Performance Impact of Manufacturing Variations for Multistage Steam Turbines

Yang, Jing; Xiong, Juntao; McBean, Ivan; Havakechian, Said; Liu, Feng; Luo, Jiaqi

doi:10.2514/1.b36022

Cited by 15 publications

(7 citation statements)

References 23 publications

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“…where, y denotes the function vector of given samples X, l is vector of ones, which is of the same size as y . More details of kriging and its implementations can be found in [ (5). Then, at a design variable location o , the mean performance (denoted by μ) and corresponding variance (denoted by σ 2 ) can be calculated by Eqs.…”

Section: Uncertainty Quantification and Robust Optimization Process Umentioning

confidence: 99%

“…Both the probabilistic approaches and deterministic methods (which incorporate non-statistical indices such as gradients [5] or sensitivities [6]) are developed for robust design. Our focus is on probabilistic robust optimization (RO), then the following four issues such as (a) uncertainty quantification (UQ), (b) dealing with uncertainty and optimization variables, (c) robustness measurement and (d) surrogate accuracy management in RO needs to be considered.…”

Section: Introductionmentioning

confidence: 99%

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Robust Optimization for Vortex Generators in U-Bend Channel of High-Temperature Blades

Guo¹,

Tao²,

Song³

2019

Proceedings of Global Power &Amp; Propulsion Society

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The uncertainties such as manufacturing errors and environmental variations are inevitably encountered in engineering design, therefore in order to find robust solutions which keep high performance over a wide range, a meanvariance multi-objective robust optimization (RO) framework was proposed. Specifically, a kriging-based uncertainty quantification (UQ) formulation was proposed, which formulates uncertainty parameters and optimization design variables in product form, thereby the optimization search and UQ are conducted simultaneously in RO. Before RO, the sequential sampling strategies were employed to build high-accurate surrogate, which was shown effective by our five-variable engineering problem. Through aero-thermal design of vortex generators (VG) in U-bend channel of hightemperature blades, some issues such as constraints selection and knowledge mining in RO space were addressed. The RO of VG was carried out with one Gaussian-distributed and one uniformly-distributed uncertainty parameter, and three optimization design variables. One deterministic optimization (DO) process at the nominal condition and several RO process with different constraints were conducted. It was shown that the proposed RO was able to find robust solutions that have high-performance and are not sensitive to uncertainty fluctuations; which were validated by CFD. Meanwhile, the solution of DO was found helpful to exclude variance-dominated solutions which have much worse performance. But some constraints based on solution of DO would make the RO solution set to be null, therefore the RO can be an iterative process, in this regard, it is attractive to build high-accurate surrogates before RO. From another perspective, the several RO with different constraints are useful to group the solutions and get a insight into black-box design space like VG, which is valuable to select the final solution from many Pareto solutions.

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Section: Uncertainty Quantification and Robust Optimization Process Umentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Optimization for Vortex Generators in U-Bend Channel of High-Temperature Blades

Guo¹,

Tao²,

Song³

2019

Proceedings of Global Power &Amp; Propulsion Society

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“…Because numerous samples are necessary for MCS to obtain enough accurate results, adjoint methods and polynomial chaos (PC) methods have been developed rapidly to further improve the efficiency of MCS. Giebmanns et al 13 and Luo et al [14][15][16] applied the first-order (FO) and second-order (SO) adjoint sensitivity methods to stochastic aerodynamic problems, respectively. However, the FO adjoint method is difficult to capture the nonlinear relationship resulting from geometrical variations.…”

Section: Introductionmentioning

confidence: 99%

“…However, the FO adjoint method is difficult to capture the nonlinear relationship resulting from geometrical variations. 13 Although the nonlinear dependence of performance variations on geometric variations were successfully captured by SO adjoint method, [14][15][16] the method is suitable for small-scale uncertainty problems. With the decrease of machining precision, the local geometric change scale of blades may increase.…”

Section: Introductionmentioning

confidence: 99%

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

Guo

Chu

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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It is essential for engineering manufacture and robust design to evaluate the impact of manufacturing variability on the aerodynamics of compressor blades efficiently and accurately. In the paper, a novel quadratic curve approximation method based on the scanning points of blade design profiles was introduced and combined with Karhunen–Loève expansion, a mathematical dimensionality reduction method for modeling manufacturing variability as truncated Normal process was proposed. Subsequently, Sparse Approximation of Moment-based Arbitrary Polynomial Chaos (SAMBA PC) and computational fluid dynamics (CFD) were applied to build a computational framework for stochastic aerodynamic analysis considering manufacturing variability. Finally, the framework was adopted to evaluate the aerodynamic variations of a high subsonic compressor cascade under the design incidence. The results illustrate that the SAMBA PC method is more efficient than the traditional methods such as Monte Carlo simulation (MCS) for stochastic aerodynamic analysis. Through uncertainty quantification, the impact of manufacturing variability on the global aerodynamic performance is primarily reflected in the fluctuation of aerodynamic losses, and the fluctuation of the total losses is mainly contributed by the fluctuation of the separation loss after the suction peak (a negative pressure spike near the leading edge (LE)) and the boundary-layer loss on the suction surface (SS). With sensitivity analysis, the most important geometric modes to aerodynamics can be revealed, which provides a useful reference for manufacturing inspection process and helps reduce computational cost in robust design.

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“…A similar adjoint approach, for the impact analysis of MVs on a gas turbine blade is used by Zamboni et al [5], who use one CMM measurement to assess the impact on aerodynamic performance. Yang et al [6] also employ an adjoint solver to study the impact of MVs on a multistage steam turbine assuming Gaussian distributed blade thickness.…”

Section: Introductionmentioning

confidence: 99%

Using adjoint CFD to quantify the impact of manufacturing variations on a heavy duty turbine vane

Liefke,

Marciniak,

Janoske

et al. 2019

Preprint

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Performance Impact of Manufacturing Variations for Multistage Steam Turbines

Cited by 15 publications

References 23 publications

Robust Optimization for Vortex Generators in U-Bend Channel of High-Temperature Blades

Robust Optimization for Vortex Generators in U-Bend Channel of High-Temperature Blades

Stochastic aerodynamic analysis for compressor blades with manufacturing variability based on a mathematical dimensionality reduction method

Using adjoint CFD to quantify the impact of manufacturing variations on a heavy duty turbine vane

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