University of Waterloo, Sept. 18-19, 1968. Hsu, Y.-Y. and Graham, R. W., rfAnAnalytical and Experimental Study of the Thermal Boundary Layer and Fbullition Cycle in Nucleate Boiling, I t TN D594, 1961, NASA, Cleveland, Ohio. Ruckenstein, E . , '!Film Boiling on a Horizontal Surface, ? * International Journal of Heat and Mass Transfer, Vol. 10, July 1967, pp. 911-919. Hamill, T. D. andBaumeister, K. J . , "FilmBoiling Heat Transfer from a Horizontal Surface a s an Optimal Boundary Value Process, m c e e d i n g s of the Third International Heat Transfer Conference, Vol. 4, AIChE. 1966, pp. 59-65. Wachters, L. H: J. andwesterling, N. A. J . , "The Heat Transfer from a Hot Wall to Impinging Water Drops i n the Spheroidal State, I sChemical Engineering Science, Vol. 21, Nov. 1966, pp. 1047-1056. Hoffman, T . W.,tlDiscussion of Leidenfrost Renomenon for Binary Liquid Solutions, Proceeding of the Third International Heat Transfer Conference, Vol. 6. AIChE. 1967, pp. 267-270. Bradfield, W. S:, "On the Effect of Subcooling on Wall Superheat in Pool Boiling, Journal of Heat Transfer, Vol. 89, NO. 3, Aug. 1967, pp. 269-270. Berenmn, P. J . , '!Transition Boiling Heat Transfer from a Horizontal Surface, I t Tech. Rep. 17, Mar. 1 , 1960, Massachusetts Institute of Technology, Cambridge, Mass.

23. Wachters, L. H. J.

Heated Wall, Temperature Distribution and Resorption, presented at the lnstitute of Mechanical Engineers Symposium on Boiling Heat Transfer in Steam Generating Units and Heat Exchangers, Manchester, England, Sept. 15-16, 1965. Simon, F. F . , Papell, S. S., and Simoneau, R. J., tfMinimum Film-Boiling Heat Flux in Vertical Flow of Liquid Nitrogen, TN D-4307, 1968, NASA, Cleveland, Ohio. Simon, F. F. andsimoneau, R. J., trTransitionfrom Film to Nucleate Boiling in Vertical Forced Flow, Paper 69-HT-26, ASME, New York, N. Y. Kutateladze, S. S. andBorishanskii, V. M.,A Concise Encyclopedia of Heat Transfer, Pergamon Press, New York, 1966. Drew, T. B. and Mueller, A . C. , ftBoiling,'f American Institute of Chemical Engineers Transactions, Vol. 33, 1937, pp. 449-471. Blaszkowska-Zakrzewska, H. , "Rate of Evaporation of Liquids from a Heated Metallic Surface, Bulletin International de 1'Academie Pblonaise, No. 4a-5aV April-May 1930, pp. 188-190. Blaszkowska, Z . , flMaximum Velocity of Evaporation of Liquids Evaporated on Heated Metallic Surfaces, ' I RocznikiChemii, Vol. 10, 1930, pp. 691-713. Boutigny, P. H. , Annales de Chimie et de Physique, Series 3, Vol. 9 , 1843, pp. 350-370; Vol. 11, 1844, pp. 16-39; Vol. 27, 1849, pp. 54-64; and Vol. 28, 1850, pp. 158-163 (as cited in reference 16). Hosler, E. R . and Westwater, J. W . , "Film Boiling on a Horizontal Plate," ARS Journal, Vol. 32, No. 4, Apr. 1962, pp. 553-558.

24.

25.

26.

27.

28.

29.

30.

20. Harvey, D. M., "The Impact and Rebound of a Small 31.

Water Drop Striking a Hot Surface, !* Ph. D. Thesis, 1967, McMaater University, Hamilton, Ont., Canada. 21. Bradfield, W. S . , IfLiquid-Solid Contact in Stable Film Boiling, ' 1 Industrial + Engineering Chemistry Fundamentals, Vol. 5, No. 2, May1966, pp. 200-204. 22. Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, 1959.

Y

E-5828

TABLE I.

- COMPARISON O F LEIDENFROST AND MINLMUM TEMPERATURES MEASURED (Degrees Centigrade)

Liquid Boiling point

Godleski Gottfried, Lee, Tamura Kutateladze Tanasawa(lO) Borishanski(15) Bell(3) and Bell(4) 1SSI I ?I ssl =I Water 100.0 78.4 Ethanol Benzene 80.0

320 175 180

[ S S ] - Stainless steel - Aluminum-Bronze alloy [Ag] - Silver [All - Aluminum [ ? ] - Not given [ A-B]

280 178 185

1

1

302 185 195

250 170 175

Tmin

TLeid, meas (large drop)

TLeid, meas (small drops) Blaszkow ska Boutigny(l8) Zakrzewka(17) [ Ag] 1A-Bl 157 112 117

142

-----

1 I

.

