miss m hallquist prof jp meyer€¦ · microsoft powerpoint - final defense.pptx author: user...

Miss M Hallquist Prof JP MeyerProf JP Meyer

6/1/2012 1

Laminar Turbulent High insulation requirements Less insulation needed

Re < 2100 Re > 3000

Insufficient energy balance Low heat transfer coefficients Low pressure drop

Good energy balances High pressure drop

p p

????Transitional

????

6/1/2012 2University of Pretoria

Department of Mechanical & Aeronautical Engineering

120

140

14.03/1

75.0Pr025.0PrRe24.1

w

bx Gr

xdNu

x

80

100m

ber [

Nu]

1923 Dx

3800Re280 160Pr40

40

60

Nus

selt

Num

Petukhov et al. (1969)ESDU (2001)Ghajar and Tam (1994)

4108.21000 Gr

8.32.1 w

b

20

40 j ( )Chilton and Colburn (1933)Dittus and Boelter (1930)Petukhov (1959)Gnielinski (1976)Churchill (1977)C

00 2000 4000 6000 8000 10000 12000 14000 16000

Reynolds Number [Re]

Constant UHF



• Applications Energy transfer in chillers Heat rejection in condensers Steam generation in power stations

• System efficiency & capacity

Steam generation in power stations

• “Best of both worlds”

• Accurate correlationAccurate correlation



• Experimental Set‐up

234 1

6

5

Data Acquisition System

1. Cold water tank2. Positive displacement pump3. Accumulator4. Bypass valve5. Flow meter (low flow rate)

7C

8

Test Section

5. Flow meter (low flow rate)6. Flow meter (high flow rate)7. DC inverter welder8. MPC controller

7 8



• Measurement Procedure Reynolds number: 450 – 10 300Reynolds number: 450 10 300

Prandtl number: 4 – 7

Nusselt number: 2 3 – 67 Nusselt number: 2.3 – 67

Grashoff number: 60 – 25 600

H t fl 1 500 W/ 2 Heat flux: − 1 500 W/m2

− 3 000 W/m2

− 4 500 W/m2

6 000 W/m2− 6 000 W/m2



• Data Reductiondh

Nu i sqh RiQ l

2 100 TTRR

Qq eleck

Nu bs TT

h

RiQelec

cALR 0

Ldq

is

1mm

Integrate wall temperatures

Average of inlet& outlet temperature

)(

)()( .,

xCpm

xdxqTxT i

iff



35

4077

• System Validation

25

30

35[°

C]

5

6

umbe

r, N

u

5

6

umbe

r, N

u

15

20

Tem

pera

ture

[

3

4

ocal

Nus

selt

Nu

3

4

ocal

Nus

selt

Nu

0

5

10Measured Wall TemperatureBulk Fluid TemperatureCalculated Fluid TemperatureLinear (Measured Wall Temperature)

1

2Lo

Ghajar and Tam (1994)

Measurements

1

2Lo

Ghajar and Tam (1994)

M t00 1 2 3 4 5 6

Tube Length [m]

00 1 2 3 4 5 6

Tube Length [m]0

0 1 2 3 4 5 6Tube Length [m]

Measurements



• System Validation60

MeasurementsGhajar and Tam (1994)

40

50

ber,

Nu

j ( )Gnielinski (1976)

20

30

e N

usse

lt nu

mb

10Ave

rage

00 1000 2000 3000 4000 5000 6000 7000

Reynolds Number, Re



• Data Reduction2

2 Pdf i 2

vLf

Measured

Average fluid bulk temperatureAverage fluid bulk temperature



0.16PoiseulleBlasius

0.12MeasurementsGhajar and Tam (1994)

• System Validation

0.1

0.12

0.14

or, f

BlasiusMeasurements

0.08

0.1r,

f

Ghajar and Tam (1994)Allen and Eckert (1964)

0.06

0.08

0.1

Fric

tion

Fact

o

0 04

0.06

Fric

tion

Fact

or

0.02

0.04

0.02

0.04

00 2000 4000 6000 8000 10000 12000

Reynolds Number, Re0

0 1000 2000 3000 4000 5000 6000 7000Reynolds Number, Re



• Heat Transfer1.E+05

6mm Tube - 1 278

2 8326 mm Tube - 1 268 W/m 2

6 mm Tube - 2 832 W/m 240

60Re = 1 500Re = 1 800Re = 2 100Re = 2 400Re = 2 700R 3 000

1.2

1.E+04

r, R

e

4 078

5 346

1 464

3 192

4 575

6 mm Tube - 4 078 W/m 2

6 mm Tube - 5 346 W/m 2

8 mm Tube - 1 464 W/m 2

8 mm Tube - 3 192 W/m 2

8 mm Tube - 4 575 W/m 2

20

Re = 3 000Re = 6 100Re = 8 900

0.8

1io

, h(x

) t/h(

x)b

1.E+03ynol

ds N

umbe

r

6 271

1 451

3 225

4 703

6 505

8 mm Tube - 6 271 W/m 2

10 mm Tube - 1 451 W/m 2

10 mm Tube - 3 225 W/m 2

10 mm Tube - 4 703 W/m 2

10 mm Tube - 6 505 W/m 2

0-60 -40 -20 0 20 40 60

0 4

0.6

at T

rans

fer R

ati

Rey 6 505

-40

-20

0.2

0.4

Loca

l Hea

1.E+021.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Raleigh Number, Ra -60Temperature [ C]

