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At least 73 records · Page 4

Shock structure in classical magnetohydrodynamics

How the structure of coplanar MHD fast and slow shocks depends upon the relative magnitudes of the dissipation coefficients contained in classical magnetohydrodynamics is examined. An asymptotic method is used in which the scale lengths for resistivity, thermal conduction, and viscosity are widely separated, and the qualitative dependence of the shock solutions upon the ordering of the scales is studied. Upper limit Mach numbers for both fast and slow shocks are defined at which resistivity and thermal conduction taken together can provide all the shock dissipation and at which viscosity is not needed.

Kennel, Charles F.↗

Guidance analysis of the aeroglide plane change maneuver as a turning point problem

The development of guidance approximations for the atmospheric (aeroglide) portion of the minimum fuel, orbital plane change, trajectory optimization problem is described. Asymptotic methods are used to reduce the two point, boundary value, optimization problem to a turning point problem from the bank angle control. The turning point problem solution, which yields an approximate optimal control policy, is given in terms of parabolic cylinder functions, which are tabulated, and integral expressions, which must be numerically computed. Comparisons of the former, over their region of validity, with optimal control solutions show good qualitative agreement. Additional work and analysis is needed to compute the guidance approximation work.

Gracey, Christopher↗

A review of instability and noise propagation in supersonic flows

Originally analytical and numerical models were to be developed for noise production in supersonic jets, wakes and free shear layers. While the effort was concentrated initially on these aspects, other topics were also pursued, most were of interest to the Jet Noise Group of the Aeroacoustics Branch. An overview is given of subjects reviewed and the investigations that were carried out. A significant effort was devoted to numerically predicting the flow field of a turbulent supersonic wall jet. This information is necessary for computing the pressure in the far field. The wall jet was selected because it represents a generic flow that can be associated with plug nozzle in supersonic engines. It combines the characteristic of a boundary layer with that of a free shear flow. The spatially evolving flow obtained using Dash's code would form the input for the stability analysis program. This analysis would determine the large scale instability wave within the flow. The far field pressure can be computed from the shape of the evolving large scale structure by asymptotic methods. Flow characteristics obtained from a program that analyses the turbulent downstream supersonic flow in a nozzle are described and compared with experimental results.

Daudpota, Q. Isa↗

Non linear evolution of a second mode wave in supersonic boundary layers

Presented here are several direct simulations of one 2-D second mode perturbation wave, superimposed upon a prescribed mean flow. Periodicity is assumed in the streamwise direction (Fourier) and the variables are expanded in Chebyshev series in the direction normal to the flat plate. The code is fully explicit and is time advanced with a 3rd order Runge-Kutta scheme. The second mode wave (R delta prime = 8000), interacts with itself to generate higher streamwise harmonics. Physical parameters are chosen to maximize the linear growth rate at the prescribed Reynolds number. Initial results indicate that the nonlinear processes begin in the critical layer region and are the result of the cubic interactions in the momentum equations, rather than due to the higher streamwise harmonics. Analysis of the various terms in the momentum equations combined with numerical experiments in which various modes are artificially suppressed, lead to the conclusion that asymptotic methods will produce the saturated state in one or two order of magnitude less computer time than that required by the direct numerical simulations.

Erlebacher, Gordon↗

Numerical computation of transition to turbulence

Current applications of numerical simulations, including studies of mildly nonlinear and strongly nonlinear effects, and incipient turbulence are reviewed, and it is observed that one mildly nonlinear application for which direct simulations need to take a leading part is in establishing confidence in the dominant instability of a flow, while direct simulations are the primary tool when nonlinear effects are stronger than can be handled by existing asymptotic methods. The characteristics of existing algorithms for transition simulations are discussed, along with algorithmic improvements which would extend the range of problems amenable to numerical simulations. Current and future issues and problems are outlined.

Zang, Thomas A.↗

Receptivity of boundary layers to acoustic and vortical free-stream disturbances

The receptivity mechanisms by which free-stream disturbances generate instability waves in laminar boundary layers are discussed. Free-stream disturbances have wavelengths which are generally much longer than those of instability waves. Hence, the transfer of energy from the free-stream disturbance to the instability wave requires a wavelength conversion mechanism. Recent analyses using asymptotic methods have shown that the wavelength conversion takes place in regions of the boundary layer where the mean flow adjusts on a short streamwise length scale. This paper reviews recent progress in the theoretical understanding of these phenomena and suggests directions for future research in this area.

