247
Chapter 7
Dynamic Similitude
© Springer Science+Business Media Dordrecht 2015
E. Dick, Fundamentals of Turbomachines, Fluid Mechanics and Its Applications 109,
DOI 10.1007/978-94-017-9627-9_7
Abstract The present chapter discusses the concept of similitude, which means
that two machines may be similar in the sense that there exist proportionality factors for geometry, velocities and forces. The performance characteristics of one of
the machines can then be derived from the known characteristics of the other. The
concept forms the basis of the initial design of a turbomachine, which means the
determination of main parameters as the rotational speed, the size and some geometric ratios. In this chapter, we discuss the theory of dynamic similitude and some
applications, including the basic design of a radial fan.
7.1 Principles of Dynamic Similitude
7.1.1 Definition of Dynamic Similitude
Two flows are dynamically similar when they are geometrically similar, when velocities at homologous points have the same direction and have a constant ratio
and when forces at homologous points have the same direction and have a constant
ratio. In other words, flows are dynamically similar when similitude is as well geometric, kinematic and dynamic.
With the simplest flows, i.e. steady flows with incompressible fluids in a stationary geometry, dynamic similitude implies kinematic similitude, as the velocity field
unambiguously results from the integration of the force field. Further, kinematic
similitude implies geometric similitude, as streamlines unambiguously result from
the integration of the velocity field. Therefore, the term dynamic similitude is applied to the common denomination of the three elements within similitude. Henceforth we simply use the term similitude. The notion dynamic similitude is limited
to the flow itself. Apart from fluid transport itself, other transport phenomena may
occur within a flow. Heat transport is an example. The notion of similitude may
be extended to these phenomena. Additional transport phenomena are not directly
relevant for the fundamental study of turbomachines. For turbomachines, work by a
rotor is an additional phenomenon compared to simple flows. In the present chapter,
the similitude study is limited to constant density fluids. An extension to compressible fluids is made in Chap. 15.
Chapter 7
Dynamic Similitude
© Springer Science+Business Media Dordrecht 2015
E. Dick, Fundamentals of Turbomachines, Fluid Mechanics and Its Applications 109,
DOI 10.1007/978-94-017-9627-9_7
Abstract The present chapter discusses the concept of similitude, which means
that two machines may be similar in the sense that there exist proportionality factors for geometry, velocities and forces. The performance characteristics of one of
the machines can then be derived from the known characteristics of the other. The
concept forms the basis of the initial design of a turbomachine, which means the
determination of main parameters as the rotational speed, the size and some geometric ratios. In this chapter, we discuss the theory of dynamic similitude and some
applications, including the basic design of a radial fan.
7.1 Principles of Dynamic Similitude
7.1.1 Definition of Dynamic Similitude
Two flows are dynamically similar when they are geometrically similar, when velocities at homologous points have the same direction and have a constant ratio
and when forces at homologous points have the same direction and have a constant
ratio. In other words, flows are dynamically similar when similitude is as well geometric, kinematic and dynamic.
With the simplest flows, i.e. steady flows with incompressible fluids in a stationary geometry, dynamic similitude implies kinematic similitude, as the velocity field
unambiguously results from the integration of the force field. Further, kinematic
similitude implies geometric similitude, as streamlines unambiguously result from
the integration of the velocity field. Therefore, the term dynamic similitude is applied to the common denomination of the three elements within similitude. Henceforth we simply use the term similitude. The notion dynamic similitude is limited
to the flow itself. Apart from fluid transport itself, other transport phenomena may
occur within a flow. Heat transport is an example. The notion of similitude may
be extended to these phenomena. Additional transport phenomena are not directly
relevant for the fundamental study of turbomachines. For turbomachines, work by a
rotor is an additional phenomenon compared to simple flows. In the present chapter,
the similitude study is limited to constant density fluids. An extension to compressible fluids is made in Chap. 15.