Boiling Heat Transfer
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Multiphase Science and Technology, Vol. 13, No. 3, pp. 207-232, 2001 CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING – AN ASSESSMENT OF CURRENT UNDERSTANDING AND FUTURE DIRECTIONS FOR RESEARCH S. G. Kandlikar Mechanical Engineering Department, Rochester Institute of Technology, Rochester, NY 14623, USA Abstract. Critical Heat Flux, or CHF, is an important condition that defines the upper limit of safe operation of heat transfer equipment employing boiling heat transfer in heat flux controlled systems. Although significant research has been conducted in this field, a clear understanding of the basic mechanisms leading to the CHF condition is still lacking. The present article covers the subcooled flow boiling CHF and reviews the parametric trends and photographic studies reported by earlier investigators. An in-depth review of the existing models is presented in light of these studies, and further research needs are identified. 1. INTRODUCTION Dissipation of large heat fluxes at relatively small temperature differences is possible in systems utilizing boiling phenomenon as long as the heated wall remains wetted with the liquid. With the wetted wall condition at the heated surface, heat is transferred by a combination of two mechanisms: (i) bubbles are formed at the active nucleation cavities on the heated surface, and heat is transferred by the nucleate boiling mechanism, and (ii) heat is transferred from the wall to the liquid film by convection and goes into the bulk liquid or causes evaporation at the liquid-vapor interface. The large amount of energy associated with the latent heat transfer (compared to the sensible energy change in the liquid corresponding to the available temperature potential in the system) in the case of nucleate boiling, or the efficient heat transfer due to liquid convection at the wall, both lead to very high heat transfer coefficients in flow boiling systems. Removal or depletion of liquid from the heated wall therefore leads to a sudden degradation in the heat transfer rate. The way in which the heated surface arrives at the liquid starved condition in a flow boiling system determines whether it is termed as Critical Heat Flux or Dryout
Transcript of Boiling Heat Transfer
Multiphase Science and Technology, Vol. 13, No. 3, pp. 207-232, 2001
CRITICAL HEAT FLUX IN SUBCOOLED FLOW
BOILING – AN ASSESSMENT OF CURRENT UNDERSTANDING AND FUTURE DIRECTIONS FOR RESEARCH
S. G. Kandlikar Mechanical Engineering Department, Rochester Institute of Technology, Rochester, NY 14623, USA
Abstract. Critical Heat Flux, or CHF, is an important condition that
defines the upper limit of safe operation of heat transfer equipment employing boiling heat transfer in heat flux controlled systems. Although significant research has been conducted in this field, a clear understanding of the basic mechanisms leading to the CHF condition is still lacking. The present article covers the subcooled flow boiling CHF and reviews the parametric trends and photographic studies reported by earlier investigators. An in-depth review of the existing models is presented in light of these studies, and further research needs are identified.
1. INTRODUCTION Dissipation of large heat fluxes at relatively small temperature differences is possible in systems utilizing boiling phenomenon as long as the heated wall remains wetted with the liquid. With the wetted wall condition at the heated surface, heat is transferred by a combination of two mechanisms: (i) bubbles are formed at the active nucleation cavities on the heated surface, and heat is transferred by the nucleate boiling mechanism, and (ii) heat is transferred from the wall to the liquid film by convection and goes into the bulk liquid or causes evaporation at the liquid-vapor interface. The large amount of energy associated with the latent heat transfer (compared to the sensible energy change in the liquid corresponding to the available temperature potential in the system) in the case of nucleate boiling, or the efficient heat transfer due to liquid convection at the wall, both lead to very high heat transfer coefficients in flow boiling systems. Removal or depletion of liquid from the heated wall therefore leads to a sudden degradation in the heat transfer rate.
The way in which the heated surface arrives at the liquid starved condition in a flow boiling system determines whether it is termed as Critical Heat Flux or Dryout
208 S. G. KANDLIKAR
condition. The evolution of the terminology itself is quite interesting. From a mechanistic viewpoint, the following definitions seem to be appropriate and are therefore recommended:
Critical Heat Flux condition represents the upper limit of heat flux (in heat flux controlled systems) followed by a drastic rise in wall temperature, or considerable degradation in heat flux with an increase in wall temperature (in temperature controlled systems) in the nucleate boiling heat transfer. A vapor blanket covers the heated surface separating the surface from the liquid. Dryout condition represents the termination of continuous liquid contact with the wall. It follows the gradual depletion of liquid due to evaporation and entrainment of the liquid film. The vapor, from the continuous vapor phase in the bulk flow, covers the heated surface, and the discrete liquid droplets flowing in the vapor core may make occasional contact with the heated surface. 1.1 Historical Perspective of Critical Heat Flux As early as 1888, Lang (1888) recognized through his experiments with high pressure water that as the wall temperature increased beyond a certain point, it resulted in a reduction in the heat flux. However, it was Nukiyama (1934) who realized that the “maximum heat transmission rate” might occur at relatively modest temperature differences. An excellent summary of the historical developments in this area was presented by Drew and Mueller (1937).
