A one-equation turbulence model for aerodynamic flows

Nomenclature c = airfoil chord CL = lift coefficient = L/!/2pV00c CLu = upper-surface lift coefficient Cp = pressure coefficient = (p -p^)/ Ap Vx 2 Mx = freestream Mach number p = static pressure Re^ = freestream Reynolds number based on airfoil chord = V^clv sp = location of leading-edge stagnation point V^ — freestream velocity v local velocity on airfoil surface x = distance along chord line F = circulation about the airfoil 7 = ratio of specific heats v = kinematic viscosity p = density () oo = freestream conditions () t e = conditions at the airfoil trailing edge

Design of Subsonic Airfoils for High Lift

A brief review of the evolutionary progress in computational aerothermodynamics is presented. The current status of computational aerothermodynamics is then discussed, with emphasis on its capabilities and limitations for contributions to the design process of hypersonic vehicles. Some topics to be highlighted include: (1) aerodynamic coefficient predictions with emphasis on high temperature gas effects; (2) surface heating and temperature predictions for thermal protection system (TPS) design in a high temperature, thermochemical nonequilibrium environment; (3) methods for extracting and extending computational fluid dynamic (CFD) solutions for efficient utilization by all members of a multidisciplinary design team; (4) physical models; (5) validation process and error estimation; and (6) gridding and solution generation strategies. Recent experiences in the design of X-33 will be featured. Computational aerothermodynamic contributions to Mars Pathfinder, METEOR, and Stardust (Comet Sample return) will also provide context for this discussion. Some of the barriers that currently limit computational aerothermodynamics to a predominantly reactive mode in the design process will also be discussed, with the goal of providing focus for future research.

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Computational Aerothermodynamic Design Issues for Hypersonic Vehicles

The problem studied is that of designing a single element airfoil which provides the maximum possible lift in an unseparated incompressible flow. First, an airfoil velocity distribution is defined and optimized using boundary-layer theory and the calculus of variations. The resulting velocity distribution is then used as an input for an inverse airfoil design program which provides the corresponding airfoil shape. Since there is no guarantee that an arbitrarily defined velocity distribution will yield a physically possible airfoil shape, some parametric adjustments in the optimized distributions are required in order to obtain realistic and practical airfoil geometries. Wind-tunnel tests of two different airfoils (one assuming a laminar rooftop and the other a turbulent rooftop) have been conducted and in both cases the results met the theoretically predicted performance; for example, the laminar section exhibited a low drag range of CD — 0.0085 from CL - 0.8 to CL = 2.2.

A Class of Airfoils Designed for High Lift in Incompressible Flow

A method is presented for the automatic synthesis of minimum drag hull shapes for axisymmetric vehicles of specified enclosed volume and constant speed submerged in incompresible, nonseparating, noncavitating flow at zero incidence. The computer-oriented optimization procedure does not consider propulsion or maneuvering; drag reduction is accomplished solely through manipulation of the vehicle hull shape. The selected optimization formulation is a nongradient algorithm in a finite, constrained parameter space. This study considers an eight-parameter class of rounded-nose tailboom bodies constrained to be well behaved as determined by previous hydrodynamic experience. The drag model, for nonseparating flows at zero incidence, is based on classical hydrodynamics and consists of computer programs from work available in the literature; the model is representative of state-of-the-art drag prediction methods. By exploiting laminar flow while avoiding turbulent separation, a body with a drag coefficient one-third below the best existing laminar design has been obtained. The evidence suggests that the method produces realistic hull shapes useful in engineering design. The optimization procedure is independent of any particular drag model so that the effects on minimum drag shapes due to alternate drag models can be studied.

Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow

A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers

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A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers