Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations

A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing frequencies. Up to now, harmonic balance methods have used a uniform time sampling of the period of interest, but in the case of several frequencies, non-necessarily multiple of each other, harmonic balance methods can face stability issues due to a bad condition number of the Fourier operator. Two algorithms are derived to find a non-uniform time sampling in order to minimize this condition number. Their behavior is studied on a wide range of frequencies, and a model problem of a 1D flow with pulsating outlet pressure, which enables to prove their efficiency. Finally, the flow in a multi-stage axial compressor is analyzed with different frequency sets. It demonstrates the stability and robustness of the present non-uniform harmonic balance method regardless of the frequency set

Le retour du juridique comme dimension constitutive des théories critiques des relations internationales ?

Dans la discipline anglo-américaine des relations internationales (ri), la frontière entre l’étude des ri et celle du droit international (di) est devenue de plus en plus étanche au cours du 20e siècle. Les théories critiques, n’échappent pas à ce traitement instrumental du di. Si plusieurs tiennent un propos plutôt empirique sur le droit, d’autres développent des stratégies théoriques afin de faire du droit une dimension constitutive de leur théorie. On se propose ici d’explorer deux tentatives des théories critiques de développer une relation plus dynamique avec les catégories juridiques. La première est celle de Jürgen Habermas de renouveler une théorie cosmopolite des ri ; la seconde est celle de Benno Teschke de faire du droit une catégorie cognitive centrale pour une sociologie historique des ri articulée autour du concept de relations sociales de propriété.In the Anglo-American discipline of International Relations (ir), the boundaries between ir and International Law (il) have become increasingly unclear during the 20th Century. Traditional and critical theories of ir altogether tend to treat il in an instrumental manner. Many theories do have something empirical to say about International Law ; however, few have managed to incorporate law as a constitutive dimension in their theoretical framework. This article seeks to explore two attempts to develop such a relation with juridical categories. The first is Jürgen Habermas’ tentative to renew a cosmopolitan vision of ir ; the second is Benno Teschke’s one to articulate an historical sociology of ir with the concept of social property regime

Two-equation modeling of turbulent rotating flows

The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a (k,epsilon) model fitted with an existing Coriolis correction [J. H. G. Howard, S. V. Patankar, and R. M. Bordynuik, "Flow prediction in rotating ducts using Coriolis-modified turbulence models", ASME Trans. J. Fluids Eng. 102, (1980)] is performed. Full analytical solutions are given for the flow predicted with this model in the situation of homogeneously sheared turbulence subject to rotation. The existence of an unphysical phenomenon of blowup at finite time is demonstrated in some range of the rotation-to-shear ratio. A direct connection is made between the slope of the mean-velocity profile in the plane-channel flow with spanwise rotation, and a particular fixed point of the dynamical system in homogeneously sheared turbulence subject to rotation. The general analysis, and the understanding of typical inaccuracies and misbehavior observed with the existing model, are then used to design a new model which is free from the phenomenon of blowup at finite time and able to account for both of the main influences of rotation on turbulence: the inhibition of the spectral transfer to high wave numbers and the shear/Coriolis instability

Description of the unsteady flow pattern from peak efficiency to near surge in subsonic centrifugal compressor stage

This paper aims to describe the flow structure modifications when the operating point moves from peak efficiency to near stall condition in a moderate pressure ratio centrifugal compressor stage consisted of a splittered unshrouded impeller and a vaned diffuser. The investigations are based on three-dimensional U-RANS simulation results. The flow is described in the impeller and in the vaned diffuser through time-averaged flow quantities and unsteady fluctuations. Results show that at low mass flow rate, the effects of secondary flow in the impeller are more pronounced, inducing both, high time-averaged values and temporal fluctuations of the flow angle near the shroud at the diffuser inlet, leading to vane suction side boundary layer separation. Pressure waves due to impeller diffuser interaction spread through the vaned diffuser generating unsteadiness which intensifies at near surge condition