Search

Direct numerical simulations of homogeneous isotropic turbulence are used to investigate the effects of turbulence on the transport of particles in gas flows or bubbles in liquid flows. The inertia associated with the bubbles or the particles leads to locally strong concentrations of these in regions of instantaneously strong vorticity for bubbles or strain-rate for particles. This alters the average settling rates and other processes. If the mass-loading of the dispersed phase is significant a random “turbulent” flow is generated by the particle settling. A simple demonstration of this is given, showing the statistically axisymmetric character of this flow and how it can modify an ambient turbulent flow.

We study the dynamic and kinematic collision statistics of cloud droplets for a range of flow Taylor microscale Reynolds numbers (up to 500), using a highly scalable hybrid direct numerical simulation approach. Accurate results of radial relative velocity (RRV) and radial distribution function (RDF) at contact have been obtained by taking advantage of their power-law scaling at short separation distances. Three specific but inter-related questions have been addressed in a systematic manner for geometric collisions of same-size droplets (of radius from 10 to 60µm) in a typical cloud turbulence (dissipation rate at 400cm 2 s 3 ). Firstly, both deterministic and stochastic forcing schemes were employed to test the sensitivity of the simulation results on the large- scale driving mechanism. We found that, in general, the results are quantitatively similar, with the deterministic forcing giving a slightly larger RDF and collision

The development of precipitating warm clouds is aected by several eects of small-scale air turbulence including enhancement of droplet-droplet collision rate by turbulence, entrainment and mixing at the cloud edges, and coupling of mechanical and thermal energies at various scales. Large-scale computation is a viable research tool for quantifying these multiscale processes. Specically, top-down large-eddy simulations (LES) of shallow convective clouds typically resolve scales of turbulent energy-containing eddies while the eects of turbulent cascade toward viscous dissipation are parameterized. Bottom-up hybrid direct numerical simulations (HDNS) of cloud microphysical processes resolve fully the dissipation-range ow scales but only partially the inertial subrange scales. it is desirable to systematically decrease the grid length in LES and increase the domain size in HDNS so that they can be better integrated to address the full range of scales and their coupling. In this paper, we discuss computational issues and physical modeling questions in expanding the ranges of scales realizable in LES and HDNS, and in bridging LES and HDNS. We review our on-going eorts in transforming our simulation codes towards PetaScale computing, in improving physical representations in LES and HDNS, and in developing better methods to analyze and interpret the simulation results.

In recent years, direct numerical simulation (DNS) approach has become a reliable tool for studying turbulent collision-coalescence of cloud droplets relevant to warm rain development. It has been shown that small-scale turbulent motion can enhance the collision rate of droplets by either enhancing the relative velocity and collision efficiency or by inertia-induced droplet clustering. A hybrid DNS approach incorporating DNS of air turbulence, disturbance flows due to droplets, and droplet equation of motion has been developed to quantify these effects of air turbulence. Due to the computational complexity of the approach, a major challenge is to increase the range of scales or size of the computation domain so that all scales affecting droplet pair statistics are simulated. Here we discuss our on-going work in this direction by improving the parallel scalability of the code, and by studying the effect of large-scale forcing on pair statistics relevant to turbulent collision. New results at higher grid resolutions show a saturation of pair and collision statistics with increasing flow Reynolds number, for given Kolmogorov scales and small droplet sizes. Furthermore, we examine the orientation dependence of pair statistics which reflects an interesting coupling of gravity and droplet clustering.