258

---

---

TABLE II.

r

- LEIDENFROST

TEMPERATURES MEASURED IN PRESENT PAPER (Degrees Centigrade)

Plate material

I

Water

0.032 ml drop

TL

1000

c

6 ml drop

I

C 100' C TL TL

26'

Pyrex glass (3-4 r m s )

515

NO0

---

Stainless steel (3-4 rms)

305

305

325

Brass (3-4 r m s )

230

235

Aluminum (3-4 rms)

230

235

---

265

155

>ZOO

t Aluminum 0 gauge (25 rms) Aluminum (fresh polish) (3-4 r m s ) B r a s s (fresh polish) (3-4 rms) Gold fresh polish (very smooth)

I

Ethanol 0.0125 ml drol

E- 5828 *

--e-+ c -

3%2%* TRANS ITION r

NAT URA L CONVEC TlON AND COND UCTlON REGIME 7

NUCLEATE BO1LING REGIME 7

- --

,

-2 3--c

a

BOILING FILM BOILING REGIME 7

I

CCI

-I -- -,-

"

LEIDENFROST FILM BOILING

---

A

-

-----

I I e

Tmin SURFACE TEMPERATURE, LOG(T) Figure 1.

- Conventional pool boiling curve.

INITIAL SURFACE TEMPERATURE, To Figure 2. - Evaporation time curve of liquid drops in contact with hot surface for drops of equal volume and equal initial temperature.

r

Figure 3.

"ISOTHERMAL" REGION

- Hot plate conduction model.

"INTERMEDIATE" REGION

h Y

-

..

"NONISOTHERMAL" REGION A

1.0

.8 00

L E W

.6-

.4.2

-

0

Figure 4.

- Effect of

N, on surface temperature.

E-5828

LEIDENFROST POINT ALU2 0 0 0 r M l N U M AND BRASS 1000

800 600 -

I

LEIDENFROST 400 POINT ALU-FIRST DROP MlNUM AND ON PLAT57 BRASS LEIDENFROST

'

LEIDENFROST POINT STAIN-

n

Y Ln

z 0

200

z!i100 e

0

a

a >

401,

20 10

100

I

150

'

200

ALUMINUM A STAINLESS STEEL OPEN SYMBOLS DENOTE TL = 26' C SOLID SYMBOLS D E N Y T:= 10O:C 0

80

A

I

IAI

,

250 300 350 400 PLATE TEMPERATURE, OC

450

500

Figure 6. - Total vaporization time of 6 m l water drops on polished aluminum, brass, and steel surfaces.

, 550

PREHEAT AT 167OC

n 600-ALUMINUM LEIDENFROST 4w-POINT

,?0.032 m l DROPS (26OC)

1

200 -

0

W

m

100 F

w"

E

80:

t!

s

_.

I-

6040:

ui

5

i=

z

0

20-

2

20 $

107

86-

4-

-

2-

4

0

17

.8

50

I 100

150

200

250

300

350

400

450

500

550

40

80

160 120 TIME, MIN

200

240

Figure 8. - Effect of increased surface contamination on vaporization time of a water drop on a n alum i n u m surface at 167".

600

200 -

4

0 ALUMINUM 0 BRASS A STAINLESS STEEL 0 GLASS

OPEN SYMBOLS DENOTE TL = 26' C SOLID SYMBOLS DENOTE TL = 100' C

LEIDENFROST POINT CONTAM(FIG. 5)

3,

4 300

100 7 80 60 40-

=-

E

0.032 m I

20 -

=

200

6 ml 0.032 ml 4

10 7

8 r

L).

64-

0

-

2-

101

BRASS (CONTAMINATED) ALUMINUM (CONTAMINATED) 0 ALUMINUM (FRESH POLISH) GOLD ON COPPER (FRESH POLISH OPEN SYMBOL= T - '62 C SOLID SYMBOL [email protected] C 0

102

1

1 120

160

200 240 280 320 PLATE TEMPERATURE, OC

360

400

Figure 9. - Lowering of Leidenfrost temperature by measurement of vaporization time on freshly polished aluminum and inert gold surfaces.

Figure 10. - Effect of surface material a n d i n i t i a l drop volume o n t h e Leidenfrost temperature of water.

ALUMINUM STAINLESS STEEL 0 GIASS OPEN SYMBOLS DENOTE TL = 26' C SOLID SYMBOLS DENOTE TL = 78.5' C 0

A

500r

/

400 0.0125 m I 7

0

STAINLESS STEEL (TBULK IN FIM BOILING

=

rSTAlNLESS STEEL (TBULK

=

r

26' C)

00 350 w-

eL

3 II-

100-

'L 0.0125

2 w a 5 +

mI

300 250

w

"LALUMINUM (TBULK IN FILM BOILING

a

150 10-1

=

100°C)

1

looo -

Figure 11. - Effect of surface material on the Leidenfrost temperature of ethanol.

100' C)

NUCLEATE BOILING

, /

4 '

I

I

I

I

40 60 80 100 120 140 TIMEAFTER LIQUID REACHES SURFACE, SEC 20

Figure 12. - TemQerature 1/32 inch beneath surface after 6 ml drop of water reaches t h e heating surface.

t 600

0

0

-I

1: E

v, Y W'

I-

400r 200k

/'

4

40-.

I-

150

20 .4

0

I

3

I 6

I 9

.8

1.2

1.6

I I 12 15

I I I I 18 21 24 27

2o:

/rSMOOTH SURFACE i 3 T O 4 RMS)

SMOOTH SURFACE 0 GAUGE SURFACE OPEN SYMBOLS DENOTE T L = 26OC SOLID SYMBOLS DENOTE TL = 100' C 0

0

I

I

I

I ,

30

Figure 13. - Minimum temperature as a function of p for n-pentane (Data - Berenson, ref. 31).

Figure 14. - Effect of surface roughness on t h e Leidenfrost temperature of 6 m l water drops o n a n a l u m i n u m surface.

1