A low-dimensional description of the compressible axisymmetric shear layer

2001 ◽  
Author(s):  
Jeffrey Taylor ◽  
Lawrence Ukeiley ◽  
Mark Glauser
Keyword(s):  
Shear Layer ◽  
Axisymmetric Shear ◽  
Low Dimensional

The stability of countercurrent mixing layers in circular jets

1991 ◽  
Vol 227 ◽  
pp. 309-343 ◽  
Author(s):  
P. J. Strykowski ◽  
D. L. Niccum
Keyword(s):  
Shear Layer ◽  
Critical Velocity ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Mean Velocity ◽  
Axisymmetric Vortex ◽  
Circular Jets ◽  
Axisymmetric Shear ◽  
The Stability

A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = ΔU/2U between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and U is the average speed of the two streams. Above a critical velocity ratio Rr = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatial order of the primary vortices inhibits the pairing process and dramatically alters the spatial development of the shear layer downstream. Consequently, the turbulence level in the jet core is significantly reduced, as is the decay rate of the mean velocity on the jet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted value of 1.315 for the transition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985).

scholarly journals Decomposition of wake dynamics in fluid–structure interaction via low-dimensional models

2019 ◽  
Vol 867 ◽  
pp. 723-764 ◽  
Author(s):  
T. P. Miyanawala ◽  
R. K. Jaiman
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
High Amplitude ◽  
Wake Flow ◽  
High Dimensional ◽  
Near Wake ◽  
Structure Interaction ◽  
Moderate Reynolds Number ◽  
Low Dimensional ◽  
Lock In

We present a dynamic decomposition analysis of the wake flow in fluid–structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational FSI solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number ($Re$). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode to detect features of the organized motions, namely, the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominant role in the drag force. We further examine the fundamental mechanism of this dynamical behaviour and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyse the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Reynolds number laminar flow. These quantitative mode energy contributions demonstrate that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake–body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake–body interaction, which provides the interrelationship between the high-amplitude motion and the dominating wake features. Through our investigation of wake–body synchronization below critical $Re$ range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of $Re=22\,000$, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake synchronization is found to be valid for the turbulent wake flow.

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.

Experiments on the Reattachment of a Turbulent Axisymmetric Shear Layer

1967 ◽  
Vol 18 (4) ◽  
pp. 379-398
Author(s):  
P. J. Finley
Keyword(s):  
Mach Number ◽  
Shear Layer ◽  
Spherical Surface ◽  
Free Shear Layer ◽  
Numerical Predictions ◽  
Axisymmetric Shear ◽  
Pressure Changes

SummarySome experiments are described in which an axisymmetric free shear layer attaches to a spherical surface, the exterior flow Mach number ranging from 0-75 to 207. The Chapman-Korst reattachment model is shown to correlate the results very well. The relation between the quantities measured and the numerical predictions of the model is discussed in detail and it is shown that the pressure changes which occur just downstream of reattachment are significantly different from those observed on flat walls.

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