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Nucleate boiling and critical heat flux of HFE-7100 in horizontal narrow spaces
Experimental Thermal and Fluid Science 35 (2011) 772–779
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Nucleate boiling and critical heat flux of HFE-7100 in horizontal narrow spaces M. Misale *, G. Guglielmini, A. Priarone DIPTEM – Sezione di Termoenergetica e Condizionamento Ambientale, Università degli Studi di Genova, Via all’Opera Pia 15a, 16145 Genova, Italy
a r t i c l e
i n f o
Article history: Available online 23 June 2010 Keywords: Nucleate pool boiling Dielectric fluid Confinement Peripheral conditions Critical heat flux
a b s t r a c t The pool boiling heat transfer and critical heat flux CHF of saturated HFE-7100 at atmospheric pressure on a confined smooth copper surface were experimentally studied. The horizontal upward boiling surface was confined by a face-to-face parallel unheated surface. We analysed the effects obtained by changing the diameter of the unheated surface and the gap between the boiling surface and the adiabatic surface. The gap values investigated were s = 0.5, 1.0, 2.0, 3.5 mm. To confine the circular boiling surface (d = 30 mm), two different Plexiglas discs were used: one with a diameter D = 30 mm, equal to that of the copper boiling surface, and the other with a diameter D = 60 mm, equal to that of the overall test section support. For each configuration, boiling curves were obtained up to the thermal crisis. For both configurations, it was observed that, at low wall superheat, the effect of confinement was not significant if Bo > 1, while for Bo 6 1 the heat transfer coefficient increased as the channel width s decreased. By contrast, at high wall superheat, a drastic reduction in both heat transfer and CHF was seen when the channel width s decreased; this reduction was less pronounced when the smaller confinement disc (D = 30 mm) was used. CHF data were also compared with the values predicted by literature correlations. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction As pool boiling is a very efficient means of thermal control in several applications, nucleate pool boiling heat transfer and critical heat flux CHF have aroused increasing attention, especially with regard to confined geometries. Moreover, the use of dielectric fluids in nucleate pool boiling is often applied in thermal systems, as it allows heat to be removed while keeping surface superheat relatively low. The use of dielectric fluids offers several further advantages: (a) low saturation temperatures at atmospheric pressure; (b) good thermal contact with all components, even in narrow spaces; (c) excellent chemical compatibility with many materials; (d) low toxicity and good environmental characteristics. Confined pool boiling has become a research subject of great importance, as it is frequently encountered in many practical situations, such as high-performance compact heat exchangers and the cooling of electronic components. The effects of confinement on pool boiling depend on the complex interaction among geometry, channel width, heat flux and fluid properties. This paper reports an experimental study on the confined pool boiling of HFE-7100, a hydrofluoroether dielectric fluid (C4F9OCH3). The effects of confinement conditions (channel width s and unheated confinement disc diameter D) on a horizontal upward-facing boiling surface were systematically investigated. * Corresponding author. Tel.: +39 010 3532576; fax: +39 010 311870. E-mail address: [email protected] (M. Misale). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.06.009
A criterion for analysing the confinement gap effect has been proposed in the literature, and is based on the Bond number Bo, which is defined as the ratio between the channel width s and the capillary length L; the capillary length L is often assumed to be proportional to the departure diameter of isolated bubbles, as it relates capillary and gravitational forces; it is calculated by:
L¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r gðql qm Þ
The capillary length for HFE-7100 (3MTM NovecTM Engineered Fluids [1]) at atmospheric saturation pressure is about 0.88 mm, which corresponds to Bo numbers ranging between Bo = 0.57 (s = 0.5 mm) and Bo = 4.0 mm (s = 3.5 mm). 2. Previous research The first studies on the effects of confinement date back to the end of the 1960s. Ishibashi and Nishikawa [2] studied the nucleate boiling of water and ethyl alcohol in vertical annuli at pressures from 1 atm (channel width 1–20 mm) to 10 atm (channel width 0.6–2 mm). In saturated boiling heat transfer in a narrow space, they found, in addition to the isolated bubble region, a coalesced bubble region with markedly different characteristics; they proposed a new type of correlating equation for the coalesced bubble region. Later, Katto et al. [3] studied the boiling of saturated water at atmospheric pressure on a horizontal upward-facing circular
M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
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Nomenclature Bo CHF d D D0 g h hlv L q00 Ra
Bond number = s/L [–] critical heat flux [W m2] boiling surface diameter [m] confinement disc diameter [m] boiling surface support diameter [m] acceleration of gravity [m s2] heat transfer coefficient [W m2 K1] latent heat of vaporisation [J kg1] capillary length [m] specific heat flux [W m2] average roughness [m]
copper surface (d = 11 mm) confined by a parallel glass surface (d/ D = 1) with channel widths down to 0.1 mm. They observed significant effects of confinement both at low heat flux (increased heat transfer performance on decreasing the channel width) and at CHF (reduced CHF values on decreasing the channel width). Yao and Chang [4] analysed the boiling of R-113, acetone and water at atmospheric pressure in vertical narrow annuli with closed bottoms (heights of 25.4 and 76.2 mm and channel widths of 0.32–2.58 mm). They proposed the Bond number as a criterion for characterising the squeezing effect on a bubble due to confinement. In addition to the Bond number, these authors considered the effect of the aspect ratio of the channel, and defined a modified boiling number as the ratio between the residence time of the bubble in the confined space and the vapour formation time; they proposed a boiling map with the Bond number and the boiling number as coordinates, on which they distinguished three boiling regimes: isolated deformed bubbles, slightly deformed bubbles and coalesced deformed bubbles. Bonjour and Lallemand [5] studied the combined effect of confinement (s = 0.3–2.5 mm) and pressure (1–3 bar) on the critical heat flux of R-113 in vertical channels. They noted a reduction in CHF on decreasing the channel gap at all pressures investigated. Subsequently, Bonjour and Lallemand [6] analysed flow patterns during the boiling of R-113 in narrow vertical spaces, and observed three different boiling regimes: nucleate boiling with isolated bubbles, nucleate boiling with coalesced bubbles, and partial dry-out; they also developed a flow pattern map for confined boiling, based on the Bond number and on a reduced heat flux. A study by Misale and Bergles [7] dealt with boiling heat transfer on three vertical in-line heaters placed in narrow channels and cooled by FC-72 or Galden HT-55; when the channel width was small, the heat transfer performance improved at low heat fluxes (q00 6 3.5 W cm2). More recently, Misale et al. [8] analysed the confined pool boiling of saturated FC-72 from square-pin finned surfaces; they found a critical channel width value below which heat transfer diminished. Geisler and Bar-Cohen [9] experimentally studied saturated boiling in vertical, rectangular parallel-plate channels immersed in FC-72 at atmospheric pressure, with spacing down to 0.3 mm. They found that enhancement of nucleate boiling at low heat flux appeared to be largely dependent on the Bond number. Passos et al. [10,11] analysed the confined (s = 0.2–13 mm) saturated boiling of FC-72 and FC-87 on a downward-facing copper disc (d = 12 mm); at low heat flux (q00 6 4 W cm2), the heat transfer coefficient was enhanced on decreasing the channel gap. Guglielmini et al. [12] performed experiments to analyse the combined effects of surface orientation (h = 0°, 45°; 90°; 135°) and confinement (channel widths s = 1–20 mm) on the nucleate pool boiling and critical heat flux of saturated HFE-7100 on a
s Tsat Tw
e k h
ql qv r DTsat
channel width [m] saturation temperature [K] surface temperature [K] mean absolute error [-] fraction of data predicted to within ±30% [-] orientation angle [deg] liquid density [kg m3] vapour density [kg m3] surface tension [N m1] wall superheat = Tw Tsat [K]
