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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Thick accretion disks - Self-similar, supercritical models

Self-similar models, characterized by near-equilibrium between gravity, centrifugal force and radiation pressure, are generated for geometrically thick, supercritical accretion disks analyzing their structure and stability. The assumption that hydrodynamic quantities scale as power laws in radius allows for computation of disk structure as a function of the angle from the rotation axis, given a viscosity law model to which the structure of the interior of the disk is sensitive. The behaviors of other hydrodynamic quantities near the surface depend on the viscosity law, but not on the degree of pressure support on the equator. All models are found to be unstable to local axisymmetric perturbations at high latitudes noting the role of convection in bringing the disk to marginal stability. It is recommended that future thick accretion disk models take into account both their convective nature and the dependence of their structure on the viscosity law.

Begelman, M. C.↗
NASA NTRS1987

On self-similarity of crack layer

The crack layer (CL) theory of Chudnovsky (1986), based on principles of thermodynamics of irreversible processes, employs a crucial hypothesis of self-similarity. The self-similarity hypothesis states that the value of the damage density at a point x of the active zone at a time t coincides with that at the corresponding point in the initial (t = 0) configuration of the active zone, the correspondence being given by a time-dependent affine transformation of the space variables. In this paper, the implications of the self-similarity hypothesis for qusi-static CL propagation is investigated using polystyrene as a model material and examining the evolution of damage distribution along the trailing edge which is approximated by a straight segment perpendicular to the crack path. The results support the self-similarity hypothesis adopted by the CL theory.

Botsis, J.↗
NASA NTRS1992

Self-similar evolution of magnetized plasmas. I - Quasi-static solution

The concept of linear expansion suggested by Wei-Hong (1989 and 1990), describes the self-similar evolution of a magnetic structure. Linear expansion can be represented by a single function which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general self-similar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasi-static solution is investigated in this paper. It is shown that a gamma = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands self-similarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding force-free magnetic field, the self-similar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasi-state modeling of a pressure confined magnetized plasmoid is analyzed.

Yang, Wei-Hong↗
NASA NTRS1996

A Numerical Study of Self-Similarity in a Turbulent Plane Wake Using Large-Eddy Simulation

Turbulent wakes are known to develop self-similarly sufficiently far downstream from obstacles that generate them. It has long been assumed that the spreading rate of the wake in the self-similar regime is independent of the details of the body generating the wake, being dependent only on the total drag (or momentum deficit). This assumption seems to be in contradiction with some recent experiments. In this study we attempt to complement these experimental investigations through a numerical study of a time-developing wake. A numerical study has the advantage of eliminating many of the uncontrolled factors present in experiments and allowing precise control of initial conditions. Large-eddy simulations employing the recently developed dynamic localization model are used to extend previous results from direct numerical simulations. The large-eddy simulation results are compared to the direct numerical simulation database, wherever such comparisons are feasible, as a check of the method. Like the experiments, the large-eddy simulations suggest that non-unique self-similar states, characterized by different spreading rates and turbulent statistics, are possible and that they can be maintained for significant time periods. The study also demonstrates the predictive capability of the dynamic localization subgrid model.

Ghosal, Sandip↗
NASA NTRS1995

Intermittency and extended self-similarity in the solar wind turbulence

Using the satellite measurements of the velocity field in the interplanetary plasma. we present some analysis which show the presence of a self-similar intermittent state in the solar wind turbulence. We used the so called Extended Self-Similarity hypothesis, which is well visible in the solar wind turbulence, showing convincing evidences for the presence of universal anomalous scaling laws. Through the Extended Self-Similarity we are able to calculate the scaling exponents of the velocity structure functions with very small uncertainties, and we show that these scaling exponents are in very good agreement with the multifractal models describing intermittency in magnetohydrodynamic flows.

Bruno, R.↗
NASA NTRS1992

Electromagnetically driven relativistic jets - A class of self-similar solutions

A class of self-similar solutions for relativistic winds driven by rotating magnetic fields is constructed. These winds are collimated to cylindrical jet flows of finite radii and may attain supermagnetosonic speeds with high Lorentz factors. Most of the flow acceleration results from the 'magnetic nozzle' effect and occurs beyond the fast magnetosonic point, which is typically located a few light cylinder radii from the rotation axis. Approximate equipartition between the electromagnetic and flow kinetic energies is generally achieved for these jets, in contrast to the radial wind case in which the flow is magnetically dominated at all radii.

