Similarity of hydraulic turbomachines

The performance of a turbomachine can be defined by the pressure (or height) curves plotted as a function of flow-volume for different values of rotational speed. These characteristics, however, may depend on other variables such as the physical properties of the working fluid. An attempt to study the variations of all the quantities involved would require an excessive number of experiments on the one hand, and make concise presentation of the results impossible on the other. Most of these complications can be overcome by using, for example, dimensional analysis, which allows the variables involved to be combined to form a smaller, more manageable number of dimensionless groupings.

As will be shown later, the head-flow characteristics of a pump, for example, can then be reasonably represented by a single curve.

Geometrically similar turbomachinery families will be studied here, with dimensions characterized by a reference length r.

This length r can be equal to the peripheral radius of the drive wheel, although for axial machines it is sometimes preferable to use the mean radius of the first drive wheel.

The nature of the incompressible fluid conveyed will be characterized by its constant density ρ, and its dynamic viscosity µ.

The two ways of approaching the study of turbomachinery similarity described briefly below, before going into greater detail later, will be considered in turn.

– The first is to use dimensional analysis. We list the variables that characterize the operation of a turbomachine, and select the ones we need to determine beforehand, in order to be able to determine the others. The former are called independent variables, the latter dependent variables.

– The flow in a turbomachine is just a special case of a fluid inside a channel. The second method, known as direct study, consists in particularizing the general laws of similarity of a fluid flow in a channel to the case of turbomachinery, and deducing from them the reduced variables characteristic of turbomachinery operation. We can only speak of similarity between two turbomachines if they are geometrically similar, since the channels in which the fluid flows must be geometrically similar.