scholarly journals Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

2014 ◽  
Vol 26 (1) ◽  
pp. 013601 ◽  
Author(s):  
Aldo Figueroa ◽  
Patrice Meunier ◽  
Sergio Cuevas ◽  
Emmanuel Villermaux ◽  
Eduardo Ramos
Keyword(s):  
Numerical Simulations ◽  
Peclet Number ◽  
Chaotic Advection ◽  
Péclet Number ◽  
Theoretical Predictions ◽  
Large Peclet Number

scholarly journals The dynamics of miscible viscous fingering from onset to shutdown

2018 ◽  
Vol 837 ◽  
pp. 520-545 ◽  
Author(s):  
Japinder S. Nijjer ◽  
Duncan R. Hewitt ◽  
Jerome A. Neufeld
Keyword(s):  
Numerical Simulations ◽  
Flow Regime ◽  
Peclet Number ◽  
Viscous Fingering ◽  
Linear Stability Theory ◽  
Late Time ◽  
Exchange Flow ◽  
Mixing Rate ◽  
Péclet Number ◽  
Single Finger

We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions.

scholarly journals The drag of a body moving transversely in a confined stratified fluid

1970 ◽  
Vol 43 (2) ◽  
pp. 407-418 ◽  
Author(s):  
M. R. Foster ◽  
P. G. Saffman
Keyword(s):  
Peclet Number ◽  
Slow Motion ◽  
Shear Layers ◽  
Stratified Fluid ◽  
Rotating Fluid ◽  
Péclet Number ◽  
Fluid Layers ◽  
Number Problem ◽  
Number Flow ◽  
Large Peclet Number

The slow motion of a body through a stratified fluid bounded laterally by insulating walls is studied for both large and small Peclet number. The Taylor column and its associated boundary and shear layers are very different from the analogous problem in a rotating fluid. In particular, the large Peclet number problem is non-linear and exhibits mixing of statically unstable fluid layers, and hence the drag is order one; whereas the small Peclet number flow is everywhere stable, and the drag is of the order of the Peclet number.

The effective diffusivity of ordered and freely evolving bubbly suspensions

2018 ◽  
Vol 840 ◽  
pp. 215-237 ◽  
Author(s):  
Aurore Loisy ◽  
Aurore Naso ◽  
Peter D. M. Spelt
Keyword(s):  
Numerical Simulations ◽  
Peclet Number ◽  
Random Media ◽  
Chemical Species ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Solid Particles ◽  
Péclet Number ◽  
Mechanical Dispersion ◽  
Fixed Beds

We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse components of this tensor with respect to the direction of averaged bubble rise velocity in a zero mixture velocity frame of reference, we focus on the convective contribution thereof, this being expected to be dominant in commonly encountered bubbly flows. We first extend the theory of Kochet al.(J. Fluid Mech., vol. 200, 1989, pp. 173–188) (which is for dispersion in fixed beds of solid particles under Stokes flow) to account for weak inertial effects in the case of ordered suspensions. In the limits of low and of high Péclet number, including the inertial effect of the flow does not affect the scaling of the effective diffusivity with respect to the Péclet number. These results are confirmed by direct numerical simulations performed in different flow regimes, for spherical or very deformed bubbles and from vanishingly small to moderate values of the Reynolds number. Scalar transport in arrays of freely rising bubbles is considered by us subsequently, using numerical simulations. In this case, the dispersion is found to be convectively enhanced at low Péclet number, like in ordered arrays. At high Péclet number, the Taylor dispersion scaling obtained for ordered configurations is replaced by one characterizing a purely mechanical dispersion, as in random media, even if the level of disorder is very low.

Mass transfer of particles located on the flow axis at large peclet number

1977 ◽  
Vol 12 (2) ◽  
pp. 218-226 ◽  
Author(s):  
Yu. P. Gupalo ◽  
A. D. Polyanin ◽  
Yu. S. Ryazantsev
Keyword(s):  
Mass Transfer ◽  
Peclet Number ◽  
Flow Axis ◽  
Péclet Number ◽  
Large Peclet Number

Sedimentation of charged particles at large péclet number

2004 ◽  
Vol 2 (6) ◽  
pp. 253-255
Author(s):  
Lianzhong Zhang ◽  
Chenbing Zhang ◽  
Wen Liu ◽  
Yizhi Ren
Keyword(s):  
Peclet Number ◽  
Charged Particles ◽  
Péclet Number ◽  
Large Peclet Number

