Abstract

In high-temperature transcritical organic Rankine cycles (ORCs), the expansion process may take place in the neighborhood of the thermodynamic critical point. In this region, many organic fluids feature a value of the fundamental derivative of gas dynamics Γ that is less than unity. As a consequence, severe nonideal gas-dynamic effects can be possibly observed. Examples of these nonideal effects are the nonmonotonic variation of the Mach number along an isentropic expansion, oblique shocks featuring an increase of the Mach number, and a significant dependence of the flow field on the upstream total state. To tackle this latter nonideal effect, an uncertainty-quantification strategy combined with Reynolds-averaged flow simulations is devised to evaluate the turbine performance in presence of operational uncertainty. The results clearly indicate that a highly nonideal expansion process leads to an amplification of the operational uncertainty. Specifically, given an uncertainty in the order of 1% in cycle nominal conditions, the mass flow rate and cascade losses vary ±4% and ±0.75 percentage points, respectively. These variations are four and six times larger than those prompted by an ideal-like expansion process. The flow delivered to the first rotating cascade is severely altered as well, leading to local variations in the rotor incidence angle up to 10 deg. A decomposition of variance contributions reveals that the uncertainty in the upstream total temperature is mainly responsible for these variations. Finally, the understanding of the physical mechanism behind these changes allows us to generalize the present findings to other organic-fluid flows.

References

References
1.
Astolfi
,
M.
,
Romano
,
M. C.
,
Bombarda
,
P.
, and
Macchi
,
E.
,
2014
, “
Binary ORC (Organic Rankine Cycles) Power Plants for the Exploitation of Medium–Low Temperature Geothermal Sources—Part A: Thermodynamic Optimization
,”
Energy
,
66
, pp.
423
434
.10.1016/j.energy.2013.11.056
2.
Freeman
,
J.
,
Hellgardt
,
K.
, and
Markides
,
C. N.
,
2015
, “
An Assessment of Solar-Powered Organic Rankine Cycle Systems for Combined Heating and Power in uk Domestic Applications
,”
Appl. Energy
,
138
, pp.
605
620
.10.1016/j.apenergy.2014.10.035
3.
Pantaleo
,
A. M.
,
Camporeale
,
S. M.
,
Miliozzi
,
A.
,
Russo
,
V.
,
Shah
,
N.
, and
Markides
,
C. N.
,
2017
, “
Novel Hybrid Csp-Biomass Chp for Flexible Generation: Thermo-Economic Analysis and Profitability Assessment
,”
Appl. Energy
,
204
, pp.
994
1006
.10.1016/j.apenergy.2017.05.019
4.
Yu
,
H.
,
Feng
,
X.
,
Wang
,
Y.
,
Biegler
,
L. T.
, and
Eason
,
J.
,
2016
, “
A Systematic Method to Customize an Efficient Organic Rankine Cycle (ORC) to Recover Waste Heat in Refineries
,”
Appl. Energy
,
179
, pp.
302
315
.10.1016/j.apenergy.2016.06.093
5.
Schuster
,
A.
,
Karellas
,
S.
, and
Aumann
,
R.
,
2010
, “
Efficiency Optimization Potential in Supercritical Organic Rankine Cycles
,”
Energy
,
35
(
2
), pp.
1033
1039
.10.1016/j.energy.2009.06.019
6.
Lai
,
N. A.
,
Wendland
,
M.
, and
Fischer
,
J.
,
2011
, “
Working Fluids for High-Temperature Organic Rankine Cycles
,”
Energy
,
36
(
1
), pp.
199
211
.10.1016/j.energy.2010.10.051
7.
Colonna
,
P.
,
Casati
,
E.
,
Trapp
,
C.
,
Mathijssen
,
T.
,
Larjola
,
J.
,
Turunen-Saaresti
,
T.
, and
Uusitalo
,
A.
,
2015
, “
Organic Rankine Cycle Power Systems: From the Concept to Current Technology, Applications, and an Outlook to the Future
,”
ASME J. Eng. Gas Turbines Power
,
137
(
10
), p.
100801
.10.1115/1.4029884
8.
Macchi
,
E.
, and
Astolfi
,
M.
