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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Boundary layer description of directional polymer crystallisation

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger–Gryte ansatz.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Random equations in aerodynamics

Literature was reviewed to identify aerodynamic models which might be treated by probablistic methods. The numerical solution of some integral equations that arise in aerodynamical problems were investigated. On the basis of the numerical studies a qualitative theory of random integral equations was developed to provide information on the behavior of the solutions of these equations (in particular, boundary and asymptotic behavior, and stability) and their statistical properties without actually obtaining explicit solutions of the equations.

Bharucha-Reid, A. T.↗
DOE OSTI2022

Spatiotemporal Route to Understanding Metal Halide Perovskitoid Crystallization

Here, a spatiotemporal experimental route is reported for the antisolvent vapor diffusion crystal growth of metal halide perovskitoids. A computational analysis combining automated image capture and diffusion modeling enables the determination of the critical concentrations required for nucleation and crystal growth from a single experiment. Five different solvent systems and ten distinct organic ammonium iodide salts were investigated with lead iodide, from which nine previously unreported compounds were discovered. Automated image capture of the mother liquor and antisolvent vials was used to determine changes in solution meniscus positions and detect the nucleation event location. Matching the observations to a numerical solution of Fick's second law diffusion model enables the calculation of reactant, solvent, and antisolvent concentrations at both the time and position of the first stable nucleation and crystal growth. A machine learning model was trained on the resulting data, and it reveals solvent- and amine-specific crystallization tendencies. Solvent systems that interact more weakly with dissolved lead species promote crystallization, while those with stronger interactions can prevent crystallization through increased solubilities. Organic amines that interact more strongly with inorganic components and exhibit greater rigidity are more likely to be incorporated into crystalline products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1975

The use of back corrections in multistep methods of numerical integration

Generalized multistep methods for the numerical solution of nonlinear systems of ordinary differential equations are introduced which allow the correction of previously computed values of the solution at internal points of the grid. These methods are shown to possess enhanced numerical stability. Preliminary numerical results indicate that for some satellite orbit problems these methods also possess greater overall efficiency. A uniformly converging theory of error propagation is presented which is valid for nonasymptotic values of the step size. Experimental results are seen to conform with theory.

Beaudet, P.↗
NASA NTRS1976

Simulated traveling interplanetary disturbances initiated by various solar phenomena

Earlier studies have shown that interplanetary disturbances observed by spacecraft at large heliocentric distances from the sun can be directly associated with various solar activities such as surges, sprays, eruptive prominences, and flares. A digital computer code to simulate these phenomena is developed. This numerical code solves a set of conservation equations for an adiabatic time-dependent spherically-symmetric fluid flow. The solar events are simulated by perturbations in the dependent variables at the lower boundary of the quiet sun corona, and the time-dependent numerical solution simulates the coronal response. Three physical cases are simulated by using the proposed numerical code: (1) part of a surge, spray and prominence; (2) a single flare; and (3) two flares whose interplanetary consequences interact in space. Results for the first two cases are compared with both ground-based and space probe observations. Fairly good agreement with observations is found. A comparison of the third case with observations is presently under way.

Dryer, M.↗
NASA NTRS1981

Heat transfer in a periodic boundary layer near an axisymmetric stagnation point on a circular cylinder

An analysis is presented to investigate the time-mean characteristics of the laminar boundary layer near an axisymmetric stagnation point when the velocity of the oncoming flow relative to the body oscillates. Different solutions are obtained for the small and high values of the reduced frequency parameter. Numerical solutions for the velocity and temperature functions are presented and the wall values of the velocity gradients are tabulated.

Gorla, R. S. R.↗
NASA NTRS1982

Solutions of the compressible Navier-Stokes equations using the integral method

The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.

Elrefaee, M. M.↗
NASA NTRS1984

Forced stationary solutions in a barotropic channel: Multiple equilibria and theory of nonlinear resonance

A barotropic flow over sinusoidal topography in a beta channel in the presence of forcing and dissipation was studied. The work is divided into two parts: (1) computation of the stationary solutions of the model, by Newton's method together with a finite difference approximation, and comparison of solutions with the solutions of the linear theory; (2) development of a nonlinear theory that reproduce the numerical solutions.

Rambaldi, S.↗
NASA NTRS1988

Excitations of low-frequency hydromagnetic waves by freshly created ions in the solar wind

Low-frequency hydromagnetic waves excited by newborn ions in the solar wind plasma are studied. The freshly created ions appear in the solar wind frame with a ring beam distribution. Both Alfven and fast magnetosonic waves are made unstable by the presence of the newborn ions. The dependence of the growth rate of both waves on the newborn ion density, the angle between the interplanetary magnetic field (IMF) and solar wind flow, and the angle of wave propagation relative to the IMF is investigated. Analytic approximations for the growth rates are presented, and numerical solutions of the dispersion equation are shown. The approximations are quite close to the numerically determined growth rates. It is found that the waves grow preferentially in the direction parallel to the IMF, and that the growth rates increase with both newborn ion density and the angle between the IMF and the solar wind flow.

Price, C. P.↗
NASA NTRS1988

Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming

In order to obtain the physically relevant discontinuous numerical solution, the steady-state inviscid Burgers' equation is singularly perturbed through the addition of a small amount of viscosity. A 'cell-centered' finite-difference scheme is proposed which employs two points for the inviscid part and four points for the viscous one. While difficulties are experienced in the capture of interior layers centered at node points, computational results for interior layers centered between node points, and for boundary layers, exhibit accurate nonoscillatory solutions whose discontinuities are captured in one cell on both coarse and fine grids.

Lavery, John E.↗
NASA NTRS1989

Moment method with isoparametric elements for three-dimensional anisotropic scatterers

A novel method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatters is presented. The method is based on a general volume integrodifferential formulation of the scattering problem and consists of the numerical solution of the coupled integral equations by the moment method and point matching. The numerical model of the scatterer is obtained by parametric volume elements, and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples.

Graglia, Roberto D.↗
NASA NTRS1992

A two-dimensional Euler solution for an unbladed jet engine configuration

A two dimensional, nonaxisymmetric Euler solution in a geometry representative of a jet engine configuration without blades is presented. The domain, including internal and external flow, is covered with a multiblock grid. In order to construct this grid, a domain decomposition technique is used to subdivide the domain, and smooth grids are dimensioned and placed in each block. The Euler solution is verified by examining five theoretical properties. The result demonstrates techniques for performing numerical solutions in complex geometries and provides a foundation for complete engine throughflow calculations.

Stewart, Mark E. M.↗
DOE OSTI2021

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗
NASA NTRS1992

Scattering from dielectric structures above impedance surfaces and resistive sheets

Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods.

Sarabandi, Kamal↗
NASA NTRS1972

Kinetic theory analysis of rarefied gas flow through finite length slots

An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.

Raghuraman, P.↗
NASA NTRS1937

Potential flow about arbitrary biplane wing sections

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

Garrick, I E↗