Research Papers

High-Fidelity Shape Optimization of Non-Conventional Turbomachinery by Surrogate Evolutionary Strategies

[+] Author and Article Information
Giacomo Persico

Laboratorio di Fluidodinamica delle Macchine (LFM), Dipartimento di Energia,
Politecnico di Milano,
Via Lambruschini 4, I-20156 Milano, Italy
e-mail: giacomo.persico@polimi.it

Pablo Rodriguez-Fernandez

Laboratorio di Fluidodinamica delle Macchine (LFM), Dipartimento di Energia,
Politecnico di Milano,
Via Lambruschini 4, I-20156 Milano, Italy
e-mail: pablorf@mit.edu

Alessandro Romei

Laboratorio di Fluidodinamica delle Macchine (LFM), Dipartimento di Energia,
Politecnico di Milano,
Via Lambruschini 4, I-20156 Milano, Italy
e-mail: alessandro.romei@polimi.it

1Present address: Plasma Science and Fusion Center, MIT, Cambridge, MA 02139.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received November 22, 2017; final manuscript received March 15, 2019; published online April 2, 2019. Assoc. Editor: Guillermo Paniagua.

J. Turbomach 141(8), 081010 (Apr 02, 2019) (11 pages) Paper No: TURBO-17-1220; doi: 10.1115/1.4043252 History: Received November 22, 2017; Accepted March 18, 2019

This paper presents a novel tool for the shape optimization of turbomachinery blade profiles operating with fluids in non-ideal thermodynamic conditions and in complex flow configurations. In novel energy conversion systems, such as organic Rankine cycles or supercritical CO2 cycles, the non-conventional turbomachinery layout as well as the complex thermodynamics of the working fluid complicate significantly the blade aerodynamic design. For such applications, the design of turbomachinery may considerably benefit from the use of systematic optimization methods, especially in combination with high-fidelity computational fluid dynamics (CFD), as it is shown in this paper. The proposed technique is implemented in the shape-optimization package FORMA (Fluid-dynamic OptimizeR for turbo-Machinery Aerofoils) developed in-house at the Politecnico di Milano. FORMA is constructed as a combination of a generalized geometrical parametrization technique based on B-splines, a CFD solver featuring turbulence models and arbitrary equations of state, and multiple surrogate-based evolutionary strategies based on either trust-region or training methods. The application to the re-design of a supersonic turbine nozzle shows the capabilities of applying a high-fidelity optimization, consisting of a 50% reduction in the cascade loss coefficient and in an increased flow uniformity at the inlet of the subsequent rotor. Two alternative surrogate-based evolutionary strategies and different fitness functions are tested and discussed, including nonlinear constraints within the design process. The optimization study reveals relevant insights into the design of supersonic turbine nozzles as well on the performance, reliability, and potential of the proposed design technique.

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Fig. 1

Flow charts for surrogate-based optimization: (a) SBLO and (b) SBGO

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Fig. 2

Baseline converging-diverging configuration

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Fig. 3

Grid dependence analysis for the calculation of the flow in the supersonic turbine nozzle in the baseline configuration, for two quantities: (a) entropy generation across the cascade and (b) standard deviation of the pressure downstream of the cascade

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Fig. 4

Baseline blade parametrization with 16 movable CPs; fixed CPs are marked as black circles; the design space is highlighted by the shadow

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Fig. 5

Convergence history for SBLO (a) and SBGO (b). The objective function (OF) is defined according to Eq. (3), expressed in Pa.

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Fig. 6

Comparison between baseline, optimal-SBLO, and optimal-SBGO blades

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Fig. 7

Convergence process for SBGO performed with finer CFD mesh resolution (150 k cells). The objective function (OF) is defined according to Eq. (3), expressed in Pa.

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Fig. 8

Convergence history of the constrained SBGO: (a) objective function and (b) constraint. The objective function is defined according to Eq. (3), expressed in Pa; the constraint is defined as the mass flow rate, expressed in kg/s.

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Fig. 9

Outcome of constrained optimization for SBGO with 16 CPs: (a) baseline and optimal blade shapes and (b) pressure distribution half an axial chord downstream of the blade

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Fig. 10

High-fidelity assessment of the optimization outcome—flow field: (a) entropy (top) and Mach number (bottom) distributions for the baseline blade configuration; and (b) entropy (top) and Mach number (bottom) distributions for the optimal blade configuration

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Fig. 11

High-fidelity assessment of the optimization outcome—processing: (a) isentropic Mach number distribution on the baseline and optimal blade and (b) axial evolution of total pressure loss coefficient downstream of the cascade

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Fig. 12

Results of SBGO performed with 13 movable CPs and the entropy production across the cascade as an objective function: (a) convergence process—objective function (J/kg K); (b) convergence process—constraint (kg/s); and (c) baseline and optimal blades



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