Page 316 - Fluid Mechanics and Thermodynamics of Turbomachinery

Hydraulic Turbines 297

FIG. 9.16. Part section of a Kaplan turbine in situ (courtesy Sulzer Hydro Ltd, Zurich).

The vanes of the runner are similar to those of an axial-flow turbine rotor but
designed with a twist suitable for the free-vortex flow at entry and an axial flow
at outlet. Because of the very high torque that must be transmitted and the large
length of the blades, strength considerations impose the need for large blade chords.
As a result, pitch/chord ratios of 1.0 to 1.5 are commonly used by manufacturers
and, consequently, the number of blades is small, usually 4, 5 or 6. The Kaplan
turbine incorporates one essential feature not found in other turbine rotors and that
is the setting of the stagger angle can be controlled. At part load operation the
setting angle of the runner vanes is adjusted automatically by a servo mechanism to
maintain optimum efficiency conditions. This adjustment requires a complementary
adjustment of the inlet guide vane stagger angle in order to maintain an absolute
axial flow at exit from the runner.
Basic equations

Most of the equations presented for the Francis turbine also apply to the Kaplan
(or propeller) turbine, apart from the treatment of the runner. Figure 9.17 shows
the velocity triangles and part section of a Kaplan turbine drawn for the mid-blade
height. At exit from the runner the flow is shown leaving the runner without a whirl
velocity, i.e. c 3 D 0 and constant axial velocity. The theory of free-vortex flows was
expounded in Chapter 6 and the main results as they apply to an incompressible fluid
are given here. The runner blades will have a fairly high degree of twist, the amount
depending upon the strength of the circulation function K and the magnitude of the
axial velocity. Just upstream of the runner the flow is assumed to be a free-vortex
and the velocity components are accordingly:

c 2 D K/r c x D a constant.

The relations for the flow angles are
K/.rc x / .9.22a/
tan ˇ 2 D U/c x tan ˛ 2 D r/c x
tan ˇ 3 D U/c x D r/c x . .9.22b/