Lawrence L. Green

Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models

This workdiscussesan approach,e rst-orderapproximation and modelmanagementoptimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower-e delity, cheaper models in iterative procedures with occasional, but systematic, recourse to highere delity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is thatit is globally convergent to a solution oftheoriginal, high-e delity problem. VariantsofAMMObased on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing optimization problemand atwo-dimensionalairfoiloptimizationproblem. Euleranalysisonmeshesof varying degrees of ree nement provides a suite of variable-e delity models. Preliminary results indicate threefold savings in terms of high-e delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem.

Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi I-D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a firstand second-order statistical moment matching procedure is performed to approximate the uncertainly in the CFD output. Efficient calculation of both firstand second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving firstorder sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values. A a b b F g k M M Nomenclature nozzle area Minf geometric shape parameter Mt geometric shape parameter N vector of independent input variables Pb vector of CFD output functions Q vector of conventional optimization constraints q number of standard deviations qt Mach number at nozzle inlet R vector of Mach number at each grid point V Vt x (Y * LTC, US Army, Ph.D. Candidate, Department of Mechanical Engineering, mputko @ tabdemo.larc.nasa.gov tSenior Research Scientist, Muhidisciplinary Optimization Branch, M/S 159, p.a.newman@larc.nasa.gov -: Associate Professor, Deparlment of Mechanical Engineering, ataylor @lions.odu.edu §Research Scientist, Multidisciplinary Optimization Branch, M/S 159, AIAA senior member, l.l.grecn@larc.nasa.gov This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United Stales. free-stream Mach number target inlet Mach number sample size normalized nozzle static back (outlet) pressure vector of flow-field variables (state variables) mass flux through nozzle target mass flux through nozzle vector of state equation residuals nozzle volume target nozzle volume used for optimization normalized axial position within nozzle standard deviation variance

Automatic Differentiation of Advanced CFD Codes for Multidisciplinary Design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier- Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man- week) not O(man-year). DOE

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

Abstract 1.0 Introduction An efficient incremental-iterative approach for dif-ferentiating advanced flow codes is successfully demon-strated on a 2D inviscid model problem. The methodemploys the reverse-mode capability of the automatic-differentiation software tool ADIFOR 3.0, and isproven to yield accurate first-order aerodynamic sensi-tivity, derivatives. A substantial reduction in CPU timeand computer memory is demonstrated in comparisonwith results from a straight-forward, black-box t:everse-mode application of ADIFOR 3.0 to the same flowcode. An ADIFOR-assisted procedure for accurate sec-ond-order aerodynamic sensitivity derivatives is suc-cessfidly verified on an inviscid transonic lifting airfoilexample problem. The method requires that first-orderderivatives are calculated first using both the fonvard(direct) and reverse (adjoint) procedures; then, a veryefficient non-iterative calculation of all second-orderderivatives can be accomplished. Accurate second de-rivatives (Le., the complete Hessian matrices) of lift,wave-drag, and pitching-moment coefficients are calcu-lated with respect to geometric-shape, angle-of-attack,and freestream Mach numberComputing sensitivity derivatives (SDs) from high-fidelity, nonlinear CFD codes is an enabling technologyfor design of advanced concept vehicles. In recent yearssignificant progress has been achieved in the efficientcalculation of accurate SDs from these CFD codes _.-The automatic differentiation (AD) software toolADIFOR (Automatic Differentiation of FORTRAN)has been proven an effective tool for extracting aerody-namlc

Multidisciplinary design optimization techniques - Implications and opportunities for fluid dynamics research

A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MD0 is a methodology for the design of, complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASAlISSMO Symposia on Multidisciplinary Analysis and Optimization, the MD0 technical community focuses on vehicle and system design tissues. This paper provides an overview of the MD0 technology field from a fluid dynamics perspective, i

Towards a Credibility Assessment of Models and Simulations

iw emphasis to suggestions of specific applications of -recent ‘MD0 technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.

An Uncertainty Structure Matrix for Models and Simulations

*† ‡ § ** †† A scale is presented to evaluate the rigor of modeling and simulation (M&S) practices for the purpose of supporting a credibility assessment of the M&S results. The scale distinguishes required and achieved levels of rigor for a set of M&S elements that contribute to credibility including both technical and process measures. The work has its origins in an interest within NASA to include a “Credibility Assessment Scale” in development of a NASA standard for models and simulations.

Transonic wall interference assessment and corrections for airfoil data from the 0.3-meter TCT adaptive wall test section

Software that is used for aerospace flight control and to display information to pilots and crew is expected to be correct and credible at all times. This type of software is typically developed under strict management processes, which are intended to reduce defects in the software product. However, modeling and simulation (M&S) software may exhibit varying degrees of correctness and credibility, depending on a large and complex set of factors. These factors include its intended use, the known physics and numerical approximations within the M&S, and the referent data set against which the M&S correctness is compared. The correctness and credibility of an M&S effort is closely correlated to the uncertainty management (UM) practices that are applied to the M&S effort. This paper describes an uncertainty structure matrix for M&S, which provides a set of objective descriptions for the possible states of UM practices within a given M&S effort. The columns in the uncertainty structure matrix contain UM elements or practices that are common across most M&S efforts, and the rows describe the potential levels of achievement in each of the elements. A practitioner can quickly look at the matrix to determine where an M&S effort falls based on a common set of UM practices that are described in absolute terms that can be applied to virtually any M&S effort. The matrix can also be used to plan those steps and resources that would be needed to improve the UM practices for a given M&S effort.

Decision Support Methods and Tools

The wall interference assessment/correction code presented is nonlinear, involves four walls, and is applicable to transonic airfoil data from wind tunnels with shaped, solid top and bottom walls. Attention is given to its application to data from the NASA 0.3-m Transonic Cryogenic Tunnel Adaptive Test Section, for two sizes of a NACA 0012 airfoil and to simulated data for an inviscid two-dimensional full-potential code. This study indicates that while adaptive wall wind tunnels significantly reduce some aspects of wall-interference effects (by comparison to straight solid and slotted wall wind tunnels), residual wall and other interference effects are present.

Sensitivity Derivatives for Advanced CFD Algorithm and Viscous Modeling Parameters via Automatic Differentiation

This paper is one of a set of papers, developed simultaneously and presented within a single conference session, that are intended to highlight systems analysis and design capabilities within the Systems Analysis and Concepts Directorate (SACD) of the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC). This paper focuses on the specific capabilities of uncertainty/risk analysis, quantification, propagation, decomposition, and management, robust/reliability design methods, and extensions of these capabilities into decision analysis methods within SACD. These disciplines are discussed together herein under the name of Decision Support Methods and Tools. Several examples are discussed which highlight the application of these methods within current or recent aerospace research at the NASA LaRC. Where applicable, commercially available, or government developed software tools are also discussed.