Detection of turbulent thermal diffusion of particles in numerical simulations

Abstract

The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the formation of large-scale inhomogeneities in the spatial distribution of inertial particles. The strength of this effect is maximum for Stokes numbers around unity, and decreases again for larger values. The dynamics of inertial particles is studied using Lagrangian modelling in forced temperature-stratified turbulence, whereas non-inertial particles and the fluid are described using DNS in an Eulerian framework.

Turbulent diffusion of chemically reacting gaseous admixtures

“…(41) and (42) [35,36] and detected in different laboratory experiments in stably and unstably temperature-stratified turbulence produced by oscillating grids or a multi-fan generator [30,38,40]. Turbulent thermal diffusion has been also detected in direct numerical simulations [42] and is shown to be important for atmospheric turbulence with temperature inversions [41] and for small-scale particle clustering in temperature-stratified turbulence [30,31].…”

“…During the decades turbulent transport of passive scalar and particles has been subject of an active research (see, e.g., handbooks [10][11][12][13][14][15] and reviews [16][17][18][19][20][21]). Many important problems, including particle clustering in isothermal [22][23][24][25][26][27][28][29] and stratified [30,31] turbulence, intermittency [32,33], effective diffusion [34], the formation of large-scale inhomogeneous structures in spatial distribution of particles or different scalar fields in small-scale turbulence [35][36][37][38][39][40][41][42] have been investigated in analytical, numerical and laboratory studies. However, impact of chemical reactions on turbulent transport have been studied mainly numerically and in the context of turbulent combustion (see, e.g., [2][3][4][5]).…”

Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

“…Turbulent thermal diffusion has been intensively investigated analytically [17,[20][21][22][23][24][25][26] using different theoretical approaches, in laboratory experiments in oscillating grid turbulence [27][28][29] and in the multi-fan produced turbulence [30]. This effect has also been detected in direct numerical simulations [31] and in atmospheric [32] and astrophysical turbulence [33].…”

Turbulent thermal diffusion: a way to concentrate dust in protoplanetary discs

“…The effects of TTD can be implemented in numerical simulations and theory as an ad-hoc velocity V TTD, but theoretical estimates are only approximate and factors of a few in α have a large impact on the concentration of particles (Equations 25, 43 and 48). Implementing TTD into numerical simulations directly will be difficult, and efforts to date have barely been able to detect the effect (Haugen et al 2012). Capturing the TTD requires a large dynamical range between the scale of the temperature variation and the scale of the turbulence, and a further large dynamical range between the integral scale of the turbulence and the scale of the turbulence which has the same correlation time as the particle's frictional stopping time.…”