experimental investigation of effect of buoyancy on...
TRANSCRIPT
Experimental investigation of effect of buoyancy on
supercritical carbon dioxide heat transfer in round tubes
The 4th International Symposium –Supercritical CO2 power cycles
Pittsburgh, PA
September 9 & 10, 2014
Sandeep Pidaparti, Mark Mikhaeil, Jacob McFarland, Devesh Ranjan, Mark Anderson
2
Contents
• Motivation for the study
• Experimental facility
• Data analysis procedure
• Results
• Summary
3
Motivation for the study
• Heat exchangers in the cycle
– High temperature recuperator (HTR)
– Low temperature recuperator (LTR)
– Cooler
• Expected operating conditions
– 7.6 – 20 MPa
– 20 – 50 KW/m2
– 200 – 300 Kg/m2s
• For these conditions, there is a needfor fundamental understanding ofeffects of buoyancy on heat transfer
– Various channel sizes From ANL Plant Dynamics Code [Moisseytsev et al]
4
Experimental facility
• Heat transfer deterioration due to buoyancy effects and flow acceleration
• Key components of the test facility – A high pressure CO2 supply pump, circulation pump,flow meter, precooler, preheater, and DC power supply
• Test section orientation can be changed with minor tubing modifications
Component Capabilities
HPLC pump Up to ~ 10,000 psi
Circulation pump 0.6 – 7.0 GPM
Coriolis flow meter 0 – 0.27 Kg/sec
Pre-heater Maximum 5.5 KW
Water chiller Maximum 5.28 KW
Pre-cooler Double tube HEX
DC power supply 0 – 5 KW
Buffer Tank ~ 0.5 m3
5
Test section
1 m
0.3 m
75 mmPT RTD
PTRTD
• Direct current volumetric heating
– 10 V, 500 A power supply
• L = 1m, Din ~ 10.9mm, Dout ~ 12.7mm
• RTD probes are calibrated against boiling water and ice bath
• Wall temperatures are measured using 20 E type thermocouples
– Calibrated against RTDs under no heat flux conditions
6
Data analysis procedure
• Data recorded for 500 s @ 1Hz
𝑄"𝑃𝑆 =𝑉𝑃𝑆𝐼𝑃𝑆
𝜋𝐷𝑖𝐿[PS – power supply]
𝑇𝑤𝑖 = 𝑇𝑤𝑜 + 𝑞
4𝑘𝑠𝑠
𝐷𝑜𝑢𝑡
2
2−
𝐷𝑖𝑛
2
2−
𝑞
2𝑘𝑠𝑠
𝐷𝑜𝑢𝑡
2
2ln
𝐷𝑜𝑢𝑡
𝐷𝑖𝑛
𝑞 =𝑉𝑃𝑆𝐼𝑃𝑆
𝜋
4𝐷𝑜𝑢𝑡2 −𝐷𝑖𝑛
2 𝐿
Where, kss is the thermal conductivity of stainless steel 316
𝑇𝑏+1 = 𝑇𝑏 +𝑄"𝑃𝑆
𝑚𝐶𝑝𝜋𝐷𝑥
• Local heat transfer coefficients and Nusselt numbers are calculated as,
ℎ =𝑄"𝑃𝑆
𝐴 𝑇𝑤𝑖−𝑇𝑏
𝑁𝑢𝑏 =ℎ𝐷
𝑘𝑏
7
Results
• Effect of
– Operating pressure
– Flow direction
– Inlet temperature
– Heat flux
Control Parameters Range of Study
Inlet Temperature 20 – 550 C
Operating pressure 7.5, 8.1, and 10.2 MPa
Mass flux 195, 320 Kg/m2sec
Heat flux 0 - 65 KW/m2
Flow direction Horizontal, Upward, and Downward
• Buoyancy factor calculations
8
Effect of operating pressure
• Test conditions
– Mass flux, 195 Kg/m2sec
– Heat flux, 13.5 KW/m2
– Downward flow
• Heat transfer enhancement close to thepseudo-critical point
• Tb < Tpc , lower operating pressure results inhigher HTC’s
