Page 326 - Fluid Mechanics and Thermodynamics of Turbomachinery

Hydraulic Turbines 307
Calculate, using an iterative process, the loss of head in the pipeline and hence, determine
for the turbine:
(1) the speed of rotation;
(2) the overall efficiency (based on the effective head);
(3) the power output;
(4) the percentage of the energy available at turbine inlet which is lost as kinetic energy at
turbine exit.

5. A Francis turbine operates at its maximum efficiency point at 0 D 0.94, corresponding
to a power specific speed of 0.9 rad. The effective head across the turbine is 160 m and the
speed required for electrical generation is 750 rev/min. The runner tip speed is 0.7 times the
spouting velocity, the absolute flow angle at runner entry is 72 deg from the radial direction
and the absolute flow at runner exit is without swirl.
Assuming there are no losses in the guide vanes and the mechanical efficiency is 100 per
cent, determine:
(1) the turbine power and the volume flow rate;
(2) the runner diameter;
(3) the magnitude of the tangential component of the absolute velocity at runner inlet;
(4) the axial length of the runner vanes at inlet.
6. The power specific speed of a 4 MW Francis turbine is 0.8, and the hydraulic efficiency
can be assumed to be 90 per cent. The head of water supplied to the turbine is 100 m. The
runner vanes are radial at inlet and their internal diameter is three-quarters of the external
diameter. The meridional velocities at runner inlet and outlet are equal to 25 and 30 per cent,
respectively, of the spouting velocity.
Determine:
(1) the rotational speed and diameter of the runner;
(2) the flow angles at outlet from the guide vanes and at runner exit;
(3) the widths of the runner at inlet and at exit.

Blade thickness effects can be neglected.
7. (a) Review, briefly, the phenomenon of cavitation in hydraulic turbines and indicate
the places where it is likely to occur. Describe the possible effects it can have upon turbine
operation and the turbine’s structural integrity. What strategies can be adopted to alleviate
the onset of cavitation?
(b) A Francis turbine is to be designed to produce 27 MW at a shaft speed of 94 rev/min
under an effective head of 27.8 m. Assuming that the optimum hydraulic efficiency is 92 per
cent and the runner tip speed to jet speed ratio is 0.69, determine:
(1) the power specific speed;
(2) the volume flow rate;
(3) the impeller diameter and blade tip speed.

(c) A 1/10 scale model is to be constructed in order to verify the performance targets of
the prototype turbine and to determine its cavitation limits. The head of water available for
the model tests is 5.0 m. When tested under dynamically similar conditions as the prototype,
the net positive suction head H S of the model is 1.35 m.
Determine for the model:

(1) the speed and the volume flow rate;