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.
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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
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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 betterunderstand 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
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9.2 BOILING CURVE
When heating a surface in a large pool of liquid, the heat fluxq is usually plotted
versus the wall superheat∆Tsat, 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
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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 lowerend of the film boiling regime (at the letterE) 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∆Tsat(defined
asT w − Tsat), 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 inq 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 pointD,
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 inq 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 pointDuntil reaching pointE, 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 constantq to the nucleate boiling
curve BC Consequently, a hysteresis loop is formed when heating a surface up
past the DNB and then bringing it below MFB whenq 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
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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 orto the walls of the vessel The vaporfilm 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
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9.3 BOILING NUCLEATION 9.3.1 Introduction
In a pool of liquid, a vapornucleus may form eitherat a heated surface orwithin 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 occuras 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 heterogehomoge-neous 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 radiusrnuc) in a liquid at uniform temperatureT Gand pressurep Gis given by the Laplace equation,
p G − p L =r2σ
nuc
(9.1)
wherep Gis the vapor pressure inside the nucleus,p Lthe 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,rnuc 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 the vapor nucleus relative to that above a planar interfacep∞at the same fluid temperature, which has been shown by Lord Kelvin (1871) to be
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Figure 9.3 Vapornucleus in a pool of liquid
p G = p∞exp
−2σv
L M
rnuc¯RT
≈ p∞
1− 2σv L
p∞rnucv G
(9.2)
whereM is the molecularweight in kg/mol, ¯R is the ideal gas constant ( ¯R = 8.3144
J/mol·K), and the specific volumes of the vaporand liquid are v Gandv L, respectively.
Introducing eq (9.1) for 2σ/rnucinto eq (9.2) and rearranging yields
p∞− p L= r2σ
nuc
1+v v L
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
= T h LG
whereTsatis in K Assuming that the vaporbehaves as a perfect gas, then
Thus, forv G v L, eq (9.4) becomes
1
p dp =
h LG M
Now integrating this expression fromp Ltop∞and fromTsattoT G, we have
lnp∞
p L = −h LG M
¯R
1
T G − 1
Tsat
= h LG M
¯RT G Tsat
(T G − Tsat) (9.7)
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Substituting (9.3) and again rearranging gives us
T G − Tsat= ¯RTsatT G
h LG M ln
1+p2σ
L rnuc
1+v v L
G
(9.8) Sincev G v Land 2σ/p L rnuc
T G − Tsat= ∆Tnuc= ¯RT2
sat
h LG M
2σ
p L rnuc
(9.9)
This expression gives the nucleation superheat∆Tnuc, which is the difference between the saturation temperature of the vapor T G at the pressure inside the nucleus p G
and the saturation temperatureTsatat the pressure in the surrounding liquidp L An equivalent and easierto use form is
∆Tnuc= 2σ
rnuc(dp/dT )sat
(9.10)
where(dp/DT )satis 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 )satinto
eq (9.1) The nucleation superheat∆Tnucrepresents the uniform superheating of the liquid required for a stable vapor bubble of radiusrnucto exist If the superheat is less than this, the nucleus will collapse, whereas if it is larger, it will grow as a bubble
If airis trapped in the nucleus with the vapor, eitherwhile filling the vessel orby 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=r2σ
nuc
(9.11)
T G − Tsat= ¯RTsatT G
h LG M ln
1+p2σ
L rnuc
−p p a
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 factorφ 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 sin2β
β = 0 fora 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
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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 ofφ 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
angleθ The apparent contact angle βforeq (9.13) is then
β= β + π − θ
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 largeθ give a value of βclosertoβ than
smallercavities, implying that largercavities will nucleate first
The contact angleβ 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 whetherornot it is clean, oxidized, fouled, polished, orwettable at all, and also depends on whetherthe interface is advancing orreceding 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 aboveTsat, a vapornucleus 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