• Tb > Tpc , higher operating pressure results inhigher HTC’s
• Attributed to variation of isobaric Prandtlnumber
0.92 0.94 0.96 0.98 1 1.02 1.04 1.0630
40
50
60
70
80
Tb/T
pc
Tw
i(C)
7.5 MPa
8.1 MPa
10.2 MPa
0.92 0.94 0.96 0.98 1 1.02 1.04 1.06500
1000
1500
2000
2500
3000
3500
4000
Tb/T
pc
h [
W /
m2K
]
7.5 MPa
8.1 MPa
10.2 MPa
9
Effect of flow direction
• Test conditions
– Mass flux, 195 Kg/m2sec
– Heat flux, 24 KW/m2
– Operating pressure, 10.2 MPa
– Bulk inlet temperature, 460 C
• Horizontal flow – Circumferential variationin wall temperature
• Upward flow – Localized spikes in walltemperature
• Downward flow – Wall temperatures aresignificantly lower than upward flow
0.2 0.4 0.6 0.8 1 1.260
70
80
90
100
110
120
x(m)
Tw
i(C)
Horizontal flow - top
Horizontal flow - bottom
Upward flow
Downward flow
0.2 0.4 0.6 0.8 1 1.20
500
1000
1500
2000
2500
3000
x(m)
h[W
/m2 K
]
Horizontal flow - top
Horizontal flow - bottom
Upward flow
Downward flow
10
Effect of flow direction
Upward flow
Wall Center
τ/τ𝑤
Buoyancy
effects
absent
1.0
0
WallCenter
τ/τ𝑤Buoyancy
effects
absent
1.0
0
Downward flow
• Upward flow – Turbulent shear stress is reduced by buoyancy force
• Downward flow – Turbulent shear stress is enhanced by buoyancy force
11
Effect of inlet temperature
• Test conditions
– Mass flux, 320 Kg/m2sec
– Heat flux, 24 KW/m2
– Operating pressure, 7.5 MPa
– Horizontal, upward and downward flow
• Horizontal flow – Severe discontinuity in thewall temperature as the inlet temperatureis changed
• Thermal entrance length effects
• Temperature differences between top andbottom sides reduce for Tb > Tpc
20 25 30 35 40 45 50 55 6030
35
40
45
50
55
60
65
70
75
Tw
i(C)
Tb(C)
Horizontal flow - top
Tin
=20o C
Tin
=26o C
Tin
=29.5o C
Tin
=31.25o C
Tin
=32.5o C
Tin
=36.5o C
20 25 30 35 40 45 50 55 6030
35
40
45
50
55
60
65
70
75
Tw
i(C)
Tb(C)
Horizontal flow - bottom
Tin
=20o C
Tin
=26o C
Tin
=29.5o C
Tin
=31.25o C
Tin
=32.5o C
Tin
=36.5o C
12
Effect of inlet temperature
• Upward flow – Location of spikes can bereadily be changed by changing the inlettemperature
• Downward flow – Sharp increase in walltemperature for Tin ~ Tpc
• Pseudo-film boiling phenomenon similar tofilm boiling at subcritical pressures
• For Tb > Tpc , wall temperatures similar forboth upward and downward flows
20 25 30 35 40 45 50 55 6030
35
40
45
50
55
60
65
70
75
Tw
i(C)
Tb(C)
Upward flow
Tin
=20o C
Tin
=26o C
Tin
=29.5o C
Tin
=31.25o C
Tin
=32.5o C
Tin
=36.5o C
20 25 30 35 40 45 50 55 6030
35
40
45
50
55
60
65
70
75
Tw
i(C)
Tb(C)
Downward flow
Tin
=20o C
Tin
=26o C
Tin
=29.5o C
Tin
=31.25o C
Tin
=32.5o C
Tin
=36.5o C
13
Effect of heat flux
• Test conditions
– Mass flux, 195 Kg/m2sec
– Operating pressure, 7.5 MPa