smooth copper surface. At low wall superheats, for channel widths greater than 2 mm (Bo > 1), the effect of confinement was negligible for all surface orientations, while for a channel width of 1 mm (Bo 1) and angles of 0° and 45°, heat transfer was clearly enhanced. At high wall superheats, boiling curves matched for channel widths greater than 5 mm, while for confinements of 3.5, 2 and 1 mm, the heat flux, heat transfer coefficient and CHF decreased as the channel width decreased. This effect was more evident for orientation angles of 0° (upward-facing surface) and 45°, whereas it was less pronounced at 90° and was almost negligible at 135°. Concerning the CHF, the effects of confinement became appreciable for s 6 3.5 mm; the CHF decreased as the channel width decreased, and the magnitude of this reduction depended on the orientation of the heated surface. Cardoso et al. [13] experimentally studied the saturated nucleate boiling of n-pentane on an upward-facing heated surface, for different degrees of confinement (s = 0.2–13 mm). The authors analysed only partial boiling curves, not up to the thermal crisis, and observed an effect of confinement only for s = 0.2 mm; they also found that the heat transfer coefficient increased when the confinement gap decreased. The effect of confinement was also analysed by Su et al. [14], who varied the gap size s and heated disc diameter (d = 100; 300 mm) of a downward-facing surface during boiling in water at atmospheric pressure under subcooled conditions. They found that the heat transfer was lower for the larger diameter of the heated plate because, in that case, the bubbles escaped less easily to the liquid pool and less intensively churned the fluid under the heated plate. The authors also suggested introducing into the analysis a new geometrical dimensionless parameter to take into account the effect of the boiling surface diameter on heat transfer: d/L, i.e. the ratio between the diameter d of the heated surface and the capillary length L. Recently, Hetsroni et al. [15] experimentally studied the boiling of water and surfactant solutions in a confined space between two vertical plates; the gap size was varied in the range of s = 1–80 mm (Bo = 0.4–47). They found that, when the gap size was the same, the addition of surfactant enhanced heat transfer in comparison with that of water boiling, and that an increase in the Bond number led to an increase in the dimensionless frequency of the temperature fluctuations of the heated wall, that are typical of the regime of high heat flux. Stutz et al. [16] experimentally analysed the nucleate and transition boiling of saturated n-pentane in narrow horizontal spaces between a heated upward-facing copper disc and an unheated surface (d/D = 1). They concluded that confinement influenced both heat transfer and CHF and that the Bond number was a good parameter to represent this behaviour. Finally, Stutz et al. [17] proposed an axisymmetric two-phase flow model to describe the growth of a single bubble squeezed
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between a horizontal upward-facing heated disc and an insulating surface placed parallel to the heated surface. No studies have dealt with the effect of the dimensions of the unheated confinement surface. In the present study, which used a horizontal upward-facing surface, the ratio between boiling surface diameter d and confinement disc diameter D significantly influenced heat transfer and CHF. 3. Experiments 3.1. Experimental set-up The apparatus (Fig. 1a) consisted of a vessel, which contained the instrumented test section immersed in the fluid. The test vessel was cubic (internal side 210 mm) and made of stainless steel (AISI
a Pressure transducer
Water condenser
304). A coil condenser, refrigerated by tap water, was positioned inside the container in the vapour zone. Five optical windows on the lateral and top sides allowed visualization of the boiling surface. The experimental apparatus was equipped with a pressure transducer, venting valve, safety valve, vacuum pump and five shielded K-type thermocouples: four thermocouples measured liquid temperature and one measured vapour temperature. One liquid thermocouple was plugged into a PID controller, which modulated electrical power to the auxiliary heaters, which were placed laterally on the external surface of the vessel. These heaters preheated the fluid and maintained it at the desired saturation temperature. In all tests HFE-7100 dielectric fluid (saturation temperature at atmospheric pressure Tsat = 61 °C) [1] was used.
Safety valve
Venting valve
Auxiliary heater
Thermocouples
Optical window to Vacuum pump
Test section
Micrometer positioning system
b
Confinement disc (black D=30 mm; gray D=60 mm)
Epoxy resin
D d
s
Thermocouples Insulator
Bakelite
Copper block
D'
Heater Stainless steel disk Insulator Support Fig. 1. (a) Test vessel for pool boiling experiments and (b) test section scheme.
M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
3.2. Test section
4. Results and discussion
The test section (Fig. 1b) consisted of a cylindrical copper (99.99%) block heated at the bottom by an electric heater. The top, flat end of the copper block constituted the boiling surface (d = 30 mm), the area of which was 7.07 cm2. The copper test section was instrumented with nine shielded thermocouples (K-type, O.D = 0.5 mm), placed in holes at different levels: 3, 21 and 39 mm below the boiling surface. At each level, the holes were positioned at 120° to each one another and the three levels were rotated so that only one thermocouple was located in each vertical direction, in order to reduce non-uniformity of temperature distribution in the copper block. The copper block was housed in a Bakelite support (D = 60 mm); the space between the copper and the Bakelite was filled with insulating material and the upper seal was made of epoxy resin (STYCAST 2651 MM). The boiling surface was roughened by sandblasting with particles of controlled dimension, and presented an average roughness Ra = 0.6 lm with an associated standard deviation of 0.02 lm. Assuming one-dimensional axial heat conduction through the copper block, the heat flux q00 and the surface temperature Tw were calculated by means of Fourier’s law, the thermal conductivity of the copper (394 W m1 K1, from supplier’s data) and the temperature gradient through the block being known. The heat transfer coefficient was defined as h ¼ q00 =DT sat . To confine the boiling surface, two different Plexiglas discs were used (diameter D = 30 and 60 mm; thickness 2.5 mm). The periphery of the space between the two surfaces was open to allow the fluid to wet the boiling surface. In all these experimental tests, the boiling surface was horizontal and faced upward. Standard techniques were followed in order to determine uncertainty [18] in the experimental measurements. The system used to collect and store the signals from the thermocouples is accurate to ±0.1 K on absolute temperature values and to ±0.02 K on differential values. Uncertainty in the determination of heat flux is dependent on operating conditions. In the single-phase natural convection zone and at the onset of nucleate boiling, the maximum error in the heat flux value is ±15%. In the fully developed nucleate boiling region, the maximum error is less than ±5%. Close to the thermal crisis, uncertainty increases to ±8%. The error associated with surface temperature in the fully developed boiling region is less than ±0.2 K. Finally, the positional error of the confinement surface is about ±0.05 mm.
4.1. Pool boiling curves and heat transfer
3.3. Test procedure To degas the fluid, the following procedure was followed: before each experimental campaign, a partial vacuum (less than 0.01 Pa) was created inside the vessel and then the bulk liquid was introduced into the vessel. The auxiliary heaters were then switched on in order to raise the internal pressure value above (+10%) of the external atmospheric pressure and to vent out noncondensable gases. This operation was repeated until a satisfactory correspondence was achieved between the pressure inside the vessel and the liquid saturation temperature. For dielectric fluids, at the onset of nucleate boiling, temperature overshoot or hysteresis phenomena may appear. To avoid these situations, the following procedure was adopted, which enabled all nucleation centres to be activated: after half an hour of vigorous boiling at about 2 W cm2 (for s = 1 mm and s = 0.5 mm, at q00 = 0.8 W cm2), the experiments were immediately started at the lowest heat flux value; all tests were then conducted under increasing heat flux conditions. For each heat flux value imposed, once steady-state conditions were reached after about 15–20 min, all measurement parameters were acquired and recorded.
