An Experimental Study on the Development of Coherent Structure in a Plane Jet (2nd Report, Spatio-temporal Velocity Structure by the Combined Analysis of KL Expnasion and Fourier Transform)

Sakai, Yasuhiko; Tanaka, Nobuhiko; Kushida, Takehiro

doi:10.1299/kikaib.71.1978

Cited by 3 publications

(5 citation statements)

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“…These frequencies are almost consistent with the frequency of the flapping motion investigated by Gotari et al [6]. In addition, the eigenspectra for the 1 st mode are relatively more similar to those for the 1 st v (crossstreamwise velocity fluctuation) mode than those for the 1 st u (streamwise velocity fluctuation) mode obtained in the previous study [18] but they are not completely consistent with those for the streamwise or cross-streamwise velocity fluctuations.…”

Section: Resultssupporting

confidence: 86%

“…Figure 6 shows the downstream variation of the eigenspectra for the 1 st mode obtained with reference to the previous study [18], where each eigenspectrum is normalized by the sum of frequency integrals of eigenspectra over all modes. Figure 6 indicates that the spectra have small peaks at x/d = 10 and 20, whose frequencies are 120 Hz and 45 Hz, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…), |・| denotes the modulus, and <・> is the ensemble average. This maximization process of the mean-square projection, which is a classical problem in the calculus of variations, leads to the following Fredholm integral eigenvalue equation [15]: (17) where the kernel is the two-point correlation function of temperature (18) and and (x) denote the eigenvalue and the eigenfunction, respectively. Because R (x, x') is a positivedefinite symmetric function, the Hilbert-Schmidt theory assures us that there is a countable infinity of eigenvalues and eigenfunctions that provides a diagonal decomposition:…”

Section: Kl-expansionmentioning

confidence: 99%

See 2 more Smart Citations

1093 Measurement of Fluctuating Temperature and Analysis of Eigenmodes by Kl Expansion in a Heated Plane Jet

Terashima

Sakai

Nagata

et al. 2013

ICJWSF

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In this study, simultaneous measurement of the temperature at two points with cold-wire sensors is performed at three different downstream locations of a heated plane jet. The measurement apparatus consists of a wind tunnel, a skimmer, a side-wall, and a heater set at the blower intake of the wind tunnel. The temperature of the jet is controlled to become 5 K higher than the ambient fluid. A thin tungsten wire whose diameter is 3.0 m is used as a sensor and is connected to the self-made constant current circuit. The output of the cold-wire sensor is compensated theoretically to increase the temporal resolution of the measurement. By applying the Karhunen-Loève (KL) expansion in space and time, the structural development of the heated plane jet is investigated from the viewpoint of both space and frequency. Results obtained in the selfpreserving region show that the energy contribution of the 1st mode of the temperature is approximately 20%. It was also found that the dominant mode of the fluctuating temperature field in a plane jet expresses and relates to a flapping motion, which is the coherent structure observed in the plane jet.

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Section: Resultssupporting

confidence: 86%

Section: Resultsmentioning

confidence: 99%

Section: Kl-expansionmentioning

confidence: 99%

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1093 Measurement of Fluctuating Temperature and Analysis of Eigenmodes by Kl Expansion in a Heated Plane Jet

Terashima

Sakai

Nagata

et al. 2013

ICJWSF

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show abstract

“…9 (a) include the small fluctuations, but the large fluctuation is dominant as a whole. Secondly, the coefficients of middlenumbered modes (the 7th mode a (7) u and the 9th mode a (9) u ) in Fig. 9 (b) are almost random signals.…”

