Droplet Velocity Profiles Research Articles

Correction to: Predicting the number of printed cells during inkjet-based bioprinting process based on droplet velocity profile using machine learning approaches

Correction to: Predicting the number of printed cells during inkjet-based bioprinting process based on droplet velocity profile using machine learning approaches

Probabilistic derivation of droplet velocity using quadrature method of moments

Abstract Accurately prediction of dispersion and polydispersity of droplet flow is not a trivial task due to the complex behavior of the droplet size distribution (DSD) and the strong state of the instantaneous velocity of a droplet on the shape and size of the droplet. Describing the distribution of sizes and velocities of droplets initially formed in sprays is an essential piece of information needed in spray modeling, which is used to define the initial state of the spray droplets in the downstream two-phase flow fields’ predictive computations. The predictive model for the droplet size and velocity distributions in sprays is formulated as the droplet’s velocity magnitude has a power–law relationship with the droplet in this study. The present model incorporates the deterministic and stochastic aspects of the spray formation process. The quadrature method of moments (QMOM) is applied to solve numerically the transport equations of the probability density function coupled with conserved source terms incompressible Navier-Stokes equations for the liquid phase. The sub-models are connected by different source terms signifying the liquid-gas interaction. Equations of transport for spray moments are derived from DSD, and closure is attained using a gamma distribution. The integer spray moments concerning the volume are used to construct the continuous distribution of QMOM. In contrast, the velocity moments are used to determine the droplet velocity as a constant function of the droplet diameter. The model is first applied to simulate a diesel spray tip penetration under nonreactive conditions with different droplet velocity profiles to validate the approach with experimental data. An additional case of a liquid nitrogen spray is applied to show the gamma distribution’s ability to describe spray drop size distribution. The model generally predicts reasonable agreement with the experimental for both cases.

Lagrangian Simulation Methodology for Large-Eddy Simulations of Prefilming Air-Blast Injectors

A Lagrangian framework is proposed to address liquid film and atomization modeling in large-eddy simulations (LESs) of aeronautical air-blast injectors. The Lagrangian liquid film model of O’Rourke and Amsden (“A Spray/Wall Interaction Submodel for the KIVA-3 Wall Film Model,” SAE International TP 2000-01-0271, Warrendale, PA, 2000) is improved by introducing a subgrid contact angle to better predict the film height and the resulting film dynamics. Next, the phenomenological the primary atomization model for prefilming air-blast injectors (PAMELA) proposed by Chaussonnet et al. (“A New Phenomenological Model to Predict Drop Size Distribution in Large-Eddy Simulations of Airblast Atomizers,” International Journal of Multiphase Flow, Vol. 80, April 2016, pp. 29–42) for primary atomization at the prefilmer edge is enhanced to deal with complex geometries. This model is able to predict the droplet-size probability density function from the prefilmer height and flow conditions. The original formulation relied on correlations valid for flat plates to determine the gas boundary-layer thickness, and it required a gas velocity at film height to be set by the user. These two points make its use difficult for complex configurations where there is no simple correlation for the gas boundary-layer thickness and the gas velocity at film height cannot be a priori estimated. An embedded methodology, named the automatic PAMELA, is therefore proposed in this work to automatically determine these two quantities in the simulation. For each cell of the prefilmer edge where atomization occurs, the gas boundary-layer thickness is estimated by analyzing the local velocity profile thanks to Lagrangian probes; and the gas velocity is computed from the local film height by assuming a logarithmic velocity profile. Finally, the film and primary atomization models are coupled to a secondary atomization model, and they are assessed on an industrial air-blast aeronautical injector. The average droplet velocity profiles and Sauter mean diameters are compared against experimental phase Doppler particle analyzer measurements, and they demonstrate the ability of the proposed framework to perform Lagrangian LESs of liquid injection in complex geometries.

Predicting the number of printed cells during inkjet-based bioprinting process based on droplet velocity profile using machine learning approaches

Predicting the number of printed cells during inkjet-based bioprinting process based on droplet velocity profile using machine learning approaches

