Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear projection”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗

Re-entry vehicle shape for enhanced performance

A convex shell structure for enhanced aerodynamic performance and/or reduced heat transfer requirements for a space vehicle that re-enters an atmosphere. The structure has a fore-body, an aft-body, a longitudinal axis and a transverse cross sectional shape, projected on a plane containing the longitudinal axis, that includes: first and second linear segments, smoothly joined at a first end of each the first and second linear segments to an end of a third linear segment by respective first and second curvilinear segments; and a fourth linear segment, joined to a second end of each of the first and second segments by curvilinear segments, including first and second ellipses having unequal ellipse parameters. The cross sectional shape is non-symmetric about the longitudinal axis. The fourth linear segment can be replaced by a sum of one or more polynomials, trigonometric functions or other functions satisfying certain constraints.

Brown, James L.↗

Visual Systems for Remotely Controlled Vehicles

The Variable Acuity Remote Viewing System is discussed. It was conceived as a technique for resolving the field of view/resolution/ bandwidth tradeoffs that exist in remote viewing systems. This system is based on the fact that integration of the human eye acuity function shows only about 130,000 pixels are required to fully support the human vision. This quantity is well within the capabilities of conventional video systems. The technique utilizes a non-linear optical system in both the sensing and display equipment. The non-linearity is achieved by a special lens which translates a uniform pixel array on its image plane into the object field as a variable angular array. This lens will record the same angular detail the eye would see when viewing the same scene and compress this detail into a uniform matrix of equal sized picture elements on its image plane. This image can be scanned with a broadcast quality tv having a 525 line raster scan. Conventional transmission equipment can then also be used to send the image information to a remote location. When received, the image is projected by a light valve projector onto a hemispherical screen by an identical non-linear lens.

Rezek, T.↗

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗

Observable-projected ensembles

Measurements in many-body quantum systems can generate non-trivial phenomena, such as preparation of long-range entangled states, dynamical phase transitions, or measurement-altered criticality. Here, we introduce a new measurement scheme that produces an ensemble of mixed states in a subsystem, obtained by measuring a local Hermitian observable on part of its complement. We refer to this as the observable-projected ensemble . Unlike standard projected ensembles-where pure states are generated by projective measurements on the complement-our approach involves projective partial measurements of specific observables. This setup has two main advantages: theoretically, it is amenable to analytical computations, especially within conformal field theories. Experimentally, it requires only a linear number of measurements, rather than an exponential one, to probe the properties of the ensemble. As a first step in exploring the observable-projected ensemble, we investigate its entanglement properties in conformal field theory and perform a detailed analysis of the free compact boson.

Milekhin, Alexey [California Institute of Technolo↗

Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory

This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.

Dukeman, Greg A.↗

System identification of the Large-Angle Magnetic Suspension Test Facility (LAMSTF)

The Large-Angle Magnetic Suspension Test Facility (LAMSTF), a laboratory-scale research project to demonstrate the magnetic suspension of objects over wide ranges of attitudes, has been developed. This system represents a scaled model of a planned Large-Gap Magnetic Suspension System (LGMSS). The LAMSTF system consists of a planar array of five copper electromagnets which actively suspend a small cylindrical permanent magnet. The cylinder is a rigid body and can be controlled to move in five independent degrees of freedom. Five position variables are sensed indirectly by using infra-red light-emitting diodes and light-receiving phototransistors. The motion of the suspended cylinder is in general nonlinear and hence only the linear, time-invariant perturbed motion about an equilibrium state is considered. One of the main challenges in this project is the control of the suspended element over a wide range of orientations. An accurate dynamic model plans an essential role in controller design. The analytical model of the LAMSTF system includes highly unstable real poles (about 10 Hz) and low-frequency flexible modes (about 0.16 Hz). Projection filters are proposed to identify the state space model from closed-loop test data in time domain. A canonical transformation matrix is also derived to transform the identified state space model into the physical coordinate. The LAMSTF system is stabilized by using a linear quadratic regulator (LQR) feedback controller. The rate information is obtained by calculating the back difference of the sensed position signals. The reference inputs contain five uncorrelated random signals. This control input and the system reponse are recorded as input/output data to identify the system directly from the projection filters. The sampling time is 4 ms and the model is fairly accurate in predicting the step responses for different controllers while the analytical model has a deficiency in the pitch axis.

