A two-dimensional aerofoil section of chord and thickness is tested in an air stream…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Separation, wakes, jets and free shear flows

Problem

A two-dimensional aerofoil section of chord

c = 1.0\,\mathrm{m}

and

12\%

thickness is tested in an air stream (

\rho = 1.20\,\mathrm{kg\,m^{-3}}

) at

U = 40\,\mathrm{m\,s^{-1}}

and angle of attack

\beta = 6^\circ

, well below its stalling angle. A Pitot rake traversed two chords behind the trailing edge, where the static pressure has recovered to the free-stream value, gives the velocity deficit

U - u

across the wake: Data (

y

in cm from the wake centre,

U-u

\mathrm{m\,s^{-1}}

(-3,\,0)

(-2,\,1.33)

(-1,\,2.67)

(0,\,4.00)

(1,\,2.67)

(2,\,1.33)

(3,\,0)

. ((a)) Use thin-aerofoil theory to estimate the lift per unit span. ((b)) Use the tabulated wake data and the momentum-deficit relation to estimate the profile drag per unit span (use the trapezoidal rule with the seven tabulated points). ((c)) Find the lift-to-drag ratio and comment on whether this is consistent with

6^\circ

being well below the stalling angle (about

15^\circ

for a

12\%

section).

Browse the problem library