Coherent Structures in the Axisymmetric Turbulent Jet Mixing Layer

Glauser, Mark; Leib, S. J.; George, William K.

doi:10.1007/978-3-642-71435-1_13

Cited by 129 publications

(95 citation statements)

References 5 publications

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“…The decomposition of this correlation tensor in one and two dimensions showed that the dominant eddy carried about 64% of the turbulent kinetic energy. Applying POD to an axisymmetric turbulent jet, Glauser et al 38 established that the dominant eigenfunction carried about 40% of the total streamwise turbulent intensity across the layer. Further, the works of Herzog 39 and Moin and Moser 40 also involved the use of POD to find the most dominating eigenvalue.…”

Section: Introductionmentioning

confidence: 99%

Direction of scalar transport in turbulent channel flow

Srinivasan

Papavassiliou

2011

Physics of Fluids

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The concept of reverse diffusion, introduced by Corrsin to describe the motion of particles as they move towards a location in the flow field, is fundamental to the understanding of mixing. In this work, direct numerical simulations in conjunction with the tracking of scalar markers are utilized in infinitely long channels to study the principal direction of transport of heat (or mass) for both forwards and backwards single particle dispersion. The viscous sub-layer, the transition region (between the viscous sub-layer and the logarithmic region), and the logarithmic region of a Poiseuille flow and a plane Couette flow channel are studied. Fluctuating velocities of scalar markers captured in these regions are used to obtain the full autocorrelation coefficient tensor forwards and backwards with time. The highest eigenvalue of the velocity correlation coefficient tensor quantifies the highest amount of turbulent heat transport, while the corresponding eigenvector points to the main direction of transport. Different Prandtl number, Pr, fluids are simulated for the two types of flow. It is found that the highest eigenvalues are higher in the case of backwards dispersion compared to the case of forwards dispersion for any Pr, in both flow cases. The principal direction for backwards and forwards dispersion is different than for forwards dispersion, for all Pr, and in all flow regions for both flows. Fluids with lower Pr behave different than the higher Pr fluids because of increased molecular diffusion effects. The current study also establishes an interesting analogy of turbulent dispersion to optics defining the turbulent dispersive ratio, a parameter that can be used to identify the differences in the direction of turbulent heat transport between forwards and backwards dispersion. A spectral analysis of the auto-correlation coefficient for both forwards and backwards dispersion shows a universal behavior with slope of À1 at intermediate frequencies.

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Section: Introductionmentioning

confidence: 99%

Direction of scalar transport in turbulent channel flow

Srinivasan

Papavassiliou

2011

Physics of Fluids

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“…The experiment conducted to obtain the data in the axisymmetric jet was first reported by Glauser and George [13] and Glauser et al [14]. The jet had an exit diameter (V) of 0.098 m with a centerline exit velocity of 2o m/s.…”

Section: Jetmentioning

confidence: 99%

“…The numerical approximations of Eq. 2 and 4 involves replacing the integrals by an appropriate quadrature rule (in this study a trapezoidal rule) as detailed by Glauser et al [13].…”

Section: Pot) Theo~mentioning

confidence: 99%

Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure

Bonnet¹,

Cole

Delville³

et al. 1994

Experiments in Fluids

225

104

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Experiments in Fluids 17 (i994) 307 314 © Springer-Verlag 1994 decomposition: ComplementaryAbstract The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in space simultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.

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“…The first successful experimental implementations of the POD, almost two decades after Lumley's proposal [1], came in the 1980s from Glauser [4] for high Reynolds number axisymmetric mixing layer and Herzog [5] for low Reynolds number pipe flow. Since then, experimental utilization of the POD has been widely used to break the turbulence scales apart [4,[6][7][8][9][10][11][12][13][14][15][16][17].…”

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confidence: 99%

“…Since then, experimental utilization of the POD has been widely used to break the turbulence scales apart [4,[6][7][8][9][10][11][12][13][14][15][16][17]. Glauser [4], Glauser and George [6], and Glauser et al [7] implemented the POD to investigate the coherent structures in an axisymmetric mixing layer. The axisymmetric shear layer was created by means of a round jet and the experiment was performed at 3 nozzle diameters downstream of the nozzle.…”

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confidence: 99%

Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disk

2008

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One-component scalar, two-component vectorial, and three-component vectorial proper orthogonal decompositions of the axisymmetric turbulent wake have been studied to investigate possible effects of the number of components comprising the two-point correlation tensor forming the kernel of the proper orthogonal decompositions integral equation. A wind-tunnel experiment has been performed 50 diameters downstream of the wake generator, which was a disk of 20 mm in diameter. The Reynolds number based on the disk diameter was 20,400. Twelve cross hot wires were used to obtain the simultaneous multipoint measurements. Six of the probes were located on a fixed rake and the other six probes were located on a movable rake, which was traversed from 10 to 180 deg in 10 deg increments. Two experiments were carried out to obtain first the streamwise and azimuthal components of the velocity, and second to obtain the streamwise and radial components of the velocity. Seven out of nine components of the two-point correlation tensor were computed using measured velocities and the remaining two two-point correlations were extracted from the data using the continuity equations. The one-component scalar, and two-and three-component vectorial decomposition results were essentially in agreement. Eigenvalues for the full vector proper orthogonal decompositions integrated over frequency showed that Fourier mode 2 was the largest in both the streamwise and azimuthal velocity. Azimuthal mode 2 peaks at the near-zero frequency, whereas azimuthal mode 1 peaks at a frequency which corresponds to the vortex shedding frequency. Similar features in turbulence kinetic energy distributions were also observed in the modally decomposed two-point cross-spectra and two-point cross-correlations. = mean velocity in streamwise direction, U x U, m=s U r = mean velocity in radial direction, U r V, m=s U = mean velocity in azimuthal direction, U W, m=s u x = fluctuating velocity in streamwise direction, u x u, m=s u r = fluctuating velocity in radial direction, u r v, m=s u = fluctuating velocity in azimuthal direction, u w, m=s x, r, = cylindrical coordinate system = proper orthogonal decomposition eigenvalues = normalized proper orthogonal decomposition eigenvalues

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Coherent Structures in the Axisymmetric Turbulent Jet Mixing Layer

Cited by 129 publications

References 5 publications

Direction of scalar transport in turbulent channel flow

Direction of scalar transport in turbulent channel flow

Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure

Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disk

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