Spray Cooling Investigation of TiO2–Water Nanofluids on a Hot Surface

Spray cooling is a heat transfer technology that has already shown its advantages and limitations. There has been increasing interest from academia and industry in combining this technology with nanofluids as coolants, owing to their potential for heat transfer enhancement. Nevertheless, there is a lack of understanding of the physical mechanism leading to this enhancement with the presence of technical problems that prevent the use of nanofluids in spray cooling applications. In this study, we investigate the effect of water-based TiO2 nanofluids on both spray characteristics and heat transfer using an industrial full-cone pneumatic nozzle. For this purpose, three mass concentrations (0.05 wt.%, 0.1 wt.%, and 0.2 wt.%) were prepared and tested. We monitored the droplet sizes and velocity profiles with a particle dynamics analysis system. Moreover, the temporal temperature decrease of a heated aluminum block from 190 to 65 °C was measured via an infrared camera to calculate the heat transfer rate and heat transfer coefficient. The presence of nanoparticles is shown not to substantially alter the spray characteristics. Moreover, heat transfer is augmented mainly in the boiling regime due to more nucleation sites formed by the deposited nanoparticles. However, in the non-boiling regime, the contribution of adsorbed nanoparticles to the heat transfer enhancement diminishes. Overall, the aluminum block is cooled down 6%, 12%, and 25% faster than the DI water by the nanofluids at 0.05 wt.%, 0.1 wt.%, and 0.2 wt.%, respectively, including boiling and non-boiling regimes.

Simulations of turbulent acetone spray flames using the conditional source term estimation (CSE) approach

Turbulent dilute acetone spray flames are simulated in an Eulerian–Lagrangian framework using Conditional Source-term Estimation (CSE) for closure of the mean reaction rate. The objective of this work is to assess the performance of the coupled CSE-spray approach, investigated for the first time for the selected configuration. One non-reacting case and four non-premixed flames, AcF1–AcF3 and AcF5 are chosen. Detailed tabulated chemistry is included. Predictions of mean axial velocity, gas temperature and spray statistics are compared with available experimental data. Good agreement between the predicted gas temperatures and experimental values is found. The peak temperature tends to be overpredicted and shifted radially outwards in the simulations, in particular farther downstream. Same trends are observed in all flames, but the predictions deteriorate with flame AcF5. Possible sources of discrepancy are inaccurate turbulent mixing field, increased level of premixing for flame AcF5, the neglect of spray effect in the chemistry tabulation and a larger experimental uncertainty in the temperatures in the high-temperature regions. The mean droplet velocity profiles are in good agreement with the experiments for the four flames. However, the velocity was underpredicted, in particular near the centreline, for flames AcF1 and AcF2.

On the near wake structure of a supersonic coaxial gas-liquid jet

The work is devoted to a complex experimental study of the near wake of supersonic coaxial gas-liquid jets with a high concentration of the dispersed phase. At the various liquid flow rates, wave structure of a gas phase was visualized, droplet velocity profiles were obtained by the LDA method, and the spray concentration was measured. The effect of the liquid phase on the supersonic underexpanded jet was studied, in particular, a change in the general wave structure, Mach disk transformation, etc. A gas velocity profile was obtained in a two-phase core of a gas-liquid jet by the method of droplet velocity profile correction taking into account their velocity relaxation.

Dynamic Contact Angles and Mechanisms of Motion of Water Droplets Moving on Nanopillared Superhydrophobic Surfaces: A Molecular Dynamics Simulation Study.

In this work, we investigate the dynamic advancing and receding contact angles, and the mechanisms of motion of water droplets moving across nanopillared superhydrophobic surfaces using molecular-dynamics simulation. We obtain equilibrium Cassie states of droplets on nanopillared surfaces with different pillar heights, groove widths, and intrinsic contact angles. We quantitatively evaluate the dynamic advancing and receding contact angles along the advancing direction of an applied body force, and find that they depend on the roughness parameters and the applied body force in a predictable way. The maximum dynamic advancing contact angle is 180°, and the minimum dynamic advancing contact angle is close to the static contact angle. On the receding side, the maximum dynamic receding contact angle is as large as 180°, while the minimum dynamic receding contact angle is close to the intrinsic contact angle of smooth surface. Interestingly, water droplets exhibit a "rolling" mechanism as they move across the surface, which is confirmed by movies of interfacial water molecules, as well as droplet velocity profiles.