Kerschen, Edward J.↗

Effects of streamwise curvature variations on Goertler vortices

The influence of wall curvature oscillations on Goertler vortices is studied using an asymptotic method. A large number of oscillations leads to a stabilization of the Goertler vortices. In addition, basic velocity profile of a flow over a wall with a large number of oscillations is similar to that over a wall without oscillation. The curvature stays positive while oscillating and the wall is concave. On a wall with curvature decreasing to zero, the Goertler vortices move outside of the boundary layer; no discrete eigenvalue of Goertler instability is found on a wall with zero curvature. In this case the discrete eigenvalues merge into a continuous spectrum.

Jallade, Sophie↗

Modeling of composite beams and plates for static and dynamic analysis

A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.

Hodges, Dewey H.↗

MHD flow past an obstacle - Large-scale flow in the magnetosheath

As a step to the study of the large-scale flow in the magnetosheath, the MHD flow past an obstacle is investigated. A time asymptotic method is used to obtain 3D steady-state solutions. The results indicate the formation of a depletion layer near the obstacle due to the increase of the magnetic field. Along the earth-sun line the plasma density increases first and then decreases from the post bow shock to the magnetopause. The local density maximum in front of the magnetopause may correspond to what was recently observed. When the interplanetary magnetic field direction is tilted from the solar wind flow, the IMF influences the shape of the bow shock as well as the location of the stagnation point at the magnetopause in a way consistent with observation. In addition, the results show the existence of a magnetosheath current in the post parallel-shock region.

Wu, C. C.↗

Modeling of composite beams and plates for static and dynamic analysis

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.

Hodges, Dewey H.↗

Studies of droplet burning and extinction

A project on droplet combustion, pursued jointly with F.L. Dryer of Princeton University, has now been in progress for many years. The project involves experiments on the burning of single droplets in various atmospheres, mainly at normal atmosperic pressure and below, performed in drop towers and designed to be performed aboard space-based platforms such as the Space Shuttle or the Space Station. It also involves numerical computations on droplet burning, performed mainly at Princeton, and asymptotic analyses of droplet burning, performed mainly at UCSD. The focus of the studies rests primarily on time-dependent droplet-burning characteristics and on extinction phenomena. The presentation to be given here concerns the recent research on application of asymptotic methods to investigation of the flame structure and extinction of hydrocarbon droplets. These theoretical studies are investigating the extent to which combustion of higher hydrocarbons - heptane, in particular - can be described by four-step reduced chemistry of the kind that has achieved a good degree of success for methane flames. The studies have progressed to a point at which a number of definite conclusions can now be stated. These conclusions and the reasoning that led to them are outlined here.

Williams, Forman A.↗

Long-wavelength asymptotics of unstable crossflow modes, including the effect of surface curvature

Stationary vortex instabilities with wavelengths significantly larger than the thickness of the underlying three-dimensional boundary layer are studied with asymptotic methods. The long-wavelength Rayleigh modes are locally neutral and are aligned with the direction of the local inviscid streamline. For a spanwise wave number Beta much less than 1, the spatial growth rate of these vortices is O(Beta(exp 3/2)). When Beta becomes O(R(exp -1/7)), the viscous correction associated with a thin sublayer near the surface modifies the inviscid growth rate to the leading order. As Beta is further decreased through this regime, viscous effects assume greater significance and dominate the growth-rate behavior. The spatial growth rate becomes comparable to the real part of the wave number when Beta = O(R(exp -1/4)). At this stage, the disturbance structure becomes fully viscous-inviscid interactive and is described by the triple-deck theory. For even smaller values of Beta, the vortex modes become nearly neutral again and align themselves with the direction of the wall-shear stress. Thus, the study explains the progression of the crossflow-vortex structure from the inflectional upper branch mode to nearly neutral long-wavelength modes that are aligned with the wall-shear direction.

