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Results for “ASYMPTOTIC METHOD”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

An asymptotic description of transient settling and ultrafiltration of colloidal dispersions

The present model for the sedimentation of colloidal systems includes a diffusion term in the governing equation which, in the regions above the sediment, acts as small perturbation to the Kynch (1952) theory. Within the sediment, diffusion is comparable to convection due to the the high solid volume fraction. An application of the method of matched asymptotic expansions to the conservation equation allows a complete description of the settling process to be formulated, with specific attention to volume-fraction evolution in the sediment.

Davis, K. E.↗
NASA NTRS2018

Vertical Profile of Cloud Optical Parameters Derived from Airborne Measurements Above, Inside and Below Clouds

Past strategies for retrieving cloud optical properties from remote sensing assumed significant limits for desired parameters such as semi-infinite optical thickness, single scattering albedo equaling unity (non-absorbing scattering), absence of spectral dependence of the optical thickness, etc., and only one optical parameter could be retrieved (either optical thickness or single scattering albedo). Here, we demonstrate a new method based on asymptotic theory for thick atmospheres, and the presence of a diffusion domain within the clouds that does not put restrictions and makes it possible to get two or even three optical parameters (optical thickness, single scattering albedo and phase function asymmetry parameter) for every wavelength independently. We applied this method to measurements of angular distribution of solar radiation above, inside and below clouds, obtained with NASA's Cloud Absorption Radiometer (CAR) over two cases of marine stratocumulus clouds; first case, offshore of Namibia and the second case, offshore of California. The observational and retrieval errors are accounted for by regularization, which allows stable and smooth solutions. Results show good potential for parameterization of the shortwave radiative properties (reflection, transmission, radiative divergence and heating rate) of water clouds.

airborne observations↗
NASA NTRS1972

Lifting-surface theory for calculating the loading induced on a wing by a flap

A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.

Johnson, W. A.↗
NASA NTRS1987

Guidance and control strategies for aerospace vehicles

A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed.

Hibey, Joseph L.↗
NASA NTRS1993

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Hagstrom, Thomas↗
NASA NTRS1992

Asymptotic modal analysis of a rectangular acoustic cavity excited by wall vibration

Asymptotic modal analysis, a method that has recently been developed for structural dynamical systems, has been applied to a rectangular acoustic cavity. The cavity had a flexible vibrating portion on one wall, and the other five walls were rigid. Banded white noise was transmitted through the flexible portion (plate) only. Both the location along the wall and the size of the plate were varied. The mean square pressure levels of the cavity interior were computed as a ratio of the result obtained from classical modal analysis to that obtained from asymptotic modal analysis for the various plate configurations. In general, this ratio converged to 1.0 as the number of responding modes increased. Intensification effects were found due to both the excitation location and the response location. The asymptotic modal analysis method was both efficient and accurate in solving the given problem. The method has advantages over the traditional methods that are used for solving dynamics problems with a large number of responding modes.

Peretti, Linda F.↗
NASA NTRS1987

The fully nonlinear development of Goertler vortices in growing boundary layers

The fully nonlinear development of small wavelength Goertler vortices in a growing boundary layer is investigated using a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall (1982b) who discussed the initial development of small amplitude vortices in a neighborhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact the system obtained by writing down the equations for the fundamental component of the vortex generate a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a square-root profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free-stream. In this situation the mean flow has essentially no relationship to the flow which exists in the absence of the vortices.

Hall, Philip↗
NASA NTRS1975

Perturbation solution of the Navier-Stokes equations and its relation to the Lighthill-Curle solution of aerodynamic sound

The aerodynamic sound described by the Lighthill-Curle solution is reexamined using a method of matched asymptotic expansions. The governing Navier-Stokes equations written in nondimensional form are expanded for a small Mach number. First- and second-order solutions for the pressure field are obtained, and the singular nature of the expansion at large distances is indicated. The nearfield pressure is governed by the Poisson equation, whereas the farfield equations describe a linear wave system in a dissipative medium. The pseudosound is related to the incompressible Reynolds stresses associated with a solenoidal velocity field, the velocity, the pressure perturbation, and their derivatives on the boundaries. A uniformly valid first-order solution for the pressure is obtained. It is shown that viscosity, thermal conductivity, and entropy in the flow do not contribute to the first-order noise generation, while the viscous stress contributes to noise only from some boundaries. The application of the proposed perturbation method to a subsonically moving surface and a hot jet is discussed.

Pan, Y. S.↗
DOE OSTI2024

Enhancing the cooling performance of thermocouples: a power-constrained topology optimization procedure

Abstract Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form $$p_k=p_{\sigma }>p_{\alpha }=1$$ p k = p σ > p α = 1 for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

Gutiérrez, G. Reales↗
DOE OSTI2025

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗
DOE OSTI2025

Moment-based adaptive time integration for thermal radiation transport

Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dynamical defects in a two-dimensional Wigner crystal: Self-doping and kinetic magnetism

We study the quantum dynamics of interstitials and vacancies in a two-dimensional Wigner crystal (WC) using a semi-classical instanton method that is asymptotically exact at low density, i.e., in the r s → ∞ limit. Here, the dynamics of these point defects mediates magnetism with much higher energy scales than the exchange energies of the pure WC. Via exact diagonalization of the derived effective Hamiltonians in the single-defect sectors, we find the dynamical corrections to the defect energies. The resulting expression for the interstitial (vacancy) energy extrapolates to 0 at r s = r mit ≈ 70 (r s ≈ 30), suggestive of a self-doping instability to a partially melted WC for some range of r s below r mit . We thus propose a “metallic electron crystal” phase of the two-dimensional electron gas at intermediate densities between a low density insulating WC and a high density Fermi fluid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1972

Analysis of an entrainment model of the jet in a crossflow

A theoretical model has been proposed for the problem of a round jet in an incompressible cross-flow. The method of matched asymptotic expansions has been applied to this problem. For the solution to the flow problem in the inner region, the re-entrant wake flow model was used with the re-entrant flow representing the fluid entrained by the jet. Higher order corrections are obtained in terms of this basic solution. The perturbation terms in the outer region was found to be a line distribution of doublets and sources. The line distribution of sources represents the combined effect of the entrainment and the displacement.

Chang, H. S.↗
NASA NTRS1973

Transonic flow about lifting configurations.

A transonic flow solution is presented for configurations with span-to-length ratios of order one. The angles of attack are sufficiently large to produce lift effects that are either dominant or comparable to the thickness effects. The analysis is performed with the aid of the method of matched asymptotic expansions. The results obtained are compared with data reported by Cheng and Hafez (1972).

Barnwell, R. W.↗
NASA NTRS1974

Viscous, radiating hypersonic flow about a blunt body

The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.

Passamaneck, R. S.↗
NASA NTRS1974

Conical flow near singular rays

The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.

Zahalak, G. I.↗
NASA NTRS1974

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

Melnik, R. E.↗
NASA NTRS1974

Some analytical results for radiative transfer in thick atmospheres

Singular eigenmode expansions are a convenient analytical tool with which to study problems of monochromatic radiative transfer in thick or semi-infinite atmospheres. Some closed-form solutions are presented for anisotropic scattering, with the neglect of polarization effects. A basic ingredient for applications to the semi-infinite medium is Chandrasekhar's H-function, which is best defined through the Wiener-Hopf factorization. The solutions of the Milne and albedo problems are discussed in order that the method of matched asymptotic approximations may be used to describe the solution for a thick atmosphere adjacent to a diffusely reflecting ground. Expressions for the emerging distributions are quoted. A possible extension of the general scheme to problems involving polarization is indicated.

Kuscer, I.↗