A self-consistent model for the saturation dynamics of the vortex shedding around the mean flow in the unstable cylinder wake

2015 ◽  
Vol 27 (7) ◽  
pp. 074103 ◽  
Author(s):  
Vladislav Mantič-Lugo ◽  
Cristóbal Arratia ◽  
François Gallaire
Keyword(s):  
Vortex Shedding ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Consistent Model ◽  
Self Consistent ◽  
The Mean

A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

2016 ◽  
Vol 800 ◽  
pp. 327-357 ◽  
Author(s):  
P. Meliga ◽  
E. Boujo ◽  
F. Gallaire
Keyword(s):  
Sensitivity Analysis ◽  
Limit Cycle ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Cycle Frequency ◽  
Flow Perturbation ◽  
Self Consistent ◽  
The Mean

We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard–von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis is performed in the frame of the semi-linear self-consistent model recently introduced by Mantič et al. (Phys. Rev. Lett., vol. 113, 2014, 084501), which allows us to describe accurately the effect of the control on the mean flow, but also on the finite-amplitude fluctuation that couples back nonlinearly onto the mean flow via the formation of Reynolds stress. The sensitivity is computed with respect to arbitrary steady and synchronous time-harmonic body forces. For a small amplitude of the control, the theoretical variations of the limit-cycle frequency predict well those of the controlled flow, as obtained from either self-consistent modelling or direct numerical simulation of the Navier–Stokes equations. This is not the case if the variations are computed in the simpler mean flow approach overlooking the coupling between the mean and fluctuating components of the flow perturbation induced by the control. The variations of the limit-cycle amplitude (that falls out the scope of the mean flow approach) are also correctly predicted, meaning that the approach can serve as a relevant and systematic guideline to control strongly unstable flows exhibiting non-small, finite amplitudes of oscillation. As an illustration, we apply the method to control by means of a small secondary control cylinder and discuss the obtained results in the light of the seminal experiments of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, pp. 71–107).

scholarly journals Self-consistent model for the saturation mechanism of the response to harmonic forcing in the backward-facing step flow

2016 ◽  
Vol 793 ◽  
pp. 777-797 ◽  
Author(s):  
V. Mantič-Lugo ◽  
F. Gallaire
Keyword(s):  
Numerical Simulations ◽  
Reynolds Stress ◽  
Linear Response ◽  
Flow Equation ◽  
Direct Numerical Simulations ◽  
Mean Flow ◽  
Saturation Process ◽  
Consistent Model ◽  
Self Consistent ◽  
The Mean

Certain flows denominated as amplifiers are characterized by their global linear stability while showing large linear amplifications to sustained perturbations. As the forcing amplitude increases, a strong saturation of the response appears when compared to the linear prediction. However, a predictive model that describes the saturation of the response to higher amplitudes of forcing in stable laminar flows is still missing. While an asymptotic analysis based on the weakly nonlinear theory shows qualitative agreement only for very small forcing amplitudes, the linear response to harmonic forcing around the mean flow computed by direct numerical simulations presents a good prediction of the saturation also at higher forcing amplitudes. These results suggest that the saturation process is governed by the Reynolds stress and thus motivate the introduction of a simple self-consistent model. The model consists of a decomposition of the full nonlinear Navier–Stokes equations in a mean flow equation together with a linear perturbation equation around the mean flow, which are coupled through the Reynolds stress. The full fluctuating response and the resulting Reynolds stress are approximated by the first harmonic calculated from the linear response to the forcing around the aforementioned mean flow. This closed set of coupled equations is solved in an iterative manner as partial nonlinearity is still preserved in the mean flow equation despite the assumed simplifications. The results show an accurate prediction of the response energy when compared to direct numerical simulations. The approximated coupling is strong enough to retain the main nonlinear effects of the saturation process. Hence, a simple physical picture is formalized, wherein the response modifies the mean flow through the Reynolds stress in such a way that the correct response energy is attained.

