LEARNING OUTCOMES

The 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

By means of active attendance of classes and individual study, the student will gain:

An operative knowledge of: the physical properties of the commonly processed fluids, the followed thermodynamic transformations, the balance equations employed for studying the flow, the similarity theory and the statistical approach, and the effect of the main aerodynamic and structural constraints on the blade design.

A basic knowledge of: the machine architecture, the features of the various parts, and the variation of fundamental fluid dynamic and thermodynamic quantities.

A basic knowledge of multi-stage axial compressors characteristic curves and relation with the trend of fluid dynamic and thermodynamic quantities along the machine.

With reference to radial and axial pumps and compressors, an operative knowledge of the one- and two dimensional flow models in the meridional and blade-to-blade planes.

A basic knowledge of anomalous operation of pumps and compressors.

PREREQUISITES

Basic knowledge of Fluid Dynamics, Thermodynamics, and Fluid Machinery.

TEACHING METHODS

Theoretical and applied classes

SYLLABUS/CONTENT

1. Basic Fluid Dynamics and Thermodynamics of turbomachinery

1.1. Physical properties of gas and liquids and related models

Vapour pressure; constitutive equation and viscosity; state equation of perfect gases, internal energy and enthalpy, specific heats, polytropic transformations; compressibility module and speed of sound. Effect of temperature on the accuracy and limits of applicability. 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 momentum and moment of momentum, Euler equation. Head and total pressure, total temperature, and total enthalpy. Direct and inverse problem and features of the related algorithms. Basic assumptions and limits of applicability.

1.3. Theory of similarity

Non-dimensionalization of the Navier-Stokes equations solution (for compressible and incompressible flow) and choice of the reference dimensional parameters. Fundamental non-dimensional parameters for turbomachinery (Mach and Reynolds number, lift and drag coefficients, flow and head coefficients, reduced flow rate and speed, compression ratio; relation with Mach number), non-dimensionalization of the characteristic curves and interpretation of their trend. Limits of applicability.

1.4. Statistical approach for turbomachinery

Specific speed and diameter, empirical correlations, relation with design constraints and effects on the geometry of the machine. Limits of applicability.

2. Architecture and operation of axial pumps and compressors

2.1. Geometrical representation of axial turbomachines: meridional and blade-to-blade view, blade cuts and velocity triangles.

2.2. Function of the rotor: velocity triangles and variation of pressure, velocity, enthalpy, and temperature; relation between blade thrust, work input and pressure rise; blade shape and analogies with an isolated airfoil. 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 temperature; blade shape; analogies and differences with rotors.

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

2.5. Two-dimensional flow in the annuli: radial equilibrium equation and common vortex laws; employ in direct and design problems.

2.6. Aerodynamic and structural constraints on the blade span.

3. Architecture and functioning of radial turbomachines

3.1. Geometrical representation of radial turbomachines: meridional and blade-to-blade view, blade cuts and velocity triangles.

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

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

3.4. Two-dimensional flow on the blade-to-blade surface: design of the blade by means of the streamline curvature method.

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

4. Anomalous operation of pumps and compressors

4.1. Surge, stall, and choking in compressors.

4.2. Pump cavitation and suction height.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes by the lecturer.

E. M. Greitzer, C. S. Tan, M. B. Graf, Internal Flow: Concepts and Applications, Ed. Cambridge University Press.

N. A. Cumpsty, Compressor Aerodynamics, Ed. Longman.

R. I. Lewis, Turbomachinery performance analysis, Ed. Arnold.