Turbomachinery

This introductory Chapter is a synthesis of the text titled “Lecture notes on Fluid Machines—Gambini and Vellini” (in Italian), 2007, adopted for the Tur-bomachinery and Energy Systems courses for students of the bachelor’s Degree in Mechanical and Energy Engineering of the University of Rome Tor Vergata. This Chapter intends to provide a summary of the basic principles of thermodynamics and fluid-dynamics applied to turbomachinery in order to define all the performance parameters (work transfer, isentropic and polytropic efficiency, nozzles and diffusers efficiency, degree of reaction, etc.) used in the proposed procedures for turbomachinery selection and preliminary design (Chaps. 2–7). After introducing the basics of the First and Second Principles of Thermodynamics (Sect. 1.1), the energy equation is deduced in the mechanical and thermodynamic form (Sect. 1.2). Then, fluid properties are introduced (Sect. 1.3). Next, we analyze work transfer in turbomachines handling compressible (Sect. 1.4) and incompressible (Sect. 1.5) fluids, and we define isentropic, polytropic (Sect. 1.4), and hydraulic efficiency (Sect. 1.5). Then, the fluid flow in turbomachinery is studied through cardinal equations, and the Euler equation is deduced (Sect. 1.6). The principles of turbomachinery operation are therefore illustrated, highlighting stator and rotor configurations and the relative energy transfer processes (Sect. 1.7). Afterwards, an energy analysis of both axial and radial turbine and compressor stages is carried out (Sect. 1.8), aimed at defining all the performance parameters (work transfer, efficiency, degree of reaction, power, etc.). Finally (Sect. 1.9), we analyze losses in turbomachinery stages by highlighting the loss sources and providing a classification of these losses for both axial and radial stages. Throughout the discussion, real fluids are considered, illustrating only a few particular applications for perfect gases.

The turbomachinery selection process, as well as the consequent preliminary design, is based on the application of the similitude theory, which allows to “capitalize” all previous experience in the turbomachinery sector by transferring the results obtained for an existing machine, considered as a model, to another machine, to be designed, which is “similar” to the reference model. First of all (Sect. 2.1), we briefly recall the similitude theory through the dimensional analysis and the Π theorem (Buckingham’s theorem), and then (Sect. 2.2), we illustrate the effective and fundamental Baljé’s method, through which we can proceed not only with the choice of the turbomachine stage configuration (axial, radial, mixed flow) but we can also define the number of stages, the speed of rotation and the characteristic diameter of the turbomachine (Sect. 2.3). The numerical application of the proposed procedure will instead be developed in Chapter 8 and will concern the selection of turbomachines for advanced conversion cycles.

With reference to an axial turbine stage, a procedure for the calculation of kinematic parameters at mean diameter (Sect. 3.1), thermodynamic parameters (Sect. 3.2), geometric parameters (Sect. 3.3), parameters in the radial direction (Sect. 3.4) and stage losses (Sect. 3.5) is provided. Then, Sect. 3.6 discusses the input parameters of this procedure and suggests their numerical values to be used in the calculations. Finally, Sect. 3.7 illustrates the procedure for extending calculations to multistage turbines. The numerical application of the proposed procedure, aimed at the preliminary design of multistage axial turbines, is instead developed in Chap. 8.

With reference to an axial compressor stage, a procedure for the calculation of kinematic parameters at mean diameter (Sect. 4.1), thermodynamic parameters (Sect. 4.2), geometric parameters (Sect. 4.3), parameters in the radial direction (Sect. 4.4) and stage losses (Sect. 4.5) is provided. Then, Sect. 4.6 discusses the input parameters of this procedure and suggests their numerical values to be used in the calculations. Finally, Sect. 4.7 illustrates the procedure for extending calculations to multistage compressors. The numerical application of the proposed procedure, aimed at the preliminary design of multistage axial compressors, is instead developed in Chap. 8.

With reference to a radial inflow turbine stage, a procedure for the calculation of kinematic parameters (Sect. 5.1), thermodynamic parameters (Sect. 5.2), geometric parameters (Sect. 5.3) and stage losses (Sect. 5.4) is provided. Then, Sect. 5.5 discusses the input parameters of this procedure and suggests their numerical values to be used in the calculations. Finally, Sect. 5.6 illustrates the procedure for extending calculations to multistage turbines. The numerical application of the proposed procedure, aimed at the preliminary design of radial turbines, is instead developed in Chap. 8.

With reference to a centrifugal compressor stage, a procedure for the calculation of kinematic parameters (Sect. 6.1), thermodynamic parameters (Sect. 6.2), geometric parameters (Sect. 6.3) and stage losses (Sect. 6.4) is provided. Then, Sect. 6.5 discusses the input parameters of this procedure and suggests their numerical values to be used in the calculations. Finally, Sect. 6.6 illustrates the procedure for extending calculations to multistage compressors. The numerical application of the proposed procedure, aimed at the preliminary design of centrifugal compressors, is instead developed in Chap. 8.

The preliminary design of a centrifugal pump is very similar to that of a centrifugal compressor, even if the fluid incompressibility and the phenomenon of cavitation, which is specific for the hydraulic machines, must be taken into account. For these reasons, we devote a specific chapter to pumps. With reference to a centrifugal pump stage, a procedure for the calculation of kinematic parameters (Sect. 7.1), thermodynamic parameters (Sect. 7.2), geometric parameters (Sect. 7.3) and stage losses (Sect. 7.4) is provided. Then, Sect. 7.5 discusses the input parameters of these procedures and suggest their numerical values to be used in the calculations. Finally, Sect. 7.6 illustrates the procedure for extending calculations to multistage pumps. The numerical application of the proposed procedure, aimed at the preliminary design of centrifugal pumps, is instead developed in Chap. 8.

In this chapter numerical applications of the procedures proposed in the previous chapters are illustrated: from the turbomachinery selection process (Chap. 2) to their preliminary design (Chaps. 3–7). The Concentrating Solar Power (CSP) sector has been chosen in order to provide design examples of turbomachinery operating with unconventional fluids (that is, fluids different from air, water, steam and flue gas used in conventional steam cycles, gas turbines and combined cycles). We will analyze power blocks integrated in a solar field equipped with a central tower; in this application, Brayton closed cycles, operating with Helium, Argon or supercritical CO₂ (sCO₂), are proposed, alone or in combination with Organic Rankine Cycles (ORC) fed by the waste heat of the Brayton cycle. First of all, we will analyze these cycles evaluating their performance and sizing 10 MWe power blocks (Sect. 8.1). Knowing the flow rates handled by turbomachines as well as their inlet and outlet conditions (inlet pressure and temperature, and outlet pressure) we will proceed (Sect. 8.2) to the selection and preliminary design of each turbomachine. It is important to highlight that when defining the thermodynamic cycle of each power block, we assume the turbomachinery efficiency; but this efficiency must necessarily be verified through the loss calculation, which requires knowledge of the kinematics, the thermodynamics and the geometry of the turbomachines (Chaps. 3–7 and this chapter), especially considering the working fluids used in these CSP applications. Otherwise, the cycle performance assessment is not realistic.