In this chapter, a turbomachinery-related nondimensional groupings of geometric dimensions and thermodynamic properties will be derived.

In this chapter, a Computational Grain is developed for direct numerical modelling of composites with nanoscale inclusions considering both interface stretching and bending effects, using a large number of CGs in a representative volume element. The CGs developed in this chapter are by far the first and the only numerical tool for direct numerical modelling of nanocomposites with a large number of inclusions with Steigman-Ogden matrix/inclusion interfaces. By using a new boundary-type multi-field variational principle together with Papkovich-Neuber potentials, the stiffness matrices of CGs can be directly evaluated and assembled. Together with the parallel algorithms, it is found that very efficient simulations of nanocomposites can be realized, for example, a SERVE containing 10,000 nano inclusions only takes fifty minutes on a sixteen-core computer. The influence of spatial distributions of the nano inclusions on the overall properties of nanocomposites is also investigated in this chapter. We also study the influence of interface bending resistance parameters on the effective modulus of nanocomposites. Numerical results show that interface bending resistance parameters affect the shear modulus of nanocomposites but their effect on the bulk modulus is negligible.

In this chapter, Trefftz trial functions which satisfy identically all the governing equations of linear elasticity in 2D and 3D problems are summarized. These Trefftz functions are later used in conjunction with boundary variational principles (since all the field equations are satisfied identically inside the Voronoi cell elements), to construct planar and 3D Computational Grains to directly model statistically equivalent representative volume elements (SERVEs) of heterogeneous materials at the microscale. In as much as the Trefftz functions are used as trial solutions, this modeling captures the correct and accurate stress solutions in the matrix, inclusions, and at their interfaces. The presented Trefftz solutions include: (1) Muskhelishvili’s complex functions for 2D problems,(2) Papkovich-Neubar solutions for 3 D problems,and (3) Harmonic functions in spherical coordinates, cylindrical coordinates, and ellipsoidal coordinates.

In this chapter, the flow-governing equations (conservation laws) are reviewed, with applications that are purposely turbomachinery related. Particular emphasis is placed on the total (or stagnation) flow properties. A turbomachinery-adapted Mach number definition is also introduced as a compressibility measure of the flow field. A considerable part of the chapter is devoted to the total-relative properties, which, together with the relative velocity, define a legitimate thermophysical state. Different means of gauging the performance of a turbomachine, and the wisdom behind each of them, are discussed. Also explored is the entropy-production principle, as a way of assessing the performance of turbomachinery components. The point is stressed that the calculation of entropy production may indeed be desirable, for it is the only meaningful performance measure that is accumulative (or addable) by its mere definition.

This chapter introduces the reader to the modelling of particle-particle collisions. We assume that two spherical particles collide along the normal axis to plane of contact – that is, we only examine a head-on impact. In the beginning, attention is paid to the contact mechanics. The objective is therefore to prepare the reader for fundamental analysis. First, we investigate a simple case of a single force acting on a surface. This problem gradually extends to a similar contact between two spherical bodies (Hertz theory). Next, these bodies are allowed to move towards each other, and we observe their deformation – i.e., a head-on collision. The collision is also elastic, so there is no mechanical energy loss upon impact. Later, this issue is expanded upon by introducing dissipative forces during the contact in addition to the elastic forces discussed above. These dissipative forces are of different types: both linear and non-linear. Finally, another topic is introduced, which is plastic deformation. Here, the colliding bodies are allowed to deform permanently.

This chapter lists the acronyms used in the text, the heat and mass balance software used for numerical examples, and key concepts to evaluate the technical and commercial viability of novel technologies.

This chapter explains the background behind the book concept, e.g., the meaning of sustainability within the electric power generation context, energy transition, and decarbonization. Technologies that are covered in the book are described in brief. The concept of operability and how it pertains to the main theme of the book is addressed.

