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Mathematical Modelling of Energy Systems and Fluid Machinery

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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 (31 October 2020) | Viewed by 48648

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Prof. Dr. Mirko Morini

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Department of Engineering and Architecture, University of Parma, I-43124 Parma, Italy
Interests: modelling; district heating networks; electrofuels
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Prof. Dr. Michele Pinelli

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Department of Engineering, University of Ferrara, Via Saragat, 1, 44122 Ferrara, Italy
Interests: turbomachinery; energy systems
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Special Issue Information

Dear Colleagues,

The ongoing digitalization of the energy sector, which will make a large amount of data available, should not be viewed as a passive ICT application for energy technology or a threat to thermodynamics and fluid dynamics, in the light of the competition triggered by data mining and machine learning techniques.

Digitalization creates opportunities, for example, for more sustainable energy systems through the smart management of renewable energy technologies, and for more reliable fluid machines through predictive maintenance.

Nevertheless, 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 is intended for a collection of contributions about mathematical modelling of energy systems and fluid machinery in order to build and consolidate the base of this 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 the 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). Besides original research papers, historical review papers are particularly welcome since they can contribute to the discussion on consolidated assumptions and methodological approaches in the light of the new capabilities provided by modern ICT.

Prof. Dr. Mirko Morini
Prof. Dr. Michele Pinelli
Guest Editors

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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.

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Keywords

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

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Published Papers (12 papers)

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Research

25 pages, 5644 KiB

Open AccessArticle

Mathematical Modelling of Active Magnetic Regenerator Refrigeration System for Design Considerations

by Aref Effatpisheh, Amir Vadiee and Behzad A. Monfared

Energies 2020, 13(23), 6301; https://doi.org/10.3390/en13236301 - 29 Nov 2020

Cited by 1 | Viewed by 2369

Abstract

A magnetic refrigeration system has the potential to alternate the compression system with respect to environmental compatibility. Refrigeration systems currently operate on the basis of the expansion and compression processes, while active magnetic refrigeration systems operate based on the magnetocaloric effect. In this study, a single layer of Gd was used as the magnetocaloric material for six-packed-sphere regenerators. A one-dimensional numerical model was utilized to simulate the magnetic refrigeration system and determine the optimum parameters. The optimum mass flow rate and maximum cooling capacity at frequency of 4 Hz are 3

L \cdot \min^{- 1}

and 580 W, respectively. The results show that the maximum pressure drop increased by 1400 W at a frequency of 4 Hz and mass flow rate of 5

L \cdot \min^{- 1}

. In this study, we consider the refrigeration system in terms of the design considerations, conduct a parametric study, and determine the effect of various parameters on the performance of the system. Full article

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

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20 pages, 12352 KiB

Open AccessArticle

Reduction of Entrained Vortices in Submersible Pump Suction Lines Using Numerical Simulations

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

Energies 2020, 13(22), 6136; https://doi.org/10.3390/en13226136 - 23 Nov 2020

Cited by 13 | Viewed by 3704

Abstract

Pump intake structure design is one area where physical models still remain as the only acceptable method that can provide reliable engineering results. Ensuring the amount of turbulence, entrained air vortices, and swirl are kept within acceptable limits requires site-specific, expensive, and time-consuming physical model studies. This study aims to investigate the viability of Computational Fluid Dynamics (CFD) as an alternative tool for pump intake design thus reducing the need for extensive physical experiments. In this study, a transient multiphase simulation of a 530 mm wide rectangular intake sump housing a 116 m³/h pump is presented. The flow conditions, vortex formation and inlet swirl are compared to an existing 1:10 reduced scaled physical model test. For the baseline test, the predicted surface and submerged vortices agreed well with those observed in the physical model. Both the physical model test and the numerical model showed that the initial geometry of the pump sump is unacceptable as per ANSI/HI 9.8 criteria. Strong type 2 to type 3 submerged vortices were observed at the floor of the pump and behind the pump. Consequently, numerical simulations of proposed sump design modification are further investigated. Two CFD models with different fillet-splitter designs are evaluated and compared based on the vortex formation and swirl. In the study, it was seen that a trident-shaped splitter design was able to prevent flow separation and vortex suppression as compared to a cross-baffle design based on ANSI/HI 9.8. CFD results for the cross-baffle design showed that backwall and floor vortices were still present and additional turbulence was observed due to the cross-flow caused by the geometry. Conversely, CFD results for the trident-shaped fillet-splitter design showed stable flow and minimized the floor and wall vortices previously observed in the first two models. Full article

