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At least 181 records · Page 10

CFD-Based Design Optimization for Single Element Rocket Injector

To develop future Reusable Launch Vehicle concepts, we have conducted design optimization for a single element rocket injector, with overall goals of improving reliability and performance while reducing cost. Computational solutions based on the Navier-Stokes equations, finite rate chemistry, and the k-E turbulence closure are generated with design of experiment techniques, and the response surface method is employed as the optimization tool. The design considerations are guided by four design objectives motivated by the consideration in both performance and life, namely, the maximum temperature on the oxidizer post tip, the maximum temperature on the injector face, the adiabatic wall temperature, and the length of the combustion zone. Four design variables are selected, namely, H2 flow angle, H2 and O2 flow areas with fixed flow rates, and O2 post tip thickness. In addition to establishing optimum designs by varying emphasis on the individual objectives, better insight into the interplay between design variables and their impact on the design objectives is gained. The investigation indicates that improvement in performance or life comes at the cost of the other. Best compromise is obtained when improvements in both performance and life are given equal importance.

Vaidyanathan, Rajkumar↗

Improved approximations of displacements for structural optimization

In most structural optimization problems the implicit behavior constraints are evaluated for successive modifications in the design. For each trial design, the analysis equations must be solved and the multiple repeated analyses usually involve extensive computational effort. This difficulty motivated several studies on explicit approximations of the structural behavior in terms of the design variables. The latter approach can considerably reduce the amount of computations, but the quality of the approximations might not be sufficient. Many of the approximate behavior models proposed in the past are valid only for relatively small changes in the design variables. The accuracy of the results is often insufficient for large changes in the design. The object of this study is to present efficient and high quality approximations of the structural behavior. It will be shown that the quality of the approximations can greatly be improved by combining scaling of the initial design, using intervening variables, and scaling a set of fictitious loads. Integrating these means, a powerful solution procedure can be introduced. In addition, the errors in satisfying the analysis equations can readily be evaluated. A numerical example illustrates the solution methodology and the effectiveness of the proposed approach.

Kirsch, Uri↗

Neural Network and Response Surface Methodology for Rocket Engine Component Optimization

The goal of this work is to compare the performance of response surface methodology (RSM) and two types of neural networks (NN) to aid preliminary design of two rocket engine components. A data set of 45 training points and 20 test points obtained from a semi-empirical model based on three design variables is used for a shear coaxial injector element. Data for supersonic turbine design is based on six design variables, 76 training, data and 18 test data obtained from simplified aerodynamic analysis. Several RS and NN are first constructed using the training data. The test data are then employed to select the best RS or NN. Quadratic and cubic response surfaces. radial basis neural network (RBNN) and back-propagation neural network (BPNN) are compared. Two-layered RBNN are generated using two different training algorithms, namely solverbe and solverb. A two layered BPNN is generated with Tan-Sigmoid transfer function. Various issues related to the training of the neural networks are addressed including number of neurons, error goals, spread constants and the accuracy of different models in representing the design space. A search for the optimum design is carried out using a standard gradient-based optimization algorithm over the response surfaces represented by the polynomials and trained neural networks. Usually a cubic polynominal performs better than the quadratic polynomial but exceptions have been noticed. Among the NN choices, the RBNN designed using solverb yields more consistent performance for both engine components considered. The training of RBNN is easier as it requires linear regression. This coupled with the consistency in performance promise the possibility of it being used as an optimization strategy for engineering design problems.

Vaidyanathan, Rajkumar↗

The Sizing and Optimization Language (SOL): A computer language to improve the user/optimizer interface

The nonlinear mathematical programming method (formal optimization) has had many applications in engineering design. A figure illustrates the use of optimization techniques in the design process. The design process begins with the design problem, such as the classic example of the two-bar truss designed for minimum weight as seen in the leftmost part of the figure. If formal optimization is to be applied, the design problem must be recast in the form of an optimization problem consisting of an objective function, design variables, and constraint function relations. The middle part of the figure shows the two-bar truss design posed as an optimization problem. The total truss weight is the objective function, the tube diameter and truss height are design variables, with stress and Euler buckling considered as constraint function relations. Lastly, the designer develops or obtains analysis software containing a mathematical model of the object being optimized, and then interfaces the analysis routine with existing optimization software such as CONMIN, ADS, or NPSOL. This final state of software development can be both tedious and error-prone. The Sizing and Optimization Language (SOL), a special-purpose computer language whose goal is to make the software implementation phase of optimum design easier and less error-prone, is presented.

Lucas, S. H.↗

Bi-Level Integrated System Synthesis (BLISS)

BLISS is a method for optimization of engineering systems by decomposition. It separates the system level optimization, having a relatively small number of design variables, from the potentially numerous sub-system optimizations that may each have a large number of local design variables. The subsystem optimizations are autonomous and may be conducted concurrently. Subsystem and system optimizations alternate, linked by sensitivity data, producing a design improvement in each iteration. Starting from a best guess initial design, the method improves that design in iterative cycles, each cycle comprised of two steps. In step one, the system level variables are frozen and the improvement is achieved by separate, concurrent, and autonomous optimizations in the local variable subdomains. In step two, further improvement is sought in the space of the system level variables. Optimum sensitivity data link the second step to the first. The method prototype was implemented using MATLAB and iSIGHT programming software and tested on a simplified, conceptual level supersonic business jet design, and a detailed design of an electronic device.

