scholarly journals Inertial particle trapping in an open vortical flow

2014 ◽  
Vol 744 ◽  
pp. 183-216 ◽  
Author(s):  
Jean-Régis Angilella ◽  
Rafael D. Vilela ◽  
Adilson E. Motter
Keyword(s):  
Vortex Pair ◽  
Stokes Number ◽  
Basins Of Attraction ◽  
Critical Distance ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Particle Trapping ◽  
Order Unity ◽  
Heavy Particles ◽  
Open Flow

AbstractRecent numerical results on advection dynamics have shown that particles denser than the fluid can remain trapped indefinitely in a bounded region of an open fluid flow. Here, we investigate this counterintuitive phenomenon both numerically and analytically to establish the conditions under which the underlying particle-trapping attractors can form. We focus on a two-dimensional open flow composed of a pair of vortices and its specular image, which is a system we represent as a vortex pair plus a wall along the symmetry line. Considering particles that are much denser than the fluid, referred to as heavy particles, we show that two attractors form in the neighbourhood of the vortex pair provided that the particle Stokes number is smaller than a critical value of order unity. In the absence of the wall, the attractors are fixed points in the frame rotating with the vortex pair, and the boundaries of their basins of attraction are smooth. When the wall is present, the point attractors describe counter-rotating ellipses in this frame, with a period equal to half the period of one isolated vortex pair. The basin boundaries remain smooth if the distance from the vortex pair to the wall is large. However, these boundaries are shown to become fractal if the distance to the wall is smaller than a critical distance that scales with the inverse square root of the Stokes number. This transformation is related to the breakdown of a separatrix that gives rise to a heteroclinic tangle close to the vortices, which we describe using a Melnikov function. For an even smaller distance to the wall, we demonstrate that a second separatrix breaks down and a new heteroclinic tangle forms farther away from the vortices, at the boundary between the open and closed streamlines. Particles released in the open part of the flow can approach the attractors and be trapped permanently provided that they cross the two separatrices, which can occur under the effect of flow unsteadiness. Furthermore, the trapping of heavy particles from the open flow is shown to be robust to the presence of viscosity, noise and gravity. Navier–Stokes simulations for large flow Reynolds numbers show that viscosity does not destroy the attracting points until vortex merging takes place, while simulation of thermal noise shows that particle trapping persists for extended periods provided that the Péclet number is large. The presence of a gravitational field does not alter the permanent trapping by the attracting points if the settling velocities are not too large. For larger settling velocities, however, gravity can also give rise to a limit-cycle attractor next to the external separatrix and to a new form of trapping from the open flow that is not mediated by a heteroclinic tangle.

scholarly journals Modelling of turbulence modulation in particle- or droplet-laden flows

2012 ◽  
Vol 706 ◽  
pp. 251-273 ◽  
Author(s):  
Daniel W. Meyer
Keyword(s):  
Isotropic Turbulence ◽  
Density Ratio ◽  
Joint Probability ◽  
Stokes Number ◽  
Navier Stokes ◽  
Grid Turbulence ◽  
Heavy Particles ◽  
Turbulence Modulation ◽  
Modelling Framework ◽  
Liquid Flows

AbstractAddition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1{\unicode{x2013}} 10)$, particle/fluid density ratio ${\rho }_{p} / \rho = 2000$, ${\Phi }_{v} = O(1{0}^{- 4} )$) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ($\mathit{St}= O(0. 1)$, ${\rho }_{p} / \rho \gtrsim 1$, ${\Phi }_{v} = O(1{0}^{- 3} )$) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible.

scholarly journals Inertial-particle accelerations in turbulence: a Lagrangian closure

2016 ◽  
Vol 798 ◽  
pp. 187-200 ◽  
Author(s):  
S. Vajedi ◽  
K. Gustavsson ◽  
B. Mehlig ◽  
L. Biferale
Keyword(s):  
Numerical Simulations ◽  
Numerical Data ◽  
Direct Numerical Simulations ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Order Unity ◽  
Heavy Particles ◽  
Preferential Sampling ◽  
Closure Scheme ◽  
Light Particles

The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial-particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of $St$, as well as the presence of a minimum/maximum for the flatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity field. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.

Numerical Investigations for the Effect of Slender Body on Dynamic Rolling Characteristics of a 80°/60° Double Delta Wing

2013 ◽  
Vol 444-445 ◽  
pp. 286-292
Author(s):  
Bing Han ◽  
Min Xu ◽  
Xi Pei ◽  
Xiao Min An
Keyword(s):  
Stokes Equations ◽  
Delta Wing ◽  
Time Lag ◽  
Slender Body ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Rolling Motion ◽  
Navier Stokes Equations ◽  
Lag Effect ◽  
Double Delta Wing

The effect of slender body on the rolling characteristics of a double delta wing is found by comparing the numerical simulation results of the double delta wing and wing-body configuration. The coupled computation system solving the Navier-Stokes equations and the rolling motion equation alternatively to obtain the unsteady vortical flow around the two configurations while rolling. The results conclusively showed the upwash effect of the slender body enhanced the energy of strake vortex and merged vortex.The aerodynamic lag of double delta wing is weak, contrarily, the time lag effect of the wing-body configuration is significant. The asymmetry vortices structure nearby the trailing edge are believed to be the main reason for the unsteady time lag effect.

