MDPI - Publisher of Open Access Journals

16 pages, 3080 KiB

Open AccessArticle

Computational Optimization of Free-Piston Stirling Engine by Variable-Step Simplified Conjugate Gradient Method with Compatible Strategies

by Chin-Hsiang Cheng and Yu-Ting Lin

Energies 2022, 15(10), 3569; https://doi.org/10.3390/en15103569 - 13 May 2022

Viewed by 1735

Abstract

This study aimed at the development of an algorithm for the computational optimization of free-piston Stirling engines. The design algorithm includes an optimization method and two compatible strategies. The optimization method is an improved version of traditional conjugate gradient method and is named the variable-step simplified conjugate gradient method (VSCGM). The free-piston Stirling engine is operable only in narrow-bounded parameter regions. Using the present approach, the operable variable combinations can be found efficiently. Two compatible strategies, the wake-up and backward-comparison strategies, are integrated with the VSCGM. The present design algorithm can handle multiple-parameter optimization with more flexible objective function definitions. Meanwhile, it features faster convergence as compared with the traditional conjugate gradient methods. Moreover, the feasibility of the VSCGM and the two compatible strategies is demonstrated in two test cases. It was found that the present approach can optimize the ten designed variables simultaneously, and the optimal designs can be yielded in a finite number of iterations. The results show that the inoperable initial designs were successfully optimized to reach a high power output. Full article

(This article belongs to the Section K: State-of-the-Art Energy Related Technologies)

► Show Figures

Figure 1

14 pages, 2521 KiB

Open AccessArticle

Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method

by Chin-Hsiang Cheng and Duc-Thuan Phung

Energies 2021, 14(23), 7835; https://doi.org/10.3390/en14237835 - 23 Nov 2021

Cited by 4 | Viewed by 2387

Abstract

This study focuses on optimizing a 100-W-class β-Type Stirling engine by combining the modified thermodynamic model and the variable-step simplified conjugate gradient (VSCGM) method. For the modified thermodynamic model, non-uniform pressure is directly introduced into the energy equation, so the indicated power and heat transfer rates can reach energy balance while the VSCGM is an updated version of the simplified conjugate gradient method (SCGM) with adaptive increments and step lengths to the optimization process; thus, it requires fewer iterations to reach the optimal solution than the SCGM. For the baseline case, the indicated power progressively raises from 88.2 to 210.2 W and the thermal efficiency increases from 34.8 to 46.4% before and after optimization, respectively. The study shows the VSCGM possesses robust property. All optimal results from the VSCGM are well-matched with those of the computational fluid dynamics (CFD) model. Heating temperature and rotation speed have positive effects on optimal engine performance. The optimal indicated power rises linearly with the charged pressure, whereas the optimal thermal efficiency tends to decrease. The study also points out that results of the modified thermodynamic model with fixed values of unknowns agree well with the CFD results at points far from the baseline case. Full article

(This article belongs to the Section K: State-of-the-Art Energy Related Technologies)

► Show Figures

Figure 1

18 pages, 2560 KiB

Open AccessFeature PaperArticle

Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm

by Chin-Hsiang Cheng and Yu-Ting Lin

Energies 2020, 13(19), 5164; https://doi.org/10.3390/en13195164 - 3 Oct 2020

Cited by 6 | Viewed by 2529

Abstract

The present study develops a novel optimization method for designing a Stirling engine by combining a variable-step simplified conjugate gradient method (VSCGM) and a neural network training algorithm. As compared with existing gradient-based methods, like the conjugate gradient method (CGM) and simplified conjugate gradient method (SCGM), the VSCGM method is a further modified version presented in this study which allows the convergence speed to be greatly accelerated while the form of the objective function can still be defined flexibly. Through the automatic adjustment of the variable step size, the optimal design is reached more efficiently and accurately. Therefore, the VSCGM appears to be a potential and alternative tool in a variety of engineering applications. In this study, optimization of a low-temperature-differential gamma-type Stirling engine was attempted as a test case. The optimizer was trained by the neural network algorithm based on the training data provided from three-dimensional computational fluid dynamic (CFD) computation. The optimal design of the influential parameters of the Stirling engine is yielded efficiently. Results show that the indicated work and thermal efficiency are increased with the present approach by 102.93% and 5.24%, respectively. Robustness of the VSCGM is tested by giving different sets of initial guesses. Full article

(This article belongs to the Section I: Energy Fundamentals and Conversion)

► Show Figures

Figure 1

Search Results (3)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (3)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI