Topics on Boiling

Tomohiko Yamaguchi , ... Mamoru Ozawa , in Boiling, 2017

6.9.1 Introduction

Boiling heat transfer enhancement leads to two important advantages. One is a decrease in the temperature difference in heat transfer for a given heat flux, and the other is an increase in the heat flux for a given temperature difference. The former advantage is efficient for cooling of electric equipment to decrease the operating temperature, and is also efficient for heat recovery by using a heat pump system to raise the evaporative temperature. The latter advantage is efficient for the compactness of heat exchanger.

As is well known, boiling heat transfer enhancement is caused by an increase in active nucleation site density. It is required for the increase in nucleation sites to decrease the wall superheat for vapor bubble generation. The wall superheat strongly depends on the heat transfer surface characteristics, such as surface roughness, cavities, microporous structure, wettability, and so on.

The simplest way is to increase the surface roughness. The effect of surface roughness was investigated in detail by Gorenflo et al., and the heat transfer enhancement factor due to the surface roughness, F WR, is expressed by the following equation independent of pressure and heat flux as shown in VDI Heat Atlas [1].

(6.9.1) F WR = ( R a R a0 ) 0.133 ,

where R a is the arithmetical mean roughness defined in DIN4768 and subscript 0 indicates a reference value.

Cavities, especially re-entrant cavities are considered to be effective in keeping nucleation sites active. Some methods have been developed on the commercial scale. Examples are the GEWA tubes produced by Wieland Werke AG and Thermoexel tubes by Hitachi Cable, Ltd, with re-entrant cavities manufactured by a mechanical process, and High Flux tubes produced by Union Carbide with a porous structure made by sintering and thermal spraying. A good overview of heat transfer enhancement techniques is given by Webb [2]. Nishikawa et al. [3] studied boiling heat transfer characteristics on a porous layer made by sintering metal particles in detail, and it was shown that an optimum ratio of the coating thickness to the particle diameter existed. Generally, such heat transfer enhancement of the surface is very effective for bubble nucleation at low heat flux; however, the heat transfer enhancement becomes weak at high heat flux due to a partial dry-out in cavities.

With the advances in manufacturing techniques, mechanical microstructures have been applied for boiling heat transfer enhancement. Wei and Honda [4] evaluated pool boiling heat transfer characteristics on a silicon chip with micro-pin-fins to clarify the combined effects of fin thickness and fin height on the boiling heat transfer. Micro-pin-fins with fin thickness of 30–50   μm and a fin height of 60–270   mm were fabricated on a silicon chip by a dry etching process. Degassed and gas-dissolved FC-72 was used as the working fluid. They reported that the micro-pin-finned chips produced a considerable heat transfer enhancement in nucleate boiling and an increase in the critical heat flux (CHF) as compared to the smooth chip.

Another method of boiling heat transfer enhancement that is different from the manufacture of the surface configuration is to control the wettability. Takata et al. [5] examined a TiO2-coated super-hydrophilic surface with dipping or sputtering processes. They reported that the TiO2-sputtered surface produced excellent heat-transfer characteristics in the nucleate boiling region and higher CHF than the non-coated surface.

The required points for boiling heat transfer are higher heat transfer coefficient, smaller wall superheat for the onset of nucleate boiling, and higher CHF. In this section, boiling heat transfer enhancement by microporous surface manufactured by thermal spray coating is introduced in detail.

As described above, boiling heat transfer enhancement can be obtained by increasing active nucleation site density. It is expected that a heat-transfer surface with the microporous structure will decrease vapor bubble departure diameters. Small vapor bubbles will be generated from the boiling heat transfer enhanced surface. Since the ratio of the interface area to the volume is smaller for smaller diameter, the gravity effect on the bubble behavior will decrease with decreasing bubble diameter. Conversely, high-performance cooling systems with boiling heat transfer are strongly required for space structures. Therefore, in order to clarify the gravity effect on pool boiling heat transfer, especially to clarify the difference in boiling behaviors between a smooth and a heat-transfer enhanced surface, pool boiling experiments for a horizontal cylinder were carried out. The results of the microgravity experiments are shown in Section 6.9.3.