Choudhari, Meelan↗

Evolution of dynamo-generated magnetic fields in accretion disks around compact and young stars

Geometrically thin, optically thick, turbulent accretion disks are believed to surround many stars. Some of them are the compact components of close binaries, while the others are throught to be T Tauri stars. These accretion disks must be magnetized objects because the accreted matter, whether it comes from the companion star (binaries) or from a collapsing molecular cloud core (single young stars), carries an embedded magnetic field. In addition, most accretion disks are hot and turbulent, thus meeting the condition for the MHD turbulent dynamo to maintain and amplify any seed field magnetic field. In fact, for a disk's magnetic field to persist long enough in comparison with the disk viscous time it must be contemporaneously regenerated because the characteristic diffusion time of a magnetic field is typically much shorter than a disk's viscous time. This is true for most thin accretion disks. Consequently, studying magentic fields in thin disks is usually synonymous with studying magnetic dynamos, a fact that is not commonly recognized in the literature. Progress in studying the structure of many accretion disks was achieved mainly because most disks can be regarded as two-dimensional flows in which vertical and radial structures are largely decoupled. By analogy, in a thin disk, one may expect that vertical and radial structures of the magnetic field are decoupled because the magnetic field diffuses more rapidly to the vertical boundary of the disk than along the radius. Thus, an asymptotic method, called an adiabatic approximation, can be applied to accretion disk dynamo. We can represent the solution to the dynamo equation in the form B = Q(r)b(r,z), where Q(r) describes the field distribution along the radius, while the field distribution across the disk is included in the vector function b, which parametrically depends on r and is normalized by the condition max (b(z)) = 1. The field distribution across the disk is established rapidly, while the radial distribution Q(r) evolves on a considerably longer timescale. It is this evolution that is the subject of this paper.

Stepinski, Tomasz F.↗

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Balsa, Thomas F.↗

Studies of droplet burning and extinction

A project on droplet combustion, pursued jointly with F. L. Dryer of Princeton University, has now been in progress for many years. The project involves experiments on the burning of single droplets in various atmospheres, mainly at normal atmospheric pressure and below, performed in drop towers and designed to be performed aboard space-based platforms such as the Space Shuttle or the Space Station and currently manifest for Spacelab in the MSL-1 flight of the Space Shuttle in April of 1997. It also involves numerical computations on droplet burning, performed mainly at Princeton, and asymptotic analyses of droplet burning, performed mainly at UCSD. The focus of the studies rests primarily on time-dependent droplet-burning characteristics and on extinction phenomena. The presentation to be given here concerns the recent research on application of asymptotic methods to investigation of the flame structure and extinction of alcohol droplets. These theoretical studies are relevant to the second of the proposed space-flight tests and are currently investigating the extent to which combustion of alcohols can be described by four-step reduced chemistry similar to that which has achieved a good degree of success for alkane flames. These studies have progressed to a point at which a number of definite conclusions can now be stated. These conclusions and the reasoning that led to them are outlined.

Williams, F. A.↗

The role of nonlinear critical layers in boundary layer transition

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

Goldstein, M.E.↗

The Effect of Nonlinear Critical Layers on Boundary Layer Transition

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear and spatially growing instability waves evolve downstream in nominally two-dimensional and spanwise periodic laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer' with the flow outside this layer consisting of a locally parallel mean flow plus an appropriate superposition of linear instability waves. The amplitudes of these waves are determined by either a single integro-differential equation or by a pair of integro-differential equations with quadratic to quartic-type nonlinearities.

Goldstein, Marvin E.↗

Interactions Between Solidification and Compositional Convection in Alloys

This project combined theoretical and experimental ground-based studies of the interactions between convection and solidification of binary melts. Particular attention was focused on the alteration of the composition and microstructure of castings caused by convective flows through the interstices of mushy layers. Two different mechanisms causing convection were investigated. (i) Compositional, buoyancy driven convection is known to cause chimneys and freckles in directionally cast alloys on Earth. The analytical studies provide quantitative criteria for the formation of chimneys that can be used to assess the expediency of producing alloys in Space. (ii) Flow of the melt is also driven by the contraction (expansion) that typically occurs during change of phase. Such convection will occur even in the absence of gravity, and may indeed be the primary cause of macrosegregation during the production of alloys in Space. The studies will employed asymptotic methods in order to determine conditions for the stability of various states of solidifying systems. Further, simple macroscopic models of complete systems were developed and solved. These analytical studies were augmented by laboratory experiments using aqueous solutions, in which the convective flows could be easily observed and the effects of convection could be readily measured. These y experiments guided the development of the theoretical models and provided data against which the predictions of the models can be tested.

Davis, S. H.↗