This chapter describes the essential aspects of geometry definition of flow channels, blades and vanes in radial compressors. The impeller blades and flow channel make up a complex three-dimensional shape, and a general method for defining such geometries using Bezier surfaces is described. The meridional channel is defined as a series of Bezier patches whose geometry is parametrised to allow changes to be made quickly and efficiently during the design. Radial compressor impeller blades are typically defined as a distribution of camber line angle and thickness on the hub and casing meridional sections. A three-dimensional shape is generated by joining the hub and casing sections by straight lines to make up a ruled surface. This simplifies simplify manufacture by flank milling. In transonic flows, a more complex definition is used in which the geometry is defined along a series of separate meridional planes. A description of the definition of asymmetric components, such as the volute, is also provided.

The design of the stationary components upstream of the impeller and downstream of the diffuser is considered. The inlet nozzle accelerates the fluid from the compressor flange to the impeller inlet, keeping losses low and avoiding distortion in the velocity profile. The impeller inlet may be axial or radial and it may be fitted with inlet guide vanes to change the swirl velocity as a way of controlling performance. Downstream of the diffuser, the flow is guided to the outlet flange, a downstream component or an intermediate cooler. The scroll, or volute, collects the flow, leaving the diffuser to take it to the outlet flange. In middle stages of multistage inline compressors, a crossover bend and a vaned return channel lead the flow to the next stage. In gas turbine applications, axial exit guide vanes remove the swirl at outlet and diffuse the flow to the low velocity needed in the combustor. Special applications may also include side-stream inlets or a secondary inlet and outlet nozzles, allowing the flow to gain access to a cooler and be returned to the compressor. The rotor–stator cavities determine the pressure field around the impeller and play a role in the axial thrust.

In many books on radial turbocompressors, the nondimensional parameter known as specific speed is often used to categorise a particular type of design. The specific speed and specific diameter are two alternative dimensionless coefficients based on the same data which are used define the flow coefficient and the head coefficients. In their definition, both the flow coefficient and the head coefficient are included. The specific speed alone is often used to specify a particular type of design of radial compressor as, broadly speaking, an optimum specific speed can be defined, rather like an optimum flow coefficient. This optimum is often presented in the form of a Cordier diagram. Both parameters are essentially incompressible in nature and are often used for hydraulic machines and in pump and ventilator design. In this chapter, the background to these parameters is described. This discussion gives clear guidance that the flow coefficient, work coefficient and tip-speed Mach number are more useful for radial turbocompressors than specific speed and specific diameter.

The concepts of fluid dynamic and thermodynamic similarity are introduced. The key nondimensional parameters of relevance to radial compressors, such as flow coefficient, work coefficient, pressure coefficient and the blade tip-speed Mach number are explained. The appropriate nondimensional parameters allow the preliminary design of a new machine to be based on features of an existing machine, even one designed for a different size, a different fluid, other flow conditions or rotational speed. Its performance can also be estimated from that of a similar machine, even though it may be larger or smaller. The principle of similarity and the associated nondimensional parameters provide an invaluable aid to the design and testing of all turbomachinery and to the proper understanding of their performance maps and stage characteristics. A good grasp of these is an excellent basis for rationalising compressor performance in different applications. Deviations from similarity in real machines are considered leading to performance corrections for changes in Reynolds number and isentropic exponent.

The important fluid dynamic principles of the flows around aerofoils, cascades of blades and the diffusing flow in radial compressor flow channels are described. The nature of decelerating flows in two-dimensional channel diffusers is explained together with their interesting flow regimes, which limit the amount of diffusion that is possible. The different nondimensional parameters used to define the fluid dynamic loading limits in compressors blade rows related to diffusion and blade loading are summarised. The primary meaning of aerodynamic loading is that there is a difference in pressure between the surfaces of a blade profile. This pressure difference leads to the forces and the torque needed to drive an impeller and to change the direction of the flow. The pressure difference between the adjacent blades may be high even if the work coefficient or pressure rise of the stage is moderate, simply by dint of having few blades. The second meaning is that the stage is designed for a particularly high work coefficient. The third meaning is related to the amount of diffusion in the flow between the inlet and the outlet of a cascade or a diffuser vane.

Aspects of the structural mechanics, vibration dynamics and rotor dynamics of compressors including impeller manufacture are described. The background knowledge required to understand the key structural issues is given with some simple analytic solutions. These identify the effects of blade thickness and blade taper on the stresses and the vibration characteristics of impellers. Such analytical solutions are only available for the simplest geometrical cases but give an insight into the fundamentals. Complex computer-based methods are used for the more detailed mechanical analysis of blades. A brief introduction to rotordynamics is also presented with the intention to guide the engineering of robust vibration-free compressor shafts. The characteristics of a simple rotor assembly, known as the Jeffcott single mass rotor, are examined using the equations of motion. Some limits on multistage compressor design introduced by rotordynamics can be derived even on the basis of the simple Jeffcott rotor; for example, the shaft should be thick and short to achieve a high critical speed. More complex rotor assemblies again need to be analysed with computer-based methods which are readily available.