775
The effects of channel width s and confinement disc diameter D were experimentally investigated for the saturated pool boiling of HFE-7100. The channel width s was the distance between the circular boiling surface (d = 30 mm) and the Plexiglas disc above it. The study analysed different configurations by varying the channel width (s = 0.5, 1, 2, 3.5 mm) and the diameter of the confinement disc (D = 60 mm, as large as the overall Bakelite support; D = 30 mm, large enough to cover only the copper boiling surface). In a previous study [12], in which a confinement disc D = 60 mm was used, no significant effects of confinement were observed for channel widths s > 3.5 mm (Bo > 4.0). Fig. 2 reports the experimental results obtained with the confinement disc of D = 30 mm: Fig. 2a shows the boiling curves and Fig. 2b the heat transfer coefficients, both as functions of DTsat. Fig. 3 reports the experimental results obtained with the disc of D = 60 mm: Fig. 3a shows the boiling curves and Fig. 3b the heat transfer coefficients. In the low wall superheat boiling region (DTsat <9 K) and for the confinement disc of D = 60 mm, heat transfer was higher at channel widths s = 1 mm (Bo 1) and s = 0.5 mm (Bo < 1) than for the unconfined surface; for the disc of D = 30 mm, the channel width seemed to have less significant effects on boiling curves, except at s = 0.5 mm. At higher wall superheats (DTsat > 9 K), a drastic reduction in both heat transfer and CHF appeared for confined boiling at channel width s 6 3.5 mm; the reduction was less pronounced when the smaller confinement disc was used. For channel spacing s = 0.5 mm (Bo = 0.57), at very low wall superheats the heat transfer for confined surfaces was higher than that of the unconfined surface, while at high superheats the heat transfer was significantly lower for both types of confinement, in particular for D = 60 mm. The great instability of the boiling process with this configuration (s = 0.5 mm), especially for D = 60 mm, causes poor repeatability of boiling curves; indeed, vapour accumulates in the gap and suddenly leaves the test section laterally in one direction or another, allowing fresh liquid to wet the boiling surface. These experimental data are in agreement with literature results [19]. The experimental results seem to partially confirm the observations made by Katto et al. [3], who found that the mechanism of nucleate boiling seems to change when the Bond number decreases to the order of magnitude of 1 or less. Indeed, between the heated surface and the base of the deformed bubble, a thin liquid film, called microlayer, evaporates. For Bo < 1 and for low wall superheats, the bubbles coalesce, increasing the area of the liquid film; this liquid microlayer, which is attached to the surface by intermolecular attractive forces [20], is pressed against the heated wall and does not evaporate completely. Consequently, the heat transfer coefficient increases. The effect of the Bond number was more evident in the D = 60 mm configuration, in which the confinement disc constituted a real obstacle to the departing bubbles. Indeed, as supposed by Cardoso et al. [13], the mechanism of escape of coalescent bubbles and surface rewetting ‘is dependent on the conditions imposed by the geometric characteristics of the heated surface and its support. Thus, the ratio between the diameters of the support and the test section can influence the residence time of the bubble in the channel’. The effects of confinement are presented in Fig. 4, where the ratio between the heat transfer coefficient in the case of the confined boiling surface and of the unconfined one (h/hunconf) is plotted versus the Bond number for different wall superheats DTsat; the data
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a
a
Unconfined
Unconfined
10
2
q" [W/cm ]
q" [W/cm2]
10
1
1
D=60 mm
D=30 mm s=3.5 mm =2 mm =1 mm =0.5 mm
s s=3.5 mm s =2 mm s =1 mm s =0.5 mm
10
10
ΔTsat [K]
b
ΔTsat [K]
b
Unconfined
4
10
Unconfined
4
2
h [W/m K]
h [W/m2K]
10
3
10
3
10 D=30 mm s=3.5 mm =2 mm =1 mm =0.5 mm
10
ΔTsat [K] Fig. 2. (a) Boiling curves and (b) heat transfer coefficient curves for D = 30 mm and different gaps.
for D = 30 mm and for D = 60 mm are shown in Fig. 4a and b, respectively. At very low wall superheats (DTsat < 9 K), heat transfer was enhanced when the gap size s was very small (s = 0.5; 1 mm; Bo 6 1); this effect was more pronounced when the larger confinement disc (D = 60 mm) was used. On increasing the wall superheat (DTsat P 9 K), heat transfer coefficients decreased as the Bond number decreased to Bo < 4 (s 6 3.5 mm). At high wall superheats, both the heat transfer coefficient and the CHF were higher, for the same channel width, when the smaller confinement disc was used; this was because the vapour bubbles could leave the boiling surface more easily. By contrast, when the larger disc was used, the departing vapour bubbles accumu-
D=60 mm s s=3.5 mm s =2 mm s =1 mm s =0.5 mm
10
ΔTsat [K] Fig. 3. (a) Boiling curves and (b) heat transfer coefficient curves for D = 60 mm and different gaps.
lated and coalesced near the boiling surface, which hindered heat transfer. Su et al. [14] noticed that, for the elongated bubbles that are typical of confined boiling, there were two characteristic length scales: bubble width (direction parallel to the heated surface) and bubble height (normal to the heated surface). The width of the bubble is more important than the height as it directly affects the area of the heated surface covered by vapour. This dimension is strongly influenced by the diameter of the boiling surface, and can expand to the same size as the boiling surface if the nucleation site is at the centre of the surface. Conversely, the height of the bubble is limited by the gap size.
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2.0
Δ Tsat = 8 K =9K = 10 K = 12 K = 15 K = 18 K = 20 K
h/hunconf
1.5
20
CHF [W/cm 2]
a
1.0
0.5
15
10
5 0.0 0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
D=30 mm
Bo
b
0
2.0
1
1.5
1.5
2.0
2.5
2.5
3
3.5
4
Fig. 5. Critical heat flux CHF vs channel width s for different confinement disc diameter D.
0.5
1.0
2
s [mm]
=9K = 10 K = 12 K = 15 K = 18 K = 20 K
1.0
0.0 0.5
0.5
Δ Tsat = 8 K
1.5
h/hunconf
D=60 mm
0
3.0
3.5
4.0
Bo Fig. 4. Effect of confinement on heat transfer coefficients: (a) D = 30 mm and (b) D = 60 mm.
4.2. Critical heat flux Boiling conditions close to the thermal crisis were also analysed. To avoid compromising the integrity of the test section, heat flux was increased by regular steps until a noticeable and rapid rise in surface temperature was measured. This condition was identified as the maximum heat flux and should be very close to the thermal crisis: this heat flux was defined as the critical heat flux CHF. For channel widths s greater than about 3.5 mm and for the larger confinement disc diameter, the effect of confinement was negligible in comparison with the unconfined boiling condition [12]. For channel widths of 3.5, 2, 1 and 0.5 mm, the presence of the confinement disc clearly impaired heat transfer performance at high wall superheats, and the CHF value decreased markedly as the channel width s decreased, in comparison with the unconfined configuration. Fig. 5 shows the values of critical heat flux CHF vs channel width s for the two different confinement disc diameters (D = 30, 60 mm); CHF decreased as channel width s decreased, for both diameters D, whereas CHF was always higher for the smaller confinement disc. Bonjour and Lallemand [6] concluded that the reduced CHF was caused by the earlier dry-out of the microlayer, since the initial thickness of the microlayer was smaller when the channel width was smaller. Geisler and Bar-Cohen [21] recently studied confined boiling between two vertical, rectangular parallel plates. They suggested that a key parameter in the CHF of confined boiling surfaces was
the channel aspect ratio (channel principal dimension/spacing, in this study D/s), which determines the propensity of vapour to accumulate in the channel and induces premature dry-out near the channel exit. With regard to the CHF of pool boiling, various theoretical and semi-empirical correlations can be found in the literature. Zuber [22] derived a classical CHF analytical expression:
CHF ¼
p n 24
0:25 q0:5 m hlm ½g rðql qm Þ
o
ð1Þ
This correlation is useful for saturated pool boiling on large, thick, upward-facing horizontal plates and represents a baseline correlation for pool boiling CHF. On the basis of Zuber’s correlation, many other correlations have been developed; these have introduced correction factors to take into account various effects, such as length scale, geometry, wall thermophysical properties, wall thickness and subcooling [23–25]. Arik and Bar-Cohen [26] introduced an expanded formulation of Zuber’s correlation, which included parametric factors which took into account the effects of heater characteristics and bulk liquid subcooling. Their correlation considered the increase in CHF observed for small heaters. Few authors, however, have obtained correlations which consider the effect of channel width s on CHF for confined surfaces. Katto and Kosho [27] studied pool boiling critical heat flux in horizontal upward-facing confined geometries using water, R113, ethyl alcohol and benzene. They used a confinement surface area equal to that of the boiling surface (d/D = 1) and proposed the following correlation:
n o 0:25 CHF ¼ q0:5 m hlm ½g rðql qm Þ
0:18 0:14 h i 2 0:5 qm g ðql rqm Þd ds 1 þ 0:00918 q
ð2Þ
l
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðql qv Þ=r > 6. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi For the present test section configuration, d/L = d gðql qv Þ=r is equal to 34. On the basis of Zuber’s expression, Misale et al. [28] proposed an empirical correlation for the CHF of horizontal upward-facing confined surfaces:
This correlation was proposed for d/L = d
n o 0:25 CHF ¼ 0:185 wðsÞ q0:5 m hlm ½g rðql qm Þ
ð3Þ
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M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
where
wðsÞ ¼
e¼ 1 1 þ 71:43 e1:32s
ð4Þ
and s is expressed in mm. In their experimental study, Misale et al. used a ratio between boiling surface diameter and confinement disc diameter d/D equal to 0.5. Fig. 6 compares the present experimental CHF data both with the predicted values yielded by the Misale et al. correlation [28] and with those yielded by Katto and Kosho’s correlation [27], for both confinement disc diameters: D = 30; 60 mm (d/D = 1; 0.5). The Misale et al. correlation predicted data for the confinement configuration with the larger disc (D = 60 mm and d/D = 0.5) quite well, but not data for D = 30 mm; Katto and Kosho’s correlation yielded a rough prediction of the experimental data for both values of confinement disc diameter. With regard to the experimental data presented in this study, the predictive methods were evaluated according to two criteria, i.e., the fraction of data predicted to within ±30%, k% and the mean absolute error, e%:
24
ð5Þ
In the correlation by Misale et al., e% and k% proved to be equal to 41 and 30, respectively; in Katto and Kosho’s correlation, e% and k% were equal to 43 and 30, respectively: for both correlations the comparison was unsatisfactory. In fact, the CHF for a confined horizontal boiling surface depends both on the channel gap s and on the ratio between the boiling surface diameter and the confinement disc diameter d/D; the size of the support of the boiling surface is also important [13], especially in the case of a downward-facing horizontal boiling surface, in which the presence of a large surface around the boiling surface hinders the escape of vapour and reduces the heat transfer performance. Table 1 shows the geometrical conditions of the experiments in the literature database on horizontal confined pool boiling; the geometry of the boiling surface, including the dimensions and configuration of the test section support, the confinement geometry and the channel width s are reported. To propose a new correlation that satisfactorily represents all the effects of geometry on critical heat flux CHF, new experimental tests will be required for different d/D and also for different d/D0 ratios.
