BOOKCOMP, Inc. — John Wiley & Sons / Page 633 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 633 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [633], (61) Lines: 2034 to 2055 ——— * 277.04701pt PgVar ——— Normal Page * PgEnds: PageBreak [633], (61) Rothman, L. S., Camy-Peyret, C., Flaud, J M., Gamache, R. R., Goldman, A., Goorvitch, D., Hawkins, R.L., Schroeder, J., Selby, J. E. A., and Wattson, R. B. (2000). HITEMP,the High- Temperature Molecular Spectroscopic Database, J. Quant. Spectrosc. Radiat. Transfer, 62, 511–562. Schmidt, E., and Eckert, E. R. G. (1935). ¨ Uber die Richtungsverteilung der W ¨ armestrahlung von Oberfl ¨ achen, Forsch. Geb. Ingenieurwes., 7, 175. Siegel, R., and Howell, J. R. (1992). Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, New York. Smith, T. F., Shen, Z. F., and Friedman, J. N. (1982). Evaluation of Coefficients for the Weighted Sum of Gray Gases Model, J. Heat Transfer, 104, 602–608. Taine, J., and Soufiani, A. (1999). Gas IR Radiative Properties: From Spectroscopic Data to Approximate Models, Vol. 33, Academic Press, New York, pp. 295–414. Touloukian, Y. S., and DeWitt, D. P., eds. (1970). Thermal Radiative Properties: Metallic Elements and Alloys, Vol.7ofThermophysical Properties of Matter, Plenum Press, New York. Touloukian, Y. S., and DeWitt, D. P., eds. (1972). Thermal Radiative Properties: Nonmetallic Solids, Vol.8ofThermophysical Properties of Matter, Plenum Press, New York. Touloukian, Y.S., DeWitt, D. P., and Hernicz, R. S., eds. (1973). Thermal Radiative Properties: Coatings, Vol.9ofThermophysical Properties of Matter, Plenum Press, New York. Weast, R. C., ed. (1988). CRC Handbook of Chemistry and Physics, 68th ed., Chemical Rubber Company, Cleveland, OH. White, F. M. (1984). Heat Transfer, Addison-Wesley, Reading, MA. BOOKCOMP, Inc. — John Wiley & Sons / Page 635 / 2nd Proofs / Heat Transfer Handbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [635], (1) Lines: 0 to 94 ——— 2.34608pt PgVar ——— Normal Page PgEnds: T E X [635], (1) CHAPTER 9 Boiling JOHN R. THOME Laboratory of Heat and Mass Transfer Faculty of Engineering Science Swiss Federal Institute of Technology Lausanne Lausanne, Switzerland 9.1 Introduction to boiling heat transfer 9.2 Boiling curve 9.3 Boiling nucleation 9.3.1 Introduction 9.3.2 Nucleation superheat 9.3.3 Size range of active nucleation sites 9.3.4 Nucleation site density 9.4 Bubble dynamics 9.4.1 Bubble growth 9.4.2 Bubble departure 9.4.3 Bubble departure frequency 9.5 Pool boiling heat transfer 9.5.1 Nucleate boiling heat transfer mechanisms 9.5.2 Nucleate pool boiling correlations Bubble agitation correlation of Rohsenow Reduced pressure correlation of Mostinski Physical property type of correlation of Stephan and Abdelsalam Reduced pressure correlation of Cooper with surface roughness Fluid-specific correlation of Gorenflo 9.5.3 Departure from nucleate pool boiling (or critical heat flux) 9.5.4 Film boiling and transition boiling 9.6 Introduction to flow boiling 9.7 Two-phase flow patterns 9.7.1 Flow patterns in vertical and horizontal tubes 9.7.2 Flow pattern maps for vertical flows 9.7.3 Flow pattern maps for horizontal flows 9.8 Flow boiling in vertical tubes 9.8.1 Chen correlation 9.8.2 Shah correlation 9.8.3 Gungor–Winterton correlation 9.8.4 Steiner–Taborek method 9.9 Flow boiling in horizontal tubes 9.9.1 Horizontal tube correlations based on vertical tube methods 635 BOOKCOMP, Inc. — John Wiley & Sons / Page 636 / 2nd Proofs / Heat Transfer Handbook / Bejan 636 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [636], (2) Lines: 94 to 151 ——— 12.0pt PgVar ——— Short Page PgEnds: T E X [636], (2) 9.9.2 Horizontal flow boiling model based on local flow regime 9.9.3 Subcooled boiling heat transfer 9.10 Boiling on tube bundles 9.10.1 Heat transfer characteristics 9.10.2 Bundle boiling factor 9.10.3 Bundle design methods 9.11 Post-dryout heat transfer 9.11.1 Introduction 9.11.2 Thermal nonequilibrium 9.11.3 Heat transfer mechanisms 9.11.4 Inverted annular flow heat transfer 9.11.5 Mist flow heat transfer 9.12 Boiling of