Droplet Size Distribution Research Articles

Detailed analysis on primary and secondary break up characteristics of liquid fuel jet in crossflow using homogeneous mixture model and large eddy simulation

The detailed breakup characteristics of the liquid jet fuel, Jet-A, in crossflow to various ranges of momentum flux ratios and Weber numbers have been investigated using a high-fidelity compressible multi-phase numerical technique. Multi-phase large eddy simulation with adaptive mesh refinement and Eulerian to Lagrangian transformation are applied to the homogeneous mixture model. The liquid surface instabilities and their frequencies inside the injector orifice are observed and analyzed. Interactions between liquid jet and crossflow result in phenomena such as horse-shoe vortex formation, boundary separation, liquid trailing, and counter-rotating vortex pair. Liquid column breakup characteristics and wave structures are analyzed from both temporal and spatial viewpoints. The Sauter mean diameter distribution and cumulative distributions of droplets resulting from secondary breakup are presented, along with the droplet size distribution derived from the momentum flux ratio and Weber number. Several engineering models, including the instability frequencies, the breakup length, and the penetration depth, are proposed in terms of the momentum flux ratio and Weber number, providing valuable insights for injector and combustor design.

Cloud droplet size distributions governed by condensation, collision–coalescence, and sedimentation. Part 1: Monte Carlo simulations and scaling relations for growth in a convection–cloud chamber

Abstract Atmospheric clouds are crucial to weather and climate, and the rate at which droplets collide and coalesce to form precipitation is one of the fundamental controlling processes. A convection-cloud chamber allows the interactions between aerosols and cloud droplets produced by condensation to be investigated within a turbulent environment. Studying the full range of microphysical conditions in atmospheric clouds is not possible, however, unless conditions for droplet growth by collision and coalescence are also achieved. In this study, we explore the conditions favorable to collision-coalescence growth in convection-cloud chambers, extending previous work on steady-state droplet size distributions due to condensation only to obtain analytic expressions for number concentration and supersaturation as a function of small-droplet injection rate, and for collision-coalescence rates. We derive several scaling laws and demonstrate consistency between these theoretical results and Monte-Carlo simulations of growth and precipitation within a convection-cloud chamber. Specifically, the coalescence rate is shown to scale as the square of the liquid water content, which in turn can be modulated in a convection-cloud chamber by varying the small-droplet injection rate as well as the applied temperature difference.

Cloud droplet size distributions governed by condensation, collision–coalescence, and sedimentation. Part 2: Analytical expressions for size distribution shape and asymptotic behavior for large-droplet tails

Abstract Droplet growth via condensation and collision-coalescence has been investigated in the limit of very weak coalescence growth: a collector-mode approximation emerges for coalescence growth that consists solely of droplets in the tail collecting droplets near the main mode of the cloud droplet size distribution, and that does not deplete the mode. In this second part, the approximation is formalized, leading to a simplified form of the collision-coalescence term in the equation governing the evolution of the droplet size distribution. This form allows for analytical solutions for transient growth and for steady-state distributions representing a balance between condensation, collision-coalescence growth, and removal by sedimentation. The solutions lead to an expression for the drizzle growth time, formally, the finite time in which a droplet approaches infinite size. The drizzle growth time is related to a transition radius at which droplet growth switches from condensation-dominated to coalescence-dominated. The solutions also provide a dimensionless group that governs the steady-state distribution shape, which is referred to as the drizzle number. The solutions are checked by comparing to a Monte Carlo model developed in Part 1, and it is found that the analytical solution is excellent when the drizzle number is much greater than unity, which is the typical situation for the microphysical conditions achievable in a convection-cloud chamber. The steady-state size distribution has the form of a modified gamma distribution, with a transition to power-law tail at sufficiently large radius. The solutions are formally valid for a convection-cloud chamber, but can also be extended to shallow, mixed-layer clouds such as mixing fogs.

