Heat and Mass Transfer Laboratory 1 Anthony Servonet Stefano Nebuloni Bruno Agostini - supervisor...

Heat and Mass Transfer Laboratory 1

Anthony ServonetStefano NebuloniBruno Agostini - supervisor

Micro-channel flow boiling correlations and 3-zone model plus comparison to recent published results

08 February 2007


– introduction to micro-channel features– heat transfer prediction models

– Kandlikar and Balasubramanian (2004)– Zhang at al. (2004)– 3 zone model – Thome-Dupont-Jacobi (2004)

– comparison with experimental data– conclusions

Contents of the presentation


– h is not dependent on mass velocity– h is not dependent on vapor quality (x>0.1)– h is dependent on heat flux– h is dependent on saturation temperature

General considerations on micro-scale flow boiling trends (from experiments)


Macro to micro-scale transition

Kandlikar and Grande : 3 mm

Mehandal et al. : micro-channels (1 – 100 μm)meso-channels (100 μm –

1mm)macro-channels (1 – 6 mm)conventional (Dh > 6 mm)

Kew and Cornwell : )(

4

VLth g

D


- this model is an extension of their macro-scale correlation to tube diameter <3mm, eliminating the dependency on Froude number

- it is based on Reynolds number ReLO (all liquid), taking into account the laminar or turbulent flow condition

Kandlikar and Balasubramanian model (1/2)

Heat transfer coefficient can be calculated in the following way:

if 100<ReLO <1600 : ),max( CBDNBDTP hhh

LOFLLONBD hFxBohxCoh 8.07.08.02.0 1105816683.0

LOFLLOCBD hFxBohxCoh 8.07.08.09.0 12.6671136.1

CNu h

LLO D

kNuh

if ReLO <100 :

LOFLLONBD hFxBohxCoh 8.07.08.02.0 1105816683.0

NBDTP hh

FFL represents the nucleation characteristic of the liquid on a given surface


Kandlikar and Balasubramanian model (2/2)

- The model predicts that nucleate boiling becomes dominant for low Reynolds numbers- convective boiling contribution becomes dominant to high vapor quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1000

2000

3000

4000

5000

6000

x - vapour quality

h [

W/K

m2]

KANDLIKAR MODEL - R22 at Tsat=15°C - G=295 - Dh=0.51mm

Q=27 KW/m2

Q=35 KW/m2

Q=45 KW/m2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1000

2000

3000

4000

5000

6000

x - vapour qualityh [

W/K

m2]

KANDLIKAR MODEL - R22 at Tsat=15°C - G=295 - Q=27 KW/m2

Dh=0.4 mm

Dh=0.5 mm

Dh=0.6 mm

The model has been implemented in a MATLAB code (Excel compatible)


- this model (2004) is a modification of the macro-scale flow boiling correlation proposed by Chen (1966) where the correlation proposed by Foster and Zuber for nucleate boiling heat transfer is used

- Chen model was developed to determine flow boiling heat transfer coefficients when both liquid and vapor phases were both in turbulent flows (Rek>2300)

S: suppression factorF: Reynolds number factor

)',1max( FF fF 64.0'

22 11

XX

Cf

Martinelli parameter

5.05.0

2 1

f

g

g

f

g

f

x

x

f

f

dzdp

dzdpX

C is a function of flow conditions (Re)

SPNBTP hFhSh

Zhang – modified Chen model (1/3)



2000ReRe046.0

1000ReRe/162.0

k

kk

kffriction factors for circular channels

for 1000<Rek<2000 an interpolation is used

- single phase heat transfer correlations are modified to take into account laminar flow conditions and channels orientation w.r.t. gravity

75.024.024.024.029.05.0

49.045.079.0

00122.0 satsatgfgf

fpffNB pT

h

Ckh

satsatwallsatsat

satwallsat

TpTpp

TTT

NuD

kh

h

fsp

17.16 Re1053.21/1 fS

Solving for the wall temperature allows to obtain the heat transfer coefficient

0 QTTTh satwwTP

The model has been implemented in a MATLAB code with a bisection method solver



- A clear transition zone is identifiable in correspondence of sharp variation of heat transfer coefficient (subordinated to Reynolds number range)

- At high vapor quality (x1-) the heat transfer coefficient diverges, due to the big contribution of convective boiling component

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11000

2000

3000

4000

5000

6000

7000

8000

9000

10000

x - vapour quality

h [W

/Km

2]

ZHANG MODEL - R22 at Tsat=15°C - Q=10KW/m2 - Dh=1.4mm

G=200

G=400

G=600

G=800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

2

3

4

5

6

7

8

9

x - vapour quality

Tw

-Tsa

t [K

]