Another aspect of historical significance is the evolution of the term Critical Heat Flux. Early investigators used various terminology to describe this condition, e.g., maximum or peak heat flux, maximum boiling rate (Drew and Mueller, 1937), and burnout heat flux. Nukiyama (1934) described it as the critical point on the boiling curve. The earliest usage of the term Critical Heat Flux is seen by Zuber (1959). Further investigation is needed to determine if publications in other languages (by investigators such as Kutateladze and Fritz) used this terminology. Well into 1980s, there was no consensus on the use of a single term. However, in the mid-1980s, the term critical heat flux, and its acronym, CHF, became widely accepted. 1.2 Application Areas for CHF Studies After establishing the terminology, let us examine the relevance and application of CHF and Dryout in the fields of current interest. The historical applications such as quenching are still valid. The major impetus for the CHF studies in the recent past was the nuclear reactor core cooling. The catastrophic nature of the disaster associated with the CHF in a nuclear reactor, leading to core meltdown, put a high premium on the CHF studies. The urgency of the problem led to exhaustive experimentation in geometries similar to the reactor core. The safe operating limits were established through compilation of data from various experiments – developing the lookup tables. In his exhaustive literature survey report, Boyd (1983a, b) points out the severe inadequacies in the theoretical modeling of the CHF phenomena leading to empiricism.
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 209
Another major impetus for research in CHF was provided by the refrigeration and power industry in determining the Dryout point in a refrigeration evaporator and the safe operating limit in a boiler. The concerns in these cases were largely regarding safety and economic optimization of the systems.
The focus for CHF and Dryout studies as we enter the new millennium has somewhat shifted. The issues related to the nuclear industries are still valid. However, the emphasis has now moved toward gaining the basic understanding of the mechanisms leading to the CHF condition. Developments in new augmentation techniques have opened a whole new area where extensive CHF data for specific systems are not available. For example, in spite of its superior performance in the flow boiling application, the microfin tubes have not been tested for their upper limits in CHF. Many new compact heat exchanger geometries are now being employed in flow boiling applications, but their dryout characteristics have not been established. These and many more challenges have emerged with the advancement in the heat transfer enhancement technologies and their microscale applications. A major evolving area is the CHF in narrow channels employed in fast response evaporators for fuel cell applications. In the present paper, the current status of our understanding of the CHF in subcooled flow boiling is reviewed, and recommendations for future work in this area are presented.
2. OVERVIEW OF PREVIOUS REVIEW ARTICLES Subcooled flow boiling has received considerable attention due to its potential for sustaining high heat fluxes in nuclear fusion applications. One of the most comprehensive reviews on this subject was presented by Boyd (1983a and b) in a two-part survey article addressing the fundamental issues, modeling, and correlations for CHF in subcooled flow boiling. Boyd (1983a) presents a list of various fusion machines and the heat flux levels sustained in them at steady state levels. He also provides an exhaustive table with the details of the experimental studies available in literature. In the second part, Boyd (1983b) presents a comprehensive table listing available correlations for predicting CHF. It is clear that the available exhaustive experiments and correlations were aimed at obtaining the CHF limits under specific operating conditions. A comprehensive model was not yet developed; the parametric trends were however identified from the data.
As mentioned in the Introduction section, the vast data available on CHF have been compiled as look-up tables by various investigators. A relatively recent paper by Groeneveld et al. (1996) presents the summary of the latest 1995 look-up table developed jointly by AECL Research (Canada) and IPEE (Obninsk, Russia). It is based on an extensive database of CHF values in tubes with vertical upflow of steam-water mixtures. The table is designed to provide CHF values for 8 mm diameter tubes at discrete values of pressure, mass flux, and dryout qualities covering the ranges 0.1 to 20 MPa, 0 to 8 Mg/m2s, and –0.5 to 1 respectively. Linear interpolation is provided for intermediate values, with an empirical correction factor for diameters different from 8 mm. The look-up table provides a tool capable of predicting data with an rms error of 7.82 percent for the 22,946 data points.
210 S. G. KANDLIKAR
A comprehensive paper by Nariai and Inasaka (1992) presents a summary of their own experimental work and presents useful parametric relationships between CHF and important system variables. A comparison with the available correlations is also presented.
A recent review of CHF fundamentals, models and correlation schemes is presented by Celata and Mariani (1999). They present a comprehensive summary of investigations of the CHF condition and reflect our current understanding of this phenomenon. Earlier review articles by Celata (1992, 1997) provide a good overview of the models describing the CHF mechanism.
Tong and Tang (1997) present a very comprehensive summary of the available literature on various aspects of flow boiling crisis. A large number of correlations have been compiled and presented from the available literature.
In view of the excellent recent surveys already available in literature, the focus of the present paper is directed toward gaining a fundamental understanding through the theoretical models and experimental observations. Areas for future research are identified to gain further insight into the mechanisms leading to CHF.