Huang, Jen-Kuang↗

Bench-Scale Testing of Monolithic PPI Structured Contactors for Direct Air Capture of CO 2

The overall project objective was to develop, optimize and bench-scale test the integrated embodiment of a leading direct air capture (DAC) sorbent composition, linear-poly(propylenimine) (l-PPI), in a structured material system, specifically a monolithic contactor for achieving low pressure drop, to justify its further scale-up in a subsequent program. The project team was led by CORMETECH, a leading monolithic gas/solid contactor manufacturer for environmental applications, and included Global Thermostat, a well-known DAC start-up, and Georgia Tech, a prominent US academic institution in carbon capture and DAC. The monolithic contactor for l-PPI in this project employed an advanced, cost-effective fabrication technique from CORMETECH, namely a porous monolith substrate directly impregnated with the amine, an approach contrasting to the traditional wash-coating methods used for activating monoliths. The l-PPI monolithic contractor is targeted for use in DAC systems such as the Global Thermostat DAC process, which involves the cyclic operation of ambient air flow over a monolithic amine contactor followed by steam-mediated thermal desorption and CO 2 collection, maximizing volumetric productivity while reducing the auxiliary power required to capture CO 2 from air. The Global Thermostat DAC process currently utilizes poly(ethyleneimine) (PEI) materials as baseline sorbents, which are subject to oxidative degradation and slow capacity fade at the elevated temperature required for efficient CO 2 removal. Georgia Tech, with Global Thermostat, had discovered in lab-scale efforts that l-PPI had superior resistance to oxidative degradation compared to PEI, with similar CO 2 adsorption capacity. While the novel l-PPI sorbent offers significant advantages over PEI for DAC, including potential design simplification and increased process efficiency, it is not commercially available, and prior to this project, had not yet been evaluated on the bench-scale in a structured contactor.

36 MATERIALS SCIENCE↗

Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations

A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.

Reddy, Tondapu S.↗

The future of the El Niño–Southern Oscillation: using large ensembles to illuminate time-varying responses and inter-model differences

Future changes in the El Niño–Southern Oscillation (ENSO) are uncertain, both because future projections differ between climate models and because the large internal variability of ENSO clouds the diagnosis of forced changes in observations and individual climate model simulations. By leveraging 14 single model initial-condition large ensembles (SMILEs), we robustly isolate the time-evolving response of ENSO sea surface temperature (SST) variability to anthropogenic forcing from internal variability in each SMILE. We find nonlinear changes in time in many models and considerable inter-model differences in projected changes in ENSO and the mean-state tropical Pacific zonal SST gradient. We demonstrate a linear relationship between the change in ENSO SST variability and the tropical Pacific zonal SST gradient, although forced changes in the tropical Pacific SST gradient often occur later in the 21st century than changes in ENSO SST variability, which can lead to departures from the linear relationship. Single-forcing SMILEs show a potential contribution of anthropogenic forcing (aerosols and greenhouse gases) to historical changes in ENSO SST variability, while the observed historical strengthening of the tropical Pacific SST gradient sits on the edge of the model spread for those models for which single-forcing SMILEs are available. Our results highlight the value of SMILEs for investigating time-dependent forced responses and inter-model differences in ENSO projections. The nonlinear changes in ENSO SST variability found in many models demonstrate the importance of characterizing this time-dependent behavior, as it implies that ENSO impacts may vary dramatically throughout the 21st century.

54 ENVIRONMENTAL SCIENCES↗

In-Process Melt Separation of Depolymerized PET in PET/PE Blends for Upcycling via Twin-Screw Extrusion

Our previous work focused on depolymerizing polyethylene terephthalate (PET) in twin-screw extrusion, as part of a broader project to continuously separate PET from polyolefins in the melt. This study focused on linear low-density polyethylene (LLDPE) and PET films and the use of ethylene glycol (EG), diethylene glycol (DEG), triethylene glycol (TEG), and bis(2-hydroxyethyl) terephthalate (BHET) to depolymerize the PET in the extruder to levels above 90% Mw. In this work, the focus will shift to achieving separation of the two polymers in the twin-screw extruder, which is made possible due to a 90% reduction in the Mw of the PET, which caused a decrease of its viscosity by several orders of magnitude. Owing to the viscosity difference and pressure buildup in the die, the low-viscosity PET preferentially exited a degassing vent instead of going through the die. This is because the flow of the PET would travel through a non-pressure vent rather than through a high-pressure die. However, owing to the higher viscosity of the LLDPE, the pressure was too high to pass through such a small diameter vent hole. Supercritical CO 2 (SCCO 2 ) was used to assist in this extraction, but SCCO 2 negatively impacted the overall degree of separation. Through analysis of the separated materials, it was concluded that a high separation of the two materials was achieved. TGA and FTIR confirmed that the material separated from the vent was 100% PET. The material removed from the die was composed of 95% LLDPE and 5% PET.