– Downward flow
• Heat transfer enhancement reduces withheat flux
• Area integrated values of Cp reduces
• Pseudo-film boiling phenomenon is evidentfor all heat fluxes
20 30 40 50 60 70 8020
40
60
80
100
120
140
160
180
200
Tb(C)
Tw
i(C)
0.96 0.98 1 1.02 1.04 1.06 1.08 1.1500
1000
1500
2000
2500
3000
3500
4000
4500
Normalized Temperature, Tb/T
pc [-]
Hea
t T
ra
nsf
er C
oeff
icie
nt,
h [
W /
m2K
]
Q" - 13.5 KW/m2
Q" - 24.0 KW/m2
Q" - 50.0 KW/m2
Q" - 62.5 KW/m2
14
Buoyancy criteria – Vertical flows
• Experimental Nusselt numbers normalized with Jackson correlation (developed for forcedconvection)
𝑁𝑢𝑗𝑎𝑐𝑘𝑠𝑜𝑛 = 0.0183𝑅𝑒𝑏0.82𝑃𝑟𝑏
0.5 ρ𝑤
ρ𝑏
0.3 𝐶𝑎𝑣
𝐶𝑝𝑏
𝑛
Where, n is defined as
𝑛 = 0.4 for Tb < Tw < Tpc and 1.2Tpc < Tb < Tw
𝑛 = 0.4 + 0.2𝑇𝑤
𝑇𝑝𝑐− 1 for Tb < Tw < Tpc
𝑛 = 0.4 + 0.2𝑇𝑤
𝑇𝑝𝑐− 1 1 − 5
𝑇𝑏
𝑇𝑝𝑐− 1 for Tpc < Tb < 1.2Tpc
• Jackson, 2013 buoyancy criteria
𝐵𝑢 = 𝐶𝐵𝐵𝑜𝑏𝐹𝑉𝑃1𝐹𝑉𝑃3𝐹𝑉𝑃4 < 0.04
𝐶𝐵 = 4600, 𝐵𝑜𝑏 =𝐺𝑟𝑏
𝑅𝑒𝑏2.625𝑃𝑟𝑏
0.4 , 𝐹𝑉𝑃1=𝜇𝑎𝑣𝜇𝑏
𝜌𝑎𝑣𝜌𝑏
−0.5
, 𝐹𝑉𝑃3 =𝑃𝑟𝑎𝑣𝑃𝑟𝑏
−0.4
, 𝐹𝑉𝑃4 =𝜌𝑏 − 𝜌𝑎𝑣𝜌𝑏 − 𝜌𝑤
15
Buoyancy criteria – Upward flow
10-2
10-1
100
101
10-1
100
101
Buoyancy Factor, CB FVP1FVP3FVP4B ob
Nu
ex
p=N
uJ
ack
son
Principle of Natural convection
Recovery from Laminarization
Normal heat transfer regime
Bu, CBFVP1FVP3FVP4Bob
Nu
ex p
/Nu
Jack
son
16
Buoyancy criteria – Downward flow
10-2
10-1
100
101
10-1
100
101
Buoyancy Factor, CB FVP1FVP3FVP4B ob
Nu
ex
p=N
uJ
ack
son
Pseudo-film boiling phenomenon near pseudo-critical region
Bu, CBFVP1FVP3FVP4Bob
Nu
ex p
/Nu
Jack
son
17
Buoyancy criteria – Horizontal flow
• Jackson, 1976 suggested a criteria to neglect buoyancy effects for horizontal flows
10-1
100
101
102
103
104
105
10-1
100
101
B oj
Nu
ex
p=N
uJ
ack
son
Horizontal Flow - Top side
Boj < 10
Flow dominated by natural convection
Forced convection regime
𝐵𝑜𝑗 =𝐺𝑟𝑏
𝑅𝑒𝑏2
𝜌𝑏
𝜌𝑤
𝑥
𝐷
2< 10
Boj < 10
Boj
Nu
ex p
/Nu
Jack
son
18
Buoyancy criteria – Horizontal flow
10-1
100
101
102
103
104
105
10-1
100
101
B oj
Nu
ex
p=N
uJ
ack
son
Horizontal Flow - Bottom side
Boj < 10
Pseudo-film boiling phenomenon near pseudo-critical region
Approaching forced convection regimeBoj < 10
Boj
Nu
ex p
/Nu
Jack
son
19
Summary
• Effect of buoyancy on heat transfer was investigated
• For Tb < Tpc , effect of buoyancy was significant resulting in
– Circumferential variation of wall temperature for horizontal flow
– Localized peaks in wall temperature for upward flow
– Enhancement in heat transfer for downward flow
• For Tb > Tpc , effect of buoyancy was minimum leading to similar walltemperature profiles for all the flow orientations
• Buoyancy criteria suggested by Jackson can be used to predict theeffect of buoyancy for both horizontal and vertical flows
Questions?
Thank you for your time!