Page 33 - Fluid Mechanics and Thermodynamics of Turbomachinery

14 Fluid Mechanics, Thermodynamics of Turbomachinery
particles in sufficient numbers. It is an interesting fact that in the absence of such
nuclei a liquid can withstand negative pressures (i.e. tensile stresses)! Perhaps the
earliest demonstration of this phenomenon was that performed by Osborne Reynolds
(1882) before a learned society. He showed how a column of mercury more than
twice the height of the barometer could be (and was) supported by the internal cohe-
sion (stress) of the liquid. More recently Ryley (1980) devised a simple centrifugal
apparatus for students to test the tensile strength of both plain, untreated tap water
in comparison with water that had been filtered and then de-aerated by boiling.
Young (1989) gives an extensive literature list covering many aspects of cavitation
including the tensile strength of liquids. At room temperature the theoretical tensile
strength of water is quoted as being as high as 1000 atm (100 MPa)! Special pre-
treatment (i.e. rigorous filtration and pre-pressurization) of the liquid is required to
obtain this state. In general the liquids flowing through turbomachines will contain
some dust and dissolved gases and under these conditions negative pressure do
not arise.
A useful parameter is the available suction head at entry to a pump or at exit
from a turbine. This is usually referred to as the net positive suction head, NPSH,
defined as
H s D .p o p //. g/ (1.10)
where p o and p are the absolute stagnation and vapour pressures, respectively, at
pump inlet or at turbine outlet.
To take into account the effects of cavitation, the performance laws of a hydraulic
turbomachine should include the additional independent variable H s . Ignoring the
effects of Reynolds number, the performance laws of a constant geometry hydraulic
turbomachine are then dependent on two groups of variable. Thus, the efficiency,
D f. , N ss / (1.11)

where the suction specific speed N ss D NQ 1/2 /.gH s / 3/4 , determines the effect of
3
cavitation, and D Q/.ND /, as before.
It is known from experiment that cavitation inception occurs for an almost
constant value of N ss for all pumps (and, separately, for all turbines) designed
to resist cavitation. This is because the blade sections at the inlet to these pumps
are broadly similar (likewise, the exit blade sections of turbines are similar) and it
is the shape of the low pressure passages which influences the onset of cavitation.
Using the alternative definition of suction specific speed  ss D Q 1/2 /.gH s / 1/2 ,
3
where  is the rotational speed in rad/s, Q is the volume flow in m /s and gH s ,is
2
2
in m /s , it has been shown empirically (Wislicehus 1947) that
 ss ' 3.0 (rad) (1.12a)
for pumps, and
 ss ' 4.0 (rad) (1.12b)
for turbines.
Pearsall (1973) described a supercavitating pump with a cavitation performance
much better that of conventional pumps. For this pump suction specific speeds,  ss