Effects of viscoelasticity in the high Reynolds number cylinder wake

2012 ◽  
Vol 693 ◽  
pp. 297-318 ◽  
Author(s):  
David Richter ◽  
Gianluca Iaccarino ◽  
Eric S. G. Shaqfeh
Keyword(s):  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Cylinder Wake ◽  
Helmholtz Instability ◽  
Newtonian Flow ◽  
Newtonian Flows ◽  
Free Shear Layers ◽  
High Reynolds ◽  
Far Wake

AbstractAt $\mathit{Re}= 3900$, Newtonian flow past a circular cylinder exhibits a wake and detached shear layers which have transitioned to turbulence. It is the goal of the present study to investigate the effects which viscoelasticity has on this state and to identify the mechanisms responsible for wake stabilization. It is found through numerical simulations (employing the FENE-P rheological model) that viscoelasticity greatly reduces the amount of turbulence in the wake, reverting it back to a state which qualitatively appears similar to the Newtonian mode B instability which occurs at lower $\mathit{Re}$. By focusing on the separated shear layers, it is found that viscoelasticity suppresses the formation of the Kelvin–Helmholtz instability which dominates for Newtonian flows, consistent with previous studies of viscoelastic free shear layers. Through this shear layer stabilization, the viscoelastic far wake is then subject to the same instability mechanisms which dominate for Newtonian flows, but at far lower Reynolds numbers.

On the spatial instability of piecewise linear free shear layers

1987 ◽  
Vol 174 ◽  
pp. 553-563 ◽  
Author(s):  
T. F. Balsa
Keyword(s):  
Velocity Profile ◽  
Numerical Solutions ◽  
Piecewise Linear ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Spatial Instability ◽  
Free Shear Layers ◽  
Linear Shear ◽  
High Reynolds ◽  
Sommerfeld Equation

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

The mechanics of the formation region of vortices behind bluff bodies

1966 ◽  
Vol 25 (2) ◽  
pp. 401-413 ◽  
Author(s):  
J. H. Gerrard
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Free Stream ◽  
Shear Layers ◽  
Bluff Bodies ◽  
Formation Region ◽  
Splitter Plates ◽  
Free Shear Layers ◽  
High Reynolds

The characteristic lengths of the oscillating wakes of bluff bodies is discussed; in particular, those used in the universal non-dimensional frequencies proposed by Roshko (1954b) and Goldburg, Washburn & Florsheim (1965). It is concluded that these are equivalent at high Reynolds number. A closer examination leads to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region, and the width to which the free shear layers diffuse. Discussion of the mechanics of the formation region results in a physical basis for the determination of the frequency by these two characteristic lengths. The ideas developed are applied to the effects of splitter plates in the wake. The possibility of a high-Reynolds-number symmetrical formation region is suggested as an explanation of the very small lift values observed in the absence of free-stream disturbances.

Correlated Compressible and Incompressible Channel Flows

1997 ◽  
Vol 119 (4) ◽  
pp. 911-915 ◽  
Author(s):  
C. Crnojevic´ ◽  
V. D. Djordjevic´
Keyword(s):  
Cross Section ◽  
High Reynolds Number ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Isothermal Flow ◽  
Governing Equations ◽  
Adiabatic Flow ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Reynolds Number Flows

Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Spatial stability analysis of subsonic corrugated jets

2019 ◽  
Vol 876 ◽  
pp. 766-791 ◽  
Author(s):  
F. C. Lajús ◽  
A. Sinha ◽  
A. V. G. Cavalieri ◽  
C. J. Deschamps ◽  
T. Colonius
Keyword(s):  
High Reynolds Number ◽  
Base Flow ◽  
Flow Profile ◽  
Azimuthal Direction ◽  
Instability Mechanism ◽  
Helmholtz Instability ◽  
Circular Jets ◽  
Unstable Solutions ◽  
High Reynolds ◽  
Axis Switching

The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin–Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin–Helmholtz instability.