D=60 mm, Misale et al. 2009 D=30 mm, Misale et al. 2009
21
5. Conclusions
D=60 mm, Katto and Kosho 1979 D=30 mm, Katto and Kosho 1979
Nucleate pool boiling of the dielectric fluid HFE-7100 on a smooth copper surface (d = 30 mm) at atmospheric pressure was experimentally studied; the boiling surface was horizontal, oriented upwards and confined by means an adiabatic disc. The study analysed the effects of confinement conditions (channel width s and diameter D of the unheated disc) on heat transfer coefficients and on critical heat flux CHF. The following conclusions can be drawn:
18
CHFpred [W/cm2]
N 1 X predict:v alue exper:v alue% N i¼1 exper:v alue
15 12 9 6
5.1. Heat transfer coefficient 3 0 0
3
6
9
12
15
18
21
24
CHFexp [W/cm2 ] Fig. 6. Predicted critical heat flux CHF vs experimental CHF data.
– in the low wall superheat boiling region (DTsat < 9 K), confinement influenced heat transfer only at s = 0.5, 1 mm (Bo 61); – at high wall superheats (DTsat > 9 K), a drastic reduction in heat transfer occurred for all confinement gaps analysed (s 6 3.5 mm), but the reduction was less pronounced when the smaller confinement disc (D = 30 mm) was used;
Table 1 Geometrical conditions of experiments in the literature database on horizontal confined pool boiling. Authors
Boiling surface geometry
Confinement geometry
Channel width s
Katto et al. [3]
Horizontal upward-facing circular d = 11 mm Support: D0 d Horizontal downward-facing circular d = 12 mm PVC support: D0 = 20 mm Horizontal upward-facing circular d = 12 mm Teflon support: D0 50 mm Horizontal downward-facing circular d = 100; 300 mm Support: D0 1.5d Horizontal upward-facing circular d = 30 mm Flush mounted with the vessel bottom: D0 = 160 mm Horizontal upward-facing circular d = 10; 20 mm Support: D0 d
Parallel circular surface D = 11 mm
Down to 0.1 mm
Bottom of the boiling chamber
s = 0.2–13 mm
Parallel circular surface D = 12 mm
s = 0.2–13 mm
Bottom of the boiling chamber: 900 750 mm
s = 10; 15; 20 mm for d = 100 mm; s = 0.9–77 mm for d = 300 mm
Parallel circular surface D = 30 mm
s = 200 lm–90 mm
d/D = 1
d/s 0–120
Passos et al. [10,11]
Cardoso et al. [13]
Su et al. [14]
Stutz et al. [16]
Katto and Kosho [27]
M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
– the influence of the Bo number was more pronounced when the larger confinement disc D = 60 mm (d/D = 0.5) was used, especially at low heat fluxes; – for the same confinement gap s, the heat transfer coefficient and critical heat flux were higher, at high wall superheat, when the diameter D of the confinement disc was smaller. 5.2. Critical heat flux (CHF) – in both confinement conditions, CHF decreased as the channel width s decreased; – at all channel widths s, CHF values were higher for the confinement disc of smaller diameter D; – CHF data were compared with the values predicted by the Katto and Kosho [27] and Misale et al. [28] correlations; for both correlations, the comparison was unsatisfactory; – new tests will be required in order to collect more data and to define a relationship that includes the effect of the ratio d/D on CHF. Acknowledgment This paper was supported by Grant MIUR COFIN 2008NHP97B. References [1] 3M™ Novec™ Engineered Fluids, 3M Center, St. Paul, Minnesota. [2] E. Ishibashi, K. Nishikawa, Saturated boiling heat transfer in narrow spaces, Int. J. Heat Mass Transf. 12 (1969) 863–894. [3] Y. Katto, S. Yokoya, K. Teraoka, Nucleate transition boiling in a narrow space between two horizontal parallel disk-surfaces, Bull. JSME 20 (143) (1977) 638– 643. [4] S.C. Yao, Y. Chang, Pool boiling heat transfer in a confined space, Int. J. Heat Mass Transf. 26 (6) (1983) 841–848. [5] J. Bonjour, M. Lallemand, Effects of confinement and pressure on critical heat flux during natural convective boiling in vertical channels, Int. Commun. Heat Mass Transf. 24 (2) (1997) 191–200. [6] J. Bonjour, M. Lallemand, Flow patterns during boiling in a narrow space between two vertical surfaces, Int. J. Multiphas. Flow 24 (1998) 947–960. [7] M. Misale, A.E. Bergles, The influence of channel width on natural convection and boiling heat transfer from simulated microelectronic components, Exp. Therm. Fluid Sci 14 (1997) 187–193. [8] M. Misale, G. Guglielmini, M. Frogheri, Pool boiling heat transfer from square pin finned surfaces confined by unheated wall in saturated FC-72, in: Proc. of 4th Int. Conference on Multiphase Flow, paper 509, New Orleans, Louisiana, USA, 2001. [9] K.J.L. Geisler, A. Bar-Cohen, Nucleate pool boiling heat transfer in narrow vertical channels, in: Proc. of 5th Int. Conference on Boiling Heat Transfer Session XII, Montego Bay, Jamaica, University of Florida, 2003.