,
2017
, “
9—Axial Flow Turbines for Organic Rankine Cycle Applications
,” Organic Rankine Cycle (ORC) Power Systems,
E.
Macchi
, and
M.
Astolfi
, eds.,
Woodhead Publishing
, Duxford, UK, pp.
299
319
.10.1016/B978-0-08-100510-1.00009-0
9.
Meroni
,
A.
,
Andreasen
,
J. G.
,
Persico
,
G.
, and
Haglind
,
F.
,
2018
, “
Optimization of Organic Rankine Cycle Power Systems Considering Multistage Axial Turbine Design
,”
Appl. Energy
,
209
, pp.
339
354
.10.1016/j.apenergy.2017.09.068
10.
Wheeler
,
A. P. S.
, and
Ong
,
J.
,
2013
, “
The Role of Dense Gas Dynamics on Organic Rankine Cycle Turbine Performance
,”
ASME J. Eng. Gas Turbines Power
,
135
(
10
), p.
102603
.10.1115/1.4024963
11.
Rinaldi
,
E.
,
Pecnik
,
R.
, and
Colonna
,
P.
,
2016
, “
Unsteady Operation of a Highly Supersonic Orc Turbine
,”
ASME J. Turbomach.
,
138
(
12
), p.
121010
.10.1115/1.4033973
12.
Pini
,
M.
,
Persico
,
G.
,
Pasquale
,
D.
, and
Rebay
,
S.
,
2015
, “
Adjoint Method for Shape Optimization in Real-Gas Flow Applications
,”
ASME J. Eng. Gas Turbines Power
,
137
(
3
), pp.
1
13
.10.1115/1.4028495
13.
Persico
,
G.
,
Rodriguez-Fernandez
,
P.
, and
Romei
,
A.
,
2019
, “
High-Fidelity Shape-Optimization of Non-Conventional Turbomachinery by Surrogate Evolutionary Strategies
,”
ASME J. Turbomach.
,
141
(
8
), p.
081010
.10.1115/1.4043252
14.
Thompson
,
P. A.
,
1971
, “
A Fundamental Derivative in Gas Dynamics
,”
Phys. Fluids
,
14
(
9
), pp.
1843
1849
.10.1063/1.1693693
15.
Thompson
,
P. A.
, and
Lambrakis
,
K. C.
,
1973
, “
Negative Shock Waves
,”
J. Fluid Mech.
,
60
(
1
), pp.
187
208
.10.1017/S002211207300011X
16.
Cramer
,
M. S.
,
1989
, “
Negative Nonlinearity in Selected Fluorocarbons
,”
Phys. Fluids A
,
1
(
11
), pp.
1894
1897
.10.1063/1.857514
17.
Colonna
,
P.
, and
Guardone
,
A.
,
2006
, “
Molecular Interpretation of Nonclassical Gasdynamics of Dense Vapors Under the Van Der Waals Model
,”
Phys. Fluids
,
18
(
5
), pp.
056101
056114
.10.1063/1.2196095
18.
Nannan
,
N. R.
,
Guardone
,
A.
, and
Colonna
,
P.
,
2013
, “
On the Fundamental Derivative of Gas Dynamics in the Vapor–Liquid Critical Region of Single-Component Typical Fluids
,”
Fluid Phase Equilib.
,
337
, pp.
259
273
.10.1016/j.fluid.2012.09.017
19.
Cramer
,
M. S.
, and
Best
,
L. M.
,
1991
, “
Steady, Isentropic Flows of Dense Gases
,”
Phys. Fluids A
,
3
(
1
), pp.
219
226
.10.1063/1.857855
20.
Vimercati
,
D.
,
Gori
,
G.
, and
Guardone
,
A.
,
2018
, “
Non-Ideal Oblique Shock Waves
,”
J. Fluid Mech.
,
847
, pp.
266
285
.10.1017/jfm.2018.328
21.
Spinelli
,
A.
,
Cammi
,
G.
,
Gallarini
,
S.
,
Zocca
,
M.
,
Cozzi
,
F.
,
Gaetani
,
P.
,
Dossena
,
V.
, and
Guardone
,
A.
