Geometric Notation

The geometry of a generalized turbomachine rotor is sketched in figure 2.1, and consists of a set of rotor blades (number = ZR) attached to a hub and operating within a static casing. The radii of the inlet blade tip, inlet blade hub, discharge blade tip, and discharge blade hub are denoted by RT1, RH1, RT2, and RH2, respectively. The discharge blade passage is inclined to the axis of rotation at an angle, ϑ, which would be close to 90° in the case of a centrifugal pump, and much smaller in the case of an axial flow machine. In practice, many pumps and turbines are of the “mixed flow” type, in which the typical or mean discharge flow is at some intermediate angle, 0 < ϑ < 90°.

The flow through a general rotor is normally visualized by developing a meridional surface (figure 2.2), that can either correspond to an axisymmetric streamsurface, or be some estimate thereof. On this meridional surface (see figure 2.2) the fluid velocity in a non-rotating coordinate system is denoted by v(r) (with subscripts 1 and 2 denoting particular values at inlet and discharge) and the corresponding velocity relative to the rotating blades is denoted by w(r). The velocities, v and w, have components vθ and wθ in the circumferential direction, and vm and wm in the meridional direction. Axial and radial components are denoted by the subscripts a and r.