In this chapter we will discuss some of the numerical methodologies that are appropriate for particle-resolved simulations of multiphase flows. Our focus will be on PR-DNS, where all the flow scales of fluid motion are resolved along with the surface of the particles. PR-DNS simulations, however, come at a computational cost. The range of multiphase flow problems that can be simulated in a particle-resolved manner is limited. This limitation does not arise from the mathematical formulation. As discussed in Section 2.4, the mathematical formulation of PR-DNS is the easiest among all approaches to dispersed multiphase flows.

Photovoltaic (PV) systems generate electricity directly from the light of the sun, and grid-connected systems are becoming increasingly important in many electricity supply networks. The photovoltaic effect is described and the use of standard test conditions to define the performance of PV equipment explained. The bond and band models are used to explain the behaviour of an illuminated silicon p–n junction and the shape of its V–I characteristic. Operation of a PV cell at varying irradiance and cell temperature is demonstrated and the importance of operating at the maximum power point explained. The equivalent circuit of a PV cell is shown. The connection of multiple cells into a PV module is described together with the metrics that are used to describe the performance of PV arrays. The principle of operation of a grid-connected PV system and its inverter are described. A final section summarizes the main technologies used to manufacture the different generations of PV cells. The chapter is supported by 7 examples, 16 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

We now have all the background information needed to explore the various computational approaches that are available for solving the wide range of multiphase flows we encounter. In fact, you may feel like you are at the cereal aisle in a grocery store wondering which one cereal among the shelf-full to pick. Fortunately, the process of picking the correct computational approach for a particular multiphase flow problem can be simplified through a rational analysis of the strengths and weaknesses of the different approaches and their suitability to the multiphase flow problem at hand.

The present importance of fossil energy is recognized and the consequences of its exponential growth explained. The mechanism of global warming from increasing greenhouse gases in the atmosphere is summarised and the need for a transition to renewable energy is identified. The units that are usually used to describe energy are listed. The consequences of exponential growth are explained. Approaches to limiting energy use and the difficulties of reducing energy use are discussed. The consequences of applying discounted cash flow analysis in the economic appraisal of energy-efficiency measures are described. The challenges of low-carbon energy electricity generation are discussed and the carbon intensity of generation illustrated. The low-capacity factors of many renewable energy sources and the high-capacity margin of an electrical power system with renewable energy generation are described. Environmental and social impacts of renewable energy schemes are summarized. The chapter is supported by 4 examples, 13 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

From Chapter 4 to Chapter 10 we have studied extensively the interaction of an ambient flow with (i) an isolated particle, (ii) an isolated particle in the presence of a nearby wall, (iii) a pair of particles, and (iv) a large collection of particles. These investigations were at the microscale and we paid great attention to solving for the complete details of the flow around the particles. These studies can be classified as “particle-resolved” or “fully resolved,” as they included all the relevant physics. As a result, these studies have yielded reliable results on the hydrodynamic force, torque, and heat transfer on the particles under varying flow conditions.

In this chapter, we will consider particle–particle interactions. Here we distinguish two kinds of interactions. The first is direct interaction between particles in the form of collisions. When two particles collide, the time history of force exchange between them is controlled by the solid mechanics of elastic and plastic deformation between the colliding particles. In the context of multiphase flow computations, such collisions are simplified and treated using either a hard-sphere or a soft-sphere collision model, which will be discussed in this chapter. As a special case we will also consider the problem of particle–wall collisions.

Most renewable energy sources depend on the sun and so vary with time and ambient conditions. Hence a consistent supply of renewable energy requires energy storage. The main approaches to storing renewable energy are described and quantified. Pumped hydro, compressed air and flywheels are discussed. Storing heat in the fabric of buildings and hot water using sensible heat are described. The increasing importance of phase change materials to store energy through latent heat is recognized. Battery technology is developing very fast; the principles of lithium-ion batteries are explained, together with their advantages and disadvantages. The various materials currently used for the positive electrode are listed. The electrochemistry of various battery technologies is summarized as well as how a large number of cells are connected to form are a useful store of energy. The principle of flow batteries is demonstrated and approaches to the estimation of the lifetime of a lithium-ion battery discussed. The chapter is supported by 10 examples, 16 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

