3

Aerodynamic Considerations

35

Fig. 3.5 Schematic diagram of stream tube boundary

The actuator disc model is based on the following assumptions like no frictional

drag, homogeneous, incompressible, steady-state fluid flow and pressure variation

or thrust per unit area over the disc, continuity of velocity through the disc and the

infinite number of blades. The idealized actuator disc concept has been used by many

entomologists for understanding hovering in insects.

Applying conservation of linear momentum across the disc,

T = ˙m(U∞−Uw).

(3.17)

Applying energy balance across the disc using the Bernoulli equation

Pd + ¹

2^{ρU 2}

R ^{= Po + 1}

2^{ρU 2}

w^,

(3.18)

Po + ¹

2^{ρU 2}

∞^{= Po + 1}

2^{ρU 2}

R^.

(3.19)

By solving the above equations for thrust on the actuator disc, power output of the

rotor can be evaluated. Finally, performance parameters such as power coefficient

(CP), thrust coefficient (CT ) and the tip speed ratio (λ) of a rotating wing can be

expressed in a dimensionless form which are given as

CP =

2P

ρU ³∞π R^{2 ,}

(3.20)

CT =

2P

ρU ²∞π R^{2 ,}

(3.21)

λ = ^R

U∞

,

(3.22)

where