Search NASA⌕ Search

SEARCH · Search NASA

Results for “parabolic problems”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Phased Array Antenna for the Mitigation of UAS Interference

The growing demand for Unmanned Aerial Systems (UAS) operating beyond the line of sight (BLOS) has resulted in an increased interest in using existing commercial satellite communication capabilities for UAS command and control (C2) communications. The World Radiocommunication Conference in 2015 designated portions of Ku-Band and Ka-Band fixed satellite service (FSS) spectrum to support UAS C2 communications, provided that potential interference with existing co-allocated users in these bands is addressed. As the user base in this new spectrum allocation expands, there is an increased potential for interference with existing terrestrial communication systems operating under fixed service (FS) allocations. The portion of Ka-Band spectrum allocated for UAS C2 avoids significant interference issues, but the Ku-Band allocation contains a co-primary FS allocation, creating potential interference problems. Therefore, UAS must identify solutions to avoid interfering with these existing FS ground sites while maintaining good links with satellite constellations. UAS operating with conventional fixed feed parabolic antennas will have difficulty in meeting interference thresholds, especially at high latitudes where the antennas will operate with low elevation angles. As a means of addressing this limitation, NASA is investigating the use of a phased array antenna to enable mitigation of interference into ground-based FS receivers. In this paper, a novel lightweight conformal phased array antenna will be presented that can use null-steering and/or beam shaping to avoid ground interference while simultaneously providing strong satellite microwave links for communications. The reduced weight of this design and ability to integrate into the fuselage of smaller UAS platforms will also be discussed as a potential solution to provide BLOS operation via spectrum sharing for an expanding user base. This paper will review design aspects of the conformal phased array antenna, describe the intended benefits in reducing interference with FS ground stations, and describe phased array development and test plans.

Beam Forming↗
NASA NTRS2018

Phased Array Antenna for the Mitigation of UAS Interference

The growing demand for Unmanned Aerial Systems (UAS) operating beyond the line of sight (BLOS) has resulted in an increased interest in using existing commercial satellite communication capabilities for UAS command and control (C2) communications. The World Radiocommunication Conference in 2015 designated portions of Ku-Band and Ka-Band fixed satellite service (FSS) spectrum to support UAS C2 communications, provided that potential interference with existing co-allocated users in these bands is addressed. As the user base in this new spectrum allocation expands, there is an increased potential for interference with existing terrestrial communication systems operating under fixed service (FS) allocations. The portion of Ka-Band spectrum allocated for UAS C2 avoids significant interference issues, but the Ku-Band allocation contains a co-primary FS allocation, creating potential interference problems. Therefore, UAS must identify solutions to avoid interfering with these existing FS ground sites while maintaining good links with satellite constellations. UAS operating with conventional fixed feed parabolic antennas will have difficulty in meeting interference thresholds, especially at high latitudes where the antennas will operate with low elevation angles. As a means of addressing this limitation, NASA is investigating the use of a phased array antenna to enable mitigation of interference into ground-based FS receivers. In this paper, a novel lightweight conformal phased array antenna will be presented that can use null-steering and/or beam shaping to avoid ground interference while simultaneously providing strong satellite microwave links for communications. The reduced weight of this design and ability to integrate into the fuselage of smaller UAS platforms will also be discussed as a potential solution to provide BLOS operation via spectrum sharing for an expanding user base. This presentation will review design aspects of the conformal phased array antenna, describe the intended benefits in reducing interference with FS ground stations, and describe phased array development and test plans.

Conformal Phased Array↗
DOE OSTI2020

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Focusing Optics for Axion Detection: Simulating Sensing Enhancements of Photons in InfraBREAD

The Broadband Reflector Experiment for Axion Detection (BREAD) will search for axions, a promising particle candidate for dark matter, in the high mass range of [$10^{-3}$,1]eV. BREAD acts like a telescope for dark matter, using a parabolic reflector to direct axion-induced photons onto a precise focal spot. InfraBREAD is the experimental version designed to detect photons resulting from axions with infrared frequency using a 1mm × 1mm Superconducting Nanowire Singe Photon Detector (SNSPD). However, at this frequency scale two problems arise: 1) the focal spot becomes smeared across an area larger than the size of the SNSPD detector; 2) any millimeter-scale misalignment shifts in the SNSPD can greatly diminish photon signal. This study performed simulations of novel optical configurations of lenses and reflectors placed around the SNSPD to achieve a greater efficiency than the SNSPD alone through both of these effects. One optical setup was identified called the “Parabolo id to Winston Cone (PTW) Configuration,” which exploits the optics of parabolic reflectors to focus incoming photons from the larger area of the smeared focal spot onto the smaller 1mm 2 area of the detector. The PTW configuration demonstrated overall improvements in efficiency by around 10% through misalignment shifts, with a maximal improvement of 55% in one region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2006

RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.