3. CHF IN SUBCOOLED FLOW BOILING The nucleate boiling heat flux at a given wall superheat in subcooleed flow boiling increases with the liquid subcooling. The bubbles generated on the heater surface condense as they leave the surface and move toward the bulk liquid. As the subcooling increases, the bubbles experience the increased condensation rate while they are still attached to the heater surface. This leads to smaller bubble diameters. Further increase in subcooling leaves the bubble layer attached to the wall. At some point, corresponding to the CHF condition, the heater surface is covered with a vapor blanket causing a significant increase in the wall temperature. Researchers obtained information regarding the mechanisms responsible for this transition by studying the parametric relationships between CHF and relevant system parameters, and by visually capturing, through high-speed photographic techniques, the physical structure of the liquid and vapor phases adjacent to the heater surface. 3.1 Parametric Effects Bergles (1963) identified five important system variables affecting the CHF in subcooled flow boiling. They are: • Pressure
• Mixed mean temperature, or local liquid subcooling
• Velocity (mass flux)
• Length
• Hydraulic Diameter
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The effect of these variables on CHF will be discussed first. It will be followed by a discussion on other variables that are believed to be important in arriving at the CHF condition. 3.1.1 Influence of Pressure Pressure has a weak influence on the CHF as shown in Fig. 1. Bergles (1963) reported an increase of only 17 percent for water when the pressure was changed from 0.14 MPa to 0.6 MPa. Celata (1992) reports no dependence of CHF on pressure, but the data was plotted for the constant inlet subcooling. The results are in general agreement with the pool boiling data, where the pressure has a strong effect near the reduced pressure values of 0 and 1 for cryogenic fluids (for example, see Bewilogua et al., 1975). In the broad region between these two limits, CHF is almost independent of pressure. For water, the results presented by Bonilla and Perry (1941) for CHF in saturated pool boiling are shown in Fig. 2. The slight increase in CHF with pressure at low pressures is very similar to the trend observed by Bergles. 3.1.2 Influence of Subcooling and Mass Flux The higher level of subcooling in the liquid requires a higher heat flux to initiate and sustain bubble activity. As the bubbles grow, they contact the subcooled liquid core causing condensation at the liquid-vapor interface. The departing bubbles condense rapidly depending on the level of liquid subcooling in the core.
0
5,000,000
10,000,000
15,000,000
0 200 400 600 800
Pressure, kPa
CH
F, W
/m2
Bergles (1963)Eperimental data
Subcooled Flow Boiling,Water(Ts - Tb)o = 22.4K G=3038kg/m2s L=15DD=2.4mm
Figure 1 Effect of pressure on subcooled flow boiling CHF of water, Bergles (1963).
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0
1,000,000
2,000,000
0 40 80 120Pressure, kPa
CH
F, W
/m2
Bonilla and Perry (1941)Experimental data
Water, Pool BoilingHorizontal Plate
Figure 2 Effect of pressure on CHF in pool boiling of hydrogen, Bonilla and Perry (1941).
Gunther (1951) presented a systematic study on the effect of velocity on CHF for a
flat 12.5 mm wide and 150 mm long heater strip placed in a rectangular section with flow of water. For this case, their experimental results were correlated by the following equation. )degin(sec)/in(0135.0sec)in./(in 5.0 FTftVsqBtuCHF sub∆= (1a) or, in SI units )(0.987,71 5.0
subTuq ∆=& (1b) where, for eq. (1b), q& -heat flux, W/m2, u- flow velocity, m/s, ∆Tsub - liquid subcooling, K.
Equations (1a) and (1b) are obviously not valid for the pool boiling case (with flow velocity u=0). Therefore a departure from the above relationship is expected at low velocities.
Bergles (1963) conducted systematic experiments to study the parametric trends in CHF for subcooled flow boiling in circular tubes. Figure 3 shows CHF as a function of liquid subcooling. Here the CHF is plotted against the difference between the saturation enthalpy and the liquid enthalpy at the bulk condition. Different sets of points correspond to different mass fluxes. Mass flux plays an important role in this plot. At low mass fluxes, the variation with subcooling is almost linear up to the saturation point. As the mass flux increases, CHF increases in the saturation region, and stays almost flat until it meets the linear portion of the curve in the high subcooling region. Figure 4
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 213
0
10,000,000
20,000,000
30,000,000
-300 -150 0 150 300
Local Excess Enthalpy at CHF, (hs - hb)o, kJ/kg
CH
F, W
/m2
G = 1519 3034 6076 13508
kg/m2 s
Po = 214kPaL = 15DD = 2.4mm
Figure 3 Effect of subcooling and mass velocity on CHF, Bergles (1963).
100,000
1,000,000
10,000,000
50 60 70 80 90 100
Water Temperature, oC
CH
F, W
/m2
Sakurai and Shiotsu (1974)Experimental data (Horizontal)
Sakurai and Masahiro (1974)Experimental data (Vertical)
Pool Boiling, WaterHorizontal and Vertical Plate
Figure 4 Effect of orientation on CHF in pool boiling, experimental data from Sakurai and Shiotsu (1974), water at 1 atm pressure.
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shows a similar plot obtained by Sakurai and Shiotsu (1974) depicting the effect of subcooling on pool boiling CHF for water at one atmospheric pressure. The two data sets are for vertical and horizontal orientations. For both data sets, a linear relationship between CHF and subcooling is seen to be valid in the entire region up to saturation.