00 1000 2000 3000 4000 5000 6000 7000 8000 9000

Reynolds number, Re



• Heat Transfer

70

80

50

60

70r [

Nu]

30

40

usse

lt N

umbe

r

10

20

Nu

1 451 W/m

3 225 W/m

4 703 W/m

2

2

2

2

00 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000


6 505 W/m2



0 18

0.21 451 W/m3 225 W/m

2

2

• Friction Factor0.05

1 451 W/m3 225 W/m

2

2

0 12

0.14

0.16

0.18

or, f

3 225 W/m4 703 W/m6 505 W/m

2

2

0.04

0.045r,

f3 225 W/m4 703 W/m6 505 W/m

2

2

0 06

0.08

0.1

0.12

Fric

tion

Fact

o

0 03

0.035

Fric

tion

Fact

or

0.02

0.04

0.06

0.025

0.03

00 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Reynolds Number, Re0.02

1800 2000 2200 2400 2600 2800 3000 3200Reynolds Number, Re



1j Factor 1 451 W/mj Factor 3 225 W/mj Factor 4 703 W/mj Factor 6 505 W/mF i ti F t 1 451 W/

j Factor 1 451 W/m 2




1

acto

r

j Factor 1 451 W/mj Factor 3 225 W/mj Factor 4 703 W/mj Factor 6 505 W/mFriction Factor 1 451 W/m





Friction Factor 1 451 W/m 2

25

30

Series1

Series2

Measurements

Nu prediction (k = factor of 4.7)kfPrSt /

232

25

30Series1Series2

Measurements

Nu prediction (k = factor of 4.7)

0.1r a

nd j

Fact

or

Friction Factor 1 451 W/mFriction Factor 3 225 W/mFriction Factor 4 703 W/mFriction Factor 6 505 W/m




Friction Factor 6 505 W/m 2 Friction Factor

0 1Cco

rrec

ted

j F

Friction Factor 1 451 W/mFriction Factor 3 225 W/mFriction Factor 4 703 W/mFriction Factor 6 505 W/m





selt

Num

ber

20

elt N

num

ber

0.01

Fric

tion

Fact

o

j Factor

0.1

on F

acto

r and

10

15

Pred

icte

d N

uss

10

15

redi

cted

Nus

se

0 0010.01

Fric

tio

0

5

P

5

Pr

0.001100 1000 10000

Reynolds Number, Re100 1000 10000

Reynolds Number, Re

00 5 10 15 20 25 30

Measured Nusselt Number

00 5 10 15 20 25 30




1 E 051.E+05

Ay = 72.971x0.0664

R² = 0.603

100

y = 5.73935x‐0.04502

R² = 0.990176.25

6.3

6.35

632417

140450

103931.

.

.

s

b.

LPrGre

ReNu

25

30

Series1

Series4Measurements

Nu prediction

1.E+04m

ber [

Gr]

B

C/d

i)0.2

875

6.15

6.2

6.25

(L/d

i)0.1

625

103931x

PrGre.

20ss

elt N

umbe

r

1.E+03

Gra

shof

f Num

D

EGr0

.085

Pr(L

/

06640

6.05

6.1

Gr0

.045

Pr0.

2 (

10

15

Cal

cula

ted

Nus

1 451 W/m3 225 W/m4 703 W/m6 505 W/m

2

2

2

2

066401404080

287500850 97172

..

s

b...

.

Nu

PrRe.

xLPrGr

5.95

6

5

C

1.E+021.E+01 1.E+02 1.E+03

Re0.8Pr0.4 (µb/µs)0.14Nu-1

101 10

Re0.5(µb/µs)0.14Nu-1

5.90 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Re0.45Pr0.2(µb/µs)0.14Nu-1

00 5 10 15 20 25 30




Consistent data for all test cases

Smooth transition between laminar and turbulent flow regimes

Transition is dependent on heat flux of the system

Secondary flow effects….?

Development of a correlation Development of a correlation

Improvements Data logger

Power supply

Calibration methods



• j Factor0.01

0.6 ]

j Fac

tor [

stPr

0

1 451 W/m3 225 W/m4 703 W/m6 505 W/m

2

2

2

2

0.001500 5000Reynolds Number [Re]

Ghajar & Tam (1994)



• Uncertainties1.16

1 1

1.12

1.14

erta

inty

[%]

1.06

1.08

1.1

t Num

ber U

nce

1.02

1.04

vera

ge N

usse

lt

1 451 W/m3 225 W/m4 703 W/m5 346 W/m

10 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Av


5 346 W/m



miss m hallquist prof jp meyer€¦ · microsoft powerpoint - final defense.pptx author: user...

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