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CHF—Transition Boiling

Hiroto Sakashita , ... Shinichi Morooka , in Boiling, 2017

3.7.5 Conclusion

Transition boiling heat transfer was examined by deriving the correlation and model, the following conclusions were obtained.

1.

As correlation of transition boiling heat transfer,

Γ = 1.000 − 0.9120 θ − 0.1343 θ 2

was presented from experimental results for water, R-113 and LN2. Here, heat flux in transition boiling was given by q tb=q CHF Γ+q MHF (1−Γ). θ is the non-dimensional temperature: θ=(T w−T CHF)/(T MHF−T CHF). Transition boiling heat transfer was well reproduced by the present correlation for some clean metal surfaces and several liquids (namely, water, R-113, and liquefied nitrogen).

2.

The prediction by the present model, taken the dependence on wall superheat of liquid–solid contact time and area into account using the present correlation and nucleate boiling heat transfer during the wet period, agreed well with the present experimental data for water in the transition boiling region, both qualitatively and quantitatively.

3.

A simulation of rewetting was performed using the present transition boiling correlation and model; the experimental cooling curves during rewetting were well reproduced by the transient heat conduction model using the present correlation of transition boiling heat transfer and the present-liquid solid contact model.

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Advances in Heat Transfer

Sujoy Kumar Saha , ... Satish G. Kandlikar , in Advances in Heat Transfer, 2011

II.4.1 Introduction

Boiling heat transfer provides an excellent mechanism for heat removal from a heated surface. High heat transfer rates are achieved through the phase change process that is aided by the localized motion of the liquid–vapor interface. This efficient boiling mechanism is a result of the liquid being able to convectively transport heat away from the heater surface, and utilize it in generating vapor that removes large amounts of heat from the liquid and provides a driving force for the localized liquid motion.

However, at higher heat transfer rates, the liquid is unable to remain in contact with the surface, thereby reducing the ability to remove heat efficiently. This condition is called critical heat flux (CHF) and may be defined as the maximum heat flux that can be transferred from a heater surface at the termination of the nucleate boiling process.

CHF in flow boiling systems is influenced by additional factors resulting from the forces caused by the bulk fluid motion. These forces become dominant at higher flow rates, thereby reducing the influence of gravitational forces. This feature makes flow boiling an attractive option in microgravity application.

Flow boiling in microchannels faces additional challenges that have a direct bearing on CHF. The small channel diameter makes the viscous and surface tension forces more important compared to the inertia force. Localized nucleation sometimes causes a very rapid bubble growth causing the flow reversal at the trailing interface of a bubble. This leads to flow instability and the flow temporarily slows down, or even reverses its direction, and exposes the regions of the heater surface to be covered by vapor for a long duration depending on the severity of the instability. This further causes the thin liquid layer underneath an expanding bubble to evaporate and bring the vapor in contact with the heater surface over an extended period of time, again depending on the severity of the instability. These events cause a dramatic reduction in the CHF. Additionally, multiple parallel microchannels experience flow maldistribution as well as parallel channel instabilities, which cause further deterioration in the CHF. It is therefore important to understand the particular events and mechanisms leading to the CHF condition. The rest of this chapter deals with a detailed description of the CHF mechanism, followed by a listing of correlations that are available to the heat exchanger designers.

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INVESTIGATION OF NUCLEATE BOILING HEAT TRANSFER ON SINTERED POROUS SURFACES FOR A BINARY CYCLE EXCHANGER

Zhai Guili , ... Associate Professor, in Energy Developments: New Forms, Renewables, Conservation, 1984

INTRODUCTION

Enhancement of boiling heat transfer has been spurred on in a number of industrial divisions such as refrigeration and chemical and in the development of low enthalpy energy sources. Many patents and papers on this enhancement technique have appeared since the sixties. The use of various porous surfaces has proved one of the best ways to achieve enhancement. There are a variety of methods to produce porous surfaces, but only the sintering method and mechanical fabrication method have been put into commercial use.

To estimate the efficiency of heat transfer, to produce optimal design, and to improve the performance of porous surfaces, investigators have given different explanations of boiling heat transfer mechanism on porous surfaces. It is known that the mechanism of boiling heat transfer on a plain surface has not been clarified adequately. Owing to the complexity of heat, mass, momentum transport in porous layer, the proposed explanations reveal only some physical features of the phenomenon to a certain extent. Their correlations cannot be satisfactorily applied to engineering practice and the optimal design method remains to be sought.

