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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Robust Airfoil Optimization in High Resolution Design Space

The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of B-spline control points as design variables yet the resulting airfoil shape is fairly smooth, and (3) it allows the user to make a trade-off between the level of optimization and the amount of computing time consumed. The robust optimization method is demonstrated by solving a lift-constrained drag minimization problem for a two-dimensional airfoil in viscous flow with a large number of geometric design variables. Our experience with robust optimization indicates that our strategy produces reasonable airfoil shapes that are similar to the original airfoils, but these new shapes provide drag reduction over the specified range of Mach numbers. We have tested this strategy on a number of advanced airfoil models produced by knowledgeable aerodynamic design team members and found that our strategy produces airfoils better or equal to any designs produced by traditional design methods.

Li, Wu↗
NASA NTRS1985

TRO-2D - A code for rational transonic aerodynamic optimization

Features and sample applications of the transonic rational optimization (TRO-2D) code are outlined. TRO-2D includes the airfoil analysis code FLO-36, the CONMIN optimization code and a rational approach to defining aero-function shapes for geometry modification. The program is part of an effort to develop an aerodynamically smart optimizer that will simplify and shorten the design process. The user has a selection of drag minimization and associated minimum lift, moment, and the pressure distribution, a choice among 14 resident aero-function shapes, and options on aerodynamic and geometric constraints. Design variables such as the angle of attack, leading edge radius and camber, shock strength and movement, supersonic pressure plateau control, etc., are discussed. The results of calculations of a reduced leading edge camber transonic airfoil and an airfoil with a natural laminar flow are provided, showing that only four design variables need be specified to obtain satisfactory results.

Davis, W. H., Jr.↗
NASA NTRS1990

Multi-disciplinary optimization of aeroservoelastic systems

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Karpel, Mordechay↗
NASA NTRS1992

Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Karpel, Mordechay↗
NASA NTRS2004

Probabilistic Aeroelastic Analysis of Turbomachinery Components

A probabilistic approach is described for aeroelastic analysis of turbomachinery blade rows. Blade rows with subsonic flow and blade rows with supersonic flow with subsonic leading edge are considered. To demonstrate the probabilistic approach, the flutter frequency, damping and forced response of a blade row representing a compressor geometry is considered. The analysis accounts for uncertainties in structural and aerodynamic design variables. The results are presented in the form of probabilistic density function (PDF) and sensitivity factors. For subsonic flow cascade, comparisons are also made with different probabilistic distributions, probabilistic methods, and Monte-Carlo simulation. The approach shows that the probabilistic approach provides a more realistic and systematic way to assess the effect of uncertainties in design variables on the aeroelastic instabilities and response.

Reddy, T. S. R.↗
NASA NTRS1993

Optimal design of composite hip implants using NASA technology

Using an adaptation of NASA software, we have investigated the use of numerical optimization techniques for the shape and material optimization of fiber composite hip implants. The original NASA inhouse codes, were originally developed for the optimization of aerospace structures. The adapted code, which was called OPORIM, couples numerical optimization algorithms with finite element analysis and composite laminate theory to perform design optimization using both shape and material design variables. The external and internal geometry of the implant and the surrounding bone is described with quintic spline curves. This geometric representation is then used to create an equivalent 2-D finite element model of the structure. Using laminate theory and the 3-D geometric information, equivalent stiffnesses are generated for each element of the 2-D finite element model, so that the 3-D stiffness of the structure can be approximated. The geometric information to construct the model of the femur was obtained from a CT scan. A variety of test cases were examined, incorporating several implant constructions and design variable sets. Typically the code was able to produce optimized shape and/or material parameters which substantially reduced stress concentrations in the bone adjacent of the implant. The results indicate that this technology can provide meaningful insight into the design of fiber composite hip implants.

Blake, T. A.↗
NASA NTRS1988

Aeroelastic optimization of a helicopter rotor

Structural optimization of a hingeless rotor is investigated to reduce oscillatory hub loads while maintaining aeroelastic stability in forward flight. Design variables include spanwise distribution of nonstructural mass, chordwise location of blade center of gravity and blade bending stiffnesses (flap, lag and torsion). A comprehensive aeroelastic analysis of rotors, based on a finite element method in space and time, is linked with optimization algorithms to perform optimization of rotor blades. Sensitivity derivatives of blade response, hub loads, and eigenvalues with respect to the design variables are derived using a direct analytical approach, and constitute an integral part of the basic blade response and stability analyses. This approach reduces the computation time substantially; an 80 percent reduction of CPU time to achieve an optimum solution, as compared to the widely adopted finite difference approach. Through stiffness and nonstructural mass distributions, a 60-90 percent reduction in all six 4/rev hub loads is achieved for a four-bladed soft-inplane rotor.

Lim, Joon W.↗
NASA NTRS1991

Aerodynamic shape optimization using sensitivity analysis on third-order Euler equations

Two major advancements of an aerodynamic optimization method with two design variables are described. The first is represnted by an improved flow prediction method that uses the third-order accurate discretization of the Euler equations. This method makes it possible to predict the flowfield of a perturbed shape which generates shocks and other large gradients without intermediate CFD analysis. The second advancement is the use of every surface grid point as a design variable in the aerodynamic shape optimization problem. The improved algorithm is demonstrated by optimizing the ramp shape of a scramjet-afterbody configuration for maximum axial thrust. It is concluded that the improved flow-field prediction method eliminates most of the flow analysis and a priori guessing of all possible shapes from which the optimum is to be selected.

Baysal, Oktay↗
NASA NTRS2002

Options for Robust Airfoil Optimization under Uncertainty

A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.

Padula, Sharon L.↗
NASA NTRS1995

An integrated optimum design approach for high speed prop rotors

The objective is to develop an optimization procedure for high-speed and civil tilt-rotors by coupling all of the necessary disciplines within a closed-loop optimization procedure. Both simplified and comprehensive analysis codes are used for the aerodynamic analyses. The structural properties are calculated using in-house developed algorithms for both isotropic and composite box beam sections. There are four major objectives of this study. (1) Aerodynamic optimization: The effects of blade aerodynamic characteristics on cruise and hover performance of prop-rotor aircraft are investigated using the classical blade element momentum approach with corrections for the high lift capability of rotors/propellers. (2) Coupled aerodynamic/structures optimization: A multilevel hybrid optimization technique is developed for the design of prop-rotor aircraft. The design problem is decomposed into a level for improved aerodynamics with continuous design variables and a level with discrete variables to investigate composite tailoring. The aerodynamic analysis is based on that developed in objective 1 and the structural analysis is performed using an in-house code which models a composite box beam. The results are compared to both a reference rotor and the optimum rotor found in the purely aerodynamic formulation. (3) Multipoint optimization: The multilevel optimization procedure of objective 2 is extended to a multipoint design problem. Hover, cruise, and take-off are the three flight conditions simultaneously maximized. (4) Coupled rotor/wing optimization: Using the comprehensive rotary wing code CAMRAD, an optimization procedure is developed for the coupled rotor/wing performance in high speed tilt-rotor aircraft. The developed procedure contains design variables which define the rotor and wing planforms.

Chattopadhyay, Aditi↗
NASA NTRS1991

Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions

Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.

Kane, James H.↗
NASA NTRS1991

General shape optimization capability

A method is described for calculating shape sensitivities, within MSC/NASTRAN, in a simple manner without resort to external programs. The method uses natural design variables to define the shape changes in a given structure. Once the shape sensitivities are obtained, the shape optimization process is carried out in a manner similar to property optimization processes. The capability of this method is illustrated by two examples: the shape optimization of a cantilever beam with holes, loaded by a point load at the free end (with the shape of the holes and the thickness of the beam selected as the design variables), and the shape optimization of a connecting rod subjected to several different loading and boundary conditions.