,
2019
, “
Experimental Evidence of Non-Ideal Compressible Effects in Expanding Flow of a High Molecular Complexity Vapor
,”
Exp. Fluids
,
59
, pp.
1
16
. 10.1007/s00348-018-2578-0
22.
Romei
,
A.
,
Vimercati
,
D.
,
Persico
,
G.
, and
Guardone
,
A.
,
2020
, “
Non-Ideal Compressible Flows in Supersonic Turbine Cascades
,”
J. Fluid Mech.
,
882
, p.
A12
.10.1017/jfm.2019.796
23.
Bufi
,
E. A.
,
Cinnella
,
P.
, and
Merle
,
X.
,
2015
, “
Sensitivity of Supersonic ORC Turbine Injector Designs to Fluctuating Operating Conditions
,”
ASME
Paper No. GT2015-42193.10.1115/GT2015-42193
24.
Razaaly
,
N.
,
Persico
,
G.
, and
Congedo
,
P. M.
,
2019
, “
Impact of Geometric, Operational, and Model Uncertainties on the Non-Ideal Flow Through a Supersonic ORC Turbine Cascade
,”
Energy
,
169
, pp.
213
227
.10.1016/j.energy.2018.11.100
25.
Thompson
,
P. A.
,
1988
,
Compressible Fluid Dynamics
,
McGraw-Hill
, New York.
26.
Thol
,
M.
,
Dubberke
,
F. H.
,
Rutkai
,
G.
,
Windmann
,
T.
,
Köster
,
A.
,
Span
,
R.
, and
Vrabec
,
J.
,
2016
, “
Fundamental Equation of State Correlation for Hexamethyldisiloxane Based on Experimental and Molecular Simulation Data
,”
Fluid Phase Equilib.
,
418
, pp.
133
151
.10.1016/j.fluid.2015.09.047
27.
Colonna
,
P.
,
Harinck
,
J.
,
Rebay
,
S.
, and
Guardone
,
A.
,
2008
, “
Real-Gas Effects in Organic Rankine Cycle Turbine Nozzles
,”
J. Propulsion Power
,
24
(
2
), pp.
282
294
.10.2514/1.29718
28.
Preißinger
,
M.
, and
Brüggemann
,
D.
,
2016
, “
Thermal Stability of Hexamethyldisiloxane (MM) for High-Temperature Organic Rankine Cycle (ORC)
,”
Energies
,
9
(
3
), p.
183
.10.3390/en9030183
29.
Keulen
,
L.
,
Gallarini
,
S.
,
Landolina
,
C.
,
Spinelli
,
A.
,
Iora
,
P.
,
Invernizzi
,
C.
,
Lietti
,
L.
, and
Guardone
,
A.
,
2018
, “
Thermal Stability of Hexamethyldisiloxane and Octamethyltrisiloxane
,”
Energy
,
165
, pp.
868
876
.10.1016/j.energy.2018.08.057
30.
Persico
,
G.
, and
Pini
,
M.
,
2017
, “
8—Fluid Dynamic Design of Organic Rankine Cycle Turbines
,”
Organic Rankine Cycle (ORC) Power Systems
,
E.
Macchi
, and
M.
Astolfi
, eds.,
Woodhead Publishing
, Duxford, UK, pp.
253
297
.
31.
Bini
,
R.
, and
Colombo
,
D.
,
2017
, “
Large Multistage Axial Turbines
,”
Energy Procedia
,
129
, pp.
1078
1084
.10.1016/j.egypro.2017.09.138
32.
Galiana
,
F. J. D.
,
Wheeler
,
A. P. S.
, and
Ong
,
J.
,
2016
, “
A Study of Trailing-Edge Losses in Organic Rankine Cycle Turbines
,”
ASME J. Turbomach.
,
138
(
12
), p.
121003
.10.1115/1.4033473
33.
Galiana
,
F. J. D.
,
Wheeler
,
A. P. S.
,
Ong
,
J.
,
de
,
C. A.
, and
Ventura
,
M.
,
2017
, “
The Effect of Dense Gas Dynamics on Loss in ORC Transonic Turbines
,”
J. Phys.: Conf. Ser.
,
821
(
1
), p.
