This chapter explains the hard-sphere model of particle-particle collision. This model exploits impulse equations that directly relate the pre-collisional and post-collisional velocities of the particles. Thus, this model does not track the deformation history that was done in the prior chapters. As a result, we obtain ready analytical solutions so that the computational time is short. First, the chapter shows a standard hard-sphere model for a “mechanical” collision of two bodies. Different strategies are presented, such as the so-called two- and three-parameter hard-sphere model. Later, an extension of these models is shown that also accounts for adhesive interactions. Although, due to its simplicity, the hard-sphere model may not account for various physical phenomena between colliding particles, it may still be used in many applications. In this chapter, the reader is again provided with a computer code.

Sometime around 2010 and thereafter, trade publications and archival journals were inundated with articles and papers filled with hyperbole and lofty claims about the closed cycle sCO2 turbines and their merits. In particular, sCO2 cycle/turbine was/is touted as a technology that can replace Rankine (steam) cycle and steam turbine in conventional fossil fuel-fired power generation, as a stand-alone or as the bottoming cycle of a gas turbine combined cycle. In this chapter, performance of sCO2 in power generation applications (including the Allam cycle) is rigorously assessed with in-depth thermodynamic analysis and cycle data. Furthermore, we will also look at the operability challenges presented by the unique structure of the sCO2 powertrain and heat exchangers.

A brief introduction to gas turbine engines was presented in Chapter 1. Review of the different engines included in this chapter reveals that most of these engine components are composed of “lifting” bodies, termed airfoil “cascades,” some of which are rotating, while others are stationary. These are all, by necessity, bound by the hub surface and the engine casing (or housing), as shown in Figures 2.1–2.5. As a result, the problem becomes one of the internal-aerodynamics type, as opposed to such traditional external-aerodynamics topics as “wing theory” and others. Referring, in particular, to the turbofan engines in Chapter 1 (e.g., Figure 1.3), these components may come in the form of ducted fans. These, as well as compressors and turbines, can be categorically summed up under the term “turbomachines.” Being unbound, however, the propeller of a turboprop engine (Figure 1.2) does not belong to the turbomachinery category.

This chapter discusses some general algorithms which are useful in the computational homogenization using the Computational Grains (CGs) method. First, an algorithm for generating a statistically equivalent representative volume element (SERVE) is presented. Then, an algorithm to divide the SERVE in to Voronoi cells (polygons in 2D and polyhedrons in 3D), and using a CG in each Voronoi cell is discussed. The role of parallel computation is also discussed.

In this chapter, a new kind of Computational Grain (CG) with embedded cylindrical elastic fibers is developed for the micromechanical modeling of fiber-reinforced composites. The trial displacement fields within the CGs are assumed using Papkovich-Neuber solutions. Cylindrical harmonics scaled by characteristic lengths are employed as the P-N potentials. A compatible displacement field is assumed at elemental surfaces and fiber–matrix interfaces, and the stiffness matrices of CGs are derived by a newly developed multi-field boundary variational principle.

Through numerical simulations, we demonstrate that the developed CGs have high computational efficiency, and they can accurately capture the localized stress distributions under various loadings. Computational Grains are also effective for estimating the effective material properties of fiber-reinforced composites, as validated by comparing with experimental results in the literature. Moreover, with the use of parallel computation, the time required for CGs is significantly decreased. Thus, we consider that the kind of CGs developed in this study is an accurate and efficient tool for the micromechanical modeling of fiber composites. Such a tool of micromechanical modeling can also be combined with meso- and macro-scale finite elements for the multi-scale analysis of laminates and composite parts, which will be given in Chapter 12.

The book’s final chapter pays attention to various issues that can be encountered when investigating multiphase flows. This chapter can be read independently, although on a few occasions it refers to some selected problems from the prior topics. First, this chapter treats a multiphase flow as a system of spherical particles with some given concentration and with some average distance between the particles. Later, the chapter looks into the particle reaction as immersed in a fluid (discussion so-called response times), and it is shown how the presence of the particles influences the fluid flow by discussing the concept of phase coupling and suspension viscosity. Next, we consider the issue of the dispersion of particles as they are subject to turbulent flows, and how the particles may gather in some selected flow zones (preferential concentration). The fact that the particles may be of different sizes is later analysed by investigating the particle size distribution. The final sections of the chapter are dedicated to collision frequency and a particular case of a flow through a particle bed.

