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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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A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗

Optimal Power Flow in DC Networks with Robust Feasibility and Stability Guarantees

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. Here, in contrast, this paper studies a DN-OPF formulation which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this paper's robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the stability set using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator set-points are obtained by optimizing over the proposed convex stability set. The validity and effectiveness of the propose algorithm is demonstrated through various DC networks adapted from IEEE test cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Generating moment matching scenarios using optimization techniques

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

97 MATHEMATICS AND COMPUTING↗

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Final Technical Report: Sparse Grid Scenario Generation and Interior Algorithms for Stochastic Optimization in a Parallel Computing Environment

The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting our main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.

97 MATHEMATICS AND COMPUTING↗

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗

Making use of x-ray optical effects in photoelectron-, Auger electron-, and x-ray emission spectroscopies: Total reflection, standing-wave excitation, and resonant effects

We present a general theoretical methodology and related open-access computer program for carrying out the calculation of photoelectron, Auger electron, and x-ray emission intensities in the presence of several x-ray optical effects, including total reflection at grazing incidence, excitation with standing-waves produced by reflection from synthetic multilayers and at core-level resonance conditions, and the use of variable polarization to produce magnetic circular dichroism. Calculations illustrating all of these effects are presented, including in some cases comparisons to experimental results. Sample types include both semi-infinite flat surfaces and arbitrary multilayer configurations, with interdiffusion/roughness at their interfaces. These x-ray optical effects can significantly alter observed photoelectron, Auger, and x-ray intensities, and in fact lead to several generally useful techniques for enhancing surface and buried-layer sensitivity, including layer-resolved densities of states and depth profiles of element-specific magnetization. The computer program used in this study should thus be useful for a broad range of studies in which x-ray optical effects are involved or are to be exploited in next-generation surface and interface studies of nanoscale systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Features of the Upgraded Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) Software

The Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) software is used at the NASA Langley Research Center to analyze global aeroheating data on wind tunnel models tested in the Langley Aerothermodynamics Laboratory. One-dimensional, semi-infinite heating data derived from IHEAT are used in the design of thermal protection systems for hypersonic vehicles that are exposed to severe aeroheating loads, such as reentry vehicles during descent and landing procedures. This software program originally was written in the PV-WAVE(Registered Trademark) programming language to analyze phosphor thermography data from the two-color, relative-intensity system developed at Langley. To increase the efficiency, functionality, and reliability of IHEAT, the program was migrated to MATLAB(Registered Trademark) syntax and compiled as a stand-alone executable file labeled version 4.0. New features of IHEAT 4.0 include the options to perform diagnostic checks of the accuracy of the acquired data during a wind tunnel test, to extract data along a specified multi-segment line following a feature such as a leading edge or a streamline, and to batch process all of the temporal frame data from a wind tunnel run. Results from IHEAT 4.0 were compared on a pixel level to the output images from the legacy software to validate the program. The absolute differences between the heat transfer data output from the two programs were on the order of 10(exp -5) to 10(exp -7). IHEAT 4.0 replaces the PV-WAVE(Registered Trademark) version as the production software for aeroheating experiments conducted in the hypersonic facilities at NASA Langley.

Mason, Michelle L.↗

Fast generation of three-dimensional computational boundary-conforming periodic grids of C-type

A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.

Dulikravich, D. S.↗

Dynamic Temperature and Pressure Measurements in the Core of a Propulsion Engine

Dynamic temperature and pressure measurements were made in the core of a TECH977 propulsion engine as part of a NASA funded investigation into indirect combustion noise. Dynamic temperature measurements were made in the combustor, the inter-turbine duct, and the mixer using ten two-wire thermocouple probes. Internal dynamic pressure measurements were made at the same locations using piezoresistive transducers installed in semi-infinite coils. Measurements were acquired at four steady state operating conditions covering the range of aircraft approach power settings. Fluctuating gas temperature spectra were computed from the thermocouple probe voltage measurements using a compensation procedure that was developed under previous NASA test programs. A database of simultaneously acquired dynamic temperature and dynamic pressure measurements was produced. Spectral and cross-spectral analyses were conducted to explore the characteristics of the temperature and pressure fluctuations inside the engine, with a particular focus on attempting to identify the presence of indirect combustion noise.

