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Mathematical Modelling of Energy Systems and Fluid Machinery 2022

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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "J: Thermal Management".

Deadline for manuscript submissions: closed (29 March 2023) | Viewed by 21586

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Special Issue Editors

Prof. Dr. Michele Pinelli

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Guest Editor

Department of Engineering, University of Ferrara, Via Saragat, 1, 44122 Ferrara, Italy
Interests: turbomachinery; energy systems
Special Issues, Collections and Topics in MDPI journals

Dr. Alessio Suman

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Guest Editor

Department of Engineering, University of Ferrara, Via Saragat, 1, 44122 Ferrara, Italy
Interests: turbomachinery; numerical simulation; measurements

Dr. Nicola Casari

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Guest Editor

Department of Engineering, University of Ferrara, Via Saragat, 1, 44122 Ferrara, Italy
Interests: turbomachinery; numerical simulation; open source software; energy systems

Special Issue Information

Dear Colleagues,

It is my pleasure to acknowledge that we are opening for submissions a Special Issue of Energies on “Mathematical Modelling of Energy Systems and Fluid Machinery 2021”. This SI is a continuation of the previous issue “Mathematical Modelling of Energy Systems and Fluid Machinery”. In fact, we experienced huge interest on these topics, and we are sure that this new SI will capture the attention of many other researchers around the world.

Regarding this topic, we underline that (as stated in the previous SI) the digitalization of the energy sector is of paramount importance and, at the same time, an ever-increasing phenomenon. For example, it is worth noting how IoT technologies and the widespread utilization of digital twins are changing the way in which energy systems and fluid machinery are conceived and designed. However, this can only be achieved if these new ICT technologies are posed on solid bases for the representation of energy systems and fluid machinery. Therefore, mathematical modelling is still relevant, and its importance cannot be underestimated.

This Special Issue, which follows the previous one that enjoyed considerable success, is intended for a collection of contributions about the mathematical modelling of energy systems and fluid machinery in order to build and consolidate this base of knowledge.

Authors are invited to submit papers dealing with all aspects of modelling techniques, from the basics of model development (e.g., problem simplification and translation, model implementation, parameter identification, and model validation) to their applications, for all purposes of interest in energy conversion (e.g., linear models for optimization, 3D CFD for component design, dynamic modelling for system control development, CAE models for production, and digital twins for diagnostics and maintenance). In particular, papers based on open source software are very welcome, especially if the source codes are made available to the community through the SI website. Besides original research papers, historical review papers are particularly welcome since they can contribute to the discussion on consolidated assumptions and methodological approaches.

Prof. Dr. Michele Pinelli
Dr. Alessio Suman
Dr. Nicola Casari
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Energies is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Mathematical modelling
Energy systems
Fluid machinery
Modelling techniques
Computational fluid dynamics
Dynamic modelling

Published Papers (10 papers)

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Research

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19 pages, 5297 KiB

Open AccessArticle

Performance Analysis of WHR Systems for Marine Applications Based on sCO₂ Gas Turbine and ORC

by Fabrizio Reale, Raffaela Calabria and Patrizio Massoli

Energies 2023, 16(11), 4320; https://doi.org/10.3390/en16114320 - 25 May 2023

Viewed by 924

Abstract

Waste heat recovery (WHR) can represent a solution to improve the efficiency of ships’ propulsion, helping to exceed stringent greenhouse gas emission limits. This is particularly suitable in the case of propulsion based on gas turbines due to their medium-high temperature level of the exhaust gases. This study analyzes the performance of a hybrid energy grid, in which the heat is recovered by the exhaust gases of an aeroderivative gas turbine, a GE LM2500+, when the bottoming system is a supercritical CO₂ gas turbine. Given the issues and peculiarities related to the onboard installation, where size and weight are fundamental concerns, six WHR schemes have been analyzed. They span from the simple cycle to partial preheated and regenerative, to a cascade layout in which an ORC system receives thermal power by the sCO₂ GT. The influence of the seawater temperature on the performance of the hybrid energy system has been also considered. The energetic and exergetic performance comparison of the different schemes has been carried out by using the commercial software Thermoflex. The results showed that an increase in overall performance by up to 29% can be obtained and that the increase in seawater temperature can lead to a decrease in the overall performance. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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15 pages, 15275 KiB

