Mechanical Energy Conversion E-Book

Mathieu Mory

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 364

Veröffentlichungsjahr: 2024

Beschreibung

This book studies the principles of mechanical energy conversion used in renewable energy sources derived from air and water: wind power, tidal power, hydroelectric power, osmotic energy, ocean thermal energy and wave energy. Mechanical Energy Conversion presents twelve application exercises and their answers. They enable the reader to first understand the physical principles of mechanical energy converters and then learn the method for sizing them. The book also reinforces the concepts of fluid mechanics and hydraulic turbo machinery, which are required to solve the exercises. This book aims to instruct readers on how to design an energy system. For each renewable energy source covered - and based on the quantity of energy or power supplied - it describes the production process, explains how it works and calculates the characteristics and dimensions of its components.

Leseprobe

Series Editor Alain Dollet

Mechanical Energy Conversion

Exercises for Scaling Renewable Energy Systems

Mathieu Mory

First published 2024 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK

www.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

www.wiley.com

© ISTE Ltd 2024The rights of Mathieu Mory to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.

Library of Congress Control Number: 2023952598

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78630-923-5

Foreword

The subtitle of this work refers to “renewable energies” and it is for this reason that I was asked by Mathieu Mory to write this foreword. My professional life has mostly been spent in the Laboratory of geophysical and industrial flows (Laboratoire des écoulements géophysiques et industriels [LEGI]), which is a Joint Research Unit (UMR 5519) of the French National Center for Scientific Research (Centre national de la recherche scientifique [CNRS]), the Institut national polytechnique de Grenoble (Grenoble INP) and the University of Grenoble-Alpes (UGA). It was in this laboratory that I launched a research program in 2000, bringing together four regional laboratories over a period of around 10 years, the objective of which was to design and ultimately produce a demonstrator of an innovative marine tidal turbine. This program was at the origin of the company HydroQuest, whose tidal turbine is mentioned in this book. Since then, I have never ceased to be involved in renewable energies, first through several studies on new converters, and at the same time by participating in various national organizations, such as group No. 5 on marine, hydraulic and wind turbine energies of the Alliance nationale de coordination de la recherche pour l’énergie (ANCRE) and like the Scientific Evaluation Committee CES 05 – Sustainable, Clean, Safe and Efficient Energy of the French National Agency for Research (ANR).

This book is original in several respects.

First of all, by its angle of attack on renewable energies that are limited to hydraulic and wind energy, that is to say from water and wind, respectively; the three other commonly accepted forms thus being not considered, namely, solar, biomass and geothermal energies, coming from the sun, from the biomass or from the earth. The original limitation appears in fact in the title itself, which implicitly specifies that only mechanical conversion will be considered in the conversion chain of the various sectors covered; thus, the part of the chain taken into account extends from the primary resource available in nature and stops upstream of the electrical generators. On the other hand, this part is very carefully treated, step by step, component by component, some of the latter possibly not being mechanical: thermal in the case of marine thermal energy or chemical in the case of converters of osmotic energy. It should be noted that the division into chapters covers the wind power sector (Chapter 3) and the six hydropower sectors (Chapters 4–8). The division is classic, except that Chapter 4 devoted to tidal energy deals with both the tidal dam sector and the marine tidal turbine sector.

Another original aspect is the introduction of an inventory, carried out with moderation, for each sector considered, appearing either at the beginning of the chapter concerned, or at the end. This inventory is not without interest for students who, at the end of their studies, wish to either join a company or undertake a thesis to develop one of the renewable energy sectors considered here. They may feel encouraged by the media which do not always have the perspective necessary to judge the maturity of the various sectors discussed here, nor the importance of the obstacles to be overcome in order to obtain acceptable costs. The resulting enthusiasm is certainly eminently positive for the decarbonization of our planet, but it must be channeled to truly meet the expectations of these students, so that they are not disappointed. For each sector, it is desirable that they can a priori place in a general context the objectives which will be proposed to them, know the part of the strictly technical or economic requirements to be raised that the innovation makes it possible in priority to overcome, and the part from scientific requirements of a more fundamental nature to optimize sectors that are beginning to be well known and exploited.