Turbomachinery Noise↗

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Fricke, C. L.↗

An Upgrade of the Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) Software

The Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) code is used at NASA Langley Research Center to analyze global aeroheating data on wind tunnel models tested in the Langley Aerothermodynamics Laboratory. One-dimensional, semi-infinite heating data derived from IHEAT are used to design thermal protection systems to mitigate the risks due to the aeroheating loads on hypersonic vehicles, such as re-entry vehicles during descent and landing procedures. This code was originally written in the PV-WAVE programming language to analyze phosphor thermography data from the two-color, relativeintensity system developed at Langley. To increase the efficiency, functionality, and reliability of IHEAT, the code was migrated to MATLAB syntax and compiled as a stand-alone executable file labeled version 4.0. New features of IHEAT 4.0 include the options to batch process all of the data from a wind tunnel run, to map the two-dimensional heating distribution to a three-dimensional computer-aided design model of the vehicle to be viewed in Tecplot, and to extract data from a segmented line that follows an interesting feature in the data. Results from IHEAT 4.0 were compared on a pixel level to the output images from the legacy code to validate the program. The differences between the two codes were on the order of 10-5 to 10-7. IHEAT 4.0 replaces the PV-WAVE version as the production code for aeroheating experiments conducted in the hypersonic facilities at NASA Langley.

Mason, Michelle L.↗

Validation of the SINDA/FLUINT code using several analytical solutions

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

Keller, John R.↗

Integrated plasma facing component calorimetry for measurement of shot integrated deposited energy in the NSTX-U

Here, the upgrade to the National Spherical Torus eXperiment (NSTX-U) increases the injected neutral beam power up to 12 MW and the plasma current up to I p = 2 MA for plasma durations up to 5 s. The graphite plasma facing components have been re-designed to handle greater heat and energy fluxes than were seen in NSTX using a castellated design. We present the experimental testing and validation of a castellated graphite target, similar to the prototype tile design, instrumented with thermocouples at various depths in the castellation. During testing, incident heat flux is provided by a programmed electron beam system and surface temperatures are measured via infrared thermography directly viewing the target surface. It was found that the thermocouple response scaled linearly with the measured surface temperature rise regardless of thermocouple depth in the castellation. A sensitivity of 14.3 °C/kJ of deposited energy was found when treating individual castellations as a semi-infinite solid.

47 OTHER INSTRUMENTATION↗

Application of phase-change technique to thin sections with heating on both surfaces

A numerical digital computer program was developed to calculate the heat-transfer coefficients for both sides of a one-dimensional finite slab subject to the boundary conditions ascribed to the phase-change coating heat-transfer technique. In a typical tunnel test situation where a thin wing was exposed to heating on both sides, the data reduction procedures for a semi-infinite slab gave heat-transfer coefficients as much as 375 percent too high on the side with the lowest heating. The results from the one-dimensional finite-slab procedure are presented in the form of correction factors to the solution for a semi-infinite slab in terms of parameters normally used with the phase-change heat-transfer technique. These correlations are not restricted to slab thickness or thermophysical properties and are easily used to obtain accurate data on thin model sections.