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

Experimental Investigation of a Tandem Cylinder System With a Yawed Upstream Cylinder

2011 ◽  
Author(s):  
Stephen J. Wilkins ◽  
Joseph W. Hall
Keyword(s):  
Experimental Investigation ◽  
Flow Field ◽  
Unsteady Flow ◽  
Surface Pressure ◽  
Vortex Shedding ◽  
Flow Direction ◽  
Pressure Fluctuations ◽  
Mean Flow ◽  
The Mean ◽  
Velocity Spectra

The unsteady flow field produced by a tandem cylinder system with the upstream cylinder yawed to the mean flow direction is investigated for upstream cylinder yaw angles from α = 60° to α = 90°. Multi-point fluctuating surface pressure and hotwire measurements were conducted at various spanwise positions on both the upstream and downstream cylinders. The results indicate that yawing the front cylinder to the mean flow direction causes the pressure and velocity spectra on the upstream and downstream cylinders to become more broadband than for a regular tandem cylinder system, and reduces the magnitude of the peak associated with the vortex-shedding. However, span-wise correlation and coherence measurements indicate that the vortex-shedding is still present and was being obscured by the enhanced three-dimensionality that the upstream yawed cylinder caused and was still present and correlated from front to back, at least for the larger yaw angles investigated. When the cylinder was yawed to α = 60°, the pressure fluctuations became extremely broadband and exhibited shorter spanwise correlation.

The distortion of turbulence by a circular cylinder

1979 ◽  
Vol 92 (2) ◽  
pp. 269-301 ◽  
Author(s):  
R. E. Britter ◽  
J. C. R. Hunt ◽  
J. C. Mumford
Keyword(s):  
Circular Cylinder ◽  
Spectral Energy ◽  
Cylinder Surface ◽  
List Type ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Mean Velocity ◽  
Number Range ◽  
Velocity Fluctuations ◽  
The Mean

The flow of grid-generated turbulence past a circular cylinder is investigated using hot-wire anemometry over a Reynolds number range from 4·25 × 103 to 2·74 × 104 and a range of intensities from 0·025 to 0·062. Measurements of the mean velocity distribution, and r.m.s. intensities and spectral energy densities of the turbulent velocity fluctuations are presented for various radial and circumferential positions relative to the cylinder, and for ratios of the cylinder radius a to the scale of the incident turbulence Lx ranging from 0·05 to 1·42. The influence of upstream conditions on the flow in the cylinder wake and its associated induced velocity fluctuations is discussed.For all measurements, detailed comparison is made with the theoretical predictions of Hunt (1973). We conclude the following. The amplification and reduction of the three components of turbulence (which occur in different senses for the different components) can be explained qualitatively in terms of the distortion by the mean flow of the turbulent vorticity and the ‘blocking’ or ‘source’ effect caused by turbulence impinging on the cylinder surface. The relative importance of the first effect over the second increases as a/Lx increases or the distance from the cylinder surface increases.Over certain ranges of the variables involved, the measurements are in quantitative agreement with the predictions of the asymptotic theory when a/Lx [Lt ] 1, a/Lx [Gt ] 1 or |k| a [Gt ] 1 (where k is the wavenumber).The incident turbulence affects the gross properties of the flow in the cylinder wake, but the associated velocity fluctuations are probably statistically independent of those in the incident flow.The dissipation of turbulent energy is greater in the straining flow near the cylinder than in the approach flow. Some estimates for this effect are proposed.

Passive pitching of splitters in the trailing edge of elliptic cylinders

2017 ◽  
Vol 826 ◽  
pp. 363-375 ◽  
Author(s):  
Y. Jin ◽  
L. P. Chamorro
Keyword(s):  
Vortex Shedding ◽  
Semimajor Axis ◽  
Wake Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Trailing Edge ◽  
Flow Measurements ◽  
High Background ◽  
Aspect Ratios ◽  
The Mean

The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ($AR$) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. $f_{p}$ and $f_{v}$, which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible $f_{v}$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low $AR$ and high $AoA$, where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero $AoA$ of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.

