On the Approximated Expression of the Axial Perturbation Velocities in the Actuator Disc Theory

Extract

Fluid motion in an annulus is described, in the absence of radial velocity, by the simple radial equilibrium equation. This equation is used to describe the flow in an axial turbomachine some distance ahead and behind the rows of blades, where radial displacements have already decayed.

In the neighbourhood of and between the blades the fluid motion is far more complex than the flow in the radial equilibrium condition. Most of the difficulties of the real problem can be overcome by introducing the actuator disc mathematical model. The actuator disc divides the complex flow field into two simpler fields, each free from blades, i.e. a simple annulus. The equations of motion in each field are easily linearised by posing some particular restrictions concerning the velocity profiles and by conceiving the velocity as the sum of the radial equilibrium solution and of small perturbed quantities. These are radial and axial perturbation velocities vanishing far from the actuator disc, and are given by a perturbation velocity potential.