Particle-laden turbulent flow is a typical non-equilibrium process characterized by particle relaxation time p and the characteristic timescale of the flows f, in which the turbulent mixing of heavy particles is related to different scales of fluid motions. The preferential concentration (PC) of heavy particles could be strongly affected by fluid motion at dissipation-range scales, which presents a major challenge to the large-eddy simulation (LES) approach. The errors in simulated PC by LES are due to both filtering and the subgrid scale (SGS) eddy viscosity model. The former leads to the removal of the SGS motion and the latter usually results in a more spatiotemporally correlated vorticity field. The dependence of these two factors on the flow Reynolds number is assessed using a priori and a posteriori tests, respectively. The results suggest that filtering is the dominant factor for the under-prediction of the PC for Stokes numbers less than 1, while the SGS eddy viscosity model is the dominant factor for the over-prediction of the PC for Stokes numbers between 1 and 10. The effects of the SGS eddy viscosity model on the PC decrease as the Reynolds number and Stokes number increase. LES can well predict the PC for particle Stokes numbers larger than 10. An SGS model for particles with small and intermediate Stokes numbers is needed to account for the effects of the removed SGS turbulent motion on the PC.

The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision-coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51-73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20µm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100cm 2 s 3 , respectively. The collision efficiency for self-collisions in a bidisperse turbulent suspension can be larger than one. Such an increase in self-collisions is related to the far- field many-body AI and depends on the volumetric concentration of droplets. The total turbulent enhancement agrees qualitatively with previous results, but differs on a quantitative level. In the case of cross-size collisions between 18 and 20µm droplets, the total turbulent enhancement can be a factor of 7 and 2 at

There have been relatively few studies of turbulent collision rate of sedimenting droplets in the context of cloud physics, for which both the gravitational settling and inertial effects must be simultaneously considered. In this study, direct numerical simulations (DNS) were used to study the geometric collision rates of cloud droplets. Both Stokes drag law and a nonlinear drag law were considered, but the droplet–droplet local aerodynamic interactions were not included. Typical droplet and turbulence parameters of convective clouds were used to determine the flow dissipation rate , characteristic Stokes numbers, and the nondimensional terminal velocities. DNS results from a large number of runs covering the range from 10 to 400 cm2 s− 3 and droplet sizes from 10 to 60 μm in radius are presented. These results show that air turbulence can increase the geometric collision kernel by up to 47%, relative to geometric collision by differential sedimentation. This is due to both a moderate enhancement of the radial relative velocity between droplets and a moderate level of pair nonuniform concentration due to local droplet clustering. The turbulence enhancements increase with the flow dissipation rate and flow Reynolds number. Comparisons with related DNS studies show that our results confirm and extend the previous findings. The mean settling velocity of droplets in a turbulent flow was also obtained, showing that a maximum increase relative to the terminal velocity occurs for 20 μm cloud droplets. This agrees with a previous theory based on simple vortex flows and confirms the importance of a new nondimensional parameter τp3g2/ν for sedimenting droplets, where τp is the droplet inertial response time, g is the gravitational acceleration and ν is the air kinematic viscosity. Limitations of DNS and future directions are also noted.

The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted if the effects of air turbulence on two kinematic pair statistics can be modeled. The first is the average radial relative velocity and the second is the radial distribution function (RDF). A survey of the literature shows that no theory is available for predicting the radial relative velocity of finite-inertia sedimenting droplets in a turbulent flow. In this paper, a theory for the radial relative velocity is developed, using a statistical approach assuming that gravitational sedimentation dominates the relative motion of droplets before collision. In the weak-inertia limit, the theory reveals a new term making a positive contribution to the radial relative velocity resulting from a coupling between sedimentation and air turbulence on the motion of finite-inertia droplets. The theory is compared to the direct numerical simulations (DNS) results in part 1, showing a reasonable agreement with the DNS data for bidisperse cloud droplets. For droplets larger than 30??m in radius, a nonlinear drag (NLD) can also be included in the theory in terms of an effective inertial response time and an effective terminal velocity. In addition, an empirical model is developed to quantify the RDF. This, together with the theory for radial relative velocity, provides a parameterization for the turbulent geometric collision kernel. Using this integrated model, we find that turbulence could triple the geometric collision kernel, relative to the stagnant air case, for a droplet pair of 10 and 20??m sedimenting through a cumulus cloud at R?=2?104 and =600?cm2?s?3. For the self-collisions of 20??m droplets, the collision kernel depends sensitively on the flow dissipation rate.