Development of a Direct Supercritical Carbon Dioxide Solar...
Transcript of Development of a Direct Supercritical Carbon Dioxide Solar...
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Development of a Direct Supercritical Carbon Dioxide Solar Receiver Based on Compact Heat Exchanger Technology
Saeb M. Besarati, D. Yogi. Goswami, Elias K. Stefanakos
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Overview
β’ Background information
β’ Computational model for a direct s-CO2 receiver
β’ Design a of a 3 MWth cavity receiver
β’ Thermal performance evaluation
β’ Summary and conclusions
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Solar power tower
Future cost of generating electricity using solar tower technology can be reduced by:
1) Lowering the cost of the heliostats
2) Including thermal storages with the systems to increase the capacity factor
3) Increasing the operational temperature and employing more efficient power cycles
Ref (5)
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Supercritical CO2 as the heat transfer and working fluids
Ref (6)
β’ Carbon dioxide seems like a proper replacement for current heat transfer fluids (HTFs), i.e. oil, molten salt, and steam.
β’ Oil has low maximum operating
temperature limit.
β’ Molten salt requires freeze protection units.
β’ Steam requires complex control systems.
β’ The main challenge about utilizing s-CO2 as the HTF is the high operating pressure.
Compact heat exchanger technology
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β’ Compact heat exchangers have already been extensively used for cooling the electronics. The high heat transfer rate in these heat exchangers is associated with the large area density (heat transfer area).
β’ Compact heat exchangers which are manufactured by diffusion bonding can tolerate very high pressures, i.e. more than 60 MPa.
Cross-section of a printed circuit heat exchanger Ref (7)
Thermal resistance network model
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π = 200, π =π π
, π =πΏπ
π ππππ =
π‘
ππ Γ π2 Γ π
π π€ππ€π€ =π2
ππ Γ π Γ π β π2
π ππππ =π
ππ Γ (π Γ π» β π Γ π)2
π π,ππππ =2
β Γ π Γ π
π π€,ππππ =
1 β Γ π Γ π
Ref (8)
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β’ Bulk fluid temperature can be found as:
ππππ€π,π(π,π) = ππ,ππ +π
οΏ½ΜοΏ½ Γ πΆποΏ½π π, π π
π=1
where π represents the row number, and π is the grid number in the axial direction. β’ The equivalent thermal resistance is given as:
π ππ π,π =ππ π β ππππ€π,π π,π
π π, π
β’ Writing the energy balance around grid π leads to:
βππ π β 1 + 2 + π πππποΏ½1
π ππ π, π
π
π€=1
ππ π β ππ π + 1 = π ππππ π + οΏ½ππππ€π,π π,ππ ππ π,π
π
π€=1
Therefore, a system of linear equations is obtained for π unknown junction temperatures.
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β’ Laminar flow (Re<=2300)
ππ = 8.235 1 β 2.0421 πΌ + 3.0853 πΌ2 β 2.4765 πΌ3 + 1.0578 πΌ4 β 0.1861 πΌ5 πΌ is the aspect ratio <=1 β’ Turbulent flow (Re>=5000)
ππ =ππ 2 π π β 1000 ππ
1 + 12.7 (Pr23β1) ππ
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,ππ = 0.25 1
1.8 logπ π β 1.5
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β’ Transition region (2300<Re<5000)
ππ = ππ2300 +ππ5000 β ππ2300
5000 β 2300 (π π β 2300)
β’ Pressure drop at the entrance and exit of the channels:
βπ =πΆπΆπ2
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where C is taken as 0.5 for the entrance, and 1 for the exit. β’ The friction loss inside the channel:
βπ =π πΏπ· πΆπ
2
2
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Model validation
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Direct s-CO2 receiver in a recompression Brayton cycle
P5 = 20 Mpa, T5 = 700β, T1 = 35β
Under Optimized Condition Ξ· = 48.6 %
T4 = 530
h5 β h4 = 213kJkg
Mass flow rate: 1 kg/s
Heat flux: 500 kW/m2
πβπ₯=0.6 m
Material selection
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β’ Inconel 625, which is a nickel based alloy, is selected as the heat exchanger material because of its good corrosion resistance in high temperature s-CO2 environment.
Melting range is 1290-1350 C, and maximum operating temperature is 982 C.
