scholarly journals Toward coherently representing turbulent wall-flow dynamics

2013 ◽  
Vol 734 ◽  
pp. 1-4 ◽  
Author(s):  
J. C. Klewicki
Keyword(s):  
Solid Surface ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Flow Dynamics ◽  
Coherent Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Formation And Evolution ◽  
Wall Flow ◽  
Turbulent Wall

AbstractThe complex dynamics of turbulent flow in the vicinity of a solid surface underlie numerous scientifically important processes, and pose persistently daunting challenges in many engineering applications. Since their discovery decades ago, coherent motions have presented a tantalizing prospective opportunity for constructing descriptions of wall-flow dynamics using only a relatively small number of elements. The veracity and reliability of such representations are, however, ultimately tied to their basis in the Navier–Stokes equations. In this regard, the study by Sharma & McKeon (J. Fluid Mech., vol. 728, 2013, pp. 196–238) constitutes an important contribution, as it not only provides insights regarding the mechanisms underlying wall-flow coherent motion formation and evolution, but does so within a Navier–Stokes framework.

Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Deformation Process of a Water Droplet Impinging on a Solid Surface

1995 ◽  
Vol 117 (3) ◽  
pp. 394-401 ◽  
Author(s):  
Natsuo Hatta ◽  
Hitoshi Fujimoto ◽  
Hirohiko Takuda
Keyword(s):  
Solid Surface ◽  
Central Region ◽  
Deformation Process ◽  
Stokes Equations ◽  
Liquid Droplet ◽  
Navier Stokes ◽  
Maximum Diameter ◽  
Navier Stokes Equations ◽  
First Case ◽  
Practical Standpoint

This paper is concerned with numerical simulations of the deformation behavior of a liquid droplet impinging on a flat solid surface, as well as the flow field inside the droplet. In the present situation, the case where a droplet impinges on the surface at room temperature with a speed in the order of a few [m/s], is treated. These simulations were performed using the MAC-type solution method to solve a finite-differencing approximation of the Navier-Stokes equations governing an axisymmetric and incompressible fluid flow. For the first case where the liquid is water, the liquid film formed by the droplet impinging on the solid surface flows radially along it and expands in a fairly thin discoid-like shape. Thereafter, the liquid flow shows a tendency to stagnate at the periphery of the circular film, with the result that water is concentrated there is a doughnut-like shape. Subsequently, the water begins to flow backwards toward the center where it accumulates in the central region. For the second case where a n-heptane droplet impinges the surface, the film continues to spread monotonically up to a maximum diameter and there is no recoiling process to cause a backwards flow towards the central region. In this study the whole deformation process was investigated from numerical as well as experimental points of view. We find that the results obtained by the present mathematical model give fairly good agreement with the experimental observations. The effects of the viscous stresses and the surface tension on the deformation process of the droplets are estimated and discussed from a practical standpoint.

Axisymmetric Low-Reynolds Motion of Drops Through Circular Microchannels

2012 ◽  
Author(s):  
Saira F. Pineda ◽  
Arjan M. Kamp ◽  
D. Legendre ◽  
Armando J. Blanco
Keyword(s):  
Pressure Gradient ◽  
Drop Size ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
System Pressure ◽  
The Continuum

Flow constituted by drops appears in a wide range of natural, biological and engineering situations. For example, liquid-liquid two phase flow inside capillaries constitutes a model commonly used to represent fluid flow in a petroleum reservoir. The typical modeling approach considers inertial forces negligible in comparison to viscous forces, allowing the use of Stokes equation to study flow dynamics. Very few numerical simulations have been made considering inertial effects. In this project, the flow of a periodic train of drops in a viscous suspending fluid, due to the influence of a fixed pressure gradient, was studied by numerical simulation considering the full Navier-Stokes equations. A numerical approach based on a Volume of Fluid (VOF) formulation was employed using JADIM software, developed by the Institut de Mécanique des Fluides de Toulouse, France. JADIM solves Navier-Stokes equations using a VOF finite volume method, second order in space and time using structured mesh. This two-fluid approach without reconstruction of the interface allows simulating two-phase flows with complex interface shapes. Densities of the drops equal to those of the suspending fluid and a constant interface tension were assumed. The effect of drop size, viscosity ratio, interfacial forces and system pressure gradient on the flow dynamics was studied. Parameters values were chosen to be representative for some particular viscous oil. The result validation shows an excellent agreement between both numerical results. However, there are relative differences between them due to the increase in flow velocity when drop relative size increase and validity of Stokes approach is questionable. Results show non-symmetric eddies in the continuum phase, in a referential frame fixed to the drop. The shape of eddies is strongly influenced by viscosity radio. Drop mobility decreases with increasing size. Additionally, drop mobility also decreases when the viscosity ratio increases. Extra pressure gradient of the system due to the presence of the drop shows a strong dependency on the size ratio between the drop and the pore. For size ratio lower than 0.5, the extra pressure gradient required to move the continuum phase is small. However, when drop to micro-channel ratio exceeds 0.5, the extra pressure gradient significantly increases when the drop size increases. Also, viscosity ratio affects on the system pressure loss, especially in cases where the viscosity ratio is high. The analysis of the capillary number effect on the dynamics of the two-phase system shows that it does not influence drop mobility for the drop sizes considered.

