Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2021/2022
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 054827 - TURBOMACHINERY A
Docente Gaetani Paolo
Cfu 10.00 Tipo insegnamento Monodisciplinare
Didattica innovativa L'insegnamento prevede  1.0  CFU erogati con Didattica Innovativa come segue:
  • Blended Learning & Flipped Classroom

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The course aims to analyse in detail the theoretical and practical fluid-dynamic features of hydraulic and thermal Turbomachinery. Thanks to the knowledge gained during the course, students will be able to proficiently face and solve the design issues as well as Turbomachinery performance testing and optimisation. As the technical scenario includes a large variety of Turbomachinery configurations, the course is focused on devices suited for energy conversion, industrial processes and aeronautical / ground transportation.

Moreover, students can improve their soft skills by holding, on a voluntary basis, seminars on specific issues to the class in the frame of a flipped classroom methodology and by doing in groups a design project.

Risultati di apprendimento attesi

By the end of the course, students will learn contents and practices according to what defined in the leaning objectives.


In terms of acquired knowledge and understanding, students will be able to:

  • describe the operating principles of turbomachinery
  • identify the different class of turbomachines and their main thermo-fluid dynamic issues
  • discuss the behaviour of turbomachinery in design and off-design conditions
  • predict the operating behaviour of turbomachinery in design and off-design conditions
  • examine the complex 3d flows in turbomachinery


Concerning the ability to apply the acquired knowledge and understanding, students will be able to:  

  • apply all scaling rules for designing experiments and foresee turbomachinery behaviour from model-test data.
  • select the best solution for turbomachinery integration in power plants and propulsion systems.
  • calculate the operating curve of turbomachinery in design and off-design conditions.


Through exercise / labs class and the design project, students will also acquire the skills to formulate a judgment, meaning to:

  • select the best stage arrangement and design
  • compare different stage design
  • analyse the turbomachinery operation
  • propose a test methodology for the performance qualification.


Furthermore, through the assigned group project and flipped class, students will gain the ability to autonomously:

  • design a multistage turbomachine in the context of an optimised load sharing.
  • assess the scientific content of paper
  • prepare a project presentation
  • improve his knowledge on the topic in an autonomous and self-directed manner, thanks to the robust bases gained in this course


Finally, students will improve their communication skills, being able to:

  • prepare and present the design project
  • discuss a scientific paper as proposed in the flipped class

Argomenti trattati

The course contents are delivered through lectures, exercise classes and lab. activities.


The course covers the following topics divided in modules as per the description below:


Module 1 – Fundamentals of Aerodynamics, Thermodynamics and Turbomachinery Flow.

Topic 1.1: Stresses in continuum media. Continuity equation, momentum balance, energy balance for open systems in both differential and integral forms, in stationary and rotating frames of reference.

Topic 1.2: Compressible flows. Viscous and turbulent flows; boundary layer. Cavitation

Topic 1.3: Euler equation.

Topic 1.4: Principle and basic equations for thermodynamics, thermodynamic process representation, loss coefficient and efficiency parameters. Reaction degree. Performance curves.


Module 2 – Operation of Turbomachinery.  

Topic 2.1: General performance curves.

Topic 2.2: Models Theory and Similarity for incompressible flows.

Topic 2.3: Reynolds effects

Topic 2.4: Compressibility effects on the similarity laws for gas/steam turbines and compressors.

Topic 2.5: Turbomachinery classification on the basis of specific speed and specific diameter.


Module 3 – Turbomachinery fluid-dynamics. 

Topic 3.1: Reference surfaces (blade to blade, meridional and secondary ones), main geometrical and fluid-dynamic quantities for turbomachinery cascades.

Topic 3.2: Force exchange on blades: Lift and drag on profiles and blades. Cascades effects.

Topic 3.3: Crocco equation and radial equilibrium.

Topic 3.4: 2D and 3D blade design concepts.

Topic 3.5: Losses in turbomachinery: Secondary flows, 3D effects, clearances and wake effects. Clearances geometries and design.

Topic 3.6: Examples of turbomachinery flows.


Module 4 – Diffusers and Compressors.

Topic 4.1: Diffusers: geometries and operation for compressible and incompressible flows.  Shape factor and main performance parameters.

Topic 4.2: Radial Compressors: classification and analysis according to 1D approach. Slip factor. Rotor geometry and Losses. Diffusers geometry and performance. Volute design.

