Typically, enhanced surfaces on the out-side of tubes are for the purpose of enhancing nucleate boiling, whereas those on the inside are for enhancing forced-convective boiling.. 9.13.1
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local flow boiling heat transfer coefficient, which is most pronounced at high vapor qualities and at high local oil mass fractions
9.13 ENHANCED BOILING
In the foregoing sections we have addressed boiling when it occurs on plain surfaces, either outside or inside tubes Boiling on specially formed microsurfaces, to enhance
nucleate boiling or convective boiling or both, is referred to as enhanced boiling and these surfaces as enhanced boiling surfaces Typically, enhanced surfaces on the
out-side of tubes are for the purpose of enhancing nucleate boiling, whereas those on the inside are for enhancing forced-convective boiling The exception is the porous lay-ered surfaces that enhance nucleate boiling whether applied inside or outside a tube
In this section, first enhancement of nucleate boiling is discussed and then enhance-ment of forced-convective boiling Both types of enhanced surfaces are used widely
in industry, particularly in the refrigeration and air-conditioning industries Refer to Bergles (1996), Thome (1990), and Webb (1994) for comprehensive treatments of this subject
9.13.1 Enhancement of Nucleate Pool Boiling
Boiling on plain, smooth surfaces is a weak function of the roughness of the sur-face, which increases nucleate pool boiling heat transfer coefficient with increas-ing roughness This is only marginal, on the order of up to 30%, and may also be temporary if the surface becomes fouled For substantial and sustainable enhance-ment, numerous geometries have been proposed and patented over the years The earliest commercially successful enhancement was the integral low finned tube (i.e.,
a continuous helical fin that is formed on the outside of an otherwise plain tube), which is still used for appropriate applications Applying a porous metallic coating
on the surface of a tube is another important historical development, giving up to 15
times the heat transfer coefficient of a plain tube In recent years, attention has
fo-cused on mechanically deformed low finned tubes, whose fins are notched, bent, and compressed to form reentrant channels, essentially mechanically emulating a porous coating
Enhanced nucleate boiling surfaces provide significant performance advantages overthose of a plain tube Forinstance, the enhancement ratio of theircoefficient relative to that of a comparable plain tube ranges from about 2 to 4 for low finned tubes and up to about 10 ormore times forporous-coated tubes and mechanically deformed low finned tubes Evaporation occurs both on the external surface of an enhanced boiling surface and inside its reentrant passageways Hence, there are four possible paths by which heat can leave such a surface (Fig 9.22):
1 As latent heat in the vapor formed within the reentrant passageways
2 As latent heat in bubbles growing on the exterior and on those emerging from the pores
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3 As sensible heat to the liquid “pumped” through the reentrant passageways
4 As sensible heat to the liquid in the external thermal boundary layer The factors contributing to the substantial increase in thermal performance of enhanced surfaces can be summarized as follows:
• Nucleation superheat Enhanced surfaces have an abundant supply of reentrant
nucleation (except forlow finned tubes) and hence initiate boiling at very low wall superheats with respect to plain surfaces
• Wetted surface area Low finned tubes have from 2 to 3.5 times the surface area
of a similar-sized plain tube, while complex enhancements have area ratios from
4 to 10 times that of a plain surface
• Thin-film evaporation Reentrant channels favor the formation of thin
evaporat-ing liquid films on the innerwalls of the passageways
• Capillary evaporation In a porous coating, the myriad of liquid menisci can
evaporate as heat is conducted into the liquid behind them
• Internal convection Liquid is pumped through the narrow channels by capillary
forces and by growth and departure of bubbles The small hydraulic diameters and entrance region effects yield very large laminar heat transfer coefficients for the liquid flow
• External convection The largernumberof active boiling sites accentuates the
external convection mechanisms (i.e., bubble agitation and thermal boundary layerstripping)
These mechanisms can be compared to those occurring on a plain surface in Section 9.5.1 The thermal effectiveness of these factors depends on the type of
2 3
4
1
5 Liquid
Vapor Liquid
Liquid
Liquid Particles
1 Thin-film evaporation
2 External evaporation
3 Convection in passageways
4 External convection
5 Capillary evaporation
Figure 9.22 Heat transfer paths for boiling on a porous-coated surface
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Figure 9.23 Low finned tube (left) and Turbo-Bii tube (right)
enhanced surface geometry and its characteristic dimensions As an example, Fig
9.23 depicts photographs of the surfaces of a low finned tube and a Turbo-Bii tube (trademark of Wolverine Tube Inc.)
