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Design optimization methods for high-performance research reactor core design

Typical objectives of high-performance research reactors include neutron scattering, materials irradiation, and isotope production. The creation of a core that optimizes these multiple objectives often presents a multidimensional (i.e., in design space), multiobjective optimization problem. The developed systematic approach discussed herein draws on response surface methodology to validate and leverage a surrogate model to serve in place of high-fidelity computational analyses. Optimization and design analysis methods leverage this surrogate model to provide a flexible tool for generating optimized designs and understanding the impact of design decisions on desired metrics. In applications to High Flux Isotope Reactor (HFIR) low-enriched uranium (LEU) core designs, neutronic, isotopic evolution, and thermal hydraulic analyses are used to generate key performance and safety metrics for assessing the feasibility and fitness of given designs. Three optimized designs that determine different desired metrics and constraints (e.g., key metric weighting and fabrication constraints) are presented, providing potential design options that satisfy the requirements for HFIR’s conversion from high enriched uranium to LEU fuel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Novel Framework for Performance Evaluation and Design Optimization of PCM Embedded Heat Exchangers for the Built Environment

This research sheds light on the performance evaluation and design optimization of PCM-HXs for the built environment, addressing several barriers to practical issues to PCM-HX commercialization such as modeling aspects (i.e., modeling expertise and computational / time investment, etc.), manufacturing aspects (i.e., at-scale manufacturing, cost assessments, etc.) and experimental performance assessment (i.e., reliable experimental data, assessment of multiple PCM-working fluid combinations, etc.). We present a novel, comprehensive, and experimentally-validated design optimization framework for PCM-HXs capable of simulating any PCM-HX geometry with reasonable accuracy and significant computational time savings when compared to traditional CFD-based design practices. The framework was validated for a wide range of PCM-HX configurations, including a design optimization for a domestic hot water heater application where TES partially replaces electrical heating input. The resulting PCM-HXs were found to deliver 34-68% of the total daily hot water supply with only 5-10% package volume increase from the water heater, thus within U.S. DOE targets for TES systems. To identify the most promising HXs for PCM applications, first-order geometry and cost analyses were conducted based on off-the-shelf HX products. As part of this work, 9 PCM-HX prototypes were manufactured using additive and conventional manufacturing methods. Detailed economy-of-scale assessments were conducted for the most promising PCM-HXs and were found to have a good outlook for the next 5-10 years. The PCM-HX design optimization framework was validated through comprehensive in-house experimental testing using newly-developed PCM-to-fluid test facilities. In total,10 total in-house component-level experiments were conducted using these prototypes, including 9 with water and 1 with refrigerant (R410A) as the working fluid. It was found that the framework can successfully predict experimental thermal-hydraulic performance within ±10-20% the first time without manual design changes, eliminating the need for time-consuming and expensive prototyping efforts as part of the design process. As part of this work, a publicly-available PCM web tool was released which includes a PCM property database (531 PCMs) and PCM-HX modeling tool to assist the design community on common PCM-HX use-cases, e.g., single/multiple flow path(s) fluid-to-PCM and air-to-fluid-to-PCM configurations (https://ceeeweb.umd.edu/pcmapp/). This work will accelerate the design and time to market for next generation PCM-HXs.

25 ENERGY STORAGE↗

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

Patnaik, Surya N.↗

Optimal design of solidification processes

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem.

Dantzig, Jonathan A.↗

Development of Building Design Optimization Methodology: Residential Building Applications

Building design optimization is a highly complex problem, requiring long computational running processes because of the many options that exist when a building is being designed. This paper introduces an integrated approach through which to perform this optimization within an acceptable time frame. The approach includes the methods of variable selection, model simplification, and a sequential optimization process. Using singular value decomposition, a large number of design variables is reduced to a smaller subset that can be solved more quickly through the optimization algorithm. To expedite the variable selection process, a modeling approach that quickly simulates annual energy consumption was developed to replace full annual energy simulations. The developed methodology was applied to two residential buildings in the US, and the results are discussed herein. To assess the accuracy of the integrated optimization methodology, the optimized life cycle costs are compaa variables demonstrating the strongest contributions in the optimization study were identified. The proposed methodology significantly shortened the time requirements for the optimization processes of the two case studies by 74% and 84%; the optimized life cycle costs were within 0.05% and 0.06%, respectively, of the optimum point.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows

A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.

Taylor, Arthur C., III↗

Design Optimization of Composite Structures under Uncertainty

Design optimization under uncertainty is computationally expensive and is also challenging in terms of alternative formulation. The work under the grant focused on developing methods for design against uncertainty that are applicable to composite structural design with emphasis on response surface techniques. Applications included design of stiffened composite plates for improved damage tolerance, the use of response surfaces for fitting weights obtained by structural optimization, and simultaneous design of structure and inspection periods for fail-safe structures.

Haftka, Raphael T.↗

Sequential ensemble-based optimal design for parameter estimation

The ensemble Kalman filter (EnKF) has been widely used in parameter estimation for hydrological models. The focus of most previous studies was to develop more efficient analysis (estimation) algorithms. On the other hand, it is intuitively understandable that a well-designed sampling (data-collection) strategy should provide more informative measurements and subsequently improve the parameter estimation. In this work, a Sequential Ensemble-based Optimal Design (SEOD) method, coupled with EnKF, information theory and sequential optimal design, is proposed to improve the performance of parameter estimation. Based on the first-order and second-order statistics, different information metrics including the Shannon entropy difference (SD), degrees of freedom for signal (DFS) and relative entropy (RE) are used to design the optimal sampling strategy, respectively. The effectiveness of the proposed method is illustrated by synthetic one-dimensional and two-dimensional unsaturated flow case studies. It is shown that the designed sampling strategies can provide more accurate parameter estimation and state prediction compared with conventional sampling strategies. Optimal sampling designs based on various information metrics perform similarly in our cases. Furthermore, the effect of ensemble size on the optimal design is also investigated. Overall, larger ensemble size improves the parameter estimation and convergence of optimal sampling strategy. Although the proposed method is applied to unsaturated flow problems in this study, it can be equally applied in any other hydrological problems.

