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Results for “mathematical programming formulations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Analysis of radiative sources with both specular and diffuse characteristics in the visible and infrared spectrum

The application of analytical concepts developed to facilitate the design and analysis of the thermal simulator for the Apollo Soyuz docking module is discussed. The functions used to mathematically formulate the irradiance from a quartzline lamp and reflector are described with examples of applications to other geometries. General information is denoted for utilization of the functions in computer programs with approximate computer storage and statement requirements.

Williams, F. U.↗
DOE OSTI2025

Recovery Simulator and Analysis Formulation: Mathematical Framework for Enhanced Resilience and Resource Allocation

This report introduces recovery simulator and analysis (RSA), a framework aimed at enhancing the resilience of electrical grids post-disruption. The RSA model leverages an optimization problem formulation that focuses on maximizing the load served (or optionally customers served) through a coordinated and cooptimized recovery of non-black start generation, transmission lines, feeders and substations subject to labor budget constraints. By integrating advanced linear programming techniques, the simulator selects efficient reocovery pathways, optimizing both short-term and long-term grid recovery strategies. The mathematical framework guides decision-making through a comprehensive evaluation of potential recovery actions, factoring in the trade-offs between labor constraints and load (or optionally customer) restoration efficacy. This enables grid operators to simulate diverse outage scenarios and delineate optimal recovery pathways, thereby prioritizing critical repair tasks and ensuring resource allocation is both economical and effective. The intended use case of RSA is to allow planners to explore many recovery scenarios quickly and determine assets most critical across a wide range of scenarios, and therefore strong candidates for hardening or additional investment. RSA might also be used in an operational setting, following a single event, for exploring efficient recovery pathways.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1982

Mathematical modeling of ice accretion on airfoils

The progress toward development of a computer model suitable for predicting icing behavior on airfoils over a wide range of environmental conditions and airfoils shapes is reported. The LEWICE program was formulated to solve a set of equations which describe the physical processes which occur during accretion of ice on an airfoil, including heat transfer in a time dependent mode, with the restriction that the flow must be describable by a two-dimensional flow code. Input data comprises the cloud liquid water content, mean droplet diameter, ambient air temperature, air velocity, and relative humidity. A potential flowfield around the airfoil is calculated, along with the droplet trajectories within the flowfield, followed by local values of water droplet collection efficiency at the impact points. Both glaze and rime ice conditions are reproduced, and comparisons with test results on icing of circular cylinders showed good agreement with the physical situation.

Macarthur, C. D.↗
NASA NTRS1990

Overcoming the Bellman's curse of dimensionality in large optimization problems

Decomposition of large problems into a hierarchic pyramid of subproblems was proposed in the literature as a means for optimization of engineering systems too large for all-in-one optimization. This decomposition was established heuristically. The dynamic programming (DP) method due to Bellman was augmented with an optimum sensitivity analysis that provides a mathematical basis for the above decomposition, and overcomes the curse of dimensionality that limited the original formulation of DP. Numerical examples are cited.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1984

The influence of wind-tunnel walls on discrete frequency noise

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Mosher, M.↗
DOE OSTI2020

A novel matching formulation for startup costs in unit commitment

Here we present a novel formulation for startup cost computation in the unit commitment problem (UC). Both our proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. Our proposed formulation is tested empirically against existing formulations on large-scale UC instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening can reduce the computational burden in comparison to existing formulations, especially for UC instances with large reserve margins and high penetration levels of renewables.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

A numerically efficient finite element hydroelastic analysis. Volume 2: Implementation in NASTRAN, part 1

Details are presented of the implementation of the new formulation into NASTRAN including descriptions of the DMAP statements required for conversion of the program and details pertaining to problem definition and bulk data considerations. Details of the current 1/8-scale space shuttle external tank mathematical model, numerical results and analysis/test comparisons are also presented. The appendices include a description and listing of a FORTRAN program used to develop harmonic transformation bulk data (multipoint constraint statements) and sample bulk data information for a number of hydroelastic problems.

Coppolino, R. N.↗
NASA NTRS2006

Predicting the Effects of Test Media in Ground-Based Propulsion Testing

This paper discusses the progress of work which began in mid-2004 sponsored by the Office of the Secretary of Defense (OSD) Test & Evaluation/Science & Technology (T&E/S&T) Program. The purpose of the work is to improve the state of the art of CFD capabilities for predicting the effects of the test media on the flameholding characteristics in scramjet engines. The program has several components including the development of advance algorithms and models for simulating engine flowpaths as well as a fundamental experimental and diagnostic development effort to support the formulation and validation of the mathematical models. The paper will provide details of current work involving the development of phenomenological models for Reynolds averaged Navier-Stokes codes, large-eddy simulation techniques and reduced-kinetics models. Experiments that will provide data for the modeling efforts will also be described, along with with the associated nonintrusive diagnostics used to collect the data.

