Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition

2000 ◽  
Vol 418 ◽  
pp. 137-166 ◽  
Author(s):  
J. H. CITRINITI ◽  
W. K. GEORGE
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Time Scale ◽  
Large Scale ◽  
Large Scale Structure ◽  
Ring Structure ◽  
Scale Structure ◽  
Orthogonal Decomposition ◽  
Potential Core ◽  
Proper Orthogonal

Experimental data are presented from 138 synchronized channels of hot-wire anemometry in an investigation of the large-scale, or coherent, structures in a high Reynolds number fully developed, turbulent axisymmetric shear layer. The dynamics of the structures are obtained from instantaneous realizations of the streamwise velocity field in a single plane, x/D = 3, downstream of a round jet nozzle. The Proper Orthogonal Decomposition (POD) technique is applied to an ensemble of these realizations to determine optimal representations of the velocity field, in a mean-square sense, in terms of an orthogonal basis. The coefficients of the orthogonal functions, which describe the temporal evolution of the POD eigenfunctions, are determined by projecting instantaneous realizations of the velocity field onto the basis.Evidence is presented to show that with a partial reconstruction of the velocity field, using only the first radial POD mode, the large-scale structure is objectively educed from the turbulent field. Further, it is shown that only five azimuthal Fourier modes (0,3,4,5,6) are necessary to represent the evolution of the large-scale structure. The results of the velocity reconstruction using the POD provide evidence for azimuthally coherent structures that exist near the potential core. In addition to the azimuthal structures near the potential core, evidence is also found for the presence of counter-rotating, streamwise vortex pairs (or ribs) in the region between successive azimuthally coherent structures as well as coexisting for short periods with them. The large-scale structure cycle, which includes the appearance of the ring structure, the advection of fluid by the ribs in the braid region and their advection toward the outside of the layer by a following ring structure, repeats approximately every one integral time scale. One surprising result was that the most spatially correlated structure in the flow, the coherent ring near the potential core which ejects fluid in the streamwise direction in a volcano-like eruption, is also the one with the shortest time scale.

scholarly journals A Review of Model Order Reduction Methods for Large-Scale Structure Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kuan Lu ◽  
Kangyu Zhang ◽  
Haopeng Zhang ◽  
Xiaohui Gu ◽  
Yulin Jin ◽  
...  
Keyword(s):  
Complex Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Large Scale Structure ◽  
Scale Structure ◽  
High Dimensional ◽  
Model Order ◽  
Reduction Methods ◽  
Proper Orthogonal

The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

Structure and dynamical processes in Saturn's rings

1984 ◽  
Vol 75 ◽  
pp. 393-395
Author(s):  
Richard J. Terrile
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Large Scale Structure ◽  
Ring Structure ◽  
Ring System ◽  
Scale Structure ◽  
Dynamical Processes ◽  
Saturn’S Rings ◽  
Saturn's Rings

The Voyager encounters have provided the first high resolution look at the Saturn ring system. Images of the rings reveal several classes of dynamical processes active in creating and maintaining large scale structure. These classes include variable ring features attributable to the influence of external satellite resonances, ring structure induced by the shepherding effects from external and possibly internal satellites, smooth eccentric ringlets contained within clear gaps in the ring and the dynamics of spokes which may represent a transient ring atmosphere.

Effects of Outlier Flow Field on the Characteristics of In-Cylinder Coherent Structures Identified by Proper Orthogonal Decomposition-Based Conditional Averaging and Quadruple Proper Orthogonal Decomposition

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Rui Gao ◽  
Li Shen ◽  
Kwee-Yan Teh ◽  
Penghui Ge ◽  
Fengnian Zhao ◽  
...  
Keyword(s):  
Flow Field ◽  
Proper Orthogonal Decomposition ◽  
Coherent Structures ◽  
Large Scale ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Engine Cylinder ◽  
Conditional Averaging ◽  
Proper Orthogonal ◽  
Engine Cycle

