Bogdan Rosa

Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation

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.

Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization

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.

Turbulent collision efficiency of heavy particles relevant to cloud droplets

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

Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations

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

Adaptation of fluid model EULAG to graphics processing unit architecture

The goal of this study is to adapt the multiscale fluid solver EULerian or LAGrangian framewrok (EULAG) to future graphics processing units (GPU) platforms. The EULAG model has the proven record of successful applications, and excellent efficiency and scalability on conventional supercomputer architectures. Currently, the model is being implemented as the new dynamical core of the COSMO weather prediction framework. Within this study, two main modules of EULAG, namely the multidimensional positive definite advection transport algorithm (MPDATA) and the variational generalized conjugate residual, elliptic pressure solver Generalized Conjugate Residual (GCR) are analyzed and optimized. In this paper, a method is proposed, which ensures a comprehensive analysis of the resource consumption including registers, shared, and global memories. This method allows us to identify bottlenecks of the algorithm, including data transfers between host and global memory, global and shared memories, as well as GPU occupancy. We put the emphasis on providing a fixed memory access pattern, padding as well as organizing computation in the MPDATA algorithm. The testing and validation of the new GPU implementation have been carried out based on modeling decaying turbulence of a homogeneous incompressible fluid in a triply‐periodic cube. Simulations performed using the standard version of EULAG and its new GPU implementation give similar solutions. Preliminary results show a promising increase in terms of computational efficiency. Copyright

Effects of gravity on the acceleration and pair statistics of inertial particles in homogeneous isotropic turbulence

Within the context of heavy particles suspended in a turbulent airflow, we study the eff ects of gravity on acceleration statistics and radial relative velocity (RRV) of inertial particles. The turbulent flow is simulated by direct numerical simulation (DNS) on a 256 3 grid and the dynamics of O(10 6 ) inertial particles by the point-particle approach. For particles/droplets with radius from 10 to 60 µm, we found that the gravity plays an important role in particle acceleration statistics: (a) a peak value of particle acceleration variance appears in both the horizontal and vertical directions at a particle Stokes number of about 1.2, at which the particle horizontal acceleration clearly exceeds the fluid-element acceleration; (b) gravity constantly disrupts quasi-equilibrium of a droplet’s response to local turbulent motion and amplifies extreme acceleration events both in the vertical and horizontal directions and thus eff ectively reduces the inertial filtering mechanism. By decomposing the RRV of the particles into three parts: (1) diff erential sedimentation, (2) local flow shear, and (3) particle diff erential acceleration, we evaluate and compare their separate contributions. For monodisperse particles, we show that the presence of gravity does not have a significant e ff ect on the shear term. On the other hand, gravity suppresses the probability distribution function (pdf) tails of the diff erential acceleration term due to a lower particle-eddy interaction time in presence of gravity. For bidisperse cases, we find that gravity can decrease the shear term slightly by dispersing particles into vortices where fluid shear is relatively low. The di ff erential acceleration term is found to be positively correlated with the gravity term, and this correlation is stronger when the diff erence in colliding particle radii becomes smaller. Finally, a theory is developed to explain the eff ects of gravity and turbulence on the horizontal and vertical acceleration variances of inertial particles at small Stokes numbers, showing analytically that gravity aff ects particle acceleration variance both in horizontal and vertical directions, resulting in an increase in particle acceleration variance in both directions. Furthermore, the eff ect of gravity on the horizontal acceleration variance is predicted to be stronger than that in the vertical direction, in agreement with our DNS results. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915121]

Kinematic and dynamic pair collision statistics of sedimenting inertial particles relevant to warm rain initiation

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.

An accurate and efficient method for treating aerodynamic interactions of cloud droplets

Motivated by a need to improve the representation of short-range interaction forces in hybrid direct numerical simulation of interacting cloud droplets, an efficient method for treating the aerodynamic interaction of two spherical particles settling under gravity is developed. An effort is made to ensure the accuracy of our method for any inter-particle separation by considering three separation ranges. The first is the long-range interaction where a multipole method is applied. After a decomposition into six simple configurations, explicit formulae for drag forces and torques are derived from an approximate Force-Torque-Stresslet (FTS) formulation. The FTS formulation is found to be accurate when the separation distance normalized by the average radius is larger than 5. The second range concerns the short-range interaction where the interaction force could be very large. Leading-order lubrication expansions are employed for this range and are found to be accurate when the normalized separation is less than about 0.01. Finally, for the intermediate range where no simple method is available, a third-order polynomial fitting is proposed to bridge the treatments for long-range and short-range interactions. After optimizing the precise form of polynomial fitting and matching locations, the force representation is found to be highly accurate when compared with the exact solution for Stokes flows. Using this method, collision efficiencies of cloud droplets sedimenting under gravity have been calculated. It is shown that the results of collision efficiency are in excellent agreement with results based on the exact Stokes flow solution. Collision efficiency results are also compared to previous results to further illustrate the accuracy of our calculations. The effects of particle rotation and the attractive van der Waals force on the collision efficiency are also studied. The efficient force representation developed here is more general than the usual lubrication expansion and thus can serve as a better approach to correct unresolved short-range interactions in particle-resolved simulations.

A study on parallel performance of the EULAG f90/95 code

The paper presents several aspects of the computational performance of the EULAG F90/95 code, originally written in Fortran 77. EULAG is a well-established research fluid solver characterized by robust numerics. It is suitable for a wide range of scales of the geophysical flows and is considered as a prospective dynamical core of a future weather forecast model of the COSMO consortium. The code parallelization is based on Message Passing Interface (MPI) communication protocol. In the paper, the numerical models parallel performance is examined using an idealized test case that involves a warm precipitating thermal developing over an undulated terrain. Also the efficiency of the basic code structures/subroutines is tested separately. It includes advection, elliptic pressure solver, preconditioner, Laplace equation solver and moist thermodynamics. In addition, the effects of horizontal domain decomposition and of the choice of machine precision on the computational efficiency are analyzed.

High-resolution simulation of turbulent collision of cloud droplets

A novel parallel implementation of hybrid DNS (Direct Numerical Simulation) code for simulating collision-coalescence of aerodynamically interacting particles in a turbulent flow has been developed. An important application of this code is to quantify turbulent collision-coalescence rate of cloud droplets, relevant to warm rain formation, under physically realistic conditions. The code enables performing high-resolution DNS of turbulent collisions so the simulation results can be used to begin addressing the question of Reynolds number dependence of pair and collision statistics. The new implementation is based on MPI (Message Passing Interface) library, and thus the code can run on computers with distributed memory. This development enables to conduct hybrid DNS with flow field solved at grid resolutions up to 5123 while simultaneously track up to several million aerodynamically-interacting droplets. In this paper we discuss key elements of the MPI implementation and present preliminary results from the high resolution simulations. The key conclusion is that, for small cloud droplets, the results on pair statistics and collision kernel appear to reach their saturation values as the flow Reynolds number is increased.