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24 SCIENTIFIC BULLETIN OF THE POLITEHNICA ± UNIVERSITY OF TIMISOARA Transactions on MECHANICS Tom 50 (64) Fascicola 2, 2005 ABOUT DESIGN OPTIMIZATION OF CROSS-FLOW HIDRAULIC TURBINES M. B Ǎ RGL Ǎ ZAN Politehnica ± University from Timi oara, B-ul Mihai Viteazul nr.1 Timi Abstract: In the present paper there are established the optima values for some geometric parameters of the cross-flow hydraulic turbine. This research is focused on the main machine elements of the turbine, namely, the radial runner and the supply nozzle. Also an automated design of the cross-flow hydraulic turbines is obtained through dedicated soft (programs) in which some parameters could be chosen and a lot of other parameters are calculated. Key wo0rds : hydraulic turbines, cross-flow turbines, Banki turbines, design and operation optimization. 1. Nomenclature. u ² tangential velocity v ² absolute velocity w ² relative velocity ² angle between u and v ± -angle between ² u and w b ² hydrodynamic runner width s ² distance between two neighbor runner blades g ² gravitational acceleration H T ² hydraulic turbine ³ s head ² h ² hydraulic efficiency k v1 ² absolute velocity entrance coefficient v u - absolute velocity ³ s projection on tangential velocity k ² nozzle exit transversal extension coefficient s 0 = k D 1 2. Introduction Nowadays between sustainable development of renewable sources of energy the hydro-energy plays an important and crucial role. Because usually the great hydropower plants are already built it remains to harness the medium and small hydropower sources. Among the different types of hydraulic turbines, the cross-flow type is a real option and viable solution from technical ² economical point of view. The cross-flow hydraulic turbines (CFHT) consist from two main hydrodynamic machine elements namely the runner and the nozzle. The CFHT is in almost all regimes of operation an impulse wheel machine. CFHT has the peculiarity that, like the Pelton hydraulic turbine, there is no connection between the rate of flow of the hydraulic turbine and the rotational speed of the runner but the width of the runner is a function of the rate of flow through the CFHT. In operation the runner is only partially immersed in water, every inter-blade channel, twice in a complete rotation of the runner. The runner has, an overall given geometry, the shape of a cylindrical annuls in which are inserted the blades. The nozzle ² conducting the water to the runner ² is a convergent pipe with rectangular cross section and with two plane parallel fixed walls and the other two walls in the shape of cylinder with evolute or spiral logarithmic generation curve (one of them sometimes mobile). 2.
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