Sobieszczanski-Sobieski, Jaroslaw↗

Bell-Curve Based Evolutionary Strategies for Structural Optimization

Evolutionary methods are exceedingly popular with practitioners of many fields; more so than perhaps any optimization tool in existence. Historically Genetic Algorithms (GAs) led the way in practitioner popularity (Reeves 1997). However, in the last ten years Evolutionary Strategies (ESs) and Evolutionary Programs (EPS) have gained a significant foothold (Glover 1998). One partial explanation for this shift is the interest in using GAs to solve continuous optimization problems. The typical GA relies upon a cumber-some binary representation of the design variables. An ES or EP, however, works directly with the real-valued design variables. For detailed references on evolutionary methods in general and ES or EP in specific see Back (1996) and Dasgupta and Michalesicz (1997). We call our evolutionary algorithm BCB (bell curve based) since it is based upon two normal distributions.

Kincaid, Rex K.↗

Bell-Curve Based Evolutionary Strategies for Structural Optimization

Evolutionary methods are exceedingly popular with practitioners of many fields; more so than perhaps any optimization tool in existence. Historically Genetic Algorithms (GAs) led the way in practitioner popularity. However, in the last ten years Evolutionary Strategies (ESs) and Evolutionary Programs (EPS) have gained a significant foothold. One partial explanation for this shift is the interest in using GAs to solve continuous optimization problems. The typical GA relies upon a cumbersome binary representation of the design variables. An ES or EP, however, works directly with the real-valued design variables. For detailed references on evolutionary methods in general and ES or EP in specific see Back and Dasgupta and Michalesicz. We call our evolutionary algorithm BCB (bell curve based) since it is based upon two normal distributions.

Kincaid, Rex K.↗

Digital robust active control law synthesis for large order systems using constrained optimization

This paper presents a direct digital control law synthesis procedure for a large order, sampled data, linear feedback system using constrained optimization techniques to meet multiple design requirements. A linear quadratic Gaussian type cost function is minimized while satisfying a set of constraints on the design loads and responses. General expressions for gradients of the cost function and constraints, with respect to the digital control law design variables are derived analytically and computed by solving a set of discrete Liapunov equations. The designer can choose the structure of the control law and the design variables, hence a stable classical control law as well as an estimator-based full or reduced order control law can be used as an initial starting point. Selected design responses can be treated as constraints instead of lumping them into the cost function. This feature can be used to modify a control law, to meet individual root mean square response limitations as well as minimum single value restrictions. Low order, robust digital control laws were synthesized for gust load alleviation of a flexible remotely piloted drone aircraft.

Mukhopadhyay, Vivek↗

On implementation of the extended interior penalty function

The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.

Cassis, J. H.↗

Model reduction in integrated controls-structures design

It is the objective of this paper to present a model reduction technique developed for the integrated controls-structures design of flexible structures. Integrated controls-structures design problems are typically posed as nonlinear mathematical programming problems, where the design variables consist of both structural and control parameters. In the solution process, both structural and control design variables are constantly changing; therefore, the dynamic characteristics of the structure are also changing. This presents a problem in obtaining a reduced-order model for active control design and analysis which will be valid for all design points within the design space. In other words, the frequency and number of the significant modes of the structure (modes that should be included) may vary considerably throughout the design process. This is also true as the locations and/or masses of the sensors and actuators change. Moreover, since the number of design evaluations in the integrated design process could easily run into thousands, any feasible order-reduction method should not require model reduction analysis at every design iteration. In this paper a novel and efficient technique for model reduction in the integrated controls-structures design process, which addresses these issues, is presented.

Maghami, Peiman G.↗

Multi-parameter optimization tool for low-cost commercial fuselage crown designs

The work in progress for developing a methodology and software tool to aid in the optimal design of composite structures is discussed. The methodology is being developed to take advantage of the ability to tailor the composite material in conjunction with the design of the structure. The composites optimization design software UWCODA was found to be very successful in preliminary testing and early experience. UWCODA is a composites design code that uses a number of plies and fiber angles as design variables, employs maximum strain failure criteria for objective function and additional constraints, includes Boeing design tools for stiffened panels, and includes stiffener geometry in the design variables.

Zabinsky, Zelda↗

Sonic Boom Ground Noise Minimization Via the Adjoint Method

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by the sonic boom of a high altitude supersonic body is presented. A Cartesian Euler flow solver is coupled with an atmospheric propagation tool to create a ground-noise analysis capability for supersonic bodies. Adjoint formulations for both the flow solver and propagation tool are also coupled to compute sensitivities of shape variations in the body in a highly efficient manner. A gradient-based optimizer is then introduced to forge a valuable design capability. Output-based mesh adaptation that is driven directly by ground-level noise is employed to increase accuracy and provide error estimation. The design method is demonstrated first on a simple axisymmetric body with few design variables to evaluate the efficacy of the optimization scheme. Guided by the results of this initial case, the problem is then repeated with somewhat different design variables to further demonstrate the capabilities of the design method. Finally, the method is applied to a real-world problem by optimizing control surface deflection settings of a low-boom aircraft to minimize ground noise while maintaining trimmed, level flight.

