Relative Velocity Distribution Research Articles

Experimental study of flow field and transition characteristics in rod bundle channel

Utilizing the particle image velocimetry (PIV) technique, this study investigates the fully developed flow field and turbulence statistics in a 5×5 rod bundle across 22 cases, with Reynolds numbers ranging from 310 to 12296.Time-averaged, statistical, and spectral analyses were performed on the full field and instantaneous velocity vectors obtained through PIV measurements to examine the velocity distribution, turbulence characteristics, and spectral features in different subchannels under various Reynolds numbers. In conjunction with a differential pressure transmitter, the flow properties and fluid transitions were also explored.The experimental results reveal that the relative velocity gradient in the rod bundle channel is more significant at lower Reynolds numbers. As the Reynolds number increases, the relative velocity distribution becomes more uniform. A comparison of experimental results from different planes indicates that the fluctuation velocity in the gap subchannel is greater than that in the inner subchannel, suggesting that tightly arranged rods can generate higher turbulence intensity. Furthermore, the transition observed through the friction factor in the rod bundle channel is less distinct than those in pipes, with the transition Reynolds number being approximately 900. A low Reynolds number effect is present in the rod bundle channel, where the dimensionless fluctuation velocity decreases as the Reynolds number increases. Upon reaching the transition Reynolds number, the area-averaged dimensionless fluctuation velocity abruptly rises. By examining the turbulence intensity variations at different positions within the rod bundle, it becomes evident that the transition Reynolds numbers vary across different subchannel positions. Ultimately, the experimental data can be employed to validate the applicability of turbulence models for different Reynolds numbers.

Numerical and Experimental Investigation of Flow Characteristics in a Fluid Self-Lubricating Centrifugal Pump with R134a Refrigerant

With the rapid development of information technology, researchers have paid attention to the pump-driven two-phase cooling loop technology for data centers, which imposes requirements on the efficiency and size of the pump. A fluid self-lubricating centrifugal pump with R134a refrigerant was developed to reach a higher rotation speed and oil-free system, resulting in a more diminutive size. Due to the high rotation speed and refrigerant pressure approaching saturated vapor pressure, the internal flow characteristics and cavitating characteristics are critical and complex. This paper focuses on the prototype’s head and cavitation performance based on experimental and numerical data. The experiments indicated that the head coefficient of the pump under design conditions is 0.9881, and the pump’s critical cavitation number and breakdown number are 0.551 and 0.412, respectively. The numerical results can predict the head and cavitation with deviations less than 2.6%. To study changing patterns in flow characteristics under the different operating conditions in the refrigerant centrifugal pump, the numerical model based on a modified Sauer-Schnerr cavitation model was built to analyze the distributions of pressure, temperature, relative velocity, and bubble volume across every hydraulic component and different degrees of cavitation, and proposed the influence of the thermal effect on refrigerant cavitating. The cavitating flow characteristics were obtained with the aim of providing guidance for the hydraulic design of a refrigerant centrifugal pump.

Surface generating mechanism in surface shape error control for thin copper plate with large-diameter based on chemical mechanical lapping

As metal plane flyer, pure copper thin plate is required with extremely low surface shape error. To achieve this goal, some researchers make a significant attempt to develop a deterministic full-aperture polishing/lapping process. However, the detail relationship of surface shape error and vital machining parameter such as machining time which benefits machining efficiency promotion is not given. Besides, the error rate of surface shape error prediction is high. To solve this problem, the surface shape prediction model considering the influence of pressure and relative velocity distribution on material removal amount is established for thin copper plate. Through the product of pressure distribution, relative velocity distribution, Preston coefficient k and machining time T, material removal distribution is obtained. According to initial surface shape characteristic, through targeted adjustment of eccentricity, lapping pad rotation speed, workpiece rotation speed to control pressure and relative velocity distribution, suitable material removal distribution is formed to smooth surface radial profile, realizing deterministic control of surface shape error. By above method, the flatness of pure copper thin plate (Φ200 mm × 2.2 mm) decreases from PV 54.8 μm to PV 1.9 μm with mean error rate of surface shape error prediction <10 %, realizing deterministic control of surface shape error.

Angiographic velocimetry analysis using contrast dilution gradient method with a 1000 frames per second photon-counting detector.

