37464 - Turbomachines M

Course Unit Page

  • Teacher Giovanni Naldi

  • Credits 6

  • SSD ING-IND/08

  • Teaching Mode Traditional lectures

  • Language Italian

  • Course Timetable from Sep 19, 2018 to Dec 17, 2018

Academic Year 2018/2019

Learning outcomes

The student masters the basic methodologies to address the thermal and fluid design of turbomachinery. The logical path adopted allows the student to acquire knowledge for the external design of the machine through the use of statistical correlations.

Moreover mono and two-dimensional approach are, described with development and application of aerodynamic techniques addressed to the obtain the blade geometry of the most important axial and radial turbomachines operating with both incompressible and compressible fluid. Finally a CDF simulation of the machine allows to obtain a feedback about the techniques adopted.

Course contents

Classification of turbomachinery. Nozzles and diffusers

Equations of the mono-dimensional flow, stationary, compressible of a perfect gas in a duct. Coefficients of loss. Performances of nozzles and diffusers. Isentropic flow through a duct of variable area. Nozzles not isentropic.

Thermodynamic analysis of the stages of axial and centrifugal turbomachines.

Real, reversible and theoretical work. Hydraulic, polytropic and isentropic efficiency. Recovery and counter-recovery factors.

Dimensionless parameters of the turbomachines operating with compressible and incompressible fluid. Maps of performances.

Geometric and fluid dynamics similarity  in turbomachinery. Specific speed. Selection diagrams, H, Q, P, n, D.

Rotating Stall and pumping.

Two-dimensional fluid dynamics of turbomachinery. Review of vector calculus. Irrotational fields, Velocity potential. Continuity equation. Equations of motion for the fixed and mobile observers.

Theory of isolated airfoils. Lift and drag, Kutta-Jukowskij Theorem. Method of singularities, the Kutta condition. Flat and cambered profiles. Sources and wells, airfoils with finite thickness. Ideal incidence. Profiles with logarithmic camber line and Jukowskij profiles.

Study of rows of airfoils with the method of singularities. Forces acting on the array. Application of the results to turbomachinery. Calls on the functions of complex variables. Cauchy theorem. Stream function. Complex potential.

Potential of elementary flows. Flow around the circle. Conformal mapping for the study of airfoils. Bieberbach series. Flat plate. Profiles with finite thickness. Profiles with cambered line. Joukowskij profiles. Method of conformal mapping to study airfoils array. Calculation of the performance of an array of a flat blade profiles.

Weinig and Eckert diagrams for arrays airfoils with  circular arc camber line. Induced drag.

Notes on the finite wing Prandtl theory. Energy losses of the of airfoils arrays. Three-dimensional flow in turbomachinery. Axisymmetric orthogonal coordinates and flows. of Stokes' current function. Simple radial balance equation. Free vortex, constant angle, rigid and forced vortex blade design. Automatic design of axial turbomachinery diagonal and centrifugal flow by computer codes. Flow simulation by means of CFD codes.


Sandrolini Sandro, Naldi Giovanni,Macchine 1: Termodinamica e fluidodinamica delle turbomacchine,Pitagora Editrice, Bologna, 1996, pp. I-XXIV, 1-805, ISBN 88-371-0827-3. (Ed. speciale, Bologna, 1997, pp. I-XXIV, 1-805, ISBN 88-371-0936-9)

Sandrolini Sandro, Naldi Giovanni,Macchine 2: Le turbomacchine motrici e operatrici,Pitagora Editrice, Bologna, pp. I-XXIV, 1-848, ISBN 88-371-0862-1.

Sandrolini Sandro, Naldi Giovanni,Macchine 3: Gli Impianti motori termici e i loro componenti,Pitagora Editrice, Bologna, 2003, pp. I-IIX, 1-685, ISBN 88-371-1317-X

Teaching methods

The arguments set out in the program by means of " chalk and blackboard "

Presentations in Power Point format (downloadable from the teacher site)

Short numerical exercises .

Assessment methods

Presentation of a home-work concerning a turbomachin describing the preliminary design stages, the generation of geometry and the simulation of performance by CFD analysis

Teaching tools

slides available at: http://www.diem.ing.unibo.it/personale/naldi/

Office hours

See the website of Giovanni Naldi