 |
Fig.F-25
|

Radial turbines:
possess quite a long history - especially as water turbines they are know almost 170 years (- neglecting more than 250 years old Euler's theoretical investigations).
Already in 1827 a French engineer Fourneyron built a radial centrifugal turbine
capable to generate mechanical power
= 4,5 kW. The name (from latin " turbo" = eddy) proposed Fourneyron's teacher Burdin. Present day turbined are centripetal (rather than centrifugal) ones first designed by Francis and Boyden in U.S.A. in 1847. In principle, the operation is a reversal of the process inside a radial pump - to the degree of there being in existence also machines capable to operate according to the need as pump or turbine (in water storage facilities - in both regimes, however, they are a compromise in which it is necessary to tolerate somewhat worse efficiency). Efficiency of present-day Francis-type turbines (especially large ones, in which there is the favourable effect offriction coefficient decrease with increasing Reynolds number) is rather high, up to about
=
mech/(
.
) = 95 %.
The governing relations for turbines are basically the same as those derived above for pumps - with the difference that it is here the inlet
which is on the larger diameter (Fig.F-25). It is usual to select the exit condition on the inner diameter of the rotor so that the absolute axit velocity is there radial. Under this condition, the Euler Turbine Theorem for the work performed by fluid simplifies to:

- the result is negative, energy of fluid decreases.
 |
 |
Fig.F-26
|
In practice, some slight rotational velocity component at exit
is welcome, since it prevents flow separation from the wall of the exit diffuser. This is used quite commonly and in case of water turbines it is called the draught tube. It connects inner space of the turbine with the bottom water surface and permits placing the turbine at convenient locations above this surface. Also small gas turbines are usually designed as the radial centripetal ones. They are typically chosen to operate in somewhat lower range of speed coefficients (this permits to increase the Reynolds number, which for them tends to be inconveniently low). Radial gas turbines are often designed with blades lying in the meridional plane as this is leads to lower stress. In this case the above expression for the lossless specific work reduces to
=
. The ideal lossless turbine power is then
= 
.
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This is page Nr. F10 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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