Thermal-fluids engineering

Summary

One of the most dazzling applications of thermodynamics is the study and design of devices to convert energy to obtain some useful effect. Modern societies are based on the extensive use of electricity, heating, and refrigeration for a broad variety of goals. These services are supplied by a system in which some sort of working substance, usually in the gas or liquid phase, flows through several devices at various temperatures. The same holds for engines, which provide the stunning mobility which is also a pillar of modern times.

Here we therefore describe and analyze systems such as stationary power plants, propulsion engines, refrigerators, heat pumps, and the like. Stationary power plants convert one kind of energy, like the chemical energy of a fuel, the thermal energy of a geothermal reservoir, or solar radiation into electricity. Propulsion engines do the same, but usually the primary energy source is a liquid fuel and the final objective is to obtain mechanical power or thrust to put something into motion. Refrigeration systems and heat pumps make use of electrical, mechanical, or thermal power in order to keep the temperature of a certain space at a value different from that of the natural environment.

Analysis of Thermodynamic Systems

Most energy systems involve a working fluid, like water or air, which is circulated through one or more components, often arranged in a cycle. The working fluid undergoes therefore a sequence of processes, which together form a thermodynamic cycle. In steam power plants (Figure 7.1a) the cycle is usually closed, but thermodynamic cycles can be open (closed by the atmosphere), as is the case for a turboprop engine (Figure 7.1b).

The basic methodology for the analysis of thermodynamic processes and systems has been laid down in Chapter 4, while in this chapter we will use that procedure, together with knowledge on the estimation of fluid properties (Chapter 6), in order to study some notable examples of energy conversion systems. In addition, we can make use of the many consequences of the second law of thermodynamics to discuss their performance and limitations.

In Section 3.6 we have already stressed the importance of thermodynamic charts and of sketching relevant processes on such charts. Graphical representation of concepts is a very powerful tool for the understanding of thermodynamics.

Summary

Application of the First and Second Laws of Thermodynamics, together with entropy analysis, has already showed us that a useful effect like work, cooling, or heating can be obtained if a thermodynamic system is not in equilibrium with its surroundings. The Carnot efficiency tells us which is the maximum amount of work (or power) that we can extract from a thermal source with a device operating between the temperature of the thermal source and a lower temperature. We also know that all the processes in a Carnot cycle are reversible, and this is an unattainable limit for real processes. Similar reasoning can be applied to refrigeration systems, whereby mechanical work is used to obtain the cooling effect. Entropy production always occurs in real processes and we generally speak of thermodynamic losses associated with entropy production.

Now we look closer at this concept, which becomes a powerful analysis and optimization tool in energy conversion engineering.

What for?

We are about to define another thermodynamic function, called exergy. This function is useful to evaluate thermodynamic losses in quantitative terms and to answer questions like:

Summary

This chapter deals with the study of mixtures of substances undergoing chemical reactions. Combustion is an example of a thermodynamic process governed by many complex chemical reactions. It is at the core of the majority of the power and propulsion systems in use today. The First Law of Thermodynamics is the basis for quantitative analysis of chemical reactions. The Second Law of Thermodynamics tells us if a certain reaction is possible, and it is at the basis of the calculation of the state of thermodynamic equilibrium reached by a reacting mixture. Here we will introduce the Third Law of Thermodynamics in order to correctly compute the entropy of different species involved in the chemical reaction. The prediction of reaction rates, and the investigation of reactions mechanisms, that is chemical kinetics, is beyond the scope of this book.

Some Concepts and Terms

Associated with every chemical reaction is a chemical equation, derived by applying the law of conservation of atoms to each of the atomic species involved in some sort of units reaction. The reaction begins with the collection of certain chemical constituents, called reactants. The chemical reaction causes a rearrangement of atoms and electrons to form different constituents, called the products.

The reaction between the reactants hydrogen and oxygen to form the product water can be expressed as

This expression indicates that two molecules of hydrogen and one molecule of oxygen can be combined to form two molecules of water. The arrows in both directions indicate that the opposite reaction may also occur. The coefficients in the chemical equation are called stoichiometric coefficients (2, 1, and 2 in this example). The number of hydrogen atoms is conserved, as is the number of oxygen atoms. Chemical equations can also be interpreted as equations relating the molar masses of the species involved in the reaction; here two moles of hydrogen and one mole of oxygen combine to form two moles of water. Note that the number of moles of the reactants may differ from the number of moles of the products.

A stoichiometric mixture of reactants is one in which the molar proportions of the reactants are exactly as given by the stoichiometric coefficients so that no excess of any constituent is present. A stoichiometric combustion is one in which all the oxygen atoms in the oxidizer react chemically to appear in the products.

Summary

In any analysis it is very important that the system being analyzed is defined precisely. Careful definition helps the analyst do the work correctly and enables the reader to understand it. In thermodynamic analysis we work with two different types of system definitions: the control mass (CM) and the control volume (CV). When we apply a basic principle, such as conservation of energy, we always apply it to one of these two types of systems. Each of the energy balances we made in previous chapters was made on a control mass. The primary purpose of this chapter is to help you learn how to make a correct energy balance on a control volume, because in many cases it is natural and simplifies the solution of problems.