Figure 5 shows another plot, also presented by Bergles (1963), representing the effect of subcooling and mass flux for a smaller diameter tube. Here, the trends are similar to those seen for the larger diameter tube in Fig. 3, but the effect of subcooling is not seen until relatively high levels of subcooling are reached.
An increase in mass flux increases the CHF as seen from Figs. 3 and 5. Celata and Mariani (1999) noted that similar trends are reported by other investigators, (Weatherhead, 1963; Moon et al., 1996, Chang et al., 1991; Mishima, 1984). 3.1.3 Effect of L, D and L/D ratio The experimental results for CHF are presented by researchers either for fixed inlet conditions or for fixed exit conditions. The inlet and outlet conditions are related through the heat flux, mass flux, tube or channel dimensions and length. Knowing the conditions at the exit location allows for the formulation of models based on the local conditions, while the effect of L/D ratio is implicitly accounted for when the inlet fluid condition is known. The two-phase flow patterns are dependent on the history of flow.
Bergles (1963) studied the effect of the L/D ratio on CHF. Their results are shown in Figs. 6 and 7. As the L/D ratio increases, the CHF decreases, becoming independent for L/D>30. The effect of diameter for a fixed outlet fluid temperature and with L/D=25 is shown in Fig. 7 for two mass fluxes. The CHF increases with decreasing tube diameter and with increasing mass flux; the effect becomes less significant for tube diameters above 5 mm.
0
20,000,000
40,000,000
-200 -100 0 100 200 300
Local Excess Enthalpy at CHF, (hs - hb)o, kJ/kg
CH
F, W
/m2
G = 3024kg/m2s
6062
13765 24276
Po = 207kPaL = 25DD = 1.2mm
Figure 5 Effect of subcooling and mass velocity on CHF, additional data from Bergles (1963).
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0
5,000,000
10,000,000
15,000,000
0 10 20 30 40
L/D
CH
F, W
/m2
Po = 207Mpa(Ts - Tb)o = 18.3KG = 3038kg/m2sD = 2.4mm
Figure 6 Effect of L/D on subcooled flow boiling CHF, Bergles (1963).
0
10,000,000
20,000,000
30,000,000
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
Tube Diameter, m
CH
F, W
/m2
G = 3038
6076
No Burnout at System Limit
Burnout with Upstream Compressible Volume
kg/m2 s
Po = 207kPa(Ts - Tb)o = 19.4K
L = 25D
Figure 7 Dependence of subcooled flow boiling CHF on tube diameter and mass flux, Bergles (1963).
Boyd (1990) performed extensive experiments to study the effect of L/D ratio on CHF. He concludes that a single value of L/D cannot be proposed beyond which the CHF is independent of the ratio. The L/D effect also depends on other flow parameters, including channel diameter, subcooling, mass velocity, and diameter.
Nariai et al. (1987) and Inasaka and Nariai (1987) conducted experiments to study the effect of tube diameter, tube length and mass flux on CHF. Figures 8 and 9 show
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0
20,000
40,000
60,000
80,000
-0.15 -0.1 -0.05 0 0.05Exit Quality
CH
F, W
/m2
1 1 1 5 2 1 2 5 3 1 3 5 1 3 2 10 2 3 3 10 3 3
D Lmm cm
D Lmm cmG = 20000kg/m2 s
Figure 8 Effect of tube diameter on subcooled flow boiling CHF at high mass flux, Inasaka and Nariai (1987).
0
20,000
40,000
60,000
-0.15 -0.1 -0.05 0 0.05Exit Quality
CH
F, W
/m2
1 1 1 5 2 1 2 5 3 1 3 5 1 3 2 10 2 3 3 10 3 3
D Lmm cm
D Lmm cmG = 7000kg/m2 s
Figure 9 Effect of tube diameter on subcooled flow boiling CHF at low mass flux, Nariai and Inasaka (1992).
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 217
their results for high and low mass fluxes respectively. At the high mass flux shown in Fig. 8, the CHF increases with a decrease of both the tube diameter and the length. At low mass fluxes however, both effects disappear for sufficiently high values of L and D. It was also noted by Nariai et al. that the CHF values are higher in the region where the L and D effects are significant.
In order to define the region of influence, Inasaka and Nariai (1987) classified the CHF into high heat flux and low heat flux regions with mass flux as a parameter. Figure 10 shows the two regions separated by a transition zone that depends on the mass flux. In the high heat flux region, the effects of L and D are significant. This region may be seen as the entrance region where the flow is still developing.
Beyond the entrance region effect, CHF may be treated as a local phenomenon. Groeneveld et al. (1995) compared the data from various sources and presented the diameter effect in a plot. Each point on the plot represents a data set from literature. The following equation summarizes this effect.
n
mm
mmDCHF
CHF
=
8in
8 (2)
The data sets were correlated well with a value of n = –1/2 for tubes below 8 mm
diameter, while n = –1/3 fitted the data better for tubes above 8 mm diameter. 3.1.4 Effect of Channel Orientation The channel orientation plays a role only when the flow rates are small. Celata and Mariani (1999) propose a criterion based on the comparison of the buoyancy to inertia forces. They used a modified Froude number, given by the following equation.
