This article outlines some of the principal issues in the development of numerical methods for the prediction of flows over aircraft and their use in the design process. These include the choice of an appropriate mathematical model, the design of shock-capturing algorithms, the treatment of complex geometric configurations, and shape modifications to optimize the aerodynamic performance.

/pdf/computational-aerodynamics-for-aircraft-design-2my12h8sny.pdf

Computational Aerodynamics for Aircraft Design

▪ Abstract Modern helicopter aerodynamics is challenging because the flow field generated by a helicopter is extremely complicated and difficult to measure, model, and predict; moreover, experiments are expensive and difficult to conduct. In this article we discuss the basic principles of modern helicopter aerodynamics. Many sophisticated experimental and computational techniques have been employed in an effort to predict performance parameters. Of particular interest is the structure of the rotor wake, which is highly three-dimensional and unsteady, and the rotor-blade pressure distribution, which is significantly affected by the strength and position of the wake. We describe the various modern methods of computation and experiment which span the range from vortex techniques to full three-dimensional Navier-Stokes computations, and from classical probe methods to laser velocimetry techniques. Typical results for the structure of the wake and the blade pressure distribution in both hover and forward fligh...

Modern helicopter aerodynamics

A practical design method is presented for three-dimensional transonic wings with prescribed pressure distributions. The method is based on an iterative "residual-correction" concept. The residual, defined as the difference between the computed and the prescribed pressure distributions at each iteration step, is determined by the use of an existing direct analysis code for a transonic wing with or without the body. The wing geometry correction to compensate for the residual can be approximately obtained from the inverse solution code developed in the present study. The inverse (correction) problem is mathematically reduced to a Dirichlet boundary value problem that is solved here by the aid of the transonic integral equation method. Some of the design results are also presented for transonic swept wings.

Iterative three-dimensional transonic wing design using integral equations

Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.

Design of supercritical swept wings

Multiobjective Genetic Algorithm for Multidisciplinary Design of Transonic Wing Planform

A numerical method is presented for analyzing the transonic potential flow past a lifting, swept wing. A finite-difference approximation to the full potential equation is solved in a coordinate system which is nearly conformally mapped from the physical space in planes parallel to the symmetry plane, and reduces the wing surface to a portion of one boundary of the computational grid. A coordinate invariant, rotated difference scheme is used, and the difference equations are solved by relaxation. The method is capable of treating wings of arbitrary planform and dihedral, although approximations in treating the tips and vortex sheet make its accuracy suspect for wings of small aspect ratio. Comparisons of calculated results with experimental data are shown for examples of both conventional and supercritical transport wings. Agreement is quite good for both types, but it was found necessary to account for the displacement effect of the boundary layer for the supercritical wing, presumably because of its greater sensitivity to changes in effective geometry.

/pdf/numerical-calculation-of-the-transonic-flow-past-a-swept-3g4cfrh2f9.pdf

Numerical calculation of the transonic flow past a swept wing. [FLO 22]

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Numerical calculation of the transonic flow past a swept wing. [FLO 22]