9.13.2 Enhancement of Internal Convective Boiling
Numerous geometries exist for enhancing in-tube evaporation: porous coatings, cor-rugations, ribs, star inserts, twisted tapes, and microfins, to name just a few The two most important geometries are the porous coating (commercially available as High Flux from UOP, Inc.) and the microfin (manufactured by numerous companies) The High Flux porous coating is used in large refrigeration systems working with propane
or ethylene as the working fluids and also in vertical thermosyphon reboilers in the petrochemical industry for evaporation of nonfouling fluids, typically mixtures Its nucleate boiling performance is so high that typically the convective contribution for forced-convective boiling becomes negligible in comparison Hence, nucleate pool boiling data can be used forthese design applications
Microfin tubes are characterized by numerous small internal fins 0.1 to 0.4 mm in height that can be eitherlongitudinal orhelical and eithertwo-dimensional (i.e., plain microfins) or three-dimensional (i.e., crosscut or notched microfins) Figure 9.24 de-picts a typical geometry The fins have a height-to-width at base ratio of about 1.0, and their fin profiles tend to be trapezoidal, triangular, or rectangular, depending on the particular tooling of the manufacturer Most microfin tubes are seemless (manufac-tured by drawing a plain tube over an externally grooved mandrel), but manufacturers now also produce these tubes from strip by first rolling the enhancement geometry onto one side of the strip and then forming a longitudinally seamed tube from the strip Microfin tubes are most commonly available in copper in diameters from about
5 to 16 mm outside diameter Several versions are available in high alloys with 14 to 22-mm internal diameters (stainless steels and titanium) and also in carbon steel and aluminum (for ammonia systems) Nearly all microfin tubes tested in university labs have been used in their original production form; in some industrial applications of microfin tubes, such as air-conditioning coils with external aluminum fins, they are
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Figure 9.24 Microfin tube
expanded mechanically into the coils, and hence their fin heights are reduced by a small margin and their internal diameters increased
In-tube evaporation inside microfin tubes has become an important research topic because of their widespread application in direct-expansion evaporators in recent years These are all horizontal units, and hence all the published test data for microfin tubes presented here will be for that orientation Microfin tubes typically provide heat transfer augmentation on the order of 1.5 up to 4 times that of a plain tube operating
at the same conditions This significant enhancement relative to plain tubes, with only
a small adverse augmentation of their two-phase pressure drops, has been attributed
to the following heat transfer enhancement mechanisms:
• Extended surface area effect Internal wetted surface area ratios for microfin
tubes relative to their equivalent plain bore tubes range from about 1.3 to 1.9, depending on the numberof fins and on theirshape, height, and helix angle
(typ-ically, the area ratio represents the lower bound on the heat transfer enhancement
level)
• Enhanced convective heat transfer Microfins augment the convective heat
trans-fer process across the annular liquid film, similar to internal ribs used for single-phase flow inside tubes, and this increases the two-single-phase convection contribution
to annularflow boiling
• Flow pattern effect The helical microfins tend to convert what would otherwise
be a stratified-wavy flow in plain tubes into the more thermally effective annular flow regime, meaning that all the internal tube wall perimeter is wetted and active rather than only the lower wetted fraction in plain tubes; this represents the principal reason for their very large augmentation ratios at low mass velocities
• Nucleate boiling heat transfer The microfins may favor the activation of
nucle-ation sites by partially shielding the potential cavities from the flow; nucleate boiling will also occur on the total wetted extended surface area
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• Swirl effects Swirl imparted to the annular liquid film by helical microfins may
retard the onset of dryout to higher vapor qualities; swirl of the continuous vapor phase in mist flow and annular flow with partial dryout will augment vapor-phase heat transfer to the dry wall, similar to a single-phase turbulent flow inside an internally ribbed tube; swirl will also drive entrained droplets to the tube wall
• Grigorig film thinning effects The convex contours at the tips of microfins will