This chapter focuses on compressed air energy storage (CAES) technology, which is one of the two commercially proven long-duration, large scale energy storage technologies (the other one is pumped hydro). The chapter covers the basic theory, economics, operability, and other aspects of CAES with numerical examples derived from the two existing plants, Huntorf in Germany and McIntosh in the USA.

Historically, the first axial turbine utilizing a compressible fluid was a steam turbine. Gas turbines were later developed for engineering applications where compactness is as important as performance. However, the successful use of this turbine type had to wait for advances in the area of compressor performance. The viability of gas turbines was demonstrated upon developing special alloys that possess high strength capabilities at exceedingly high turbine inlet temperatures.

The first chapter describes the main structure of the book, but also reveals an algorithm that the book is built on. The ultimate goal is the creation of a strategy that can be used for modelling fluid flows laden with particles. Therefore, this chapter depicts the main steps: first, modelling the flow with a single particle, then introducing two particles that may interact, and finally, modelling of the whole set of particles. The details are provided in the subsequent chapters.

Figure 4.1 shows a general-type mixed-flow compressor rotor. The thermophysical states 1 and 2 represent average conditions over the entire inlet and exit stations, respectively. The rotor-blade-to-blade hub-to-casing passage is the control volume, and other than the continuity and energy equations (Chapter 3), we are now left with the momentum-conservation principle to implement.

This chapter outlines the basic knowledge required from the reader in order for them to follow the narrative in the book. Key terms and concepts are introduced with brief descriptions. The chapter also lists books, articles, and papers by the author, which deal with the subject matter covered in the book in a more detailed fashion.

Whilst the previous chapter focused solely on head-on collisions, this chapter also considers tangential contact. The objective is to extend the previous analysis to include oblique collisions. The strategy also resembles the prior chapter. First, we pay attention to contact mechanics by analysing tangential forces acting on a surface. The analysis is later enhanced to a contact of two spherical bodies. This knowledge is exploited in the subsequent sections of the chapter, where we consider a full oblique collision of two bodies. The collision process is described in detail by following a study case, which is solved using a computer code provided for readers.

By rearranging the weakly singular boundary, integral equations developed by Han and Atluri, an SGBEM-CG, which is abbreviated as CG, is developed in this chapter. The CG, representing a single grain of a material, can include arbitrarily shaped voids, inclusions (of a different material), and microcracks. The CG has a stiffness matrix and a load vector, which have similar physical meanings to the traditional displacement FEM. The stiffness matrix is symmetric, positive-definite, and has the same number of rigid-body modes. Different CGs, each with different isotropic material properties, can be directly coupled by the assembly procedure, and are used to directly and efficiently model the microstructure of heterogeneous composite materials. Some examples are also presented, with microcracks interacting with inclusions and holes. This provides some insight of a possible future study of the micro-cracking and damage of heterogeneous material. By introducing stochastic variations of the shapes of CG, and stochastic variations of the properties of the constituent materials, the realistic statistical bounds on the overall properties of composite materials will be determined in future studies.

Well-known intermittency and low capacity factors of solar and wind resources prevent these technologies from fulfilling the demands of the energy transition on their own – at least in the near future. They require backup in the form of dispatchable resources, e.g., fossil-fired power plants and energy storage systems. Such systems must be nimble enough to address short-term fluctuations and maintain grid stability in addition to taking over the base load generation when renewable resources are not available. Aeroderivative gas turbines, small industrial gas turbines, gas-fired recip engines, and energy storage systems such as CAES, LAES, pumped hydro (PHS), and electric batteries are readily available technologies that can accomplish these tasks. Large-scale, long-duration systems such as CAES and PHS are discussed elsewhere in the book. Herein, the focus is on BESS and its integration with gas turbines and solar PV.

This chapter is dedicated to the elementary problem, which concerns interactions between a single particle and the surrounding fluid. First, we explore the drag force, which is the most common interaction. It is shown how this force is derived and applied in practice. This topic is further expanded upon by introducing Basset and added mass force – both are crucial for unsteady cases such as accelerating particles. Next, lift forces (Magnus and Saffman) are shown that may result in the particle’s motion in the lateral direction. To some extent, this is associated with the next issue explained in the chapter: the torque acting on a particle. The following sections pay attention to other interactions: Brownian motion, rarefied gases and the thermophoretic force. These interactions play a role for tiny particles, perhaps of nano-size. Ultimately, we deliberate heat effects when the particle and fluid have different temperatures. Thus, this last section scrutinise convective and radiative heat transfer.