The Effects of Forced Convection on the Power Dissipation of Constant-Temperature Thermal Conductivity Sensors

1997 ◽  
Vol 119 (1) ◽  
pp. 30-37 ◽  
Author(s):  
Y. Huang ◽  
H. H. Bau
Keyword(s):  
Thermal Conductivity ◽  
Forced Convection ◽  
Constant Temperature ◽  
Power Dissipation ◽  
Peclet Number ◽  
Asymptotic Theory ◽  
Time Dependent ◽  
Péclet Number ◽  
Theoretical Predictions ◽  
On Line

The effect of forced convection on the power dissipation of cylindrical and planar, constant temperature, thermal conductivity detectors (TCDs) is investigated theoretically. Such detectors can be used either for on-line continuous sensing of fluid thermal conductivity or for determining the sample concentrations in gas chromatography. A low Peclet number, asymptotic theory is constructed to correlate the TCD’s power dissipation with the Peclet number and to explain experimental observations. Subsequently, the effect of convection on the TCD’s power dissipation is calculated numerically for both time-independent and time-dependent flows. The theoretical predictions are compared with experimental observations.

Chloride transport models for wick action in concrete at large Peclet number

1998 ◽  
Vol 10 (3) ◽  
pp. 566-575 ◽  
Author(s):  
Y. T. Puyate ◽  
C. J. Lawrence ◽  
N. R. Buenfeld ◽  
I. M. McLoughlin
Keyword(s):  
Peclet Number ◽  
Chloride Transport ◽  
Transport Models ◽  
Péclet Number ◽  
Large Peclet Number

Sensitive enhanced diffusivities for flows with fluctuating mean winds: a two-parameter study

2001 ◽  
Vol 445 ◽  
pp. 345-375 ◽  
Author(s):  
JAMES BONN ◽  
RICHARD M. McLAUGHLIN
Keyword(s):  
Steady Flow ◽  
Strouhal Number ◽  
Diffusion Coefficients ◽  
Peclet Number ◽  
Large Scale ◽  
Three Dimensional ◽  
Temporal Fluctuation ◽  
Péclet Number ◽  
Enhanced Diffusion ◽  
Large Peclet Number

Enhanced diffusion coefficients arising from the theory of periodic homogenized averaging for a passive scalar diffusing in the presence of a large-scale, fluctuating mean wind superimposed upon a small-scale, steady flow with non-trivial topology are studied. The purpose of the study is to assess how the extreme sensitivity of enhanced diffusion coefficients to small variations in large-scale flow parameters previously exhibited for steady flows in two spatial dimensions is modified by either the presence of temporal fluctuation, or the consideration of fully three-dimensional steady flow. We observe the various mixing parameters (Péclet, Strouhal and periodic Péclet numbers) and related non-dimensionalizations. We document non-monotonic Péclet number dependence in the enhanced diffusivities, and address how this behaviour is camouflaged with certain non-dimensional groups. For asymptotically large Strouhal number at fixed, bounded Péclet number, we establish that rapid wind fluctuations do not modify the steady theory, whereas for asymptotically small Strouhal number the enhanced diffusion coefficients are shown to be represented as an average over the steady geometry. The more difficult case of large Péclet number is considered numerically through the use of a conjugate gradient algorithm. We consider Péclet-number-dependent Strouhal numbers, S = QPe−(1+γ), and present numerical evidence documenting critical values of γ which distinguish the enhanced diffusivities as arising simply from steady theory (γ < −1) for which fluctuation provides no averaging, fully unsteady theory (γ ∈ (−1, 0)) with closure coefficients plagued by non-monotonic Péclet number dependence, and averaged steady theory (γ > 0). The transitional case with γ = 0 is examined in detail. Steady averaging is observed to agree well with the full simulations in this case for Q [les ] 1, but fails for larger Q. For non-sheared flow, with Q [les ] 1, weak temporal fluctuation in a large-scale wind is shown to reduce the sensitivity arising from the steady flow geometry; however, the degree of this reduction is itself strongly dependent upon the details of the imposed fluctuation. For more intense temporal fluctuation, strongly aligned orthogonal to the steady wind, time variation averages the sensitive scaling existing in the steady geometry, and the present study observes a Pe1 scaling behaviour in the enhanced diffusion coefficients at moderately large Péclet number. Finally, we conclude with the numerical documentation of sensitive scaling behaviour (similar to the two-dimensional steady case) in fully three dimensional ABC flow.

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