Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

1／2亚谐共振──主参数共振情况下非线性振动系统的余维2退化分叉

本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性.     

Delay Model for a Cycling Transport Through Porous Medium

A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed.     

Stick-slip instability analysis

A theoretical investigation of friction-induced self-excited oscillations for systems with one degree of freedom is proposed. The friction force is assumed as an odd function of the relative sliding velocity with a jump discontinuity at a value of zero for the relative sliding velocity. The friction characteristic is approximated with a piecewise linear function, i.e. straight line segments with a suitable slope. For the generic system belonging to the class in question, the stick-slip instability region is located on a suitable dimensionless map.

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Sommario Viene proposta un'indagine teorica sulle oscillazioni autoeccitate indotte dall'attrito per sistemi ad un grado di libertà. La forza d'attrito viene assunta come funzione dispari della velocità relativa tra le superfici accoppiate, con una discontinuità di prima specie in corrispondenza del valore nullo della velocità. La caratteristica d'attrito viene approssimata mediante una funzione lineare a tratti con segmenti di opportuna pendenza. Per il generico sistema appartenente alla classe in esame, si perviene all'individuazione, su opportuna mappa adimensionale, della regione di instabilità da stick-slip.

     

Turbulent Channel Flow with an Artificial Two-Dimensional Wall Layer

Turbulent flow of an incompressible fluid in a plane channel with parallel walls is considered. The three-dimensional time-dependent Navier-Stokes equations are solved numerically using the spectral finite-difference method. An artificial force which completely suppresses lateral oscillations of the velocity is introduced in the near-wall zone (10 % of the channel half-width in the neighborhood of each wall). Thus, the three-dimensional flow zone, in which turbulent oscillations can develop, is separated from the wall by a fluid layer. It is found that the elimination of three-dimensionality in the neighborhood of the walls leads to a significant reduction in the drag. However, complete laminarization does not occur. The flow in the stream core remains turbulent and can be interpreted as a turbulent flow in a channel with walls located on the boundary of the two-dimensional layer and traveling at the local mean-flow velocity. The oscillations developing inside the two-dimensional layer, which have significant amplitude, distort the flow only in the adjacent zone. Beyond this zone the distributions of the mean characteristics and the structure of instantaneous fields completely correspond to ordinary turbulent flow in a channel with rigid walls. The results obtained confirm the hypothesis of the unimportance of the no-slip boundary conditions for the fluctuating velocity component in the mechanism of onset and self-maintenance of turbulence in wall flows.     

Numerical analysis of pressure oscillations over axisymmetric spiked blunt bodies at Mach 6.80

The pressure oscillations over a forward facing spike attached to an axisymmetric blunt body are simulated by solving time-dependent compressible Navier–Stokes equations. The governing fluid flow equations are discretized in spatial coordinates employing a finite volume approach which reduces the equations to semidiscretized ordinary differential equations. Temporal integration is performed using the two-stage Runge–Kutta time stepping scheme. A global time step is used to obtain a time-accurate numerical solution. The numerical computation is carried out for a freestream Mach number of 6.80 and for spike length to hemispherical diameter ratios of 0.5, 1.0 and 2.0. The flow features around the spiked blunt body are characterized by a conical shock wave emanating from the spike tip, a region of separated flow in front of the hemispherical cap, and the resulting reattachment shock wave. Comparisons of the numerical results are made with the available experimental results, such as schlieren pictures and the surface pressure distribution along the spiked blunt body. They are found to be in good agreement. Spectral analysis of the computed pressure oscillations are performed employing fast Fourier transforms. The surface pressure oscillations over the spike and phase plots exhibit a behaviour analogous to that of the Van der Pol equation for a self-sustained oscillatory flow. Received 28 February 2001 / Accepted 17 January 2002     

Oscillations and global attractivity in models of hematopoiesis

LetP(t) denote the density of mature cells in blood circulation. Mackey and Glass (1977) have proposed the following equations:

Multiple Scales via Galerkin Projections: Approximate Asymptotics for Strongly Nonlinear Oscillations

The method of multiple scales and the related method of averaging are commonly used tostudy slowly modulated oscillations. If the system of interest is a slightlyperturbed harmonic oscillator, then these techniques can be applied easily. If the unperturbed system is strongly nonlinear (though possiblyconservative), then these methods can run into difficulties due to the impossibilityof carrying out required analytical operations in closed form.In this paper, we abandon the requirement of closed form analyticaltreatment at all stages. Instead, Galerkin projections are used toobtain approximate realizations of the method of multiple scales. Thispaper adapts recent work using similar ideas for approximaterealizations of the method of averaging. A key contribution of thepresent work is in the systematic identification and removal of secularterms in the general nonlinear case, a procedure that is more difficultthan for the perturbed harmonic oscillator case, and that is unnecessaryfor averaging.A strength of the present work is that the heuristics (Galerkin)and asymptotics (multiple scales) are kept distinct,leaving room for systematic refinement of the formerwithout compromising the asymptotic features of the latter.     

The response of nonlinear systems to modulated high-frequency input

We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.