Journal of Fluid Mechanics

Theoretical analysis of inertially irrotational and solenoidal flow in two-dimensional radial-flow pump and turbine impellers with equiangular blades

F. C.  Visser a1, J. J. H.  Brouwers a1 and R.  Badie a1
a1 Faculty of Mechanical Engineering, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

Article author query
visser fc   [Google Scholar] 
brouwers jj   [Google Scholar] 
badie r   [Google Scholar] 


Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radialflow pump and turbine impellers fitted with equiangular blades is analysed. Exact solutions are given for the fluid velocity along straight radial pump and turbine impeller blades, while for logarithmic spiral pump impeller blades solutions are given which hold asymptotically as (r1/r2)n[rightward arrow]0, in which r1 is impeller inner radius, r2 is impeller outer radius and n is the number of blades. Both solutions are given in terms of a Fourier series, with the Fourier coefficients being given by the (Gauss) hypergeometric function and the beta function respectively. The solutions are used to derive analytical expressions for a number of parameters which are important for practical design of radial turbomachinery, and which reflect the two-dimensional nature of the flow field. Parameters include rotational slip of the flow leaving radial impellers, conditions to avoid reverse flow between impeller blades, and conditions for shockless flow at impeller entry, with the number of blades and blade curvature as variables. Furthermore, analytical extensions to classical one-dimensional Eulerian-based expressions for developed head of pumps and delivered work of turbines are given.

(Published Online April 26 2006)
(Received April 1 1993)
(Revised December 18 1993)