Contrast dilution gradient (CDG) analysis is a quantitative method allowing blood velocity estimation using angiographic acquisitions. Currently, CDG is restricted to peripheral vasculature due to the suboptimal temporal resolution of current imaging systems. We investigate extension of CDG methods to the flow conditions of proximal vasculature using 1000 frames per second (fps) high-speed angiographic (HSA) imaging. We performed in-vitro HSA acquisitions using the XC-Actaeon detector and 3D-printed patient-specific phantoms. The CDG approach was used for blood velocity estimation expressed as the ratio of temporal and spatial contrast gradients. The gradients were extracted from 2D contrast intensity maps synthesized by plotting intensity profiles along the arterial centerline at each frame. In-vitro results obtained at various frame rates via temporal binning of 1000 fps data were retrospectively compared to computational fluid dynamics (CFD) velocimetry. Full-vessel velocity distributions were estimated at 1000 fps via parallel line expansion of the arterial centerline analysis. Using HSA, the CDG method displayed agreement with CFD at or above 250 fps [mean-absolute error (MAE): , ]. Relative velocity distributions correlated well with CFD at 1000fps with universal underapproximation due to effects of pulsatile contrast injection (MAE: 4.3cm/s). Using 1000fps HSA, CDG-based extraction of velocities across large arteries is possible. The method is sensitive to noise; however, image processing techniques and a contrast injection, which adequately fills the vessel assist algorithm accuracy. The CDG method provides high resolution quantitative information for rapidly transient flow patterns observed in arterial circulation.

Wide-binary Stars Formed in the Turbulent Interstellar Medium

The ubiquitous interstellar turbulence regulates star formation and the scaling relations between the initial velocity differences and the initial separations of stars. We propose that the formation of wide binaries with initial separations r in the range ∼103 au ≲ r ≲ 105 au is a natural consequence of star formation in the turbulent interstellar medium. With the decrease of r, the mean turbulent relative velocity v tur between a pair of stars decreases, while the largest velocity v bon at which they still may be gravitationally bound increases. When v tur < v bon, a wide binary can form. In this formation scenario, we derive the eccentricity distribution p(e) of wide binaries for an arbitrary relative velocity distribution. By adopting a turbulent velocity distribution, we find that wide binaries at a given initial separation generally exhibit a superthermal p(e), irrespective of the exact turbulent velocity scaling. This provides a natural explanation for the observed superthermal p(e) of the wide binaries in the solar neighborhood.

Resonance Scattering Treatment with the Windowed Multipole Formalism

A new method for directly sampling the resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches, which require pointwise energy data, are particularly well suited to the windowed multipole cross-section representation. The new method, called multipole analytic resonance scattering, overcomes these limitations by inverse transform sampling from the target relative velocity distribution where the cross section is expressed in the multipole formalism. The closed-form relative speed distribution contains a novel special function we deem the incomplete Faddeeva function, and we present the first results on its efficient numerical evaluation.

Power Production and Blade Fatigue of a Wind Turbine Array Subjected to Active Yaw Control

This study investigated the power production and blade fatigue of a three-turbine array subjected to active yaw control (AYC) in full-wake and partial-wake configurations. A framework of a two-way coupled large eddy simulation (LES) and an aeroelastic blade simulation was applied to simulate the atmospheric boundary layer (ABL) flow through the turbines and the structural responses of the blades. The mean power outputs and blade fatigue loads were extracted from the simulation results. By exploring the feasible AYC decision space, we found that in the full-wake configuration, the local power-optimal AYC strategy with positive yaw angles endures less flapwise blade fatigue and more edgewise blade fatigue than the global power-optimal strategy. In the partial-wake configuration, applying positive AYC in certain inflow wind directions achieves higher optimal power gains than that in the full-wake scenario and reduces blade fatigue from the non-yawed benchmark. Using the blade element momentum (BEM) theory, we reveal that the aforementioned differences in flapwise blade fatigue are due to the differences in the azimuthal distributions of the local relative velocity on blade sections, resulting from the vertical wind shear and blade rotation. Furthermore, the difference in the blade force between the positively and negatively yawed front-row turbine induces different wake velocities and turbulence distributions, causing different fatigue loads on the downwind turbine exposed to the wake.

