In this article we will discuss about:- 1. Performance of a Turbine under Unit Head 2. Specific Speed of Turbine as a Type Number 3. Model Testing 4. Characteristic Curves.
Performance of a Turbine under Unit Head:
In the studies of comparison of the performances of turbines of different output, and speeds and different heads, it is convenient to determine the output, the speed and the discharge, when the head on the turbine is reduced to unity, i.e. 1 metre. The conditions of the turbine under unit head are such that the efficiency of the turbine remains unaffected. Thus, the velocity triangles under the working conditions and under unit head are geometrically similar.
Given a turbine every velocity vector (v Vw Vf V etc.) is a function of √H where H is the head on the turbine. With this basic property, we can determine the speed, discharge and power under unit head.
Thus, if the speed, discharge and power developed by a turbine under a certain head are known, the corresponding quantities for any other head can be determined easily.
Specific Speed of a Turbine:
The specific speed of a turbine is the speed at which a geometrically similar turbine will run when developing 1 kilo watt under a head of 1 metre. This is the type characteristic of the turbine. Within certain known limits, every type of turbine has its own value of the specific speed. For example, Francis turbines have a specific speed in the range 50 to 260. Such a range- exists because all the Francis turbines are not geometrically similar. For a set of geometrically similar turbines, the specific speed will have the same value.
Derivation of the Specific Speed:
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Consider a series of geometrically similar turbines. Suppose these turbines are Francis turbines.
Specific Speed of Turbine as a Type Number:
This is another representation of specific speed of a turbine. In this representation the specific speed is expressed as a non- dimensional quantity given by –
Model Testing of Turbines:
The performance of a prototype turbine can be determined by model analysis. Tests are conducted on a dynamically similar model and from the properties of the model turbine, the corresponding properties of the prototype turbine can be determined.
By dimensional analysis, it can be shown that the power developed by a turbine is a functions of some non-dimensional parameters and can be expressed as –
Characteristic Curves of a Turbine:
These are curves which are characteristic of a particular turbine which help us in studying the performance of the turbine under various conditions. These curves pertaining to any turbine are supplied by its manufacturers, based on actual tests.
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The data that must be obtained in testing a turbine are the following:
1. The speed of the turbine N
2. The discharge Q
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3. The net head H
4. The power developed P
5. The overall efficiency ƞ0
6. Gate opening (this refers to the percentage of the inlet passages provided for water to enter the turbine).
The characteristic curves obtained are the following:
(i) Constant head curves or main characteristic curves
(ii) Constant speed curves or operating characteristic curves
(iii) Constant efficiency curves, or Muschel curves.
(i) Constant Head Curves or Main Characteristic Curves:
Maintaining a constant head, the speed of the turbine is varied by admitting different rates of flow by adjusting the percentage of gate opening. The power P developed is measured mechanically. From each test, the unit power Pu, the unit speed Nu, the unit quantity Qu and the overall efficiency ƞ0 are determined.
The characteristic curves drawn are:
(a) Unit quantity vs unit speed
(b) Unit power vs unit speed
(c) Overall efficiency vs unit speed
Fig. 23.1. shows the main characteristic curves of the Pelton and Kaplan turbines respectively.
(ii) Constant Speed Curves or Operating Characteristic Curves:
In this case tests are conducted at a constant speed varying the head H and suitably adjusting the discharge Q. The power developed P is measured mechanically. The overall efficiency is aimed at its maximum value.
(iii) Constant Efficiency Curves (Muschel Curves):
These curves are plotted from data which can be obtained from the constant head and constant speed curves. The object of obtaining this curve is to determine the zone of constant efficiency so that we can always run the turbine with maximum efficiency.
This curve also gives a good idea about the performance of the turbine at various efficiencies.