Measurements of local droplet velocities in horizontal gas-liquid pipe flow with low liquid loading

New data on streamwise droplet velocity profiles for low liquid loading pipe flows are reported. The fluids used in the experiments are SF6 (gas-phase) and Exxsol D60 (oil-phase). Experiments are conducted in a 10 cm pipe diameter high-pressure (∼780 kPa, absolute) flow loop to reproduce gas-condensate field conditions. Instantaneous streamwise velocity data, obtained using the non-intrusive Laser Doppler Anemometry (LDA) technique, are used to calculate mean and root-mean-squared (RMS) local velocities. Asymmetric droplet velocity profiles with respect to the pipe center-line are observed especially for the stratified low atomization flow conditions. However, as the flow momentum increases, the droplet velocity profiles seem to become more symmetric. Also, these data suggest that, irrespective of the conditions studied, the single-phase gas flow characteristics are preserved closer to the top pipe wall. The data from the LDA imply that the bottom pipe half region is highly influenced by the gas-liquid interfacial characteristics. This results in high streamwise turbulence intensity in the region influenced by the interfacial waves (interfacial turbulence). An isokinetic sampling instrument is also used to measure the local instantaneous dynamic pressure. The dynamic pressure and the locally extracted liquid (droplets) volume rate under isokinetic conditions are used to calculate local fluid velocity. Excellent agreement has been obtained when comparing this calculated local velocity from the isokinetic instrument to the LDA data.

Comparison of droplet evaporation models for a turbulent, non-swirling jet flame with a polydisperse droplet distribution

The current investigation aims to present the numerical results of a turbulent spray jet flame in the framework of Large Eddy Simulation. The injection of n-heptane liquid fuel is achieved through the use of a pressure-swirl atomiser generating a lifted spray flame. The evolution of the sub-grid probability density function of relevant scalars is accounted for by the Eulerian stochastic field method. A non-reactive spray computation is conducted in a preliminary stage. The simulation allows for a stochastic breakup formulation in combination with a stochastic dispersion model to confirm their predictive capabilities. This is achieved as the liquid properties such as droplet diameter and velocity profiles are found to be in excellent agreement between the simulated results and measurements. The main target of the work is to assess the performance of the most widely accepted evaporation models in a turbulent droplet-laden flame. In this paper, a detailed comparison of the evaporation models is conducted thanks to a recent development in measurement techniques which allow to permit the spray temperature profiles. The time-averaged droplet temperature across the spray flame is therefore investigated in order to validate several droplet vaporisation models. All the models under consideration are found to capture the formation of a double reaction zone flame and the measured lift-off height is reproduced within a satisfactory level of accuracy. This good reproduction of the flame morphology additionally confirms the performance of the pdf approach as a closure for the unknown turbulence–chemistry interaction in this type of spray flames. However, the simulated wet-bulb temperature in the hot burnt gas between the two reaction zones in addition to the profile along the spray centreline show a large discrepancy when compared to measurements. This large difference thus requires further investigation both in the modelling of evaporation and in the accuracy of measurement techniques.

Numerical simulation of the gas-liquid interaction of a liquid jet in supersonic crossflow

The gas-liquid interaction process of a liquid jet in supersonic crossflow with a Mach number of 1.94 was investigated numerically using the Eulerian-Lagrangian method. The KH (Kelvin-Helmholtz) breakup model was used to calculate the droplet stripping process, and the secondary breakup process was simulated by the competition of RT (Rayleigh-Taylor) breakup model and TAB (Taylor Analogy Breakup) model. A correction of drag coefficient was proposed by considering the compressible effects and the deformation of droplets. The location and velocity models of child droplets after breakup were improved according to droplet deformation. It was found that the calculated spray features, including spray penetration, droplet size distribution and droplet velocity profile agree reasonably well with the experiment. Numerical results revealed that the streamlines of air flow could intersect with the trajectory of droplets and are deflected towards the near-wall region after they enter into spray zone around the central plane. The analysis of gas-liquid relative velocity and droplet deformation suggested that the breakup of droplets mainly occurs around the front region of the spray where gathered a large number of droplets with different sizes. The liquid trailing phenomenon of jet spray which has been discovered by the previous experiment was successfully captured, and a reasonable explanation was given based on the analysis of gas-liquid interaction process.

Effect of Nozzle Orientation on Droplet Size and Droplet Velocity from Vineyard Sprays

Spray drift has become an important issue in pesticide application. Vineyard spraying is particularly interesting to consider, as pesticide droplets are not directed towards the ground but rather towards the targeted crop. The aim of this study was to investigate the influence of nozzle orientation on droplet size and droplet velocity using three different nozzles (IDK, TVI, and TXA) used in vineyards. Two series of measurement were performed in order to assess the effect of the gravity on sprays. Droplet size and one-dimensional droplet velocity characteristics were measured using a phase Doppler particle analyser (PDPA). Two planes, i.e., one horizontal and one vertical, were considered. Results suggest that the nozzle orientation slightly affects the size distribution, which is shifted towards larger droplets when nozzles spray horizontally compared to vertically spray. However, droplet axial velocity distribution is shifted towards lower values. Supposing that the only droplets which can reach the crop are those with an axial velocity greater than 1 m/s and a diameter larger than 100 μm, results showed significant differences according to the nozzle and orientation. More than 98.6% of the spray volume would reach the target whatever the orientation of the IDK nozzle, 78.8% of the spray volume would reach the crop when the TVI nozzle sprays horizontally, while only 16.0% of the spray volume would reach the crop when TXA nozzle sprays horizontally. This paper offers new perspectives in the comprehension and the optimization of the deposition process into the vegetation based from droplet size and velocity profiles from horizontally oriented sprays from flat fan or hollow cone nozzles.

