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 Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

2017 ◽  
Vol 825 ◽  
pp. 515-549 ◽  
Author(s):  
L. Sciacovelli ◽  
P. Cinnella ◽  
F. Grasso
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Equations Of State ◽  
Vapour Phase ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Dense Gas ◽  
Homogeneous Isotropic Turbulence ◽  
Third Invariant ◽  
Strong Expansion

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics $\unicode[STIX]{x1D6E4}$ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
Author(s):  
Andras Nemes ◽  
Teja Dasari ◽  
Jiarong Hong ◽  
Michele Guala ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Response Times ◽  
Field Measurements ◽  
Stokes Number ◽  
Inertial Particles ◽  
Natural Setting ◽  
Scale Particle ◽  
Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay

2017 ◽  
Vol 818 ◽  
pp. 697-715 ◽  
Author(s):  
M. Meldi ◽  
P. Sagaut
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
The Other ◽  
Grid Turbulence ◽  
Physical Domain ◽  
Simulation Studies ◽  
Homogeneous Isotropic Turbulence ◽  
Free Decay ◽  
Reynolds Number Effects ◽  
New Guidelines

The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.

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.

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.

Kinetic energy transfer in compressible isotropic turbulence

2018 ◽  
Vol 841 ◽  
pp. 581-613 ◽  
Author(s):  
Jianchun Wang ◽  
Minping Wan ◽  
Song Chen ◽  
Shiyi Chen
Keyword(s):  
Energy Transfer ◽  
Mach Number ◽  
Kinetic Energy ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Average Kinetic Energy ◽  
Small Scales ◽  
Strong Compression ◽  
Mach Numbers ◽  
Kinetic Energy Transfer

Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales.

Kármán–Howarth solutions of homogeneous isotropic turbulence

2021 ◽  
Vol 932 ◽  
Author(s):  
L. Djenidi ◽  
R.A. Antonia
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Order Moment ◽  
Homogeneous Isotropic Turbulence ◽  
The Difference ◽  
Decaying Turbulence ◽  
The Impact ◽  
Good Agreement

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

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