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Research Papers: Gas Turbines: Microturbines and Small Turbomachinery

Shape Optimization of an Organic Rankine Cycle Radial Turbine Nozzle

[+] Author and Article Information
David Pasquale

e-mail: david.pasquale@ing.unibs.it

Antonio Ghidoni

e-mail: antonio.ghidoni@ing.unibs.it

Stefano Rebay

e-mail: stefano.rebay@ing.unibs.it
Dipartimento di Ingegneria,
Meccanica e Industriale,
Universita degli Studi di Brescia,
Via Branze, 38,
25123 Brescia, Italy

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received February 29, 2012; final manuscript received September 13, 2012; published online March 18, 2013. Assoc. Editor: Joost J. Brasz.

J. Eng. Gas Turbines Power 135(4), 042308 (Mar 18, 2013) (13 pages) Paper No: GTP-12-1061; doi: 10.1115/1.4023118 History: Received February 29, 2012; Revised September 13, 2012

During the last decade, organic Rankine cycle (ORC) turbogenerators have become very attractive for the exploitation of low-temperature heat sources in the small to medium power range. Organic Rankine cycles usually operate in thermodynamic regions characterized by high pressure ratios and strong real-gas effects in the flow expansion, therefore requiring a nonstandard turbomachinery design. In this context, due to the lack of experience, a promising approach for the design can be based on the intensive use of computational fluid dynamics (CFD) and optimization procedures to investigate a wide range of possible configurations. In this work, an advanced global optimization strategy is coupled with a state-of-the-art CFD solver in order to assist in the design of ORC turbines. In particular, a metamodel assisted genetic algorithm, based on the so-called `off-line trained’ metamodel technique, has been employed. The numerical solutions of the two-dimensional (2D) Euler equations are computed with the in-house built code zFlow. The working fluid is toluene, whose thermodynamic properties are evaluated by an accurate equation of state, available in FluidProp. The computational grids created during the optimization process have been generated through a fully automated 2D unstructured mesh algorithm based on the advancing-Delaunnay strategy. The capability of this procedure is demonstrated by improving the design of an existing one-stage impulse radial turbine, where a strong shock appears in the stator channel due to the high expansion ratio. The goal of the optimization is to minimize the total pressure losses and to obtain a uniform axisymmetric stream at the stator discharge section, in terms of both the velocity magnitude and direction of the flow.

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Figures

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Fig. 1

Layout of the optimization procedure

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Fig. 2

Two-dimensional radial blade parameterization. Blade camberline and nozzle meanline definition: (a) detailed view of the throat region, and (b) trailing edge.

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Fig. 3

Example of a two-dimensional unstructured coarse mesh generated during the optimization process. The figures are deformed since the design is the confidential property of the manufacturer.

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Fig. 4

Convergence rate comparison between genetic algorithm optimizations assisted by Kriging with different parameters of the metamodel. (a) Gaussian, and (b) exponential correlation functions coupled with regression surfaces with an increasing polynomial order.

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Fig. 5

Convergence rate comparison between genetic algorithm optimizations assisted by feed-forward neural network with different parameters of the metamodel. In the case that the ‘early-stopping’ technique (est) is employed, the database is divided into two groups, i.e., the validation and training sets. (a) Different splitting ratios are compared. (b) Different network layouts in terms of the number of hidden layers (hl) and hidden neurons (hn) are compared.

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Fig. 6

Convergence rate comparison between standard genetic algorithm and genetic algorithm assisted by the Kriging and feed-forward neural network metamodels with optimal settings

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Fig. 7

Comparison of the convergence history of metamodel assisted optimizations performed by using the Kriging model and the feed-forward neural network with optimal settings in the case of a fixed throat location

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Fig. 8

Comparison of the Mach number (top) and total pressure (bottom) fields between the baseline (left) and the optimized geometries with a fixed throat location (right). The figures are deformed since the design is the confidential property of the manufacturer.

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Fig. 9

(a) Comparison of the absolute flow angle, (b) Mach number, and (c) total pressure distributions along the discharge boundary corresponding to one nozzle passage between the baseline and the optimized geometries with a fixed throat location

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Fig. 10

Comparison of the convergence history of metamodel assisted optimizations performed by using the Kriging model and the feed-forward neural network with optimal settings in the case of a throat with two degrees of freedom

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Fig. 11

Comparison of the Mach number (top) and total pressure (bottom) fields between the baseline (left) and the optimized geometry with a variable throat location (right). The figures are deformed since the design is the confidential property of the manufacturer.

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Fig. 12

(a) Comparison of the absolute flow angle, (b) Mach number, and (c) total pressure distributions along the discharge boundary corresponding to one nozzle passage between the baseline and the optimized geometry with a variable throat location

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Fig. 13

Comparison of the convergence history of metamodel assisted optimizations performed by using the Kriging model and the feed-forward neural network with optimal settings in the case of a throat with two degrees of freedom and half the number of blades

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Fig. 14

Comparison of the Mach number (top) and total pressure (bottom) fields between the baseline (left) and the optimized geometry with half the number of blades (right). The figures are deformed since the design is the confidential property of the manufacturer.

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Fig. 15

(a) Comparison of the absolute flow angle, (b) Mach number, and (c) total pressure distributions along the discharge boundary between the baseline and the optimized geometry with half the number of blades corresponding to two original nozzle passages

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