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

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30 pages, 37230 KiB

Open AccessArticle

Derivation and Uncertainty Quantification of a Data-Driven Subcooled Boiling Model

by Jerol Soibam, Achref Rabhi, Ioanna Aslanidou, Konstantinos Kyprianidis and Rebei Bel Fdhila

Energies 2020, 13(22), 5987; https://doi.org/10.3390/en13225987 - 16 Nov 2020

Cited by 4 | Viewed by 2078

Abstract

Subcooled flow boiling occurs in many industrial applications where enormous heat transfer is needed. Boiling is a complex physical process that involves phase change, two-phase flow, and interactions between heated surfaces and fluids. In general, boiling heat transfer is usually predicted by empirical or semiempirical models, which are horizontal to uncertainty. In this work, a data-driven method based on artificial neural networks has been implemented to study the heat transfer behavior of a subcooled boiling model. The proposed method considers the near local flow behavior to predict wall temperature and void fraction of a subcooled minichannel. The input of the network consists of pressure gradients, momentum convection, energy convection, turbulent viscosity, liquid and gas velocities, and surface information. The outputs of the models are based on the quantities of interest in a boiling system wall temperature and void fraction. To train the network, high-fidelity simulations based on the Eulerian two-fluid approach are carried out for varying heat flux and inlet velocity in the minichannel. Two classes of the deep learning model have been investigated for this work. The first one focuses on predicting the deterministic value of the quantities of interest. The second one focuses on predicting the uncertainty present in the deep learning model while estimating the quantities of interest. Deep ensemble and Monte Carlo Dropout methods are close representatives of maximum likelihood and Bayesian inference approach respectively, and they are used to derive the uncertainty present in the model. The results of this study prove that the models used here are capable of predicting the quantities of interest accurately and are capable of estimating the uncertainty present. The models are capable of accurately reproducing the physics on unseen data and show the degree of uncertainty when there is a shift of physics in the boiling regime. Full article

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

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12 pages, 7028 KiB

Open AccessArticle

CFD-DEM Simulation for the Distribution and Motion Feature of Solid Particles in Single-Channel Pump

by Cheng Tang and Youn-Jea Kim

Energies 2020, 13(19), 4988; https://doi.org/10.3390/en13194988 - 23 Sep 2020

Cited by 17 | Viewed by 2850

Abstract

Since various foreign bodies can cause clogging and wear in single-channel pumps, considerable attention has been focused on the numerical study of solid-liquid flows in the single-channel pump. However, conventional numerical simulation cannot responsibly assess the significant effect of the particle material properties, inter-particle collision, and size on the pump. In consideration of the particle features and behaviors, the Computational Fluid Dynamics (CFD)-Discrete Element Method (DEM) coupling method was applied for the first time to simulate the solid-liquid flows in a single-channel pump. The results showed that the smaller particles possessed a wider velocity distribution range and velocity peak, while the larger particles exerted a greater contact force. Additionally, the pie-shaped particles had the most severe collisions, and spherical particles had the least in total. Furthermore, the hub and shroud wall suffered a minor contact force, but the blade and volute wall both sustained a considerable contact force. This paper could present some supply data for future research on the optimization of a single-channel pump. Full article

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

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13 pages, 6147 KiB

Open AccessArticle

Two-Objective Optimization of a Kaplan Turbine Draft Tube Using a Response Surface Methodology

by Riccardo Orso, Ernesto Benini, Moreno Minozzo, Riccardo Bergamin and Andrea Magrini