012021
.10.1088/1742-6596/821/1/012021
34.
Zanellato
,
L.
,
Astolfi
,
M.
,
Serafino
,
A.
,
Rizzi
,
D.
, and
Macchi
,
E.
,
2020
, “
Field Performance Evaluation of Geothermal ORC Power Plants With a Focus on Radial Outflow Turbines
,”
Renewable Energy
,
147
, pp.
2896
2904
.10.1016/j.renene.2018.08.068
35.
Romei
,
A.
,
Vimercati
,
D.
,
Guardone
,
A.
, and
Persico
,
G.
,
2019
, “
The Role of Operational Variability on the Non-Ideal Flow in Supersonic Turbines for Supercritical Organic Rankine Cycles
,”
Proceedings of the Fifth International Seminar on ORC Power Systems
, Athens, Greece, Sept. 9–11, p.
184
.https://crealab.polimi.it/wp-content/uploads/2019/04/orc2019_abstract_romei.pdf
36.
Lemmon
,
E. W.
,
Huber
,
M. L.
, and
McLinden
,
M. O.
,
2013
, “
Reference Fluid Thermodynamic and Transport Properties–REFPROP, Version 9.1
,” Standard Reference Data Program, NIST, Gaithersburg, MD, Database No.
23
.https://www.nist.gov/publications/nist-standard-reference-database-23-reference-fluid-thermodynamic-and-transport
37.
Maître
,
O. L.
, and
Knio
,
O. M.
,
2012
,
Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics
,
Scientific Computation
,
Springer Netherlands
, Heidelberg, Germany.
38.
Askey
,
B. K.
, and
Wilson
,
J.
,
1985
,
Some Basic Hypergeometric Orthogonal Polynomials That Generalize Jacobi Polynomials
,
American Mathematical Society
, Providence, RI.
39.
Crestaux
,
T.
,
Le Maître
,
O.
, and
Martinez
,
J.-M.
,
2009
, “
Polynomial Chaos Expansion for Sensitivity Analysis
,”
Reliab. Eng. Syst. Saf.
,
94
(
7
), pp.
1161
1172
.10.1016/j.ress.2008.10.008
40.
Mee
,
D. J.
,
Baines
,
N. C.
,
Oldfield
,
M. L. G.
, and
Dickens
,
T. E.
,
1992
, “
An Examination of the Contributions to Loss on a Transonic Turbine Blade in Cascade
,”
ASME J. Turbomach.
,
114
(
1
), pp.
155
162
.10.1115/1.2927979
41.
Denton
,
J. D.
, and
Xu
,
L.
,
1990
, “
The Trailing Edge Loss of Transonic Turbine Blades
,”
ASME J. Turbomach.
,
112
(
2
), pp.
277
285
.10.1115/1.2927648
42.
Bufi
,
E. A.
, and
Cinnella
,
P.
,
2018
, “
Preliminary Design Method for Dense-Gas Supersonic Axial Turbine Stages
,”
ASME J. Eng. Gas Turbines Power
,
140
(
11
), p.
112605
.10.1115/1.4039837
43.
Gaetani
,
P.
,
Persico
,
G.
, and
Osnaghi
,
C.
,
2010
, “
Effects of Axial Gap on the Vane-Rotor Interaction in a Low Aspect Ratio Turbine Stage
,”
J. Propulsion Power
,
26
(
2
), pp.
325
334
.10.2514/1.37616
44.
Macchi
,
E.
,
2017
, “
1—Theoretical Basis of the Organic Rankine Cycle
,”
Organic Rankine Cycle (ORC) Power Systems
,
E.
Macchi
, and
M.
Astolfi
, eds.,
Woodhead Publishing
, Duxford, UK, pp.
3
24
.
45.
Dickes
,
R.
,
Dumont
,
O.
,
Guillaume
,
L.
,
Quoilin
,
S.
, and
Lemort
,
V.
,
2018
, “
Charge-Sensitive Modelling of Organic Rankine Cycle Power Systems for Off-Design Performance Simulation
,”
Appl. Energy
,
212
, pp.
1262
1281
.10.1016/j.apenergy.2018.01.004
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