Drummond, J. Philip↗
NASA NTRS2007

Supersonic Combustion Research at NASA

This paper discusses the progress of work to model high-speed supersonic reacting flow. The purpose of the work is to improve the state of the art of CFD capabilities for predicting the flow in high-speed propulsion systems, particularly combustor flowpaths. The program has several components including the development of advanced algorithms and models for simulating engine flowpaths as well as a fundamental experimental and diagnostic development effort to support the formulation and validation of the mathematical models. The paper will provide details of current work on experiments that will provide data for the modeling efforts along with the associated nonintrusive diagnostics used to collect the data from the experimental flowfield. Simulation of a recent experiment to partially validate the accuracy of a combustion code is also described.

Drummond, J. P.↗
NASA NTRS2007

Modeling Combustion in Supersonic Flows

This paper discusses the progress of work to model high-speed supersonic reacting flow. The purpose of the work is to improve the state of the art of CFD capabilities for predicting the flow in high-speed propulsion systems, particularly combustor flow-paths. The program has several components including the development of advanced algorithms and models for simulating engine flowpaths as well as a fundamental experimental and diagnostic development effort to support the formulation and validation of the mathematical models. The paper will provide details of current work on experiments that will provide data for the modeling efforts along with with the associated nonintrusive diagnostics used to collect the data from the experimental flowfield. Simulation of a recent experiment to partially validate the accuracy of a combustion code is also described.

Drummond, J. Philip↗
NASA NTRS2009

Development of Methods to Predict the Effects of Test Media in Ground-Based Propulsion Testing

This report discusses work that began in mid-2004 sponsored by the Office of the Secretary of Defense (OSD) Test & Evaluation/Science & Technology (T&E/S&T) Program. The work was undertaken to improve the state of the art of CFD capabilities for predicting the effects of the test media on the flameholding characteristics in scramjet engines. The program had several components including the development of advanced algorithms and models for simulating engine flowpaths as well as a fundamental experimental and diagnostic development effort to support the formulation and validation of the mathematical models. This report provides details of the completed work, involving the development of phenomenological models for Reynolds averaged Navier-Stokes codes, large-eddy simulation techniques and reduced-kinetics models. Experiments that provided data for the modeling efforts are also described, along with with the associated nonintrusive diagnostics used to collect the data.

Drummond, J. Philip↗
NASA NTRS1971

Monopropellant hydrazine resisto jet

Mathematical models for the electrothermal hydrazine thruster are provided which can be utilized to aid in preliminary design definition, interpretation of test data, and the evaluation of design and operational changes. Three computer programs were formulated to provide the necessary steady state and transient performance design tools. These included: preliminary evaluation of the energy balance characteristics of the thruster; a means of evaluating steady state performance relative to the primary design, configuration, and operational parameters; and a model to provide a means of evaluating transient (pulse mode) operation of the thruster relative to primary design and operational parameters.

Muenzer, F. B.↗
NASA NTRS1975

Segregation effects during solidification in weightless melts

Computer programs are developed and used in the study of the combined effects of evaporation and solidification in space processing. The temperature and solute concentration profiles during directional solidification of binary alloys with surface evaporation were mathematically formulated. Computer results are included along with an econotechnical model of crystal growth. This model allows: prediction of crystal size, quality, and cost; systematic selection of the best growth equipment or alloy system; optimization of growth or material parameters; and a maximization of zero-gravity effects. Segregation in GaAs crystals was examined along with vibration effects on GaAs crystal growth. It was found that a unique segregation pattern and strong convention currents exist in GaAs crystal growth. Some beneficial effects from vibration during GaAs growth were discovered. The implications of the results in space processing are indicated.

Li, C.↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Modifications to give HOPE/MDC 2.0 the capability to solve for or consider vent forces: Mission planning, mission analysis, and software formulation

The modifications are described as necessary to give the Houston Operations Predictor/Estimator (HOPE) program the capability to solve for or consider vent forces for orbit determination. The model implemented in solving for vent forces is described along with the integrator problems encountered. A summary derivation of the mathematical principles applicable to solve/consider methodology is provided.

Zyla, L. V.↗
DOE OSTI2019

PAO

PAO supports the formulation and analysis of mathematical models for complex optimization applications. This capability is commonly associated with algebraic modeling languages (AMLs), which support the description and analysis of mathematical models with a high-level language. PAO is derived from the Pyomo subpackage pyomo.bilevel, which has been deprecated. PAO supports the formulation and solution of optimization models that explicitly represent adversarial behavior. This includes variances of bilevel programming, including methods that represent challenging problems with discrete decisions and uncertain model parameters.

Hart, William↗