Compressors increase the pressure and density of gases, whereas pumps increase the pressure of a liquid at constant density. To understand the compression process in gases a thermal equation of state is needed to give the relationships between the intensive thermodynamic variables (p, T and v) and a caloric equation of state for internal energy and enthalpy (u and h). The simplest equation of state is that for a perfect gas. Centrifugal compressors are used with such a wide range of fluids that complex real gas models are often needed to characterise the behaviour of the fluid. The law of corresponding states and the van der Waals equation of state are introduced. Generalised cubic equations of state are described, and an example of this type, the Aungier–Redlich–Kwong equation of state, is given in more detail. The real gas equations not only change the relationship between the intensive properties but also require special care in determination of the integration of a polytropic process to determine the aerodynamic work. Different methods of carrying out this integration (from Schulz, Mallen and Saville and from Huntington) are discussed.

Classifications of different types of turbomachines are reviewed to define precisely what is meant by a radial flow turbocompressor. Single-stage compressors and different configurations of multistage compressors are introduced. The basic operating principle of turbocompressors, the Euler turbine equation, is valid for all turbomachines. Numerous applications of radial flow turbocompressors are described, including gas turbines for power generation and propulsion, turbochargers, oil and gas processing, wastewater treatment and the compression of industrial gases in refrigeration and industrial processes. Newer applications in fuel cells and in microcompressors are introduced. This gives an overview of the large range of duty in terms of volume flow rate and pressure ratio for which these machines are used. Some of the special aerodynamic features that are relevant to their design in different applications are highlighted. Aspects of the history of compressors are also given together with a short overview of other books, technical journals and conferences on this topic.

Modern computational fluid dynamics (CFD) methods are described. CFD simulations of whole compressor stages using the Reynolds-averaged Navier–Stokes equations (RANS), with a steady-state rotor–stator interaction model between the blade rows and a two-equation turbulence model, are the basis of aerodynamic calculations for the design of radial compressors. More detailed simulations using unsteady RANS (URANS) equations with unsteady rotor–stator interaction models are now used in a research environment. The source of errors and the importance of validating the CFD methods are described. The prediction of the turbulent flow is one of the main error sources in CFD simulations, and an overview is given of turbulence models. Up-to-date guidelines are provided on the use of CFD for the design and development of components in radial turbocompressors. A practical description of the CFD process is given, including the technologies used to support the calculations, such as geometry generation, mesh generation and postprocessing.

One-dimensional models are described that can be used for preliminary analysis of the performance of a radial turbocompressor stage. The simple 1D mean-line steady flow analysis given here facilitates a general understanding of the influence of the design parameters on performance and provides a good basis for the preliminary design. The important loss mechanisms and their contribution to the stage efficiency are explained. The physical background to different loss sources is explained, including profile losses, leading-edge losses, trailing-edge losses, end-wall losses, tip clearance losses and leakage losses. An overview of the available correlations is given. A broad outline is given of the state-of-the-art performance levels that can be achieved and the associated design parameters. A meanline calculation procedure for a compressor stage is described for preliminary performance estimation and initial compressor sizing. The effect of parasitic losses on performance is described.

Mechanical energy is the most useful energy form to humans. This motivates the question: given an energy resource – fossil or nuclear fuel, wind, solar, geothermal – what is the maximum mechanical energy one may extract? A similar question is: what is the difference between the low-temperature waste heat of a nuclear power plant and the high-temperature heat in the nuclear reactor? The combination of the first and second laws of thermodynamics, in conjunction with the characteristics of the environment where energy conversion processes occur, offers a definitive answer to these and similar questions: exergy is the thermodynamic variable that describes the maximum mechanical work that may be extracted from energy resources, the concept that quantifies the quality of energy. This chapter elucidates the concept of exergy and its relationship to the energy resources. It derives useful expressions for the exergy of primary energy sources including: fossil fuels, geothermal, solar, wind, hydraulic, tidal, wave, and nuclear. The effects of the environment on the exergy of energy sources, the energy conversion processes, and the exergetic efficiencies of the processes are also elucidated.

The application of the exergy methodology reveals the system components where high exergy dissipation occurs and improvements may be accomplished to conserve energy resources. The method is applied to several systems: heat exchangers, including boilers and condensers; vapor and gas power cycles, including cogeneration units; jet engines; and geothermal units. Calculations on exergy dissipation identify the processes and components where improvements would save energy resources. The calculations reveal that combustion processes waste a great deal of exergy, leading to the conclusion that direct energy conversion devices, such as fuel cells, utilize fossil fuels in a sustainable way. The exergy method is also applied to photovoltaic cells and thermal solar power plants, as well as to solar collectors that deliver heat. Significant exergy destruction occurs in wind turbines because of Betz’s limit and the wind turbine characteristics. A large number of examples in this chapter elucidate the exergy calculations and provide guidance and resources for the application of the exergy methodology to power and heat generation systems and processes.

The use of energy has defined our civilization and governs our lives. Throughout the day and night modern humans consume enormous quantities of energy resources for: food preparation; transportation; lighting, heat, ventilation and air-conditioning of buildings; entertainment; and a myriad other applications that define modern life. A gigantic global energy industry transports and inconspicuously transforms the energy resources to convenient forms (gasoline, diesel, electricity) that are vital to the functioning of the modern society. This introductory chapter surveys the types of the global primary energy sources, how they are transformed to useful energy, and how they are used. The chapter introduces the two laws of thermodynamics that govern the conversion of energy from one form to another; explains the methodology of thermodynamics, which is essential for the understanding of energy conversion processes; and delineates the limitations on energy conversion. The thermodynamic cycles for the generation of power and refrigeration are reviewed and the thermodynamic efficiencies of the cycles and energy conversion equipment (turbines, compressors, solar cells, etc.) are defined.