Based on the results obtained by other researchers in the studies of boiling heat transfer, heat and mass transfer in porous bodies, and two-phase flow in a capacity tube, the authors suggest a modified comprehensive model of boiling heat transfer on sintered porous surfaces.

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Critical Heat Flux for Boiling in Microchannels

P.K. Das , A.K. Das , in Microchannel Phase Change Transport Phenomena, 2016

Abstract

During boiling heat transfer, the unique phenomenon of critical heat flux (CHF) is very complex and is detrimental for most of the practical applications. Though CHF during flow boiling through microchannels is a well-researched topic, there are many controversial issues and competing physical models. On the other hand, CHF during flow boiling through microchannels is a topic of recent origin and is understood only poorly. The present chapter reviews the major experimental investigations on CHF in microchannels and brings out the effect of important parameters on this phenomenon. A large number of correlations have been used for the prediction of CHF through microchannels. Some of them are modification of the existing correlations while the others have been developed afresh. An overview of the key correlations has been provided in this chapter in a tabular form. Lately, some efforts have also been made to develop mechanistic models for CHF in microchannels. The CHF has been associated with the flow of elongated bubbles or annular flow. Local dry patch formation has also been thought of a probable reason for CHF. Finally, the gray areas of this topic have been highlighted and the specific research needs have been suggested.

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Volume 3

Junghoon Yeom , Mark A. Shannon , in Comprehensive Microsystems, 2008

3.16.3.2.3.(ii) Two-phase cooling

Flow boiling heat transfer and two-phase hydrodynamics have been heavily studied and are currently investigated by many researchers. The Mudawar group experimentally determined hydrodynamic and heat transfer correlations in two-phase μHEX and predicted pressure drops and CHFs for various geometries and applications ( Lee and Mudawar 2005a, b, Qu and Mudawar 2002, 2003a, b, c, 2004). Experiments in micromachined silicon channels with a range of 27–171   μm in hydraulic diameter and with varying surface roughness were conducted to investigate the boiling process and two-phase flow behavior such as bubble nucleation, flow patterns, and transient pressure fluctuations (Zhang et al. 2005a). Faulkner et al. at MicroEnergy Technologies reported a prototype of a 1000   W   cm−2 cooling system for microwave electronics, employing flow boiling heat transfer in a parallel μHEX. Heat fluxes up to 125   W   cm−2 for saturated boiling and 280   W   cm−2 for subcooled (25   °C) boiling were removed with water as a coolant and a flow rate of 0.75   l   min−1 (Faulkner et al. 2003). Researchers at Intel studied the effects of nonuniform heating conditions on the thermal performance of the two-phase μHEX to address cooling of local hot spots and observed temperature fluctuation as high as 30   °C (Prasher et al. 2005).

Thin-film and flexible microchannel heat exchangers were developed by the Shannon group (Pourmohamadian et al. 2004, Selby et al. 2001). These heat exchangers, shown in Figure 22 , are made from heat-sealable Kapton (special polyimide films from Dupont) and range from a thickness of 200 to 250   μm. The outer panels, or caps, in the figure are 50   μm thick. Even with a relatively low thermal conductivity (∼   1   W   m−1  °C−1) of the Kapton, the thermal resistance is still small (order 5   ×   10−5  °C   W−1). When the four panels shown in Figure 22(a), which have channels cut for the heat exchanger, manifold, and caps are bonded and assembled into a single unit, the result is a flexible microchannel heat exchanger that can withstand pressures over 18   atm. The maximum pressure is determined by delamination and/or rupture at the critical point shown in Figure 22(b). Under pressure, the polymer channels inflate, increasing the effective cross-sectional area. These flexible heat exchangers were developed for two-phase heat transfer, specifically for R-134a (∼   13   atm absolute pressure at room temperature). Applications for these types of heat exchangers include insertion into cooling garments for people working in hot environments, and for providing large area, light weight, thin-film heat exchangers for electronics.

