scholarly journals Synchronization of low Reynolds number plane Couette turbulence

2021 ◽  
Vol 933 ◽  
Author(s):  
Marios-Andreas Nikolaidis ◽  
Petros J. Ioannou
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Fourier Decomposition ◽  
Critical Wavelength ◽  
Small Scales ◽  
Flow Components ◽  
Negative Characteristic ◽  
Active Subspace

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$ , that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

On the impulsively started rotating sphere

1967 ◽  
Vol 27 (4) ◽  
pp. 779-788 ◽  
Author(s):  
K. E. Barrett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Series Solutions ◽  
Rotating Sphere ◽  
Boundary Layer Equations ◽  
Small Times ◽  
3 Omega

The velocity field generated in a fluid of viscosity, v, by impulsively starting at time t = 0, a sphere of radius a spinning with angular velocity Ω about a diameter is described using a new expansion variable 2 √vt/r. It is first shown how the standard time-dependent boundary-layer equations can be modified to give series solutions satisfying all the boundary conditions. Next, that these new solutions are relevant when the Reynolds number R = a2Ω/v goes to infinity in such a way that $R^{\frac{1}{3}} \Omega t$ is large. Lastly, solutions are given, applicable at small times for non-zero Reynolds numbers. These last expansions show that the velocity components decay algebraically rather than exponentially at large distances.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Numerical Analysis of Vortex Dynamics in a Double Expansion

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Allan I. J. Love ◽  
Donald Giddings ◽  
Henry Power
Keyword(s):  
Reynolds Number ◽  
Vortex Dynamics ◽  
Experimental Studies ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
Reynolds Stress Model ◽  
Main Flow ◽  
Time Dependent ◽  
Ansys Fluent ◽  
Flow Through

The turbulent flow through a 3D diffuser featuring a double expansion is investigated using computational fluid dynamics. Time dependent simulations are reported using the stress omega Reynolds stress model available in ANSYS FLUENT 13.0. The flow topography and characteristics over a range of Reynolds numbers from 42,000 to 170,000 is reported, and its features are consistent with those investigated for other similar geometries. A transition from a chaotic separated flow to one featuring one large recirculation in one corner of the diffuser is predicted at a Reynolds number of 80,000. For a Reynolds number of 170,000 a precessing/flapping motion of the main flow field was identified, the frequency of which is consistent with other numerical and experimental studies.

Linear stability theory of oscillatory Stokes layers

1974 ◽  
Vol 62 (4) ◽  
pp. 753-773 ◽  
Author(s):  
Christian Von Kerczek ◽  
Stephen H. Davis
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Stability Theory ◽  
Absolute Stability ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Full Time ◽  
Full Theory ◽  
The Stability

The stability of the oscillatory Stokes layers is examined using two quasi-static linear theories and an integration of the full time-dependent linearized disturbance equations. The full theory predicts absolute stability within the investigated range and perhaps for all the Reynolds numbers. A given wavenumber disturbance of a Stokes layer is found to bemore stablethan that of the motionless state (zero Reynolds number). The quasi-static theories predict strong inflexional instabilities. The failure of the quasi-static theories is discussed.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

scholarly journals Dynamical interactions between the coherent motion and small scales in a cylinder wake

2014 ◽  
Vol 749 ◽  
pp. 201-226 ◽  
Author(s):  
F. Thiesset ◽  
L. Danaila ◽  
R. A. Antonia
Keyword(s):  
Reynolds Number ◽  
Energy Budget ◽  
Reynolds Numbers ◽  
Structure Functions ◽  
Coherent Motion ◽  
Order Structure ◽  
Cylinder Wake ◽  
Major Question ◽  
Dynamical Interaction ◽  
Small Scales

AbstractMost turbulent flows are characterized by coherent motion (CM), whose dynamics reflect the initial and boundary conditions of the flow and are more predictable than that of the random motion (RM). The major question we address here is the dynamical interaction between the CM and the RM, at a given scale, in a flow where the CM exhibits a strong periodicity and can therefore be readily distinguished from the RM. The question is relevant at any Reynolds number, but is of capital importance at finite Reynolds numbers, for which a clear separation between the largest and the smallest scales may not exist. Both analytical and experimental tools are used to address this issue. First, phase-averaged structure functions are defined and further used to condition the RM kinetic energy at a scale $r$ on the phase $\phi $ of the CM. This tool allows the dependence of the RM to be followed as a function of the CM dynamics. Scale-by-scale energy budget equations are established on the basis of phase-averaged structure functions. They reveal that energy transfer at a scale $r$ is sensitive to an additional forcing mechanism due to the CM. Second, these concepts are tested using hot-wire measurements in a cylinder wake, in which the CM is characterized by a well-defined periodicity. Because the interaction between large and small scales is most likely enhanced at moderate/low Reynolds numbers, and is also likely to depend on the amplitude of the CM, we choose to test our findings against experimental data at $R_{\lambda } \sim 10^2$ and for downstream distances in the range $10 \leq x/D \leq 40$. The effects of an increasing Reynolds number are also discussed. It is shown that: (i) a simple analytical expression describes the second-order structure functions of the purely CM. The energy of the CM is not associated with any single scale; instead, its energy is distributed over a range of scales. (ii) Close to the obstacle, the influence of the CM is perceptible even at the smallest scales, the energy of which is enhanced when the coherent strain is maximum. Further downstream from the cylinder, the CM clearly affects the largest scales, but the smallest scales are not likely to depend explicitly on the CM. (iii) The isotropic formulation of the RM energy budget compares favourably with experimental results.