ARMD↗

Computer method for design of acoustic liners for turbofan engines

A design package is presented for the specification of acoustic liners for turbofans. An estimate of the noise generation was made based on modifications of existing noise correlations, for which the inputs are basic fan aerodynamic design variables. The method does not predict multiple pure tones. A target attenuation spectrum was calculated which was the difference between the estimated generation spectrum and a flat annoyance-weighted goal attenuated spectrum. The target spectrum was combined with a knowledge of acoustic liner performance as a function of the liner design variables to specify the acoustic design. The liner design method at present is limited to annular duct configurations. The detailed structure of the liner was specified by combining the required impedance (which is a result of the previous step) with a mathematical model relating impedance to the detailed structure. The design procedure was developed for a liner constructed of perforated sheet placed over honeycomb backing cavities. A sample calculation was carried through in order to demonstrate the design procedure, and experimental results presented show good agreement with the calculated results of the method.

Minner, G. L.↗

Review of Controllers for Low-Power Free-Piston Stirling Convertors

This work provides a complete review of controller strategies for free-piston Stirling convertors (FPSCs) and design recommendations for future controller development efforts. First, basic operating principles for the control of FPSCs and design variables for the FPSC controllers are described. Next, past controller approaches are reviewed and categorized based on the design variables. State-of-the-art controllers are also summarized by their key features, which are then hypothetically extended to flight designs to compare their critical metrics such as the estimated size, weight, and power with cost (SWaP-C) and reliability. Finally, design recommendations are suggested to improve the state-of-the-art controllers for future flight development projects.

Free-Piston Stirling Convertor Controller↗

Automated optimum design of wing structures. Deterministic and probabilistic approaches

The automated optimum design of airplane wing structures subjected to multiple behavior constraints is described. The structural mass of the wing is considered the objective function. The maximum stress, wing tip deflection, root angle of attack, and flutter velocity during the pull up maneuver (static load), the natural frequencies of the wing structure, and the stresses induced in the wing structure due to landing and gust loads are suitably constrained. Both deterministic and probabilistic approaches are used for finding the stresses induced in the airplane wing structure due to landing and gust loads. A wing design is represented by a uniform beam with a cross section in the form of a hollow symmetric double wedge. The airfoil thickness and chord length are the design variables, and a graphical procedure is used to find the optimum solutions. A supersonic wing design is represented by finite elements. The thicknesses of the skin and the web and the cross sectional areas of the flanges are the design variables, and nonlinear programming techniques are used to find the optimum solution.

Rao, S. S.↗

Distributed Space Mission Design for Earth Observation Using Model-Based Performance Evaluation

Distributed Space Missions (DSMs) are gaining momentum in their application to earth observation missions owing to their unique ability to increase observation sampling in multiple dimensions. DSM design is a complex problem with many design variables, multiple objectives determining performance and cost and emergent, often unexpected, behaviors. There are very few open-access tools available to explore the tradespace of variables, minimize cost and maximize performance for pre-defined science goals, and therefore select the most optimal design. This paper presents a software tool that can multiple DSM architectures based on pre-defined design variable ranges and size those architectures in terms of predefined science and cost metrics. The tool will help a user select Pareto optimal DSM designs based on design of experiments techniques. The tool will be applied to some earth observation examples to demonstrate its applicability in making some key decisions between different performance metrics and cost metrics early in the design lifecycle.

Constellation↗

Global, Multi-Objective Trajectory Optimization With Parametric Spreading

Mission design problems are often characterized by multiple, competing trajectory optimization objectives. Recent multi-objective trajectory optimization formulations enable generation of globally-optimal, Pareto solutions via a multi-objective genetic algorithm. A byproduct of these formulations is that clustering in design space can occur in evolving the population towards the Pareto front. This clustering can be a drawback, however, if parametric evaluations of design variables are desired. This effort addresses clustering by incorporating operators that encourage a uniform spread over specified design variables while maintaining Pareto front representation. The algorithm is demonstrated on a Neptune orbiter mission, and enhanced multidimensional visualization strategies are presented.

trajectory design↗

Structural tailoring of engine blades (STAEBL) theoretical manual

This Theoretical Manual includes the theories included in the Structural Tailoring of Engine Blades (STAEBL) computer program which was developed to perform engine fan and compressor blade numerical optimizations. These blade optimizations seek a minimum weight or cost design that satisfies practical blade design constraints, by controlling one to twenty design variables. The STAEBL constraint analyses include blade stresses, vibratory response, flutter, and foreign object damage. Blade design variables include airfoil thickness at several locations, blade chord, and construction variables: hole size for hollow blades, and composite material layup for composite blades.

Brown, K. W.↗