Study of Buoyancy Induced Suppression of Cylinder Wake Instability Using Schlieren-Interferometry

2007 ◽  
Author(s):  
S. K. Singh ◽  
P. K. Panigrahi
Keyword(s):  
Vortex Shedding ◽  
Heat Input ◽  
Richardson Number ◽  
Shear Layers ◽  
Vortex Structures ◽  
Schlieren Image ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Experimental Conditions ◽  
Thermal Buoyancy

The control of horizontal square cylinder wake using thermal buoyancy has been experimentally investigated at low Reynolds numbers. The cylinder with an aspect ratio of 60 is mounted in a vertical test cell. The cylinder is electrically heated such that the buoyancy aids to the inertia of the mean flow. The operating parameters i.e. Reynolds number (87–118) and Richardson number (0.065–0.171) are varied to examine the flow behaviour over a range of experimental conditions. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. The complete vortex shedding sequence has been recorded using a highspeed camera. The suppression of vortex shedding by heat input has been demonstrated by schlieren image visualization, time traces of light intensity, corresponding power spectra and Strouhal number. The study provides new experimental information on processes and mechanisms involved in the heat-induced changes of the vortex structures under the influence of buoyancy. The formation length of the vortex structures increases with increase in Richardson number i.e. heating level. The sequence of instantaneous schlieren images show that shape of vortex structures becomes slender at a sufficiently high Richardson number and the vortices from opposite shear layers rub with each other without increasing the circulation level and the two shear layers combine to form a single plume. The plume becomes steady at critical value of heat input leading to suppression of vortex shedding. The corresponding spectra evolve from having a clear peak at the vortex shedding frequency to broadband spectra when vortex shedding is suppressed.

The Effect of Sound on Vortex Shedding From Single and Tandem Cylinders

2002 ◽  
Author(s):  
Joseph W. Hall ◽  
Samir Ziada ◽  
David S. Weaver
Keyword(s):  
Vortex Shedding ◽  
Sound Field ◽  
Open Circuit ◽  
Mean Flow ◽  
Number Range ◽  
Single Cylinder ◽  
Tandem Cylinders ◽  
Vortex Shedding Frequency ◽  
The Mean ◽  
Lock In

A single cylinder and two tandem cylinders configurations with longitudinal pitch ratios L/D = 1.75 and 2.5 were rigidly mounted in an open circuit windtunnel and a sound field was applied so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. Tests were performed for a Reynolds number range of 5000 < ReD < 24000. The effect of sound on the vortex shedding was investigated by instrumenting the cylinders with pressure taps and hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing (L/D = 1.75) was broader still than either the single cylinder, or the L/D = 2.5 tandem cylinder case.

The Spanwise Dependence of Vortex-Shedding From Yawed Circular Cylinders

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
James D. Hogan ◽  
Joseph W. Hall
Keyword(s):  
Vortex Shedding ◽  
Flow Direction ◽  
Rapid Decrease ◽  
Circular Cylinders ◽  
Mean Flow ◽  
Independence Principle ◽  
Simultaneous Measurements ◽  
Vortex Shedding Frequency ◽  
The Mean ◽  
Shedding Frequency

Simultaneous measurements of the fluctuating wall pressure along the cylinder span were used to examine the spanwise characteristics of the vortex-shedding for yaw angles varying from α=60 deg to α=90 deg. The Reynolds number based on the diameter of the cylinder was 56,100. The results indicate that yawing the cylinder to the mean flow direction causes the vortex-shedding in the wake to become more disorderly. This disorder is initiated at the upstream end of the cylinder and results in a rapid decrease in correlation length, from 3.3D for α=90 deg to 1.1D for α=60 deg. The commonly used independence principle was shown to predict the vortex-shedding frequency reasonably well along the entire cylinder span for α>70 deg, but did not work as well for α=60 deg.

Sign in / Sign up

Export Citation Format

Share Document