Open AccessArticle

CFD-Based Analysis of Installed Fuel Consumption and Aerodynamics of Transonic Transport Aircraft during Cruise Flight

by Andrea Magrini, Denis Buosi, Francesco Poltronieri, Elena De Leo and Ernesto Benini

Energies 2023, 16(8), 3323; https://doi.org/10.3390/en16083323 - 8 Apr 2023

Cited by 1 | Viewed by 1624

Abstract

Gas turbine fuel burn for an aircraft engine can be obtained analytically using thermodynamic cycle analysis. For large-diameter ultra-high bypass ratio turbofans, the impact of nacelle drag and propulsion system integration must be accounted for in order to obtain realistic estimates of the installed specific fuel consumption. However, simplified models cannot fully represent the complexity of installation effects. In this paper, we present a method that combines thermodynamic cycle analysis with detailed Computational Fluid Dynamics (CFD) modelling of the installation aerodynamics to obtain the fuel consumption at a given mission point. The flow field and propulsive forces arising in a transport aircraft powered by an ultra-high bypass ratio turbofan at cruise are first examined to characterise the operating conditions and measure the sensitivity to variations of the incidence at transonic flight. The proposed methodology, in which dynamic balance of the vehicle is achieved at each integration point, is then applied along a cruise segment to calculate the cumulative fuel burn and the change in the specific fuel consumption. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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25 pages, 5229 KiB

Open AccessArticle

Simulation of Particle Trajectories in Gas Turbine Components and Assessment of Unsteady Effects Using an Efficient Eulerian-Lagrangian Technique

by Stefano Oliani, Nicola Casari, Michele Pinelli and Mauro Carnevale

Energies 2023, 16(6), 2810; https://doi.org/10.3390/en16062810 - 17 Mar 2023

Viewed by 1243

Abstract

In recent years, CFD has proven to be a very useful asset to help with predicting complex flows in a wide range of situations, including multiphase and gas-particle flows. On this track, numerical modelling of particle-laden flows in multistage turbomachinery has become an important step in helping to analyse the behaviour of a discrete phase in gas turbines. Furthermore, unsteady effects due, for example, to rotor–stator interaction may have an effect on trajectories and capture efficiencies of the discrete phase. Unfortunately, computational times for transient simulations can be exceedingly high, especially if a discrete-phase needs also to be simulated. For this reason, this work reports a new method for the efficient and accurate simulation of particle-laden flows in gas turbine engines components. The Harmonic Balance Method is exploited to gain orders of magnitude speedup exploiting the idea that once the flow field has been embedded in the spectral basis, it can be reconstructed at any desired time. In this way, not only can the computational time needed to reach convergence of the flow field be dramatically reduced, but there is also no need to keep simulating the flow field during particle tracking. On the contrary, the continuous phase field can be retrieved at any desired time through flow reconstruction. This technique is conceptually simple, but, to the authors’ knowledge, has never been applied so far in particle-laden flow simulations and represents a novelty in the field. First, the implementation of the method is described, and details are given on how phase-lagged boundary conditions can be applied to flow and particles to further speed up the calculation. Then, some relevant case studies are presented to highlight the performance of the method. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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16 pages, 7495 KiB

Open AccessArticle

Performance Degradation of a Shell-and-Tube Heat Exchanger Due to Tar Deposition

by Nicola Aldi, Nicola Casari, Michele Pinelli, Alessio Suman and Alessandro Vulpio

Energies 2022, 15(4), 1490; https://doi.org/10.3390/en15041490 - 17 Feb 2022

Cited by 3 | Viewed by 2424

Abstract

Biomass represents a programmable renewable energy source that is useful for reducing issues related to the transfer from fossil fuels to the renewable energy era. The exploitation of biomass is strongly related to the development of power technologies that are designed to improve efficiency; however, at the same time, they have to be designed to improve the life cycle of the entire installation—especially in relation to maintenance operations. In this paper, a numerical analysis is proposed to assess the performance of a heat exchanger used for separating condensing tar from syngas generated by the gasification of lignocellulosic wood chips and pellets. The analysis included clean, fouled, and clogged conditions. Flow maldistribution characterized the inlet section of shell-and-tube configurations and was responsible for clogging phenomena. Starting from field detection, analyses of fouled and clogged conditions showed a reduction in the effectiveness of the heat exchanger, causing dangerous conditions for the internal combustion engine used to exploit the syngas flow. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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18 pages, 5760 KiB

