On the interaction of Taylor length scale size droplets and isotropic turbulence

2016 ◽  
Vol 806 ◽  
pp. 356-412 ◽  
Author(s):  
Michael S. Dodd ◽  
Antonino Ferrante
Keyword(s):  
Surface Tension ◽  
Surface Area ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Droplet Surface ◽  
Rate Of Change ◽  
Length Scale ◽  
Fluid Viscosity ◽  
Carrier Fluid ◽  
Two Fluid

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Modulation of isotropic turbulence by particles of Taylor length-scale size

2010 ◽  
Vol 650 ◽  
pp. 5-55 ◽  
Author(s):  
FRANCESCO LUCCI ◽  
ANTONINO FERRANTE ◽  
SAID ELGHOBASHI
Keyword(s):  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Density Ratio ◽  
Particle Diameter ◽  
Finite Size ◽  
Rate Of Change ◽  
Spherical Particles ◽  
Length Scale ◽  
Frequency Spectra ◽  
Scale Size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.In contrast to particles with d < η, the effect of the particles in this study, with d > η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

The Gating Mechanism of Mechanosensitive Channels in Droplet Interface Bilayers

2015 ◽  
Vol 1722 ◽  
Author(s):  
Joseph S. Najem ◽  
Eric Freeman ◽  
Sergei Sukharev ◽  
Donald J. Leo
Keyword(s):  
Surface Tension ◽  
Surface Area ◽  
Duty Cycle ◽  
Large Scale ◽  
Droplet Surface ◽  
Lipid Monolayer ◽  
Low Frequencies ◽  
Area Change ◽  
Gating Mechanism ◽  
Relative Change

ABSTRACTMscL, a large-conductance mechanosensitive channel, is a ubiquitous osmolyte release valve that aids bacteria in surviving abrupt hypo-osmotic shocks. The large scale of its tension-driven opening transition makes it a strong candidate to serve as a transducer in novel stimuli-responsive biomolecular materials. In the previous work, a low-threshold gain-of-function V23T mutant of MscL produced a reliable activation behavior in a droplet interface bilayer (DIB) with applied axial droplet compression. Near the maximal compression, the aqueous droplets deform and the resulting increase in surface area leads to an increase in tension in the water-lipid-oil interface. This increase in tension is the product of the relative change in the droplet surface area and the elastic modulus of the DPhPC lipid monolayer (∼120 mN/m). This paper, presents a study of the physical processes that cause MscL gating in the DIB. Analysis of video during compression and relaxation of the droplets is utilized to estimate the change in the surface area of the droplet and the variation on monolayer surface tension. The monolayer surface tension is proportional to the area change of the droplet normalized to the original surface area. The results demonstrate that the area change in the droplet is negligible at frequencies above 1 Hz, but is approximately 2% at frequencies in the range of 100 mHz. In addition, at low frequencies (∼0.2 Hz) bilayer thinning occurs at maximum compression, proving an increase in bilayer tension. However, this study also shows that gating at frequencies higher than 0.2 Hz could be achieved through the application of high duty cycle oscillation (∼75%). The relative change in monolayer area increases significantly at higher duty cycle oscillations where the compression stroke is much faster than the relaxation stroke.

Direct particle–fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence

2017 ◽  
Vol 819 ◽  
pp. 188-227 ◽  
Author(s):  
Lennart Schneiders ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Kinetic Energy ◽  
Strain Rate ◽  
Viscous Dissipation ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Bulk Flow ◽  
Small Scale ◽  
Length Scale ◽  
Kolmogorov Length Scale ◽  
Scale Size

