Preferred location of droplet collisions in turbulent flows

2016

J. Fluid Mech.

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This study uses the eigenvalues of the local velocity gradient tensor to categorize the local flow structures in incompressible turbulent flows into different types of saddle nodes and vortices and investigates their effect on the local collision kernel of heavy particles. Direct numerical simulation (DNS) results show that most of the collisions occur in converging regions with real and negative eigenvalues. Those regions are associated not only with a stronger preferential clustering of particles, but also with a relatively higher collision kernel. To better understand the DNS results, a conceptual framework is developed to compute the collision kernel of individual flow structures. Converging regions, where two out of three eigenvalues are negative, posses a very high collision kernel, as long as a critical amount of rotation is not exceeded. Diverging regions, where two out of three eigenvalues are positive, have a very low collision kernel, which is governed by the third and negative eigenvalue. This model is not suited for particles with Stokes number St 1, where the contribution of particle collisions from caustics is dominant.

Section: Dns Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of the eigenvalues of the velocity gradient tensor on particle collisions

2016

J. Fluid Mech.

Self Cite

“…The velocity of the flow field at the particle position is computed using trilinear interpolation. For more details, see Perrin and Jonker [30].…”

Section: Numerical Setupmentioning

confidence: 99%

“…043022-2 In order to construct the PDF of the relative velocities, we use the algorithm of Allen and Tildesley [31] to find neighboring particle pairs (see also Chen et al [32] and Perrin and Jonker [30]). This algorithm uses cell indexing and linked lists to check only particle pairs which could collide within one time step and therefore avoids the prohibitive O(N 2 p ) scaling of the computational cost.…”

Section: Numerical Setupmentioning

confidence: 99%

Relative velocity distribution of inertial particles in turbulence: A numerical study

2015

Phys. Rev. E

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The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.

“…The algorithm of Allen and Tildesley (1987) is used to detect collisions, which uses cell indexing and linked lists to check only droplet pairs that could collide within one time step [see also Chen et al (1999) and Perrin and Jonker (2014)]. Coalescence can instantaneously be enacted if required.…”

Section: Numerical Setupmentioning

confidence: 99%

Lagrangian Droplet Dynamics in the Subsiding Shell of a Cloud Using Direct Numerical Simulations

Journal of the Atmospheric Sciences

2015

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This study investigates the droplet dynamics at the lateral cloud-environment interface in shallow cumulus clouds. A mixing layer is used to study a small part of the cloud edge using direct numerical simulation combined with a Lagrangian particle tracking and collision algorithm. The effect of evaporation, gravity, coalescence, and the initial droplet size distribution on the intensity of the mixing layer and the evolution of the droplet size distribution is studied. Mixing of the droplets with environmental air induces evaporative cooling, which results in a very characteristic subsiding shell. As a consequence, stronger horizontal velocity gradients are found in the mixing layer, which induces more mixing and evaporation. A broadening of the droplet size distribution is observed as a result of evaporation and coalescence. Gravity acting on the droplets allows droplets in cloudy filaments detrained from the cloud to sediment and remain longer in the unsaturated environment. While this effect of gravity did not have a significant impact in this case on the mean evolution of the mixing layer, it does contribute to the broadening of the droplet size distribution and thereby significantly increases the collision rate. Although more but smaller droplets result in more evaporative cooling, more droplets also increase small-scale fluctuations and the production of turbulent dissipation. For the smallest droplets considered with a radius of 10 mm, the authors found that, although a more pronounced buoyancy dip was present, the increase in dissipation rate actually led to a decrease in the turbulent intensity of the mixing layer. Extrapolation of the results to realistic clouds is discussed.