Buoyancy-Driven Two Phase Flow and Boiling Heat Transfer in Narrow Vertical Channels CFD Simulation...

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

L = 20 mm

Tin = Tsat

= insulated/non-conducting

Heater Surface

L = 20 mm

Tin = Tsat

Heater Surface

5 mm channel

liquid

liquid phase volume fraction

time in secondseach frame = 5 ms

0.7 mm channel

liquid

0.3 mm channel

liquid

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

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:

wb ρρg

245aJ000465.0 E (F.2)

satfaJh

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.

Bubble Departure Frequency

Also following Tong et al. (1990), the bubble departure frequency is evaluated using the

Malenkov (1968) correlation:

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).

Nucleation Site Density (1)

Benjamin and Balakrishnan (1997) nucleation site density correlation is employed,

following Chai et al. (2000).

3sat63.1

fPr8.218

N (F.6)

where the surface-liquid interaction parameter is given as

and the dimensionless roughness parameter is

aa 4.05.45.14

PRPR (F.8)

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:

N 1059

N 1013

C25ΔC5

μm 17.1μm 02.0

5Pr7.1

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.

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

onContributiHeat Latent Fractionalfgg

(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).

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

ND (F.10)

or, equivalently

ND (F.11)

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

(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.

Vapor Inlet Mass Flux

Combining this with Eq. (F.12) yields an expression for the average vapor mass flux over

the bubble growth time.

(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.

Boiling parameter predictions for saturated FC-72 at atmospheric pressure (101 kPa)

Boiling Heat Flux

(kW/m2)

Latent Heat Contribution

Bubble Departure Diameter

Bubble Frequency

Bubble Period (ms)

Bubble Growth Time (ms)

Nucleation Site

Density

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

Mikic and Rohsenow (1969) bubble growth rate correlation

0 0.005 0.01 0.015 0.02

Time (s)

0.00E+00

5.00E-11

1.00E-10

1.50E-10

2.00E-10

2.50E-10

3.00E-10

Bubble Radius

Bubble Volume

slope = 1.39E-8

w 1132

satfJah

CFD Model Geometry

L = 20 mm

Tin = Tsat

Heater Surface

L = 20 mm

Tin = Tsat

Heater Surface

GAMBIT screen-shot of model geometry showing vertices, edges, and faces

GAMBIT screen-shot showing mesh details in vicinity of vapor inlet

Comparison of temperature results from single phase numerical simulations

Velocity results for initial steady-state single phase solution

Nucleation site mass flux profiles

0.000 0.005 0.010 0.015

Time (s)

liquid

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

Phase contour plots at 4 ms time steps from the beginning of the VOF simulation through the first four bubble generations

Velocity contour plot at end of VOF simulation, 5 mm channel

Inlet and outlet mass flow rates as a function of time, 5 mm channel

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Simulated Time (s)

Outlet

Heater top and bottom heat flux as a function of time, 5 mm channel

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Simulated Time (s)

Top Half

Bottom Half

Two Phase SimulationTemperature Results Comparison

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

Local Surface Heat Flux (kW/m2)

VOF Solution 1.34 s

Single Phase

Surface heat flux profiles

0 5 10 15 20 25

Local Surface Heat Flux (kW/m2)

0.3 mm

0.7 mm

single phase

two phase

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

Buoyancy-Driven Two Phase Flow and Boiling Heat Transfer in Narrow Vertical Channels CFD Simulation...

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