2/1cosFr
−=
L
GLL gD
m
ρρρρ
φ& (3)
where Fr – Froude number, m& - mass flux, kg/m2s, φ - angle of inclination of the tube with horizontal, Lρ , Gρ - liquid and vapor density, kg/m3, g – acceleration due to gravity, m2/s, and D – tube diameter, m.
The effects due to orientation and stratification disappear for the modified Froude number greater than 5-7. Although high mass fluxes are often employed in the nuclear applications, the mass fluxes may be quite small in some of the new application areas, such as electronic cooling. In such applications, the orientation effects may become significant. In terms of the parametric trends at low mass fluxes, the CHF is highest for the vertical upflow, lowest for the vertical downflow, and intermediate for the horizontal case in the subcooled region.
Mirshak and Towell (1961) found that the CHF in vertical upflow increased with subcooling, while it had very little effect in downflow at low mass velocities. Similar
218 S. G. KANDLIKAR
Figure 10 High and low heat flux regions defined by Nariai and Inasaka (1992). observations were made by Papell et al. (1966) based on their experimental study with liquid nitrogen in a 12.5 mm diameter tube. In certain cases at low mass velocities, the CHF was reduced to a very low value. It clearly demonstrates the role that buoyancy plays in arriving at the CHF condition. It may also be noted that none of the existing models on CHF explicitly account for the buoyancy effect in their formulation. 3.1.5 Additional important variables that need to be investigated The similarity between the CHF in subcooled flow boiling and in pool boiling is quite remarkable. Specifically, the following observations can be made: a) The weak influence of pressure on the CHF is identical in flow boiling CHF and pool
boiling CHF (see Figs. 1 and 2).
b) The influence of subcooling on the CHF is very similar in the two cases (see Figs. 3 and 4).
c) Orientation has a definite effect on CHF in pool boiling, a vertical plate has a lower CHF than a horizontal plate. In flow boiling, the effect is complicated due to flow direction and the presence of inertia forces which affect the bubble removal. At low
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 219
mass fluxes, the vertical upflow has a higher CHF, while the vertical downflow has a lower CHF compared to the horizontal flow case.
From the above comparison, it can be seen that the essential characteristics of the pool boiling CHF are retained in the flow boiling CHF as well, especially at low mass fluxes. With this in mind, the following three important parameters, which have been long recognized to influence the pool boiling CHF, are recommended for further investigation.
1. Effect of Contact Angle
2. Effect of Surface Roughness
3. Effect of Surface Tension
Kandlikar (2000) summarizes these effects on pool boiling CHF. Figure 11 shows the variation of CHF with contact angle as reported by Dhir and Liaw (1989). As the contact angle increases, the CHF decreases. In fact, according to Gaertner (1963), it approaches a dangerously low value for contact angles above 130 degrees. It is therefore expected that the variation in contact angle will have a significant influence on the flow boiling CHF as well. Effects of contact angle on CHF in flow boiling have not been investigated in the literature. This is an area where further research is warranted.
Surface roughness affects CHF in two ways. A very large roughness structure causes changes in the liquid flow over the heater surface. The apparent effect of such a structure is similar to an increase in mass flux or the presence of inserts. The presence of large roughness structures therefore results in an improvement in CHF.
Haramura (1999) presents a detailed discussion on the influence of surface roughness and surface tension in pool boiling CHF. The influence of surface roughness on nucleate boiling heat transfer and CHF in pool boiling provides some insight into the CHF mechanism of subcooled flow boiling. As Ramilison and Lienhard (1987) and Haramura (1991) report, increasing the surface roughness from a mirror finish to that obtained with a #80 emery paper resulted in a 25-35% improvement in CHF. However, since the effect of nucleation site density or the surface structure was not reported in these studies, the mechanism for this enhancement is not clearly understood.
Effect of surface roughness on CHF for vertical downward annular flow was studied by Durant and Mirshak (1960). When the roughness induced friction factor was changed by a factor of 2.9 over a smooth tube of the same dimensions, CHF increased by 100%. This effect was believed to be due to the increased turbulence caused by the roughness structures.
A number of studies conducted by previous researchers on roughness effect on CHF indicate the enhancement to be due to the increased turbulence at the wall. Merely changing the roughness using simple polishing techniques does not change the nucleation characteristics as was observed by Kandlikar and Spiesman (1997). It is therefore recommended that a porous structure, or other structured surface, such as Thermoexcel-E or Gewa-T, be employed in flow boiling to distinguish the surfaces from the viewpoint of nucleation characteristics. Yilmaz and Westwater (1981) report
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Figure 11 Effect of contact angle on CHF in pool boiling, experimental data of Liaw and Dhir (1986), water on vertical plate, 1 atm pressure. significant enhancement in CHF for such structured surfaces in pool boiling; these surfaces may possess potential for CHF enhancement in flow boiling as well.
Avedisian and Koplik (1987) studied the Leidenfrost phenomenon for methanol droplet falling on a porous hot surface. They obtained dramatic improvements in the Leidenfrost temperature, up to 620 K, with the porous surface. The improved wetting characteristics of the surface was responsible for the continuation of nucleate boiling mechanism at such high wall superheat conditions (saturation temperature of methanol was 338 K). The Leidenfrost temperatures measured by Avedisian and Koplik for the plain surface, and surfaces with porosities of 10% and 25% were 443 K, 570 K and 645 K respectively. For the surface with 40% porosity, the Leidenfrost temperature could not be reached due to the system limitations.
