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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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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Domain-based method↗
NASA NTRS1995

Closed-form Static Analysis with Inertia Relief and Displacement-Dependent Loads Using a MSC/NASTRAN DMAP Alter

Solving for the displacements of free-free coupled systems acted upon by static loads is commonly performed throughout the aerospace industry. Many times, these problems are solved using static analysis with inertia relief. This solution technique allows for a free-free static analysis by balancing the applied loads with inertia loads generated by the applied loads. For some engineering applications, the displacements of the free-free coupled system induce additional static loads. Hence, the applied loads are equal to the original loads plus displacement-dependent loads. Solving for the final displacements of such systems is commonly performed using iterative solution techniques. Unfortunately, these techniques can be time-consuming and labor-intensive. Since the coupled system equations for free-free systems with displacement-dependent loads can be written in closed-form, it is advantageous to solve for the displacements in this manner. Implementing closed-form equations in static analysis with inertia relief is analogous to implementing transfer functions in dynamic analysis. Using a MSC/NASTRAN DMAP Alter, displacement-dependent loads have been included in static analysis with inertia relief. Such an Alter has been used successfully to solve efficiently a common aerospace problem typically solved using an iterative technique.

Barnett, Alan R.↗
NASA NTRS1985

Distributed reacceleration of cosmic rays

A model is developed in which cosmic rays, in addition to their initial acceleration by a strong shock, are continuously reaccelerated while propagating through the Galaxy. The equations describing this acceleration scheme are solved analytically and numerically. Solutions for the spectra of primary and secondary cosmic rays are given in a closed analytic form, allowing a rapid search in parameter space for viable propagation models with distributed reeacceleration included. The observed boron-to-carbon ratio can be reproduced by the reacceleration theory over a range of escape parameters, some of them quite different from the standard leaky-box model. It is also shown that even a very modest amount of reacceleration by strong shocks causes the boron-to-carbon ratio to level off at sufficiently high energies.

Wandel, Amri↗
NASA NTRS1994

Steepened structures in equatorial spread F. 2: Theory

This paper investigates the properties of a one-dimensional fluid model of plasma convection in the equatorial F region ionosphere. The model equations are similar in form to Burgers equation except for additional higher-order spatial derivatives. Like Burgers equation, solution to the model have the form of propagating, shocklike structures. Numerical simulations of the model closely resemble the steepened structures observed by sounding rocket plasma density probes within equatorial spread F. Simulated denstiy power spectra, like the spectra computed from in situ data, seem to possess power law forms with a break at wavelengths of about 100 m. The precise wavenumber of the spectral break is determined by the ambipolar diffusion coefficient. The model predicts that electric field fluctuations perpendicular to the direction of plasma steepening should be proportional to the plasma density fluctuations. Electric field fluctuations parallel to the steepening will be due primarily to the ambipolar field and have a Boltzmann relationship with density (square of the absolute value of delta E) approximately equal to (K(exp 2))(square of the absolute value of (delta n/n)). At wavelengths less than about 300 m, the ambipolar field should be the dominant component of the total field intensity.

Hysell, D. L↗
NASA NTRS1987

Distributed reacceleration of cosmic rays

We develop a model in which cosmic rays, in addition to their initial acceleration by a strong shock, are continuously reaccelerated (e.g., by weak shocks) while propagating through the galaxy. The equations describing this acceleration scheme are solved analytically (approximating ionization losses by a cutoff) and numerically. Solutions for the spectra of primary and secondary cosmic rays are given in a closed analytic form, and they allow a rapid search in parameter space for viable propagation models with distributed reacceleration included. The observed boron-to-carbon ratio can be reproduced by the reacceleration theory over a range of escape parameters, some of them quite different from the standard "leaky box" model. It is also shown that even a very modest amount of reacceleration by strong shocks causes the boron-to carbon ratio to level off at sufficiently high energies, and this effect may be observed in the CRNE data. Several other curiosities in the data may be explained naturally if a modest amount of distributed reacceleration is invoked, including (a) the apparent truncation at low energy in the otherwise exponential pathlength distribution associated with the leaky box model, (b) the sub-iron isotopic anomalies and other effects noted by Silberberg et al., and (c) the discrepancy between the reported 10Be lifetime and the lifetime of cosmic rays in the dense strata of the galactic disk.

NASA Discipline Radiation Health↗
NASA NTRS2006

Approximations of distant retrograde orbits for mission design

Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.

Distant Retrograde Orbits (DRO)↗
NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗
DOE OSTI2020

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Mathematical model for predicting human vertebral fracture

Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.

