buoyancy-driven two phase flow and boiling heat transfer in narrow vertical channels cfd simulation...
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Buoyancy-Driven Two Phase Flow and Boiling Heat Transfer in Narrow Vertical Channels
CFD Simulation of Two Phase Channel Flow
Karl J.L. Geisler, Ph.D. http://www.menet.umn.edu/~kgeisler
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 2
CFD Model
2-D FLUENT VOF multiphase simulation of channel flow
Evaluate convective enhancement mechanism
Estimated bubble parameters at selected operating point
Tsat = 12.3°C
Db = 0.78 mm
f = 59.3 Hz = (16.9 ms)-1
g = 4.2 ms
N/A = 96354 1/m2
g
L = 20 mm
5 mm
15 mm
Tin = Tsat
= insulated/non-conducting
Heater Surface
10 mm
10 mm
g
L = 20 mm
5 mm
15 mm
Tin = Tsat
= insulated/non-conducting
Heater Surface
10 mm
10 mm
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 3
5 mm channel
liquid
liquid phase volume fraction
vapor
time in secondseach frame = 5 ms
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 4
0.7 mm channel
liquid
liquid phase volume fraction
vapor
time in secondseach frame = 5 ms
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 5
0.3 mm channel
liquid
liquid phase volume fraction
vapor
time in secondseach frame = 5 ms
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 6
CFD Observations and Conclusions
Unconfined boiling heat flux nearly 50% due to enhanced convection Disruption of thermal boundary layer by bubble motion ≈3x single phase natural convection
Narrow channels show higher mass flux, enhanced single phase convection below nucleation site
Sensible heat rise in 0.3 mm channel yields reduced heat flux compared to 0.7 mm channel
Maximum enhancement observed for 0.7 mm channel 0.7 mm channel only 20% better than unconfined
0.7 mm experiment 50–150% better 0.3 mm experiment 150–500% better
Enhanced liquid convection likely NOT dominant enhancement mechanism
CFD Background and Additional Results
For details, see:http://www.menet.umn.edu/~kgeisler/Geisler_PhD_Dissertation.pdf
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 8
Bubble Departure Diameter
Tong et al. (1990) explored the suitability of a variety of bubble correlations for highly-
wetting liquids, including FC-72. They determined that the Cole and Rohsenow (1969)
departure diameter model fit available experimental data best:
gf
wb ρρg
ED
(F.1)
where
245aJ000465.0 E (F.2)
and
fgg
satfaJh
Tcp
(F.3)
with the saturation temperature is specified in absolute degrees. Tong et al. (1990)
modified the Cole and Rohsenow (1969) to include the wall temperature dependence of
departure diameter by evaluating the surface tension in Eq. (F.1) at the wall temperature.
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 9
Bubble Departure Frequency
Also following Tong et al. (1990), the bubble departure frequency is evaluated using the
Malenkov (1968) correlation:
qhU
UDf
fggb1
1-1
bb
(F.4)
where
gfbgf
gfbb
2
2
D
gDU (F.5)
Further, it is assumed that the bubble growth time, g, is one-quarter of the overall bubble
departure period (1/f), with the waiting time, w, equal to the remainder (Sateesh et al.,
2005) (Van Stralen et al., 1975).
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 10
Nucleation Site Density (1)
Benjamin and Balakrishnan (1997) nucleation site density correlation is employed,
following Chai et al. (2000).
4.0
3sat63.1
fPr8.218
T
A
N (F.6)
where the surface-liquid interaction parameter is given as
f
h
kc
kc
p
p
(F.7)
and the dimensionless roughness parameter is
2
aa 4.05.45.14
PRPR (F.8)
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 11
Nucleation Site Density (2)
In Eq. (F.8), Ra is the centerline average surface roughness, assumed equal to 1 m
following the discussion of Section 4.2, and P is the system pressure (101 kPa). This
nucleation site density correlation was validated using a large set of experimental data
from a variety of sources and covers the following parameter ranges:
1422m
N 1059
m
N 1013
C25ΔC5
μm 17.1μm 02.0
937.4
5Pr7.1
3-3-
a
Θ.
