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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 163 records · Page 9
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NASA NTRS1999

A Generalized Wall Function

The asymptotic solutions, described by Tennekes and Lumley (1972), for surface flows in a channel, pipe or boundary layer at large Reynolds numbers are revisited. These solutions can be extended to more complex flows such as the flows with various pressure gradients, zero wall stress and rough surfaces, etc. In computational fluid dynamics (CFD), these solutions can be used as the boundary conditions to bridge the near-wall region of turbulent flows so that there is no need to have the fine grids near the wall unless the near-wall flow structures are required to resolve. These solutions are referred to as the wall functions. Furthermore, a generalized and unified law of the wall which is valid for whole surface layer (including viscous sublayer, buffer layer and inertial sublayer) is analytically constructed. The generalized law of the wall shows that the effect of both adverse and favorable pressure gradients on the surface flow is very significant. Such as unified wall function will be useful not only in deriving analytic expressions for surface flow properties but also bringing a great convenience for CFD methods to place accurate boundary conditions at any location away from the wall. The extended wall functions introduced in this paper can be used for complex flows with acceleration, deceleration, separation, recirculation and rough surfaces.

Shih, Tsan-Hsing↗
NASA NTRS1998

Re-examination of a Classic Experiment to Measure the Positronium-Helium Cross Section

In 1975, before the advent of positronium beams, a clever experiment was carried out in an attempt to measure low-energy Ps-atom scattering cross-sections, especially that of Ps-He. A series of parallel thin plates was placed in the vessel containing the sample of gas, and positrons were allowed to enter the chamber from a radioactive source. The time spectrum of annihilation radiation was observed in the traditional way, and the pickoff annihilation due to thermalized Ps striking one of the plates was to be the special feature of the experiment. Using a diffusion analysis the authors derived cross- sections for several gases, and for helium the value obtained was sigma = 0.0166 pi(alpha)(sub o, sup 2). Even then this value was thought to be very much too small, while recent measurements and some calculations suggest a more reasonable value would be sigma = 3 to 13 pi(alpha)(sub o,sup 2). It has always been puzzling that an apparently well-designed experiment should give such an unsatisfactory result. We have now re-examined the analysis of the data with some interesting consequences which may explain the discrepancy. Two main observations support our re-analysis. First, we note that the mean free path for Ps-He scattering would be quite long if the cross-section were as small as that quoted above; the diffusion method itself would seem to be questionable. For the larger values, however, there would be no such problem. Second, it was assumed that when the annihilation rate had settled down and was following an exponential decay curve the asymptotic solution of the diffusion equation had been reached. We find, instead, that a superposition of exponentials can accurately represent the decay curve, consistent with the higher cross-section value.

Drachman, Richard J.↗
NASA NTRS2005

Measurement of the Shear Lift Force on a Bubble in a Channel Flow

Two-phase flow systems play vital roles in the design of some current and anticipated space applications of two-phase systems which include: thermal management systems, transfer line flow in cryogenic storage, space nuclear power facilities, design and operation of thermal bus, life support systems, propulsion systems, In Situ Resource Utilization (ISRU), and space processes for pharmaceutical applications. The design of two-phase flow systems for space applications requires a clear knowledge of the behaviors of the dispersed phase (bubble), its interaction with the continuous phase (liquid) and its effect on heat and mass transfer processes, The need to understand the bubble generation process arises from the fact that for all space applications, the size and distribution of bubbles are extremely crucial for heat and mass transfer control. One important force in two-phase flow systems is the lift force on a bubble or particle in a liquid shear flow. The shear lift is usually overwhelmed by buoyancy in normal gravity, but it becomes an important force in reduced gravity. Since the liquid flow is usually sheared because of the confining wall, the trajectories of bubbles and particles injected into the liquid flow are affected by the shear lift in reduced gravity. A series of experiments are performed to investigate the lift force on a bubble in a liquid shear flow and its effect on the detachment of a bubble from a wall under low gravity conditions. Experiments are executed in a Poiseuille flow in a channel. An air-water system is used in these experiments that are performed in the 2.2 second drop tower. A bubble is injected into the shear flow from a small injector and the shear lift is measured while the bubble is held stationary relative to the fluid. The trajectory of the bubble prior, during and after its detachment from the injector is investigated. The measured shear lift force is calculated from the trajectory of the bubble at the detachment point. These values for the shear lift are then compared with the theoretical predictions from various published works on shear lift in the open literature, which include asymptotic solutions at low bubble Reynolds number, potential flow predictions and numerical studies that deal with intermediate bubble Reynolds numbers.

