The density of organized vortices in a turbulent mixing layer

It is argued on the basis of exact solutions for uniform vortices in straining fields that vortices of finite cross-section in a row will disintegrate if the spacing is too small. The results are applied to the organized vortex structures observed in turbulent mixing layers. An explanation is provided for the disappearance of these structures as they move downstream and it is deduced that the ratio of average spacing to width should be about 3·5, the width being defined by the maximum slope of the mean velocity. It is shown in an appendix that walls have negligible effect.

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On the periodically excited plane turbulent mixing layer, emanating from a jagged partition

Journal of Fluid Mechanics ◽

10.1017/s0022112007007884 ◽

2007 ◽

Vol 589 ◽

pp. 479-507 ◽

Cited By ~ 18

Author(s):

E. KIT ◽

I. WYGNANSKI ◽

D. FRIEDMAN ◽

O. KRIVONOSOVA ◽

D. ZHILENKO

Keyword(s):

Turbulent Mixing ◽

Mixing Layer ◽

Two Dimensional ◽

Streamwise Vortices ◽

Mean Flow ◽

Trailing Edge ◽

Mean Velocity ◽

Turbulent Mixing Layer ◽

Arithmetic Average ◽

The Mean

The flow in a turbulent mixing layer resulting from two parallel different velocity streams, that were brought together downstream of a jagged partition was investigated experimentally. The trailing edge of the partition had a short triangular ‘chevron’ shape that could also oscillate up and down at a prescribed frequency, because it was hinged to the stationary part of the partition to form a flap (fliperon). The results obtained from this excitation were compared to the traditional results obtained by oscillating a two-dimensional fliperon. Detailed measurements of the mean flow and the coherent structures, in the periodically excited and spatially developing mixing layer, and its random constituents were carried out using hot-wire anemometry and stereo particle image velocimetry.The prescribed spanwise wavelength of the chevron trailing edge generated coherent streamwise vortices while the periodic oscillation of this fliperon locked in-phase the large spanwise Kelvin–Helmholtz (K-H) rolls, therefore enabling the study of the inter- action between the two. The two-dimensional periodic excitation increases the strength of the spanwise rolls by increasing their size and their circulation, which depends on the input amplitude and frequency. The streamwise vortices generated by the jagged trailing edge distort and bend the primary K-H rolls. The present investigation endeavours to study the distortions of each mode as a consequence of their mutual interaction. Even the mean flow provides evidence for the local bulging of the large spanwise rolls because the integral width (the momentum thickness, θ), undulates along the span. The lateral location of the centre of the ensuing mixing layer (the location where the mean velocity is the arithmetic average of the two streams,y0), also suggests that these vortices are bent. Phase-locked and ensemble-averaged measurements provide more detailed information about the bending and bulging of the large eddies that ensue downstream of the oscillating chevron fliperon. The experiments were carried out at low speeds, but at sufficiently high Reynolds number to ensure naturally turbulent flow.

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The interaction between the mean flow and coherent structures in turbulent mixing layers

Journal of Fluid Mechanics ◽

10.1017/s0022112094003447 ◽

1994 ◽

Vol 260 ◽

pp. 81-94 ◽

Cited By ~ 8

Author(s):

J. Cohen ◽

B. Marasli ◽

V. Levinski

Keyword(s):

Velocity Profile ◽

Coherent Structures ◽

Turbulent Mixing ◽

Mixing Layer ◽

Mixing Layers ◽

Mean Flow ◽

Mean Velocity ◽

Turbulent Mixing Layer ◽

Self Similar ◽

The Mean

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional turbulent mixing layer is addressed. Based on considerations from stability theory, previous experimental results, in particular the modification of the mean velocity profile, the peculiar growth of the forced shear-layer thickness and the spatial growth of the disturbance amplitude, are explained. A model that assumes a quasi-parallel mean flow having a self-similar mean velocity profile is developed. The model is capable of predicting the downstream evolution of turbulent mixing layers subjected to external excitations.

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Energetics of a linear array of hollow vortices of finite cross-section

Journal of Fluid Mechanics ◽

10.1017/s0022112080000523 ◽

1980 ◽

Vol 99 (1) ◽

pp. 97-100 ◽

Cited By ~ 2

Author(s):

Gregory R. Baker

Keyword(s):

Cross Section ◽

Ideal Fluid ◽

Turbulent Mixing ◽

Linear Array ◽

Mixing Layer ◽

Vortex Structures ◽

Turbulent Mixing Layer

The energetics of a linear array of hollow or stagnant-cored vortices of finite cross-section in an ideal fluid is studied in this paper. The results are useful in a discussion of the amalgamation of vortex structures in a turbulent mixing layer.

