44 research outputs found

    Localized Dispersive States in Nonlinear Coupled Mode Equations for Light Propagation in Fiber Bragg Gratings.

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    Dispersion effects induce new instabilities and dynamics in the weakly nonlinear description of light propagation in fiber Bragg gratings. A new family of dispersive localized pulses that propagate with the group velocity is numerically found, and its stability is also analyzed. The unavoidable different asymptotic order of transport and dispersion effects plays a crucial role in the determination of these localized states. These results are also interesting from the point of view of general pattern formation since this asymptotic imbalance is a generic situation in any transport-dominated (i.e., nonzero group velocity) spatially extended system

    Asymptotic description of maximum mistuning amplification of bladed disk forced response

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    The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the Asymptotic Mistuning Model (AMM), to determine which are the key ingredients of this amplification process are, and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model

    Streaky 3D Structures in the Boundary Layer

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    It has been recently shown [Choi, Nature, April 06 - Cossu, PRL, February 06] that 3D streaky structures in the boundary layer can remain laminar longer than the 2D Blasius °ow. The aim of this investigation is to study the possibility of promoting these 3D streaky structures via surface roughness, computing them and evaluat- ing the resulting stabilization using the Reduced Navier Stokes equations (RNS). The RNS are derived from Navier-Stokes making use of the fact that two very di®erent scales are present: one slow (streamwise direc- tion) and two short (spanwise and wall-normal direction). The RNS allows us to perform these 3D computations in a standard PC, without using CPU costly DNS simulations

    Computation of nonlinear streaky structures in boundary layer flow

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    In this work, the Reduced Navier Stokes (RNS) are numerically integrated, and used to calculate nonlinear finite amplitude streaks. These structures are interesting since they can have a stabilizing effect and delay the transition to the turbulent regime. RNS formulation is also used to compute the family of nonlinear intrinsic streaks that emerge from the leading edge in absence of any external perturbation. Finally, this formulation is generalized to include the possibility of having a curved bottom wal

    Forced Response of Mistuned Bladed Disks: Quantitative Validation of the Asymptotic Description

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    The effect of small mistuning in the forced response of a bladed disk is analyzed using a recently introduced methodology: the asymptotic mistuning model. The asymptotic mistuning model is an extremely reduced, simplified model that is derived directly from the full formulation of the mistuned bladed disk using a consistent perturbative procedure based on the relative smallness of the mistuning distortion. A detailed description of the derivation of the asymptotic mistuning model for a realistic bladed disk configuration is presented. The asymptotic mistuning model results for several different mistuning patterns and forcing conditions are compared with those from a high-resolution finite element model. The asymptotic mistuning model produces quantitatively accurate results, and, probably more relevant, it gives precise information about the factors (tuned modes and components of the mistuning pattern) that actually play a role in the vibrational forced response of mistuned bladed disks