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[10] J.C. Passos, F.R. Hirata, L.F.B. Possamai, M. Balsamo, M. Misale, Confined boiling of FC-72 and FC-87 on a downward facing heating copper disk, Int. J. Heat Fluid Flow 25 (2004) 313–319. [11] J.C. Passos, L.F.B. Possamai, F.R. Hirata, Confined and unconfined FC-72 and FC87 boiling on a downward-facing disc, Appl. Therm. Eng. 25 (2005) 2543– 2554. [12] G. Guglielmini, M. Misale, A. Priarone, Combined orientation and confinement effects on saturated pool boiling of a dielectric liquid, in: Proc. of 13th Int. Heat Transfer Conference, Sydney, Australia, 2006. [13] E.M. Cardoso, J.C. Passos, B. Stutz, M. Lallemand, Confined boiling of n-pentane in a horizontal space, in: Proc. of EBECEM 2008, Florianópolis, 28–29 April, 2008. [14] G.H. Su, Y.W. Wu, K. Sugiyama, Subcooled pool boiling of water on a downward-facing stainless steel disk in a gap, Int. J. Multiphas. Flow 34 (2008) 1058–1066. [15] G. Hetsroni, A. Mosyak, R. Rozenblit, E. Pogrebnyak, Z. Segal, Natural convection boiling of water and surfactant solutions having negligible environmental impact in vertical confined space, Int. J. Multiphas. Flow 35 (2009) 20–33. [16] B. Stutz, M. Lallemand, F. Raimbault, J. Passos, Nucleate and transition boiling in narrow horizontal spaces, Heat Mass Transf. 45 (2009) 929–935. Special Issue. [17] B. Stutz, R. Goulet, J. Passos, Bubble growth in narrow horizontal space, in: Proceedings of ECI Int. Conf. on Boiling Heat Transfer, Florianopolis-SC-Brazil, 3–7 May; 2009. [18] R.J. Moffat, Using uncertainty analysis in the planning of an experiment, J. Fluid. Eng. (1985) 107–173. [19] K.J.L. Geisler, A. Bar-Cohen, Numerical and experimental investigations of boiling enhancement in buoyancy driven microchannels, in: Proc. of 11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 28–31 May; 2008. [20] J. Straub, The role of surface tension for two-phase heat and mass transfer in the absence of gravity, Exp. Therm. Fluid Sci. 9 (1994) 253–273. [21] K.J.L. Geisler, A. Bar-Cohen, Confinement effect on nucleate boiling and critical heat flux in buoyancy-driven microchannels, Int. J. Heat Mass Transf. 52 (2009) 2427–2436. [22] N. Zuber, Hydrodynamic aspects of boiling heat transfer, AEC report No. AECU4439, Physics and Mathematics, 1959. [23] A. Bar-Cohen, A. McNeil, Parametric effects on pool boiling critical heat flux in highly wetting liquids, in: Proc. of Engineering Foundation Conference on Pool and External Flow Boiling, CA; 1992. pp. 171–176. [24] A.A. Watwe, A. Bar-Cohen, Modelling of conduction effects on pool boiling CHF of dielectric liquids, in: Proc. of National Heat Transfer Conference. vol. 35, 1997. [25] I. Golobic, A.E. Bergles, Effects of heater side factors on the saturated pool boiling critical heat flux, Exp. Therm. Fluid Sci. 5 (1997) 43–51. [26] M. Arik, A. Bar-Cohen, Effusivity-based correlation of surface property effects in pool boiling CHF of dielectric liquids, Int. J. Heat Mass Transf. 46 (2003) 3755–3764. [27] Y. Katto, Y. Kosho, Critical heat flux of saturated natural convection boiling in a space bounded by two horizontal co-axial disks and heated from below, Int. J. Multiphas. Flow 5 (1979) 219–224. [28] M. Misale, G. Guglielmini, A. Priarone, HFE-7100 pool boiling heat transfer and critical heat flux in inclined narrow spaces, Int. J. Refrig. 32 (2009) 235–245.
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Nucleate boiling and critical heat flux of HFE-7100 in horizontal narrow spaces M. Misale *, G. Guglielmini, A. Priarone DIPTEM – Sezione di Termoenergetica e Condizionamento Ambientale, Università degli Studi di Genova, Via all’Opera Pia 15a, 16145 Genova, Italy
a r t i c l e
i n f o
Article history: Available online 23 June 2010 Keywords: Nucleate pool boiling Dielectric fluid Confinement Peripheral conditions Critical heat flux
a b s t r a c t The pool boiling heat transfer and critical heat flux CHF of saturated HFE-7100 at atmospheric pressure on a confined smooth copper surface were experimentally studied. The horizontal upward boiling surface was confined by a face-to-face parallel unheated surface. We analysed the effects obtained by changing the diameter of the unheated surface and the gap between the boiling surface and the adiabatic surface. The gap values investigated were s = 0.5, 1.0, 2.0, 3.5 mm. To confine the circular boiling surface (d = 30 mm), two different Plexiglas discs were used: one with a diameter D = 30 mm, equal to that of the copper boiling surface, and the other with a diameter D = 60 mm, equal to that of the overall test section support. For each configuration, boiling curves were obtained up to the thermal crisis. For both configurations, it was observed that, at low wall superheat, the effect of confinement was not significant if Bo > 1, while for Bo 6 1 the heat transfer coefficient increased as the channel width s decreased. By contrast, at high wall superheat, a drastic reduction in both heat transfer and CHF was seen when the channel width s decreased; this reduction was less pronounced when the smaller confinement disc (D = 30 mm) was used. CHF data were also compared with the values predicted by literature correlations. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction As pool boiling is a very efficient means of thermal control in several applications, nucleate pool boiling heat transfer and critical heat flux CHF have aroused increasing attention, especially with regard to confined geometries. Moreover, the use of dielectric fluids in nucleate pool boiling is often applied in thermal systems, as it allows heat to be removed while keeping surface superheat relatively low. The use of dielectric fluids offers several further advantages: (a) low saturation temperatures at atmospheric pressure; (b) good thermal contact with all components, even in narrow spaces; (c) excellent chemical compatibility with many materials; (d) low toxicity and good environmental characteristics. Confined pool boiling has become a research subject of great importance, as it is frequently encountered in many practical situations, such as high-performance compact heat exchangers and the cooling of electronic components. The effects of confinement on pool boiling depend on the complex interaction among geometry, channel width, heat flux and fluid properties. This paper reports an experimental study on the confined pool boiling of HFE-7100, a hydrofluoroether dielectric fluid (C4F9OCH3). The effects of confinement conditions (channel width s and unheated confinement disc diameter D) on a horizontal upward-facing boiling surface were systematically investigated. * Corresponding author. Tel.: +39 010 3532576; fax: +39 010 311870. E-mail address: [email protected] (M. Misale). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.06.009
A criterion for analysing the confinement gap effect has been proposed in the literature, and is based on the Bond number Bo, which is defined as the ratio between the channel width s and the capillary length L; the capillary length L is often assumed to be proportional to the departure diameter of isolated bubbles, as it relates capillary and gravitational forces; it is calculated by:
L¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r gðql qm Þ
The capillary length for HFE-7100 (3MTM NovecTM Engineered Fluids [1]) at atmospheric saturation pressure is about 0.88 mm, which corresponds to Bo numbers ranging between Bo = 0.57 (s = 0.5 mm) and Bo = 4.0 mm (s = 3.5 mm). 2. Previous research The first studies on the effects of confinement date back to the end of the 1960s. Ishibashi and Nishikawa [2] studied the nucleate boiling of water and ethyl alcohol in vertical annuli at pressures from 1 atm (channel width 1–20 mm) to 10 atm (channel width 0.6–2 mm). In saturated boiling heat transfer in a narrow space, they found, in addition to the isolated bubble region, a coalesced bubble region with markedly different characteristics; they proposed a new type of correlating equation for the coalesced bubble region. Later, Katto et al. [3] studied the boiling of saturated water at atmospheric pressure on a horizontal upward-facing circular
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773
Nomenclature Bo CHF d D D0 g h hlv L q00 Ra