Topic 4.3: Axial Compressors: classification and analysis according to 1D approach. Blade aerodynamics. Prediction of flow angle, losses and blades number by semi-empirical criteria. Blade loading criteria. Supersonic and chocked cascades. Off design operation.

Topic 4.4: Compressors Instability:  Helmholtz theory. Blade stall and rotating stall. Surge and machine – plant interaction.


Module 5: Turbines.

Topic 5.1: classification and analysis according to 1D approach for different reaction degrees. Discussion on optimisation parameters.

Topic 5.2: axial turbines: Semi-empirical criteria for flow angle and losses prediction downstream subsonic and supersonic cascades. Blade loading criteria.

Topic 5.3: Gas turbines: blade cooling, thermal aspects for cooled blade, aero-engine architecture.

Topic 5.4: radial turbines: architectures and semiempirical loss correlation for stator and rotor.


Module 6: additional tools and features in turbomachinery.

Topic 6.1: labs experiments: blades, turbomachinery and aeroengine models overview and discussion. Turbocharger operation analysis.

Topic 6.2: flipped classroom and design project tutoring

Topic 6.3: Computational schemes for Turbomachinery: lumped parameter approach, 1D-2D and 3D schemes, issues for unsteady solutions.

Topic 6.4: Mechanical issues for Turbomachinery blades: periodic aerodynamic forcing, aero-elastic effects, flutter, mechanical damping.

Topic 6.5: Seminars on specific topics, yearly setup.


Students must have acquired the following skills in fluid dynamic, thermodynamics and fluid machines:

  • Continuity, momentum and energy balances
  • Basic flow equation and gas-dynamics, basic boundary layer theory.
  • basic knowledge on thermodynamics and different processes
  • fluid machines: basic knowledge on velocity triangles, Euler equation for work exchange, different kind of turbines, compressors.


A comprehensive review of the basic concepts can be found in: Dixon S.L., Hall C., Fluid Mechanics and Thermodynamics of Turbomachinery, Editore: Butterworth-Heinemann

This reference holds for all students, included who got his bachelor at Politecnico di Milano

Modalità di valutazione

The course will offer lectures and exercises. Seminars, held by experts on specific topics (different year by year), are also foreseen. On voluntary basis, few labs can be also attended.

Course attendance is warmly suggested. Students’ skills and knowledge will be evaluated by an oral exam and by a short project: the project is mandatory for Turbomachinery A and on a voluntary basis for Turbomachinery B.

In the oral exam, the student is expected to:

  1. a) discuss and present the turbomachines operational laws
  2. b) discuss and present the different design methodologies on a quality level
  3. c) quantify the main analytical relationship describing the thermo-fluid dynamic processes occurring in turbomachines
  4. d) apply the design criteria and methodologies: for those who does the design project this part consists in the design project discussion, for all the others a specific question will be asked in the oral exam.
  5. e) show their ability in seeking new possible turbomachinery application thanks to an autonomous and self-directed in-depth study.


By the design project, soft skills in oral presentation and work group are enhanced and improved.

On a voluntary basis, few students could hold seminars on specific issues to the class in the frame of a flipped classroom methodology.

Depending on the class (Turbomachinery A – B, marked out by different credits) slightly different programs are foreseen:

  • Turbomachinery B: Modules 1- 5. 
  • Turbomachinery A: All Modules.


Final Grading

To pass the course, students must successfully pass the oral exam and present the design project if done. The design project has a grade range of 0-3 points.

Risorsa bibliografica facoltativaE.A. Baskharone, Principles of turbomachinery in air breathing engines, Editore: cambridge university press, Anno edizione: 2014, ISBN: 978-1-107-41740-3
Risorsa bibliografica facoltativaM. Schobeiri, Turbomachinery Flow Physics and Dynamic Performance, Editore: Springer
Risorsa bibliografica facoltativaDixon S.L., Hall C., Fluid Mechanics and Thermodynamics of Turbomachinery, Editore: Butterworth-Heinemann
Risorsa bibliografica facoltativaF. White, Viscous Fluid Flow, Editore: Mc Graw Hill
Risorsa bibliografica facoltativaC. Osnaghi, Teoria delle Turbomacchine, Editore: Esculapio

Software utilizzato
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Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 104:46 145:13

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