σ
T
R
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 12
Nucleation Site Density (3)
While values for the current system of interest are well within range for most of these
parameters, the Prandtl number for FC-72, 9.6, is high. In addition, its surface tension,
8.310-3 N/m is somewhat low. In fact, is it the low surface tension that also drives the
roughness parameter, Θ, out of range to a calculated value of 19. It is unclear exactly
what the impact of these deviations might be, though nucleation site density curves were
shown to flatten out at larger surface roughnesses (Benjamin and Balakrishnan, 1997).
Therefore, extrapolation outside the upper limit of Θ (and lower limit of ) is expected to
be less problematic than extrapolation on the lower end. Thus, Eq. F.8 is expected to
produce at least representative predictions of nucleation site density and will be used in
the absence of more accurate data/correlations.
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 13
Latent Heat Contribution
The latent heat contribution to the total boiling heat flux was calculating as the time-
averaged vapor volume generation rate multiplied by the product of the vapor density and
latent heat.
FluxHeat Boiling Total
23
4
onContributiHeat Latent Fractionalfgg
2
b hfA
ND
(F.10)
The values shown in Table F.1 appear to be congruent, in at least an order-of-magnitude
sense, with experimentally-observed measurements reported in the literature for FC-72
and similar highly-wetting organic fluids, e.g. (Bonjour et al., 2000) (El-Genk and
Bostanci, 2003) (Pioro et al., 2004) (Kim et al., 2006).
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 14
2-D Bubble Volume
The point on the pool boiling curve corresponding to the generation of a total vapor
volume (number of bubbles times the bubble departure volume) equivalent to the volume
of a single 2-D (cylindrical) bubble of the same diameter was chosen as the operating
point for the simulations. This point may be expressed mathematically as
2
b
3
b
223
4
D
HHLA
ND (F.10)
or, equivalently
2
3b L
A
ND (F.11)
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 15
Vapor Generation Rate
Given the bubble parameters in Table F.1 corresponding to a boiling surface superheat of
12.3°C, the mass flow rate for the vapor inlet representing the nucleation site may be
calculated. The average vapor mass generation rate over the bubble growth time is
g
g2
b
2
HD
m
(F.12)
As discussed in the following section, the vapor inlet representing the nucleation site in
the CFD model was taken to be 0.1 mm in size. This dimension is not representative of
expected nucleation sites but instead represents a compromise between computation
resources and bubble behavior—i.e. 0.1 mm is large enough to maintain a reasonable
number of computational cells, while it is, at the same time, sufficiently smaller than the
bubble departure diameter.
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 16
Vapor Inlet Mass Flux
Combining this with Eq. (F.12) yields an expression for the average vapor mass flux over
the bubble growth time.
g
g2
b
2
s
DG
(F.13)
where s is the size of the vapor inlet, 0.1 mm, and the channel depth once factors out of
the problem. For the chosen operating point, Eq. (F.13) evaluates to 15.18 kg/m2s.
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 17
Boiling parameter predictions for saturated FC-72 at atmospheric pressure (101 kPa)
T sat
(°C)
Boiling Heat Flux
(kW/m2)
Latent Heat Contribution
Bubble Departure Diameter
(mm)
Bubble Frequency
(Hz)
Bubble Period (ms)
Bubble Growth Time (ms)
Nucleation Site
Density
(m-2)
5.0 3.1 3% 0.811 51.4 19.5 4.9 64286.0 3.7 5% 0.806 51.9 19.3 4.8 111087.0 4.8 6% 0.802 52.7 19.0 4.7 176398.0 6.4 7% 0.797 53.6 18.7 4.7 263319.0 8.5 7% 0.793 54.7 18.3 4.6 3749010.0 11.0 8% 0.789 56.0 17.9 4.5 5142711.0 13.7 8% 0.784 57.4 17.4 4.4 6844912.0 16.6 9% 0.780 58.8 17.0 4.3 8886612.3 17.7 9% 0.778 59.3 16.9 4.2 9635413.0 19.8 10% 0.775 60.4 16.6 4.1 11298514.0 23.1 10% 0.771 62.1 16.1 4.0 14111515.0 26.7 11% 0.766 63.8 15.7 3.9 173566