Bond number = s/L [–] critical heat flux [W m2] boiling surface diameter [m] confinement disc diameter [m] boiling surface support diameter [m] acceleration of gravity [m s2] heat transfer coefficient [W m2 K1] latent heat of vaporisation [J kg1] capillary length [m] specific heat flux [W m2] average roughness [m]
copper surface (d = 11 mm) confined by a parallel glass surface (d/ D = 1) with channel widths down to 0.1 mm. They observed significant effects of confinement both at low heat flux (increased heat transfer performance on decreasing the channel width) and at CHF (reduced CHF values on decreasing the channel width). Yao and Chang [4] analysed the boiling of R-113, acetone and water at atmospheric pressure in vertical narrow annuli with closed bottoms (heights of 25.4 and 76.2 mm and channel widths of 0.32–2.58 mm). They proposed the Bond number as a criterion for characterising the squeezing effect on a bubble due to confinement. In addition to the Bond number, these authors considered the effect of the aspect ratio of the channel, and defined a modified boiling number as the ratio between the residence time of the bubble in the confined space and the vapour formation time; they proposed a boiling map with the Bond number and the boiling number as coordinates, on which they distinguished three boiling regimes: isolated deformed bubbles, slightly deformed bubbles and coalesced deformed bubbles. Bonjour and Lallemand [5] studied the combined effect of confinement (s = 0.3–2.5 mm) and pressure (1–3 bar) on the critical heat flux of R-113 in vertical channels. They noted a reduction in CHF on decreasing the channel gap at all pressures investigated. Subsequently, Bonjour and Lallemand [6] analysed flow patterns during the boiling of R-113 in narrow vertical spaces, and observed three different boiling regimes: nucleate boiling with isolated bubbles, nucleate boiling with coalesced bubbles, and partial dry-out; they also developed a flow pattern map for confined boiling, based on the Bond number and on a reduced heat flux. A study by Misale and Bergles [7] dealt with boiling heat transfer on three vertical in-line heaters placed in narrow channels and cooled by FC-72 or Galden HT-55; when the channel width was small, the heat transfer performance improved at low heat fluxes (q00 6 3.5 W cm2). More recently, Misale et al. [8] analysed the confined pool boiling of saturated FC-72 from square-pin finned surfaces; they found a critical channel width value below which heat transfer diminished. Geisler and Bar-Cohen [9] experimentally studied saturated boiling in vertical, rectangular parallel-plate channels immersed in FC-72 at atmospheric pressure, with spacing down to 0.3 mm. They found that enhancement of nucleate boiling at low heat flux appeared to be largely dependent on the Bond number. Passos et al. [10,11] analysed the confined (s = 0.2–13 mm) saturated boiling of FC-72 and FC-87 on a downward-facing copper disc (d = 12 mm); at low heat flux (q00 6 4 W cm2), the heat transfer coefficient was enhanced on decreasing the channel gap. Guglielmini et al. [12] performed experiments to analyse the combined effects of surface orientation (h = 0°, 45°; 90°; 135°) and confinement (channel widths s = 1–20 mm) on the nucleate pool boiling and critical heat flux of saturated HFE-7100 on a
s Tsat Tw
e k h
ql qv r DTsat
channel width [m] saturation temperature [K] surface temperature [K] mean absolute error [-] fraction of data predicted to within ±30% [-] orientation angle [deg] liquid density [kg m3] vapour density [kg m3] surface tension [N m1] wall superheat = Tw Tsat [K]
smooth copper surface. At low wall superheats, for channel widths greater than 2 mm (Bo > 1), the effect of confinement was negligible for all surface orientations, while for a channel width of 1 mm (Bo 1) and angles of 0° and 45°, heat transfer was clearly enhanced. At high wall superheats, boiling curves matched for channel widths greater than 5 mm, while for confinements of 3.5, 2 and 1 mm, the heat flux, heat transfer coefficient and CHF decreased as the channel width decreased. This effect was more evident for orientation angles of 0° (upward-facing surface) and 45°, whereas it was less pronounced at 90° and was almost negligible at 135°. Concerning the CHF, the effects of confinement became appreciable for s 6 3.5 mm; the CHF decreased as the channel width decreased, and the magnitude of this reduction depended on the orientation of the heated surface. Cardoso et al. [13] experimentally studied the saturated nucleate boiling of n-pentane on an upward-facing heated surface, for different degrees of confinement (s = 0.2–13 mm). The authors analysed only partial boiling curves, not up to the thermal crisis, and observed an effect of confinement only for s = 0.2 mm; they also found that the heat transfer coefficient increased when the confinement gap decreased. The effect of confinement was also analysed by Su et al. [14], who varied the gap size s and heated disc diameter (d = 100; 300 mm) of a downward-facing surface during boiling in water at atmospheric pressure under subcooled conditions. They found that the heat transfer was lower for the larger diameter of the heated plate because, in that case, the bubbles escaped less easily to the liquid pool and less intensively churned the fluid under the heated plate. The authors also suggested introducing into the analysis a new geometrical dimensionless parameter to take into account the effect of the boiling surface diameter on heat transfer: d/L, i.e. the ratio between the diameter d of the heated surface and the capillary length L. Recently, Hetsroni et al. [15] experimentally studied the boiling of water and surfactant solutions in a confined space between two vertical plates; the gap size was varied in the range of s = 1–80 mm (Bo = 0.4–47). They found that, when the gap size was the same, the addition of surfactant enhanced heat transfer in comparison with that of water boiling, and that an increase in the Bond number led to an increase in the dimensionless frequency of the temperature fluctuations of the heated wall, that are typical of the regime of high heat flux. Stutz et al. [16] experimentally analysed the nucleate and transition boiling of saturated n-pentane in narrow horizontal spaces between a heated upward-facing copper disc and an unheated surface (d/D = 1). They concluded that confinement influenced both heat transfer and CHF and that the Bond number was a good parameter to represent this behaviour. Finally, Stutz et al. [17] proposed an axisymmetric two-phase flow model to describe the growth of a single bubble squeezed
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between a horizontal upward-facing heated disc and an insulating surface placed parallel to the heated surface. No studies have dealt with the effect of the dimensions of the unheated confinement surface. In the present study, which used a horizontal upward-facing surface, the ratio between boiling surface diameter d and confinement disc diameter D significantly influenced heat transfer and CHF. 3. Experiments 3.1. Experimental set-up The apparatus (Fig. 1a) consisted of a vessel, which contained the instrumented test section immersed in the fluid. The test vessel was cubic (internal side 210 mm) and made of stainless steel (AISI
a Pressure transducer
Water condenser
304). A coil condenser, refrigerated by tap water, was positioned inside the container in the vapour zone. Five optical windows on the lateral and top sides allowed visualization of the boiling surface. The experimental apparatus was equipped with a pressure transducer, venting valve, safety valve, vacuum pump and five shielded K-type thermocouples: four thermocouples measured liquid temperature and one measured vapour temperature. One liquid thermocouple was plugged into a PID controller, which modulated electrical power to the auxiliary heaters, which were placed laterally on the external surface of the vessel. These heaters preheated the fluid and maintained it at the desired saturation temperature. In all tests HFE-7100 dielectric fluid (saturation temperature at atmospheric pressure Tsat = 61 °C) [1] was used.
Safety valve
Venting valve
Auxiliary heater
Thermocouples
Optical window to Vacuum pump
Test section
Micrometer positioning system
b
Confinement disc (black D=30 mm; gray D=60 mm)
Epoxy resin
D d
s
Thermocouples Insulator
Bakelite
Copper block
D'
Heater Stainless steel disk Insulator Support Fig. 1. (a) Test vessel for pool boiling experiments and (b) test section scheme.
