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Ebook Turbomachinery performance analysis: Part 2

(BQ) Part 2 book "Turbomachinery performance analysis" has contents: Mixed-flow and radial turbomachines; ducted propellers and fans; selected supporting fluid dynamic analysis; vorticity production in turbomachines and its influence upon meridional flows. | 6 Vorticity production I n turbomachines and its influence upon meridional flows Introduction The title of this chapter has been chosen with good reason, for turbomachines operate, as the Latin turbo suggests, by creating a whirling motion or vortex (again, Latin for whirlpool). Vorticity production is the prime mechanism for both the development of blade lift, as we have shown in Chapter 2, and energy transfer between fluid and rotating shaft, Chapters 1 and 5. In the last chapter flee-vortex machines, for which the swirl velocity obeys the law cor = constant, were shown to exhibit very simple meridional flow characteristics. Thus for incompressible flow through axial turbomachines with cylindrical hub and casing the axial velocity Cx and stagnation pressure Po are then constant, satisfying the radial equilibrium equation (5.14) for cylindrical flow. On the other hand a designer may prefer to specify some other swirl and/or stagnation pressure distributions. Radial equilibrium and actuator disc theory have been presented in Chapter 5 as two means for prediction of the consequent meridional disturbances. Similar design problems arise in non-cylindrical or 'mixed-flow' turbomachines as illustrated by Fig. 6.1. If the blades of a mixed-flow fan are designed to generate equal stagnation pressure rise Po2-Pol for all meridional streamlines, the swirl velocity co2 will obey the free-vortex law co2r= constant. In this case, as for cylindrical machines, the meridional flow (defined as the circumferential average or equivalent axisymmetric flow) and streamline pattern will be uninfluenced by the presence of the blades, Fig. 6.1(a). Should the designer depart from free-vortex swirl, on the other hand, the blades will produce tangential vorticity COowhich will cause meridional flow disturbances as illustrated by Fig. 6.1(b). c~ c~ ~3 ~2 ~'1 (a) ~0 (b) Fig. 6.1 Meridional streamlines in a mixed-flow fan: (a) meridional flow through empty annulus or with free-vortex .