37464 - Turbomachines M

Learning outcomes

The student masters the basic methodologies to deal with the thermo-fluid dynamic design of turbomachinery. The logical path adopted allows the student to acquire knowledge for the sizing of machines, through the use of statistical correlations, the one-dimensional sizing and the two-dimensional approach, with the development and application of aerodynamic techniques, considering driving and operating machines with incompressible and compressible fluid.

Course contents

THREE-DIMENSIONAL FLUID DYNAMICS OF TURBOMACHINES

Equations of motion (continuity, momentum and energy, Crocco's formula) for a compressible fluid in a three-dimensional space and in cylindrical coordinates.
Constitutive equation for the stress tensor. Navier Sotkes equations.
Rotor in cylindrical coordinates: vorticity. Irrotational flow field, the vector potential and its properties. Solenoid motion field: the velocity potential and its properties. Orthogonality of lines iso potential velocity iso potential vector.

FUNCTIONS OF COMPLEX VARIABLES
Cauchy conditions Reiemann and holomorphic functions. The complex potential and the complex velocity. The conformal transformation and the maintenance of the angles between the tangents to the curves in a plane and the corresponding tangents to the curves in the transformed plane.
Complex potential in the case of a point source and in the case of a free vortex source.

NACA PROFILES
Classification. Building a 4-digit NACA profile. Profile libraries available in literature and online (airfoiltools).

FORCE ON AN ISOLATED PROFILE
Lift, lift and pressure coefficient for an airfoil. Using the complex force to determine the Blasius formula for an isolated profile. Correlation between lift and circulation for an isolated profile. Th. of Joukowsky. Condition of Kutta. Determination of the coefficient of lift and resistance for a profile placed in rows in the case of absence and presence of leaks. Analytical expression for the Coefficient of lift and drag for a mobile airfoil.

THREE-DIMENSIONAL FLOW APPROXIMATION IN TURBOMACHINES
Axisymmetric flows. Orthogonal axisymmetric coordinates. Stokes current function. Expression of the Stokes current function on the S2 surface (meridian plane) and in the case of S1 surface blade to blade.
Flow analysis in a flow channel using dedicated software (Mathematica, Matlab, Fluent, OpenFoam).

TRANSONIC COMPRESSORS
Normal and oblique shock waves. Bow wave and normal shock in a transonic compressor blade channel; energy losses.

ENERGY LOSSES IN BLADE CASCADE
Losses due to laminar and turbulent motion.
Losses due to deflection defect for axial (Konig theory) and radial (Busemann theory) profiles.
Hub and tip endwall losses;  tip clearance losses, horsesohoe losses;

DESIGN and SIZING OF A TURBO MACHINE
Radial blades; determination of the profile of a radial blade by conformal transformation. Use of CAD software for 3D blade design.
Axial blades; Simple radial balance. Types of blading design using the free vortex design method (work, degree of reaction, alpha and beta angles). Circumferential velocity trend with Constant reaction design and Exponential design. Method comparison.

 

A video presentation of the course is available via the link at the top right of this page.

Readings/Bibliography

Lecture notes provided by the teacher.

Teaching methods

Explanation in the classroom using an electronic blackboard. I use turbomachinery modeling software.

Assessment methods

The student will have to face a final oral test on the developed program and comment on a work carried out in a group relating to the moderation of the flow in a blade channel or to the design of a radial or axial blading of a turbomachinery.

Teaching tools

Using software for flow and blade analysis in the turbomachinery in both 2D and 3D.
Parts of Turbines and Compressors brought to class and explained to students.

Links to further information

https://youtu.be/ApgdrFq4KHM

Office hours

See the website of Antonio Peretto