Improving Thermal Conductivity and Tribological Performance of Polyimide by Filling Cu, CNT, and Graphene

The thermal conductivity, mechanical, and tribological properties of polyimide (PI) composites filled by copper (Cu), carbon nanotube (CNT), graphene nanosheet (GNS), or combination were investigated by molecular dynamics simulation (MD). The simulated results suggested that Cu can improve thermal stability and thermal conductivity, but it reduces mechanical properties and tribological properties. CNT and GNS significantly improved the thermal and tribological properties at low content, but they decreased the properties at high content. In this study, the modification mechanism, friction, and wear mechanism of different fillers on polyimide were revealed by observing the frictional interface evolution process from the atomic scale, extracting the atomic relative concentration, the temperature and velocity distribution at the friction interface, and other microscopic information.

Velocity-dependent J-factors for Milky Way dwarf spheroidal analogues in cosmological simulations

We study the impact of the dark matter velocity distribution modelling on signals from velocity-dependent dark matter annihilation in Milky Way dwarf spheroidal galaxies. Using the high resolution APOSTLE simulations, we identify analogues corresponding to Milky Way dwarf spheroidal galaxies, and from these directly determine the dark matter pair-wise relative velocity distribution, and compare to best-fitting Maxwell-Boltzmann distribution models. For three velocity-dependent annihilation models, p-wave, d-wave, and the Sommerfeld model, we quantify the errors introduced when using the Maxwell-Boltzmann parameterization. We extract a simple power-law relation between the maximum circular velocity of the dwarf spheroidal analogue and the peak speed of the Maxwell-Boltzmann distribution. We show that this relation can be used to accurately calculate the dark matter relative velocity distribution, and find that it allows us to estimate the dark matter annihilation signal without the need to directly calculate the relative velocity distribution for each galaxy. The scatter in the J-factors calculated from the analogues dominates the uncertainty obtained when compared to the J-factor as determined from the observational data for each dwarf spheroidal, with the largest scatter from d-wave models and the smallest from Sommerfeld models.

Effect of Packing Structure Evolution on the Flow Characteristics in a Binary Composite Packed Bed Based on DEM-CFD Method

The evolution of mesoscale structures of particle packing in binary composite packed beds and their effects on flow characteristics and wall effects were investigated using the discrete element method (DEM) and computational fluid dynamics (CFD). The DEM model was used to build a series of randomly mixed packing structures of particles in accordance with the dynamic change of mass ratio between particles in two size ranges, which were then confirmed by the findings of an X-ray tomography (CT) scan. The results show that the packing structure of b25s75 was conducive to reducing the influence of wall effect in packed bed reactors. For b25s75, the dimensionless distance of radial porosity fluctuation from the wall is 0.3705, which is the smallest among the five packing models, indicating that this structure plays a suppressive role on the wall effect. In addition, the uniformity of velocity and temperature distributions in both the radial and axial directions of different packing structures were compared. The standard deviations of radial relative velocity distributions in the packed beds of b100, b75s25, b25s75 and s100 are 0.28, 0.178, 0.139 and 0.156, respectively, indicating that the stacking mode of b25s75 can make the fluid flow and the gas–solid interactions more uniform.

Biradial turbine rotor aerodynamic design and parametric analysis

The paper presents a study on the aerodynamic design of self-rectifying biradial turbine rotors for applications in wave energy conversion. The aim is to improve the biradial turbine efficiency and understand the specific speed range for which the turbine operation is most efficient. A rotor geometry generation method is presented, adding more degrees of freedom to the original method by improving the rotor meridional profile definition and relative flow velocity distribution. The new meridional channel definition allows tuning the rotor specific speed in the design phase. The prescribed relative flow velocity distribution improves the rotor inlet-to-outlet pressure gradient distribution. The research comprises geometry parametrisation, and three-dimensional flow simulations with a Reynolds-averaged Navier–Stokes equations solver to understand the effect of the design parameters on the rotor performance. The increase in total-to-total efficiency of the new rotor design is near 1%, demonstrating the good aerodynamic performance of the original design. It is shown that the turbine’s specific speed can increase by 5.4%, and the specific diameter can decrease by 6.0% compared to the original design without reducing turbine efficiency.