4. MODELING OF CHF IN SUBCOOLED POOL BOILING The size of the bubbles over a heated surface decreases as the subcooling increases. In their photographic study, Mattson et al. (1973) show that the bubble population in the vicinity of the heater surface and the bubble size both decrease as the subcooling increases. It therefore seems that, at a higher subcooling at least, the bubble crowding or liquid starvation to the heated surface may not be valid mechanisms leading to CHF condition. 4.1 Photographic Observations
Earlier studies by Gunther (1951) and Mattson et al. (1973) provide useful insights
into the mechanism leading to the departure from nucleate boiling. Although these
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 221
studies are over 25-50 years old, they are still one of the best resources available in developing our understanding of the CHF phenomenon.
Gunther (1951) obtained high speed photographs at 20,000 frames per second and noted that the bubbles became smaller as the subcooling increased. Eventually, with an increase in heat flux, a local vapor film was formed on the heater surface leading to the CHF condition. Mattson et al. focused their study to determine whether the boundary layer separation was the cause for the transition to the CHF condition. They noted that “There were no macroscopic flow pattern changes which could be characterized as abrupt or violent, and there were no oscillations in (a) bubble flow trajectories above the DNB location, (b) slope of the bubble boundary layer near the DNB location, and (c) velocity and trajectory of the vapor. None of these changes were observed.” In light of these observations, it may be concluded that CHF condition is a local phenomenon initiated by conditions existing in the immediate vicinity of the heater surface.
A number of studies have been conducted to obtain photographic evidence at the CHF location. Tippets (1962) obtained pictures at a frame rate of 4300 frames per second in both subcooled and low quality regions. He observed vapor streams coming from the edges of a heater ribbon close to the CHF location. Hosler (1965), Kirby et al. (1965), and Tong et al. (1966) conducted photographic studies near the CHF condition. Hosler observed vapor patches developing on the heater surface just prior to CHF, Kirby et al. observed that at high subcoolings and high heat fluxes, bubbles coalesced and slid along the heater surface. However, they also confirm Gunther’s (1951) observation that there were no noticeable changes in the flow pattern at the CHF location. Tong (1972) measured temperature along the length of the heated surface in the flow direction and noted temperature fluctuations in the wall near the CHF location.
The photographic studies carried out by Chandra and Avedisian (1991, 1992) on a droplet impinging on a hot surface reveal interesting information regarding the initiation of the CHF condition. Although the liquid droplet is spreading on the heater surface, the rapid evaporation at the edges causes the edges to curl back with a significant increase in the contact angle. This effect increases with increasing wall temperatures. The absence of any vapor plumes near the CHF suggests that this phenomenon is highly localized at the solid-liquid-vapor contact line and is dictated by the movement of the contact line and the spreading of a vapor film as postulated by Kandlikar (2000). 4.2 Theoretical Models
Celata (1999) summarizes the previous models in the following five categories.
1. Boundary Layer Ejection Model
2. Critical Enthalpy in the Bubble Layer Model
3. Liquid Flow Blockage Model
4. Vapor Removal Limit and Near-wall Bubble Crowding Model, and
5. Liquid Sublayer Dryout Model
222 S. G. KANDLIKAR
Boundary Layer Ejection Model. This model was originally proposed by Kutatleadze and Leont’ev (1966). The boiling mechanism is compared with the injection of a gas stream into the liquid flow through a permeable plate. The ejection of bubbles into the mainstream is postulated to be the cause of the boundary layer separation at the heater surface. However, the photographic study conducted by Mattson et al. (1973) does not show any abrupt changes in the macroscopic structure of the flow near the CHF location. The high velocity vapor ejection from the heater surface into the flow was also not observed.
Critical Enthalpy In The Bubble Layer Model. This model was proposed by Tong et al. (1966). They assume that a layer of small bubbles flowing adjacent to the heater surface traps the liquid between the bubble layer and the heated surface. This bubble layer separates the trapped superheated liquid layer from the mainstream. They postulated that the CHF condition is reached when this superheated liquid layer attains a certain limiting enthalpy. This model does not provide a clear explanation of the CHF phenomenon other than stating the existence of a critical liquid enthalpy in the superheated liquid layer. Fiori and Bergles (1970) suggest that, based on their observations, the CHF condition results from a periodic wall temperature rise followed by a disruption of the liquid film caused by nucleate boiling. Kirby et al. (1965) observed such wall temperature behavior near the CHF location; however, the actual CHF mechanism is not clearly described by this model.
Liquid Flow Blockage Model. Bergel’son (1980) proposed this model based on the assumption that the flow of the liquid toward the heated surface is blocked by the outflow of vapor from the heater surface. This behavior may be feasible under very low mass flux conditions where the liquid and vapor flow structure is similar to that in the case of pool boiling. However, the vapor flow away from the wall is not seen to be a limiting factor in subcooled flow boiling. Due to the inadequate evidence supporting this mechanism, this model is not being pursued by other researchers.
