Floquet stability analysis of viscoelastic flow over a cylinder

Richter, David H.; Shaqfeh, Eric S. G.; Iaccarino, Gianluca

doi:10.1016/j.jnnfm.2011.02.005

Cited by 22 publications

(16 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(More technical details about Floquet stability analysis and its application to hydrodynamic instability are presented in, for example, [2,6,8,11,35]. )…”

Section: B Floquet Stability Analysismentioning

confidence: 99%

Three-dimensional transition after wake deflection behind a flapping foil

Deng

Caulfield

2015

Phys. Rev. E

View full text Add to dashboard Cite

We report the inherently three-dimensional linear instabilities of a propulsive wake, produced by a flapping foil, mimicking the caudal fin of a fish or the wing of a flying animal. For the base flow, three sequential wake patterns appear as we increase the flapping amplitude: Bénard-von Kármán (BvK) vortex streets; reverse BvK vortex streets; and deflected wakes. Imposing a three-dimensional spanwise periodic perturbation, we find that the resulting Floquet multiplier |μ| indicates an unstable "short wavelength" mode at wave number β=30, or wavelength λ=0.21 (nondimensionalized by the chord length) at sufficiently high flow Reynolds number Re=Uc/ν≃600, where U is the upstream flow velocity, c is the chord length, and ν is the kinematic viscosity of the fluid. Another, "long wavelength" mode at β=6 (λ=1.05) becomes critical at somewhat higher Reynolds number, although we do not expect that this mode would be observed physically because its growth rate is always less than the short wavelength mode, at least for the parameters we have considered. The long wavelength mode has certain similarities with the so-called mode A in the drag wake of a fixed bluff body, while the short wavelength mode appears to have a period of the order of twice that of the base flow, in that its structure seems to repeat approximately only every second cycle of the base flow. Whether it is appropriate to classify this mode as a truly subharmonic mode or as a quasiperiodic mode is still an open question however, worthy of a detailed parametric study with various flapping amplitudes and frequencies.

show abstract

“…(More technical details about Floquet stability analysis and its application to hydrodynamic instability are presented in, for example, [2,6,8,11,35]. )…”

Section: B Floquet Stability Analysismentioning

confidence: 99%

Three-dimensional transition after wake deflection behind a flapping foil

Deng

Caulfield

2015

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…At larger Reynolds number, polymer elasticity suppresses the secondary three-dimensional mode which dominates the structure of the near-wake for Newtonian fluids. Later, the same authors investigated Instability of shear-thinning and shear-thickening fluids past a circular cylinder 203 the viscoelastic effects on the stability of the cylinder wake using linear theory (Richter, Shaqfeh & Iaccarino 2011). They found that viscoelasticity modifies the underlying base flow which results in a reduction of vorticity intensity and strain rate in the wake and successively a decrease in the production of perturbation energy.…”

Section: Cylinder Flow Of Non-newtonian Fluidsmentioning

confidence: 99%

First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder

et al. 2012

View full text Add to dashboard Cite

The first bifurcation and the instability mechanisms of shear-thinning and shear-thickening fluids flowing past a circular cylinder are studied using linear theory and numerical simulations. Structural sensitivity analysis based on the idea of a ‘wavemaker’ is performed to identify the core of the instability. The shear-dependent viscosity is modelled by the Carreau model where the rheological parameters, i.e. the power-index and the material time constant, are chosen in the range 0.4

show abstract

“…To solve Eqs. (5)-(8), the code described in our previous works was utilized [4,5], and only a brief description will be provided here.…”

Section: Methodsmentioning

confidence: 99%

“…Perhaps the most common example of this is in the area of turbulent drag reduction, where skin friction drag over flat surfaces can be reduced up to 80% in the presence of polymer additives [1][2][3]. Beyond drag reduction, however, we have recently shown that viscoelasticity can significantly alter the flow within a bluff body wake, effectively delaying the Newtonian modes of turbulent transition [4][5][6]. Specifically, we investigated the flow of homogeneous dilute polymer solutions at large Reynolds numbers (Re ¼ 3900), and viscoelasticity was found to stabilize the shear layer immediately behind the surface of the cylinder, causing the wake to appear qualitatively similar to the Newtonian structure observed at much lower Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Polymer Injection in Turbulent Flow Past a Circular Cylinder

Richter

Shaqfeh

Iaccarino

2011

Journal of Fluids Engineering

Self Cite

View full text Add to dashboard Cite

Using a code developed to compute high Reynolds number viscoelastic flows, polymer injection from the upstream stagnation point of a circular cylinder is modeled at Re=3900. Polymer stresses are represented using the FENE-P constitutive equations. By increasing polymer injection rates within realistic ranges, significant near wake stabilization is observed. Rather than a turbulent detached shear layer giving way to a chaotic primary vortex (as seen in Newtonian flows at high Re), a much more coherent primary vortex is shed, which possesses an increased core pressure as well as a reduced level of turbulent energy.

show abstract

Floquet stability analysis of viscoelastic flow over a cylinder

Cited by 22 publications

References 26 publications

Three-dimensional transition after wake deflection behind a flapping foil

Three-dimensional transition after wake deflection behind a flapping foil

First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder

Numerical Simulation of Polymer Injection in Turbulent Flow Past a Circular Cylinder

Contact Info

Product

Resources

About