**About the Editors**

**Mirko Morini** graduated with a Bachelor of Science in Material Engineering in 2003, with a Master of Science in Material Engineering in 2004, and with a PhD in Industrial Engineering at the University of Ferrara in 2008. During his PhD, he had an internship at Alstom (now Ansaldo Energia) in Baden (CH). He is currently Associate Professor in Energy Systems and Fluid Machinery at the Department of Engineering and Architecture of the University of Parma. His main research activities have focused on (i) smart district energy, (ii) energy and economic analyses of energy chains based on biomass and biofuels, (iii) micro-CHP systems analysis, (iv) dynamic models for the simulation of turbomachines, (v) experimental investigation of turbomachine instabilities, (vi) analysis of the effect of blade deterioration on turbomachine performance, and (vii) analysis of start-up transients of heavy-duty gas turbines for cost-killing and reliability enhancement. This activity is documented by more than 100 scientific articles.

**Michele Pinelli** received his MSc Degree in Mechanical Engineering at the University of Bologna in 1997 and his PhD in 2001. Since 2010, he has been Associate Professor of Fluid Machinery at the Engineering Department in Ferrara. His research activity has been carried out in the field of fluid machinery and energy systems and recently has mainly dealt with the development of techniques for the numerical estimation of turbine and compressor behavior in deteriorated conditions (fouling and erosion), the development of a small-scale compressor test rig for the analysis of transient behavior, water ingestion, stall and surge conditions of small-scale compressors, and the study of innovative energy systems in micro-cogeneration applications, with particular attention to thermophotovoltaics and organic Rankine Cycle systems. His research activity is documented by more than 200 scientific articles. He received the Best Paper Award of the Oil and Gas Committee at the ASME Turbo Expo in Barcelona 2006, Montreal 2007, Orlando 2009, and Montreal 2015. He is the coordinator of a research group comprising PhD students and research fellows. He is also responsible for research collaborations with Imperial College of London (UK), St. John's College of Oxford (UK), University of Bath (UK), Institut fur Luftfahrtantriebe—Universit ¨ at Stuttgart (D), Southwest Research Institute ¨ (SwRI) (US), and Solar Turbines (US).

## **Preface to "Mathematical Modelling of Energy Systems and Fluid Machinery"**

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 managemen<sup>t</sup> 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. The aim of this Special Issue was to collect contributions about mathematical modelling of energy systems and fluid machinery in order to build and consolidate the base of this knowledge. In this Special Issue, we collected papers dealing with many 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 (e.g., models for optimization, 3D CFD for component design, CAE models). In this context, a relevant number of fluid machinery (e.g., axial and radial pumps, hydroturbines, turboexpanders) and energy system (e.g., thermal energy storage, refrigeration systems) typologies have been taken into consideration and studied by means of the above-mentioned models.

> **Mirko Morini, Michele Pinelli** *Editors*

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

**Nora Cadau 1, Andrea De Lorenzi 1, Agostino Gambarotta 1,2, Mirko Morini 2,\* and Michele Rossi 2**


Received: 24 September 2019; Accepted: 7 November 2019; Published: 9 November 2019

**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.

**Keywords:** thermal energy storage; stratification; dynamic simulation; heating