Multi-modal framework to model wet milling through numerical simulations and artificial intelligence (part 1)

Stirred media mills are used in many industries from mechanochemistry, to ore crushing, battery production and pharmaceutics. Investigation and modelling can be a costly, difficult and time consuming endeavour, limiting the investigable parameter space with some aspects only being accessible via numerical methods such as simulations or artificial intelligence (AI). Simulations allow investigations of inner mechanisms and generate large quantities of data while being computationally demanding. AI requires large data quantities yet is applicable with limited computing power for large parameter spaces. For this reason, the intelligent integration of different methods holds great promise to achieve maximum benefits at minimum cost by synergistically combining respective advantages. Here, a multi-modal framework is demonstrated, combining experiments, simulations and AI. In this first paper direct magnetic measurements via a tracer particle are compared with simulations of wet mills. With two way coupled CFD-DEM simulations inner mechanisms like the impact of disc geometry, tip speed and grinding bead size are investigated. Differences in translational and relative velocity distributions are investigated, showing a consistent displacement of a factor three toward higher energies throughout the complete distribution for the hole disc in comparison to the full disc, and less consistent deviations for translational velocity, specifically for the higher energy collisions, being larger by a factor of 8. Also comparisons with the existing mechanistic model of Kwade are performed. An additional indirect influence of diameter on tip speed could be detected. In a second publication AI modelling will be performed on the basis of the simulations.

Dust dynamics in ramses – I. Methods and turbulent acceleration

ABSTRACT Supernova ejecta and stellar winds are believed to produce interstellar dust grains with relatively large sizes. Smaller grains can be produced via the shattering of large grains that have been stochastically accelerated. To understand this stochastic acceleration, we have implemented novel magnetohydrodynamic (MHD) particle-in-cell methods into the astrophysical fluid code ramses. We treat dust grains as a set of massive ‘superparticles’ that experience aerodynamic drag and Lorentz force. We subject our code to a range of numerical tests designed to validate our method in different physical conditions, as well as to illustrate possible mechanisms by which grains can be accelerated. As a final test as well as a foundation for future work, we present the results of decaying dusty MHD turbulence simulations with grain parameters chosen to resemble 1–2 μm grains in typical cold neutral medium conditions. We find that in these conditions, these grains can be effectively accelerated to well beyond their shattering velocities. This is true for both electrically charged and neutral grains. While the peak of the gas-grain relative drift velocity distribution is higher for neutral grains, the drift velocity distribution of charged grains exhibits an extended exponential tail out to much greater velocities. Even so, the shapes of the distributions are such that the extra gas-grain coupling provided by the Lorentz force offers grains relative protection from shattering. We also discuss the connection between our simulations and the relatively pristine ∼μm-sized pre-solar grains that do not appear to have undergone significant wear in their lifetimes.

Multi-modal framework to model wet milling through numerical simulations and artificial intelligence (part 2)

Modelling of stirred media mills is crucial because of their broad utilisation in various industries, ranging from mechanochemistry and mining to the production of batteries and pharmaceuticals. Stirred media mills are responsible for a considerable portion of the global energy demand. However, requirements exist regarding highly specific or uniform particle sizes, process conditions, and reduced wear or abrasion. Multi-modal modelling, which is the intelligent integration of different approaches, such as experiments, simulations, and AI, benefits from respective advantages of each approach. In the first study, results of an experiment conducted via magnetic tracking of a tracer bead was compared with those of simulations, and the inner mill mechanisms were investigated. The two-way coupled computer fluid dynamics discrete element method (CFD-DEM) simulations allowed the investigation of subsequent modelling through AI methods [1]. A novel AI training technique called “genetic reinforcement learning” (hereinafter, GRL), which combines neural nets with genetic algorithms, was demonstrated for cases with limited data. Furthermore, genetic programming was applied to derive transparent mathematical equations based on the generated data. Using these methods and experimentally validated simulation data, predictive models were trained, and mathematical equations were derived. Relative velocity distributions in the entire simulation domain as well as spatial distributions via heatmaps were predicted and evaluated for independent cases. Systematic predictions for the characteristic relative velocity values were generated instantaneously for varying tip speeds and bead diameters in a parameter space, which would have required 1–10 years through simulations. Finally, a transparent equation was generated via genetic programming.

2D vessel contrast dilution gradient (CDG) analysis using 1000 fps high speed angiography (HSA) for velocity distribution estimation.