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3.2. Test section
4. Results and discussion
The test section (Fig. 1b) consisted of a cylindrical copper (99.99%) block heated at the bottom by an electric heater. The top, flat end of the copper block constituted the boiling surface (d = 30 mm), the area of which was 7.07 cm2. The copper test section was instrumented with nine shielded thermocouples (K-type, O.D = 0.5 mm), placed in holes at different levels: 3, 21 and 39 mm below the boiling surface. At each level, the holes were positioned at 120° to each one another and the three levels were rotated so that only one thermocouple was located in each vertical direction, in order to reduce non-uniformity of temperature distribution in the copper block. The copper block was housed in a Bakelite support (D = 60 mm); the space between the copper and the Bakelite was filled with insulating material and the upper seal was made of epoxy resin (STYCAST 2651 MM). The boiling surface was roughened by sandblasting with particles of controlled dimension, and presented an average roughness Ra = 0.6 lm with an associated standard deviation of 0.02 lm. Assuming one-dimensional axial heat conduction through the copper block, the heat flux q00 and the surface temperature Tw were calculated by means of Fourier’s law, the thermal conductivity of the copper (394 W m1 K1, from supplier’s data) and the temperature gradient through the block being known. The heat transfer coefficient was defined as h ¼ q00 =DT sat . To confine the boiling surface, two different Plexiglas discs were used (diameter D = 30 and 60 mm; thickness 2.5 mm). The periphery of the space between the two surfaces was open to allow the fluid to wet the boiling surface. In all these experimental tests, the boiling surface was horizontal and faced upward. Standard techniques were followed in order to determine uncertainty [18] in the experimental measurements. The system used to collect and store the signals from the thermocouples is accurate to ±0.1 K on absolute temperature values and to ±0.02 K on differential values. Uncertainty in the determination of heat flux is dependent on operating conditions. In the single-phase natural convection zone and at the onset of nucleate boiling, the maximum error in the heat flux value is ±15%. In the fully developed nucleate boiling region, the maximum error is less than ±5%. Close to the thermal crisis, uncertainty increases to ±8%. The error associated with surface temperature in the fully developed boiling region is less than ±0.2 K. Finally, the positional error of the confinement surface is about ±0.05 mm.
4.1. Pool boiling curves and heat transfer
3.3. Test procedure To degas the fluid, the following procedure was followed: before each experimental campaign, a partial vacuum (less than 0.01 Pa) was created inside the vessel and then the bulk liquid was introduced into the vessel. The auxiliary heaters were then switched on in order to raise the internal pressure value above (+10%) of the external atmospheric pressure and to vent out noncondensable gases. This operation was repeated until a satisfactory correspondence was achieved between the pressure inside the vessel and the liquid saturation temperature. For dielectric fluids, at the onset of nucleate boiling, temperature overshoot or hysteresis phenomena may appear. To avoid these situations, the following procedure was adopted, which enabled all nucleation centres to be activated: after half an hour of vigorous boiling at about 2 W cm2 (for s = 1 mm and s = 0.5 mm, at q00 = 0.8 W cm2), the experiments were immediately started at the lowest heat flux value; all tests were then conducted under increasing heat flux conditions. For each heat flux value imposed, once steady-state conditions were reached after about 15–20 min, all measurement parameters were acquired and recorded.
775
The effects of channel width s and confinement disc diameter D were experimentally investigated for the saturated pool boiling of HFE-7100. The channel width s was the distance between the circular boiling surface (d = 30 mm) and the Plexiglas disc above it. The study analysed different configurations by varying the channel width (s = 0.5, 1, 2, 3.5 mm) and the diameter of the confinement disc (D = 60 mm, as large as the overall Bakelite support; D = 30 mm, large enough to cover only the copper boiling surface). In a previous study [12], in which a confinement disc D = 60 mm was used, no significant effects of confinement were observed for channel widths s > 3.5 mm (Bo > 4.0). Fig. 2 reports the experimental results obtained with the confinement disc of D = 30 mm: Fig. 2a shows the boiling curves and Fig. 2b the heat transfer coefficients, both as functions of DTsat. Fig. 3 reports the experimental results obtained with the disc of D = 60 mm: Fig. 3a shows the boiling curves and Fig. 3b the heat transfer coefficients. In the low wall superheat boiling region (DTsat <9 K) and for the confinement disc of D = 60 mm, heat transfer was higher at channel widths s = 1 mm (Bo 1) and s = 0.5 mm (Bo < 1) than for the unconfined surface; for the disc of D = 30 mm, the channel width seemed to have less significant effects on boiling curves, except at s = 0.5 mm. At higher wall superheats (DTsat > 9 K), a drastic reduction in both heat transfer and CHF appeared for confined boiling at channel width s 6 3.5 mm; the reduction was less pronounced when the smaller confinement disc was used. For channel spacing s = 0.5 mm (Bo = 0.57), at very low wall superheats the heat transfer for confined surfaces was higher than that of the unconfined surface, while at high superheats the heat transfer was significantly lower for both types of confinement, in particular for D = 60 mm. The great instability of the boiling process with this configuration (s = 0.5 mm), especially for D = 60 mm, causes poor repeatability of boiling curves; indeed, vapour accumulates in the gap and suddenly leaves the test section laterally in one direction or another, allowing fresh liquid to wet the boiling surface. These experimental data are in agreement with literature results [19]. The experimental results seem to partially confirm the observations made by Katto et al. [3], who found that the mechanism of nucleate boiling seems to change when the Bond number decreases to the order of magnitude of 1 or less. Indeed, between the heated surface and the base of the deformed bubble, a thin liquid film, called microlayer, evaporates. For Bo < 1 and for low wall superheats, the bubbles coalesce, increasing the area of the liquid film; this liquid microlayer, which is attached to the surface by intermolecular attractive forces [20], is pressed against the heated wall and does not evaporate completely. Consequently, the heat transfer coefficient increases. The effect of the Bond number was more evident in the D = 60 mm configuration, in which the confinement disc constituted a real obstacle to the departing bubbles. Indeed, as supposed by Cardoso et al. [13], the mechanism of escape of coalescent bubbles and surface rewetting ‘is dependent on the conditions imposed by the geometric characteristics of the heated surface and its support. Thus, the ratio between the diameters of the support and the test section can influence the residence time of the bubble in the channel’. The effects of confinement are presented in Fig. 4, where the ratio between the heat transfer coefficient in the case of the confined boiling surface and of the unconfined one (h/hunconf) is plotted versus the Bond number for different wall superheats DTsat; the data
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a
a
Unconfined
Unconfined
10
2
q" [W/cm ]
q" [W/cm2]
10
1
1
D=60 mm
D=30 mm s=3.5 mm =2 mm =1 mm =0.5 mm
s s=3.5 mm s =2 mm s =1 mm s =0.5 mm
10
10
ΔTsat [K]
b
ΔTsat [K]
b
Unconfined
4
10
Unconfined
4
2
h [W/m K]
h [W/m2K]
10
3
10
3
10 D=30 mm s=3.5 mm =2 mm =1 mm =0.5 mm
10
ΔTsat [K] Fig. 2. (a) Boiling curves and (b) heat transfer coefficient curves for D = 30 mm and different gaps.
for D = 30 mm and for D = 60 mm are shown in Fig. 4a and b, respectively. At very low wall superheats (DTsat < 9 K), heat transfer was enhanced when the gap size s was very small (s = 0.5; 1 mm; Bo 6 1); this effect was more pronounced when the larger confinement disc (D = 60 mm) was used. On increasing the wall superheat (DTsat P 9 K), heat transfer coefficients decreased as the Bond number decreased to Bo < 4 (s 6 3.5 mm). At high wall superheats, both the heat transfer coefficient and the CHF were higher, for the same channel width, when the smaller confinement disc was used; this was because the vapour bubbles could leave the boiling surface more easily. By contrast, when the larger disc was used, the departing vapour bubbles accumu-
D=60 mm s s=3.5 mm s =2 mm s =1 mm s =0.5 mm
10
ΔTsat [K] Fig. 3. (a) Boiling curves and (b) heat transfer coefficient curves for D = 60 mm and different gaps.
lated and coalesced near the boiling surface, which hindered heat transfer. Su et al. [14] noticed that, for the elongated bubbles that are typical of confined boiling, there were two characteristic length scales: bubble width (direction parallel to the heated surface) and bubble height (normal to the heated surface). The width of the bubble is more important than the height as it directly affects the area of the heated surface covered by vapour. This dimension is strongly influenced by the diameter of the boiling surface, and can expand to the same size as the boiling surface if the nucleation site is at the centre of the surface. Conversely, the height of the bubble is limited by the gap size.
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2.0
Δ Tsat = 8 K =9K = 10 K = 12 K = 15 K = 18 K = 20 K
h/hunconf
1.5
20
CHF [W/cm 2]
a
1.0
0.5
15
10
5 0.0 0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
D=30 mm
Bo
b
0
2.0
1
1.5
1.5
2.0
2.5
2.5
3
3.5
4
Fig. 5. Critical heat flux CHF vs channel width s for different confinement disc diameter D.