54 ENVIRONMENTAL SCIENCES↗

Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft

The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best “truss” configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Lock’s fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples.

Kapania, Rakesh K.↗

Multidisciplinary design optimization using response surface analysis

Aerospace conceptual vehicle design is a complex process which involves multidisciplinary studies of configuration and technology options considering many parameters at many values. NASA Langley's Vehicle Analysis Branch (VAB) has detailed computerized analysis capabilities in most of the key disciplines required by advanced vehicle design. Given a configuration, the capability exists to quickly determine its performance and lifecycle cost. The next step in vehicle design is to determine the best settings of design parameters that optimize the performance characteristics. Typical approach to design optimization is experience based, trial and error variation of many parameters one at a time where possible combinations usually number in the thousands. However, this approach can either lead to a very long and expensive design process or to a premature termination of the design process due to budget and/or schedule pressures. Furthermore, one variable at a time approach can not account for the interactions that occur among parts of systems and among disciplines. As a result, vehicle design may be far from optimal. Advanced multidisciplinary design optimization (MDO) methods are needed to direct the search in an efficient and intelligent manner in order to drastically reduce the number of candidate designs to be evaluated. The payoffs in terms of enhanced performance and reduced cost are significant. A literature review yields two such advanced MDO methods used in aerospace design optimization; Taguchi methods and response surface methods. Taguchi methods provide a systematic and efficient method for design optimization for performance and cost. However, response surface method (RSM) leads to a better, more accurate exploration of the parameter space and to estimated optimum conditions with a small expenditure on experimental data. These two methods are described.

Unal, Resit↗

Design optimization of gas generator hybrid propulsion boosters

A methodology used in support of a contract study for NASA/MSFC to optimize the design of gas generator hybrid propulsion booster for uprating the National Space Transportation System (NSTS) is presented. The objective was to compare alternative configurations for this booster approach, optimizing each candidate concept on different bases, in order to develop data for a trade table on which a final decision was based. The methodology is capable of processing a large number of independent and dependent variables, adjusting the overall subsystems characteristics to arrive at a best compromise integrated design to meet various specified optimization criteria subject to selected constraints. For each system considered, a detailed weight statement was generated along with preliminary cost and reliability estimates.

Weldon, Vincent↗

Design Optimization of Gas Generator Hybrid Propulsion Boosters

A methodology used in support of a study for NASA/MSFC to optimize the design of gas generator hybrid propulsion booster for uprating the National Space Transportation System (NSTS) is presented. The objective was to compare alternative configurations for this booster approach, optimizing each candidate concept on different bases, in order to develop data for a trade table on which a final decision was based. The methodology is capable of processing a large number of independent and dependent variables, adjusting the overall subsystems characteristics to arrive at a best compromise integrated design to meet various specific optimization criteria subject to selected constraints. For each system considered, a detailed weight statement was generated along with preliminary cost and reliability estimates.

Weldon, Vincent↗

Low Space Harmonic Content Windings (LSHWs) Applied to Improve the Pareto Front in Design Optimization of Electric Machines

In design optimization of high performance electric machines where the power density is increasingly a key metric, it is often desirable to maximize the average torque output within a given volume. However, if a smooth output is also required, the torque ripple may become a hurdle as it tends to increase with the average torque for conventional windings. A direct benefit of low space harmonic content windings (LSHWs), featuring the suppression or elimination of targeted non-working orders in the winding magnetomotive force (MMF), is the torque ripple reduction. This paper provides a detailed analysis of torque ripple pairs and the space-time harmonic order mapping, with concise results that applies to both distributed windings and fractionalslot concentrated windings (FSCWs) of any slot/pole combination. Metamodel-based optimizations are performed to compare two LSHWs with a conventional winding. Improved Pareto fronts are validated, which confirms higher torque producing capabilities at various torque ripple thresholds for LSHWs.

33 ADVANCED PROPULSION SYSTEMS↗

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

Gumbert, Clyde R.↗

Preliminary Design Optimization For A Supersonic Turbine For Rocket Propulsion

In this study, we present a method for optimizing, at the preliminary design level, a supersonic turbine for rocket propulsion system application. Single-, two- and three-stage turbines are considered with the number of design variables increasing from 6 to 11 then to 15, in accordance with the number of stages. Due to its global nature and flexibility in handling different types of information, the response surface methodology (RSM) is applied in the present study. A major goal of the present Optimization effort is to balance the desire of maximizing aerodynamic performance and minimizing weight. To ascertain required predictive capability of the RSM, a two-level domain refinement approach has been adopted. The accuracy of the predicted optimal design points based on this strategy is shown to he satisfactory. Our investigation indicates that the efficiency rises quickly from single stage to 2 stages but that the increase is much less pronounced with 3 stages. A 1-stage turbine performs poorly under the engine balance boundary condition. A portion of fluid kinetic energy is lost at the turbine discharge of the 1-stage design due to high stage pressure ratio and high-energy content, mostly hydrogen, of the working fluid. Regarding the optimization technique, issues related to the design of experiments (DOE) has also been investigated. It is demonstrated that the criteria for selecting the data base exhibit significant impact on the efficiency and effectiveness of the construction of the response surface.

Papila, Nilay↗