Nahra, Henry K.↗
NASA NTRS2003

Detecting Moving Targets by Use of Soliton Resonances

A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

Zak, Michael↗
NASA NTRS2013

Zero-gravity Mean Free Surface Curvature of a Confined Liquid in a Radially-Vaned Container

A variety of increasingly intricate container geometries are under consideration for the passive manipulation of liquids aboard spacecraft where the impact of gravity may be neglected. In this study we examine the mean curvature of a liquid volume confined within a radial array of disconnected vanes of infinite extent. This particular geometry possesses a number of desirable characteristics relevant to waste water treatment aboard spacecraft for life support. It is observed that under certain conditions the slender shape of the free surface approaches an asymptote, which can be predicted analytically using new hybrid boundary conditions proposed herein. This contribution represents possibly the final extension of what has been referred to as the method of de Lazzer et al. (1996). The method enables the integration of the Young-Laplace equation over a domain with its boundaries, including the wetted portion of the solid boundaries, symmetry planes, and circular arcs representing free surfaces at the center plane of the liquid body. Asymptotic solutions at several limits are obtained and the analysis is confirmed with numerical computations.

Chen, Yongkang↗
NASA NTRS1992

Comparison of numerical oblique detonation solutions with an asymptotic benchmark

In order to have confidence in a numerical method, the verification of its reproduction of known benchmark analytic solutions for simple model problems is of great importance. Attention is presently given to a novel benchmarking procedure for numerical models of high speed, reactive 2D flows. The procedure is illustrated by comparing asymptotic and numerical solutions for oblique detonations in which an attached oblique shock is followed by an exothermic reaction with a thick reaction zone.

Grismer, Matthew J.↗
NASA NTRS1988

An invariant asymptotic formula for solutions of second-order linear ODE's

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

Gingold, H.↗
NASA NTRS1994

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Yakhot, A.↗
NASA NTRS1989

Asymptotic structure and similarity solutions for three-dimensional turbulent boundary layers

The asymptotic structure of the three-dimensional turbulent boundary layer is investigated in the limit of large Reynolds numbers. A self-consistent, but relatively complex, two-layer structure exists and the simplest situation, corresponding to a plane of symmetry, is considered in this paper as a first step. The adjustment of the streamwise velocity to relative rest, through an outer defect layer and then an inner wall layer, is similar to that in two-dimensional flow. The adjustment of the cross-streamwise velocity is more complicated and it is shown that two terms in the expansion are required to obtain useful results, and in particular to obtain the velocity skew angle at the wall near the symmetry plane. The conditions under which self-similarity is achieved near a plane of symmetry are investigated. A set of ordinary differential equations is developed which describe the streamwise and cross-streamwise velocities near a plane of symmetry in a self-similar flow through two orders of magnitude. Calculated numerical solutions of these equations yield trends which are consistent with experimental observations.

Degani, A. T.↗
NASA NTRS1985

Three-dimensional convection in horizontal cylinders - Numerical solutions and comparison with experimental and analytical results

The results of a three-dimensional numerical simulation of Boussinesq free convection in a horizontal differentially heated cylinder are presented. The computation was based on a Samarskii-Andreyev scheme (described by Leong, 1981) and a false-transient advancement in time, with vorticity, velocity, and temperature as dependent variables. Solutions for velocity and temperature distributions were obtained for Rayleigh numbers (based on the radius) Ra = 74-18,700, thus covering the core- and boundary-layer-driven regimes. Numerical solutions are compared with asymptotic analytical solutions and experimental data. The numerical results well represent the complex three-dimensional flows found experimentally.

Smutek, C.↗
NASA NTRS1990

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Shaw, Stephen J.↗
NASA NTRS1992

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Shaw, Stephen J.↗