In this chapter, viscoelasticity effects in composites are studied. Three-dimensional CGs with linear viscoelastic matrices, containing linearly elastic spherical inclusions with or without interphases/coatings are treated. For each CG, the independent displacement fields are developed by the characteristic-length-scaled Papkovich-Neuber solutions and spherical harmonics. A compatible boundary displacement field is also assumed with Wachspress coordinates as nodal shape functions on each of the polygonal faces. Multi-field boundary variational principles are used to develop the CG stiffness matrices. After the establishment of CGs in Laplace transform domain, the homogenized and localized responses are transformed back to the time domain using the Zakian technique. With different kinds of models to describe the property of the viscoelastic polymers, the generated homogenized moduli and localized stress distributions are validated against the experimental data, simulations by commercial FE software, and predictions by composite spherical assemblage models. Parametric studies are also carried out to investigate the influence of material and geometric parameters on the behavior of viscoelastic composites. Finally, the viscoelastic CGs are also used to study the effect of the negative Young’s modulus of particles on the stability and loss tangent of viscoelastic composites.

From a historical viewpoint, the centrifugal compressor configuration was developed and used, even in the propulsion field, well before axial-flow compressors were. Due to their large envelope and weight (Figure 11.1), the common belief that such a “bulky” compressor type has no place except in aerospace applications is not exactly accurate. For example, with a typical total-to-total pressure ratio of, for example, 5:1, it would take up to three axial-compressor stages to absorb similar amounts of shaft work that a single centrifugal compressor stage would. In fact, the added engine length, with so many axial stages, would increase the skin friction drag on the engine exterior, almost as much as the profile drag, which is a function of the frontal area.

Interactions between particles in multiphase flow may also involve adhesion – i.e., an attraction between the particles. This issue is the main topic of this chapter. The first sections of the chapter, however, focus on a primary case: forces acting between two solid surfaces close to each other. A typical example is an interaction between two spherical bodies, which mimic two particles in a multiphase flow. This situation is later extended to a more complex case: the bodies change their shape due to these adhesive interactions. For this, two theories were developed in the literature (JKR and DMT), and they are fully described in the chapter. Later, it is shown how these theories can be adopted to investigate particle-particle collisions in a multiphase flow. In other words, this topic constitutes an extension of the previous chapter, where the focus was on purely “mechanical” interactions without considering any adhesive forces. Finally, the last section of the chapter describes rough surfaces. There is a brief description of how this real-life issue influences the adhesion between two bodies in contact.

While coal seems to be out of the picture in the energy transition, there are technologies that make sustainable use of this abundant resource. This chapter covers several technologies, i.e., gasification, magnetohydrodynamics, and coal slurry, which, when combined with carbon capture, can make this a reality.

One of the parameters that describe particle-particle collision is a coefficient of restitution. This can be simply defined as a ratio of the post-collisional and pre-collisional relative velocity. This chapter is devoted to this topic. As it is straightforward to measure this parameter experimentally, different practical techniques have been used by the researchers, and they are depicted here. Factors such as material properties and pre-collisional conditions are discussed, and it is shown how they influence the value of the coefficient of restitution. It is worth noting that the coefficient of restitution can also be found theoretically by exploiting the relationships previously discussed in the book, especially in Chapter 3. This is described in detail in this chapter. The chapter therefore returns to the previously considered mathematical models. Finally, the chapter concludes with two additional sections focusing on special cases: collisions of granules and nanoparticles., respectively. These particular types of particles have unique features that greatly influence the collision process and restitution coefficient.

This chapter summarises the topics previously discussed in Chapters 2-8. The objective is to illustrate how to create a computer code that simulates a flow of solid particles in a fluid. First, a model is shown that accounts for the motion of particles due to various particle-fluid forces introduced in Chapter 2. Later, it is emphasised that the particles may collide, and this can be described using the techniques mentioned in Chapters 3-8. Finally, a new problem is introduced (not considered in the previous chapters) – collision detection. This issue is crucial for deciding which particles flowing in a system could potentially collide during a time step. The chapter also unveils an algorithm in which the collision detection mode is implemented.

This chapter covers the basics of energy storage, i.e., why it is needed, when it is used, how it is used, its benefits, and the types of energy storage technologies. Special attention is given to thermal energy storage due to its usage in a variety of guises in renewable power applications.