Vapor Removal Limit And Near-Wall Bubble Crowding Model. This model is based on the limit of the turbulent interchange between the bubbly layer and the bulk of the liquid, and the crowding of the bubbles preventing the liquid access to the heated wall (Hebel et al., 1981).
Weisman and Pei (1983) consider the existence of a bubbly layer adjacent to the wall at subcooled or low quality conditions. Although their model assumes the existence of a bubbly layer, the enthalpy transport from this bubbly layer to the bulk flow is considered as the limiting factor leading to the CHF condition. They consider the CHF to be a local phenomenon. The liquid region in the immediate vicinity of the heater fills with bubbles building a bubbly layer. In this region, the turbulent eddy size is insufficient to transport the bubbles away from the heater surface. At the CHF location, this layer is assumed to be at its maximum thickness. It is postulated that the CHF condition occurs when the volume fraction of vapor in the bubbly layer just exceeds the critical volume fraction at which an array of ellipsoidal bubbles can be maintained without significant contact between the bubbles. Weisman and Pei used the homogeneous flow model in the bubbly layer. The resulting model has three adjustable empirical constants that are evaluated from the experimental data. This model includes the two-phase considerations that are readily extendable to the saturated flow conditions as well.
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 223
Liquid Sublayer Dryout Model. Katto and Yokoya (1968) proposed a preliminary model describing the macrolayer dryout as the mechanism leading to CHF in pool boiling. Later, Haramura and Katto (1983) completed the model development by introducing the mechanism for macrolayer formation in both pool and flow boiling. Further description of the pool boiling CHF model is given by Haramura (1999). Figure 12 shows a schematic of the macrolayer model. According to this model, as a result of the Helmholtz instability, the columnar structure of vapor stems collapses with a vapor film blanketing a thin liquid film on the heater surface. Numerous vapor stems emerge on the heater surface thorough this liquid film. Under flow conditions, both the liquid sublayer and the vapor film move in the flow direction. Entrainment and deposition phenomena are ignored because they are presumed to be scarce. Under these conditions, liquid is fed into the film from the upstream end, while it depletes along the flow direction due to evaporation. CHF condition is reached when the heat supplied by the heater surface provides the necessary latent heat required to completely evaporate the liquid entering the film. Katto (1990a, b) provided a detailed description of the model based on the macrolayer evaporation. Their model uses several empirical constants in determining the liquid film thickness, the liquid film flow rate, and temperature of the liquid entering into the sublayer.
Lee and Mudawar (1988) considered the effect of velocity in the subcooled flow in terms of stretching the large bubble in Haramura and Katto (1983) model to a vapor blanket of length equal to the critical Helmholtz wavelength, as shown in Fig. 13. The vapor blanket separates the bulk flow from a thin sublayer trapped between the vapor blanket and the heated surface. The bubble moves at a velocity ub while the sublayer moves at a velocity of um. The sublayer is depleted if the rate of evaporation from the sublayer exceeds the rate at which the sublayer is replenished due to the difference in velocities of the sublayer and the vapor blanket. The sublayer mass velocity, its thickness, and the vapor blanket length were calculated by considering the buoyancy and drag forces acting on the vapor blanket. Their modeling resulted in a correlation scheme with three empirical constants, which were determined from a large set of experimental data.
Celata et al. (1994) eliminated the empirical constants in the Katto, and Lee and Mudawar models by using the homogeneous flow model and by introducing appropriate correlations from available literature to calculate the sublayer thickness, flow rate, enthalpies, and vapor blanket length. However, the basic features of the model are similar to those proposed by Lee and Mudawar (1988).
224 S. G. KANDLIKAR
Figure 12 Macrolayer dryout model schematic proposed by Haramura and Katto (1983). Figure 13 Schematic representation of the onset of the subclayer dryout leading to CHF in subcooled flow boiling, Lee and Mudawar (1988). 4.3 Comparison of Correlations
Inasaka and Nariai (1996) compared the correlations by Gunther (1951 ), Knoebel et al. (1993), modified Tong (1975) correlation, Weisman and Pei (1983), Celata et al. (1994), and Katto (1991). The Celata correlation provided the best predictions, while the Tong, and Weisman and Pei correlations yielded reasonably good agreement with the data. From a predictive standpoint, the Celata correlation is perhaps the best among the available correlations.
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 225
Due to the lack of a reliable mechanistic model, it is necessary to rely on the experimental CHF data specific to a system being considered. Tong and Tang (1997) provide a good collection of available correlations from various sources for specific flow and fluid conditions. 4.4 Comments on current models for describing CHF mechanism in subcooled flow boiling
The photographic studies conducted by Gunther (1951), Mattson et al. (1973) and others as described earlier are perhaps the best direct evidence of the conditions existing at the heated wall near the CHF condition. The discrete nature of bubbles seen in Gunther’s photographs just prior to CHF confirm that CHF is a local phenomenon and the conditions existing adjacent to the heater surface are most critical. The absence of any severe changes in the flow following CHF, as evidenced by Mattson et al.’s photographs, confirms the existence of a thin vapor film covering the heater surface. The temperature excursion experienced by the heater surface cannot be overlooked in describing the CHF phenomenon.
