2 Aerodynamics
89
Fig. 2.16 The law of lifting circulation of Kutta–Joukowsky
Kutta and Joukowsky’s law of lift circulation (as shown in Fig. 2.16), namely
L = ρV ∞
where L is the lift acting on the object, ρ is the air density of the inflow, V ∞ is
the velocity of the inflow, and is the velocity circulation around the object.
When different circulation values bypass the airfoil, there may be three
different flow pictures of the rear stagnation point located on the upper
wing surface, the lower wing surface, and the trailing edge point. When the
rear stagnation point is located on the upper and lower wing surfaces, the
airflow should bypass the trailing edge of the tip. According to the potential flow theory, there will be infinite velocity and negative pressure there,
which is physically impossible. Therefore, the possible flow picture in physics
is that the stagnation point coincides with the trailing edge point, or the
airflow smoothly flows through the trailing edge of the airfoil from the
upper and lower wing surfaces, and the velocity value of the trailing edge
remains limited. The flow experiment also confirms this analysis. Kutta and
Joukowsky use this condition to give the unique condition for determining
the attached circulation.
According to Kelvin’s law of conservation, for an ideal incompressible fluid,
under the action of a potential force, the velocity circulation around the
closed circumference composed of the same fluid particles does not change
with time, i.e., d/dt = 0. All airfoils accelerate from static state to steady
state. According to the law of vortex conservation, the circulation of velocity
caused by airfoil motion should be zero everywhere as in the static state, but
a non-zero circulation value is obtained by the Kutta condition, which is a
contradiction. How to understand the physical cause of circulation?
89
Fig. 2.16 The law of lifting circulation of Kutta–Joukowsky
Kutta and Joukowsky’s law of lift circulation (as shown in Fig. 2.16), namely
L = ρV ∞
where L is the lift acting on the object, ρ is the air density of the inflow, V ∞ is
the velocity of the inflow, and is the velocity circulation around the object.
When different circulation values bypass the airfoil, there may be three
different flow pictures of the rear stagnation point located on the upper
wing surface, the lower wing surface, and the trailing edge point. When the
rear stagnation point is located on the upper and lower wing surfaces, the
airflow should bypass the trailing edge of the tip. According to the potential flow theory, there will be infinite velocity and negative pressure there,
which is physically impossible. Therefore, the possible flow picture in physics
is that the stagnation point coincides with the trailing edge point, or the
airflow smoothly flows through the trailing edge of the airfoil from the
upper and lower wing surfaces, and the velocity value of the trailing edge
remains limited. The flow experiment also confirms this analysis. Kutta and
Joukowsky use this condition to give the unique condition for determining
the attached circulation.
According to Kelvin’s law of conservation, for an ideal incompressible fluid,
under the action of a potential force, the velocity circulation around the
closed circumference composed of the same fluid particles does not change
with time, i.e., d/dt = 0. All airfoils accelerate from static state to steady
state. According to the law of vortex conservation, the circulation of velocity
caused by airfoil motion should be zero everywhere as in the static state, but
a non-zero circulation value is obtained by the Kutta condition, which is a
contradiction. How to understand the physical cause of circulation?