Hunt, J. L.↗

Acoustic Database for Turbofan Engine Core-Noise Sources: Volume - I

In this program, a database of dynamic temperature and dynamic pressure measurements were acquired inside the core of a TECH977 turbofan engine to support investigations of indirect combustion noise. Dynamic temperature and pressure measurements were recorded for engine gas dynamics up to temperatures of 3100 degrees Fahrenheit and transient responses as high as 1000 hertz. These measurements were made at the entrance of the high pressure turbine (HPT) and at the entrance and exit of the low pressure turbine (LPT). Measurements were made at two circumferential clocking positions. In the combustor and inter-turbine duct (ITD), measurements were made at two axial locations to enable the exploration of time delays. The dynamic temperature measurements were made using dual thin-wire thermocouple probes. The dynamic pressure measurements were made using semi-infinite probes. Prior to the engine test, a series of bench, oven, and combustor rig tests were conducted to characterize the performance of the dual wire temperature probes and to define and characterize the data acquisition systems. A measurement solution for acquiring dynamic temperature and pressure data on the engine was defined. A suite of hardware modifications were designed to incorporate the dynamic temperature and pressure instrumentation into the TECH977 engine. In particular, a probe actuation system was developed to protect the delicate temperature probes during engine startup and transients in order to maximize sensor life. A set of temperature probes was procured and the TECH977 engine was assembled with the suite of new and modified hardware. The engine was tested at four steady state operating speeds, with repeats. Dynamic pressure and temperature data were acquired at each condition for at least one minute. At the two highest power settings, temperature data could not be obtained at the forward probe locations since the mean temperatures exceeded the capability of the probes. The temperature data were processed using software that accounts for the effects of convective and conductive heat transfer. The software was developed under previous NASA sponsored programs. Compensated temperature spectra and compensated time histories corresponding to the dynamic temperature of the gas stream were generated. Auto-spectral and cross-spectral analyses of the data were performed to investigate spectral features, acoustic circumferential mode content, signal coherence, and time delays. The dynamic temperature data exhibit a wideband and fairly flat spectral content. The temperature spectra do not change substantially with operating speed. The pressure spectra in the combustor and ITD exhibit generally similar shapes and amplitudes, making it difficult to identify any features that suggest the presence of indirect combustion noise. Cross-spectral analysis reveal a strong correlation between pressure and temperature fluctuations in the ITD, but little correlation between temperature fluctuations at the entrance of the HPT and pressure fluctuations downstream of it. Temperature fluctuations at the entrance of the low pressure turbine were an order of magnitude smaller than those at the entrance to the high pressure turbine. Time delay analysis of the temperature fluctuations in the combustor was inconclusive, perhaps due to the substantial mixing that occurs between the upstream and downstream locations. Time delay analysis of the temperature fluctuations in the ITD indicate that they convect at the mean flow speed. Analysis of the data did not reveal any convincing indications of the presence of indirect combustion noise. However, this analysis has been preliminary and additional exploration of the data is recommended including the use of more sophisticated signal processing to explore subtle issues that have been revealed but which are not yet fully understood or explained.

Aeroacoustics↗

Polarized Bidirectional Reflectance of Optically Thick Sparse Particulate Layers: an Efficient Numerically Exact Radiative-Transfer Solution

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 44 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/ mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.

radiative transfer↗

Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) Version 4.0: User Manual

The IHEAT v4.0 software is a data reduction code for global thermography data acquired in the NASA Langley Aerothermodynamics Laboratory (LAL) hypersonic wind tunnels. IHEAT uses red and green color-intensity data from two-dimensional images of wind tunnel models to compute temperatures and heat-transfer rates using a semi-infinite, one-dimensional heat transfer approximation at each image pixel. Multiple automated tools in IHEAT v4.0 decrease the time required to reduce the data from a phosphor thermography wind tunnel run. Data at one or all of the image pixel locations can be exported to computer files for further analysis. The prior version of IHEAT, v3.2, was written in PV-WAVE® (now owned by Rogue Wave® Software) in 1994 and was limited in functionality to fit within the memory constraints of the available computers at the time. IHEAT v4.0 is written in MATLAB® by MathWorks® and contains several new features that leverage the increase in available memory of the current computers. A Piecewise tool permits the user to extract data along a segmented line cut that can follow interesting features in the image better than the single, straight line cuts that were possible with the legacy Length and Profile tools. The new Load Run and Batch tools facilitate batch processing by loading in all of the input files and images for a run at the same time. Load Run permits the user to process the available run images manually, while Batch automatically saves heat transfer data from all of the images based on the analysis previously performed on a single frame. IHEAT v4.0 also can automatically calculate the temporal collapse of reference line cuts from the time history heating data for a run to indicate the appropriate frame to reduce for each run. The IHEAT v4.0 source code was compiled into a standalone executable file that can be accessed remotely from several computers with different operating systems, simultaneously. The software is run through the MATLAB® Compiler Runtime engine, and therefore, IHEAT does not require a software license to run. Any software commands executed in the IHEAT v4.0 code will not affect other similar applications running on the same machine. Similarly, changes to the parent software do not affect a compiled code. These features of IHEAT v4.0 are improvements over the legacy v3.2 code, which required regular maintenance to avoid losing functionality as the PVWAVE ® programming language was upgraded.

Mason, Michelle L.↗