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Implementation of a Mixing Length Turbulence Formulation Into the Dynamic Wake Meandering Model

Journal of Solar Energy Engineering ◽

10.1115/1.4006038 ◽

2012 ◽

Vol 134 (2) ◽

Cited By ~ 13

Author(s):

Rolf-Erik Keck ◽

Dick Veldkamp ◽

Helge Aagaard Madsen ◽

Gunner Larsen

Keyword(s):

Cross Section ◽

Turbulent Mixing ◽

Eddy Viscosity ◽

High Fidelity ◽

Mixing Length ◽

Two Dimensional ◽

Wake Region ◽

Mean Velocity ◽

The Mean ◽

The Difference

The work presented in this paper focuses on improving the description of wake evolution due to turbulent mixing in the dynamic wake meandering (DWM) model. From wake investigations performed with high-fidelity actuator line simulations carried out in ELLIPSYS3D, it is seen that the current DWM description, where the eddy viscosity is assumed to be constant in each cross-section of the wake, is insufficient. Instead, a two-dimensional eddy viscosity formulation is proposed to model the shear layer generated turbulence in the wake, based on the classical mixing length model. The performance of the modified DWM model is verified by comparing the mean wake velocity distribution with a set of ELLIPSYS3D actuator line calculations. The standard error (defined as the standard deviation of the difference between the mean velocity field of the DWM and the actuator line model), in the wake region extending from 3 to 12 diameters behind the rotor, is reduced by 27% by using the new eddy viscosity formulation.

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Statistically Targeted Forcing (STF) Method for Synthetic Turbulence Generation of Initial Conditions in Three-Dimensional Turbulent Mixing Layer Flow

10.1115/fedsm2021-65916 ◽

2021 ◽

Author(s):

Olalekan O. Shobayo ◽

D. Keith Walters

Keyword(s):

Vortex Dynamics ◽

Turbulent Mixing ◽

Initial Conditions ◽

Numerical Study ◽

Mixing Layer ◽

Turbulent Stress ◽

Mean Velocity ◽

Turbulent Mixing Layer ◽

Layer Flow ◽

Turbulence Generation

Abstract Computational fluid dynamics (CFD) results are presented for synthetic turbulence generation of initial conditions for the canonical test case of a temporally-developing turbulent mixing layer (TTML) flow. This numerical study investigates the performance of a newly proposed Statistically Targeted Forcing (STF) method, and its capability to act as a restoring force to match the target mean velocity and turbulent stress in a temporally-developing flow where highly unsteady destabilizing mechanisms and influence are evident. Several previous investigations exist documenting vortex dynamics of the turbulent mixing layer, but limited investigations exist on synthetic turbulence generation forcing methods to prescribe initial conditions. The objective of this study is to evaluate the performance of the newly proposed STF method to capture the vortex dynamics and effectively match target mean velocity and resolved turbulent stress predictions using large-eddy simulation. Results are interrogated and compared to statistical velocity and turbulent stress distributions obtained from DNS simulations available in the literature. Results show that the STF method can successfully reproduce desired statistical distributions in a turbulent mixing layer flow.

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The forced mixing layer between parallel streams

Journal of Fluid Mechanics ◽

10.1017/s0022112082002973 ◽

1982 ◽

Vol 123 ◽

pp. 91-130 ◽

Cited By ~ 450

Author(s):

D. Oster ◽

I. Wygnanski

Keyword(s):

Turbulent Mixing ◽

Mixing Layer ◽

Resonance Region ◽

Spreading Rate ◽

Initial Energy ◽

Two Dimensional ◽

Velocity Difference ◽

Mean Velocity ◽

Order Of Magnitude ◽

The Mean

The effect of periodic two-dimensional excitation on the development of a turbulent mixing region was studied experimentally. Controlled oscillations of variable ampli- tude and frequency were applied at the initiation of mixing between two parallel air streams. The frequency of forcing was at least an order of magnitude lower than the initial instability frequency of the flow in order to test its effect far downstream. The effect of the velocity difference between the streams was also investigated in this experiment. A typical Reynolds number based on the velocity difference and the momentum thickness of the shear layer was l04.It was determined that the spreading rate of the mixing layer is sensitive to periodic surging even if the latter is so small that it does not contribute to the initial energy of the fluctuations. Oscillations at very small amplitudes tend to increase the spreading rate of the flow by enhancing the amalgamation of neighbouring eddies, but at higher amplitudes the flow resonates with the imposed oscillation. The resonance region can extend over a significant fraction of the test section depending on the Strouhal number and a dimensionless velocity-difference parameter. The flow in the resonance region consists of a single array of large, quasi-two-dimensional vortex lumps, which do not interact with one another. The exponential shape of the mean-velocity distribution is not affected in this region, but the spreading rate of the flow with increasing distance downstream is inhibited. The Reynolds stress in this region changes sign, indicating that energy is extracted from the turbulence to the mean motion; the intensity of the spanwise fluctuations is also reduced, suggesting that the flow tends to become more two-dimensional.Amalgamation of large coherent eddies is resumed beyond the resonance region, but the flow is not universally similar. There are many indications suggesting that the large eddies in the turbulent mixing layer at fairly large Re are governed by an inviscid instability.

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