Hail netting changes to spray droplets and patterns in grape canopies

While hail netting in vineyards provides effective protection to wine grapes (Vitis vinifera L.) from hail, pests, and bird damage, it may also affect the spray efficacy. This study tested the interaction between hail netting and location within the canopy in determining spray droplet characteristics. Two grape cultivars (Petite Sirah FPS 04 and Touriga Nacional FPS 05) grafted onto 1103P rootstock were examined to assess spray coverage, droplet size distribution, and deposition within grapevine canopies under netted and unnetted conditions. Spray droplets were measured using spray cards placed at five locations within the canopy. Significant interactions were observed primarily at the base of the canopy directly above the cordon, where grape clusters are most concentrated. Unnetted Touriga Nacional exhibited higher spray coverage compared to Petite Sirah, attributed to its looser cluster structure. Hail netting standardized all parameters across both cultivars, mitigating the influence of canopy and cluster differences. Hail netting created smaller, uniformly distributed droplets within the canopy, an essential characteristic of effective pest and disease control. Conversely, without netting, larger droplets were unevenly distributed, predominantly settling on the outer and lower canopy sections. Hail netting also maintained deposit densities within recommended ranges, supporting effective pest and disease management without compromising spray coverage. The consistent spray coverage achieved with hail netting across all canopy locations highlights its role in improving application uniformity and grapevine health, leading to evenly ripened, high-quality fruit. Contrary to the perceived risk of reducing spray efficacy, hail netting appears to enhance vineyard spraying outcomes, potentially offsetting netting costs.

Predicting Leidenfrost Temperature and Effects of Impact Conditions on Droplet Size Distribution in Film-Boiling Regime

Abstract The interaction of a droplet with a solid wall is relevant in various engineering applications. The properties of the resulting secondary droplets are determined by the wall temperature, ambient pressure, impact momentum, and impact angle. This paper presents a comprehensive characterization of drop-wall interactions and the subsequent atomization as a function of the combined effects of such parameters. A drop-wall interaction model is derived for F-24 droplets using smoothed particle hydrodynamics (SPH). The model can predict different impact outcome regimes (deposition, rebound, contact-splash, and film-splash) for different ambient pressures, wall temperatures, and impact parameters. The model also addresses the effect of ambient pressure on the Leidenfrost behavior. Size distributions of secondary droplets are compared for vertical and nonvertical impacts of F-24 droplets on superheated surfaces in the film-boiling regime. The non-dimensional Sauter mean diameter (SMD) of the secondary droplets varies based on the position in the impact plane for all the nonvertical impacts but remains almost unchanged for vertical impacts. The leading arc for nonvertical impact consists of larger secondary droplets, and the size decreases toward the trailing arc. An empirical relation is proposed to represent this trend. This research sheds light on successive droplet impacts by studying the effects of impact frequency on SMD evolution. The results are compared to single droplet impact cases for different fuels and Weber numbers. The size of secondary droplets for successive impacts is observed to be nearly indistinguishable from that of single-droplet vertical impacts.

Prediction of MRI relaxometry in the presence of hepatic steatosis by Monte Carlo simulations.

To develop Monte Carlo simulations to predict the relationship of with liver fat content at 1.5T and 3.0T. For various fat fractions (FFs) from 1% to 25%, four types of virtual liver models were developed by incorporating the size and spatial distribution of fat droplets. Magnetic fields were then generated under different fat susceptibilities at 1.5T and 3.0T, and proton movement was simulated for phase accrual and MRI signal synthesis. The synthesized signal was fit to single-peak and multi-peak fat signal models for and proton density fat fraction (PDFF) predictions. In addition, the relationships between and PDFF predictions were compared with in vivo calibrations and Bland-Altman analysis was performed to quantitatively evaluate the effects of these components (type of virtual liver model, fat susceptibility, and fat signal model) on predictions. A virtual liver model with realistic morphology of fat droplets was demonstrated, and and PDFF values were predicted by Monte Carlo simulations at 1.5T and 3.0T. predictions were linearly correlated with PDFF, while the slope was unaffected by the type of virtual liver model and increased as fat susceptibility increased. Compared with in vivo calibrations, the multi-peak fat signal model showed superior performance to the single-peak fat signal model, which yielded an underestimation of liver fat. The -PDFF relationships by simulations with fat susceptibility of 0.6ppm and the multi-peak fat signal model were ( , ) at 1.5T and ( , ) at 3.0T. Monte Carlo simulations provide a new means for -PDFF prediction, which is primarily determined by fat susceptibility, fat signal model, and magnetic field strength. Accurate -PDFF calibration has the potential to correct the effect of fat on quantification, and may be helpful for accurate measurements in liver iron overload. In this study, a Monte Carlo simulation of hepatic steatosis was developed to predict the relationship between and PDFF. Furthermore, the effects of fat droplet morphology, fat susceptibility, fat signal model, and magnetic field strength were evaluated for the -PDFF calibration. Our results suggest that Monte Carlo simulations provide a new means for -PDFF prediction and this means can be easily generated for various regimes, such as simulations with higher fields and different echo times, as well as correction of magnetic susceptibility measurements for liver iron quantification.

