33927 - Machines M

Learning outcomes

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

Course contents

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. Rotor losses.

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.

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

Curtis Wheel Turbine scheme and operating principle. The velocity triangles. Maximum work evaluation for a Curtis Wheel Turbine. Total to static efficiency. Comparison with the impulse turbine efficiency.

The Multiple impulse 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.

Axial Compressors. Three dimensional flow: evaluation of vorticity and the rotation. Curl c in cilindrical coordinates.

Momentum Balance in radial, axial and circonferential directions. Energy Balance in cilindrical coordinate and Cracco's formula. Application of Cracco's Formula to the problem of 3D flow. Variation of circonferential speed with radius.

Design of the compressor blade with the method of Free vortex design (work and reaction rate), Constant ratio (work and axial velocity). Circonferential speed in the case of Exponential Design. Comparison of the incidence angles, Mach number and reaction rate for the three methods. 

Performance curves of an axial compressor, Suge line and rotation stall.

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.

Readings/Bibliography

For arguments related tu "Steam Turbines" see "Sistemi Energetici" 1 – MACCHINE A FLUIDO, G: Negri di Montenegro, M. Bianchi A. Peretto – Pitagora Editore

For arguments related "Compressors" see draft of the Teacher on the Assial Compressor  (on line on Virtuale web site)

For arguments related "Hydralulic Turbines" see draft of the Teacher on Hydraulic Machines  (on line on Virtuale web site)

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:

• De Laval Turbine

•  Curtis Wheel

• Multiple stage impulse Turbine

• Reaction Turbine

•  Pelton Turbine, oleo-dynamic and mechanical nozzle

• 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