High Reynolds Number Airfoil Simulations Using the Immersed Boundary Method

2012 ◽  
Author(s):  
James P. Johnson ◽  
Gianluca Iaccarino ◽  
Kuo-Huey Chen ◽  
Bahram Khalighi
Keyword(s):  
Immersed Boundary Method ◽  
High Reynolds Number ◽  
Aerodynamic Force ◽  
Reynolds Numbers ◽  
Computational Approach ◽  
Immersed Boundary ◽  
Pressure Distributions ◽  
Boundary Method ◽  
High Reynolds ◽  
Naca 0012

The Immersed-Boundary Method is coupled to an incompressible-flow RANS solver, based on a two-equation turbulence model, to perform unsteady numerical simulations of airflow past the NACA-0012 airfoil for several angles of attack and Reynolds numbers of 5.0×105 and 1.8×106. Qualitative characterizations of the flow in the vicinity of the airfoil are obtained to show the need for locally refined grids to capture the thin boundary layers close to the airfoil leading edges. Quantitative analysis of aerodynamic force coefficients and wall pressure distributions are also reported and compared to experimental results and those from body-fitted grid simulations using the same solver to assess the accuracy and limitations of this approach. The Immersed-Boundary simulations compared well to the experimental and body-fitted results up to the occurrence of separation. After that point, neither computational approach provided satisfactory solutions.

Spectral energy transfer in high Reynolds number turbulence

1977 ◽  
Vol 79 (2) ◽  
pp. 337-359 ◽  
Author(s):  
K. N. Helland ◽  
C. W. Van Atta ◽  
G. R. Stegen
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Spectrum ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Second Order ◽  
Spectral Energy ◽  
Local Isotropy ◽  
High Reynolds ◽  
Good Agreement

The spectral energy transfer of turbulent velocity fields has been examined over a wide range of Reynolds numbers by experimental and empirical methods. Measurements in a high Reynolds number grid flow were used to calculate the energy transfer by the direct Fourier-transform method of Yeh & Van Atta. Measurements in a free jet were used to calculate energy transfer for a still higher Reynolds number. An empirical energy spectrum was used in conjunction with a local self-preservation approximation to estimate the energy transfer at Reynolds numbers beyond presently achievable experimental conditions.Second-order spectra of the grid measurements are in excellent agreement with local isotropy down to low wavenumbers. For the first time, one-dimensional third-order spectra were used to test for local isotropy, and modest agreement with the theoretical conditions was observed over the range of wavenumbers which appear isotropic according to second-order criteria. Three-dimensional forms of the measured spectra were calculated, and the directly measured energy transfer was compared with the indirectly measured transfer using a local self-preservation model for energy decay. The good agreement between the direct and indirect measurements of energy transfer provides additional support for both the assumption of local isotropy and the assumption of self-preservation in high Reynolds number grid turbulence.An empirical spectrum was constructed from analytical spectral forms of von Kármán and Pao and used to extrapolate energy transfer measurements at lower Reynolds number to Rλ = 105 with the assumption of local self preservation. The transfer spectrum at this Reynolds number has no wavenumber region of zero net spectral transfer despite three decades of $k^{-\frac{5}{3}}$. behaviour in the empirical energy spectrum. A criterion for the inertial subrange suggested by Lumley applied to the empirical transfer spectrum is in good agreement with the $k^{-\frac{5}{3}}$ range of the empirical energy spectrum.

Thin Shear Layers in High Reynolds Number Turbulence—DNS Results

2013 ◽  
Vol 91 (4) ◽  
pp. 895-929 ◽  
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda ◽  
Julian C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Shear Layers ◽  
High Reynolds

Entry Lengths of Laminar Pipe and Channel Flows

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Yash Joshi ◽  
B. R. Vinoth
Keyword(s):  
Reynolds Numbers ◽  
Channel Flows ◽  
Newtonian Flow ◽  
Low Reynolds Numbers ◽  
Entry Length ◽  
Newtonian Flows ◽  
Integral Measure ◽  
Displacement Thickness ◽  
Inlet Conditions ◽  
New Entry

Numerical simulations of laminar pipe and channel flows were carried out: (i) to understand the effect of inlet conditions, viz., flat inlet and streamtube inlet, on entry lengths, and (ii) to investigate the flow development in radial/transverse locations. Results show that hydrodynamic entry lengths from the streamtube inlet simulations are significantly lower compared to the entry lengths from the flat inlet simulations for low Reynolds numbers. Moreover, results from the current study (Newtonian flow with no-slip) as well as the results from the literature (non-Newtonian flow with no-slip) showed that for many flow situations, the slowest development of axial velocity in the transverse location happens to be very near to the wall. For the above cases, the existing entry length criteria (centerline as well as global entry length) are not appropriate to define the entry length. We have proposed a new entry length criterion based on the displacement thickness which is an integral measure of the velocity profile. A new entry length correlation using the displacement thickness criterion is proposed for Newtonian flows in pipe and channel based on simulations with the streamtube inlet condition.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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