Low-Dimensional Models of a Temporally Evolving Free Shear Layer

2006 ◽  
Author(s):  
Mingjun Wei ◽  
Clarence Rowley
Keyword(s):  
Shear Layer ◽  
Free Shear Layer ◽  
Dimensional Models ◽  
Low Dimensional

Low-dimensional models of a temporally evolving free shear layer

2009 ◽  
Vol 618 ◽  
pp. 113-134 ◽  
Author(s):  
MINGJUN WEI ◽  
CLARENCE W. ROWLEY
Keyword(s):  
Numerical Simulations ◽  
Shear Layer ◽  
Direct Numerical Simulations ◽  
Rate Of Change ◽  
Galerkin Projection ◽  
Free Shear Layer ◽  
Nonlinear Saturation ◽  
Complex Modes ◽  
Dimensional Models ◽  
Low Dimensional

We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analysed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g. pairing). In the present paper, two-dimensional direct numerical simulations of a spatially periodic, temporally developing shear layer are performed. Low-dimensional models for the dynamics are obtained using a modified version of proper orthogonal decomposition (POD)/Galerkin projection, in which the basis functions can scale in space as the shear layer spreads. Equations are obtained for the rate of change of the shear-layer thickness. A model with two complex modes can describe certain single-wavenumber features of the system, such as vortex roll-up, nonlinear saturation, and viscous damping. A model with four complex modes can describe interactions between two wavenumbers (vortex pairing) as well. At least two POD modes are required for each wavenumber in space to sufficiently describe the dynamics, though, for each wavenumber, more than 90% energy is captured by the first POD mode in the scaled space. The comparison of POD modes to stability eigenfunction modes seems to give a plausible explanation. We have also observed a relation between the phase difference of the first and second POD modes of the same wavenumber and the sudden turning point for shear-layer dynamics in both direct numerical simulations and model computations.

scholarly journals Low-dimensional models of subcritical transition to turbulence

1997 ◽  
Vol 9 (4) ◽  
pp. 1043-1053 ◽  
Author(s):  
Jeffrey S. Baggett ◽  
Lloyd N. Trefethen
Keyword(s):  
Transition To Turbulence ◽  
Dimensional Models ◽  
Low Dimensional

Deformable bubbles in a free shear layer

1997 ◽  
Vol 23 (5) ◽  
pp. 977-1001 ◽  
Author(s):  
E. Loth ◽  
M. Taeibi-Rahni ◽  
G. Tryggvason
Keyword(s):  
Shear Layer ◽  
Free Shear Layer

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

2021 ◽  
Vol 931 ◽  
Author(s):  
D. Li ◽  
J. Komperda ◽  
A. Peyvan ◽  
Z. Ghiasi ◽  
F. Mashayek
Keyword(s):  
Shear Layer ◽  
Compressible Flows ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Correlation Coefficients ◽  
Free Shear Layer ◽  
Smagorinsky Model ◽  
Reynolds Analogy ◽  
Velocity Fluctuations ◽  
Scale Similarity

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

CFD analysis of free shear layer approximations for a pulsed air jet

2014 ◽  
Vol 43 ◽  
pp. 49-58
Author(s):  
Nawel Khaldi ◽  
Salwa Marzouk ◽  
Hatem Mhiri ◽  
Philippe Bournot
Keyword(s):  
Shear Layer ◽  
Cfd Analysis ◽  
Free Shear Layer ◽  
Air Jet
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