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Can the Kutta Joukowski condition be derived from the Navier Stokes equations in the limit of vanishing viskosity?
Is there some literature on this point?
Is there some literature on this point?
vanhees71 said:Have a look at Wikipedia as a first introduction to the subject:
http://en.wikipedia.org/wiki/Kutta–Joukowski_theorem
The Kutta Joukowski condition is a fundamental principle in aerodynamics that states that the lift generated by an airfoil is directly proportional to the circulation around the airfoil and the airspeed. It is named after German mathematician Martin Wilhelm Kutta and Russian physicist Nikolai Zhukovsky, who independently derived the condition in the early 1900s.
The Kutta Joukowski condition can be derived by combining Bernoulli's equation and the conservation of circulation around an airfoil. This results in the well-known equation L = ρVΓ, where L is the lift, ρ is the air density, V is the airspeed, and Γ is the circulation. This equation shows the direct relationship between lift and circulation.
The Kutta Joukowski condition is significant because it provides a theoretical basis for understanding lift generation in airfoils. It also allows for the calculation of lift and other aerodynamic parameters for a wide range of airfoil shapes and operating conditions, making it a valuable tool in aircraft design and analysis.
Yes, there are some limitations to the Kutta Joukowski condition. It assumes that the flow around the airfoil is two-dimensional, inviscid, and incompressible. In reality, there are always some three-dimensional and viscous effects present in real-world aerodynamics. However, the Kutta Joukowski condition is still a useful approximation for many practical applications.
The Kutta Joukowski condition has numerous practical applications in aerodynamics, including the design and analysis of airfoils for aircraft wings, propellers, and turbines. It is also used in the development of mathematical models for predicting the performance of aircraft and other vehicles. Additionally, the Kutta Joukowski condition is used in wind tunnel testing and computational fluid dynamics simulations to study and improve the aerodynamic characteristics of various objects.