Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex un...Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex unsteady control volumes, and show the close relationship between a single aerofoil and an infinite cascade. The modification of lift due to the presence of another lifting body is similarly derived for a wing in ground effect, a biplane, and tandem aerofoils. The results are identical to those derived from the vector form of the Kutta-Joukowsky equation.展开更多
The Kutta Joukowski(KJ) theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. However, this theorem was only prov...The Kutta Joukowski(KJ) theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. However, this theorem was only proved for inviscid flow and it is thus of academic importance to see whether there is a viscous equivalent of this theorem. For lower Reynolds number flow around objects of small size, it is difficult to measure the lift force directly and it is thus convenient to measure the velocity flow field solely and then, if possible, relate the lift to the circulation in a similar way as for the inviscid KJ theorem. The purpose of this paper is to discuss the relevant conditions under which a viscous equivalent of the KJ theorem exists that reduces to the inviscid KJ theorem for high Reynolds number viscous flow and remains correct for low Reynolds number steady flow. It has been shown that if the lift is expressed as a linear function of the circulation as in the classical KJ theorem, then the freestream velocity must be corrected by a component called mean deficit velocity resulting from the wake. This correction is small only when the Reynolds number is relatively large. Moreover, the circulation, defined along a loop containing the boundary layer and a part of the wake, is generally smaller than that based on inviscid flow assumption. For unsteady viscous flow, there is an inevitable additional correction due to unsteadiness.展开更多
This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is ne...This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.展开更多
文摘Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex unsteady control volumes, and show the close relationship between a single aerofoil and an infinite cascade. The modification of lift due to the presence of another lifting body is similarly derived for a wing in ground effect, a biplane, and tandem aerofoils. The results are identical to those derived from the vector form of the Kutta-Joukowsky equation.
基金supported by the National Natural Science Foundation of China(Grant No.11472157)the National Basic Research Program of China(Grant No.2012CB720205)
文摘The Kutta Joukowski(KJ) theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. However, this theorem was only proved for inviscid flow and it is thus of academic importance to see whether there is a viscous equivalent of this theorem. For lower Reynolds number flow around objects of small size, it is difficult to measure the lift force directly and it is thus convenient to measure the velocity flow field solely and then, if possible, relate the lift to the circulation in a similar way as for the inviscid KJ theorem. The purpose of this paper is to discuss the relevant conditions under which a viscous equivalent of the KJ theorem exists that reduces to the inviscid KJ theorem for high Reynolds number viscous flow and remains correct for low Reynolds number steady flow. It has been shown that if the lift is expressed as a linear function of the circulation as in the classical KJ theorem, then the freestream velocity must be corrected by a component called mean deficit velocity resulting from the wake. This correction is small only when the Reynolds number is relatively large. Moreover, the circulation, defined along a loop containing the boundary layer and a part of the wake, is generally smaller than that based on inviscid flow assumption. For unsteady viscous flow, there is an inevitable additional correction due to unsteadiness.
文摘This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.