Although the macrolayer evaporation models utilizing either empirical constants (Katto, 1990a, 1990b, 1992, or Lee and Mudawar, 1988) or empirical correlations (Celata et al., 1994) provide satisfactory modeling capabilities, it is far from clear how the CHF is actually initiated. The phenomenon is highly localized and occurs very rapidly. Photographing the heater surface is complicated by the presence of nucleating bubbles, the two-phase flow, and the rapidly moving interface.
The current state of available information therefore indicates that the CHF mechanism is still not completely understood. A better model description will be arrived at after gaining further insight into the leading causes of the vapor blanketing of a heater surface.
5. AUGMENTATION OF CHF IN SUBCOOLED FLOW BOILING Detailed surveys of the augmentation techniques and devices are provided by Boyd (1985) and Celata (1999). The augmentation techniques can be classified as: Passive techniques
• Twisted tapes and swirl flow devices
• Helically coiled tubes
• Surface roughness
• Extended surfaces
Active techniques
• Vibrations
226 S. G. KANDLIKAR
• Electric field effect
• Gas injection
Only the first three passive techniques will be considered in this review. 5.1 Twisted Tapes inserts and Swirl Flow Devies Twisted tapes have been studied by Gambill and Greene (1958), Gambill et al. (1961), Nariai et al. (1991), Cardella et al. (1992), Doeffer et al. (1996), Doeffer and Groeneveld et al. (1999), and Doeffer et al. (2000). These studies show that, for almost all cases, CHF increases with twisted tape inserts. The enhancement is higher as the spacing becomes shorter, or in the case of helically corrugated tubes, as the obstruction area increases. The enhancement increases with the twist ratio, reaching a threefold value over a plain tube for the largest twist ratio and largest mass flux tested. Similar enhancements were observed for helically coiled tubes by Jensen and Bergles (1981), and Berthoud and Jayanti (1990). Sturgis and Mudawar (1999) conducted a study to understand the mechanism of CHF enhancement under the influence of acceleration caused by the curvature. Curved and straight channels, 5x2.5 mm in cross-section, and curved with a 32.3 mm radius, were tested. The outer wall of the curved channel, 5 mm wide, was heated with a curved heater. Sturgis and Mudawar found that the vapor removal process was affected by the presence of the induced buoyancy. Large vapor bubbles were torn away from the heater surface in the curved channel. The effect was seen through the changes in the wetting front of the liquid rewetting the heater surface, immediately following the passage of a large vapor bubble. For all tests conducted with the curved channel, an enhancement in CHF over straight channel was noted. The following mechanisms were proposed as being responsible for the enhancement. • Better vapor removal by pinching the bubbles off from the heated outer wall,
• Buoyancy force providing better rewetting characteristics, and
• Increase in the subcooling due to increased pressure at the outer wall of the curved channel.
Figure 14 shows the three mechanisms suggested by Sturgis and Mudawar. They
obtained clear pictures of the side view of the flow channel supporting the above mechanisms.
Twisted tape inserts and swirl flow devices are the leading techniques for enhancing the CHF in flow boiling systems. The buoyancy force provided by the centrifugal acceleration is seen as the key factor responsible for the enhancement.
5.2 Suggestions for Future Research on Subcooled Flow Boiling CHF
The current efforts by researchers on modeling CHF in subcooled flow boiling have been largely focused on the flow in plain tubes. As the new technologies emerge, the
CRITICAL HEAT FLUX IN SUBCOOLED FLOW BOILING 227
(a) (b) (c) Figure 14 Heat transfer mechanism suggested by Sturgis and Mudawar (1999) showing (a) the inward motion of the bubble due to buoyancy forces, (b) increased pressure on liquid-vapor interface at wetting fronts, and (c) increased subcooling at the wall. system configuration could change to miniaturized passages. The bubble behavior in small passages, such as microchannels is not well understood.
Another area that merits further study is the effect of contact angle, surface tension, and surface characteristics. All these parameters are known to influence the CHF in pool boiling. There are no systematic studies available in literature that describe the effects of these parameters on subcooled flow boiling CHF.
The augmentation of CHF is an important area in improving the high-flux device capabilities. The following two types of surfaces have been used extensively in the pool/flow boiling enhancement, but relatively little attention has been given to them from the CHF standpoint.
• Microfin surfaces
• Structured (Gewa-T and Thermoexcel-E type) and porous surfaces
Since nucleate boiling is the underlying mechanism leading to the CHF condition, significant enhancements are expected with porous and microfin surfaces in flow boiling application as well. Experiments are needed to confirm this so that the current CHF limit in many high-flux systems could be extended considerably.
6. NOMENCLATURE D tube diameter, m Fr Froude number g acceleration due to gravity, m2/s m& mass flux, kg/m2s
228 S. G. KANDLIKAR
q& heat flux, W/m2 u flow velocity, m/s
subT∆ liquid subcooling, K φ angle of inclination of the tube with horizontal
Lρ , Gρ liquid and vapor density, kg/m3
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