ZHANG MODEL - R22 at Tsat=15°C - Q=10KW/m2 - Dh=1.4mm

G=200

G=400

G=600

G=800


3-Zone model - Thome-Jacobi-Dupont (2004) (1/6)- A three zone flow boiling model of the evaporation of elongated

bubbles in micro-channels- the sequential passages of a liquid slug, an evaporating bubble and a

vapor slug are assumed as a qualitative description of the flow pattern

- local heat transfer coefficient is then obtained by a time average (over the period of the passage of the triple):

zht

zht

zht

zh vv

filmfilm

ll


3-Zone model - Thome-Jacobi-Dupont (2004) (2/6)Major hypothesis:- liquid film remains attached to the wall (shear stresses are

assumed negligible) and is assumed very small compared to channel radius

- homogeneous flow (vapor and liquid velocities are the same)- heat flux is uniform and constant in time- neither liquid or the vapor phases are superheated

Bubble departure frequency:- bubbles are assumed to grow until r= R where the fluid reaches

saturation temperature (x=0)- from bubble departures frequency f =1/ it is possible to

evaluate the length of the liquid slug and the residence time of vapor and liquid

B

mass and volume conservation l

P

GRL 3

40

V L


3-Zone model - Thome-Jacobi-Dupont (2004) (3/6)

Local heat transfer coefficient: liquid slug and dry zone

l

vv

x

xt

11

g

ll

x

xt

11

Residence time:

The flow is assumed to be hydrodynamically and thermally developing

RePr455.0 3

zL

dzNulam

3/2

3/2 3

11

1Pr8/7.121

Pr1000Re8/

zL

dzNutrans

210 64.1Relog82.1

if Re 2300:London and Shah correlation

if Re> 2300:Gnielinski correlation

(homogeneous flow)

Asymptotic method (Churchill and Usagi) 4/144translam hhh



Thin film evaporation modelEnergy balance across the liquid layer gives the following evolution with timeof the layer:

th

qztz

lvl

0, min0

z

q

hzt lvl

filmdry

Since h tends to infinity if end tends to zero(and the choice of end is quite complicate)

filmt

endend

ll

film

kdt

tz

k

th

0

0

0

1 ln,

1

mean heat transfer coefficient

end

lkh

0

22

Liquid film thicknessThe prediction of initial liquid film thickness is based on the work done by doneby Moriyama and Inoue (a correlation including a further constant C0)

8

1

88

41.0

84.0

0 1.007.030

Bo

dUC

d p

l



The constant C0. the bubble departure frequency and the end constitute the 3parameter of the model that can be optimized on a specific database

0

50

100

150

200

250

300

0.00 0.50 1.00 1.50 2.00Time [ms]

Hea

t Tra

nsfe

r C

oeffi

cien

t [kW

/m2 K

]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1Vapor Quality

Rel

ativ

e L

engt

hs [

-]

L.S.: Liquid Slug [-]

E.B.: Elongated Bubble [-]

V.S.: Vapor Slug (Dry Zone) [-]

periodic heat transfer coefficient(vapor quality 8%)



R22 ; Tsat = 15 [°C] ; Q = 10 [kW/m̂ 2] ; DH = 1.4 [mm]

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Vapor quality [-]

Hea

t tra

nsfe

r co

effic

ient

[kW

/m̂2K

]

G = 200G = 400G = 600G = 800

R22 ; Tsat = 15 [°C] ; Q = 10 [kW/m̂ 2] ; DH = 1.4 [mm]

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Vapor qualitiy [-]W

all s

uper

heat

[K]

l

G = 200

G = 400

G = 600

G = 800

The two models (basic version – logarithm – and modified version) have beenprovided for the project development


Threshold diameter criteria

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0 0.5 1 1.5 2 2.5 3 3.5 4

Dh [mm]

Dh

/Dth

[-]

mini-channels conventional channels

macro-scale

micro-scale

Kew and Cornwellthreshold

Kandlikar and Grandethreshold

)(

4

VLth g

D

Transitional diameter depends on the refrigerant properties


Sources

Analysed 890 data in database of 2767 values (32%)Fluids : CO2, R11, R22, R134a, R141b, R410A, Water.