Energies 2020, 13(18), 4899; https://doi.org/10.3390/en13184899 - 18 Sep 2020

Cited by 9 | Viewed by 2885

Abstract

The overall cost of a hydropower plant is mainly due to the expenses of civil works, mechanical equipment (turbine and control units) and electrical components. The goal of a new draft tube design is to obtain a geometry that reduces investment costs, especially the excavation ones, but the primary driver is to increase overall machine efficiency, allowing for a reduced payback time. In the present study, an optimization study of the elbow-draft tube assembly of a Kaplan turbine was conducted. First, a CFD model for the complete turbine was developed and validated. Next, an optimization of the draft tube alone was performed using a design of experiments technique. Finally, several optimum solutions for the draft tube were obtained using a response surface technique aiming at maximizing pressure recovery and minimizing flow losses. A selection of optimized geometries was subsequently post-checked using the validated model of the entire turbine, and a detailed flow analysis on the obtained results made it possible to provide insights into the improved designs. It was observed that efficiency could be improved by 1% (in relative terms), and the mechanical power increased by 1.8% (in relative terms) with respect to the baseline turbine. Full article

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

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26 pages, 9751 KiB

Open AccessArticle

Fast Design Procedure for Turboexpanders in Pressure Energy Recovery Applications

by Gaetano Morgese, Francesco Fornarelli, Paolo Oresta, Tommaso Capurso, Michele Stefanizzi, Sergio M. Camporeale and Marco Torresi

Energies 2020, 13(14), 3669; https://doi.org/10.3390/en13143669 - 16 Jul 2020

Cited by 10 | Viewed by 4732

Abstract

Sustainable development can no longer neglect the growth of those technologies that look at the recovery of any energy waste in industrial processes. For example, in almost every industrial plant it happens that pressure energy is wasted in throttling devices for pressure and flow control needs. Clearly, the recovery of this wasted energy can be considered as an opportunity to reach not only a higher plant energy efficiency, but also the reduction of the plant Operating Expenditures (OpEx). In recent years, it is getting common to replace throttling valves with turbine-based systems (tuboexpander) thus getting both the pressure control and the energy recovery, for instance, producing electricity. However, the wide range of possible operating conditions, technical requirements and design constrains determine highly customized constructions of these turboexpanders. Furthermore, manufacturers are interested in tools enabling them to rapidly get the design of their products. For these reasons, in this work we propose an optimization design procedure, which is able to rapidly come to the design of the turboexpander taking into account all the fluid dynamic and technical requirements, considering the already obtained achievements of the scientific community in terms of theory, experiments and numeric. In order to validate the proposed methodology, the case of a single stage axial impulse turbine is considered. However, the methodology extension to other turbomachines is straightforward. Specifically, the design requirements were expressed in terms of maximum allowable expansion ratio and flow coefficient, while achieving at least a minimum assigned value of the turbine loading factor. Actually, it is an iterative procedure, carried out up to convergence, made of the following steps: (i) the different loss coefficients in the turbine are set-up in order to estimate its main geometric parameters by means of a one dimensional (1D) study; (ii) the 2D blade profiles are designed by means of an optimization algorithm based on a “viscous/inviscid interaction” technique; (iii) 3D Computational Fluid Dynamic (CFD) simulations are then carried out and the loss coefficients are computed and updated. Regarding the CFD simulations, a preliminary model assessment has been performed against a reference case, chosen in the literature. The above-mentioned procedure is implemented in such a way to speed up the convergence, coupling analytical integral models of the 1D/2D approach with accurate local solutions of the finite-volume 3D approach. The method is shown to be able to achieve consistent results, allowing the determination of a turbine design respectful of the requirements more than doubling the minimum required loading factor. Full article

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

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23 pages, 8495 KiB

Open AccessArticle

Effect of Fins on the Internal Flow Characteristics in the Draft Tube of a Francis Turbine Model

by Seung-Jun Kim, Young-Seok Choi, Yong Cho, Jong-Woong Choi, Jung-Jae Hyun, Won-Gu Joo and Jin-Hyuk Kim

