Tangling clustering of inertial particles in stably stratified turbulence

Abstract

We have predicted theoretically and detected in laboratory experiments a new type of particle clustering (namely, tangling clustering of inertial particles) in a stably stratified turbulence with imposed mean vertical temperature gradient. In the stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, i.e., the inertial particles are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid, and a non-zero gradient of the mean particle number density, ∇N , is formed. It causes generation of fluctuations of the particle number density by tangling of the large-scale gradient, ∇N , by velocity fluctuations. In addition, the mean temperature gradient, ∇T , produces the temperature fluctuations by tangling of the large-scale gradient, ∇T , by velocity fluctuations. The anisotropic temperature fluctuations contribute to the two-point correlation function of the divergence of the particle velocity field, i.e., they increase the rate of formation of the particle clusters in small scales. We have demonstrated that in the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering (preferential concentration) that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter ≈ 10 µm and Reynolds numbers based on turbulent length scale and rms velocity, Re = 250. In the experiments the correlation function for the inertial clustering in isothermal turbulence is much smaller than that for the tangling clustering in nonisothermal turbulence. The size of the tangling clusters is of the order of several Kolmogorov length scales. The clustering described in our study is found for inertial particles with small Stokes numbers and with the material density that is much larger than the fluid density. Our theoretical predictions are in a good agreement with the obtained experimental results.

Detection of turbulent thermal diffusion of particles in numerical simulations

“…This effect is robust and the results of the numerical simulations are in agreement with theoretical studies [29,38], laboratory experiments [31,33,34] and atmospheric observations [35]. When St > 1, this effect is decreasing with Stokes number.…”

“…The phenomenon of turbulent thermal diffusion has been predicted theoretically in [29] and detected in different laboratory experiments in stably and unstably temperature-stratified turbulence [30][31][32][33][34]. This phenomenon is shown to be important for atmospheric turbulence with temperature inversions [35] and for smallscale particle clustering in temperature-stratified turbulence [34], but it is also expected to be significant for different kinds of heat exchangers, e.g., industrial boilers where Reynolds numbers and temperature gradients are large.…”

“…This phenomenon is shown to be important for atmospheric turbulence with temperature inversions [35] and for smallscale particle clustering in temperature-stratified turbulence [34], but it is also expected to be significant for different kinds of heat exchangers, e.g., industrial boilers where Reynolds numbers and temperature gradients are large.…”

Acceleration of raindrop formation due to the tangling-clustering instability in a turbulent stratified atmosphere

“…Contrary to the inertia induced preferential concentration, the pressure fluctuations in stratified turbulence with a nonzero mean temperature gradient are increased due to additional temperature fluctuations generated by tangling of the mean temperature gradient by velocity fluctuations. This is a reason why clustering of water droplets is much more effective in stratified turbulence [30,32] in comparison with a non-stratified turbulence [12].…”

Turbophoresis in forced inhomogeneous turbulence

“…In such cases, the HIPs are found to accumulate in the vicinity of the minima of mean temperature. This large-scale clustering phenomenon, which can be described by turbulent thermal diffusion, was predicted in an analytical study [18,[48][49][50][51][52] and detected in laboratory experiments [53][54][55], DNS [56] and atmospheric observations [57].…”