OVERVIEW

The course explores in depth the architecture and operating principles of axial and radial turbomachines, providing a strong theoretical foundation for their analysis and design.

AIMS AND CONTENT

LEARNING OUTCOMES

he course aims at providing the fundamental information for designing axial and radial turbomachines and for understanding flow and functioning principles. Preliminarly, the architecture of the most common turbomachines is described and the basic equations of Fluid dynamics and Thermodynamics are recalled, together with the interesting physical properties of the fluids.

AIMS AND LEARNING OUTCOMES

Through active participation in lectures and problem-solving sessions, together with independent study, students will acquire:

• an operational knowledge of the physical properties of the fluids commonly processed by turbomachines, the thermodynamic transformations involved, the conservation equations used for flow analysis, similarity theory, and statistical methods;
• a basic understanding of the architecture of the main types of power-absorbing turbomachines, the functions of their components, and the variations of the principal fluid-dynamic and thermodynamic quantities within them;
• with specific reference to axial power-absorbing turbomachines, an operational knowledge of one-dimensional and two-dimensional flow models in the meridional plane and on the blade-to-blade surface;
• with specific reference to multistage axial compressors, a basic understanding of the variation of the principal fluid-dynamic and thermodynamic quantities along the machine, as well as of the characteristic curves;
• with specific reference to radial power-absorbing turbomachines, an operational knowledge of one-dimensional flow models in the meridional plane and on the blade-to-blade surface;
• a basic understanding of the fluid-dynamic and structural constraints governing the design and operation of axial and radial power-absorbing turbomachines;
• an understanding of compressor off-design operating phenomena, including stall, surge, and choking.

PREREQUISITES

Students are expected to have a basic knowledge of Fluid Dynamics, Thermodynamics, and Fluid Machinery.

TEACHING METHODS

Theoretical lectures and applied sessions.

Students with a certified Specific Learning Disorder (SLD), disability, or other special educational needs are invited to contact the course instructor before the start of classes in order to agree on teaching arrangements that, while respecting the learning objectives of the course, take individual learning needs into account and provide appropriate compensatory tools.

In addition, any request for compensatory measures and/or exemptions to be applied during the examination must be submitted using the form available at the following link: https://modulionline.unige.it/richiesta-adattamenti#no-back. The request must then be sent to the course instructor, the DIME contact person (federico.scarpa@unige.it), and the University Office for Services for the Inclusion of Students with Disabilities and Specific Learning Disorders (inclusione.studenti@info.unige.it) at least seven working days before the examination, in accordance with the guidelines available at https://unige.it/disabilita-dsa/richiesta-servizi

SYLLABUS/CONTENT

1. Review of Fluid Dynamics and Thermodynamics for Turbomachinery

1.1. Fundamental physical properties of fluids and fluid models

Vapour pressure; constitutive equation and viscosity; state equation of perfect gases, internal energy and enthalpy, specific heats, polytropic transformations; bulk modulus of compressibility and speed of sound. Limits of applicability of the various models and the effect of temperature. Recurrent integrals in the work exchange computation. Adiabatic and polytropic efficiency.

1.2. One-dimensional balance equations for turbomachines

Continuity equation (for compressible and incompressible flow), energy equation (for compressible and incompressible flow, in mechanical and thermal form, in the absolute and relative frame), equations of linear and angular momentum, Euler equation. Head and total pressure, total temperature, and total enthalpy increments. Basic assumptions and limits of applicability. Design and performance-analysis problems and features of the related algorithms. Applications of the energy equation: pump operation in a hydraulic circuit, fan efficiency, reheat effect and polytropic efficiency in compression, characteristic curve of a nozzle, and Rayleigh flow.

1.3. Theory of similarity

Non-dimensionalization of solutions of the Navier-Stokes equations (for compressible and incompressible flow), choice of the reference dimensional parameters. Fundamental non-dimensional parameters for turbomachinery: Mach and Reynolds numbers; pressure coefficient, lift and drag coefficients, incidence, adverse pressure gradient, boundary-layer separation, and stall; flow and head coefficients, non-dimensionalization of the characteristic curves of pumps and fans, interpretation of their trends; corrected flow rate, corrected rotational speed, compression ratio, and their relationship with the Mach number; non-dimensionalization of axial-compressor characteristic curves, interpretation of their trends, compressor–turbine matching, and gas-turbine operation. Limits of applicability.

1.4. Statistical Methods and Empirical Correlations in Turbomachinery Design and Analysis

Specific speed and specific diameter, empirical correlations, relation with design constraints and their influence on machine geometry. Limits of applicability.