Chargin, Mladen K.↗
NASA NTRS2005

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Mason, Brian H.↗
NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗
NASA NTRS1990

New evidence favoring multilevel decomposition and optimization

The issue of the utility of multilevel decomposition and optimization remains controversial. To date, only the structural optimization community has actively developed and promoted multilevel optimization techniques. However, even this community acknowledges that multilevel optimization is ideally suited for a rather limited set of problems. It is warned that decomposition typically requires eliminating local variables by using global variables and that this in turn causes ill-conditioning of the multilevel optimization by adding equality constraints. The purpose is to suggest a new multilevel optimization technique. This technique uses behavior variables, in addition to design variables and constraints, to decompose the problem. The new technique removes the need for equality constraints, simplifies the decomposition of the design problem, simplifies the programming task, and improves the convergence speed of multilevel optimization compared to conventional optimization.

Padula, Sharon L.↗
NASA NTRS2002

Risk-Based Probabilistic Approach to Aeropropulsion System Assessment

In an era of shrinking development budgets and resources, where there is also an emphasis on reducing the product development cycle, the role of system assessment, performed in the early stages of an engine development program, becomes very critical to the successful development of new aeropropulsion systems. A reliable system assessment not only helps to identify the best propulsion system concept among several candidates, it can also identify which technologies are worth pursuing. This is particularly important for advanced aeropropulsion technology development programs, which require an enormous amount of resources. In the current practice of deterministic, or point-design, approaches, the uncertainties of design variables are either unaccounted for or accounted for by safety factors. This could often result in an assessment with unknown and unquantifiable reliability. Consequently, it would fail to provide additional insight into the risks associated with the new technologies, which are often needed by decision makers to determine the feasibility and return-on-investment of a new aircraft engine. In this work, an alternative approach based on the probabilistic method was described for a comprehensive assessment of an aeropropulsion system. The statistical approach quantifies the design uncertainties inherent in a new aeropropulsion system and their influences on engine performance. Because of this, it enhances the reliability of a system assessment. A technical assessment of a wave-rotor-enhanced gas turbine engine was performed to demonstrate the methodology. The assessment used probability distributions to account for the uncertainties that occur in component efficiencies and flows and in mechanical design variables. The approach taken in this effort was to integrate the thermodynamic cycle analysis embedded in the computer code NEPP (NASA Engine Performance Program) and the engine weight analysis embedded in the computer code WATE (Weight Analysis of Turbine Engines) with the fast probability integration technique (FPI). FPI was developed by Southwest Research Institute under contract with the NASA Glenn Research Center. The results were plotted in the form of cumulative distribution functions and sensitivity analyses and were compared with results from the traditional deterministic approach. The comparison showed that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system. The current work addressed the application of the probabilistic approach to assess specific fuel consumption, engine thrust, and weight. Similarly, the approach can be used to assess other aspects of aeropropulsion system performance, such as cost, acoustic noise, and emissions. Additional information is included in the original extended abstract.

Tong, Michael T.↗
NASA NTRS1984

A new implementation of the programming system for structural synthesis (PROSSS-2)

This new implementation of the PROgramming System for Structural Synthesis (PROSSS-2) combines a general-purpose finite element computer program for structural analysis, a state-of-the-art optimization program, and several user-supplied, problem-dependent computer programs. The results are flexibility of the optimization procedure, organization, and versatility of the formulation of constraints and design variables. The analysis-optimization process results in a minimized objective function, typically the mass. The analysis and optimization programs are executed repeatedly by looping through the system until the process is stopped by a user-defined termination criterion. However, some of the analysis, such as model definition, need only be one time and the results are saved for future use. The user must write some small, simple FORTRAN programs to interface between the analysis and optimization programs. One of these programs, the front processor, converts the design variables output from the optimizer into the suitable format for input into the analyzer. Another, the end processor, retrieves the behavior variables and, optionally, their gradients from the analysis program and evaluates the objective function and constraints and optionally their gradients. These quantities are output in a format suitable for input into the optimizer. These user-supplied programs are problem-dependent because they depend primarily upon which finite elements are being used in the model. PROSSS-2 differs from the original PROSSS in that the optimizer and front and end processors have been integrated into the finite element computer program. This was done to reduce the complexity and increase portability of the system, and to take advantage of the data handling features found in the finite element program.

Rogers, James L., Jr.↗
NASA NTRS1981

Calculation of sensitivity derivatives in thermal problems by finite differences

The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.

Haftka, R. T.↗