TY - JOUR
T1 - Theoretical analysis of inertially irrotational and solenoidal flow in two-dimensional radial-flow pump and turbine impellers with equiangular blades
AU - Visser, F.C.
AU - Brouwers, J.J.H.
AU - Badie, R.
PY - 1994
Y1 - 1994
N2 - Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radial-flow 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 [Arrow Right] 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.
AB - Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radial-flow 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 [Arrow Right] 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.
U2 - 10.1017/S0022112094001503
DO - 10.1017/S0022112094001503
M3 - Article
SN - 0022-1120
VL - 269
SP - 107
EP - 141
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -