# Lift and drag in two-dimensional steady viscous and compressible flow

@article{Liu2015LiftAD,
title={Lift and drag in two-dimensional steady viscous and compressible flow},
author={L. Q. Liu and J. Y. Zhu and J. Z. Wu},
journal={Journal of Fluid Mechanics},
year={2015},
volume={784},
pages={304 - 341}
}
• Published 4 November 2015
• Engineering
• Journal of Fluid Mechanics
This paper studies the lift and drag experienced by a body in a two-dimensional, viscous, compressible and steady flow. By a rigorous linear far-field theory and the Helmholtz decomposition of the velocity field, we prove that the classic lift formula $L=-{\it\rho}_{0}U{\it\Gamma}_{{\it\phi}}$ , originally derived by Joukowski in 1906 for inviscid potential flow, and the drag formula $D={\it\rho}_{0}UQ_{{\it\psi}}$ , derived for incompressible viscous flow by Filon in 1926, are universally true…
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## References

SHOWING 1-10 OF 33 REFERENCES
Longitudinal–transverse aerodynamic force in viscous compressible complex flow
• L. Q. Liu
• Engineering
Journal of Fluid Mechanics
• 2014
Abstract We report our systematic development of a general and exact theory for diagnosis of total force and moment exerted on a generic body moving and deforming in a calorically perfect gas. The
A dynamic counterpart of Lamb vector in viscous compressible aerodynamics
• Physics, Engineering
• 2014
The Lamb vector is known to play a key role in incompressible fluid dynamics and vortex dynamics. In particular, in low-speed steady aerodynamics it is solely responsible for the total force acting
On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon’s paradox
• I. Imai
• Mathematics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1951
The asymptotic behaviour of flow at a considerable distance from an arbitrary cylindrical obstacle immersed in an otherwise uniform flow of an incompressible viscous fluid is considered on the basis
Interactions between a solid surface and a viscous compressible flow field
• Physics
Journal of Fluid Mechanics
• 1993
This paper presents a general theory and physical interpretation of the interaction between a solid body and a Newtonian fluid flow in terms of the vorticity ω and the compression/expansion variable
Problems in the Theory of Viscous Compressible Fluids
• Engineering
• 1949
The present study was suggested by several problems and difficulties that had appeared in previous experimental and theoretical investigations of viscosity effects in compressible fluids. The
The far–field Oseen velocity expansion
• Mathematics
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
• 1998
Consider uniform, steady, incompressible fluid flow in an unbounded domain past a fixed, closed body. In the far field the Oseen equations approximately hold. We give the Oseen velocity and pressure
Aerodynamic force by Lamb vector integrals in compressible flow
• Physics, Engineering
• 2014
A new exact expression of the aerodynamic force acting on a body in steady high Reynolds number (laminar and turbulent) compressible flow is proposed. The aerodynamic force is obtained by integration
The forces on a cylinder in a stream of viscous fluid
It has long been known that an infinite cylinder moving transversely with uniform velocity in a perfect liquid, or at rest in a uniform stream of such fluid, experiences no resistance if there be no
UNIQUENESS AND THE FORCE FORMULAS FOR PLANE SUBSONIC FLOWS
• Mathematics
• 1958
Introduction. The first proof of uniqueness of a plane subsonic flow of a compressible fluid past an obstacle was given by Bers [1]. This proof utilizes an elaborate mathematical apparatus
The Origin of Lift Revisited: I. A Complete Physical Theory
• Physics
• 2015
We revisit the theoretical basis and underlying physical mechanisms of the most fundamental problem in flight science — the origin of lift, confined to the simplest but most fundamental case for