Contrast dilution gradient (CDG) analysis is a technique used to extract velocimetric 2D information from digitally subtracted angiographic (DSA) acquisitions. This information may then be used by clinicians to quantitatively assess the effects of endovascular treatment on flow conditions surrounding pathologies of interest. The method assumes negligible diffusion conditions, making 1000 fps high speed angiography (HSA), in which diffusion between 1 ms frames may be neglected, a strong candidate for velocimetric analysis using CDG. Previous studies have demonstrated the success of CDG analysis in obtaining velocimetric one-dimensional data at the arterial centerline of simple vasculature. This study seeks to resolve velocity distributions across the entire vessel using 2D-CDG analysis with HSA acquisitions. HSA acquisitions for this study were obtained in vitro with a benchtop flow loop at 1000 fps using the XC-Actaeon (Direct Conversion Inc.) photon counting detector. 2D-CDG analyses were compared with computational fluid dynamics (CFD) via automatic co-registration of the results from each velocimetry method. This comparison was performed using mean absolute error between pixel values in each method (after temporal averaging). CDG velocity magnitudes were slightly under approximated relative to CFD results (mean velocity: 27 cm/s, mean absolute error: 4.3 cm/s) as a result of incomplete contrast filling. Relative 2D spatial velocity distributions in CDG analysis agreed well with CFD distributions qualitatively. CDG may be used to obtain velocity distributions in and surrounding vascular pathologies provided diffusion is negligible relative to convection in the flow, given a continuous gradient of contrast.

Experimental study on fiber suspension in a centrifugal pump by PIV

Abstract To study the influence of fiber particles on the flow field within the passages of an open impeller centrifugal pump, an experiment was performed. The hair fiber was used as solid particle phase in this experiment. After measuring the performance characteristic and PIV data, the flow field in impeller was measured and analyzed. It was shown that at the concentration of 0.1%, a varied distribution of relative velocity from different flow channels was observed. The outlet velocity of the impeller in the second flow channel was obviously higher than that in the first flow channel. The variation of the relative velocity near the hub tended to be consistent at the position of the front plane and the middle plane of the impeller. At 0.2% concentration, the relative velocity at the suction surface of the two channels changes more sharply than the other positions. Within the second channel, it was found that the relative velocity under low flow condition was obviously higher than that under rated and large flow rates. Under different concentrations, the increase of the relative velocity at low flow rate changed intensely compared with the other two conditions. The low velocity zone will be formed near the middle part of the suction surface of the flow channel which gradually decreases with the increase of the flow rate. The external characteristic test shows that the efficiency of the pump and the drag reducing feature increase with the increase of concentration.

Lattice Boltzmann simulation of flow and sound fields around an axial flow fan

Abstract In this study, not only the flow field but the aerodynamic sound field around the axial flow fan were directly simulated using the lattice Boltzmann method (LBM). To validate the LBM results obtained in this study, they were compared with the experimental results in terms of the pressure rise performance characteristics. In order to investigate the change in the flow and sound fields due to different operating points, calculations were conducted at two operating points; one is the low flow rate point where the fan is stalled and the other is the high flow rate point where the flow field in the fan is sound. In the comparison of the performance characteristics, the calculation results showed good agreement with the experimental results, and the flow fields were well reproduced with high accuracy. The analysis in terms of the vortical flow structures and the relative velocity distributions showed that the tip vortex was generated by the pressure difference between both sides of the fan blade at the high flow rate point while at the low flow rate point the flow field near the fan tip was covered with the low velocity region and the leading edge separation occurred on the tip side of the fan blade. Therefore, it was confirmed from the flow field as well as the performance that the fan blade was stalled with the blade loading lost at the low flow rate point. Large pressure fluctuations on the fan blade surface were caused by the interaction with the tip vortex from the adjacent blade at the high flow rate point and the occurrence of leading edge separation at the low flow rate point. With regard to the comparison of the far field sound spectrum, the calculation results for both two flow rate points were in good agreement with the experimental results in a low frequency range, and the aerodynamic sounds generated from the fan were predicted well with the LBM simulation.

Electron-induced dissociation dynamics studied using covariance-map imaging.