The last original aspect and certainly the most important: the approach used to transfer the information transmitted over the chapters based on a pedagogy that can be described as participatory. The succession of exercises provided in each sector in this book, exercises which break down into a succession of questions, followed by the succession of corresponding answers, invites students to think for themselves to discover independently. These exercises relate to situations drawn from well-described applications that become significant for them; they are in a way on a bridge between statements of very theoretical and abstract problems and statements of problems containing too technical details. Said exercises are finally relevant without being too complex: they do not require elaborate numerical approaches. We can imagine that they are themselves the fruit of experiments, trial and error, resulting from lectures, and exercise sessions offered by the author to his students.

To conclude, I would like to indicate the reasons for which I agreed to write this foreword for this book. Mathieu Mory is a friend that I have known since 1982 and I know his many qualities. However, I would be careful not to make a panegyric, but I simply want to communicate the word that comes to mind when I think of him. This word is rigor, moral as well as intellectual rigor. This rigor explains his professional trajectory since leaving the Ecole Polytechnique. He was then offered a post of high responsibility in the R&D department of a large company, which he refused because of a knowledge which he then considered insufficient of the technical-scientific activities of this department. This is how he chose and pursued a university career in which teaching was never disdained in favor of a research activity that remained of a high level. This book is an illustration of that.

Jean-Luc ACHARD Emeritus Research Director at the CNRS

Preface

Despite all the efforts, it is certain that errors remain in this work, since the last proofreading still reveals some…

When we were working on the exercises in class, the numerical applications were carried out with an Excel spreadsheet. I invite the reader to do the same. This makes it possible to see the effect of the parameters on the result and errors in numerical application are more easily identified.

The results that appear in the exercise tables are copies of the spreadsheet results. If the reader finds different numerical results, they are not necessarily the one who is making an error.

I invite the readers, if they discover an error, if they have a comment or a question, to let me know. Reach out to me at the e-mail address1 created in connection with this book. I will try to answer as best I can.

Please accept my apologies and thanks in advance.

February 2024

Note

1

[email protected]

.

Acknowledgments

I would like to thank my colleagues Didier Graebling, Daniel Broseta and Jean-Luc Achard for their advice on this manuscript.

To students of the international master’s degree in Simulation and Optimization of Energy Systems (SIMOS):

– Alireza Abbasi (Iran);

– Shayan Baghi (Iran);

– Sarad Basnet (Nepal);

– Yacine Bounekta (Algeria);

– Angelica Chacon (Venezuela);

– Mohamed Chouaikhia (Tunisia);

– Arpan Dutta (India);

– Godswill Ighedosa (Nigeria);

– Gholamhossein Kahid Baseri (Iran);

– Mukesh Kumar (Pakistan);

– Shubham Manchanda (India);

– Armin Mokhtari Shargi (Iran);

– Samandar Nabiev (Uzbekistan);

– Christopher Offor (Nigeria);

– Asaph Palencia (Philippines);

– Mohammad Sadr (Afghanistan);

– Karan Shahi (India);

– Ivan Vasilev (Russia).

Without you, without your attention, without your questions, without your presence, this course would not have been developed and this book would not have been written.

In dedicating this work to you, I want to express my friendship in return for that which you have shown me.

1Revision of Fluid Mechanics

This chapter summarizes the knowledge in fluid mechanics necessary for the resolution of the exercises. It is a tool to help the reader avoid having to look for equations in fluid mechanics books. The reader should refer to these works1 to read the mathematical proofs that are not reproduced here. This chapter presents the scientific approach and identifies the specificities of the treated flows.

1.1. Euler’s equations

Euler’s equations are the equations whose solution is the velocity field and the pressure field in a fluid domain for a fluid of zero viscosity. From the velocity field, we determine the trajectory of a fluid particle, whose position is at the point M0 at the moment . At the moment t, the fluid particle is at point M and the positions and velocities are mathematically described by the following equations:

A current line is schematized in Figure 1.1. When a flow is permanent, the velocity field and the pressure field are independent of time. Streamlines and trajectories are identical. It is then interesting to describe the flow in the intrinsic coordinate frame, linked to the trajectory of the particles. The displacement of a fluid particle can be measured by its curvilinear abscissa s(t)along the trajectory; it is the distance traveled on this line from an origin position M0.