Proper orthogonal decomposition (POD) offers an approach to quantify cycle-to-cycle variation (CCV) of the flow field inside the internal combustion engine cylinder. POD decomposes instantaneous flow fields (also called snapshots) into a series of orthonormal flow patterns (called POD modes) and the corresponding mode coefficients. The POD modes are rank-ordered by decreasing kinetic energy content, and the low-order, high-energy modes are interpreted as constituting the large-scale coherent flow structure that varies from engine cycle to engine cycle. Various POD-based analysis techniques have thus been proposed to characterize engine flow field CCV using these low-order modes. The validity of such POD-based analyses rests, as a matter of course, on the reliability of the underlying POD results (modes and coefficients). Yet a POD mode can be disproportionately skewed by a single outlier snapshot within a large data set, and an algorithm exists to define and identify such outliers. In this paper, the effects of a candidate outlier snapshot on the results of POD-based conditional averaging and quadruple POD analyses are examined for two sets of crank angle-resolved flow fields on the midtumble plane of an optical engine cylinder recorded by high-speed particle image velocimetry (PIV). The results with and without the candidate outlier are compared and contrasted. In the case of POD-based conditional averaging, the presence of the outlier scrambles the composition of snapshot subsets that define large-scale flow pattern variations, and thus substantially alters the coherent flow structures that are identified; for quadruple POD, the shape of coherent structures and the number of modes to define them are not significantly affected by the outlier.

Coherence between large-scale jet-mixing structure and its pressure field

1982 ◽  
Vol 116 ◽  
pp. 31-57 ◽  
Author(s):  
M. R. Davis
Keyword(s):  
Strouhal Number ◽  
Large Scale ◽  
Pressure Field ◽  
Large Scale Structure ◽  
Harmonic Excitation ◽  
Scale Structure ◽  
Exit Plane ◽  
Cross Sectional ◽  
Potential Core ◽  
Jet Mixing

A schlieren system has been arranged to sense the total fluctuation over a cross-section of the flow and thus becomes very sensitive to large-scale azimuthally coherent structures in the flow. For a natural unexcited jet it is found that there is a concentration of the large-scale structure at a characteristic Strouhal number which is not sensitive to the beam thickness and which reduces progressively with distance from the nozzle. This large-scale structure exhibits a coherence of over 70 % with the near-field pressure and convects at between 75 % and 95 % of the jet velocity. The coherence between the potential core-pressure field and the large-scale structure downstream increases rapidly with distance from the nozzle exit plane, rather limited coherence being found at the exit plane for these observations at a jet-exit Mach number Mj = 0·7. Movement of a central microphone from x = 0 to x = 2D introduced a solid centre body over the first 2·5 diameters of flow and gave rise to a set of discrete components in the flow structure in the range 0.6 < S < 1·4.With harmonic excitation at S = 1·12 a subharmonic at S = 0·55 occurs at x/D = 3 and a second at S = 0.26, x/D = 6. The flow cross-sectional-average sensing thus appears to show up the vortex-pairing mechanism at greater distances from the nozzle than is easily detectable by other means. Under strong impulse excitation a set of discrete components was observed in a transient response extending over times of 400D/Uj. These had a strongest component which decreases more rapidly in Strouhal number with distance than that associated with natural or harmonically excited conditions.

Zeitstrukturen im Jazz

2014 ◽  
Vol 59 (1) ◽  
pp. 79-92
Author(s):  
Alexander Becker
Keyword(s):  
Large Scale ◽  
Large Scale Structure ◽  
Time Frame ◽  
Scale Structure ◽  
Classical Form ◽  
Jazz Music ◽  
The Moment

Wie erlebt der Hörer Jazz? Bei dieser Frage geht es unter anderem um die Art und Weise, wie Jazz die Zeit des Hörens gestaltet. Ein an klassischer Musik geschultes Ohr erwartet von musikalischer Zeitgestaltung, den zeitlichen Rahmen, der durch Anfang und Ende gesetzt ist, von innen heraus zu strukturieren und neu zu konstituieren. Doch das ist keine Erwartung, die dem Jazz gerecht wird. Im Jazz wird der Moment nicht im Hinblick auf ein Ziel gestaltet, das von einer übergeordneten Struktur bereitgestellt wird, sondern so, dass er den Bewegungsimpuls zum nächsten Moment weiterträgt. Wie wirkt sich dieses Prinzip der Zeitgestaltung auf die musikalische Form im Großen aus? Der Aufsatz untersucht diese Frage anhand von Beispielen, an denen sich der Weg der Transformation von einer klassischen zu einer dem Jazz angemessenen Form gut nachverfolgen lässt.<br><br>How do listeners experience Jazz? This is a question also about how Jazz music organizes the listening time. A classically educated listener expects a piece of music to structure, unify and thereby re-constitute the externally given time frame. Such an expectation is foreign to Jazz music which doesn’t relate the moment to a goal provided by a large scale structure. Rather, one moment is carried on to the next, preserving the stimulus potentially ad infinitum. How does such an organization of time affect the large scale form? The paper tries to answer this question by analyzing two examples which permit to trace the transformation of a classical form into a form germane to Jazz music.

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