Analysis of Radial Flow Reaction Turbines

Velocities at entrance (1) and exit (2) of vane on impeller: V = U + W where

V = the absolute fluid velocity measured in the inertial frame of reference

U = the velocity of the vane rotating about the z-axis

W = the velocity of the fluid relative to the vane

where e_r = unit vector in radial direction, e_t = unit vector in tangential direction

n₁= unit vector along vane at the entrance (attached to vane)

n₂ = unit vector along vane at the exit (attached to vane)

ω = absolute angular speed of impeller

r₁ = radius at entrance section of vane, r₂ = radius at exit section of vane

V₁ = absolute velocity of fluid striking the turbine at 1 at angle α₁

β₁ = angle of vane at entrance, β₂ = angle of vane at exit

At entrance 1: At exit 2:

U₁ = ˗ r₁ ω e_t U₂ = ˗ r₂ ω e_t

W₁ = ˗ w₁ n₁ W₂ = ˗ w₂ n₂

V₁ = ˗ V₁ cos α₁ e_t + ˗ V₁ sin α₁ e_r V₂ = ˗ r₂ ω e_t ˗ w₂ n₂