Figure 22. (a) Four polyimide panels comprising the flexible microheat exchangers. (b) Cross-sectional view of the four bonded layers, showing 75 by 750   μm channel. (Permission of the Society of Manufacturing Engineers, Copyright 2001, from the NAMRC Conference Proceedings) (Source: Selby J C, Philpott M L, Shannon M A 2001 Fabrication of mesoscopic, flexible, high pressure, microchannel heat exchangers (MHEx). Trans. NAMRI/SME, XXIX, pp. 469–76).

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THERMOCAPILLARY DRIVEN FLOW IN THE MACROLAYER FOR NUCLEATE BOILING AT HIGH HEAT FLUXES

F.M. WANG , CHIN. PAN , in Transport Phenomena in Heat and Mass Transfer, 1992

ABSTRACT

Nucleate boiling heat transfer at high heat fluxes is characterized by the existence of a macrolayer between the heating surface and hovering bubble with vapor stems penetrating the layer nourishing vapor to the growing bubble. Heat transfer from the heating surface results in temperature variations along the stem–liquid and bubble–liquid interfaces which lead to the surface tension gradients along these interfaces. As a result, thermocapillary driven flow may be induced in the macrolayer. This paper develops a heat and mass transfer model in the macrolayer with consideration of surface tension gradient and evaporation at the vapor–liquid interfaces. The mathematical model thus developed is then solved numerically by a finite difference scheme. It is concluded that the thermocapillary driven flow in conjunction with the evaporation at the stem-liquid and bubble–liquid interfaces is the major heat transfer mechanism for nucleate boiling at high heat fluxes. Several circulating vortexes are generated in the macrolayer. The flow carries energy from the heating surface to the stem–liquid interface as well as the bubble–liquid interface, where the liquid is cooled by evaporation and subsequently flows back to the heating surfaces. The average wall superheat at a given heat flux predicted by the model is well below that evaluated by the pure conduction model and agrees reasonably well with experimental data. It is also found that the major part (about 98%) of the energy from the heating surface is transported by evaporation at the bubble–liquid interface and only a small percentage (about 2%) is by the evaporation at the stem–liquid interface.

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A Study of Micro-scale Boiling by Infrared Techniques

Gad Hetsroni , Albert Mosyak , in Advances in Heat Transfer, 2013

6.1 Properties of surfactants

In boiling heat transfer, it is usually desirable to transfer the largest possible heat flux with the smallest possible temperature difference between the heating surface and the boiling liquid, and to maximize the CHF. Various means have been developed with this aim in mind, including the use of additives to modify the liquid properties. The process of nucleate boiling is the total sum of the processes of bubble initiation, growth, and departure. Though these individual processes have been studied much, it is difficult to predict the effect of the physical properties of surface active agents (surfactants) on the main boiling characteristics, such as the relationship between the heat flux and the temperature difference.

In contrast to the momentum and scalar transfer in turbulent pipe flow with surfactants, which shows a reduction in the friction factor and the heat transfer coefficient, the study of surfactant solutions in the pool boiling shows a significant enhancement of the boiling mechanism. The role of surface-active solutes was explored for 0.1–1.0% aqueous solutions of a commercial surfactant. They found that the boiling curves (q vs. Δt) were shifted laterally in varying degrees, such that heat transfer was higher than that for pure water (q is the heat flux, Δt  = t s–t sat is the superheat, t s is the average surface temperature of the heater, t sat is the saturation temperature of the solution). This is an important fact because, if proved to be applicable under industrial boiling conditions, it may lead to a considerable increase in the power level of all boilers without any increase in size or operating temperature. One interesting field of application of boiling and evaporation is in desalination of seawater, which is becoming essential in some arid regions. It was already shown by Sephton [91] that addition of small amounts of surfactants to seawater can substantially enhance the boiling process and reduce the price of the desalinated water to an acceptable level. At that time, the research was discontinued because the environmental impact of surfactants was not known.