Section: Eigenfunctionsmentioning

confidence: 96%

On the Development of Coherent Structure in a Plane Jet

Sakai

Tanaka

Yamamoto

et al. 2006

JSME international journal. Ser. B, Fluids and thermal engineer

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In order to clarify the dynamics of the coherent structure in a turbulent plane jet, the simultaneous measurement of the main streamwise velocity at 21 points in the self-preserving region of a turbulent plane jet has been performed by an array of I-type hot-wire probes. Then the KL (Karhunen-Loève) expansion was applied to extract the coherent structure in the jet. The total number of eigenfunctions (modes) is N = 21, which corresponds to the number of probes. The eigenfunctions (modes) are numbered in order of magnitude of their corresponding eigenvalues. From the investigation of the random coefficients and the eigenfunctions (modes), it is found that the low-numbered (energetic) modes represent the large scale (coherent) structure, the middle-numbered modes represent the finer (small-scale) random structure, and the higher-numbered modes contribute mainly to the intermittent structure in the outer edge region. From the spatio-temporal velocity field reconstructed by the first KL mode, it is found that there exist a pair of fluid lumps with the positive and negative streamwise velocity fluctuation on the opposite sides of the jet centerline, and the signs of velocity fluctuation for those fluid lumps change alternately as time proceeds. These characteristics are consistent with the so called "jet flapping" phenomenon.

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“…It was found that the Kelvin-Helmholtz instability appeared first when the jet lost its stability, and then with the increasing of the nonlinear effects, the secondary instability appeared and the streamwise vortices formed. Recently, Sakai et al [10,11] used hot wire probe and proper orthogonal decomposition (POD) to study the characteristics of coherent structures in different regions in the plane jet. They used the eigenvalues and eigenfunctions as well as the spatial velocity correlations to characterize the development of coherent structures and found that the characteristics of coherent structures could be identified by the reconstructed two-point spatial velocity correlation.…”

mentioning

confidence: 99%

On coherent structures in a three-dimensional transitional plane jet

Luo

Yan

Fan

et al. 2008

Sci. China Ser. E-Technol. Sci.

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Direct numerical simulation of coherent structures in the three-dimensional transitional jet with a moderate Reynolds number of 5000 was conducted. The finite volume method was used to discretize the governing equations in space and the low-storage, three-order Runge-Kutta scheme was used for time integration. The comparisons between the statistical results of the flow field and the related experimental data were performed to validate the reliability of the present numerical schemes. The emphasis was placed on the study of the spatial evolution of the three-dimensional coherent vortex structures as well as their interactions. It is found that the evolution of the spanwise vortex structures in three-dimensional space is similar to that in two-dimensional jet. The spanwise vortex structures are subject to three-dimensional instability and induce the formation of the streamwise and lateral vortex structures. Going with the breakup and mixing of the spanwise vortex structures, the streamwise and transverse vortex tubes also fall to pieces and the mixing arranged small-scale structures are formed in the flow field. Finally, the arrangement relationship among the spanwise, the streamwise and the lateral vortex structures was analyzed and their interactions were also discussed. coherent structures, three-dimensional plane jet, direct numerical simulation, finite volume method, interactions Due to the particular flow characteristics itself, the fundamental study on the plane jet not only helps to deeply understand the free shear turbulence and provides convenience for evaluating different physical models, but also offers reference for related engineering applications. Therefore, the study on plane jet has always been one of the hot topics in turbulence research for the recent 40 years.Most of the early studies focused on the statistic and correlation quantities in plane jets by means of experiments [1,2] . With the discovery of turbulent coherent structure and its important effects on turbulent transport, noise and mixing enhancement, some researchers also tried to investigate the development of coherent structures in plane jet [3] . To identify the existence of co-

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An Experimental Study on the Development of Coherent Structure in a Plane Jet (2nd Report, Spatio-temporal Velocity Structure by the Combined Analysis of KL Expnasion and Fourier Transform)

Cited by 3 publications

References 0 publications

1093 Measurement of Fluctuating Temperature and Analysis of Eigenmodes by Kl Expansion in a Heated Plane Jet

1093 Measurement of Fluctuating Temperature and Analysis of Eigenmodes by Kl Expansion in a Heated Plane Jet

On the Development of Coherent Structure in a Plane Jet

On coherent structures in a three-dimensional transitional plane jet

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