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

Time-domain harmonic balance method for aerodynamic and aeroelastic simulations of turbomachinery flows

A time-domain Harmonic Balance method is applied to simulate the blade row interactions and vibrations of state- of-the-art industrial turbomachinery configurations. The present harmonic balance approach is a time-integration scheme that turns a periodic or almost-periodic flow problem into the coupled resolution of several steady computations at different time samples of the period of interest. The coupling is performed by a spectral time-derivative operator that appears as a source term of all the steady problems. These are converged simultaneously making the method parallel in time. In this paper, a non-uniform time sampling is used to improve the robustness and accuracy regardless of the considered frequency set. Blade row interactions are studied within a 3.5-stage high-pressure axial compressor representative of the high-pressure core of modern turbofan engines. Comparisons with reference time-accurate computations show that four frequencies allow a fair match of the compressor performance, with a reduction of the computational time up to a factor 30. Finally, an aeroelastic study is performed for a counter-rotating fan stage, where the rear blade is submitted to a prescribed harmonic vibration along its first torsion mode. The aerodynamic damping is analysed, showing possible flutter

Multi-frequential harmonic balance approach for the computation of unsteadiness in multi-stage turbomachines

In turbomachines, the relative motion of fixed and rotating blades gives rise to deterministic unsteady interactions at frequencies termed BPFs (Blade Passing Frequencies). In a multi-stage turbomachine, a row sandwiched between two other rows is submitted to (at least) two BPFs, hence the need for multiple frequency methods. Initially developed for single frequency problems, harmonic methods have been extended to account for multiple frequencies. All the variations of the Harmonic Balance (HB) technique proposed in the literature rely on a uniform time sampling of the longest period of interest (though the number of samples can differ). This can compromise the efficiency of the method, as too many time samples are computed. Besides, as demonstrated in the present contribution, uniform time sampling can also raise stability issues. To overcome these computational limitations, a new approach using non-uniform time sampling is proposed in the present contribution. This paper will be organized as follows: first, the multi-frequency HB methods is presented, and the impact of time sampling on numerical stability is discussed. Then, algorithms for an automatic choice of the time samples are presented and compared. The proposed non-uniform sampling is assessed for a model problem (i.e. a pulsating channel). Finally, a section is dedicated to the application to a turbomachinery configuration, with emphasis on the choice of frequencie

Attachment style impacts behavior and early oculomotor response to positive, but not negative, pictures

The present study investigated whether oculomotor behavior is influenced by attachment styles. The Relationship Scales Questionnaire was used to assess attachment styles of forty-eight voluntary university students and to classify them into attachment groups (secure, preoccupied, fearful, and dismissing). Eye-tracking was recorded while participants engaged in a 3-seconds free visual exploration of stimuli presenting either a positive or a negative picture together with a neutral picture, all depicting social interactions. The task consisted in identifying whether the two pictures depicted the same emotion. Results showed that the processing of negative pictures was impermeable to attachment style, while the processing of positive pictures was significantly influenced by individual differences in insecure attachment. The groups highly avoidant regarding to attachment (dismissing and fearful) showed reduced accuracy, suggesting a higher threshold for recognizing positive emotions compared to the secure group. The groups with higher attachment anxiety (preoccupied and fearful) showed differences in automatic capture of attention, in particular an increased delay preceding the first fixation to a picture of positive emotional valence. Despite lenient statistical thresholds induced by the limited sample size of some groups (p < 0.05 uncorrected for multiple comparisons), the current findings suggest that the processing of positive emotions is affected by attachment styles. These results are discussed within a broader evolutionary framework.We are grateful to all the volunteers who participated in this study. This work was partially supported by Portuguese Science Funding Agency - FCT grant (SFRH / BPD / 80910 / 2011) awarded to Catarina Silva. Catarina Silva and Thierry Chaminade contributed equally to this work

Le domaine de la protection de l’enfance

L’auteur résume brièvement les principales notions de la théorie de l’attachement particulièrement pertinentes pour l’enrichissement des pratiques dans le domaine de la protection de l’enfance. Les principales applications cliniques détaillées sont ensuite l’attachement désorganisé et le paradoxe de l’attachement dans la maltraitance, les liens entre non sécurité de l’attachement et psychopathologie et enfin le problème des décisions de maintien ou de séparation des liens entre un enfant et ses parents « inadéquats ». L’importance de l’évaluation et l’engagement de l’institution dans les réponses thérapeutiques sont soulignés

Violences conjugales et attachement des jeunes enfants

Introduction. La violence conjugale met en jeu la sécurité de l’attachement de l’enfant : elle lui fait peur, elle est source de stress et donc augmente son besoin d’attachement. Méthode. Ce travail rapporte les éléments tirés de la littérature sur les facteurs de gravité de cette exposition, liés à l’enfant ou á la situation. Il expose les mécanismes de cet effet, à travers les notions d’attachement désorganisé, et de celle de coparentage. Résultats. L’exposition à la violence conjugale des jeunes enfant est très fréquente. Les enfants de moins de 6 ans, qui ont été témoins de violences conjugales, ont plus de risque de présenter des troubles psychopathologiques, que ce soit sous forme de symptômes interna- lisés ou externalisés. Conclusion. Le paradigme de la peur est au cœur de la théorie de l’attachement. L’enfant témoin de la violence conjugale ne peut compter sur l’aide de ses parents comme une source de régulation des affects bouleversants qui le submergent