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
6/1/2012 3University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 4University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 5University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 6University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 7University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
6/1/2012 8University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 9University of Pretoria
Department of Mechanical & Aeronautical Engineering
• Data Reduction2
2 Pdf i 2
vLf
Measured
Average fluid bulk temperatureAverage fluid bulk temperature
6/1/2012 10University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
6/1/2012 11University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
6/1/2012 12University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
Reynolds Number [Re]
6 505 W/m2
6/1/2012 13University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
6/1/2012 14University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
j Factor 3 225 W/m 2
j Factor 4 703 W/m 2
j Factor 6 505 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
j Factor 1 451 W/m 2
j Factor 3 225 W/m 2
j Factor 4 703 W/m 2
j Factor 6 505 W/m 2
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 1 451 W/m 2
Friction Factor 3 225 W/m 2
Friction Factor 4 703 W/m 2
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
Friction Factor 1 451 W/m 2
Friction Factor 3 225 W/m 2
Friction Factor 4 703 W/m 2
Friction Factor 6 505 W/m 220
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
Measured Nusselt Number
6/1/2012 15University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
Measured Nusselt Number
6/1/2012 16University of Pretoria
Department of Mechanical & Aeronautical Engineering
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
6/1/2012 17University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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)
6/1/2012 18University of Pretoria
Department of Mechanical & Aeronautical Engineering
• 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
Reynolds Number [Re]
5 346 W/m
6/1/2012 19University of Pretoria
Department of Mechanical & Aeronautical Engineering