Figure 1.1.Definition of the intrinsic coordinate system

To describe the movement in the intrinsic coordinate system, the tangent vector and the vector normal to the trajectory are used. Two results of differential geometry are useful.

The tangent vector is calculated by the expression:

The vector normal to the trajectory line, directed toward the interior of the curve, is such that:

R designates the radius of curvature of the trajectory. In Figure 1.1, point C is the center of curvature of the trajectory. This figure also indicates the acceleration of gravity , along the direction opposite the unit vector , and the altitude z of point M.

The velocity at the point M, collinear with the unit vector , is written as:

Euler’s equations are then written, for a permanent flow in the plane ():

– according to the unit vector :

– according to the unit vector :

Euler’s equations are the Navier–Stokes equations for a fluid whose viscosity is zero. By definition, an ideal fluid is a fluid of zero viscosity. We avoid using the term ideal fluid in this work because, we will explain later why, the application of this term is ambiguous. It is not a property of the fluid if we can use Euler’s equations but a property of the flow.

We use Euler’s equations under conditions where the flow is steady, the fluid is incompressible and the flow is isothermal. The density ρ is therefore taken as a constant.

Some additional calculations, from the spring of the differential geometry, allow transforming the terms of gravity and writing the Euler’s equations:

We then finally write:

– according to the unit vector

Under the assumption that the quantity inside the parenthesis is a continuously differentiable function along the streamline, Bernoulli’s theorem (see section 1.2) follows from this first equation:

– according to the unit vector :

The consequences of this second equation are discussed in section 1.3.

1.2. Head and Bernoulli’s theorem

Euler’s equation according to the tangent vector leads to introduce the head, defined as the quantity:

Bernoulli’s theorem is deduced by integrating Euler’s equation according to the tangent vector : the head is conserved along a streamline.

This very simple proof of Bernoulli’s theorem assumes incompressible fluid, steady and isothermal flow, and zero viscosity. It also makes the assumption that the head is a continuously differentiable function along the streamline. Nothing states that this is always the case.

The problem with the term ideal fluid is that the application of Bernoulli’s theorem is then prohibited for common fluids such as water and air, since their viscosity is not zero, although low. Bernoulli’s theorem is however very useful, in water as in air, and it would be very regrettable to refrain from using it for scientific rigor. Experience shows that the head can be retained on certain portions of a streamline without being on other portions of the same streamline. It is therefore a property of the flow when the head is conserved or not. It is not a property of the fluid. The notion of ideal fluid does not explain why the head is kept along a streamline portion and not along another portion of this same streamline.

To explain this point with an example, we discuss the emptying flow of a tank filled with water, schematized in Figure 1.2. The upper reservoir is filled with water to a height H above an orifice (point B) through which the fluid flows with a flow rate velocity UB. The flow in the upper reservoir, with the jet exiting it, is called the Torricelli flow. We extend this flow by an equally classic configuration where the jet of water issuing from point B of the upper reservoir flows into the air before plunging into a lower reservoir where, sooner or later, any fluid particle coming from the upper container ends up having zero velocity. We therefore consider the flow along a streamline between a point A placed on the surface of the water in the upper container and a point D on the surface of the water in the lower container. The pressure is the atmospheric pressure in A and in D since we are on the surface of the water in contact with the air. The value of the head is easily calculated at A and at D, since the kinetic energy is negligible at these points (when the tanks are large), and it can be seen that:

The head is therefore not conserved on the current line which leads from point A to point D. However, the first use made classically of Bernoulli’s theorem consists of applying it between points A and B to determine the velocity of the jet UB at B and deduce Torricelli’s formula from it . It is therefore downstream of point B that the head loss occurs.

Figure 1.2.Drainage flow from a tank

Before going further, note that the head has an energetic significance since its dimension, the Pascal, is also understood as a Joule per unit volume. The head is the sum of three mechanical energies per unit volume: pressure, potential energy and kinetic energy. A flow (in steady state) is therefore characterized by transfers between these three forms of energy. By considering the values of the head indicated in Figure 1.2 at points A, B, C and D, we can therefore see that:

– The kinetic energy increases between A and B, compensated by a drop in potential energy. The same is true between B and C.