Benedict, J. V.↗
NASA NTRS1997

An Application of the Difference Potentials Method to Solving External Problems in CFD

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Ryaben 'Kii, Victor S.↗
DOE OSTI2024

Pairing a Global Optimization Algorithm with EXAFS to Characterize Lanthanide Structure in Solution

Ensemble-average sampling of structures from ab initio molecular dynamics (AIMD) simulations can be used to predict theoretical extended X-ray absorption fine structure (EXAFS) signals that closely match experimental spectra. However, AIMD simulations are time-consuming and resource-intensive, particularly for solvated lanthanide ions, which often form multiple nonrigid geometries with high coordination numbers. Here, to accelerate the characterization of lanthanide structures in solution, we employed the Northwest Potential Energy Surface Search Engine (NWPEsSe), an adaptive-learning global optimization algorithm, to efficiently screen first-shell structures. As case studies, we examine two systems: Eu(NO 3 ) 3 dissolved in acetonitrile with a terpyridine ligand (terpyNO 2 ), and Nd(NO 3 ) 3 dissolved in acetonitrile. The theoretical spectra for structures identified by NWPEsSe were compared to both experimental and AIMD-derived EXAFS spectra. The NWPEsSe algorithm successfully identified the proper solvation structure for both Eu(NO 3 ) 3 (terpyNO 2 ) and Nd(NO 3 )(acetonitrile) 3 , with the calculated EXAFS signals closely matching the experimental spectra for the Eu-ligand complex and showing good similarity for the Nd salt; the better agreement with the ligand-containing structure is attributed to a less dynamic coordination environment due to the rigid ligand. The key advantage of the global optimization algorithm lies in its ability to sample the coordination environment across the potential energy surface and reduce the time required to identify structures from generally a month to within a week. Additionally, this approach is versatile and can be adapted to characterize main-group metal complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2014

Solar Metal Sulfate-Ammonia Based Thermochemical Water Splitting Cycle for Hydrogen Production

Two classes of hybrid/thermochemical water splitting processes for the production of hydrogen and oxygen have been proposed based on (1) metal sulfate-ammonia cycles (2) metal pyrosulfate-ammonia cycles. Methods and systems for a metal sulfate MSO.sub.4--NH3 cycle for producing H2 and O2 from a closed system including feeding an aqueous (NH3)(4)SO3 solution into a photoctalytic reactor to oxidize the aqueous (NH3)(4)SO3 into aqueous (NH3)(2)SO4 and reduce water to hydrogen, mixing the resulting aqueous (NH3)(2)SO4 with metal oxide (e.g. ZnO) to form a slurry, heating the slurry of aqueous (NH4)(2)SO4 and ZnO(s) in the low temperature reactor to produce a gaseous mixture of NH3 and H2O and solid ZnSO4(s), heating solid ZnSO4 at a high temperature reactor to produce a gaseous mixture of SO2 and O2 and solid product ZnO, mixing the gaseous mixture of SO2 and O2 with an NH3 and H2O stream in an absorber to form aqueous (NH4)(2)SO3 solution and separate O2 for aqueous solution, recycling the resultant solution back to the photoreactor and sending ZnO to mix with aqueous (NH4)(2)SO4 solution to close the water splitting cycle wherein gaseous H2 and O2 are the only products output from the closed ZnSO4--NH3 cycle.

Huang, Cunping↗
NASA NTRS1985

Simultaneous Earth observations from 2 satellites

Simultaneous co-located observations from two different orbits lead to several advantages (i.e., cross calibration of sensors and a wider range of solar-zenith and sensor look angles). The question was asked how many times per year (on the average) do the sub-satellite points of two satellites simultaneously come within D kilometers of each other?. For the Space Station (altitude: 500 km, inclination: 28 deg) and a Sun synchronous satellite (altitude 705 km, inclination 98.21 deg) the answers are 16, 41 and 82 times per year for encounter distances D of 20, 50, and 100 km espectively. The relationship between encounters per year and distance D is linear. The answers were obtained in two ways: (1) a closed form statistical approach which led to a simple algebraic expression, and (2) a Monte Carlo type computer solution. The largest difference between the two solutions was less than 12%.

Montgomery, H. E.↗
NASA NTRS1986

Simultaneous earth observations from two satellites

Simultaneous co-located observations from two different orbits lead to several advantages (i.e., cross calibration of sensors and a wider range of solar-zenith and sensor look angles). The question was asked how many times per year (on the average) do the sub-satellite points of two satellites simultaneously come within D kilometers of each other? For the Space Station (altitude: 500 km, inclination: 28 deg) and a Sun synchronous satellite (altitude 705 km, inclination 98.21 deg) the answers are 16, 41 and 82 times per year for encounter distances D of 20, 50, and 100 km respectively. The relationship between encounters per year and distance D is linear. The answers were obtained in two ways: (1) a closed form statistical approach which led to a simple algebraic expression, and (2) a Monte Carlo type computer solution. The largest difference between the two solutions was less than 12 percent.

Montgomery, H. E.↗
NASA NTRS1987

Computational structures for robotic computations

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.

Lee, C. S. G.↗
NASA NTRS1989

An explicit Runge-Kutta method for turbulent reacting flow calculations

The paper presents a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flow in two-dimensional geometries, in both Cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-epsilon model, where low Reynolds number and compressibility effects are included, and a modified eddy-break up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit multi-stage dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.

Boretti, A. A.↗
NASA NTRS1957

Thin airfoil theory based on approximate solution of the transonic flow equation

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

WING-SECTION THEORY↗