On the concept and theory of induced drag for viscous and incompressible steady flow

• Published in: Physics of fluids (1994) Vol. 31; no. 6
• Main Authors: Zou, Shu-Fan, Wu, J. Z., Gao, An-Kang, Liu, Luoqin, Kang, Linlin, Shi, Yipeng
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.06.2019
• Subjects: Aircraft; Aircraft industry; Computational fluid dynamics; Fields (mathematics); Flow separation; Fluid dynamics; Fluid flow; Incompressible flow; Induced drag; Integrals; Numerical dissipation; Physics; Steady flow; Theory; Viscous flow
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5090165

For steady flow, one usually decomposes the total drag into different components by wake-plane integrals and seeks their reduction strategies separately. Unlike the body-surface stress integral, the induced drag as well as the profile drag has been found to depend on the streamwise location of the wake plane used for drag estimate. It gradually diminishes as the wake plane moves downstream, which was often attributed to numerical dissipation. In this paper, we present an exact general force-breakdown theory and its numerical demonstrations for viscous incompressible flow over an arbitrary aircraft to address this puzzling issue. Based on the theory, the induced and profile drags do depend inherently on the wake-plane location rather than being merely caused by numerical dissipation. The underlying mechanisms are identified in terms of the components, moments, and physical dissipation of the Lamb-vector field produced by the aircraft motion. This theoretical prediction is fully consistent with the linear far-field force theory that the induced drag finally vanishes and the profile drag increases to the total drag at an infinitely far field for viscous flow. Moreover, as a product of this exact theory, a new compact midwake approximation for the induced drag is proposed for the convenience of routine wake survey in industry. Its prediction is similar to conventional formulas for attached flow but behaves much better for separated flow.