Unified Theoretical Foundations of Lift and Drag in Viscous and Compressible External Flows by Luo-Qin Liu

Author:Luo-Qin Liu
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

3.1.2 Far-Field Force Theory in Three Dimensions

The corresponding incompressible problem in three dimensions has been treated in two papers by Goldstein [4, 5], who followed Filon [3] to apply the Oseen approximation at a great distance from the solid. In his first paper Goldstein [4] discussed two series of solutions of the equations, which corresponds exactly to the longitudinal velocity and the transversal velocity given by (3.1.1). The first series yields a set of particular integrals of the longitudinal field (see (3.3.11a) below), in which the longitudinal velocities are associated with certain values of the pressure. In the second series, which is a set of particular integrals of the transverse field (see (3.3.11b) below) and of the nature of a complementary function, the velocities are rotational, while the pressure does not appear. Thus, Filon’s drag formula (3.1.10) is shown to still hold for 3D incompressible flow, where the transversal inflow is equivalent to the longitudinal outflow,

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