On the Volume Fraction Effects of Inertial Colliding Particles in Homogeneous Isotropic Turbulence

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Martin Ernst ◽  
Martin Sommerfeld
Keyword(s):  
Fluid Flow ◽  
Particle Motion ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Particle System ◽  
Free Particle ◽  
Particle Diameter ◽  
Homogeneous Isotropic Turbulence ◽  
Particle Collisions ◽  
Carrier Fluid

Abstract The main objective of the present study is the investigation of volume fraction effects on the collision statistics of nonsettling inertial particles in a granular medium as well as suspended in an unsteady homogeneous isotropic turbulent flow. For this purpose, different studies with mono-disperse Lagrangian point-particles having different Stokes numbers are considered in which the volume fraction of the dispersed phase is varied between 0.001 and 0.01. The fluid behavior is computed using a three-dimensional Lattice-Boltzmann method. The carrier-fluid turbulence is maintained at Taylor microscale Reynolds number 65.26 by applying a spectral forcing scheme. The Lagrangian particle tracking is based on considering the drag force only and a deterministic model is applied for collision detection. The influence of the particle phase on the fluid flow is neglected at this stage. The particle size is maintained at a constant value for all Stokes numbers so that the ratio of particle diameter to Kolmogorov length scale is fixed at 0.58. The variation of the particle Stokes number was realized by modifying the solids density. The observed particle Reynolds and Stokes numbers are in between [1.07, 2.61] and [0.34, 9.79], respectively. In the present simulations, the fluid flow and the particle motion including particle-particle collisions are based on different temporal discretization. Hence, an adaptive time stepping scheme is introduced. The particle motion as well as the occurrence of inter-particle collisions is characterized among others by Lagrangian correlation functions, the velocity angles between colliding particles and the collision frequencies. Initially, a fluid-free particle system is simulated and compared with the principles of the kinetic theory to validate the implemented deterministic collision model. Moreover, a selection of results obtained for homogeneous isotropic turbulence is compared with in literature available DNS and LES results as well. According to the performed simulations, the collision rate of particles with large Stokes numbers strongly depends on the adopted volume fraction, whereas for particles with small Stokes numbers the influence of particle volume fraction is less pronounced.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

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.

DNS/DPS of Inertial Droplet Coalescence in Homogeneous Isotropic Turbulence and Comparison With PDF Model Predictions Using the Direct Quadrature Method of Moments

2009 ◽  
Author(s):  
Dirk Wunsch ◽  
Roel Belt ◽  
Pascal Fede ◽  
Olivier Simonin
Keyword(s):  
Particle Size ◽  
Method Of Moments ◽  
Isotropic Turbulence ◽  
Particle Diameter ◽  
Diameter Distribution ◽  
Quadrature Method ◽  
Homogeneous Isotropic Turbulence ◽  
Droplet Coalescence ◽  
Particle Inertia ◽  
Quadrature Method Of Moments

To analyze in detail the coalescence mechanisms and validate modeling approaches, deterministic Lagrangian simulations of droplet trajectories (DPS) coupled with Direct Numerical Simulations (DNS) of a Homogeneous Isotropic Turbulence (HIT) are performed. The influence of the colliding particle velocity correlations induced by the fluid turbulence on the rate of droplet coalescence is investigated for different particle inertia. The results are compared to predictions using the Direct Quadrature Method of Moments (DQMOM) accounting for coalescence. The particle diameter distribution is written as a summation of Dirac functions. This allows to derive Eulerian transport equations for the dispersed phase statistics, which account for coalescence and conserve the low-order moments of the particle size distribution. The collision terms are modeled applying the molecular chaos assumption in order to account for coalescence. Particle size distributions and moments obtained from DQMOM are compared to those of the DNS/DPS simulations in function of particle inertia.