Li, Zhi-Yun↗
NASA NTRS1988

Self-similar dynamics of polytropic gaseous spheres

The fundamental equations governing the self-similar dynamics of 'polytropic' gaseous spheres are derived, and the asymptotic solutions are given. The solutions divide into cases with and without 'critical points' in closed analogy with the solar wind solutions of Holzer and Axford (1970). Properties for solutions with critical points are discussed, and their behavior around the critical point is derived explicitly for n = 1. Numerical examples of self-similar solutions for n = 1 and n = 2 - gamma are presented, and the properties of the solutions are discussed.

Suto, Yasushi↗
NASA NTRS2001

A New Look at Self-Similarity in Strained Plane Wakes

In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.

Rogers, Michael M.↗
NASA NTRS1990

Self-similar evolution of the nonlinear magnetic buoyancy instability

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.

Shibata, K.↗
NASA NTRS1980

Self-similar solutions and their stability for the flow of relativistic fluids through channels

The paper analyzes the flow of a perfect relativistic fluid in a circular confining channel of variable cross-section, a situation which is currently thought to be relevant for models of beams protruding from radio galaxies. Families of self-similar solutions are found, and some of their topological characteristics are illustrated. However, a perturbative investigation of the solutions indicates that all such self-similar modes are unstable and would eventually evolve into some non-self-similar form.

Lerche, I.↗
NASA NTRS1987

Self-similar potential in the near wake

The plasma potential is measured near the edge of an electrically floating obstacle placed in a steady-state, supersonic, unmagnetized, neutral plasma flow. Equipotential contours show the sheath of the upstream side of the obstacle wrapping around the edge of the obstacle and fanning out into the near wake. Both fluid theory and the data find the near-wake plasma potential to be self-similar when ionization, charge exchange, and magnetic field can be neglected. The theory also finds that fluid velocity is self-similar, the near wake is nonneutral, and plasma density is not self-similar. Strong electric fields are found near the obstacle and equipotential contours are found to conform to all boundaries.

Diebold, D.↗
NASA NTRS1998

Self-Similar Compressible Free Vortices

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

vonEllenrieder, Karl↗
NASA NTRS1994

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

Rogers, Michael M.↗
NASA NTRS1972

A parametric study of self-similar blast waves.

Comprehensive examination of self-similar blast waves with respect to two parameters, one describing the front velocity and the other the variation of the ambient density immediately ahead of the front. All possible front trajectories are taken into account, including limiting cases of the exponential and logarithmic form. The structure of the waves is analyzed by means of a phase plane defined in terms of two reduced coordinates. Loci of extrema of the integral curves in the phase plane are traced, and loci of singularities are determined on the basis of their intersections. Boundary conditons are introduced for the case where the medium into which the waves propagate is at rest. Representative solutions, pertaining to all the possible cases of blast waves bounded by shock fronts propagating into an atmosphere of uniform density, are obtained by evaluating the integral curves and determining the corresponding profiles of the gasdynamic parameters. Particular examples of integral curves for waves bounded by detonations are given, and all the degenerate solutions corresponding to cases where the integral curve is reduced to a point are delineated.

Oppenheim, A. K.↗
NASA NTRS1972

On self-similar blast waves headed by the Chapman-Jouguet detonation.

Consideration of the whole class of self-similar solutions for blast waves bounded by Chapman-Jouguet detonations that propagate into a uniform, quiescent, zero counterpressure atmosphere of a perfect gas with constant specific heats. Since such conditions can be approached quite closely by some actual chemical systems at NTP, this raises the interesting possibility of the existence of Chapman-Jouguet detonations of variable velocity. The principal virtue of the results presented is, however, more of theoretical significance. They represent the limiting case for all the self-similar blast waves headed by gasdynamic discontinuities associated with a deposition of finite amounts of energy, and they exhibit some unique features owing to the singular nature of the Chapman-Jouguet condition.

Oppenheim, A. K.↗
NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗
NASA NTRS1984

Experimental observations of self-similar plasma expansion

The present investigation is concerned with measurements of the plasma potential profile of an expanding plasma, taking into account the demonstration of the self-similar behavior of such a plasma. The obtained experimental results are consistent with self-similar solutions reported by Crow et al. (1975). It is found that the quasi-neutrality condition breaks down early during the experiment. A consideration of the effect of charge separation is, therefore, required. Attention is given to the evolution of the potential profiles of the expanding plasma as a function of time, the accelerated ion fronts, and the sheath formation of the expanding plasma into a floating boundary.

Chan, C.↗