Mizuno, Yosuke↗
NASA NTRS2011

Excitation of a Parallel Plate Waveguide by an Array of Rectangular Waveguides

This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.

Rengarajan, Sembiam↗
NASA NTRSDate not supplied

Documentarian’s Support Role: Recording Active Research for Outreach

The Space Crop Production Team at NASA’s Kennedy Space Center recently conducted a campaign of parabolic flights to study the best techniques for harvesting and collecting microgreens in microgravity. During this process, the research team invited a student with scientific training to the field sites, contributing as the documentarian and aiding in recording audio visual data. The documentarian was tasked with photographing and filming the preparation of experiments for parabolic flight, hardware installation in the parabolic flight plane, the crew performing their experiments, and the harvesting hardware and samples post-flight. Through having a documentarian on the team during experiments, the processes of problem-solving, teamwork, and data collection were able to be captured. This allows for these methods to be reflected upon post-experiment as a means of improving the procedures for the future. Additionally, the picture and video evidence became data that were analyzed following the flight test. The Space Crop Production team benefited by having a documentarian present, as they were able to develop a 45 second social media video with the intent of being published through official NASA outlets. Longer videos for classroom use are also in work. In addition to outreach usage, the collection of footage and visual data the documentarian provides has the potential to be scientifically published both in video-based scientific journals, and as supplemental data in online journal publications. Capturing research in this manner helps share an unseen side of the research practices with a larger audience and increases the potential for scientific engagement and activation.

Christopher Bermudez↗
NASA NTRS1989

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Steger, Joseph L.↗
NASA NTRS1976

A finite element solution of unsteady transonic flow problems for three-dimensional wings and bodies

A computerized finite element method has been developed to solve a form of the three-dimensional inviscid, irrotational unsteady transonic equation for pointed and rectangular wings and wing-body combinations. The equation is a 'parabolized' version of the full unsteady transonic equation which includes the effect of the advancing wave and the acceleration in the steady flow field thus including a thickness effect. Automatic mesh generation using conformal mapping has the advantage of allowing relatively arbitrary cross-sections to be closely approximated while taking advantage of the body's similarity to a more simple configuration. Plunge, pitch, and roll modes are computed

Kimble, K. R.↗
NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗
DOE OSTI2021

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.↗
DOE OSTI2016

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical example of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.

42 ENGINEERING↗
DOE OSTI2024

Energy and Environmental Analyses of a Solar–Gas Turbine Combined Cycle with Inlet Air Cooling

Sensitivity to ambient air temperatures, consuming a large amount of fuel, and wasting a significant amount of heat dumped into the ambient atmosphere are three major challenges facing gas turbine power plants. This study was conducted to simultaneously solve all three aforementioned GT problems using solar energy and introducing a new configuration that consists of solar preheating and inlet-air-cooling systems. In this study, air was preheated at a combustion chamber inlet using parabolic trough collectors. Then, inlet air to the compressor was cooled by these collectors by operating an absorption cooling cycle. At the design point conditions, this novel proposed integration resulted in a 6.87% relative increase in generated power and a 10.53% relative decrement in fuel consumption, achieving a 19.45% relative increment in the plant’s thermal efficiency. This was accompanied by a reduction of 0.026 kg/s, 4.2 kg/s, and 0.278 kg/s in CO 2 , CO, and NOx emissions, respectively. Finally, spider diagrams were employed to assess the impact of the operating parameters on the overall system’s performance and its associated environmental implications.

14 SOLAR ENERGY↗
NASA NTRS1973

Research on the sonic boom problem. Part 2: Flow field measurement in wind tunnel and calculation of second order F-function

An experimental investigation has been carried out in a wind tunnel to test some of the results of Landahl's second order theory. The slender models consisted of a parabolic spindle, tested at M = 3, and a wing body configuration, suggested by Ferri, and tested at M = 2.7. The theory indicates that shock position and strength at an arbitrary distance can be calculated by means of near field measurements. The results show that this method is an appropriate one for simple bodies and for bodies with complicated geometries as well.

Landahl, M.↗