Recently, covariance analysis has found significant use in the field of chemical reaction dynamics. When coupled with data from product time-of-flight mass spectrometry and/or multi-mass velocity-map imaging, it allows us to uncover correlations between two or more ions formed from the same parent molecule. While the approach has parallels with coincidence measurements, covariance analysis allows experiments to be performed at much higher count rates than traditional coincidence methods. We report results from electron-molecule crossed-beam experiments, in which covariance analysis is used to elucidate the dissociation dynamics of multiply-charged ions formed by electron ionisation over the energy range from 50 to 300 eV. The approach is able to isolate signal contributions from multiply charged ions even against a very large 'background' of signal arising from dissociation of singly-charged parent ions. Covariance between the product time-of-flight spectra identifies pairs of fragments arising from the same parent ions, while covariances between the velocity-map images ('recoil-frame covariances') reveal the relative velocity distributions of the ion pairs. We show that recoil-frame covariance analysis can be used to distinguish between multiple plausible dissociation mechanisms, including multi-step processes, and that the approach becomes particularly powerful when investigating the fragmentation dynamics of larger molecules with a higher number of possible fragmentation pathways.

Collision statistics and settling velocity of inertial particles in homogeneous turbulence from high-resolution DNS under two-way momentum coupling

Statistical quantities related to the motion of low inertia particles in homogeneous isotropic turbulence are investigated by means of direct numerical simulations applying the Eulerian–Lagrangian approach and the point-particle approximation. The modelled systems imitate, among others, the microphysical processes relevant for cloud droplets in typical atmospheric flows. To complement former studies, the turbulent flow is simulated using high-resolution grids, covering a wide range of Reynolds numbers, up to Rλ≈500. The effect of mutual interaction of the carrier and dispersed phases, known as two-way momentum coupling, is considered, and the new results are compared with those obtained under one-way coupling. The droplet kinematic statistics, including the radial relative velocity and radial distribution functions, and dynamic properties, such as the collision kernel and settling velocity, are reported over a wide range of mass loadings. The results show that the radial distribution function of “nearly touching” droplets decreases as the mass loading increases when gravity is not considered. In the presence of gravity there is an enhancement in clustering for dilute systems while a reduction occurs when the two-way coupling effect becomes considerable. An opposite trend is observed for relative velocities due to transfer of momentum from droplets to the fluid, decorrelating the motion of neighbouring droplets. By increasing Rλ, or equivalently enlarging the domain size at fixed energy dissipation rate, the clustering weakens if gravity is considered, while relative velocities augment, ultimately leading to a higher collision kernel. The average settling velocity increases with Rλ. It also increases with mass loading, especially for low-inertia droplets. When performing simulations of small particles at considerable mass loadings a parameterisation is unavoidable to reduce the numerical cost. We use the super-droplet approach and demonstrate its impact on physical fidelity of the modelled systems. The effect of the large-scale forcing scheme, deterministic or stochastic, on the droplet dynamic statistics is also investigated.

In situ cloud particle tracking experiment

The collision-coalescence process of inertial particles in turbulence is held responsible for the quick growth of cloud droplets from ∼15 to ∼50 µm in diameter, but it is not well understood. Turbulence has two effects on cloud droplets: (1) it brings them closer together, preferentially concentrating them in certain parts of the flow, and (2) it sporadically creates high accelerations, causing droplets to detach from the underlying flow. These turbulence-cloud droplet interactions are difficult to study numerically or in the laboratory due to the large range of scales involved in atmospheric turbulence, so in situ measurements are needed. Here, we present a Lagrangian particle tracking (LPT) experimental setup situated close to the summit of Mt. Zugspitze at an altitude of 2650m above the sea level on top of the environmental research station Schneefernerhaus. Clouds naturally occur at this location about a quarter of the time. The LPT experiment probes a volume of ∼40 × 20 × 12mm3, has a spatial resolution of 5 µm and a temporal resolution of 0.1ms, and measures accelerations to within 0.1ms-2. Furthermore, the experiment can slide over a set of rails, driven by a linear motor, to compensate for the mean wind. It can slide up to 7.5ms-1. By doing so, the average residence time of the particles in the measurement volume increases. The mean wind compensation allows us to study various dynamical quantities, such as the velocity autocorrelation, or the dynamics of clustering. Moreover, it is beneficial for particle tracking, in general, since longer particle tracks allow us to apply better filtering to the tracks and thus increase accuracy. We present the radial distribution function, which quantifies clustering, the longitudinal relative velocity distribution, and the Lagrangian velocity autocorrelation, all computed from cloud droplet trajectories.