Non-linear vibration of rectangular reticulated shallow shell structures

ＮＯＮ－ＬＩＮＥＡＲＶＩＢＲＡＴＩＯＮＯＦＲＥＣＴＡＮＧＵＬＡＲＲＥＴＩＣＵＬＡＴＥＤＳＨＡＬＬＯＷＳＨＥＬＬＳＴＲＵＣＴＵＲＥＳＮｉｅＧｕｏ－ｈｕａ（聂国华）（ＤｅｐａｒｔｍｅｎｔｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈａｎｉｃｓ,ＴｏｎｇｊｉＵｎｉｖｅ...     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

Non-linear elastic theory of rectangular reticulated shallow shell structures

ＮＯＮ－ＬＩＮＥＡＲＥＬＡＳＴＩＣＴＨＥＯＲＹＯＦＲＥＣＴＡＮＧＵＬＡＲＲＥＴＩＣＵＬＡＴＥＤＳＨＡＬＬＯＷＳＨＥＬＬＳＴＲＵＣＴＵＲＥＳＮｉｅＧｕｏ－ｈｕａ（聂国华）（ＤｅｐａｒｔｍｅｎｔｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈａｎｉｃｓ,ＴｏｎｇｊｉＵ...     

Correlative analysis of organised structures in turbulent jets

An approach to characterise jets by analysing the locations of large-scale instantaneous structures is presented. Planar imaging is used to identify instantaneous large-scale structures in flow fields. ??Correlation Images?? are generated from the auto-correlation of identified large-scale structures in instantaneous planar images. A ??Structure Correlation Survey?? is produced by the sum of Correlation Images from an ensemble. A Structure Correlation Survey provides a measure of the underlying large-scale structures, namely the characteristic distances and angles between large-scale structures, number densities of large-scale structures in the image field and their dominant modes of flow. The approach is assessed analytically and applied to experimental data. Four generic flow patterns are identified and used individually, or in combination, to classify jet flows. Results show that the proposed method can be used successfully to characterise jet flows based on large-scale structures in an instantaneous flow field.     

Mixing and coherent vortices in turbulent coaxial jets

Direct numerical simulations associated with mixing in constant-density round coaxial jets are performed. They are validated by comparison against laboratory experiments. The mixing process is studied by seeding a passive tracer first in the outer annular jet, then in the inner jet. We demonstrate the important role played by coherent vortices in the mixing mechanisms. The turbulent mixing exhibits an intermittent character as a consequence of fluid ejections caused by the counter-rotating streamwise vortices. We quantify also the domination of the outer jet and show that the fluid issuing from the central jet remains confined. To cite this article: G. Balarac, M. Si-Ameur, C. R. Mecanique 333 (2005).     

Uncovering large-scale coherent structures in natural and forced turbulent wakes by combining PIV,POD, and FTLE

Planar velocity data of the unsteady separated flow in the turbulent wake of a circular cylinder obtained by particle image velocimetry (PIV) are analyzed in order to visualize the large-scale coherent structures associated with alternating vortex shedding at a Reynolds number of 2,150. Two different cases are examined: unforced vortex shedding in the natural wake and vortex lock-on incited by forced perturbations superimposed in the inflow velocity. Proper orthogonal decomposition (POD) is employed to reconstruct the low-order wake dynamics from randomly sampled snapshots of the velocity field. The reconstructed flow is subsequently used to determine the evolution of the finite-time Lyapunov exponent (FTLE) fields which identify the Lagrangian coherent structures. The results demonstrate that the combination of methods employed offers a powerful visualization tool to uncover large-scale coherent structures and to exemplify vortex dynamics in natural and forced bluff-body wakes.     