Geometry and interaction of structures in homogeneous isotropic turbulence

2012 ◽  
Vol 710 ◽  
pp. 453-481 ◽  
Author(s):  
T. Leung ◽  
N. Swaminathan ◽  
P. A. Davidson
Keyword(s):  
Spatial Distribution ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Circular Cross Section ◽  
Homogeneous Isotropic Turbulence ◽  
Systematic Analysis ◽  
Turbulence Structures ◽  
Classical Energy ◽  
Filter Width ◽  
Extensional Strain

AbstractA strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number ${\mathit{Re}}_{\lambda } = 141$ is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, $L$. The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, ‘planarity’ and ‘filamentarity’, obtained using the Minkowski functionals. The planarity increases gradually by a small amount as $L$ is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as $L$ decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale $L$ are most likely to align with the largest extensional strain at a scale 3–5 times larger than $L$. This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the $5\eta $ scale (where $\eta $ is the Kolmogorov scale) are more concentrated near the ones that are 3–5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

scholarly journals Dense gas effects in inviscid homogeneous isotropic turbulence

2016 ◽  
Vol 800 ◽  
pp. 140-179 ◽  
Author(s):  
L. Sciacovelli ◽  
P. Cinnella ◽  
C. Content ◽  
F. Grasso
Keyword(s):  
Speed Of Sound ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Numerical Study ◽  
Dense Gas ◽  
Homogeneous Isotropic Turbulence ◽  
Perfect Gas ◽  
Strong Compression ◽  
Strong Expansion

A detailed numerical study of the influence of dense gas effects on the large-scale dynamics of decaying homogeneous isotropic turbulence is carried out by using the van der Waals gas model. More specifically, we focus on dense gases of the Bethe–Zel’dovich–Thompson type, which may exhibit non-classical nonlinearities in the transonic and supersonic flow regimes, under suitable thermodynamic conditions. The simulations are based on the inviscid conservation equations, solved by means of a ninth-order numerical scheme. The simulations rely on the numerical viscosity of the scheme to dissipate energy at the finest scales, while leaving the larger scales mostly unaffected. The results are systematically compared with those obtained for a perfect gas. Dense gas effects are found to have a significant influence on the time evolution of the average and root mean square (r.m.s.) of the thermodynamic properties for flows characterized by sufficiently high initial turbulent Mach numbers (above 0.5), whereas the influence on kinematic properties, such as the kinetic energy and the vorticity, are smaller. However, the flow dilatational behaviour is very different, due to the non-classical variation of the speed of sound in flow regions where the dense gas is characterized by a value of the fundamental derivative of the gas dynamics (a measure of the variation of the speed of sound in isentropic compressions) smaller than one or even negative. The most significant differences between the perfect and the dense gas case are found for the repartition of dilatation levels in the flow field. For the perfect gas, strong compressions occupy a much larger volume fraction than expansion regions, leading to probability distributions of the velocity divergence highly skewed toward negative values. For the dense gas, the volume fractions occupied by strong expansion and compression regions are much more balanced; moreover, strong expansion regions are characterized by sheet-like structures, unlike the perfect gas which exhibits tubular structures. In strong compression regions, where compression shocklets may occur, both the dense and the perfect gas exhibit sheet-like structures. This suggests the possibility that expansion eddy shocklets may appear in the dense gas. This hypothesis is also supported by the fact that, in dense gas, vorticity is created with equal probability in strong compression and expansion regions, whereas for a perfect gas, vorticity is more likely to be created in the strong compression ones.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian super-droplet simulations

2021 ◽  
Vol 21 (5) ◽  
pp. 4059-4077
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Isotropic Turbulence ◽  
Cloud Droplet ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. The increase in the spectral width of an initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated by applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or a Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase in the spectral width. We apply a large computational domain (643 m3), one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence integral timescale is much larger than the droplet phase relaxation timescale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 µm is only sufficient for the lowest droplet concentration (26 cm−3). For the highest droplet concentration (650 cm−3), an order of magnitude smaller bin size is barely sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high-TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and a relatively small number of Lagrangian particles that are used in the particle-based microphysics.

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