mixtures 9.12.1 Vapor–liquid equilibria and properties 9.12.2 Nucleate boiling of mixtures 9.12.3 Flow boiling of mixtures 9.12.4 Evaporation of refrigerant–oil mixtures 9.13 Enhanced boiling 9.13.1 Enhancement of nucleate pool boiling 9.13.2 Enhancement of internal convective boiling Nomenclature References 9.1 INTRODUCTION TO BOILING HEAT TRANSFER When heat is applied to a surface in contact with a liquid, if the wall temperature is sufficiently above the saturation temperature, boiling occurs on the wall. Boiling may occur under quiescent fluid conditions, which is referred to as pool boiling, or under forced-flow conditions, which is referred to as forced convective boiling. In this chapter a review of the fundamentals of boiling is presented together with numerous predictive methods. First the fundamentals of pool boiling are addressed and then those of flow boiling. To better understand the mechanics of flow boiling, a section is also presented on two-phase flow patterns and flow pattern maps. Then the effects of mixture boiling are described. Finally, the topic of enhanced heat transfer is introduced. For more exhaustive treatments of boiling heat transfer, the following books are recommended for consultation: Tong (1965), Wallis (1969), Hsu and Graham (1976), Ginoux (1978), van Stralen and Cole (1979), Delhaye et al. (1981), Whalley (1987), Thome (1990), Carey (1992) and Collier and Thome (1994). In addition, Rohsenow (1973) provides a detailed historical presentation of boiling research. BOOKCOMP, Inc. — John Wiley & Sons / Page 637 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING CURVE 637 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [637], (3) Lines: 151 to 168 ——— 0.897pt PgVar ——— Short Page PgEnds: T E X [637], (3) 9.2 BOILING CURVE When heating a surface in a large pool of liquid, the heat flux q is usually plotted versus the wall superheat ∆T sat , which is the temperature difference between the surface and the saturation temperature of the liquid. First constructed by Nukiyama (1934), the boiling curve depicted in Fig. 9.1 is also referred to as Nukiyama’s curve, where four distinct heat transfer regimes can be identified: 1. Natural convection. This is characterized by single-phase natural convection from the hot surface to the saturation liquid without formation of bubbles on the surface. 2. Nucleate boiling. This is a two-phase natural convection process in which bubbles nucleate, grow, and depart from the heated surface. 3. Transition boiling. This is an intermediate regime between the nucleate boiling and film boiling regimes. Figure 9.1 Nukiyama’s boiling curve. BOOKCOMP, Inc. — John Wiley & Sons / Page 638 / 2nd Proofs / Heat Transfer Handbook / Bejan 638 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [638], (4) Lines: 168 to 189 ——— 0.0pt PgVar ——— Short Page PgEnds: T E X [638], (4) 4. Film boiling. This mode is characterized by a stable layer of vapor that forms between the heated surface and the liquid, such that the bubbles form at the free interface and not at the wall. Between these four regimes are three transition points. The first is called incipience of boiling (IB) or onset of nucleate boiling (ONB), at which the first bubbles appear on the heated surface. The second is the peak in the curve at the top of the nucleate boiling portion of the curve, referred to as departure from nucleate boiling (DNB), the critical heat flux (CHF), or peak heat flux. The last transition point is located at the lower end of the film boiling regime (at the letter E) and is called the minimum film boiling (MFB) point. These are all denoted in Fig. 9.1, while a representation of these regimes is shown in Fig. 9.2. In the natural convection part of the curve, the wall temperature rises as the heat flux is increased until the first bubbles appear, signaling the incipience of boiling. These bubbles form (or nucleate) at small cavities in the heated surface, which are called nucleation sites. The active nucleation sites are located at pits and scratches in the surface. Increasing the heat