CFD Online Discussion Forums - anyone has got this paper?

American Institute of Aeronautics and Astronautics 1 WING DRAG PREDICTION AND DECOMPOSITION D.D. Chao* and C.P. van Dam** University of California, Davis Abstract This paper presents the status of current research into using wake integration to predict the aerodynamic characteristics of three-dimensional wings in viscous subsonic and transonic flows. Results indicate that wake integration is viable as a method of drag prediction, and compared to surface integration, has the added benefit of being able to provide a decomposition of the total drag into its physical components of profile, induced, and wave drag for a wing in viscous, transonic flow. Future work will involve using wake integration to post process the flow information around more complex configurations for which this study provides a sound basic framework. Nomenclature ∞ subscript; denotes freestream conditions Λ wing sweep angle Î" total circulation α angle of attack αi induced angle of attack ξ x-component of vorticity ψ streamfunction τ viscous stress ρ density H total enthalpy M∞ freestream Mach number R universal gas constant T temperature [ ] T stress tensor ∞ U freestream velocity V r velocity vector b wing span h enthalpy nr normal vector p pressure q velocity magnitude rr position vector s entropy x, y, z Cartesian coordinates * Post Doctoral Researcher, Department of Mechanical and Aeronautical Engineering ** Professor, Department of Mechanical and Aeronautical Engineering Copyright ©2004 by D.D. Chao and C.P. van Dam. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Introduction The aerodynamic drag of a transport aircraft flying at transonic speeds can be separated into viscous (or profile) drag, induced drag, and wave drag. Viscous drag consists of skin friction and form drag and is generated through the action of viscosity within the boundary layer. Induced drag is the result of the shedding of vorticity that accompanies the production of lift. Wave drag arises from the radiation of energy away from the aircraft in the form of pressure waves. Accurate prediction of the drag during the various stages of the development process of an aircraft is of importance to the efficiency of this process as well as to the economic success of the aircraft. Additionally, knowledge about the physical components of the drag is of importance to the prediction of scale effects on aircraft drag. The most common technique to calculate the drag of an airfoil, wing or complete configuration is based on the integration of the pressure and shear stress acting on the surface of the configuration. This so-called near-field technique can lead to inaccuracies in the drag calculation as illustrated in Fig. 1. In Fig. 1 the surface pressure is plotted as a function of the vertical surface coordinate for a typical airfoil at incompressible conditions. -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.04 -0.02 0 0.02 0.04 0.06 Upper surface Lower surface C p z/c Drag Thrust Thrust Trailing edge Leading edge Fig. 1 Pressure distribution as a function of vertical surface coordinate for a cambered airfoil at zero angle of attack. From this figure it is clear that determining the formdrag contribution to the total drag from surface integration involves subtraction of a large force component in the thrust direction from a slightly larger force component in the drag direction. Thus 22nd Applied Aerodynamics Conference and Exhibit 16 - 19 August 2004, Providence, Rhode Island AIAA 2004-5074 Copyright © 2004 by D.D. Chao and C.P. van Dam. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.