Control Mass and Control Volume

Control mass

A control mass is a defined piece of matter. The matter may move around, and the boundaries of the control mass follow the matter wherever it goes. By definition, no matter can enter or leave a control mass, and therefore (neglecting relativistic effects) the mass of a control mass is always the same. In a control mass energy analysis, the only forms of energy transfer across the boundary are work and heat.

Control volume

A control volume is a defined region in space. Matter may enter or leave a control volume, and the matter in a control volume is whatever happens to be in it at any moment. For example, a control volume can be defined as the space around an aircraft jet engine, or the space inside a balloon. The control volume boundary may move through space (as with the jet engine), and may change shape and volume (as with a balloon). The important thing is that the boundary must be well defined at all times. In a control volume energy balance, the possible energy transfers across the boundary include heat, work, and energy transfer associated with mass flow across the boundary. The primary point of this chapter is to derive the correct expression for this mass-associated energy transfer.

Example of Flow System Analysis: Tank Charging

Flow systems can be analyzed using either a control volume or control mass approach. In either case one must identify the energy inputs, energy outputs, and energy accumulation in the control volume or control mass, and combine these properly in the energy balance.

Summary

The examples of energy analysis in Chapter 2 show that, in order to obtain quantitative results from energy balances, we need to evaluate the thermodynamic properties of fluids at the relevant states of the processes. We used the ideal gas model with constant specific heat to calculate pressure, temperature, specific volume, and internal energy, an anticipation of what is explained and generalized in this chapter. In order to treat problems in which the working fluid can be a liquid, or a vapor, and in all cases in which the fluid does not obey the ideal gas law, we have to learn how we can obtain this information first from tables and charts, then using software. Before we master how to use these tools, we must learn in a more systematic way what thermodynamic properties and states of fluids are, understand the relations and transitions between the various possible states of matter, and how they can be visualized on appropriate diagrams, revealing their complex interaction.

Concepts of Property and State

Properties

A property is any characteristic or attribute of matter that can be quantitatively evaluated. Volume, mass, density, energy, charge, temperature, pressure, magnetic dipole moment, electric dipole moment, internal energy, momentum, surface tension, velocity, entropy, viscosity, and color are all properties. Work and heat are not properties because they are not something that matter has, but instead are amounts of energy transfer to or from matter.

States

The state of a system is its condition as described by the values of all of its properties. Usually we are content to describe a more limited aspect of the system. For example, the geometric state of a solid object can be described by the values of its various dimensions, which are the geometric properties. The dynamical state of a rigid body would be specified by its geometric state plus its three components of translational velocity and three angular rotation rates.

Intensive and extensive properties

An extensive property of a system is the sum of the values of that property for the parts of the system. Volume, mass, energy, charge, magnetic dipole moment, internal energy, momentum, and entropy are extensive properties; they depend on the extent of the system.

Summary

Inspiring Principles

Bill and I talked many times about his idea of writing a new book on thermodynamics for engineers. We observed that there are many books on this subject which have one thing in common: They are very thick and every chapter becomes thicker with every new edition, by adding ever more examples and auxiliary material. We believed instead that the explanation of the very few founding concepts of classical thermodynamics, beautiful and challenging to the mind and expressed in formally very simple equations, would benefit from a much more essential treatment, which always starts with the description of the physical world at microscopic level. Concepts like energy and entropy must first be understood in their essence from situations that can be visualized with a few carefully conceived examples. Once these notions are clear, they can then be used to solve the inexhaustible variety of problems involving thermodynamics by means of a systematic approach, which always begins with applying these founding concepts.

This method is also a key element of this textbook. Illustrating or trying to solve a multitude of problems does not help deep understanding: It is better that students approach few but longer and more challenging exercises, with the intent of solving them using founding concepts and a rigorous method. Repetitively solving many examples, hoping that the mechanistic application of mysterious formulas will lead to the correct solution, is to be avoided, and this tendency is often stimulated by the availability of too many examples and exercises. The complexity and variety of the reality we want to model with thermodynamics is just excessive for the empirical approach based on learning from examples. To this purpose we recall the words of Leonardo da Vinci: “Quelli che s'innamorano della pratica senza la scienza sono come i nocchieri ch'entrano in mare sopra nave senza timone o bussola, che mai non hanno certezza dove si vadino”, or, “Those who fall in love with practice without science are like helmsmen who come on board and sail the seas without helm or compass, and never gain certainty of where they are heading.”

Thermal-fluids engineering

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B - Mathematical Relations between Partial Derivatives

Index

7 - Energy Conversion Systems

Summary

A - Thermodynamic Properties of Fluids

Notation

Epigraph

Appendices

Acknowledgments

E - The Method of Lagrange Multipliers

8 - Thermodynamic Properties of Multicomponent Fluids

9 - Exergy Analysis

Summary

10 - Thermodynamics of Reacting Mixtures

Summary

C - Numerical Schemes for Saturation Point and Flash Calculations

4 - Control Volume Energy Analysis

Summary

D - Chemical Equilibrium

Frontmatter

3 - Properties and States

Summary

Preface

Summary

6 - Thermodynamics of State

Contents

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