2. Architecture and Operation of Axial Flow Pumps and Compressors

2.1. Geometrical representation of axial turbomachines: meridional and cylindrical blade-to-blade views, blade sections, and velocity triangles.

2.2. Function of the rotor: velocity triangles and variation of pressure, velocity, and enthalpy; relation between blade thrust, work input and pressure rise. Flow deviation, losses and characteristic curve.

2.3. Function of the stator in single- and multistage machines: velocity triangles and variation of pressure, velocity, and enthalpy; blade shape; analogies and differences with rotors.

2.4. Cascade aerodynamics: non dimensional cascade parameters and non dimensional velocity triangles; relationship between velocity triangles, blade thrust, work exchange, and pressure rise; relationship between velocity triangles, lift coefficient of a blade cascade, and the behaviour of an isolated airfoil.

2.5. Multistage axial compressors: velocity trend and axial distribution of work input, pressure ratio and degree of reaction. Effect of the Mach number. Characteristic curves.

2.6. Two-dimensional flow in the annuli: radial equilibrium equation and common vortex laws; radial shift of the meridional streamlines and radial non uniformity of losses; application to design and performance-analysis problems.

2.7. Criteria for determining maximum blade loading: pressure-coefficient distribution over an airfoil and its parameterization; relationship with boundary-layer separation and the von Kármán integral equation; de Haller criterion and Diffusion Factor.

2.8. Aerodynamic and structural constraints on the blade span.

3. Architecture and Operation of Mixed- and Radial Flow Pumps and Compressors

3.1. Geometrical representation of mixed- and radial flow turbomachines: meridional and blade-to-blade view, blade sections and velocity triangles. Effect of radius variation on work exchange and compression.

3.2. Function of the radial rotor: velocity triangles and variation of pressure, velocity, and enthalpy; relation between blade thrust, work input and pressure rise. Typical blade geometries and their influence on the characteristic curve. Outlet blade angle, slip effect and related correlations.

3.3. Function of the radial stator and volute: bladed and unbladed diffuser, velocity triangles and variation of pressure, velocity, and enthalpy; blade shape; design of the volute.

3.4. Flow on the blade-to-blade flow surface: blade loading and blade design.

3.5. Aerodynamic and structural constraints on blade curvature and thickness.

4. Abnormal Operating Conditions of Compressors

4.1. Surge, stall, and choking in compressors.

RECOMMENDED READING/BIBLIOGRAPHY

For examination preparation:

• Course notes prepared by the instructor and other teaching materials available on the AulaWeb course website for the relevant academic year.

For further study of specific topics:

• E. M. Greitzer, C. S. Tan, M. B. Graf, Internal Flow: Concepts and Applications, Cambridge University Press.
• N. A. Cumpsty, Compressor Aerodynamics, Longman.
• R. I. Lewis, Turbomachinery Performance Analysis, Arnold.

The course notes, available on AulaWeb, constitute the reference teaching material for exam preparation, while the other recommended texts may be used for further study of specific topics.

Students with Specific Learning Disorders (SLDs) and working students may contact the course instructor for any clarification and to agree on ways of accessing and using the teaching material that are compatible with their needs, while respecting the learning objectives of the course.

TEACHERS AND EXAM BOARD

Exam Board

ANDREA CATTANEI (President)

MATTEO DELLACASAGRANDE

EDWARD CANEPA (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/en/corsi/11960/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam at the end of the course, normally every Tuesday. Please contact the lecturer at Andrea.Cattanei@unige.it at least one week in advance.

Students with a certified Specific Learning Disorder (SLD), disability, or other special educational needs are invited to contact the course instructor before the start of classes in order to agree on teaching arrangements that, while respecting the learning objectives of the course, take individual learning needs into account and provide appropriate compensatory tools.

In addition, any request for compensatory measures and/or exemptions to be applied during the examination must be submitted using the form available at the following link: https://modulionline.unige.it/richiesta-adattamenti#no-back. The request must then be sent to the course instructor, the DIME contact person (federico.scarpa@unige.it), and the University Office for Services for the Inclusion of Students with Disabilities and Specific Learning Disorders (inclusione.studenti@info.unige.it) at least seven working days before the examination, in accordance with the guidelines available at https://unige.it/disabilita-dsa/richiesta-servizi

ASSESSMENT METHODS

Discussion of topics covered during the course based on two questions. The examination is intended to assess the student's understanding of the physical meaning and engineering relevance of the subjects discussed.