Energies 2020, 13(11), 2806; https://doi.org/10.3390/en13112806 - 1 Jun 2020

Cited by 16 | Viewed by 6123

Abstract

Undesirable flow phenomena in Francis turbines are caused by pressure fluctuations induced under conditions of low flow rate; the resulting vortex ropes with precession in the draft tube (DT) can degrade performance and increase the instability of turbine operations. To suppress these DT flow instabilities, flow deflectors, grooves, or other structures are often added to the DT into which air or water is injected. This preliminary study investigates the effects of anti-cavity fins on the suppression of vortex ropes in DTs without air injection. Unsteady-state Reynolds-averaged Navier–Stokes analyses were conducted using a scale-adaptive simulation shear stress transport turbulence model to observe the unsteady internal flow and pressure characteristics by applying anti-cavity fins in the DT of a Francis turbine model. A vortex rope with precession was observed in the DT under conditions of low flow rate, and the anti-cavity fins were confirmed to affect the mitigation of the vortex rope. Moreover, at the low flow rate conditions under which the vortex rope developed, the application of anti-cavity fins was confirmed to reduce the maximum unsteady pressure. Full article

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

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17 pages, 8390 KiB

Open AccessArticle

Effects of the Impeller Blade with a Slot Structure on the Centrifugal Pump Performance

by Hongliang Wang, Bing Long, Chuan Wang, Chen Han and Linjian Li

Energies 2020, 13(7), 1628; https://doi.org/10.3390/en13071628 - 2 Apr 2020

Cited by 54 | Viewed by 4458

Abstract

An impeller blade with a slot structure can affect the velocity distribution in the impeller flow passage of the centrifugal pump, thus affecting the pump’s performance. Various slot structure geometric parameter combinations were tested in this study to explore this relationship: slot position p, slot width b₁, slot deflection angle β, and slot depth h with (3–4) levels were selected for each factor on an L₁₆ orthogonal test table. The results show that b₁ and h are the major factors influencing pump performance under low and rated flow conditions, while p is the major influencing factor under the large flow condition. The slot structure close to the front edge of the impeller blade can change the low-pressure region of the suction inlet of the impeller flow passage, thus improving the fluid velocity distribution in the impeller. Optimal slot parameter combinations according to the actual machining precision may include a small slot width b₁, slot depth h of ¼ b, slot deflection angle β of 45°–60°, and slot position p close to the front edge of the blade at 20–40%. Full article

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

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19 pages, 6550 KiB

Open AccessFeature PaperArticle

Multi-Disciplinary Optimization Design of Axial-Flow Pump Impellers Based on the Approximation Model

by Lijian Shi, Jun Zhu, Fangping Tang and Chuan Wang

Energies 2020, 13(4), 779; https://doi.org/10.3390/en13040779 - 11 Feb 2020

Cited by 78 | Viewed by 5587

Abstract

This study adopts a multi-disciplinary optimization design method based on an approximation model to improve the comprehensive performance of axial-flow pump impellers and fully consider the interaction and mutual influences of the hydraulic and structural designs. The lightweight research on axial-flow pump impellers takes the blade mass and efficiency of the design condition as the objective functions and the head, efficiency, maximum stress value, and maximum deformation value under small flow condition as constraints. In the optimization process, the head of the design condition remains unchanged or varies in a small range. Results show that the mass of a single blade was reduced from 0.947 to 0.848 kg, reaching a decrease of 10.47%, and the efficiency of the design condition increased from 93.91% to 94.49%, with an increase rate of 0.61%. Accordingly, the optimization effect was evident. In addition, the error between the approximate model results and calculation results of each response was within 0.5%, except for the maximum stress value. This outcome shows that the accuracy of the approximate model was high, and the analysis result is reliable. The results provide guidance for the optimal design of axial-flow pump impellers. Full article

