624 Chapter 10 ..
Boiling and Condensation
a low boiling point organic fluid at the tube outer surface and thereby obtain
, , ~ u U ' ' ' b portion of the boiling curve.
I 0.3.2 Modes of Pool Boiling
<lnr,rp('IMlrln for the physical mechanisms may be obtained by
of pool These are
in the boiling curve of Figure 1004. The specific curve pertains to water at 1
although similar trends characterize the behavior of other fluids. From
10.3 we note that q; on the convection coefficient h, as well as on
excess temperature Different may be delineated ac(;ofclmg
the value of
Free Convection Boiling Free convection
where ~ soc. The sUlface tf'.n1nf'f::lh
uration temperature in order to sustain bubble formation. As the excess t.'"1"pr,hlm
is bubble will occur, but below A
Free convection
Boi Ii ng regi mes
Nucleate
Isolated Jets and
bubbles columns
Transition
. Critical heat flux, q;;'"
I
Boiling crisis
Film
Leidenfrost point.
120 1000
FInnE lOA
function of temperature,
curve for water at 1 aim: surface heat flux q:' as a
T-
.<
10.3 .. j
10.3 II Pool Boiling
the onset of nucleate boiling, ONB), fluid motion is determined principally by free
convection effects. to whether the flow is laminar or turbulent, h varies as
to the or power, in which case varies as to the or j
power. For a horizontal plate, the fluid flow is turbulent and Equation 9.31
can be used to predict the free convection of the boiling curve, as shown in
10.4.
Nucleate Boiling Nucleate boiling exists in the range cS
where !::.T
e
.
c
= 30C. In this range, two different flow may be distin-
In A-B, isolated bubbles form at nucleation sites and separate from
the surface, as illustrated in Figure 10.2. This induces considerable fluid
mixing near the substantially In this most of the
heat is direct transfer from the surface to liquid in motion at the
and not through the vapor bubbles from the surface. As is
increased beyond !::.Te,B' more nucleation sites become active and increased bubble
formation causes bubble interference and coalescence. In the the vapor
escapes as or columns, which subsequently merge into slugs of the vapor. This
condition is illustrated in Figure 10.5a. Interference between the
bubbles inhibits the motion of liquid near the surface. Point P of
to an inflection in the boiling curve at which the heat transfer coefficient is
a maximum. At this point h begins to decrease with increasing !::.T" although
which is the product of h and continues to increase. This trend results
for > the relative increase in exceeds the relative reduction
in h. At however, further increase in is balanced by the reduction in h.
The maximum heat flux, q':.c is usually termed the critical heat flux, and in
water at pressure it exceeds 1 MW/m
2
At the point of this
considerable vapor is formed, it difficult for to continuously
wet the surface,
Because heat transfer rates and convection coefficients are associated with
small values of the excess temperature, it is desirable to operate many
devices in the nucleate boiling The of the convec-
tion coefficient may be inferred by curve of
Figure 10.4. Dividing by it is evident that convection coefficients in excess
of W/m
2
K are characteristic of this These values are considerably
than those normally to convection with no change.
Transition corresponding to cS tJ.Te,o, where
"" 120
a
C, is termed transition unstable film or film
Bubble formation now so that a vapor film or blanket begins to
form on the surface, At any point on the surface, conditions may oscillate between
film and nucleate boiling, but the fraction of the total surface covered by the film
increases with !::.Te Because the thermal conductivity of the vapor is
much less than that of the h (and cD must decrease with
Film Boiling Film boiling exists for tJ.Te 2: !::.T
e
.
D
. At
curve, referred to as the the heat flux is a
and the surface is completely covered by a vapor blanket. Heat transfer from the
surface to the liquid occurs by conduction and radiation through the vapor. It was
Leidenfrost who in 1756 observed that water droplets supported by the vapor film
626 Chapter 10 II Boiling mul Condetl.Salion
F!G!.HE 10,5
Nucleate boiling in the jets and columns regime.
courtesy of Professor J. W. Westwater,
slowly boil away as they move about a hot surface. As the surface temperature is
radiation through the vapor film becomes more and the heat
flux increases with
10.5 illustrates the nature of the vapor formation and bubble dynamics
associated with nucleate and film boiling. The photographs were obtained for the
boiling of methanol on a horizontal tube.
Although the discussion of the boiling curve assumes that control may
be maintained over it is important to remember the NUkiyama experiment and the
many applications that involve controlling (e.g., in a nuclear reactor or in an electric
Consider at some Pin 10.4 and
The value of and hence the value of
lowing the boiling curve to point C. any increase in beyond this point will
induce a sharp departure from the boiling curve in which surface conditions change
abruptly from !J.Te.C to !J.Te,E Ts,E Because T
S
E
may exceed the point
of the solid, destruction or failure of the system may occur. For this reason point C
often termed the bunwut point or the boiling crisis, and accurate of the
ical heatfiux q;.c is important. We may want to
surface close to this value, but would we want to exceed it.
10.4 III I
Boiling
K
it provides a value
10.5 .. Forced Convecti<Jn Boiling 637
For external flow over a heated plate, the heat flux can be estimated by standard
forced convection correlations up to the of As the temperature of
the heated plate is nucleate boiling will occur, the heat flux to
increase. If vapor is not extensive and the is subcooled, Bergles
and Rohsenow suggest a method for estimating the total heat flux in terms of
components associated with pure forced convection and pool
Both forced convection and subcooling are known to increase the critical heat
flux for nucleate Experimental values as as 35 MW/m2
with 1.3 MW/m2 for pool of water at 1 atm) have been reported [25J. For a
of velocity V in cross flow over a of diameter D, Lienhard
and Eichhorn [26] have the following expressions for low- and high-
where properties are evaluated at the saturation temperature.
Low Velocity:
(10.12)
High
(10.13)
The Weber number
form
is the ratio of inertia to surface tension forces and has the
(10.
The and low-velocity respectively, are detennined by whether the
heat flux Pvhfg V is less than or greater than + I).
10.12 and 10.13 correlate data within 20%.
10.5.2 Two-Phase Flow
Internal forced convection is associated with bubble formation at the inner
surface of a heated tube through which a liquid is flowing. Bubble and sepa-
influenced by the flow and hydrodynamic effects differ
from those to pool The process is '>N'n"","
by the existence of a flow
Consider flow development in a vertical tube that is to a constant sur-
face heat as shown in 10.8. Heat transfer to the subcooled liquid that
enters the tube is by convection and may be predicted
using the correlations of Chapter 8. Farther down the tube, the wall
exceeds the saturation of the liquid, and is initiated in the
subcooled flow boiling This region is characterized by significant radial
638 Chapter 10 III and Condensation
Vapor
Vapor
slug
Core
bubbles
i
Mist
Sat "rated
flow boi:ing
Subcooled
flow bOiling
Liquid
-+ ___ Liquid
convection
t
.')(;( HE 0.8 Flow for forced conveclion
with bubbles
in lube.
cooled liquid flowing near the center of the tube. The thickness of the bubble
increases farther downstream, and the core of the reaches the sat
uration temperature of the fluid. Bubbles can then exist at any radial location, and
the time-averaged mass fraction of vapor in the I exceeds zero at any radial
location. This marks the beginning of the boiling region. Within !he
saturated How region, the mean vapor mass fraction defined as
pu(r,x)XdA
c
x
m
increases and, due to the large difference between the
the mean velocity of the fluid, Un!' increases significantly.
The first stage of the saturated flow region to the bubbly
regime. As X increases individual bubbles coalesce to form slugs of
'This term is often referred 10 as the quality of a fluid.
10.5 III
wall and sub-
the bubble region
reaches the sat-
location, and
zero at any radial
Within the
id as
vapor and liquid
to form
10.5 II Forced ConlJction 639
vapor. This slug-flow is followed by an regime in which the
liquid forms a film on the tube wall. This film moves along the inner surface of the
tube, while vapor moves at a through the core of the tube. spots
appear on the inner surface of the tube and grow in size within a transi-
the entire tube surface is dry, and all
is in the form of droplets that travel at high within the core of the
tube in the mist After the are completely vaporized, the fluid con-
sists of vapor in a second forced convection The
increase in the vapor fraction along the tube dif-
ference in the densities of the liquid and vapor increases the mean velocity
of the fluid by several orders of between the first and the second
forced convection
The local heat transfer coefficient varies as X and 1
m
decrease and
the of the tube, x. In the heat transfer
coefficient can increase by approximately an order of magnitude through the sub-
cooled flow boiling region. Heat transfer coefficients are further increased in the
stages of the saturated flow boiling Conditions become more complex
in the saturated flow region since the convection defined
in Equation either increases or decreases with increasing X, on the
fluid and tube wall material. Typically, the smallest convection coefficients exist in
the second (vapor) forced convection owing to the low thermal conductivity
of the vapor relative to that of the liquid.
The following correlation has been developed for the saturated flow boiling
in smooth circular tubes 28]:
h
yl XO
l6
(I
h,p
( )
007
+ 1058 -'-11- (1
m h
fg
(10.15a)
or
h
(p YAS
hsp
1.136 p:. X
(
q; )
0
7
+ 667.2 -:-;;-, (l -
m IFn
J6
(lO.ISb)
o <X 0.8
where in" is the mass flow rate per unit cross-sectional area. In
the value of the heat transfer coefficient, h, should be used.
In this expression, the phase Froude number is Fr = (in"/Plf/gD and the
coefficient on the surface-liquid combination, with representative vaI-
10.2. lO.15 applies for horizontal as well as vertical
parameter,f(Fr), accounts for stratification of the liq-
uid and vapor that may occur for horizontal mbes. Its value is unity for verti-
cal tubes and for horizontal tubes with Fr ;;;:: 0.04. For horizontal tubes with Fr :s
0.04, f(Fr) . All are evaluated at the saturation temperature,
The convection is associated with the liquid forced
convection region of 10.8 and is obtained from 8.62 with proper-
ties evaluated at Because 8.62 is for turbulentftow, it is recommended
that Equation 10.15 not be to situations where the