Wavelet analysis of coherent structures in a three-dimensional mixing layer

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists. The project supported by the Research Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation for Outstanding Youth of China (19925210)     

POD analysis of flow structures in a scale model of a ventilated room

Measurements with particle image velocimetry have been carried out in a scale model of the Annex 20 room. Data were taken in a plane near the inlet. The flow consisted of a wall jet (Re=5,000) and a low-velocity region below the jet. POD was used to analyze dominant flow structures. The analysis showed that the flow some of the time has flow structures very different from the mean velocity field. A time-resolved data series was projected onto the orthonormal basis derived from the POD for analysis of the time variation of the POD amplitudes.     

Nonlinear analysis of doubly curved symmetrically laminated shallow shells with rectangular planform

Summary A multi-mode solution to the dynamic Marguerre-type nonlinear equations is presented for the nonlinear free vibration of doubly curved, symmetrically laminated, imperfect shallow shells of rectangular planform on a Winkler-Pasternak elastic foundation. The shell edges are assumed to be transversely supported and the variation of rotational stiffness is identical along opposite edges. Generalized double Fourier series with time-dependent coefficients and the method of harmonic balance are used in the solution. The boundary condition for the varying rotational stiffness is fulfilled by replacement of bending moments along the four edges by an equivalent lateral pressure. Based on a single-mode approximation numerical results for the amplitude-frequency response of doubly curved isotropic, orthotropic, cross-ply and angle-ply shallow shells with square planform are presented for various boundary conditions, material properties, curvature ratios, initial imperfections, edge tensions, and moduli of the elastic foundation. Graphical results for postbuckling behavior of an imperfect angle-ply cylindrical panel are also presented as a special case.

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Nichtlineares Verhalten zweifach gekrümmter, symmetrisch geschichteter dünner Schalen mit rechteckigem Grundriß

Übersicht Vorgestellt wird eine Mehrfachwellenform-Lösung der dynamischen Gleichungen vom Marguerre-Typ für die nichtlinearen Eigenschwingungen zweifach gekrümmter dünner Schalen aus symmetrischen Schichtungen, die geometrisch imperfekt sind und über einen rechteckigen Grundriß auf einer elastischen Winkler-Pasternak-Bettung lagern. Angenommen wird eine gelenkige Lagerung der Plattenränder mit einer veränderlichen Drehbehinderung, die auf gegenüberliegenden Rändern gleich ist. Zur Lösung werden verallgemeinerte zweifache Fourier-Reihen mit zeitabhängigen Koeffizienten und die Methode der harmonischen Balance benutzt. Die Randbedingung für die veränderliche Drehbehinderung wird dadurch erfüllt, daß die Randmomente durch einen äquivalenten Vertikaldruck ersetzt werden. Mit der Näherung nur einer Wellenform werden numerische Ergebnisse für die Beziehung zwischen Amplitude und Frequenz angegeben; variiert werden dabei die Randbedingungen, die anfänglichen Imperf ektionen, die Krümmungsverhältnisse, die Bettungszahlen und die Materialkonstanten, wobei die Platte entweder isotrop oder bei recht- und schiefwinkliger Schichtung orthotrop ist. Als Sonderfall wird auch das Nachbeulverhalten einer imperfekten, schiefwinklig geschichteten Zylinderschale graphisch dargestellt.

     

The application of classical POD and snapshot POD in a turbulent shear layer with periodic structures

The classical and snapshot proper-orthogonal-decomposition was applied to data taken in a one-stream mixing layer in a narrow channel. Due to this particular geometry the flow develops large periodic structures. POD-analysis of simultaneously measured velocity components in spanwise direction identify as largest mode not only their periodic fraction, but also higher Fourier modes of the two-dimensional fluctuation. The energy content of the plane motion reaches values of about 90%. The amplitude of small three-dimensional vortices embedded in higher POD modes is correlated with the phase of the large structures, which indicates their influence on the entire turbulent motion. Application of scalar snapshot POD on phase averaged data of the entire flow field allows separation into modes. The eigenvalues and eigenvectors show identical distribution for theu- andv-component. Comparison of streakline plots of the reconstructed velocity field from different numbers of modes with flow visualization exhibits that the largest physical structure is described by only the first two modes. This is also supported by calculation of the vorticity component inz-direction. The total energy content of the largest structure is approximately 60%.Supported by the Deutsche Forschungsgemeinschaft under Grant No. Fi 178/28.     