The second edition of this popular textbook has been extensively revised and brought up-to-date with new chapters addressing energy storage and off-grid systems. It provides a quantitative yet accessible overview of the renewable energy technologies that are essential for a net-zero carbon energy system. Covering wind, hydro, solar thermal, photovoltaic, ocean and bioenergy, the text is suitable for engineering undergraduates as well as graduate students from other numerate degrees. The technologies involved, background theory and how projects are developed, constructive and operated are described. Worked examples demonstrate the simple calculation techniques used and engage students by showing them how theory relates to real applications. Tutorial chapters provide background material supporting students from a range of disciplines, and there are over 150 end-of-chapter problems with answers. Online resources, restricted to instructors, provide additional material, including copies of the diagrams, full solutions to the problems and examples of extended exercises.

Waterwheels have been used for centuries for grinding corn, and the first hydro turbine was built almost 200 years ago. Hydro power now produces around 16% of worldwide electrical energy. The hydrological cycle is described and the use of flow duration curves to quantify the resource is demonstrated. The power that can be generated from the hydro resource is calculated, as well as the energy that can be stored in a reservoir. The difference between impulse and reaction turbines is explained with illustrations, and simple approaches to their analysis described. High-, medium- and low-head hydro schemes are described. The use of specific speed to choose the type of turbine for a site is demonstrated. The environmental impact of hydro schemes is discussed. The development of small hydro schemes is addressed as well as the use of Archimedes screw generators. The chapter is supported by 6 examples, 16 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

Wind energy is a major source renewable electricity generation in many countries and the diameter of wind turbine rotors is increasing. Onshore and offshore wind farms are described. The principles of wind turbine operation is explained and the importance of the power curve identified. Wind turbine rotors are analysed using axial momentum theory and the Betz limit; the power and torque coefficients are derived using the axial momentum factor. The generation of torque through lift on the blades is described and the principles of pitch and stall power regulation discussed. Fixed- and variable-speed operation of wind turbine rotors is described and variable-speed operations using two full-power converters demonstrated. Site wind speeds are described in terms of Weibull statistics and the method of bins discussed. The importance of wind turbulence and its effect on turbines is identified. Development of wind farms and the use of measure–correlate–predict to estimate long-term windspeeds is reviewed. The chapter is supported by 3 examples, 14 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

Many renewable energy sources produce electricity, and the fundamental operation of a national alternating current electric power system is described. The difference between real and reactive power is explained. The impact of renewable energy sources on the voltage of the power system is demonstrated through an example and approaches to controlling network voltages are discussed. The control of frequency is described and the importance of maintaining sufficient inertia is highlighted. Scheduling generation in a power system with significant fraction of renewable energy generation is explained. Approaches to demand-side participation and the importance of this concept are discussed. The connection of onshore and offshore wind farms to the power system is discussed. Approaches to the design of PV farms are illustrated. The chapter is supported by 6 examples, 10 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

In Chapter 4, we started with a rigorous derivation of force on a spherical particle in the limit of zero Reynolds number in a time-dependent uniform ambient flow, which led to the BBO equation. We then extended the analysis to spatially varying flows in the Stokes limit and obtained the MRG equation. At finite Reynolds number, due to the introduction of fluid inertia, we saw how difficult a complete solution of the hydrodynamic force on a particle can become. In this chapter, we plan to boldly venture into the difficult topic of interaction between a particle and a turbulent flow.

Communities living far from a grid network are increasingly being supplied by off-grid renewable energy systems. However, a consensus of the best approach to their design has yet to emerge. A number of options are being trialled and these are described. Small dc photovoltaic systems with batteries are well established but can only supply limited amounts of power. An example of the supply of power to a remote health facility is shown. Microgrids combine a number of energy sources connected using either ac or dc. These connection architectures are demonstrated. An example of an operating ac microgrid is shown, together with the initial design calculations of the scheme. The concept of community energy is explained with a demonstration of the potential benefits of peer-to-peer energy trading. The chapter is supported by 4 examples, 7 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.