Geometric optimization
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β’ Design variables 1) Number of rows 3 β€ π β€ 10 2) Hydraulic diameter 0.5 ππ β€ π·β < 3ππ 3) Horizontal distance between the channels 1ππ β€ π‘π < 5ππ β’ Objective functions
1) Pressure drop 2) RR = Tsurface,meanβTinlet
Q" Γ 10000 KW cm2
β’ Constraints
1) Mechanical strength of the system (Checked by ASME pressure vessel code)
Pareto front of two objective optimization
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Dh = 2.8 mm, tf = 5mm, number of rows = 3
Optimization results
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S-CO2 temperature inside the channels
Surface temperature
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Design of a 3MWth receiver
Tilt angle of the receiver found by optimization: 35Β°
Tilt angle of the receiver is 35 Β°
Total number of panels that is required for a 3 MWth receiver to heat s-CO2 from 530β to 700β at 20 Mpa is:
ππππππ€π = 3000213
β 14
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β’ Natural convection (Clausing method) ππ = πΆβπβ πππ΄π(ππ β πβ )
ππ = π π½ ππ β πβ πΏπ , ππ = 0.5 πΆ3ππ 2 + πΆ4ππ€πππ 2 0.5
ππ = βππππ π΄πππ (ππππ ππππ β ππ ππ)
ππ = 0.082 (πΊπ. Pr)13 [β0.9 + 2.4
ππππ πππππβ
β 0.5 ππππ πππππβ
2
]
ππ = ππ
β’ Forced convection (Siebers, D. and Kraabel, J., 1984)
πππππ πππ = 0.287 π π π€0.8 ππ1/3
β’ Combined convective heat transfer coefficient is given by: βπππ₯ = βπππππ ππ€ + βπππ πππ β’ For each panel the convective heat loss is calculated by:
πππππ,π€πππ,π = βπππ₯,π π΄π (ππ β ππππ€π)
Convective heat loss
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Radiative heat loss (model developed by Teichel)
οΏ½ΜοΏ½π ππ,πβππ πππ€,π,π = ππ,πβππ π ππ,πβππ π π π΄π πΉοΏ½π,π,πβππ π 1 β π0βππ π π π ,ππ ππ4 β 1 β π0βππ π π π ,ππ ππ4
+ππ,πππ€ππ ππ,πππ€ππ π΄π πΉοΏ½π,π,πππ€ππ π0βππ π π π ,ππππ4 β π0βππ π π π ,ππππ
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οΏ½ΜοΏ½π ππ,πππ€ππ ,π,π= π0βππ π π π ,ππ π π πΉοΏ½π,π,πππ€ππ π΄π ππππ€ππ ,π ππππ€ππ ,π πΉπππ₯πππ€ππ ,π β πΉπππ₯πππ€ππ ,π
+ 1 β π0βππ π π π ,ππ π π π΄π πΉοΏ½π,π,πβππ π ππ,πβππ π ππ,πβππ π πΉπππ₯πππ€ππ ,π β πΉπππ₯πππ€ππ ,π
οΏ½ΜοΏ½π ππ,π,π = οΏ½ΜοΏ½π ππ,πβππ πππ€,π,π + οΏ½ΜοΏ½π ππ,πππ€ππ ,π,π
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Energy balance on cavity surfaces
1) Active surfaces: πΉπππ₯π π΄π = πππππ,π + πππππ,π€πππ,π + ππ ππ,π€πππ,π
2) Passive surfaces:
0 = 0 + πππππ,π€πππ,π + ππ ππ,π€πππ,π
ππ ππ ππ,π€πππ,π = π΄ποΏ½ βπ ππ,πβππ π,π,π (ππ β ππ) π
π=1
+ οΏ½ΜοΏ½π ππ,πππ€ππ ,π
ππ =π΄π β βπ ππ,πβππ π,π,πππ β οΏ½ΜοΏ½π ππ,πππ€ππ ,π + π΄πβπππ₯,πππππ€ππ
π=1
π΄π β (βπ ππ,πβππ π,π,π) + π΄πβπππ₯,πππ=1
3) Corners: πΉπππ₯π π΄π = 0 + πππππ,π€πππ,π + ππ ππ,π€πππ,π
ππ =πΉπππ₯π π΄π + π΄π β βπ ππ,πβππ π,π,πππ β οΏ½ΜοΏ½π ππ,πππ€ππ ,π + π΄πβπππ₯,πππππ€ππ
π=1
π΄π β (βπ ππ,πβππ π,π,π) + π΄πβπππ₯,πππ=1
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Field parameters
Solar field
Location Dagget, CA
Heliostats Number of heliostats 92
Width 8.84 m Height 7.34 m
Reflectivity 0.88
Receiver Tower height 115 m
Tilt angle of the aperture 35Β°
Aperture width 3.6 m Aperture height 2.7 m
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Flux density distribution (π€π€/π¦π)
without aiming strategy with aiming strategy
March 21st , noon
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Flux density distribution (ππππ)
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Wind speed profile for Dagget (TMY3 data)
π1π2
= π§1π§2
0.14(Duffie, J. A., Beckman, W.A., 2006)
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Temperature distribution inside the cavity (β)
BlackβSurface Temperature RedβFluid temperature
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Other important information β’ Mean temperature of s-CO2 leaving the receiver: 691β
β’ Maximum surface temperature: 843β (Maximum allowable temperature for Inconel 625 is
982β.
β’ Receiver efficiency: ππ ππ =
ππ π‘π‘π π π‘π π‘π π‘ π π‘ π π‘π π‘ππ ππ‘
ππ‘π ππ πππ π‘ ππ π π‘π π‘π ππ πππ π‘Γ 100 = 81.22 %
β’ Temperatures of the passive surfaces:
Top surface 169β
Bottom surface 170β
Left surface 173β
Right surface 167β
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β’ A direct s-CO2 receiver was designed based on the principles of compact heat exchangers. β’ The receiver is expected to heat s-CO2 from 530β to 700β. The geometry of the receiver was
determined using multi-objective the Pareto based optimization approach by the simultaneous minimization of the unit thermal resistance and the pressure drop.
β’ A 3MWth cavity receiver was designed using 14 individual panels.
β’ The heliostat field was designed, and the corresponding flux distribution on the receiver surface was obtained for March 21st.
β’ The radiative and convective heat transfer models were developed, and the bulk fluid and surface temperatures were obtained.
β’ The results showed that the s-CO2 reached the design temperature while the surface temperatures remained below the maximum temperature limit of Inconel 625. The receiver efficiency was obtained as 81.22%, which is highly promising.
β’ The efficiency can be further improved by optimizing the geometry of the cavity receiver. Considering the appropriate thermal and mechanical performance of the CHEs, they can be seriously considered for the next generation of high temperature pressurized solar receivers.
Summary and conclusion
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Thank you for your attention, Questions?
References
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