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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.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.

Mendelson, A.↗
NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.

Mendelson, A.↗
DOE OSTI2016

ASYMPTOTIC STEADY-STATE SOLUTION TO A BOW SHOCK WITH AN INFINITE MACH NUMBER

The problem of a cold gas flowing past a stationary obstacle is considered. We study the bow shock that forms around the obstacle and show that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The profiles of the hydrodynamic variables in the interior of the shock are obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force on the obstacle is also calculated. Finally, we use these results to model the bow shock around an isolated neutron star.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1980

The OMNIUM-G HTC-25 tracking concentrator

A point focusing, two axis tracking, high concentration ratio parabolic reflector is described. Field experience coupled with engineering improvements are shown to have manifested a design that is economic in the areas of manufacturing, packaging, delivering, installing, and commissioning the system into operation. The initial problems specifically with the OMNIUM-G model HTC-25 tracking concentrator are addressed.

Zelinger, S.↗
NASA NTRS1985

Development of a boundary-layer-type solver based on simultaneous iteration technique for axisymmetric separated flows

A boundary-layer-type solver is developed for the numerical solution of axisymmetric separated flows. A new fully implicit coupling scheme for the viscous and inviscid regions is demonstrated. This fully implicit coupling technique is similar to the work of Carter, Veldman, and an extension of an earlier work of Halim and Hafez. A comparison is made for the convergence rate using this new fully implicit coupling technique and the semiimplicit coupling of Halim and Hafez. Numerical results using the fully implicit coupling are obtained for laminar incompressible separated flows, including a boattail and a series of trough geometries. Also, the near-wake flow problem is considered using the present formulation. A clear conclusion of this investigation is that the present scheme using the fully implicit coupling method converges at a faster rate than the semiimplicit coupling and the partially parabolized Navier-Stokes (PPNS) procedures.

Halim, A. A. M.↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS1983

State and model error estimation for elliptic systems: Applications to large antenna static shape determination

This paper outlines the application of various estimation approaches to the problem of static shape determination for large antenna systems. The problem consists of estimating the shape of an antenna surface from measurements of its static deflection. The estimation schemes are based on any one of the modeling options of a single PDE for early insight and understanding, coarse-resolution multiple-PDE models for parametric studies and fine-resolution piecewise-continuum models for detailed design. For any one of these three models, estimator design can be developed using an infinite-dimensional approach, where the necessary finite-element truncation and approximation is conducted after the analytical design has taken place, or it can be based on a finite-dimensional approach, where the model is truncated before the estimation problem is formulated. One of the main objectives of the paper is to develop both approaches while simultaneously investigating their differences and similarities. Simulation results of an application of the finite-dimensional approach to a large parabolic reflector are presented.

Rodriguez, G.↗
NASA NTRS1998

Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience with a Carbon-Carbon Composite Prototype Heat Pipe

This report discusses the design implications for spacecraft radiators made possible by the successful fabrication and Proof-of-concept testing of a graphite-fiber-carbon-matrix composite (i.e., carbon-carbon (C-C)) heat pipe. The proto-type heat pipe, or space radiator element, consists of a C-C composite shell with integrally woven fins. It has a thin-walled furnace-brazed metallic (Nb-1%Zr) liner with end caps for containment of the potassium working fluid. A short extension of this liner, at increased wall thickness beyond the C-C shell, forms the heat pipe evaporator section which is in thermal contact with the radiator fluid that needs to be cooled. From geometric and thermal transport properties of the C-C composite heat pipe tested, a specific radiator mass of 1.45 kg/m2 can be derived. This is less than one-fourth the specific mass of present day satellite radiators. The report also discusses the advantage of segmented space radiator designs utilizing heat pipe elements, or segments, in their survivability to micro-meteoroid damage. This survivability is further raised by the use of condenser sections with attached fins, which also improve the radiation heat transfer rate. Since the problem of heat radiation from a fin does not lend itself to a closed analytical solution, a derivation of the governing differential equation and boundary conditions is given in appendix A, along with solutions for rectangular and parabolic fin profile geometries obtained by use of a finite difference computer code written by the author.