0.5
1.0
2
s [mm]
=9K = 10 K = 12 K = 15 K = 18 K = 20 K
1.0
0.0 0.5
0.5
Δ Tsat = 8 K
1.5
h/hunconf
D=60 mm
0
3.0
3.5
4.0
Bo Fig. 4. Effect of confinement on heat transfer coefficients: (a) D = 30 mm and (b) D = 60 mm.
4.2. Critical heat flux Boiling conditions close to the thermal crisis were also analysed. To avoid compromising the integrity of the test section, heat flux was increased by regular steps until a noticeable and rapid rise in surface temperature was measured. This condition was identified as the maximum heat flux and should be very close to the thermal crisis: this heat flux was defined as the critical heat flux CHF. For channel widths s greater than about 3.5 mm and for the larger confinement disc diameter, the effect of confinement was negligible in comparison with the unconfined boiling condition [12]. For channel widths of 3.5, 2, 1 and 0.5 mm, the presence of the confinement disc clearly impaired heat transfer performance at high wall superheats, and the CHF value decreased markedly as the channel width s decreased, in comparison with the unconfined configuration. Fig. 5 shows the values of critical heat flux CHF vs channel width s for the two different confinement disc diameters (D = 30, 60 mm); CHF decreased as channel width s decreased, for both diameters D, whereas CHF was always higher for the smaller confinement disc. Bonjour and Lallemand [6] concluded that the reduced CHF was caused by the earlier dry-out of the microlayer, since the initial thickness of the microlayer was smaller when the channel width was smaller. Geisler and Bar-Cohen [21] recently studied confined boiling between two vertical, rectangular parallel plates. They suggested that a key parameter in the CHF of confined boiling surfaces was
the channel aspect ratio (channel principal dimension/spacing, in this study D/s), which determines the propensity of vapour to accumulate in the channel and induces premature dry-out near the channel exit. With regard to the CHF of pool boiling, various theoretical and semi-empirical correlations can be found in the literature. Zuber [22] derived a classical CHF analytical expression:
CHF ¼
p n 24
0:25 q0:5 m hlm ½g rðql qm Þ
o
ð1Þ
This correlation is useful for saturated pool boiling on large, thick, upward-facing horizontal plates and represents a baseline correlation for pool boiling CHF. On the basis of Zuber’s correlation, many other correlations have been developed; these have introduced correction factors to take into account various effects, such as length scale, geometry, wall thermophysical properties, wall thickness and subcooling [23–25]. Arik and Bar-Cohen [26] introduced an expanded formulation of Zuber’s correlation, which included parametric factors which took into account the effects of heater characteristics and bulk liquid subcooling. Their correlation considered the increase in CHF observed for small heaters. Few authors, however, have obtained correlations which consider the effect of channel width s on CHF for confined surfaces. Katto and Kosho [27] studied pool boiling critical heat flux in horizontal upward-facing confined geometries using water, R113, ethyl alcohol and benzene. They used a confinement surface area equal to that of the boiling surface (d/D = 1) and proposed the following correlation:
n o 0:25 CHF ¼ q0:5 m hlm ½g rðql qm Þ
0:18 0:14 h i 2 0:5 qm g ðql rqm Þd ds 1 þ 0:00918 q
ð2Þ
l
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðql qv Þ=r > 6. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi For the present test section configuration, d/L = d gðql qv Þ=r is equal to 34. On the basis of Zuber’s expression, Misale et al. [28] proposed an empirical correlation for the CHF of horizontal upward-facing confined surfaces:
This correlation was proposed for d/L = d
n o 0:25 CHF ¼ 0:185 wðsÞ q0:5 m hlm ½g rðql qm Þ
ð3Þ
778
M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
where
wðsÞ ¼
e¼ 1 1 þ 71:43 e1:32s
ð4Þ
and s is expressed in mm. In their experimental study, Misale et al. used a ratio between boiling surface diameter and confinement disc diameter d/D equal to 0.5. Fig. 6 compares the present experimental CHF data both with the predicted values yielded by the Misale et al. correlation [28] and with those yielded by Katto and Kosho’s correlation [27], for both confinement disc diameters: D = 30; 60 mm (d/D = 1; 0.5). The Misale et al. correlation predicted data for the confinement configuration with the larger disc (D = 60 mm and d/D = 0.5) quite well, but not data for D = 30 mm; Katto and Kosho’s correlation yielded a rough prediction of the experimental data for both values of confinement disc diameter. With regard to the experimental data presented in this study, the predictive methods were evaluated according to two criteria, i.e., the fraction of data predicted to within ±30%, k% and the mean absolute error, e%:
24
ð5Þ
In the correlation by Misale et al., e% and k% proved to be equal to 41 and 30, respectively; in Katto and Kosho’s correlation, e% and k% were equal to 43 and 30, respectively: for both correlations the comparison was unsatisfactory. In fact, the CHF for a confined horizontal boiling surface depends both on the channel gap s and on the ratio between the boiling surface diameter and the confinement disc diameter d/D; the size of the support of the boiling surface is also important [13], especially in the case of a downward-facing horizontal boiling surface, in which the presence of a large surface around the boiling surface hinders the escape of vapour and reduces the heat transfer performance. Table 1 shows the geometrical conditions of the experiments in the literature database on horizontal confined pool boiling; the geometry of the boiling surface, including the dimensions and configuration of the test section support, the confinement geometry and the channel width s are reported. To propose a new correlation that satisfactorily represents all the effects of geometry on critical heat flux CHF, new experimental tests will be required for different d/D and also for different d/D0 ratios.
D=60 mm, Misale et al. 2009 D=30 mm, Misale et al. 2009
21
5. Conclusions
D=60 mm, Katto and Kosho 1979 D=30 mm, Katto and Kosho 1979
Nucleate pool boiling of the dielectric fluid HFE-7100 on a smooth copper surface (d = 30 mm) at atmospheric pressure was experimentally studied; the boiling surface was horizontal, oriented upwards and confined by means an adiabatic disc. The study analysed the effects of confinement conditions (channel width s and diameter D of the unheated disc) on heat transfer coefficients and on critical heat flux CHF. The following conclusions can be drawn:
18
CHFpred [W/cm2]
N 1 X predict:v alue exper:v alue% N i¼1 exper:v alue
15 12 9 6
5.1. Heat transfer coefficient 3 0 0
3
6
9
12
15
18
21
24
CHFexp [W/cm2 ] Fig. 6. Predicted critical heat flux CHF vs experimental CHF data.
– in the low wall superheat boiling region (DTsat < 9 K), confinement influenced heat transfer only at s = 0.5, 1 mm (Bo 61); – at high wall superheats (DTsat > 9 K), a drastic reduction in heat transfer occurred for all confinement gaps analysed (s 6 3.5 mm), but the reduction was less pronounced when the smaller confinement disc (D = 30 mm) was used;
Table 1 Geometrical conditions of experiments in the literature database on horizontal confined pool boiling. Authors
Boiling surface geometry
Confinement geometry
Channel width s
Katto et al. [3]
Horizontal upward-facing circular d = 11 mm Support: D0 d Horizontal downward-facing circular d = 12 mm PVC support: D0 = 20 mm Horizontal upward-facing circular d = 12 mm Teflon support: D0 50 mm Horizontal downward-facing circular d = 100; 300 mm Support: D0 1.5d Horizontal upward-facing circular d = 30 mm Flush mounted with the vessel bottom: D0 = 160 mm Horizontal upward-facing circular d = 10; 20 mm Support: D0 d
Parallel circular surface D = 11 mm
Down to 0.1 mm
Bottom of the boiling chamber
s = 0.2–13 mm
Parallel circular surface D = 12 mm
s = 0.2–13 mm
Bottom of the boiling chamber: 900 750 mm
s = 10; 15; 20 mm for d = 100 mm; s = 0.9–77 mm for d = 300 mm
Parallel circular surface D = 30 mm
s = 200 lm–90 mm
d/D = 1
d/s 0–120
Passos et al. [10,11]
Cardoso et al. [13]
Su et al. [14]
Stutz et al. [16]
Katto and Kosho [27]
M. Misale et al. / Experimental Thermal and Fluid Science 35 (2011) 772–779
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