Production of Monodisperse Large Drop Emulsions by Means of High Internal Phase Pickering Emulsions-Processing and Formulation.

High internal phase Pickering emulsions (HIPPE) have received significant research attention in the last two decades due to their potential for a wide range of applications. The appropriate processing of such high-viscosity emulsions, hundreds of times more viscous than that of the continuous phase, and the control of the final droplet size remain challenges to be tackled. Our research targeted this knowledge gap by examining the influence of the emulsion formulation and the processing conditions on the final droplet size. The dispersed phase fraction (100 cSt silicon oil) ranged between 75 and 80%. The emulsions were produced in a regular mixing tank equipped with a helical ribbon impeller rotating at a low speed (100-150 rpm). The effective viscosity of the continuous phase was obtained from the experimental torque measurements. The droplet size distributions were measured after emulsification and dilution in the continuous phases. It is shown that the capillary number obtained from the observed emulsification performance can help predict the final droplet size. Our approach provides a straightforward methodology to generate concentrated Pickering emulsions with controlled and predictable droplet size.

Sound of natural and artificial rain impact on ETFE membranes

Thin membranes are known to produce a drum-like effect when subjected to rainfall. Rain noise affects acoustic comfort and might disrupt communication, speech intelligibility and cognitive task performance. Therefore, assessment of the characteristics of noise produced by impact of rain on membranes in different architectural settings is important. Given inherent disparities between natural and artificial precipitation-primarily in terms of droplet size distribution and terminal velocities-underscores the importance of conducting evaluations using natural rain noise. The focus of this study is on the comparative assessment of the sound generated by natural rainfall versus the sound generated by the impact of individual droplet in a semi-anechoic room on single Ethylene tetrafluoroethylene (ETFE) membranes. The study assesses the extent of spectral variations of the rain sound produced in both approaches and the corresponding absolute value of noise intensity.

Effect of Spray Characteristic Parameters on Friction Coefficient of Ultra-High-Strength Steel against Cemented Carbide.

Ultra-high-strength steels have been considered an essential material for aviation components owing to their excellent mechanical properties and superior fatigue resistance. When machining these steels, severe tool wear frequently results in poor surface quality and low machining efficiency, which is intimately linked to the friction behavior at the tool-workpiece interface. To enhance the service life of tools, the adoption of efficient cooling methods is paramount. However, the understanding of friction behavior at the tool-workpiece interface under varying cooling conditions remains limited. In this work, both air atomization of cutting fluid (AACF) and ultrasonic atomization of cutting fluid (UACF) were employed, and their spray characteristic parameters, including droplet size distribution, droplet number density, and droplet velocity, were evaluated under different air pressures. Discontinuous sliding tests were conducted on the ultra-high-strength steel against cemented carbide and the effect of spray characteristic parameters on the adhesion friction coefficient was studied. The results reveal that ultrasonic atomization significantly improved the uniformity of droplet size distribution. An increase in air pressure resulted in an increase in both droplet number density and droplet velocity under both AACF and UACF conditions. Furthermore, the thickness of the liquid film was strongly dependent on the spray characteristic parameters. Additionally, UACF exhibited a reduction of 4.7% to 9.8% in adhesion friction coefficient compared to AACF. UACF provided the appropriate combination of spray characteristic parameters, causing an increased thickness of the liquid film, which subsequently exerted a positive impact on reducing the adhesion friction coefficient.

Multi-scale flow atomization characteristics of Jatropha biodiesel swirl liquid film breakup

The characteristics of the spray and droplets produced by liquid film breakup are crucial for understanding the atomization process in industrial furnace atomizers. This study employed high-speed camera technology to capture images of Jatropha biodiesel (JB) spray at various pressures and Ohnesorge numbers (Oh). Image processing methods were employed to analyze the evolution morphology and proper orthogonal decomposition (POD) of fuel swirl spray, revealing the instability, breakup length, spray cone angle, fractal characteristics of the liquid film breakup zone, and droplet distribution characteristics. The results indicated that the JB jet evolution progressed through stages: cylindrical jet, torsion liquid film, open swirl, complete swirl, and fully developed mode. The evolution and disintegration of the liquid film exhibited a complex structure with ligaments, perforations, and droplet separation. Flow disturbances induced the Klystron effect, characterizing microscopic droplet motion. As spray pressure increased, the growth rate of the disturbance wave increased, the breakup length decreased, the atomization cone angle enlarged, and the fractal dimension (FD) of the liquid film breakup zone increased. The droplet size distribution followed a log-normal distribution, with a substantial increase in the number of small droplets as injection pressure increased. This study provides valuable insights into the multi-scale flow atomization of biodiesel in industrial furnace, and is of great significance for the design, operation, and optimization of spraying systems in various industrial applications.