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

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20 pages, 5801 KiB

Open AccessArticle

Influence of Critical Wall Roughness on the Performance of Double-Channel Sewage Pump

by Xiaoke He, Yingchong Zhang, Chuan Wang, Congcong Zhang, Li Cheng, Kun Chen and Bo Hu

Energies 2020, 13(2), 464; https://doi.org/10.3390/en13020464 - 17 Jan 2020

Cited by 34 | Viewed by 3345

Abstract

The numerical method on a double-channel sewage pump was studied, while the corresponding experimental result was also provided. On this basis, the influence of wall roughness on the pump performance was deeply studied. The results showed that there was a critical value of wall roughness. When the wall roughness was less than the critical value, it had a great influence on the pump performance, including the head, efficiency, and shaft power. As the wall roughness increased, the head and efficiency were continuously reduced, while the shaft power was continuously increased. Otherwise, the opposite was true. The effect of wall roughness on the head and hydraulic loss power was much smaller than that on the efficiency and disk friction loss power, respectively. With the increase of wall roughness, mechanical efficiency and hydraulic efficiency reduced constantly, leading to the decrement of the total efficiency. With the increase of flow rate, the effect of wall roughness on the head and efficiency gradually increased, while the influence on the leakage continuously reduced. The influence of the flow-through component roughness on the pump performance was interactive. Full article

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

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22 pages, 8866 KiB

Open AccessArticle

Development and Analysis of a Multi-Node Dynamic Model for the Simulation of Stratified Thermal Energy Storage

by Nora Cadau, Andrea De Lorenzi, Agostino Gambarotta, Mirko Morini and Michele Rossi

Energies 2019, 12(22), 4275; https://doi.org/10.3390/en12224275 - 9 Nov 2019

Cited by 20 | Viewed by 5991

Abstract

To overcome non-programmability issues that limit the market penetration of renewable energies, the use of thermal energy storage has become more and more significant in several applications where there is a need for decoupling between energy supply and demand. The aim of this paper is to present a multi-node physics-based model for the simulation of stratified thermal energy storage, which allows the required level of detail in temperature vertical distribution to be varied simply by choosing the number of nodes and their relative dimensions. Thanks to the chosen causality structure, this model can be implemented into a library of components for the dynamic simulation of smart energy systems. Hence, unlike most of the solutions proposed in the literature, thermal energy storage can be considered not only as a stand-alone component, but also as an important part of a more complex system. Moreover, the model behavior has been analyzed with reference to the experimental results from the literature. The results make it possible to conclude that the model is able to accurately predict the temperature distribution within a stratified storage tank typically used in a district heating network with limitations when dealing with small storage volumes and high flow rates. Full article

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

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14 pages, 2571 KiB

Open AccessArticle

Research on the Prediction Method of Centrifugal Pump Performance Based on a Double Hidden Layer BP Neural Network

by Wei Han, Lingbo Nan, Min Su, Yu Chen, Rennian Li and Xuejing Zhang

Energies 2019, 12(14), 2709; https://doi.org/10.3390/en12142709 - 15 Jul 2019

Cited by 49 | Viewed by 3480

Abstract

With the aim of improving the shortcomings of the traditional single hidden layer back propagation (BP) neural network structure and learning algorithm, this paper proposes a centrifugal pump performance prediction method based on the combination of the Levenberg–Marquardt (LM) training algorithm and double hidden layer BP neural network. MATLAB was used to establish a double hidden layer BP neural network prediction model to predict the head and efficiency of a centrifugal pump. The average relative error of the head between the experimental and prediction obtained by the double hidden layer BP neural network model was 4.35%, the average relative error of the model prediction efficiency and the experimental efficiency was 2.94%, and the convergence time was 1/42 of that of the single hidden layer. The double hidden layer BP neural network model effectively solves the problems of low learning efficiency and easy convergence into local minima—issues that were common in the traditional single hidden layer BP neural network training. Furthermore, the proposed model realizes hydraulic performance prediction during the design process of a centrifugal pump. Full article

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

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