FIELD OF THE INVENTION
The present invention relates to an improved Francis turbine runner reducing
runaway speed of the turbine without compromising efficiency and cavitation
characteristic.
BACKGROUND OF THE INVENTION
Francis turbines are employed in hydroelectric power plants.
Runway speed of a turbine runner is the maximum possible rotating speed
achieved by the runner under specific operating conditions. The Run-away speed
is an important design parameter both for Hydro Turbine and Hydro Generator
with a strong bearing on cost of the machine.
Francis turbines are employed in hydroelectric power plants for extracting the
potential energy of water and converting it into the rotational energy of the
turbine shaft. Water flows past the turbine runner blades such that it transmits
its' energy to the runner. The energy transmitted to the runner depends upon
the flow rate of water flowing through it. If large uncontrolled volumes of water
are allowed to flow through the turbine in events such as load throw-off from the
grid and simultaneous failure of discharge control mechanism, then the speed of
the turbine increases beyond its' synchronous speed and reaches 'runaway'
speed. The turbine and the generator (which is directly coupled to the turbine
shaft) have to be designed to withstand the stresses generated during operation
at this runaway speed. Hence, higher the runaway speed, higher is the cost of

the turbine and the generator. Any reduction in the value of runaway speed
leads to a very significant reduction in the cost of the turbine as well as the
generator.
A Francis turbine runner comprises of a crown, a plurality of blades and a band.
The shape of runner blades is a function of parameters.'ξ ' and 'θ ',
Where, 'ξ' is defined as the product of number of blades (z ) and the span-wise
average of another parameter 'β ' (Fig 1 a) given by

and 'θ' is defined as the span angle of the blade in the plan view averaged in
the span-wise direction (Fig 1 b).
ξ = β x z
Both parameters 'ξ ' and 'θ ' are functions of the specific speed of the turbine.
US Patent No. 7,195,495 and US Patent No. 6,135,716, focus on the efficiency
and cavitation characteristics of Francis turbine.
OBJECT OF THE INVENTION
It is therefore an object of the invention to propose an improved Francis turbine
runner reducing runaway speed of the turbine without compromising efficiency
and cavitation characteristic

Another object of the invention is to propose an improved Francis turbine runner
reducing runaway speed of the turbine without compromising efficiency and
cavitation characteristic, which reduces the cost of turbine and hydrogenerator.
SUMMARY OF THE INVENTION
Accordingly, there is provided an improved Francis turbine runner reducing
runaway speed of the turbine without compromising efficiency and cavitation
characteristic, the improvement is characterized in that the maximum permissible
value of technical parameter 'ξ' and specific speed of the turbine runner are
selected for construction according to the technical relationship:
ξ= A[(N]s)3-B[(N]s)2 + C[(N]s)+D
Where, A = 3.702E-08
B = 4.804E-04
C = 3.447E-01
D = 3.473E+01
According to the present invention, Francis turbine runner blades are configured
and positioned between the crown and the band of the runner such that the
value of configured parameter 'ξ ' follows a particular relationship with respect to
the specific speed of the turbine, maintaining corresponding value of 'θ' and 'z '
as per classic calculations and as a result, achieving reduced values of runaway
speed in a range 4% to 10 % as compared to the prior art.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Figure la - shows a meridional view of a Francis turbine blade
Figure lb - shows a plan view of a Francis turbine blade
Figure 2 - shows a comparison between the values of 'ξ' and Ns as
per the present invention and that of prior art
Figures 3a,3b and 3c shows the effect of determined parameter 'ξ' on the
efficiency of Francis turbine runners.
DETAIL DESCRIPTION OF THE INVENTION
As per the invention, the parameter 'ξ' is determined to follow a particular
relationship with respect to the specific speed of the turbine, where 'ξ' is defined
as the product of number of blades (z ) and span-wise average of another
technical parameter 'β', where 'β ' is defined as :

Where, M = Meridional length
R = Distance from the axis of rotation
'ξ' is achieved by averaging the value of 'ξ' for a number of streamlines in the
span-wise direction i.e. from the crown to the band and multiplying it with the

number of blades 'Z'. The definition of all above parameters has been explained
in Figures la and lb.
The specific speed of a turbine is a characteristic quantity which dictates
construction of the turbine to a large extent. It is defined as

where, N = rotational speed (rpm)
P = power output (kW)
H = net head (m)
In order to achieve a low value of runaway speed, the turbine runner needs to
satisfy the technical relationship between 'ξ' and its' specific speed which is
defined by a device relationship:
ξ= A[(N]s)3-B[(N]s)2 + C[(N]s)+D
Where, A = 3.702E-08
B = 4.804E-04
C = 3.447E-01
D = 3.473E+01
The values of 'ξ' determined as hereinabove constitute the maximum values of
'ξ' to be used for a given specific speed of the turbine runner. The same has
been explained in Figure 2 in greater details.

Based on a detailed CFD analysis followed by experimental model tests, it is
technically recognized by the present inventors that Francis turbine runners
constructed based on disclosed embodiment of the invention, generate much
reduced values of runaway speeds without compromising optimum performance
parameters like efficiency or cavitation. It has been established using 3-D
numerical simulation using Computational Fluid Dynamics analysis followed by
detailed experimental model tests that Francis turbine runners constructed
according to the embodiment of the invention, have a runaway speed lower by
4% to 10% as compared to prior art. However, if the values of 'ξ ' are increased
beyond the disclosed threshold values, then a drop in the efficiency is observed,
which may be attributed to an increase in the skin friction drag over the blade
surface. The effect of the determined value of parameter 'ξ' on the efficiency of
the runner has been explained in Figures 3a, 3b and 3c in detail.

WE CLAIM
1. An improved Francis turbine runner reducing runaway speed of the
turbine without compromising efficiency and cavitation characteristic, the
improvement is characterized in that the maximum permissible value of
technical parameter 'ξ' and specific speed of the turbine runner are
selected for construction according to the technical relationship:
ξ= A[(N]s)3-B[(N]s)2 + C[(N]s)+D
Where, A = 3.702E-08
B = 4.804E-04
C = 3.447E-01
D = 3.473E+01
2. Francis turbine runner as claimed in claim 1, wherein the parameter 'ξ' is
a product of number of blades (z) of the runner, and a parameter 'ξ' is
defined by a technical relationship of

which, M is the Meridional length of each runner blade, and R is the
distance from the axis of rotation of the runner.

ABSTRACT

The invention relates to an improved Francis turbine runner reducing runaway
speed of the turbine without compromising efficiency and cavitation
characteristic, the improvement is characterized in that the maximum permissible
value of technical parameter 'ξ' and specific speed of the turbine runner are
selected for construction according to the technical relationship:
ξ= A[(N]s)3-B[(N]s)2 + C[(N]s)+D
Where, A = 3.702E-08
B = 4.804E-04
C = 3.447E-01
D = 3.473E+01