if m be the indefinite but large mass flow in the wind, and actuator disk is placed
m perpendicular to the flow direction of wind, exerts a finite axial force is Dax, in this picture below no external force acts on the flow, so momentum is conserved and the flow does not expand further.
The velocity change obtained from the momentum relation is connected to the change of the kinetic power in the wind, by use this formula
at this is the formula that use to describe change of the kinetic power in the flow due to the axial force when the outer flow is included
Where :
A(delta)P is : the change of the kinetic power in the flow in the stream tube when it crosses the actuator disk
m : large mass flow in the wind
U : is velocity of wind until little past actuator boundary (see picture above)
V : is velocity of wind after fake boundary (see pincture)
Dax : Finite axial force
a : constant value from dynamic pressure function is 16/27 or 1/3
e : is fraction flows trough the stream tube
Aerodynamics of Horizontal-Axis Wind Turbines
To study the aerodynamics of wind turbines some knowledge of fluid dynamics in general is necessary and, in particular, aircraft aerodynamics, we can use Bernoulli theorem for steady, incom pressible flow is required together with the concept of continuity, and then use The Biot亡avart law, which will be familiar to those with a knowledge of electric and magnetic fields, is used to determine velocities induced by vortices
Aerodynamics of Horizontal-Axis Wind Turbines
As the air passes through the rotor disc, by design, there is a drop in static pressure such that, on leaving, the air is below the atmospheric pressure level. The air then proceeds downstream with reduced speed and static pressure ・this region
of the flow is called the wake. Eventually, far downstream, the static pressure in the wake must return to the atmospheric level for equilibrium to be achieved. The rise in static pressure is at the expense of the kinetic energy and so causes a further slowing down of the wind. Thus, between the far upstream and far wake conditions, no changein static pressure exists but there is a reduction in kinetic energy.
