# 33927 - Machines M

## Learning outcomes

The student learns about the energy production systems and related machines

## Course contents

MODULE I

Multiple extraction steam power plants. Efficiency evaluation and optimization of steam extraction pressure. Analysis and optimization of steam plant performance by means of commercial calculation codes. Mixing and surface heat exchangers: TTD and DCA. Three extraction steam power plant. Governing equations in the exchangers and their employment within an optimized computer solver. Condenser mass flow rate and pumps power consumption. Three extraction steam power plant. Governing equations in the exchangers and power equation, T-s and Mollier thermodynamics diagrams

Compressible flow turbomachines. Static and total quantities. Equations of fluid motion in moving channels. The speed of sound and flow regimes. Compressible fluid flow equations. Stodola Ellipse. The chocking. Maximum mass flow rate and flow parameter. Link between transversal area and flow in a channel depending on the regime of motion: Hugoniot equation. Converging channel and converging-diverging channel. Mass flow rate and flow parameter as function of the ratio between downstream pressure and upstream total pressure.

Stator losses, representation of physical states in the enthalpy diagram. Enthalpy diagram for converging channel and converging-diverging channel.

Euler equation and equation with the differences of kinetic energy for a rotor row. Degree of reaction. Total to total and total to static efficiencies, representation of physical states in the enthalpy diagram. Rotorlosses.

The axial turbines reaction stage: velocity triangles. Normal stage. Maximum work and velocity triangles. Total to total efficiency definition and maximum point.

The impulse stage: the velocity triangles, the maximum work, physical states on the enthalpy diagram. Total to static efficiency. comparison between reaction stage and impulse stage losses.

The De Laval Turbine scheme and operating principle. De Laval Turbine limitations on the enthalpy change.

Two velocity stages turbine scheme and operating principle. The velocity triangles.

MODULE II

Maximum work evaluation for a two velocity stages turbine. Total to static efficiency. Comparison with the impulse turbine efficiency.

The pressure stage turbine scheme and operating principle. Total to static efficiency and recovery factor.

The reaction turbine scheme and operating principle. The role of balancing drum. Limits on input and output volumetric flow of a reaction turbine. Analytic expression of the input and output volumetric flow. The mixed and double flow turbines.

Steam turbine off-design. Stodola Ellipse for the finite and infinite stages number machine. Sonic block of the turbine. Catenary performance curve.

Pelton Turbine. Scheme and operating principle. Distributor outlet velocity and flow rate evaluation. Inlet and outlet rotor velocity triangles. Maximum work, total and hydraulic efficiencies. Manual and oleo-dynamic regulating Doble nozzles. Minimum and maximum blades number. Off-design and characteristic curves: flow rate as function of rotational speed and efficiency as function of flow rate.

Mechanical, kinematical, dynamical and geometrical similarity: hydraulic similarity. Specific speed. Specific diameter and non-dimensional impeller speed. Multi-jet Pelton turbines, scheme and operating principle.

Francis Turbine. Scheme and operating principle. Balance of the axial forces on the turbine rotor and design solutions. Degree of reaction. Inlet and outlet rotor velocity triangles. Maximum work. Fink distributor effect on inlet rotor velocity triangles. Importance of the discharge duct in a Francis turbine plant and description of the outlet pressure trend as a function of design parameters at the duct outlet. Achievable work with and without the discharge duct. Pressure at the Francis discharge section. The cavitation problem and Thomanumber definition. Description of the sudden off-design problems and solutions. Off-design and characteristic curves. Rotor shape improvements as a function of specific speed in (high flow rate and low head).

Propeller and Kaplan Turbine. Scheme and operating principle. Inlet and outlet rotor velocity triangles from hub to tip of the impeller. Off-design and characteristic curves. Kaplan Turbine, operating principle and load regulation curves.

Steam Power Plant load variazioni and control. Lay out of the control system. Watt tachymeter. Static equation and working point in the case of pre load positive and negative. dynamic equation of the tachymeter and Laplace transform and transfer function. Jw, s diagram.

Hydraulic system 2-corner drawer, scheme and equations that determine the operational behavior. Laplace transform and transfer function.

Complete steam power plant lay out control system. Tachymeter, Hydraulic system, valve and Turbogenerator, close chain equations, transfer function and stability analysis.

"Sistemi Energetici" 1 – MACCHINE A FLUIDO, G: Negri di Montenegro, M. Bianchi A. Peretto – Pitagora Editore

"Sistemi Energetici" 2 – COMPLEMENTI, M. Bianchi, F. Melino, A. Peretto – Pitagora Editore

Appunti di Macchine Idrauliche

## Teaching methods

Lessons developed in the classroom.

## Assessment methods

Exam

Oral examination, generally composed by three questions about the lessons program.

Required diagrams

(the student must know how to draw the diagram in a realistic manner):

• T,s diagram of water with isobaric curves inside and outside of the liquid-vapor region
• H,s diagram of water with isobaric and isothermal curves inside and outside of the liquid-vapor region

Required layouts:

• Steam plants and the Steam Power Plant control system. In general all the schemes shown during the lessons.

Required drawings:

• PeltonTurbine, oleo-dynamic and mechanical nozzle
• FrancisTurbine
• Propeller Turbine
• Tachymeter
• Hydraulic system 2-corner drawer

## Teaching tools

Parts of Machines given and explained to the students in the classroom during the lessons.

## Office hours

See the website of Antonio Peretto