Since the concentrations are usually low, addition of the surfactant to water causes no significant change in the saturation temperature and the majority of other physical properties, except for the surface tension and, in some cases, the viscosity. There have been a large number of studies to determine the boiling enhancement mechanism caused by addition of surfactants to water. Frost and Kippenhan [92] investigated boiling of water with varying concentrations of surfactant "Ultra Wet 60   L." They found an increase in heat transfer and concluded that it resulted from the reduced surface tension. Heat transfer in nucleate pool boiling of dilute aqueous polymer solutions was measured by Kotchaphakdee and Williams [93] and compared with results for pure water. Photographs showed distinct differences in bubble size and dynamics between polymeric and nonpolymeric liquids. Gannett and Williams [94] concluded that surface tension was not relevant in explaining the enhancement effect and reported that viscosity could be a generally successful correlating parameter. Nucleate boiling curves for aqueous solutions of drag-reducing polymers have been measured experimentally by Shah and Darby [95] and by Paul and Abdel-Khalik [96]. The explanation of observed changes in the boiling curves was based only on how the polymer additives changed the solution viscosity. Polymer type, concentration, and molecular weight were important only insofar as they affect the solution viscosity. Yang and Maa [97] studied pool boiling of dilute surfactant solutions. The surfactants used in this study were sodium lauryl benzene sulfonate and sodium dodecyl sulfate (SDS). Since all experiments were carried out under very low concentrations, it was concluded that these additives had no notable influence over the physical properties of the boiling liquid, except surface tension, which was significantly reduced. This study showed that the surface tension of the boiling liquid had significant influence on the boiling heat transfer coefficient.

Pool boiling experiments were carried out by Tzan and Yang [98], for relatively wide ranges of surfactant concentration and heat fluxes. The results verify again that a small amount of surface-active additive makes the nucleate boiling heat transfer coefficient of water considerably higher. It was also found that there is an optimum additive concentration for the highest heat flux. Beyond this optimum point, further increase in the concentration of the additive lowers the boiling heat transfer coefficient. Wu et al. [99–101] reported experimental data on the effect of surfactants on nucleate boiling heat transfer in water with nine additives. Anionic, cationic, and nonionic surfactants were studied at concentration up to 400   ppm (parts per million). The enhancement of heat transfer was related to the depression of static surface tension. Boiling heat transfer coefficients were measured by Ammerman and You [102] for an electrically heated platinum wire immersed in saturated water, and in water mixed with three different concentrations of SDS (an anionic surfactant). Their results showed that addition of an anionic surfactant to water caused an increase in the convection component and a corresponding reduction in the latent heat component of the heat flux in the fully developed boiling region. The enhancement of heat transfer at boiling of water, which is caused by the addition of an anionic surfactant, appears to be influenced by this relative change in these heat flux components. The comprehensive reviews on the heat transfer in nucleate pool boiling of aqueous surfactants and polymeric solutions have been published by Kandlikar and Alves [103] and by Wasekar and Manglik [104]. It is shown that surfactant additives at low concentrations can enhance the nucleate boiling heat transfer significantly.

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Instability control of two-phase flow in microchannel heat exchangers

Mengjie Song , ... Yingjie Xu , in Advanced Analytic and Control Techniques for Thermal Systems with Heat Exchangers, 2020

2.1 Flow patterns and instability mechanism

Flow boiling heat transfer and two-phase pressure drop are closely related with the liquid and vapor phase distribution within the microchannels. In flow boiling, the two-phase flow patterns change along the heated surface. Various types of patterns have been identified by different researchers, but the ones most widely described were bubbly flow, plug flow, slug flow, and wavy and annular flow in horizontal tubes [12–14]. It is well known that the heat transfer characteristics of flow boiling are greatly related to the flow patterns. The bubble behaviors in a microchannel during flow boiling were investigated and reported by Yin and Jia [15]. In the inlet region, the flow is single-phase, or some bubbles generate to dispersed bubble flow. With an increase of temperature along the channel, the bubbles continue to grow to the channel size and becomes elongated bubbles. In the outlet region of the microchannel, the continuous elongated bubbles and the neighboring elongated bubbles merged into the annular flow. Also, the flow boiling of HFE-7100 in microchannels was studied by Zaidi et al. [16]. The main flow patterns are concluded, including bubbly, slug, churn, and annular flow. Near the channel inlet, the ONB occurred and then numerous small nucleating bubbles were observed. The small bubbles continue to grow to bigger ones, the size of which is confined by the channel. This is followed by a vapor slug, which was observed near the channel middle. When the vapor slug velocity became higher due to an increase in evaporation rate along the channel, the slug shape was distorted and changed into churn flow. The flow pattern transmissions were classified into five procedures by Kim and Mudawar [17]: buddy flow, slug flow, annular flow, mist flow, and vapor. Based on the heat transfer property, these five procedures were further classified into two types: nucleate boiling dominant heat transfer and convective boiling dominant heat transfer. For the nucleate boiling dominant type, the bubbly and slug flow are the dominant flow patterns, where the heat transfer weakened along the channel due to the reduction of nucleate boiling. However, for the convective boiling dominant type, the annular flow was the dominant flow pattern, and the HTC increases along the channel due to gradual thinning of the annular liquid film.