A new aerosol delivery approach for enhanced long-term respiratory care in resource-poor settings

Continuous aerosol therapy is safe, superior, and the mainstay in the therapy of patients with severe asthma, cystic fibrosis, chronic obstructive pulmonary disease (COPD), and coronavirus disease (COVID-19). However, continuous nebulization has been perceived as highly expensive and labor-intensive, which often requires specialized medical equipment. Moreover, it is difficult to maintain consistent aerosol output and particle size delivery over an extended period without operator intervention. This work proposes a simple and reliable continuous nebulization method using a conventional gas jet nebulizer and intravenous (IV) bottle/bag. The present work reports detailed experimental studies on a gas jet nebulizer with Particle image velocimetry (PIV), Particle/droplet Imaging Analysis (PDIA), and Mie scattering techniques to demonstrate the feasibility of the proposed technique. The preliminary investigation shows that the proposed method provides continuous liquid output delivery without external supervision. The liquid delivery rate and mass median diameter (MMD) of the nebulizer mainly depend on the gas flow rate and suction height. The MMD of the primary generated droplets is reported to vary between 100 and 230 μm for a ± 10 cm suction height and 500–1000 mlph nebulization gas flow rate. Most importantly, the nebulizer spray angle, stability, droplet size distribution, and the axial and radial velocities of the droplets are marginally affected by the suction height. Therefore, the proposed system is a versatile, safe, and cost-effective method of continuous nebulization therapy, especially in resource-poor countries or contagious disease outbreak situations.

Evaluation of Autoconversion Representation in E3SMv2 Using an Ensemble of Large‐Eddy Simulations of Low‐Level Warm Clouds

AbstractIn numerical atmospheric models that treat cloud and rain droplet populations as separate condensate categories, precipitation initiation in warm clouds is often represented by an autoconversion rate , which is the rate of formation of new rain droplets through the collisions of cloud droplets. Being a function of the cloud droplet size distribution (DSD), the local is commonly parameterized as a function of DSD moments: cloud droplet number and mass concentrations. When applied in a large‐scale model, the grid‐mean must also include a correction, or enhancement factor, to account for the horizontal variability of the cloud properties across the model grid. In this study, we evaluate the Au representation in the Energy Exascale Earth System Model version 2 (E3SMv2) climate model using large‐eddy simulations (LES), which explicitly resolve cloud droplet spectra, and therefore the local , as well as its spatial variability. The analysis of an ensemble of warm low‐level cloud cases shows that the E3SMv2 formulation represents the reasonably well compared to the horizontally averaged explicitly computed rate from LES. The agreement, however, comes from a combination of an underestimated E3SM‐tuned local rate and an overestimated subgrid cloud variability enhancement factor. The latter bias is traced to neglecting the horizontal variability of and its co‐variability with in parameterizing the grid‐mean .

Model for atomization droplet size and energy distribution ratio at the distal end of an electrostatic nozzle

Electrostatic atomization minimum quantity lubrication (EMQL) employs the synergistic effect of multiple physical fields to atomize minute quantities of lubricant. This innovative methodology is distinguished by its capacity to ameliorate the atomization attributes of the lubricant substantially, which subsequently augments the migratory and infiltration proficiency of the droplets within the complex and demanding milieu of the cutting zone. Compared with the traditional minimum quantity lubrication (MQL), the EMQL process is further complicated by the multiphysical field influences. The presence of multiple physical fields not only increases the complexity of the forces acting on the liquid film but also induces changes in the physical properties of the lubricant itself, thus making the analysis of atomization characteristics and energy distribution particularly challenging. To address this objective reality, the current study has conducted a meticulous measurement of the volume average diameter, size distribution span, and the percentage concentration of inhalable particles of the charged droplets at various intercept positions of the EMQL nozzle. A predictive model for the volume-averaged droplet size at the far end of the EMQL nozzle was established with the observed statistical value F of 825.2125, which indicates a high regression accuracy of the model. Furthermore, based on the changes in the potential energy of surface tension, the loss of kinetic energy of gas, and the electric field work at different nozzle orifice positions in the EMQL system, an energy distribution ratio model for EMQL was developed. The energy distribution ratio coefficients under operating conditions of 0.1 MPa air pressure and 0 to 40 kV voltage on the 20 mm cross-section ranged from 3.094‰ to 3.458‰, while all other operating conditions and cross-sections had energy distribution ratios below 2.06‰. This research is expected to act as a catalyst for the progression of EMQL by stimulating innovation in the sphere of precision manufacturing, providing theoretical foundations, and offering practical guidance for the further development of EMQL technology.

