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.

Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence

2003 ◽  
Vol 474 ◽  
pp. 193-225 ◽  
Author(s):  
G. BRETHOUWER ◽  
J. C. R. HUNT ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Scalar Field ◽  
Isotropic Turbulence ◽  
Numerical Study ◽  
Compressive Strain ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Length Scale ◽  
Random Forcing ◽  
Kolmogorov Length Scale

This paper presents an analysis and numerical study of the relations between the small-scale velocity and scalar fields in fully developed isotropic turbulence with random forcing of the large scales and with an imposed constant mean scalar gradient. Simulations have been performed for a range of Reynolds numbers from Reλ = 22 to 130 and Schmidt numbers from Sc = 1/25 to 144.The simulations show that for all values of Sc [ges ] 0.1 steep scalar gradients are concentrated in intermittently distributed sheet-like structures with a thickness approximately equal to the Batchelor length scale η/Sc½ with η the Kolmogorov length scale. We observe that these sheets or cliffs are preferentially aligned perpendicular to the direction of the mean scalar gradient. Due to this preferential orientation of the cliffs the small-scale scalar field is anisotropic and this is an example of direct coupling between the large- and small-scale fluctuations in a turbulent field. The numerical simulations also show that the steep cliffs are formed by straining motions that compress the scalar field along the imposed mean scalar gradient in a very short time period, proportional to the Kolmogorov time scale. This is valid for the whole range of Sc. The generation of these concentration gradients is amplified by rotation of the scalar gradient in the direction of compressive strain. The combination of high strain rate and the alignment results in a large increase of the scalar gradient and therefore in a large scalar dissipation rate.These results of our numerical study are discussed in the context of experimental results (Warhaft 2000) and kinematic simulations (Holzer & Siggia 1994). The theoretical arguments developed here follow from earlier work of Batchelor & Townsend (1956), Betchov (1956) and Dresselhaus & Tabor (1991).

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

Internal Stresses and Breakup of Porous Aggregates in Homogeneous Isotropic Turbulence

2014 ◽  
Author(s):  
Marco Vanni
Keyword(s):  
Numerical Simulation ◽  
Isotropic Turbulence ◽  
Internal Stresses ◽  
Length Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Stokesian Dynamics ◽  
Disordered Structure ◽  
Kolmogorov Length Scale ◽  
Primary Particles ◽  
Internal Forces

The stresses acting on aggregates smaller than the Kolmogorov length scale in homogeneous isotropic turbulence were estimated by a two-scale numerical simulation. The fluid dynamics at the scales larger than the Kolmogorov length scale was calculated by a Direct Numerical Simulation of the turbulent flow, in which the aggregates were modeled as point particles. Then, we adopted Stokesian Dynamics to evaluate the phenomena governed by the smooth velocity field of the smallest scales. At this level the disordered structure of the aggregates was modeled in detail, in order to take into account the role that the primary particles have in generating and transferring the internal stress. From this result, it was possible to evaluate the internal forces acting at intermonomer contacts and determine the occurrence of breakup as a consequence of the failure of intermonomer bonds. The method was applied to disordered aggregates with isostatic and highly hyperstatic structures, respectively.

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.

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.

Scale-to-scale energy and enstrophy transport in two-dimensional Rayleigh–Taylor turbulence

2015 ◽  
Vol 786 ◽  
pp. 294-308 ◽  
Author(s):  
Quan Zhou ◽  
Yong-Xiang Huang ◽  
Zhi-Ming Lu ◽  
Yu-Lu Liu ◽  
Rui Ni
Keyword(s):  
Kinetic Energy ◽  
Thermal Energy ◽  
Scaling Laws ◽  
Isotropic Turbulence ◽  
Thermal Dissipation ◽  
Small Scale ◽  
Two Dimensional ◽  
Space Technique ◽  
Small Scales ◽  
The Mean

We apply a recently developed filtering approach, i.e. filter-space technique (FST), to study the scale-to-scale transport of kinetic energy, thermal energy, and enstrophy in two-dimensional (2D) Rayleigh–Taylor (RT) turbulence. Although the scaling laws of the energy cascades in 2D RT systems follow the Bolgiano–Obukhov (BO59) scenario due to buoyancy forces, the kinetic energy is still found to be, on average, dynamically transferred to large scales by an inverse cascade, while both the mean thermal energy and the mean enstrophy move towards small scales by forward cascades. In particular, there is a reasonably extended range over which the transfer rate of thermal energy is scale-independent and equals the corresponding thermal dissipation rate at different times. This range functions similarly to the inertial range for the kinetic energy in the homogeneous and isotropic turbulence. Our results further show that at small scales the fluctuations of the three instantaneous local fluxes are highly asymmetrically distributed and there is a strong correlation between any two fluxes. These small-scale features are signatures of the mixing and dissipation of fluids with steep temperature gradients at the fluid interfaces.

scholarly journals Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

2015 ◽  
Vol 112 (31) ◽  
pp. 9530-9535 ◽  
Author(s):  
Jörg Schumacher ◽  
Paul Götzfried ◽  
Janet D. Scheel
Keyword(s):  
Kinetic Energy ◽  
Prandtl Number ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Turbulent Convection ◽  
Principal Strain ◽  
Small Scale ◽  
Strain Rates ◽  
Mean Values ◽  
Liquid Mercury

Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications.

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