tend to thin the evaporating liquid film on the fins, similar to that which occurs for film condensation on external low finned tubes, increasing the evaporating heat transfer coefficients on the microfins significantly
In recent years, numerous methods have been proposed for predicting the flow boiling heat transfer coefficients in microfin tubes Refer to Webb (1999) and Thome (1999) fora summary of these methods
NOMENCLATURE
Roman Letter Symbols
a drag constant, dimensionless
empirical constant, dimensionless
a L liquid thermal diffusivity, m2/s
A cross-sectional area, m2
bubble growth parameter, m/s
A G cross-sectional area of vapor, m2
A Gd dimensionless cross-sectional area of vapor, dimensionless
A L cross-sectional area of liquid, dimensionless
A Ld dimensionless cross-sectional area of liquid, m2
b empirical exponent, dimensionless
B bubble growth parameter, m/s1/2
c empirical exponent, dimensionless
c pL liquid specific heat, J/kg · K
C empirical constant, dimensionless
inverted annular flow constant, dimensionless
C D drag coefficient, dimensionless
C0 boiling constant, dimensionless
C sf surface factor, dimensionless
C1 lead constant, dimensionless
d b bubble base diameter, m
d i tube diameter, m
d i,0 reference tube diameter, m
d o bubble departure diameter, m
d oF bubble departure diameter of Fritz, m
D outside tube diameter, m
droplet diameter, m
e empirical constant, dimensionless
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E convection enhancement factor, dimensionless
E2 stratified flow correction factor, dimensionless
f bubble departure frequency, s−1
empirical constant, dimensionless Fanning friction factor, dimensionless friction factor, dimensionless
f cd cumulative deposition factor, dimensionless
f G vapor-phase friction factor, dimensionless
F drag force, N
two-phase multiplier, dimensionless constant of Shah, dimensionless
F1(q) nondimensional exponent, dimensionless
F1(q) nondimensional exponent, dimensionless
F b buoyancy force, N
bundle boiling factor, dimensionless
F c mixture boiling correction factor, dimensionless
F D drag force, N
F i inertia force, N
F (M) residual correction factor, dimensionless
F nb nucleate boiling correction factor, dimensionless
F p excess pressure force, N
reduced pressure factor, dimensionless
F pf pressure correction factor, dimensionless
F PF pressure correction factor, dimensionless
F tp two-phase multiplier, dimensionless
F wG radiative view factor from wall to vapor, dimensionless
F wL radiative view factor from wall to liquid droplets,
dimensionless
Fσ surface tension force, N
g acceleration of gravity, m/s2
empirical exponent, dimensionless
h liquid height, m
h G,a actual vaporenthalpy, J/kg
h G,e equilibrium vapor enthalpy, J/kg
h G,sat enthalpy of saturated vapor, J/kg
h Ld dimensionless liquid height, dimensionless
h LG latent heat of vaporization, J/kg
h L,sat enthalpy of saturated liquid, J/kg
H characteristic height, m
H dimensionless height, dimensionless
L characteristic length, m
L dimensionless length, dimensionless
exponent, dimensionless
˙m total mass velocity of liquid and vapor, kg/s · m2
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˙mbubbly bubbly flow transition mass velocity, kg/s · m2
˙mhigh value of wavy (new) flow mass velocity transition at
χ, kg/s · m2
˙mlow value of stratified low mass velocity transition atχ, kg/s · m2
˙mmin minimum mist flow transition mass velocity, kg/s · m2
˙mmist mist flow transition mass velocity, kg/s · m2
˙mstrat stratified flow transition mass velocity, kg/s · m2
˙mwavy wavy flow transition mass velocity, kg/s · m2
˙mwavy(new) new wavy flow transition mass velocity, kg/s · m2
M molecularweight, kg/mol
n exponent, dimensionless
nf nucleate boiling exponent, dimensionless
N dimensionless parameter, dimensionless
p pressure, N/m2
∆p pressure difference, N/m2
∆psat saturation pressure difference, N/m2
p a partial pressure of air, N/m2
pcrit critical pressure, N/m2
p G vapor pressure, N/m2
p L liquid pressure, N/m2
p r reduced pressure, dimensionless
psat saturation pressure, Pa
p∞ vapor pressure at planar interface, N/m2
P characteristic perimeter, m
P characteristic perimeter, m
P G vaporperimeter, m
P Gd dimensionless vaporperimeter, dimensionless
P i length of liquid–vaporinterface, m
P id interface length, dimensionless
P L wetted perimeter, m
P Ld liquid perimeter, dimensionless
P v dry perimeter, m
q heat flux, W/m2
qDNB heat flux at DNB, W/m2
qDNB,z heat flux at DNB according to Zuber, W/m2
q G heat flux resulting from wall-to-droplet evaporation, W/m2
q L heat flux resulting from droplet evaporation, W/m2
qMFB heat flux at MFB, W/m2
qONB heat flux at onset of nucleate boiling, W/m2
qrad radiation heat flux, W/m2
q0 reference heat flux, W/m2
r b bubble base radius, m
r i internal radius of tube, m