In microscopic channels, the main reason that causes flow boiling instability is the bubble dynamics that resulted from bubble generation during boiling. With the increase of vapor fraction, different flow patterns occur [18], for example, isolated bubble, elongated bubble, annular flow, and mist flow. Fig. 3 shows the vapor bubble growing and the flow transition. First, the heat transfer results in the bubble nucleation at the channel wall, and then bubbles disperse in the liquid when their size reach the bubble departure diameter [19]. As seen in Fig. 3A and B, the insolated bubbles will merge as bigger ones in the channel, although it also grows at the same time. The bubble continually increases to the channel diameter, increases further in the axial direction, and then quickly transmits to the elongated bubble [20], as shown in Fig. 3C. The continuous supply of heat flux will cause more liquid to evaporate into vapor, which causes two types of phenomenon. One is liquid evaporation, which causes the flow pattern to change to annular flow, where a thin liquid film is adjacent to the wall. The further evaporation will lead to dryout of the thin liquid film, and the channel is occupied by the vapor, resulting in deterioration of heat transfer, as shown in Fig. 3D and E. The other is the growth of bubbles may result in bubble clogging, as shown in Fig. 3F. There will be positive pressure at both of the two sides of the bubble clogging. When the bubble growth stops and loses the force to prevent fluid entering the channel, the fresh liquid reverses to the microchannel, which results in flow oscillation [21].

Fig. 3

Fig. 3. Vapor bubble growing and the flow transition. (A) Isolated bubbles, (B) bubble coalescence, (C) elongated bubble, (D) annular flow pattern, (E) mist flow pattern, and (F) clogging.

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Heat transfer in nuclear thermal hydraulics

P.L. Kirillov , H. Ninokata , in Thermal-Hydraulics of Water Cooled Nuclear Reactors, 2017

7.8.6 Heat transfer in film boiling, and superheated vapor flow in channels

Film boiling heat transfer has been extensively investigated during the last half century. Excellent reviews are found in text books by Tong (1965), Tong and Tang (1997), Collier and Thome (1980), Delhaye et al. (1981), Butterworth and Hewitt (1977), a handbook by Hetsroni (1982), and articles by Ganic and Rohsenov (1977), Mayinger and Langer (1978), Tong (1978), Sergeev (1978, 1987, 2007), Groeneveld and Snoek (1986), Groeneveld (1992), Yadigaroglu and Andreani (1989), Sakurai (1990), Andreani and Yadigaroglu (1989, 1994), and in the proceedings of the 1st International Symposium on Fundamental Aspects of Post-CHF Heat Transfer (1984). A good summary of the literature survey is given in (published in 2001 in the context of the IAEA's Coordinated Research Project on Thermohydraulic Relationships for Advanced Water Cooled Reactors (IAEA TECDOC, 1203, 2001)).

In the context that follows in this section, we discuss on a number of two-phase flow heat transfer regions depicted previously in Fig. 7.54 by region 5—liquid deficient region (degraded heat transfer), region 6—superheated vapor forced convection, region 7—subcooled film boiling ( T f < T S ), region 8—Saturated film boiling T f = T S , and region 9—liquid deficient and heat transfer crisis; in Fig. 7.53 by region 3—dispersed-annular, region 4—mist and region 5—single-phase superheated vapor; and in Fig. 7.52 by region G (liquid deficient) and region H (super heated vapor).