The modulation of decaying isotropic turbulence by 45 000 spherical particles of Kolmogorov-length-scale size is studied using direct particle–fluid simulations, i.e. the flow field over each particle is fully resolved by direct numerical simulations of the conservation equations. A Cartesian cut-cell method is used by which the exchange of momentum and energy at the fluid–particle interfaces is strictly conserved. It is shown that the particles absorb energy from the large scales of the carrier flow while the small-scale turbulent motion is determined by the inertial particle dynamics. Whereas the viscous dissipation rate of the bulk flow is attenuated, the particles locally increase the level of dissipation due to the intense strain rate generated near the particle surfaces due to the crossing-trajectory effect. Analogously, the rotational motion of the particles decouples from the local fluid vorticity and strain-rate field at increasing particle inertia. The high level of dissipation is partially compensated by the transfer of momentum to the fluid via forces acting at the particle surfaces. The spectral analysis of the kinetic energy budget is supported by the average flow pattern about the particles showing a nearly universal strain-rate distribution. An analytical expression for the instantaneous rate of viscous dissipation induced by each particle is derived and subsequently verified numerically. Using this equation, the local balance of fluid kinetic energy around a particle of arbitrary shape can be precisely determined. It follows that two-way coupled point-particle models implicitly account for the particle-induced dissipation rate via the momentum-coupling terms; however, they disregard the actual length scales of the interaction. Finally, an analysis of the small-scale flow topology shows that the strength of vortex stretching in the bulk flow is mitigated due to the presence of the particles. This effect is associated with the energy conversion at small wavenumbers and the reduced level of dissipation at intermediate wavenumbers. Consequently, it damps the spectral flux of energy to the small scales.

Flow Induced Dynamics of a Pinned Droplet on the Surface of a Channel

2005 ◽  
Author(s):  
Amirreza Golpaygan ◽  
Nasser Ashgriz
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Liquid Droplet ◽  
Equilibrium Shape ◽  
High Surface ◽  
Droplet Surface ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Droplet Deformation ◽  
Newtonian Liquids

Dynamic behavior of a droplet adhering to the surface of a channel has been modeled under the influence of surrounding fluid. The numerical solution is based on solving Navier-Stokes equations for Newtonian liquids. The study includes the effect of interfacial forces with constant surface tension, also effect of adhesion between the wall and droplet accounted by implementing contact angle at the wall. The Volume-Of-Fluid method is used to numerically determine the deformation of free surface. Droplet deformation and final shapes have been predicted. A reduction in the surface tension allows the droplet to deform much easier. However, an increase in the fluid viscosity, although increases the shear force on the droplet, may not result in the deformation at high surface tension. It is shown that deformation of droplet significantly influences structure of channel flow. Effects of liquid droplet and channel fluid properties, namely density and viscosity, inlet velocity, surface tension and channel geometry on dynamics of the problem have been studied. Two different outcomes have been considered: the first one droplet with equilibrium shape and the other one when breakup of the droplet occurs. The border line between the disintegration region and equilibrium region is determined for different droplet surface tensions.

scholarly journals Kármán–Howarth theorem for the Lagrangian-averaged Navier–Stokes–alpha model of turbulence

2002 ◽  
Vol 467 ◽  
pp. 205-214 ◽  
Author(s):  
DARRYL D. HOLM
Keyword(s):  
Energy Spectrum ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Energy Dissipation Rate ◽  
Navier Stokes ◽  
Length Scale ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Third Order ◽  
Kinetic Energy Spectrum

The Lagrangian averaged Navier–Stokes–alpha (LANS-α) model of turbulence is found to possess a Kármán–Howarth (KH) theorem for the dynamics of its second-order autocorrelation functions in homogeneous isotropic turbulence. This KH result implies that alpha-filtering in the LANS-α model of turbulence does not affect the exact Navier–Stokes relation between second and third moments at separation distances large compared to the model's length scale α. Moreover, at separations r that are smaller than α, the KH scaling between energy dissipation rate and longitudinal third-order autocorrelation changes to match the scaling found in two-dimensional incompressible flow. This is consistent with the corresponding change in scaling of the kinetic energy spectrum from k−5/3 for larger scales with kα < 1, which switches to k−3 for smaller scales with kα > 1, as discovered in Foias, Holm & Titi (2001).