Deformation of a two-dimensional drop at non-zero Reynolds number in time-periodic extensional flows: numerical simulation

2001 ◽  
Vol 436 ◽  
pp. 177-206 ◽  
Author(s):  
KAUSIK SARKAR ◽  
WILLIAM R. SCHOWALTER
Keyword(s):  
Reynolds Number ◽  
Interfacial Tension ◽  
Vortex Flow ◽  
Extensional Flow ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Drop Deformation ◽  
Two Dimensional ◽  
Extensional Flows ◽  
Potential Vortex

The shape of a two-dimensional viscous drop deforming in several time-dependent flow fields, including that due to a potential vortex, has been studied. Vortex flow was approximated by linearizing the induced velocity field at the drop centre, giving rise to an extensional flow with rotating axes of stretching. A generalization of the potential vortex, a flow we have called rotating extensional flow, occurs when the frequency of revolution of the flow is varied independently of the shear rate. Drops subjected to this forcing flow exhibit an interesting resonance phenomenon. Finally we have studied drop deformation in an oscillatory extensional flow.Calculations were performed at small but non-zero Reynolds numbers using an ADI front-tracking/finite difference method. We investigate the effects of interfacial tension, periodicity, viscosity ratio, and Reynolds number on the drop dynamics. The simulation reveals interesting behaviour for steady stretching flows, as well as time-dependent flows. For a steady extensional flow, the drop deformation is found to be non-monotonic with time in its approach to an equilibrium value. At sufficiently high Reynolds numbers, the drop experiences multiple growth–collapse cycles, with possible axes reversal, before reaching a final shape. For a vortex flow, the long-time deformation reaches a steady value, and the drop attains a revolving steady elliptic shape. For rotating extensional flows as well as oscillatory extensional flows, the maximum value of deformation displays resonance with variation in parameters, first increasing and then decreasing with increasing interfacial tension or forcing frequency. A simple ODE model with proper forcing is offered to explain the observed phenomena.

An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe

1975 ◽  
Vol 70 (3) ◽  
pp. 519-527 ◽  
Author(s):  
Arnold F. Bertelsen
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Velocity Field ◽  
Viscous Flow ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Cross Sectional ◽  
Curved Pipe ◽  
Sectional Plane ◽  
Steady Velocity

This paper deals with nonlinear streaming effects in an oscillating fluid in a curved pipe. The secondary steady velocity field in the cross-sectional plane of the pipe is studied in detail. Our experimental results are compared with the theory of Lyne (1970; that part of his theory which is valid for Reynolds numbers Rs [Lt ] 1) and the theory of Zalosh & Nelson (1973). On the basis of these comparisons we conclude that the theories are in practice valid for higher Reynolds numbers Rs than was formally expected.

Intermittency and scaling of pressure at small scales in forced isotropic turbulence

1999 ◽  
Vol 396 ◽  
pp. 257-285 ◽  
Author(s):  
TOSHIYUKI GOTOH ◽  
ROBERT S. ROGALLO
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Isotropic Turbulence ◽  
Gaussian Approximation ◽  
Reynolds Numbers ◽  
Theoretical Explanation ◽  
Effective Length ◽  
Small Scale ◽  
Small Scales ◽  
Reynolds Number Dependence

The intermittency of pressure and pressure gradient in stationary isotropic turbulence at low to moderate Reynolds numbers is studied by direct numerical simulation (DNS) and theoretically. The energy spectra scale in Kolmogorov units as required by the universal-equilibrium hypothesis, but the pressure spectra do not. It is found that the variances of the pressure and pressure gradient are larger than those computed using the Gaussian approximation for the fourth-order moments of velocity, and that the variance of the pressure gradient, normalized by Kolmogorov units, increases roughly as [Rscr ]1/2λ, where [Rscr ]λ is the Taylor microscale Reynolds number. A theoretical explanation of the Reynolds number dependence is presented which assumes that the small-scale pressure field is driven by coherent small-scale vorticity–strain domains. The variance of the pressure gradient given by the model is the product of the variance of ui,juj,i, the source term of the Poisson equation for pressure, and the square of an effective length of the small-scale coherent vorticity–strain structures. This length can be expressed in terms of the Taylor and Kolmogorov microscales, and the ratio between them gives the observed Reynolds number dependence. Formal asymptotic matching of the spectral scaling observed at small scales in the DNS with the classical scaling at large scales suggests that at high Reynolds numbers the pressure spectrum in these forced flows consists of three scaling ranges which are joined by two inertial ranges, the classical k−7/3 range and a k−5/3 range at smaller scale. It is not possible, within the classical Kolmogorov theory, to determine the length scale at which the inertial range transition occurs because information beyond the energy dissipation rate is required.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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