Flow structures and particle deposition patterns in double-bifurcation airway models. Part 2. Aerosol transport and deposition

2001 ◽  
Vol 435 ◽  
pp. 55-80 ◽  
Author(s):  
J. K. COMER ◽  
C. KLEINSTREUER ◽  
C. S. KIM
Keyword(s):  
Particle Deposition ◽  
Air Flow ◽  
Reynolds Numbers ◽  
Companion Paper ◽  
Stokes Number ◽  
Vortical Flow ◽  
Flow Structures ◽  
Particle Distributions ◽  
Deposition Patterns ◽  
Inlet Conditions

The flow theory and air flow structures in symmetric double-bifurcation airway models assuming steady laminar, incompressible flow, unaffected by the presence of aerosols, has been described in a companion paper (Part 1). The validated computer simulation results showed highly vortical flow fields, especially around the second bifurcations, indicating potentially complex particle distributions and deposition patterns. In this paper (Part 2), assuming spherical non-interacting aerosols that stick to the wall when touching the surface, the history of depositing particles is described. Specifically, the finite-volume code CFX (AEA Technology) with user-enhanced FORTRAN programs were validated with experimental data of particle deposition efficiencies as a function of the Stokes number for planar single and double bifurcations. The resulting deposition patterns, particle distributions, trajectories and time evolution were analysed in the light of the air flow structures for relatively low (ReD1 = 500) and high (ReD1 = 2000) Reynolds numbers and representative Stokes numbers, i.e. StD1 = 0.04 and StD1 = 0.12. Particle deposition patterns and surface concentrations are largely a function of the local Stokes number, but they also depend on the fluid–particle inlet conditions as well as airway geometry factors. While particles introduced at low inlet Reynolds numbers (e.g. ReD1 = 500) follow the axial air flow, secondary and vortical flows become important at higher Reynolds numbers, causing the formation of particle-free zones near the tube centres and subsequently elevated particle concentrations near the walls. Sharp or mildly rounded carinal ridges have little effect on the deposition efficiencies but may influence local deposition patterns. In contrast, more drastic geometric changes to the basic double-bifurcation model, e.g. the 90°-non-planar configuration, alter both the aerosol wall distributions and surface concentrations considerably.

Large Eddy Simulation of the Flow Around a Diffuser-Equipped Bluff Body in Ground Effect

2011 ◽  
Author(s):  
Lara Schembri Puglisevich ◽  
Gary Page
Keyword(s):  
Large Eddy Simulation ◽  
Bluff Body ◽  
Vortex Formation ◽  
Ground Effect ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Flow Structures ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Flow Features

Unsteady Large Eddy Simulation (LES) is carried out for the flow around a bluff body equipped with an underbody rear diffuser in close proximity to the ground, representing an automotive diffuser. The goal is to demonstrate the ability of LES to model underbody vortical flow features at experimental Reynolds numbers (1.01 × 106 based on model height and incoming velocity). The scope of the time-dependent simulations is not to improve on Reynolds-Averaged Navier Stokes (RANS), but to give further insight into vortex formation and progression, allowing better understanding of the flow, hence allowing more control. Vortical flow structures in the diffuser region, along the sides and top surface of the bluff body are successfully modelled. Differences between instantaneous and time-averaged flow structures are presented and explained. Comparisons to pressure measurements from wind tunnel experiments on an identical bluff body model shows a good level of agreement.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

Flow/Acoustic Mechanisms in Three-Dimensional Vortices Undergoing Sinusoidal-Wave Instabilities

2007 ◽  
Author(s):  
Wenhua Li ◽  
Z. C. Zheng ◽  
Ying Xu
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Particle Method ◽  
Acoustic Signals ◽  
Short Wave ◽  
Vortical Flow ◽  
Vortex Particle Method ◽  
Structure Changes ◽  
Wave Instabilities

It has been identified that vorticity in a vortex core directly relates to the frequency of a significant sound peak from an aircraft wake vortex pair where each of the vortices is modeled as an elliptic core Kirchhoff vortex. In three-dimensional vortices, sinusoidal instabilities at various length scales result in significant flow structure changes in these vortices, and thus influence their radiated acoustic signals. In this study, a three-dimensional vortex particle method is used to simulate the incompressible vortical flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula that enables computation of acoustic signals radiated from an approximated incompressible flow field. Cases of vortex rings and a pair of counter-rotating vortices are studied when they are undergoing both long- and short-wave instabilities. Both inviscid and viscous interactions are considered and effects of turbulence are simulated using sub-grid-scale models.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

Hypersonic weak-interaction solutions for flow past a very slender axisymmetric body

1969 ◽  
Vol 38 (3) ◽  
pp. 547-564 ◽  
Author(s):  
Arthur K. Cross ◽  
William B. Bush
Keyword(s):  
Weak Interaction ◽  
Free Stream ◽  
Axisymmetric Body ◽  
Absolute Temperature ◽  
The Body ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Order Unity ◽  
Specific Heats ◽  
Viscous Heat

The Navier–Stokes hypersonic weak-interaction theory is presented for the flow of a viscous, heat-conducting, compressible fluid past a very slender axisymmetric body, when the ratio of the radius of the body to the radial thickness of the viscous region, produced and supported by the body, is much less than unity. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Solutions are studied for the free-stream Mach number, the free-stream Reynolds number based on the axial length of the body, and the reciprocal of the weak-interaction parameter much greater than unity.It is shown that, for the viscosity-temperature exponent ω less than 1, seven distinct layers span the region between the shock wave and the body, which is of arbitrary shape. The leading approximations for the behaviour of the flow in these seven layers are analyzed, and the restrictions imposed on the theory are obtained.

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