Estimation of energy available in rain droplets from meteorological rainfall data

Abstract Even though the amount of rainfall is well documented in the reports of the India Meteorological Department (IMD), the rainfall energy available in different parts of India is unknown to the best of our knowledge. This paper reports a theoretical framework to convert the meteorological rainfall data to rainfall energy. The amount of rainfall over the south-west Monsoon period of 2022 is first converted to an average rainfall rate. Using the information on rain droplet size distribution for a rainfall of a given rainfall rate, the total energy contained in the rainfall is derived. In this, both the kinetic and surface energies of rain droplets of different sizes are considered. Based on the developed theoretical framework, rainfall map of India is converted to rainfall energy map showing states/union territories with maximum and minimum rainfall energy. Furthermore, for selected states in India, the districts showing maximum and minimum rainfall energy are also highlighted. The framework developed in the present study would help attempts to develop efficient rain energy harvesting systems.

Experimental study of fuel distribution and combustion characteristics under subatmospheric pressure in an afterburner

The fuel distribution and ignition characteristics of an afterburner with typical components under subatmospheric inlet conditions are important references for improving the performance of the afterburner at high flight altitudes. In this work, lean ignition limits, outlet temperature distributions, fuel droplet size distributions and flame propagation processes in the afterburner were obtained experimentally. The results show that with increasing fuel injection angle, the fuel atomization characteristics improve, but the flame intensity fluctuation increases, and the ignition performance deteriorates; thus, a proper ratio of liquid-phase fuel to vapor-phase fuel is one of the key elements for successful ignition. On the one hand, the increased stabilizer blockage ratio results in a localized flow velocity increase near the trailing edge of the stabilizer, which effectively promotes fuel atomization in the shear layer, resulting in a fuel droplet size reduction of 25–30 μm. On the other hand, the extent of the recirculation zone increases, and a large low-pressure and low-turbulence recirculation zone is not conducive to fuel atomization in the flow direction. During the ignition process in an afterburner with all the typical components, the flame kernel first propagates along the flow direction for a certain distance and then propagates and anchors toward the shear layer. At subatmospheric pressures, the decrease in the intensity of the combustion reaction causes a reduction in the heat released by combustion, and the fuel droplet size increases by 10–25 μm, which requires more heat for evaporation. Therefore, the flame propagates an increased distance along the flow as the pressure decreases. Furthermore, the difficulty of ignition increases, and the ignition equivalence ratio increases by 0.1–0.15.

Computationally cost-efficient analysis of the flow behavior of twin-fluid atomizers using computational fluid dynamics

In industrial-scale operations, wet electrostatic precipitators (WESPs) are used to minimize particulate matter, employing atomizers such as single-fluid and twin-fluid atomizers (TFAs). While TFAs provide several benefits over single-fluid atomizers, quantifying their spray characteristics is more complex, necessitating comprehensive case studies to design the internal structure of the spray and achieve desired properties. This study employed computational fluid dynamics (CFD) to simulate the internal and external flow phenomena of TFAs in industrial-scale WESPs, aiming to facilitate various parametric studies by reducing the high computational costs associated with analyzing high-speed internal flows and particle dynamics within the spray system. To decrease computational costs, the simulation was divided into two parts using stepwise segregated scenarios: Part I focused on the high-cost internal flow analysis, examining the spatiotemporal evolution of internal flow until it is fully developed, followed by droplet size distribution estimation at the nozzle. Part II computed the external flow of the spray, assessed potential cost reductions by examining the interactions between dispersed droplets, and validated the spray angle, penetration, and coverage against experimental data. The segregated strategy employed mapping techniques to integrate the two parts seamlessly. The simulation results closely matched the experimental benchmarks for spray angle, penetration, and coverage within a minimal error margin (<5%), demonstrating the model’s accuracy in capturing actual spray phenomena in TFAs. This approach significantly reduced the computational cost by more than twentyfold compared to conventional one-step solvers, offering a viable method for conducting various case studies in spray CFD simulations.