Droplet Necking and Morphology Variations Induced by Changing the Gap Height During Transport in Digital Microfluidic Systems

In this paper, we show that the droplet morphology varies significantly during the transport process in digital microfluidic (DMF) systems depending on the gap height between the top and bottom plates. The experimental results elucidate the effect of changing the gap height on the initiation and progression of droplet motion. For example, extreme necking is observed during transport from one electrode to another at low gap heights. In essence, this necking is unlike the previously reported necking occurring during the splitting process over three electrodes. Pronounced elongation of droplets at certain stages during the droplet motion was examined. The effect of changing the gap height on the droplet velocity profile is illustrated. We found that prolonged actuation time is needed to transport the droplet successfully at low gap heights. This paper entails detailed experimental and numerical characterization of droplet morphology to insinuate useful design and prototyping tips for enhanced DMF devices. Such deformation, elongation, and necking corroborate that the existing analytical models may be inadequate for certain gap heights as they typically assume a circular shape for the droplet during motion. [2014-0292]

Numerical and experimental investigation on droplet dynamics and dispersion of a jet engine injector

In the case of turbine combustors operating with liquid fuel the combustion process is governed by the liquid fuel atomization and its dispersion in the combustion chamber. By highly unsteady flow field conditions the transient interaction between the liquid and the gaseous phase is of interest, because it results in a temporal variation of air–fuel ratio which leads to a fluctuating temperature distribution. The objective of this research was the investigation of transient flow field phenomena (e.g. large coherent structures) on droplet dynamics and dispersion of an isothermal flow (of inert water droplets) as a necessary first step towards a full analysis of spray combustion in real-life devices. The advanced injector system for lean jet engine combustors PERM (Partial Evaporated Rapid Mixing) was applied, generating a dilute polydispersed spray in a swirled flow field. Experiments were performed using Phase Doppler Anemometry (PDA) and a patternator to determine the droplet polydispersity, concentration maps, and velocity profiles in the flow. An important finding is the effect of large-scale coherent structures due mainly to the precessing of the vortex core (PVC) of the swirling air jet on the particle dispersion patterns. The experimental results then serve as reference data to assess the accuracy of the Eulerian–Lagrangian computations using a Large Eddy Simulation (LES), a Unsteady Reynolds-Average Navier–Stokes Simulation (URANS) and two simplified (steady-state) simulations. There, a simplified droplet injection model was used and the required boundary conditions of injected droplet sizes were obtained from measurements. Important transient effects of deterministic droplet separation observed during experiments, could be perfectly replicated with this injection model. It is convincingly shown, through extensive computations, that the resolution of instantaneous vortical structures is indeed crucial; hence the LES, or a reasonably-well resolved URANS are preferred over the steady-state solutions with additional, stochastic-type, turbulent dispersion models.

Spray and combustion characteristics of biodiesel: Non-reacting and reacting

The cold spray and spray combustion characteristics of palm biodiesel were investigated and compared with baseline Jet-A1 fuel. Both fuel sprays were generated from an airblast type atomizer and compared under the same atomizing air-to-liquid mass ratio (ALR). Under non-reacting spray condition, droplet velocity profiles for both sprays peak at the centerline due to high atomizing air momentum, while the droplet size is smallest at the spray core. Palm biodiesel generated slightly larger droplet size compared to Jet-A1 due to the effect of higher viscosity and lower volatility. Utilising an airblast atomizer-based swirl burner, spray flames of Jet-A1 and palm biodiesel were established and compared under continuous, steady swirl conditions. The droplet velocity and diameter distributions within the reacting spray flames were significantly different compared to non-reacting spray due to interaction with swirl air flow and flame within the combustor. Spray flame reaction zones obtained via OH* chemiluminescence imaging showed that fuel droplets evaporated rapidly within 20 mm from the burner outlet. Reacting Jet-A1 flame showed smaller droplet size compared to biodiesel due to higher vaporisation rate and close proximity to flame reaction zone. Palm biodiesel showed consistently lower NOx but slightly higher CO emissions per unit energy compared to Jet-A1 under a range of ALR tested.

