Manuel D. Salas

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Some observations on grid convergence

It is claimed that current practices in grid convergence studies, particularly in the field of external aerodynamics, are flawed. The necessary conditions to properly establish grid convergence are presented. A theoretical model and a numerical example are used to demonstrate these ideas. It is shown that anomalously low or high observed convergence rates can be exhibited by otherwise well-behaved algorithms because of improper use of grid refinement ratios in different directions.

Digital Flight: The Last CFD Aeronautical Grand Challenge

A case is made for a computational fluid dynamics (CFD) effort to predict aircraft flight characteristics, with a focus on stability and control. Problems in predicting stability and control are discussed. The state-of-the-art in CFD, as it relates to aircraft flight predictions, is reviewed. Problems affecting grid convergence studies are analyzed. The computer resources needed to address flight simulation problems are estimated. The status of critical technologies is briefly discussed.

Recent developments in transonic Euler flow over a circular cylinder

Numerical solutions to the Euler equations for transonic flow over a circular cylinder indicate that the inviscid flow separates ahead of the rear stagnation point. Our understanding of this phenomenon and various solutions presented at a workshop on this subject are discussed.

Vortex breakdown simulation: a circumspect study of the steady, laminar, axisymmetric model

Abstract The incompressible, axisymmetric, steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order, central difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination and Newton iteration. Solutions are presented for Reynolds numbers based on vortex core radius ranging from 100 to 1800 and swirl parameter ranging from 0.9 to 1.1. The effects of inflow boundary conditions, location of farfield and outflow boundaries and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques. Previously announced in STAR as N82-28061

OPTIMUM TRANSONIC AIRFOILS BASED ON THE EULER EQUATIONS

We solve the problem of determining airfoils that approximate, in a least square sense, given surface pressure distributions in transonic flight regimes. The flow is modeled by means of the Euler equations and the solution procedure is an adjoint-based minimization algorithm that makes use of the inverse Theodorsen transform in order to parameterize the airfoil. Fast convergence to the optimal solution is obtained by means of the pseudo-time method. Results are obtained using three different pressure distributions for several free stream conditions. The airfoils obtianed have given a trailing edge angle.

ENTROPY JUMP ACROSS AN INVISCID SHOCK WAVE

The Shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure and shown to be the same, however, density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy propagation equation cannot be used as a conservation law.

Computational Electromagnetics and Its Applications

This publication documents the proceedings of the first Workshop on Computational Electromagnetics (CEM) and Applications, hosted by the Institute for Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center, Hampton, Virginia, 29-31 May, 1996, and attended by approximately 70 people from academia, government laboratories, and industry. ICASEs charter mission in 1972 remains today - to explore novel computer environments (vector in the 1970s; parallel in the 1990s) for scientific computing. These proceedings provide a necessary foundation for symposia in computational electromagnetics for future aerospace applications. The objectives of this CEM Workshop were to provide a forum for many of the leaders of the community to assess the state of CEM technology and to discuss areas of research for future programmatic planning activities. Workshop sessions included topics on optimization, industrial applications, algorithms, and a special panel session was provided during which issues were discussed and future research areas were identified. Hopefully, this publication will stimulate and improve communication among multidisciplinary researchers as well as highlighting several CEM areas that need improvement - especially for highly challenging problems. The two most important criteria in the selection of speakers for the workshop were their substantial contribution to large-scale CEM problems and their ability to articulate the issues confronting the CEM research community. Based on the results obtained, it is anticipated that this publication will be useful to government, industry, and university researchers to plan future research tasks in CEM analytical methods and applications.

Numerical analysis of viscous one-dimensional flows☆

Abstract The flow of a viscous, heat-conducting gas produced by an accelerating piston is analyzed numerically. The formation of a shock in a viscous flow is studied. A discussion of accuracy and practicality of a numerical analysis of the problem is given. It is concluded that, although very accurate results may be obtained, in principle, regardless of the Reynolds number of the flow, the assumption of a shock as a sharp discontinuity is the only practical way to handle flows whose Reynolds number per unit length is higher than 100.