36 MATERIALS SCIENCE↗

In‐Process Melt Separation of PE/PET Blends for Upcycling via Twin‐Screw Extrusion. Impact of Catalyst Reagents on PET Depolymerization

Part 1 of this work focused on depolymerizing polyethylene terephthalate (PET) in twin-screw extrusion, as part of a broader project to continuously separate PET from polyolefins in the melt. This study focused on linear low-density polyethylene (LLDPE) and PET films and the use of ethylene glycol (EG), diethylene glycol (DEG), triethylene glycol (TEG), and bis(2-hydroxyethyl) terephthalate (BHET) to depolymerize the PET in the extruder to levels above 90% Mw. In part 2, the focus will shift to achieving separation of the two polymers in the twin-screw extruder, which is made possible due to a 90% reduction in the Mw of the PET, which caused a decrease of its viscosity by several orders of magnitude. Owing to the viscosity difference and pressure buildup in the die, the low-viscosity PET preferentially exited a degassing vent instead of going through the die. This is because the flow of the PET would travel through a non-pressure vent rather than through a high-pressure die. However, owing to the higher viscosity of the LLDPE, the pressure was too high to pass through such a small diameter vent hole. Supercritical CO₂ (SCCO₂) was used to assist in this extraction, but SCCO₂ negatively impacted the overall degree of separation. Through analysis of the separated materials, it was concluded that a very high separation of the two materials was achieved. TGA and FTIR confirmed that the material separated from the vent was 100% PET. The material removed from the die was composed of 90% LLDPE and 10% PET.

36 MATERIALS SCIENCE↗

AMR-Wind [SWR-20-85]

AMR-Wind is a massively parallel, block-structured adaptive-mesh, incompressible flow solver for wind turbine and wind farm simulations. The solver is built on top of the AMReX library. AMReX is developed at LBNL , NREL , and ANL as part of the Block-Structured AMR Co-Design Center in DOE's Exascale Computing Project. AMReX library provides the mesh data structures, mesh adaptivity, as well as the linear solvers used for solving the governing equations. The primary applications for AMR-Wind are: performing large-eddy simulations (LES) of atmospheric boundary layer (ABL) flows, simulating wind farm turbine-wake interactions using actuator disk or actuator line models for turbines, and as a background solver when coupled with a near-body solver with overset methodology to perform blade-resolved simulations of multiple wind turbines within a wind farm.

Ananthan, Shreyas↗

Materials Data on BaTiO3 by Materials Project

BaTiO3 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Ba2+ is bonded in a linear geometry to two equivalent O2- atoms. Both Ba–O bond lengths are 2.52 Å. Ti4+ is bonded in a square co-planar geometry to four equivalent O2- atoms. All Ti–O bond lengths are 2.06 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to two equivalent Ti4+ and two equivalent O2- atoms. Both O–O bond lengths are 2.06 Å. In the second O2- site, O2- is bonded to two equivalent Ba2+ and four equivalent O2- atoms to form distorted corner-sharing OBa2O4 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

Materials Data on AgAuS2 by Materials Project

AuAgS2 crystallizes in the orthorhombic Pccm space group. The structure is three-dimensional. Au3+ is bonded in a linear geometry to two equivalent S2- atoms. Both Au–S bond lengths are 2.31 Å. Ag1+ is bonded in a 4-coordinate geometry to four equivalent S2- atoms. All Ag–S bond lengths are 2.62 Å. S2- is bonded to one Au3+, two equivalent Ag1+, and one S2- atom to form a mixture of edge and corner-sharing SAg2AuS tetrahedra. The S–S bond length is 2.13 Å.

36 MATERIALS SCIENCE↗

Materials Data on Cs2CuO2 by Materials Project

Cs2CuO2 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. Cs1+ is bonded in a linear geometry to two O2- atoms. Both Cs–O bond lengths are 2.64 Å. Cu2+ is bonded in a square co-planar geometry to four O2- atoms. There are two shorter (2.40 Å) and two longer (2.42 Å) Cu–O bond lengths. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a square co-planar geometry to two equivalent Cs1+ and two equivalent Cu2+ atoms. In the second O2- site, O2- is bonded in a square co-planar geometry to two equivalent Cs1+ and two equivalent Cu2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on NaLi2N by Materials Project

NaLi2N crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Na1+ is bonded in a linear geometry to two equivalent N3- atoms. Both Na–N bond lengths are 2.38 Å. Li1+ is bonded in a trigonal planar geometry to three equivalent N3- atoms. All Li–N bond lengths are 2.11 Å. N3- is bonded to two equivalent Na1+ and six equivalent Li1+ atoms to form a mixture of edge and corner-sharing NNa2Li6 hexagonal bipyramids.

36 MATERIALS SCIENCE↗