flux, more and more nucleation sites become activated until the surface is covered with bubbles that grow and depart in rapid succession. The heat flux increases dramatically for relatively modest increases in ∆T sat (defined as T w − T sat ), noting that the scale is log-log. Increasing the heat flux even further, departing bubbles coalesce into vapor jets, changing the slope of the nucleate boiling curve. A further increase in q eventually prohibits the liquid from reaching the heated surface, which is referred to as the DNB or CHF, such that complete blanketing of the surface by vapor occurs, accompanied by a rapid rise in the surface temperature to dissipate the applied heat flux. Following DNB, the process follows a path that depends on the manner in which the heat flux is applied to the surface. For heaters that impose a heat flux at the surface, such as electrical-resistance elements or nuclear fuel rods, the process progresses on a horizontal line of constant heat flux so that the wall superheat jumps to point D , where film boiling prevails as shown in Fig. 9.1, and whose vapor bubbles grow and depart from the vapor–liquid interface of the vapor layer, not from the surface. A ulterior increase in q may bring the surface to the burnout point (letter F), where the surface temperature reaches the melting point of the heater. Reducing the heat flux, the film boiling curve passes below point D until reaching point E, the MFB point. Here again, the process path depends on the mode of heating. For an imposed heat flux, the process path jumps horizontally at constant q to the nucleate boiling curve B C. Consequently, a hysteresis loop is formed when heating a surface up past the DNB and then bringing it below MFB when q is the boundary condition imposed. When the wall temperature is the externally controlled variable, such as by varying the saturation temperature of steam condensing inside a tube with boiling on the outside, the process path moves from the DNB to the MFB point, and vice versa, following the transition boiling path. In transition boiling, the process vacillates between nucleate boiling and film boiling, where each mode may coexist next to the BOOKCOMP, Inc. — John Wiley & Sons / Page 639 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING CURVE 639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [639], (5) Lines: 189 to 195 ——— 0.097pt PgVar ——— Short Page PgEnds: T E X [639], (5) Figure 9.2 Pool boiling regimes. another on the heated surface or may alternate at the same location on the surface. In film boiling, the wall is blanketed completely by a thin film of vapor, and therefore heat is conveyed by heat conduction across the vapor film and by radiation from the wall to the liquid or to the walls of the vessel. The vapor film is stable in that liquid does not normally wet the heater surface and relatively large bubbles are formed by evaporation at the free vapor–liquid interface, which then depart and rise up through the liquid pool. In the next sections, important aspects of the boiling curve, its phenomena, and predictive methods are described. BOOKCOMP, Inc. — John Wiley & Sons / Page 640 / 2nd Proofs / Heat Transfer Handbook / Bejan 640 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [640], (6) Lines: 195 to 219 ——— 7.36005pt PgVar ——— Normal Page PgEnds: T E X [640], (6) 9.3 BOILING NUCLEATION 9.3.1 Introduction In a pool of liquid, a vapor nucleus may form either at a heated surface or within the liquid itself if it is sufficiently superheated, a process called nucleation. If there is a preexistent vapor space above the liquid pool which is at its saturation temperature, then upon heating, vapor forms at the free interface without nucleation, which is referred to as evaporation. If nucleation is attained instead by reducing the pressure of the fluid rapidly or locally, this is called cavitation (e.g., that occurring on a rapidly rotating propeller of a ship). Nucleation occurring in the bulk of a superheated, perfectly clean liquid is referred to as homogeneous nucleation, which