Juhasz, Albert J.↗
NASA NTRS2002

Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience With a Carbon-Carbon Composite Prototype Heat Pipe

This report discusses the design implications for spacecraft radiators made possible by the successful fabrication and proof-of-concept testing of a graphite-fiber-carbon-matrix composite (i.e., carbon-carbon (C-C)) heat pipe. The prototype heat pipe, or space radiator element, consists of a C-C composite shell with integrally woven fins. It has a thin-walled furnace-brazed metallic (Nb-1%Zr) liner with end caps for containment of the potassium working fluid. A short extension of this liner, at increased wall thickness beyond the C-C shell, forms the heat pipe evaporator section which is in thermal contact with the radiator fluid that needs to be cooled. From geometric and thermal transport properties of the C-C composite heat pipe tested, a specific radiator mass of 1.45 kg/sq m can be derived. This is less than one-fourth the specific mass of present day satellite radiators. The report also discusses the advantage of segmented space radiator designs utilizing heat pipe elements, or segments, in their survivability to micrometeoroid damage. This survivability is further raised by the use of condenser sections with attached fins, which also improve the radiation heat transfer rate. Since the problem of heat radiation from a fin does not lend itself to a closed analytical solution, a derivation of the governing differential equation and boundary conditions is given in appendix A, along with solutions for rectangular and parabolic fin profile geometries obtained by use of a finite difference computer code written by the author.

Juhasz, Albert J.↗
DOE OSTI2026

Analysis of Molten Salt Thermal Energy Storage Tank Sizing and Preheating

Molten Salt Thermal energy storage (TES) is essential for concentrating solar power (CSP) plants, enhancing their capacity factor and dispatchability to ultimately reduce electricity costs. This technology is becoming more important for other technologies including nuclear power, thermal-electrical storage, and concentrating solar thermal (CST). While molten salt TES tanks have been successfully deployed in lower-temperature parabolic-trough plants, the current state-of-the-art central receiver systems operating at temperatures up to 565 degrees Celsius have experienced costly and frequent failures. These failures are associated with the immaturity of the technology and problems in tank design, fabrication, commissioning and, sometimes, aggressive operation. A primary contributing factor is the absence of a dedicated technical standard for high-temperature molten nitrate TES tanks; designers must currently rely on existing codes like API 650 and ASME Section II, which are insufficient because they fail to account for the unique demands of high temperatures, thermal cycling, and transient conditions.

25 ENERGY STORAGE↗
NASA NTRS1960

An Exploratory Statistical Analysis of a Planet Approach-Phase Guidance Scheme Using Angular Measurements with Significant Error

An exploratory analysis of vehicle guidance during the approach to a target planet is presented. The objective of the guidance maneuver is to guide the vehicle to a specific perigee distance with a high degree of accuracy and minimum corrective velocity expenditure. The guidance maneuver is simulated by considering the random sampling of real measurements with significant error and reducing this information to prescribe appropriate corrective action. The instrumentation system assumed includes optical and/or infrared devices to indicate range and a reference angle in the trajectory plane. Statistical results are obtained by Monte-Carlo techniques and are shown as the expectation of guidance accuracy and velocity-increment requirements. Results are nondimensional and applicable to any planet within limits of two-body assumptions. The problem of determining how many corrections to make and when to make them is a consequence of the conflicting requirement of accurate trajectory determination and propulsion. Optimum values were found for a vehicle approaching a planet along a parabolic trajectory with an initial perigee distance of 5 radii and a target perigee of 1.02 radii. In this example measurement errors were less than i minute of arc. Results indicate that four corrections applied in the vicinity of 50, 16, 15, and 1.5 radii, respectively, yield minimum velocity-increment requirements. Thrust devices capable of producing a large variation of velocity-increment size are required. For a vehicle approaching the earth, miss distances within 32 miles are obtained with 90-percent probability. Total velocity increments used in guidance are less than 3300 feet per second with 90-percent probability. It is noted that the above representative results are valid only for the particular guidance scheme hypothesized in this analysis. A parametric study is presented which indicates the effects of measurement error size, initial perigee, and initial energy on the guidance requirements. Measurement error size significantly affects both guidance accuracy and velocity-increment expenditure. The initial trajectory, as given by its perigee and energy, affects the velocity-increment expenditure but not final guidance accuracy.

Friedlander, Alan L.↗