Determination of Drag From Three-Dimensional Viscous and Inviscid Flowfield Computations

A momentum balance approach is used to extract the drag from flowfield computations for wings and wing/bodies in subsonic/transonic flight. The drag is decomposed into vorticity, entropy, and enthalpy components which can be related to the established engineering concepts of induced drag, wave and profile drag, and engine power and efficiency. This decomposition of the drag is useful in formulating techniques for accurately evaluating drag using computational fluid dynamics calculations or experimental data. A formulation for reducing the size of the region of the crossflow plane required for calculating the drag is developed using cut-off parameters for viscosity and entropy. This improves the accuracy of the calculations and decreases the computation time required to obtain the drag results. The improved method is applied to a variety of wings, including the M6, W4, and Ml65 wings, Lockheed Wing A, a NACA 0016 wing, and an Elliptic wing. The accuracy of the resulting drag calculations is related to various computational aspects, including grid type (structured or unstructured), grid density, flow regime (subsonic or transonic), boundary conditions, and the level of the governing equations (Euler or Navier-Stokes). The results show that drag prediction to within engineering accuracy is possible using computational fluid dynamics, and that numerical drag optimization of complex aircraft configurations is possible. * Project Supervisor, CFD Research Group, email: [email protected]. Member AIAA. t Professor, Aeronautical Engineering Department, email: [email protected]. Associate Fellow, AIAA. $ Rolls-Royce Reader in CFD, email: [email protected]. Member AIAA. Copyright © 1997 by D.L. Hunt, R.M. Cummings, and M.B. Giles. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Introduction As computational fluid dynamics (CFD) has matured over recent years, it has become a goal of CFD researchers to be able to predict aerodynamic drag from numerical simulations. Early attempts at accomplishing this were usually met with frustration, as most approaches involved integrating the pressure and skin friction over the surface of the body in order to calculate forces (the computational equivalent of force measurements in wind tunnels). Surface integration has met with difficulties, however, due to the need to approximate the curved surfaces of the body with flat facets. Calculation of the pressure and skin friction at the surface is also difficult at times. This has led various researchers to look at the experimental wake integral methods of Betz [1], Maull and Bearman [13], Maskell [11], Wu et al [22], and Brune and Bogataj [2], and to attempt to apply them to CFD computations. A good survey of drag computations methods was recently prepared by Takahashi [16] and may be useful to future researchers in understanding the uses and limitations of the experimental approaches. Computational methods involving wake integration have been shown to be reasonably accurate at predicting profile and vortex drag, as shown by van Dam and Nikfetrat [20], Chatterjee and Janus [4], and Van Der Vooren and Sloof [21]. An equivalent lifting-line approach by Mathias et al [12] has also been shown to be able to accurately compute induced drag. A reformulation of the momentum balance equations for lift and drag has shown that near-field calculations could be performed which were as accurate as the traditional far-field analysis methods [6]. These improved integral relations need to be validated and applied to a variety of cases, including both Euler and Navier-Stokes computations, in order to determine the effect of the numerical approach on the accuracy of the drag extraction. Various contributing factors, such as the type of grid (structured or unstructured), the grid density in the wake region, the flow regime (subsonic or transonic), boundary conditions, outer boundary distances from the body, and the level of the governing equations (Euler or Navier-Stokes) need to be evaluated for their influence on the accuracy of the drag estimation. Once methods are developed which will make accurate drag calculations possible, then these procedures can be applied to design optimization algorithms which can be used to reduce the total drag of full configurations (including wings, bodies, and engine nacelles), including power effects. It will then be possible to optimally design an aircraft for overall reductions in total drag.