may occur as a photon passes through a bubble chamber of superheated liquid hydrogen, leaving behind a photographic trace ob- served in early particle physics experiments. Homogeneous nucleation occurs when the free energy of formation of a cluster of molecules in the liquid phase is sufficient to form a vapor interface remote from the walls of the vessel. Instead, heterogeneous nucleation initiates at a solid surface when the free energy of formation there, or in a cavity in a surface, forms a vapor nucleus, or when a preexisting vapor nucleus in such a cavity reaches a superheat sufficient to initiate bubble growth. For homoge- neous or heterogeneous nucleation to occur, the temperature must be elevated above the saturation temperature of the liquid to form or activate vapor nuclei. Hence, boil- ing does not begin when the saturation temperature is reached but instead, when a certain superheat is attained. Typically, nucleation occurs from a preexisting vapor nucleus residing within a cavity or from a vapor nucleus that protrudes into the ther- mal boundary layer formed at the wall. 9.3.2 Nucleation Superheat The superheating of the liquid with respect to the saturation temperature that is required for nucleation to be achieved is referred to as the nucleation superheat. First, we consider the process of homogeneous nucleation. In Fig. 9.3 the mechanical equilibrium of forces at the interface of a spherical vapor nucleus (of radius r nuc )ina liquid at uniform temperature T G and pressure p G is given by the Laplace equation, p G − p L = 2σ r nuc (9.1) where p G is the vapor pressure inside the nucleus, p L the local liquid pressure, and σ the surface tension. Since p G >p L , the surface tension balances the pressure difference across the interface and the pressure difference increases with decreasing nucleation radius, r nuc . In addition, there is an effect of the curvature of the interface on the vapor pressure curve of the fluid, which lowers the pressure in thevapor nucleus relative to that above a planar interface p ∞ at the same fluid temperature, which has been shown by Lord Kelvin (1871) to be BOOKCOMP, Inc. — John Wiley & Sons / Page 641 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING NUCLEATION 641 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [641], (7) Lines: 219 to 258 ——— -2.64287pt PgVar ——— Normal Page * PgEnds: Eject [641], (7) Figure 9.3 Vapor nucleus in a pool of liquid. p G = p ∞ exp −2σv L M r nuc ¯ RT ≈ p ∞ 1 − 2σv L p ∞ r nuc v G (9.2) where M is the molecular weight in kg/mol, ¯ R is the ideal gas constant ( ¯ R = 8.3144 J/mol·K), and the specific volumes of the vapor and liquid are v G and v L , respectively. Introducing eq. (9.1) for 2σ/r nuc into eq. (9.2) and rearranging yields p ∞ − p L = 2σ r nuc 1 + v L v G (9.3) For a planar vapor–liquid interface, the slope of the vapor pressure curve is given by the Clausius–Clapeyron equation, dp dT sat = h LG T sat (v G − v L ) (9.4) where T sat is in K. Assuming that the vapor behaves as a perfect gas, then Mp G v G = ¯ RT (9.5) Thus, for v G v L , eq. (9.4) becomes 1 p dp = h LG M ¯ RT 2 dT (9.6) Now integrating this expression from p L to p ∞ and from T sat to T G ,wehave ln p ∞ p L =− h LG M ¯ R 1 T G − 1 T sat = h LG M ¯ RT G T sat (T G − T sat ) (9.7) BOOKCOMP, Inc. — John Wiley & Sons / Page 642 / 2nd Proofs / Heat Transfer Handbook / Bejan 642 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [642], (8) Lines: 258 to 319 ——— 2.23616pt PgVar ——— Short Page PgEnds: T E X [642], (8) Substituting (9.3) and again rearranging gives us T G − T sat = ¯ RT sat T G h LG M ln 1 + 2σ p L r nuc 1 + v L v G (9.8) Since v G v L and 2σ/p L r nuc 1, this simplifies to T G − T sat = ∆T nuc = ¯ RT 2 sat h LG M 2σ p L r nuc (9.9) This expression gives the nucleation superheat ∆T nuc , which is the difference between the saturation temperature of the vapor T G at the pressure inside the nucleus p G and the saturation temperature T sat at the pressure in the surrounding liquid p L .An equivalent and easier to use form is ∆T nuc = 2σ r nuc (dp/dT ) sat (9.10) where (dp/DT ) sat is obtained with eq. (9.4) or, more accurately, from the equation of state of the fluid. Expression (9.10) is also obtainable by introducing (dp/dT ) sat into eq. (9.1). The nucleation superheat ∆T nuc represents the uniform superheating of the liquid required for a stable vapor bubble of radius r nuc to exist. If the superheat is less than this, the nucleus will collapse, whereas if it is larger, it will grow as a bubble. If air is trapped in the nucleus with the vapor, either while filling the vessel or by degasing of the liquid itself, the partial pressure of the gas, p a , must be taken into consideration in eq. (9.1), so that p G + p a − p L = 2σ r nuc (9.11) T G − T sat = ¯ RT sat T G h LG M ln 1 + 2σ p L r nuc − p a p L (9.12) Presence of a noncondensable gas thus reduces the nucleation superheat required to initiate boiling. For heterogeneous nucleation at a flat surface, the free energy of formation re- quired to create a vapor embryo is smaller than for homogeneous nucleation. Their respective nucleation superheats can be related by multiplying that for homogeneous nucleation by a factor φ. As illustrated in Fig. 9.4a φ depends on the contact angle β between the surface and the liquid: φ = 2 + 2 cos β cos β sin 2 β 4 (9.13) β = 0 for a liquid that completely wets the surface, so in that case φ = 1. If the surface is completely nonwetting, β = π, and thus in this case, φ = 0 (i.e., no superheat is BOOKCOMP, Inc. — John Wiley & Sons / Page 643 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING NUCLEATION 643 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [643], (9) Lines: 319 to 356 ——— 0.27704pt PgVar ——— Short Page PgEnds: T E X [643], (9) Figure 9.4 Nucleation: (a) plane surface; (b–d) triangular cavity. required for nucleation). Typically, the contact angle ranges from 0 < β < π/2, so possible values of φ are 1 2 < φ < 1. However, bubbles are normally generated at microcavities in the solid surface, such as that illustrated in Fig. 9.4b with an included angle θ. The apparent contact angle β for eq. (9.13) is then β = β + π − θ 2 (9.14) As a consequence, the energy required for formation of a bubble is less at these cavities than on a planar surface or in the bulk, and therefore bubble nucleation occurs preferentially at a cavity. Larger cavities with large θ give a value of β closer to β than smaller cavities, implying that larger cavities will nucleate first. The contact angle β between the wall and the liquid–vapor interface is generally unknown for most fluid–surface combinations, and no reliable prediction method is available, which also complicates the prediction of the nucleation superheat. Contact angle is a function of the surface finish, such as whether or not it is clean, oxidized, fouled, polished, or wettable at all, and also depends on whether the interface is advancing or receding. Table 9.1 lists contact angles of some common fluids on surfaces polished with emery paper. The mechanics of nucleation at a cavity are essentially as follows. As T w of the cavity increases above T sat , a vapor nucleus trapped in a cavity expands until it reaches the mouth of the cavity. If the liquid surrounding the protruding nucleus is superheated, the bubble will grow. As a bubble grows, less superheat is required to maintain its mechanical stability. Thus, it is this radius of the cavity mouth that determines the degree of superheat required to activate a boiling site. . Subcooled boiling heat transfer 9.10 Boiling on tube bundles 9.10.1 Heat transfer characteristics 9.10.2 Bundle boiling factor 9.10.3 Bundle design methods 9.11 Post-dryout heat transfer 9.11.1. transfer 9.11.1 Introduction 9.11.2 Thermal nonequilibrium 9.11.3 Heat transfer mechanisms 9.11.4 Inverted annular flow heat transfer 9.11.5 Mist flow heat transfer 9.12 Boiling of mixtures 9.12.1 Vapor–liquid. the topic of enhanced heat transfer is introduced. For more exhaustive treatments of boiling heat transfer, the following books are recommended for consultation: Tong (1 965) , Wallis (1969), Hsu