Introduction E is an honor and challenge to present the Dryden Lecture ..i Research for 1979. Since my topic concerns a new trend in fluid mechanics, it should not be surprising that some aspects of this paper involve basic mechanics of turbulence, a field enriched by numerous contributions of Dr. Hugh L. Dryden. Having worked in related fields of fluid mechanics during past years, and long respected both his professional contributions and personal integrity, it is a special pleasure to present this Dryden lecture. The field of computational fluid dynamics during recent years has developed sufficiently to initiate some changes in traditional methods of aerodynamic design. Both computer power and numerical algorithm efficiency are simultaneously improving with time, while the energy resource for driving large wind tunnels is becoming progressively more valuable. Partly for these reasons it has been advocated that the impact of computational aerodynamics on future methods of aircraft design will be profound. ' Qualitatively, the changes taking place are not foreign to past experience in other fields of engineering. For example, trajectory mechanics and neutron transport mechanics already have been largely revolutionized by the computer. Computations rather than experiments now provide the principal source of detailed information in these fields. The amount of reactor experimentation required has been much reduced over former years; experiments now are performed mainly on clear, physically describable arrays of elements aimed at further confirmation of computational techniques; and better designs are achieved than with former experimental methods alone. Similar changes in the relative roles of experimental and computational aerodynamics are anticipated in the future. There are three compelling motivations for vigorously developing computational aerodynamics. One is to provide important new technological capabilities that cannot be provided by experimental facilities. Because of their fundamental limitations, wind tunnels have rarely been able to simulate, for example, Reynolds numbers of aircraft flight, flowfield temperatures around atmosphere entry vehicles, aerodynamics of probes entering planetary atmospheres, aeroelastic distortions present in flight, or the propulsiveexternal flow interaction in flight. In addition, transonic wind tunnels are notoriously limited by wall and support interference; and stream nonuniformities of wind tunnels severely affect laminar-turbulent transition. Moreover, the dynamic-aerodynamic interaction between vehicle motion in flight and transition-dependent separated flow also is inaccessible to wind-tunnel simulation. In still different ways ground facilities for turbomachinery experiments are limited in their ability, for example, to simulate flight inlet-flow nonuniformities feeding into a compressor stage, or to determine detailed flowfields between rotating blades. Numerical flow simulations, on the other hand, have none of these fundamental limitations, but have their own: computer speed and memory. These latter limitations are fewer, but previously have been much more restrictive overall because the full Navier-Stokes equations are of such great complexity that only highly truncated and approximate forms could be handled in the past. In recent years the Navier-Stokes equations have begun to yield under computational attack with the largest current computers. Since the fundamental limitations of computational speed and memory are rapidly decreasing with time, whereas the fundamental limitations of experimental facilities are not, numerical simulations offer the potential of mending many ills of wind-tunnel and turbomachinery experiments, and of providing thereby important new technical capabilities for the aerospace industry. A second compelling motivation concerns energy conservation. The large developmental wind tunnels require large amounts of energy, whereas computers require comparatively

Computational Aerodynamics Development and Outlook

Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review

For three-dimensional fluid flows in complex geometries, it is convenient to make predictions using a non-orthogonal boundary-fitted mesh. The present paper describes an economical method of solving the equations of motion for two and three dimensional problems using such meshes. The locations on the mesh at which the depenent variables are calculated, and the methods used to solve the equations, are key issues in the development of a successful algorithm; these are discussed in the present paper. Results obtained when the proposed method is applied to several problems are also described. The method is intended for flows in which compressibility effects do not dominate.

A method for computing three dimensional flows using non‐orthogonal boundary‐fitted co‐ordinates

FLOW visualization and near-surface hot-wire experiments were performed in the U.S.A.F Academy Aeronautics Laboratory subsonic wind tunnel on an airfoil undergoing large-amplitude pitching motions about its quarter chord. The experiments were conducted using a NACA 0015 airfoil at an airfoil Reynolds number of 45,000. Two cases are presented in which the angular pitching rate a is maintained constant during the motion. These two cases represent two different nondimensional pitching rates a+, where ot+ is equal to 6; nondimensionalized by the chord c and the freestream velocity U^ (a + ^ac/U^). Data for the two cases where values of a+ are equal to 0.2 and 0.6 show the dramatic effect of pitch rate on flow structure. Largescale vortical structures are seen in both cases at high angles of attack but appear much later and are of a different form for the case with the larger a+ value. These structures are very energetic, producing reverse flow velocities near the airfoil surface of 1.0-2.1 times the freestream velocity.

An Experimental Investigation of an Airfoil Undergoing Large-Amplitude Pitching Motions

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Implicit Algorithm for the Conservative Transonic Full-Potential Equation Using an Arbitrary Mesh

Boundary-fitted curvilinear coordinate systems are optimized for viscous flows about arbitrary airfoils at angles of attack such that boundary-layer-dependent grid systems for high Reynolds numbers are generated efficiently. The grid systems are utilized in implicit finite-difference solutions. Solution of a one-dimensional model equation is compared with the theoretical solution. The unsteady Navier-Stokes equations are solved for the incompressible flow around a cylinder and around NACA airfoils approaching stall. The predicted flows around a NACA 6412 airfoil near stall at Reynolds numbers of 4x 10 and 2x 10 are compared with the experimental observations obtained in a smoke tunnel.

Thomas E. Miller

Papers

Numerical Solution for Airfoils near Stall in Optimized Boundary-Fitted Curvilinear Coordinates