    Inestabilidad oscilatoria y sus aplicaciones en mecánica de fluidos y combustión

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    Se analiza la aparición de la inestabilidad oscilatoria en sistemas tales que una de sus dimensiones espaciales es grande frente a la longitud de onda típica de la inestabilidad. Esta es una de las maneras genéricas en que los estados estacionarios pierden estabilidad para dar paso a estados más complicados, que involucran una frecuencia temporal y un número de onda espacial, y consisten en dos trenes de ondas que se propagan en sentidos opuestos a lo largo de la dimensión espacial grande. En las proximidades del punto de pérdida de estabilidad, se deducen las ecuaciones (ya conocidas) que describen la evolución débilmente no lineal de las amplitudes de los trenes de ondas, y se obtienen las cuatro condiciones de contorno (dos de ellas son nuevas) necesarias; estas condiciones expresan el efecto de las paredes laterales en la dirección espacial en la que es grande. Se'trata de un sistema de dos ecuaciones complejas acopladas de tipo Ginzburg-Landau para las amplitudes, que contiene términos de distinto orden de magnitud; dependiendo de los tamaños relativos de la longitud espacial grande (L ^> 1) y del parámetro de bifurcación (£ < 1), se llega a dos límites distinguidos. En el primero, que es válido en el comienzo de la bifurcación (sL2 ~ 1), se tiene un problema parabólico no local cuyas soluciones se estudian en el caso de paredes laterales perfectamente reflectoras y de paredes con coeficientes de reflexión muy grandes o muy pequeños. El segundo límite corresponde a valores mayores del parámetro de bifurcación (sL ~ 1) y en él aparece una nueva longitud característica intermedia, pequeña frente a la longitud total del dominio pero grande frente a la longitud de onda básica de la inestabilidad. Suponiendo que sólo se tienen escalas del orden de L, se obtiene un sistema de ecuaciones hiperbólicas no lineales para los módulos de las amplitudes. Para este sistema se analizan las soluciones estacionarias y su estabilidad, así como sus soluciones no estacionarias persistentes, encontrándose comportamientos periódicos, casiperiódicos y caóticos. También se analiza la validez del modelo hiperbólico, es decir, cuando las escalas intermedias permanecen efectivamente inhibidas. Por último, se comparan los resultados obtenidos con los de los de los experimentos presentes en la literatura. ABSTRACT The onset of the oscillatory instability is analyzed, in systems whose size in one spatial direction is large as compared with the characteristic wavelength of the instability . This instability is one of the generic bifurcations form steady states to more complex behavior; it involves a temporal frecuency and a spatial wavenumber and yields a pair of counter propagating wavetrains along the large spatial dimensión. The (already known) amplitude equations governing the weakly nonlinear evolution of the system near the bifurcation point are obtained, along with the four boundary conditions that are needed (two of them are new); those conditions take account of the effect of the sidewalls. The amplitude equations are two coupled complex Ginzburg-Landau equations that generically contains terms of different order of magnitude; depending on the relative size of the- large system length (L ^> 1) and the bifurcation parameter (e «C 1), two distinguished limits are considered. In the first one, that applies at the begining of the bifurcation (eL2 ~ 1), the system evolves according to a nonlocal parabolic problem, whose solutions are analyzed in the limiting cases of perfectly reflecting sidewalls and sidewalls with very large or very small reflection coefflcient. The second limit corresponds to higher valúes of the bifurcation parameter and involves a new intermedíate characteristic length. This scale is small as compared with the system length but still large as compared with typical instablity wavelength. A nonlinear hyperbolic system is derived for the evolution without intermediate scales. The steady states of this system and their stability are analyzed, and also some more complex large time behaviors (periodic, quasiperiodic and chaotic) are numerically described for representative valúes of the parameters. It is also elucidated whether these solutions without intermediate scales are good approximations of the solutions of the original amplitude equations. Finally, some comparisons with experiments in the literature are given

    Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

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    The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude

    Tranversal motion and flow structure of fully nonlinear streaks in a laminar boundary layer

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    Typical streak computations present in the literature correspond to linear streaks or to small amplitude nonlinear streaks computed using DNS or nonlinear PSE. We use the Reduced Navier-Stokes (RNS) equations to compute the streamwise evolution of fully non-linear streaks with high amplitude in a laminar flat plate boundary layer. The RNS formulation provides Reynolds number independent solutions that are asymptotically exact in the limit Re1Re \gg 1, it requires much less computational effort than DNS, and it does not have the consistency and convergence problems of the PSE. We present various streak computations to show that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, that end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results

    Analysis of the influence of the plasma thermodynamic regime in the spectrally resolved and mean radiative opacity calculations of carbon plasmas in a wide range of density and temperature

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    In this work the spectrally resolved, multigroup and mean radiative opacities of carbon plasmas are calculated for a wide range of plasma conditions which cover situations where corona, local thermodynamic and non-local thermodynamic equilibrium regimes are found. An analysis of the influence of the thermodynamic regime on these magnitudes is also carried out by means of comparisons of the results obtained from collisional-radiative, corona or Saha–Boltzmann equations. All the calculations presented in this work were performed using ABAKO/RAPCAL code

    Relativistic screened hydrogenic radial integrals

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    The computation of dipole matrix elements plays an important role in the study of absorption or emission of radiation by atoms in several fields such as astrophysics or inertial confinement fusion. In this work we obtain closed formulas for the dipole matrix elements of multielectron ions suitable for using in the framework of a Relativistic Screened Hydrogenic Model
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