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.

SourceResearch connectionFrom yearThrough year

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

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

NASA NTRS1999

Unified CFD Methods Via Flowfield-Dependent Variation Theory

This paper addresses the flowfield-dependent variation (FDV) methods in which complex physical phenomena are taken into account in the final form of partial differential equations to be solved so that finite difference methods (FDM) or finite element methods (FEM) themselves will not dictate the physics, but rather are no more than simply the options how to discretize between adjacent nodal points or within an element. The variation parameters introduced in the formulation are calculated from the current flowfield based on changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkohler numbers between adjacent nodal points, which play many significant roles such as adjusting the governing equations (hyperbolic, parabolic, and/or e!liptic), resolving various physical phenomena, and controlling the accuracy and stability of the numerical solution. The theory is verified by a number of example problems addressing the physical implications of the variation parameters which resemble the flowfield itself, shock capturing mechanism, transitions and interactions between inviscid/viscous, compressibility/incompressibility, and laminar/turbulent flows.

Chung, T. J.↗

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.

Phased Array↗

NASA NTRS2018

Phased Array Antenna for the Mitigation of UAS Interference

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↗

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↗

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.↗

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.↗

NASA NTRS1975

Accurate integration of geostationary orbits with Burdet's focal elements

The theory of Burdet's focal elements (1969) is outlined. The differential equations are presented, and the initial value problem is described together with the transformation to rectangular coordinates and classical elements. The focal elements are well defined for zero eccentricity and inclination and can be adopted for the computation of elliptic, parabolic, and hyperbolic motion. For the numerical integration of near-geostationary orbits, a comparison of the efficiency is made between focal elements, Kustaanheimo-Stiefel (1971) theory, and rectangular coordinates. For this class of orbits, a higher accuracy has been obtained by integrating elements than integrating rectangular coordinates.

Flury, W.↗

NASA NTRS1979

A viscous flow analysis for the tip vortex generation process

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

Shamroth, S. J.↗

NASA NTRS1984

A second-order accurate parabolized Navier-Stokes algorithm for internal flows

A parabolized implicit Navier-Stokes algorithm which is of second-order accuracy in both the cross flow and marching directions is presented. The algorithm is used to analyze three model supersonic flow problems (the flow over a 10-degree edge). The results are found to be in good agreement with the results of other techniques available in the literature.

Chitsomboon, T.↗

NASA NTRS1991

Hypersonic cone flow predictions using an implicit upwind space-marching code

Solutions have been computed and results are presented for Problem 1, the case of Mach 9 transitional flow past a 7 deg half-angle cone at zero incidence. The solutions were computed using a code developed for the integration of the parabolized Navier-Stokes equations. The algorithm employed in the code is based on a Roe-type flux-difference-splitting scheme applied following a finite-volume approach. The basic algorithm has been modified to make it implicit and second-order accurate in the crossflow directions. Results are presented in terms of surface pressure and heat transfer as well as boundary layer profiles of pitot pressure, Mach number, and tangential velocity. The case was recalculated several times in an effort to determine sensitivities to such parameters as grid density, wall temperature, turbulence model parameters, as well as freestream expansion. Comparisons with the experimental data are presented and discussed.

Lawrence, Scott L.↗

NASA NTRS1982

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗

NASA NTRS1985

An optical technology study on large aperture telescopes

The difficult and crucial problem of selecting a suitable telescope concept for an advanced space observatory was examined. To this end two and four mirror telescopes were analyzed and compared. Both configurations are very practical and structurally similar. Parabolic primary and spherical primary four mirror telescope were compared with respect to their performance and the alignment sensitivities of the three correction mirrors. A 1 meter class afocal telescope system with lag angle compensation, to be used in a LIDAR experiment, was examined.

Korsch, D.↗