rmax maximum nucleation radius, m
rmin minimum nucleation radius, m
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rnuc nucleation radius, m
R bubble radius, m
characteristic radius, m
R radius, dimensionless
R+ bubble radius, dimensionless
¯R ideal gas constant, J/mol · K
R p mean surface roughness,µm
R p0 reference mean surface roughness,µm
R p,0 reference mean surface roughness,µm
S nucleation suppression factor, dimensionless
S2 stratified flow correction factor, dimensionless
t bubble growth time, s
t+ bubble growth time, dimensionless
t g bubble growth time, s
t w bubble waiting time, s
T absolute temperature, K
Tbub bubble point temperature, K
Tcrit critical temperature, K
T D droplet temperature, K
Tdew dew point temperature, K
T G vapor temperature, K
T G,a actual bulk vapor temperature, K
T G,f film temperature of vapor, K
T L subcooled liquid temperature, K
Tsat saturation temperature, K or °C
T w wall temperature, K or °C
T∞ bulk liquid temperature, K or °C
∆T wall superheat, K
∆T bp boiling range or temperature glide of mixture, K
∆T id ideal wall superheat, K
∆Tnuc nucleation superheat, K
∆Tsat wall superheat, K
u velocity, m/s
u d droplet deposition velocity, m/s
u G vaporvelocity, m/s
u H velocity forhomogeneous flow, m/s
v G vaporspecific volume, m3/kg
v L liquid specific volume, m3/kg
w local mass fraction of oil, kg/kg
winlet inlet mass fraction of oil before expansion valve, kg/kg
x mole fraction of liquid, dimensionless
X tt Martinelli parameter, dimensionless
y mole fraction of vapor, dimensionless
Y multiplying factor, dimensionless
z axis along tube, m
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z a length from inlet where liquid is actually completely
evaporated, m
z DO length from inlet where dryout occurs, m
z e length from inlet under equilibrium conditions, m
Z G mixture boiling parameter, dimensionless
Greek Letter Symbols
α mist flow heat transfer coefficient, W/m2· K
αb bundle boiling heat transfer coefficient, W/m2· K αcb convective boiling heat transfer coefficient, W/m2· K
αD convective boiling heat transfer coefficient from vapor to
droplet, W/m2· K
αeff effective mixture flow boiling heat transfer coefficient,
W/m2· K
αf b film boiling heat transfer coefficient, W/m2· K
αFZ Forster–Zuber nucleate boiling heat transfer coefficient,
W/m2· K
αG vaporheat transfercoefficient, W/m2· K
αid ideal pure fluid boiling heat transfer coefficient, W/m2· K
αL liquid only heat transfer coefficient, W/m2· K
αmixt mixture boiling heat transfer coefficient, W/m2· K
αnb nucleate boiling heat transfer coefficient, W/m2· K αnb,0 reference nucleate boiling heat transfer coefficient for flow
boiling, W/m2· K αnc natural convection heat transfer coefficient, W/m2· K
αrad radiation heat transfer coefficient, W/m2· K αst single-tube nucleate boiling heat transfer coefficient, W/m2· K
αtotal total heat transfer coefficient, W/m2· K αtp two-phase flow boiling heat transfer coefficient, W/m2· K
αvapor vapor-phase heat transfer coefficient on dry wall, W/m2· K
αwet wet wall heat transfer coefficient, W/m2· K
α0 reference nucleate boiling heat transfer coefficient, W/m2· K
α(z) local heat transfer coefficient at positionz, W/m2· K
β contact angle, rad
β apparent contact angle, rad
βL mass transfer coefficient, m/s
δ thickness of annularliquid layer, m
boundary layer thickness, m
ε void fraction, dimensionless
θdry dry angle around top perimeter of tube, rad
θmax dry angle atχmax, r ad
θstrat stratified angle around bottom perimeter of tube, rad
κ ratio of droplet heat flux to total heat flux, dimensionless
λ thermal conductivity, W/m2· K
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λd1 one-dimensional Taylorwavelength, m
λd2 two-dimensional Taylorwavelength, m
λH Helmholtz wavelength, m
µ dynamic viscosity, N· s/m2
µoil dynamic viscosity of oil, N· s/m2
µref dynamic viscosity of refrigerant, N· s/m2
µref −oil dynamic viscosity of refrigerant-oil mixture, N· s/m2
ξP h friction factor,
ξw emissivity of the wall, dimensionless
ρ density, kg/m3
σ surface tension, N/m
σSB Stephan–Boltzmann constant, W/m2· K4
φ heterogeneous nucleation factor, dimensionless
χ vaporquality, kg/kg
χa actual local vaporquality, dimensionless
χDO vaporquality at dryout, dimensionless
χe local equilibrium vapor quality, dimensionless
χmax vapor quality at intersection of mist and wavy flow transition
curves, kg/kg
ψ mist flow parameter, dimensionless
Dimensionless Numbers
Bo boiling number
FrL Froude number of liquid phase
GrG Grashof number of vapor
Ja Jakob number
Nu Nusselt number
Re Reynolds number
Rebub bubble Reynolds number
ReG Reynolds numberof vaporphase
ReGH Reynolds numberforvaporin homogeneous flow
ReL Reynolds numberof liquid phase
Retp two-phase Reynolds number
We Webernumber
Subscripts
e equilibrium
H homogeneous