• diameter between 0.263 et 2.87 [mm],• mass velocity between 23 and 6673 [kg/m2s],• saturation temperature between -18 and 105 [°C],• heat flux between 4.4 and 938 [kW/m2],• vapour qualities between 0 to 1,• heat transfer coefficient measured between 0.2 and

286 [kW/m2K]

Author Refrigerant Dh / L [mm] G [kg/m^2s] Tsat [°C] q [kW/m^2] h [kW/m^2K] X

0.77 / 695 467

2.01 / 690 83

Bang Choo (2004) R22 1.67 / 305 600 9.5 5, 10, 20, 30 0.7 - 4.7 Up to 0.92

Bao et al (2000) R11 1.95 / 270 167, 279, 335, 446, 560 58 - 75 39 - 125 0.9 14.1 Up to 0.85

Huai et al (2004) CO2 1.31 / 500 283, 310 5.2, 107 6.8 - 17.3 0.9 - 12 Up to 0.91

Kew and Cornewell R141b 1.39, 2.87, 3.69 / ? 188, 212, 478, 1480 32 9.7 - 90 0.4 - 7.2 Up to 0.90

Kim et al (2004) R22 1.41 / 455 200, 400, 600 5, 15 5, 10, 15 2.5 - 7.4 0.1 - 0.9

Koyama(2001) CO2 1.8 / 340 250, 260 0, 10 32, 37 19 - 25 Up to 82

Lee and Mudawar R134a 0.35 / ? 440 - 6673 (-18) - 25 159 - 938 1.6 - 49.6 0.25 - 0.86

Lin et al (2001) R141b 1.1 / 380 510 47.5 18 - 72 1 - 5.9 Up to 1

Owhaib and Palm (2003) R134a 0.8, 1.2, 1.7 / 220 100, 200, 300, 400, 500 24 10, 20, 30 2.9 - 10 Up to 0.6

Pamitran et al (2003) R410A 1.5 / 1500 and 3.0 / 3000 300, 400, 600 10 5, 10, 15 0.2 - 7.2 Up to 1

Pettersen(2004) CO2 0.8 / 540 190, 280, 380, 570 0, 10, 20, 25 5, 10, 15, 20 1.8 - 27.4 0.1 - 0.78

Qu and Mudawar Water 0.35 / ? 135, 202, 254, 323, 400 30, 60 5.2 - 318 23.1 - 44.6 Up to 0.17

Steinke Water 0.203 / ? 157; 366; 671; 1022 22 55 - 700 31 - 286 Up to 0.96

Sumith et al (2003) Water 1.45 / 100 23, 44, 57, 71, 107, 153 100 - 105 36, 101, 209, 391 7.6 - 33 Up to 0.6

Yan and Lin (1998) R134a 2/ 200 50, 100, 200 5, 15, 31 5, 10 ,15, 20 1.3 - 6.3 0.08 - 0.8

CO2 1.14, 1.53, 1.54 / ? 200, 300, 400 5 10, 15, 20 5.8 - 13 0.23 - 0.83

R410A 1.36, 1.44 200, 300, 400 0, 5, 10 10, 15, 20 6.2 - 19.8 0.06 - 0.90

Up to 0.971.8 - 11

Yun et al (2005)

Agostini et al(2003) R134a 9.3 4.4 - 14.6


Description of project


Previous database (collected by Ribatski G.)

Ribatski data (without water)

0

5000

10000

15000

20000

25000

30000

0 5000 10000 15000 20000 25000 30000

h_experimental [W/m̂ 2K]

h_m

odel

[W/m̂

2K]

l

Kandlikar

Zhang

TZM

In interval ± 30% :•Kandlikar =6.2 %•Zhang = 11.4 %•TZM = 28.4 %

MAPE(Mean Absolute Percentage Error) :•Kandlikar =74 %•Zhang = 116 %•TZM = 83 %


New database(Kew and Cornewell, Steinke, Lee and Mudawar, Qu and Mudawar)

All new data

0

10000

20000

30000

40000

50000

60000

0 10000 20000 30000 40000 50000 60000

h_experimental [w/m̂ 2K]

h_m

odel

[W/m̂

2K]

l

Kandikhar

Zhang

TZM

In interval ± 30% :• Kandlikar =12.6

%• Zhang = 43.7

%• TZM = 32.9 %

MAPE :• Kandlikar =75 %• Zhang = 87%• TZM = 49 %


Conclusions

• Kandlikar model is simple to be implemented,

but the prediction error is quite significant• Zhang model predicts the heat transfer

coefficient with a higher accuracy but with higher dispersion and it predicts trends which are not resulting from experiments

• Three zones model is the most promising one, approaching the problem from the physics of the phenomena and therefore producing better results.

A new set of experimental data of flow boiling heattransfer coefficient has been acquired and compared withthree different models :

Date post:	25-Dec-2015
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Heat and Mass Transfer Laboratory 1 Anthony Servonet Stefano Nebuloni Bruno Agostini - supervisor...

Documents