SLIDING FRICTION IN VISCOUS HYDRODYNAMICS: THE ROUGH SURFACE AS VORTICITY SOURCE

1989 ◽  
Vol 03 (05) ◽  
pp. 393-397
Author(s):  
H. DEKKER
Keyword(s):  
Friction Coefficient ◽  
Viscous Fluid ◽  
Rough Surface ◽  
Solid Surface ◽  
Sliding Friction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Source ◽  
Viscous Hydrodynamics

Basset’s collective friction coefficient for a viscous fluid flowing past a rough solid surface is obtained — analytically — as an intrinsic consequence of the Navier-Stokes equations by treating the surface as a source of vorticity.

scholarly journals Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

2012 ◽  
Vol 707 ◽  
pp. 405-443 ◽  
Author(s):  
Romain Bonhomme ◽  
Jacques Magnaudet ◽  
Fabien Duval ◽  
Bruno Piar
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Air Bubbles ◽  
Fluid Interface ◽  
Navier Stokes Equations ◽  
Film Drainage ◽  
Two Fluids

AbstractThe dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid–fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier–Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.

scholarly journals Colour of turbulence

2017 ◽  
Vol 812 ◽  
pp. 636-680 ◽  
Author(s):  
Armin Zare ◽  
Mihailo R. Jovanović ◽  
Tryphon T. Georgiou
Keyword(s):  
Order Statistics ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Second Order ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Second Order Statistics

In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that coloured-in-time excitation of the Navier–Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization and control design.

scholarly journals Exact coherent structures at extreme Reynolds number

2016 ◽  
Vol 794 ◽  
pp. 1-4 ◽  
Author(s):  
G. P. Chini
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Tollmien Schlichting ◽  
Turbulent Wall

Exact coherent structures (ECS), unstable three-dimensional solutions of the Navier–Stokes equations, play a fundamental role in transitional and turbulent wall flows. Dempsey et al. (J. Fluid Mech., vol. 791, 2016, pp. 97–121) demonstrate that at large Reynolds number reduced equations can be derived that simplify the computation and facilitate mechanistic understanding of these solutions. Their analysis shows that ECS in plane Poiseuille flow can be sustained by a novel inner–outer interaction between oblique near-wall Tollmien–Schlichting waves and interior streamwise vortices.

Precession of a rapidly rotating cylinder flow: traverse through resonance

2015 ◽  
Vol 782 ◽  
pp. 63-98 ◽  
Author(s):  
Francisco Marques ◽  
Juan M. Lopez
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Nonlinear Models ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Small Scale ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear

Recent experiments using a rapidly rotating and precessing cylinder have shown that for specific values of the precession rate, aspect ratio and tilt angle, sudden catastrophic transitions to turbulence occur. Even if the precessional forcing is not too strong, there can be intermittent recurrences between a laminar state and small-scale chaotic flow. The inviscid linearized Navier–Stokes equations have inertial-wave solutions called Kelvin eigenmodes. The precession forces the flow to have azimuthal wavenumber $m=1$ (spin-over mode). Depending on the cylinder aspect ratio and on the ratio of the rotating and precessing frequencies, additional Kelvin modes can be in resonance with the spin-over mode. This resonant flow would grow unbounded if not for the presence of viscous and nonlinear effects. In practice, one observes a rapid transition to turbulence, and the precise nature of the transition is not entirely clear. When both the precessional forcing and viscous effects are small, weakly nonlinear models and experimental observations suggest that triadic resonance is at play. Here, we used direct numerical simulations of the full Navier–Stokes equations in a narrow region of parameter space where triadic resonance has been previously predicted from a weakly nonlinear model and observed experimentally. The detailed parametric studies enabled by the numerics reveal the complex dynamics associated with weak precessional forcing, involving symmetry-breaking, hysteresis and heteroclinic cycles between states that are quasiperiodic, with two or three independent frequencies. The detailed analysis of these states leads to associations of physical mechanisms with the various time scales involved.

On reduction of turbulent wall friction through spanwise wall oscillations

1999 ◽  
Vol 383 ◽  
pp. 175-195 ◽  
Author(s):  
M. R. DHANAK ◽  
C. SI
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Wall Friction ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Streamwise Vortices ◽  
Navier Stokes Equations ◽  
Turbulent Wall

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier–Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations.

Flow Past a Forced Oscillating Cylinder: A Three-Dimensional Numerical Study

2019 ◽  
Author(s):  
Huan Ping ◽  
Yan Bao ◽  
Dai Zhou ◽  
Zhaolong Han
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Two Dimensional Flow

Abstract In this paper, we conducted a three-dimensional investigation of flow past a cylinder undergoing forced oscillation. The flow configuration is similar to the work of Blackburn & Henderson (1999) [1], in which Reynolds number equals to 500 and a fixed motion amplitude of A/D = 0.25. The oscillation frequencies are varied in the range near to the natural shedding frequency of a stationary cylinder. The flow dynamics are governed by Navier-Stokes equations and the solutions are obtained by employing high-order spectral/hp element method. It is found that the flow dynamics are significantly distinguished from the study of two-dimensional flow by Blackburn & Henderson (1999) [1]. The values of hydrodynamic forces are smaller compared to that in the two-dimensional study. However, lock-in boundary we identified is broader. In addition, a different type of hysteresis loop of energy transfer coefficient is obtained.

Sign in / Sign up

Export Citation Format

Share Document