In boiling two-phase flows in a heated channel, a drastic deterioration of heat transfer (heat transfer crisis) may occur, which shows an increase in temperature on the heat-transfer surface, or reduction in the heat flux q. The heat transfer mode between the onset location of the crisis and its downstream region where the flow becomes single-phase superheated vapor flow is called as film boiling. In this regime, at a constant heat flux, an increase in the surface temperatures is observed and the offset of the crisis in the region of low steam quality with increasing q (see Fig. 7.59).

Fig. 7.59. Wall temperature dependence on the vapor quality and heat flux at ρw  =   1400   kg/(m2  s); p  =   9.8   MPa.

The film boiling is characterized by an aggravated mode, temperature fluctuations due to the variable surface contact modes of liquid and vapor. This regime is implemented in the steam generator but is to be avoided in the case of nuclear fuel rod bundle cooling. Nevertheless, some experiments show that a short-term operation of fuel rods in such a regime under certain parameters is possible if the excess temperature of the fuel cladding surface and the amplitude of the oscillations do not exceed permissible limits. From this point of view, perhaps a more accurate calculation of heat transfer is necessary. The temperature jump at a crisis decreases with increasing mass flow rate and pressure, and increases with increasing heat flux. Two-phase flow structure in this region is different depending on the nature of the crisis, i.e., DNB ([A] in Fig. 7.54) or film dry-out ([D] in Fig. 7.54).

If a crisis occurs in the subcooled two-phase flow, or two-phase flow of low steam quality, i.e., due to DNB, the realized two-phase flow mode is called as "inverted annular flow" where the superheated vapor flow flowing along the wall separates the subcooled layer from the wall. The inverse-annular flow regime is preceded by the transition boiling section in the upstream region which is bounded by the DNB point (CHF) and the quench front or the minimum heat flux of the film boiling on the boiling curve.

As described in Section 7.5.4 on the boiling curve in the pool boiling, the location of the minimum film boiling temperature (T MFB) separates the high temperature region of the inefficient film boiling or vapor cooling, from the lower-temperature region of more efficient transition boiling region. Thus it provides a limit to application of the transition boiling and film boiling correlations. T MFB also represents a temperature boundary beyond which surface properties and surface conditions generally do not affect the heat transfer. Wettability or contact angle although important in nucleate and transition boiling, are not applicable in the film boiling regime, and the conduction along the surface becomes less important when nucleate and film boiling no longer occur one-by-one.

It is noted that, while the critical heat flux has been extensively studied and can be predicted fairly well by a variety of correlations, the minimum heat flux under forced convective conditions has undergone less investigation. There is no general consensus on the effect of the various system parameters on T MFB under the conditions but it should be affected by flow, pressure, fluid properties, and heated surface conditions in the same way as in the pool boiling described in Section 7.5.4.

In the "dispersed-annular flow" regime, the crisis is usually associated with the liquid film dry-out on the heated surface. In this case, the heated wall is cooled by the vapor flow, which is superheated while flowing along the channel. In this vapor flow region, liquid droplets exist and gradually evaporate exchanging heat with the superheated vapor.

In general, the dispersed two-phase flow in this zone is in thermally nonequilibrium, and the wall surface temperature is determined by several processes: the convective heat transfer by the vapor flow, radiation, and evaporation of the droplets. The actual flow parameters depend on the evaporation of droplets and heat-transfer area in the vapor flow, whose temperature may exceed the saturation temperature. In simple calculations, thermal equilibrium between liquid and vapor phases is often assumed. There the boundary between this region and a superheated vapor flow region of the channel is considered where the equilibrium steam quality x  =   1.

Depending on the operating conditions and the channel geometry, the flowing vapor in the post-CHF zone may be superheated in the inverse-annular regime where the liquid is separated from the heated surface by the vapor film (downstream of the DNB point and the transition boiling region), or in the dispersed-annular flow regime (downstream of the film dry-out point) where the liquid droplets are distributed in the vapor core flow.

Structure of two-phase flow in the postminimum heat flux region is stable and most of the liquid phase decays into droplets toward the downstream region and the flow becomes dispersed which is a dominant flow regime in the heat transfer crisis. Higher surface temperature in this zone is due to the fact that the superheated vapor is primarily in contact with the wall.

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