Normalized dissipation rate in a moderate Taylor Reynolds number flow

2017 ◽  
Vol 818 ◽  
pp. 184-204 ◽  
Author(s):  
Alejandro J. Puga ◽  
John C. LaRue
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Integral Length Scale ◽  
Length Scale ◽  
Velocity Correlation ◽  
Time Resolved ◽  
Reynolds Number Flow ◽  
Active Grid

Time-resolved velocity measurements are obtained using a hot-wire in a nearly homogeneous and isotropic flow downstream of an active grid for a range of Taylor Reynolds numbers from$191$to$659$. It is found that the dimensionless dissipation rate,$C_{\unicode[STIX]{x1D716}}$, is nearly a constant for sufficiently high values of Taylor Reynolds number,$R_{\unicode[STIX]{x1D706},u_{q}}$, and is approximately equal to$0.87$. This value is approximately$5\,\%$less than the value reported by Boset al.(Phys. Fluids, vol. 19 (4), 2007, 045101), which is obtained using DNS/LES (direct numerical simulation combined with large eddy simulation) for decaying homogeneous and isotropic turbulence, and is in excellent agreement with the active grid experiment of Thormann & Meneveau (Phys. Fluids, vol. 26 (2), 2014, 025112.). The results presented herein show that deviation from isotropy may cause inconsistencies in the computation of$C_{\unicode[STIX]{x1D716}}$. As a result, it is suggested that the velocity scale be the square root of the turbulence kinetic energy. The integral length scale measurements obtained from the longitudinal velocity correlation are in close agreement with the integral length scale measured from the peak of the energy spectrum,$\unicode[STIX]{x1D705}E_{11}(\unicode[STIX]{x1D705})$, where$\unicode[STIX]{x1D705}$is the wavenumber and$E_{11}(\unicode[STIX]{x1D705})$is the one-dimensional power spectrum of the downstream velocity.

MOLECULAR DYNAMICS CALCULATIONS OF NEAR-CRITICAL LIQUID OXYGEN DROPLET SURFACE TENSION

2005 ◽  
Vol 15 (4) ◽  
pp. 413-422 ◽  
Author(s):  
Michael M. Micci ◽  
S. J. Lee ◽  
B. Vieille ◽  
C. Chauveau ◽  
Iskendar Gokalp
Keyword(s):  
Molecular Dynamics ◽  
Surface Tension ◽  
Droplet Surface ◽  
Liquid Oxygen ◽  
Molecular Dynamics Calculations

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

2008 ◽  
Vol 46 (3) ◽  
pp. 499-515 ◽  
Author(s):  
J. de Jong ◽  
L. Cao ◽  
S. H. Woodward ◽  
J. P. L. C. Salazar ◽  
L. R. Collins ◽  
...  
Keyword(s):  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Rate Estimation

Effects of surface tension and viscosity on airway reopening

1990 ◽  
Vol 69 (1) ◽  
pp. 74-85 ◽  
Author(s):  
D. P. Gaver ◽  
R. W. Samsel ◽  
J. Solway
Keyword(s):  
Surface Tension ◽  
Fluid Viscosity ◽  
Opening Pressure ◽  
Viscous Forces ◽  
Considerable Portion ◽  
Airway Opening ◽  
Wall Compliance ◽  
Large Opening ◽  
Surface Tension Forces ◽  
The Relationship

We studied airway opening in a benchtop model intended to mimic bronchial walls held in apposition by airway lining fluid. We measured the relationship between the airway opening velocity (U) and the applied airway opening pressure in thin-walled polyethylene tubes of different radii (R) using lining fluids of different surface tensions (gamma) and viscosities (mu). Axial wall tension (T) was applied to modify the apparent wall compliance characteristics, and the lining film thickness (H) was varied. Increasing mu or gamma or decreasing R or T led to an increase in the airway opening pressures. The effect of H depended on T: when T was small, opening pressures increased slightly as H was decreased; when T was large, opening pressure was independent of H. Using dimensional analysis, we found that the relative importance of viscous and surface tension forces depends on the capillary number (Ca = microU/gamma). When Ca is small, the opening pressure is approximately 8 gamma/R and acts as an apparent “yield pressure” that must be exceeded before airway opening can begin. When Ca is large (Ca greater than 0.5), viscous forces add appreciably to the overall opening pressures. Based on these results, predictions of airway opening times suggest that airway closure can persist through a considerable portion of inspiration when lining fluid viscosity or surface tension are elevated.

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