Open AccessArticle

Research on Capacity Allocation Optimization of Commercial Virtual Power Plant (CVPP)

by Songkai Wang, Rong Jia, Xiaoyu Shi, Chang Luo, Yuan An, Qiang Huang, Pengcheng Guo, Xueyan Wang and Xuewen Lei

Energies 2022, 15(4), 1303; https://doi.org/10.3390/en15041303 - 11 Feb 2022

Cited by 7 | Viewed by 1394

Abstract

Commercial virtual power plants (CVPP) connect the form of renewable energy resource portfolio to the power market and reduce the risk of the unstable operation of a single renewable energy. Combining different kinds of large-scale renewable energy in CVPP to provide capacity services like base load, peak shaving, and valley-filling, etc., for the system loads is an urgent problem to be solved. Therefore, it is valuable to analyze the capacity allocation ratio of the CVPP to maximize the utilization of all kinds of energy, especially for the large-scale multi-energy base. This paper proposed a multi-energy coordinated operation framework by considering various load demands, including base load and peak shaving for the capacity allocation of CVPP based on the world’s largest renewable energy resource base on the upstream area of the Yellow River. The main procedures of this framework are as follows: (1) A paratactic model satisfying base load and peak shaving is proposed to determine the ability of the CVPP operation model’s capacity services to meet the different demands of the power system load. (2) A hybrid dimension reduction algorithm with a better convergence rate and optimization effect solves the proposed paratactic model based on the ReliefF and the Adaptive Particle Swarm Optimization (APSO). The results show that the large-scale CVPP with different compositions can achieve both of the goals of a stable base load output and stable residual load under different weather conditions. Compared with the operation on sunny days, the base load fluctuation and residual load fluctuation of CVPP on rainy days are reduced by 14.5% and 21.9%, respectively, proving that CVPP can alleviate renewable energy’s dependence on weather and improve energy utilization. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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14 pages, 984 KiB

Open AccessArticle

Numerical Modeling of Combustion and Detonation in Aqueous Foams

by Alexey Kiverin and Ivan Yakovenko

Energies 2021, 14(19), 6233; https://doi.org/10.3390/en14196233 - 30 Sep 2021

Cited by 4 | Viewed by 1432

Abstract

Combustible aqueous foams and foamed emulsions represent prospective energy carriers. This paper is devoted to the overview of model assumptions required for numerical simulations of combustion and detonation processes in aqueous foams. The basic mathematical model is proposed and used for the analysis of the combustion development in the wet aqueous foam containing bubbles filled with reactive gas. The numerical results agree with the recent experimental data on combustion and detonation in aqueous foams containing premixed hydrogen–oxygen. The obtained results allowed for distinguishing the mechanisms of flame acceleration, transition to detonation, detonation propagation, and decay. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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21 pages, 94250 KiB

Open AccessArticle

Numerical Investigation of the Performance of a Submersible Pump: Prediction of Recirculation, Vortex Formation, and Swirl Resulting from Off-Design Operating Conditions

by Virgel M. Arocena, Binoe E. Abuan, Joseph Gerard T. Reyes, Paul L. Rodgers and Louis Angelo M. Danao