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 18
Mikic and Rohsenow (1969) bubble growth rate correlation
0
0.1
0.2
0.3
0.4
0 0.005 0.01 0.015 0.02
Time (s)
Bu
bb
le R
adiu
s (m
m)
0.00E+00
5.00E-11
1.00E-10
1.50E-10
2.00E-10
2.50E-10
3.00E-10
Bu
bb
le V
olu
me
(m3)
Bubble Radius
Bubble Volume
slope = 1.39E-8
ww
sat
w 1132
T
TTJar
f
fgg
satfJah
Tc p
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 19
CFD Model Geometry
g
L = 20 mm
5 mm
15 mm
Tin = Tsat
= insulated/non-conducting
Heater Surface
10 mm
10 mm
g
L = 20 mm
5 mm
15 mm
Tin = Tsat
= insulated/non-conducting
Heater Surface
10 mm
10 mm
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 20
GAMBIT screen-shot of model geometry showing vertices, edges, and faces
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 21
GAMBIT screen-shot showing mesh details in vicinity of vapor inlet
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 22
Comparison of temperature results from single phase numerical simulations
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 23
Velocity results for initial steady-state single phase solution
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 24
Nucleation site mass flux profiles
0
20
40
60
80
100
120
0.000 0.005 0.010 0.015
Time (s)
Vap
or
Ma
ss F
lux
(kg
/m2s)
vapor
liquid
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 25
Phase contour plots at 4 ms time steps from the beginning of the VOF simulation through the first four bubble generations
t = 4 ms t = 8 ms t = 12 ms t = 16 ms t = 20 ms t = 24 ms t = 28 ms
t = 32 ms t = 36 ms t = 40 ms t = 44 ms t = 48 ms t = 52 ms t = 56 ms
t = 60 ms t = 64 ms t = 68 ms t = 72 ms t = 76 ms t = 80 ms t = 84 ms
t = 88 ms t = 92 ms t = 96 ms t = 100 ms t = 104 ms t = 108 ms t = 112 ms
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 26
Phase contour plots at 4 ms time steps from the beginning of the VOF simulation through the first four bubble generations
t = 4 ms t = 8 ms t = 12 ms t = 16 ms t = 20 ms t = 24 ms t = 28 ms
t = 32 ms t = 36 ms t = 40 ms t = 44 ms t = 48 ms t = 52 ms t = 56 ms
t = 60 ms t = 64 ms t = 68 ms t = 72 ms t = 76 ms t = 80 ms t = 84 ms
t = 88 ms t = 92 ms t = 96 ms t = 100 ms t = 104 ms t = 108 ms t = 112 ms
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 27
Velocity contour plot at end of VOF simulation, 5 mm channel
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 28
Inlet and outlet mass flow rates as a function of time, 5 mm channel
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Simulated Time (s)
Mas
s F
low
Rat
e (k
g/s
)
Inlet
Outlet
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 29
Heater top and bottom heat flux as a function of time, 5 mm channel
0
2
4
6
8
10
12
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Simulated Time (s)
Hea
t F
lux
(W/m
2)
Top Half
Bottom Half
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 30
Two Phase SimulationTemperature Results Comparison
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 31
Surface heat flux profiles for 5 mm channel single phase natural convection solution and VOF simulation results at t = 1.34 s
0
5
10
15
20
0 5 10 15
Local Surface Heat Flux (kW/m2)
Dis
tan
ce A
lon
g H
eate
r (m
m)
VOF Solution 1.34 s
Single Phase
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 32
Surface heat flux profiles
0
5
10
15
20
0 5 10 15 20 25
Local Surface Heat Flux (kW/m2)
Dis
tan
ce
Alo
ng
Hea
ter
(mm
)
0.3 mm
0.7 mm
single phase
two phase
Karl J.L. Geisler, Ph.D. January 2007 http://www.menet.umn.edu/~kgeisler 33
5 0.7 0.3 5 0.7 0.3
0.0169 0.0079 0.0021 0.28 0.10 0.026
3.4 11 7.0 56 143 87top 2.09 1.72 0.32 9.96 9.63 6.99
bottom 3.12 3.40 2.47 4.86 8.45 8.38average 2.60 2.56 1.39 7.41 9.04 7.69
211 207 113 600 732 622
216 215 118
7.5105 288 9.7
Two PhaseSingle Phase
Heat Flux (kW/m2)
Elenbaas Number
Prediction via Eq. (6.15)
(W/m2K)
Channel Mass Flow Rate (kg/s)
Average Heat Transfer
Coefficient (W/m2K)
Channel Spacing, (mm)
Channel Mass Flux (kg/m2s)
CFD Simulation Results Summary