Stabilization of microbial strains in long-lasting double emulsions as a new strategy for liquid biofertilizer formulation

The need for innovative biofertilizers has been increasing in recent years as a consequence of the loss of soil microbial biodiversity. In this context, symbiotic agriculture, which involves the application of beneficial microorganisms to the soil, is an emerging and promising reality. A key point is related to the choice of an adequate formulation strategy for the microbial systems to maintain their vitality and shelf-life. The use of a liquid formulation is an alternative to the traditional dry powder formulation, but currently a successful stabilization in a liquid biofertilizer is still not available. Therefore, the aim of this study is to stabilize different microorganisms by using a double emulsion to obtain a liquid product. The emulsion formulation and production conditions were optimized for strain encapsulation and emulsions were characterized by analysing droplet size distribution, concentration and vitality of microorganisms after the production process and stability of the product over time. A final product obtained by the mixture of the different emulsions was then obtained with the objective of delivering of a complete pool of beneficial microorganisms. The mixture was stable for 5 months at room temperature and microorganism concentration was maintained constant indicating that no antagonistic activity within the microbial consortium was present.

Edible jammed deep eutectic solvent-in-oil emulsions for 3D food printing

Concentrated emulsions, when their volume fractions exceed a critical value, tend to adopt a jammed structure and exhibit solid-like behavior. In this work, we develop a novel, edible high internal phase emulsion that incorporates an edible deep eutectic solvent (DES) as the dispersed phase, along with sunflower oil and Span 80 as the continuous phase, to formulate DES-in-oil emulsions. The rheological properties of the resulting DES-in-oil emulsions are thoroughly examined, focusing on the yield stress and storage modulus, which are indicative of solid-like characteristics. Additionally, the emulsion’s microstructure is analyzed using optical microscopy to determine the size distribution of the DES droplets. Our study further explores the impact of agitation time on the emulsion’s formation, revealing that prolonged agitation strengthens the emulsion’s mechanical properties by reducing droplet sizes. This innovative emulsion showcases potential applications in 3D food printing, where it can be used to directly form predefined solid structures. Such printed food can assume various shapes without requiring post-processing, maintaining shape integrity and self-sustainability for up to four months.

Investigation on the effect of vertical baffle plate on droplet size distribution and mixing efficiency in Taylor Reactor

The Taylor reactor is a dynamic mixer based on the principles of Taylor vortex flow. However, traditional Taylor reactors feature smooth inner and outer cylinder surfaces, presenting challenges in achieving uniform mixing and efficient mass transfer. These limitations do not meet the requirements of modern chemical processes for highly efficient mixing equipment. This article introduces a novel Taylor reactor equipped with vertical baffle plates, designed to overcome these challenges. A comprehensive methodology combining CFD-PBM and experimental techniques was employed to investigate both droplet size distribution and mixing performance in the annular gap. Compared to traditional designs, the new device demonstrates significantly lower COV at 0.018 and Sauter mean diameter at 38.3 μm. Optimal mixing efficiency is achieved at rotating Reynolds number (Re) of 1.17 × 105 and inlet Reynolds number (Rei) of 2.65 × 103. Numerical simulation results suggest that vertical baffles effectively enhance liquid-liquid interactions including collision, interface contact, and droplet residence time within the annular gap. Moreover, increased turbulent stress in the flow field contributes to greater vorticity, turbulence intensity, and turbulent kinetic energy resulting in smaller droplet sizes and improved mixing efficiency. These findings provide a theoretical foundation for hydraulic structural optimization design as well as widespread application of Taylor reactors.

Two approaches for constructing multivariate injection models for prefilming airblast atomizers

More realistic droplet starting conditions for Euler–Lagrangian simulations enable e.g. more precise soot prediction in jet engines. Up to now, mainly the droplet size distribution of sprays is considered, but not the multivariate dependence structure of droplet size, starting position and initial velocity. A novel concept for extracting multivariate spray data efficiently from detailed simulations of the atomizing process into high fidelity Euler–Lagrangian simulations of spray combustion is presented in this paper. Therefore, simulations of a prefilming airblast atomizer using the Smoothed Particle Hydrodynamics method are considered. The multivariate dependence structure in the spray is identified using rank transformation. Two models of different nature are proposed which are able to reproduce the multivariate dependence structure. The first model follows a data-driven approach using vine copulas and marginal distributions. In contrast, the second model is based on human knowledge and assumptions enabling deeper insights into the atomization process. Both models demonstrated to reproduce the multivariate character of the spray data effectively. An assessment of their capabilities reveals that the first model might be more suitable for spray data of annular injectors.