Energies 2021, 14(16), 5082; https://doi.org/10.3390/en14165082 - 18 Aug 2021

Cited by 8 | Viewed by 2070

Abstract

Like any other turbomachinery, it is essential that the hydraulic behavior and performance of mixed-flow pumps are evaluated way in advance prior to manufacturing. Pump performance relies heavily on the proper design of the intake structure. Intake structures should be accurately designed in order to minimize and avoid unnecessary swirl and vortex formations. Ensuring the optimum performance condition as well as predicting how a particular intake structure affects the efficiency of the pump often requires either physical model studies or theoretical evaluations. Unfortunately, physical models are costly, time-consuming, and site-specific. Conversely, design and performance predictions using a theoretical approach merely gives performance values or parameters, which are usually unable to determine the root cause of poor pump performance. This study evaluates the viability of using Computational Fluid Dynamics (CFD) as an alternative tool for pump designers and engineers in evaluating pump performance. A procedure for conducting CFD simulations to verify pump characteristics such as head, efficiency, and flow as an aid for preliminary pump design is presented. Afterwards, a multiphase simulation using the VOF approach is applied to compare the fluid dynamics between four different pump intake structures. A full-sized CFD model of the pump sump complete with the pump’s active components was used for the intake structure analysis in order to avoid scaling issues encountered during the reduced-scale physical model test. The results provided a clear illustration of the hydraulic phenomena and characteristic curves of the pump. A performance drop in terms of reduction in TDH was predicted across the various intake structure designs. The CFD simulation of intake structure provided a clear insight on the varying degree of swirl, flow circulation, and effect on pump efficiency between all four cases. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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20 pages, 7126 KiB

Open AccessArticle

Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

by Farzad Mohebbi and Mathieu Sellier

Energies 2021, 14(16), 5073; https://doi.org/10.3390/en14165073 - 18 Aug 2021

Cited by 5 | Viewed by 2369

Abstract

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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15 pages, 16532 KiB

Open AccessArticle

Prediction of Abrasive and Impact Wear Due to Multi-Shaped Particles in a Centrifugal Pump via CFD-DEM Coupling Method

by Cheng Tang, You-Chao Yang, Peng-Zhan Liu and Youn-Jea Kim

Energies 2021, 14(9), 2391; https://doi.org/10.3390/en14092391 - 23 Apr 2021

Cited by 15 | Viewed by 2437

Abstract

Since solid particles suspended in the fluid can cause wear in centrifugal pumps, intensive attention has been focused on the numerical prediction for the wear of flow parts in centrifugal pumps. However, most numerical studies have focused on only one wear model and a sphere particle model. The impact of particle shape on the wear of flow parts in centrifugal pumps is under-studied, particularly considering abrasive and impact wear simultaneously. In this work, the Computational Fluid Dynamics (CFD)-Discrete Element Method (DEM) coupling method with an abrasive and impact wear prediction model was adopted to study the wear characteristics of a centrifugal pump. Moreover, four regular polyhedron particles and a sphere particle with the same equivalent diameter but different sphericity were mainly analyzed. The results demonstrate that more particles move closer to the blade pressure side in the impeller passage, and particles tend to cluster in specific areas within the volute as sphericity increases. The volute suffers the principal wear erosion no matter what the shapes of particles and wear model are. Both the impact and abrasive wear within the impeller occur primarily on the blade leading edge. The pump’s overall impact wear rate decreases first and then increases with particle sphericity rising, while the pump’s overall abrasive wear rate grows steadily. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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Review

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24 pages, 2861 KiB

Open AccessReview

Numerical Modeling of Energy Systems Based on Micro Gas Turbine: A Review

by Fabrizio Reale and Raniero Sannino

Energies 2022, 15(3), 900; https://doi.org/10.3390/en15030900 - 26 Jan 2022

Cited by 17 | Viewed by 4282

Abstract

In the context of the great research pulse on clean energy transition, distributed energy systems have a key role, especially in the case of integration of both renewable and traditional energy sources. The stable interest in small-scale gas turbines can further increase owing to their flexibility in both operation and fuel supply. Since their not-excellent electrical efficiency, research activities on micro gas turbine (MGT) are focused on the performance improvements that are achievable in several ways, like modifying the Brayton cycle, integrating two or more plants, using cleaner fuels. Hence, during the last decades, the growing interest in MGT-based energy systems encouraged the development of many numerical approaches aimed to provide a reliable and effective prediction of the energy systems’ behavior. Indeed, numerical modeling can help to individuate potentialities and issues of each enhanced layout or hybrid energy system, and this review aims to discuss the various layout solutions proposed by researchers, with particular attention to recent publications, highlighting the adopted modeling approaches and methods. Full article

(This article belongs to the Special Issue Mathematical Modelling of Energy Systems and Fluid Machinery 2022)

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