An analysis of energy transport processes in the presence of coherent structures

The paper deals with the influence exterted by the presence of coherent structures upon the energy transfer processes in turbulent flow. The round free jet has been stimulated by the acoustic field with the frequency corresponding to the shedding of column-mode vortices (the so called helical structures). The results of hot-wire measurements enabled to calculate the particular terms of coherent energy transport equations that in turn made it possible to trace the energy transfer processes realized in the presence of helical-mode structures. The results obtained suggest that the organized motion modifies substantially the energy transfer processes in the flow considered.     

Interaction of turbulent coherent structures and small scale structures

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Cut-off analysis of coherent vortical structure identification in a three-dimensional external flow

Vortical structure identification has more recently been applied in the study of the transport of vortical structures in low Reynolds number three-dimensional complex geometry flows. An important issue in this identification procedure is to choose an appropriate cut-off value ${\lambda }_2$ which takes into consideration the finite precision vortex interfaces. This cut-off choice is studied in this Note and applied to an external flow around a curved cylinder. The vortex identification technique at different cut-off values is compared to the threshold of the vorticity field showing the efficiency of choosing the optimal tolerance gap. The computations are performed with a fully three-dimensional spectral/hp element method. To cite this article: A. Miliou et al., C. R. Mecanique 333 (2005).     

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of Re = 105, which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous exper-imental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent struc-tures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The m = 0, 1 modes have high coherence of near-field pres-sure for both jets, while the coherence of m = 0 modes is enhanced greatly by heating. Based on the coherent struc-tures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heat-ing would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.     

Development of shock wave and vortex structures in unsteady jets

The paper deals with the formation of a gaseous jet behind a sonic nozzle. The nozzle was located at the end wall of a shock tube. A specially made two-direction shadow system, which ensured a simultaneous recording of side-on and head-on images of the jet, as well as a diffraction interferometer were used. On the basis of the data obtained, an analysis of the vortex structure of the jet was carried out, the amplitude of the azimuthal instability was measured and the spatial distribution of the density in the gaseous flow was obtained. Comparison between the experimental density distribution, numerical results and a nonself-similar point source blast wave model was conducted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

LBE simulation of coherent vortex motion and heat transfer in jets of cross flow

Lattice Boltzmann equation method is used to simulate the coherent vortex motions and interactions and the heat transfer characteristics of jets in cross flow (JICFs) via TD2G9 model. After validation, the characteristics of cross flow under different Reynolds numbers are illustrated, including the mean profiles, the Reynolds stress tensor, the vortex and temperature fields, the temperature gradients near the walls, and the coherent correlation of vortex motions. The results show that the velocity profiles in JICF can be characterized by three basic regions, which are mainly caused by the mergence of JICF with the main flow. The temperature gradient near the walls can also be categorized by four basic regions, which are caused mainly by the impulse of JICFs too. Coherent vortex motions are found in JICF for Re = 3000, which are proved by strong periodic correlation of flow variables over a fixed area.     

Coherent structures in the near field of round jets

The present paper reports measurements of axial and radial velocities obtained with laser-Doppler anemometry in the transitional region of a round jet. The predominant frequencies of the coherent structures detected in the non-artificially excited jet, correspond to Strouhal numbers, around 0.33 and 0.55 and an interpretation of these observations is made. The use of external excitation can modify some characteristics of the jets disturbing the balance between the different flow structures, namely those corresponding to the two values of St. The jet diameter was 30.0 mm and the velocities ranged from near zero up to 15 m/s, corresponding to Reynolds number of 2.87 × 10⁴.To obtain the velocity probability distributions, power spectral distributions and auto-correlations, together with mean and rms velocities a LDA with double Bragg cell system was used. The Doppler signal was analysed with a counter interfaced to an Apple II microcomputer and a Racal magnetic tape.     

Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation

The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.