# 33927 - Machines M

• Campus: Bologna
• Corso: Second cycle degree programme (LM) in Mechanical Engineering (cod. 5724)
• from Feb 19, 2024 to Jun 05, 2024

## Learning outcomes

The Student improve in the knowledge of Turbines (Steam and Hydraulic) and Compressors.

## Course contents

STEAM TURBINE

Fluid equations of motion for fixed pipes. Total quantities and the speed of sound, motion regimes. The outflow of a compressible fluid from an environment with a defined physical state. Flow rate and flow parameter trend in a duct as a function of the ratio between the downstream pressure and the total upstream pressure. The chocking. Maximum flow rate, flow parameter. Stodola's ellipse. The trend of the passage areas through a duct of assigned flow rate according to the flow regime: Hugoniot equation. Convergent and convergent-divergent duct.

Duct in off-design condition; normal shock wave. Output Mach number as a function of wave input Mach number. Positioning of the shock wave along the divergent. Evaluation of the entropy variation along a shock wave. Fanno and Reyleigh curves. Unitary Mach at the maximum entropy for the Fanno curve.

Axial and radial stages; absolute relative and circumferential speeds. Convergent and convergent-divergent duct design. Losses in the stator. Diagram h,s in the stator. Diagram h,s for a converging and converging-diverging duct. Euler equation for one stage. Kinetic energy difference equation. Total to total and total to static efficiency. Degree of reaction. The physical states of a reaction stage in the h,s diagram. Leakage in the rotor.

The reaction stage of axial turbines; speed triangles. Normal proportioning. Maximum work and related speed triangles. Total to total efficiency of the reaction stage and maximum condition.

The impulse stage; the speed triangles, the maximum work, representation of the stator/rotor input/output physical states on the enthalpy diagram. Total to static return. Comparison between the losses of the impulse stage and those of the reaction stage.

Scheme and operating principle of a simple impulse De Laval turbine. Limits of the De Laval turbine relating to the maximum disposable enthalpy head. Maximum volume flow, maximum density and maximum power.

Curtis turbine; scheme and principle of operation. Speed triangles in the two impellers and rectifier. Evaluation of the maximum work of a turbine at two speed jumps. Total to static return. Comparison with the efficiency of a single acting turbine.

Pressure jump turbine; scheme and principle of operation. Total to static efficiency and recovery factor of a pressure drop turbine.

Reaction turbine; scheme and principle of operation. The function of the balancing drum. Reaction turbine inlet and outlet flow limits. Analytical expression of the flow rate entering and leaving the reaction turbine. The mixed turbine and the dual flow turbine.

Analysis of sealing labyrinths; representations of the transformations on the Fanno curve in the case of subsonic and sonic motion. Evaluation of flow rate and critical flow flowing through a labyrinth seal. Introduction of the parameter FI and its comparison with the experimental data.

The balancing of axial thrusts in a reaction turbine; determination of the thrust that occurs in the rotating drum and sizing of the drum surface in the case of a degree of reaction equal to 0.5 and a drum with a constant radius. "Stepped" balancing drum.

Dynamic compressors. Operational differences between axial and centrifugal compressors. Limits on the flow that can be disposed of by an axial compressor.

Degree of reaction, flow rate, load rate. Link between load rating and degree of reaction. Speed triangles entering the compressor and their degree of reaction.

h,s diagram of an axial compressor. Stallo, surge and choking.

The centrifugal compressor. Triangles of speed and work obtainable with forward and reverse blades. Real head diagram as a function of the flow rate.

CONTROL OF ENERGY SYSTEMS

Regulator system of a steam turbine. Transducer, actuator and regulation system.

Watt's tachymeter, diagram and operating principle. The dynamic equation that determines its operation and its Laplace transform.

The drawer-motor hydraulic system, diagram and operating principle. Equation of the flow rate flowing from the linearized drawer in the neighborhood of a centered drawer. Dynamic equations of operation of the engine spool group (eq. of the flow rate flowing from the spool and equation of the flow rate as volume variation of the cylinder, in the hypothesis of an incompressible fluid, eq. of the piston) and their Laplace transforms. Block diagram of the operation of the motor drawer assembly.

Dynamic equations of operation of the steam group system (eq. of the tachymeter, of the engine spool group and of the post steam turbine in closed chain) and their Laplace transforms. Block diagram of the operation of the motor drawer assembly. Study of the stability of the system and design of the root locus, determination of the permanent error. Isodromic and non isodromic systems. Coupling of two steam groups.

HYDRAULIC MACHINES

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.

Three books:

- Turbine a vapore, Vol.1 - M. Bianchi, A. Peretto - Ed.BONOMO

- Compressori dinamici ed elementi di controllo dei sistemi energetici, Vol.2 - A. Peretto. Ed. BONOMO

- Turbomacchine Idrauliche Motrici, Vol.3 - , F. Melino, A. Peretto - Ed.BONOMO

## Teaching methods

Lessons developed in the classroom with electronic pad

## Assessment methods

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 drawings:

• Convergence and convergence-divergence duct

• De Laval Turbine

•  Curtis Wheel

• Multiple stage impulse Turbine

• Reaction Turbine

• Watt Tachymeter

• Drawer hydraulic motor

• Isodromic steam power plant

• NON isodromic steam power plant

•  Pelton Turbine, with oleo-dynamic and mechanical nozzle

• 4 jet Pelton turbine

• Francis Turbine

• Propeller and Kaplan Turbine

## Teaching tools

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

## Office hours

See the website of Antonio Peretto

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.