Decaying versus stationary turbulence in particle-laden isotropic turbulence: Turbulence modulation mechanism

2012 ◽  
Vol 24 (1) ◽  
pp. 015106 ◽  
Author(s):  
Abouelmagd H. Abdelsamie ◽  
Changhoon Lee
Keyword(s):  
Isotropic Turbulence ◽  
Turbulence Modulation ◽  
Stationary Turbulence

scholarly journals A Lagrangian direct-interaction approximation for homogeneous isotropic turbulence

1997 ◽  
Vol 345 ◽  
pp. 307-345 ◽  
Author(s):  
SHIGEO KIDA ◽  
SUSUMU GOTO
Keyword(s):  
Energy Spectrum ◽  
Differential Equations ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Direct Interaction ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Stationary Turbulence ◽  
Direct Interaction Approximation ◽  
Velocity Derivative

A set of integro-differential equations in the Lagrangian renormalized approximation (Kaneda 1981) is rederived by applying a perturbation method developed by Kraichnan (1959), which is based upon an extraction of direct interactions among Fourier modes of a velocity field and was applied to the Eulerian velocity correlation and response functions, to the Lagrangian ones for homogeneous isotropic turbulence. The resultant set of integro-differential equations for these functions has no adjustable free parameters. The shape of the energy spectrum function is determined numerically in the universal range for stationary turbulence, and in the whole wavenumber range in a similarly evolving form for the freely decaying case. The energy spectrum in the universal range takes the same shape in both cases, which also agrees excellently with many measurements of various kinds of real turbulence as well as numerical results obtained by Gotoh et al. (1988) for a decaying case as an initial value problem. The skewness factor of the longitudinal velocity derivative is calculated to be −0.66 for stationary turbulence. The wavenumber dependence of the eddy viscosity is also determined.

A consequence of the zero fourth cumulant approximation

1962 ◽  
Vol 13 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Edward E. O'Brien ◽  
George C. Francis
Keyword(s):  
Energy Spectrum ◽  
Numerical Computation ◽  
Root Mean Square ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Passive Scalar ◽  
Turbulent Energy ◽  
Length Scale ◽  
Mean Square ◽  
Stationary Turbulence

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.

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.

Numerical Study of Noise from Isotropic Turbulence

1997 ◽  
Vol 05 (03) ◽  
pp. 317-336 ◽  
Author(s):  
A. Witkowska ◽  
D. Juvé ◽  
J. G. Brasseur
Keyword(s):  
Isotropic Turbulence ◽  
Numerical Study ◽  
Acoustic Power ◽  
Turnover Time ◽  
Turbulence Structure ◽  
Sound Generation ◽  
Acoustic Analogy ◽  
Eddy Simulation ◽  
Stationary Turbulence ◽  
Theoretical Predictions

A numerical study of sound radiation by isotropic turbulence is carried out by combining turbulence simulation with Lighthill's acoustic analogy. In the first study we analyze sound generation by decaying isotropic turbulence obtained both with 643 Direct Numerical Simulation (DNS) and 163 Large Eddy Simulation (LES). Both simulations lead to similar results for acoustic power, in agreement with the numerical results of Sarkar and Hussaini, but slightly different from theoretical predictions of Proudman and Lilley. In the second study we analyze sound generation by forced stationary turbulence, simulated with 1283 DNS using a forcing scheme which preserves turbulence structure. The acoustic power computed from the stationary turbulence is in good agreement with results obtained for decaying isotropic turbulence. The acoustic spectrum shows that the characteristic frequency of the generated sound is approximately four times the inverse eddy turnover time. The contributions of different turbulence scales to the generated noise are computed separately from filtered velocity fields. For the low Reynolds number turbulence analyzed, the scales which most contribute to noise generation are 2–3 times smaller than the energy-containing scales and lie between the energy and dissipation-rate spectral peaks.

Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence

2017 ◽  
Vol 832 ◽  
pp. 438-482 ◽  
Author(s):  
Qi Dai ◽  
Kun Luo ◽  
Tai Jin ◽  
Jianren Fan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Rotational Motion ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Stokes Number ◽  
Systematic Investigation ◽  
Turbulence Modulation ◽  
Physical Mechanisms ◽  
Preferential Concentration

In this paper, a systematic investigation of turbulence modulation by particles and its underlying physical mechanisms in decaying compressible isotropic turbulence is performed by using direct numerical simulations with the Eulerian–Lagrangian point-source approach. Particles interact with turbulence through two-way coupling and the initial turbulent Mach number is 1.2. Five simulations with different particle diameters (or initial Stokes numbers, $St_{0}$) are conducted while fixing both their volume fraction and particle densities. The underlying physical mechanisms responsible for turbulence modulation are analysed through investigating the particle motion in the different cases and the transport equations of turbulent kinetic energy, vorticity and dilatation, especially the two-way coupling terms. Our results show that microparticles ($St_{0}\leqslant 0.5$) augment turbulent kinetic energy and the rotational motion of fluid, critical particles ($St_{0}\approx 1.0$) enhance the rotational motion of fluid, and large particles ($St_{0}\geqslant 5.0$) attenuate turbulent kinetic energy and the rotational motion of fluid. The compressibility of the turbulence field is suppressed for all the cases, and the suppression is more significant if the Stokes number of particles is close to 1. The modifications of turbulent kinetic energy, the rotational motion and the compressibility are all related with the particle inertia and distributions, and the suppression of the compressibility is attributed to the preferential concentration and the inertia of particles.

On the Average Settling Rate of Heavy Particles in Decaying Homogeneous Isotropic Turbulence

1998 ◽  
Vol 14 (3) ◽  
pp. 111-118
Author(s):  
C. Y. Yang ◽  
U. Lei
Keyword(s):  
Time Scale ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Solid Particles ◽  
Settling Rate ◽  
Stationary Turbulence ◽  
Turbulence Decay ◽  
Decaying Turbulence ◽  
Inertia Response

ABSTRACTThe average settling rate of spherical solid particles, 〈vs〉, under a body force field is studied numerically in decaying homogeneous isotropic turbulent flows generated by the direct numerical simulation of the continuity and Navier-Stokes equations. The increase of the average settling rate, 〈Δvs〉, is maximized when Tp/Tk ≈ 1 and vd/u′ ≈ 0.5, and is of order 0.lu′, which is qualitatively similar to that in stationary turbulence. Here 〈Δvs〉 = 〈vs〉 − vd, Tp is the particle's relaxation time, Tk is the Kolmogorov time scale, vd is the settling rate of particles in still fluid, and u′ is the root mean square of the fluid velocity fluctuation. However, the magnitude of the maximum value of 〈Δvs〉 in decaying turbulence is substantially greater (about 40%) than that in the corresponding stationary turbulence due to the inertia response of particles to turbulence decay. Although 〈Δvs〉/u′ does not reach a stationary state as the flow is evolving, it is a slowly time varying function for the parameters of interest as Tp (≈ Tk when 〈Δvs〉 is maximized) is in general of one order less than the time scale of turbulence decay.

A new time scale for turbulence modulation by particles

2019 ◽  
Vol 880 ◽  
Author(s):  
Izumi Saito ◽  
Takeshi Watanabe ◽  
Toshiyuki Gotoh
Keyword(s):  
Time Scale ◽  
Isotropic Turbulence ◽  
Turnover Time ◽  
Scaling Analysis ◽  
Inertial Particles ◽  
Cloud Droplets ◽  
Turbulence Modulation ◽  
Important Time ◽  
Loading Parameter ◽  
New Time

A new time scale for turbulence modulation by particles is introduced. This time scale is inversely proportional to the number density and the radius of particles, and can be regarded as a counterpart of the phase relaxation time, an important time scale in cloud physics, which characterizes the interaction between turbulence and cloud droplets by condensation–evaporation. Scaling analysis and direct numerical simulations of dilute inertial particles in homogeneous isotropic turbulence suggest that turbulence modulation by particles with a fixed mass-loading parameter can be expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the new time scale.

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