Influence of spray characteristics on local light gas mixing in nuclear containment reactor applications

The action of spray on the mixing of different gases is used in numerous industrial applications, such as the chemical industry or the nuclear containment. The present paper concerns the impact of a spray on the break-up of a light gas layer (helium) initially confined in the top of a closed volume. Numerical calculations were performed in order to simulate the evolution of the helium concentration when the spray is activated. The objective of the paper is to show how the boundary conditions used for describing the spray can be important on the local gas mixing. Several sensitivity studies were performed that show the importance of the droplet boundary conditions: droplet size distribution, droplet velocity profiles, number of droplet classes, etc. Influence of these parameters on local gas concentration can be even higher than the one induced by a different turbulence model or some numerical parameters. Influence of the nozzle position inside the vessel is also analyzed. Extrapolation to an industrial application based on nuclear reactor containment is then discussed and recommendations are given for CFD simulations on the impact of spray systems on the gas mixing in nuclear reactors.

PDPA Investigation on an Electrostatically-Assisted Twin-Fluid Atomization Flow

The Phase Doppler Particle Analyzer (PDPA) technique is utilized for characterizing the droplet sizes and velocity profiles in an electrostatic spray flow which is atomized using the aerodynamic forces assisted with electrostatic forces. An electrostatically-assisted twin-fluid atomization system is presented and spatial distributions of the droplet size and two-dimensional velocity components are measured simultaneously at each specified point. The droplets are firstly ejected from a liquid jet through the nozzle by aerodynamic shear forces, and the breakup mechanism of such an electrostatically-assisted twin-fluid atomization is investigated using the Rayleigh instability conditions through studying the specific surface charges on these droplets measured by a Faraday canister. The discrepancies between experiment data and Rayleigh limit for specific charges of droplets are presented and discussed due to energy transforming from electrical energy to surface energy, energy loss, Taylor instability breakup and nonexcess charge polarization. The measured average velocity profiles and their RMS (root mean square) velocity values for two different scale drops further reveal the effects of the aerodynamic and electrostatic forces on the atomization process.

Investigation of pressure profile evolution during confined microdroplet formation using a two-phase level set method

The formation of droplets at a T-junction in a microchannel network is primarily influenced by the pressure difference across the interface in the squeezing regime. Accurate measurements of droplet velocity and pressure profiles are difficult to obtain experimentally, yet these are the basic parameters required for understanding the physics governing the droplet formation process and for shaping the optimum design of microfluidic devices. The current work presents predictions from two dimensional numerical simulations of microdroplet generation at a T-junction. The simulation results are validated with the experimental observations. Detailed profiles of the predicted pressure evolution across the channel upstream of the T-junction indicate that the pressure variation is sensitive to small changes in the wetting properties of the continuous phase.

Droplet size and velocity distributions for spray modelling

Methods for constructing droplet size distributions and droplet velocity profiles are examined as a basis for the Eulerian spray model proposed in Beck and Watkins (2002,2003) [5,6]. Within the spray model, both distributions must be calculated at every control volume at every time-step where the spray is present and valid distributions must be guaranteed. Results show that the Maximum Entropy formalism combined with the Gamma distribution satisfy these conditions for the droplet size distributions. Approximating the droplet velocity profile is shown to be considerably more difficult due to the fact that it does not have compact support. An exponential model with a constrained exponent offers plausible profiles.

Evaluation of the Eulerian-Lagrangian spray atomisation (ELSA) in spray simulations

Many approaches have been used to simulate the spray structure especially in modelling fuel sprays, i.e., Eulerian, Lagrangian, Lagrangian- Eulerian, Eulerian-Eulerian and Eulerian-Lagrangian approaches. The present study uses an Eulerian-Lagrangian spray atomisation (ELSA) method which is an integrated model for capturing the whole spray evolution starting directly from injector nozzle still the end. Our goal in this study is to evaluate the ELSA model which is implementing into the commercial software Star-CD, for numerical modelling of diesel sprays. There are two key studies in these validations, at first we examine the turbulent parameters through the three different scenarios and then we study mesh dependency. The results show in form of liquid penetrations, droplet velocity, and axial velocity profiles. All numerical results are compared with experimental data from our research institute, CMT-Motores Termicos.