Spray Model Research Articles

Modeling Multivariate Spray Characteristics with Gaussian Mixture Models

With the increasing demand for efficient and accurate numerical simulations of spray combustion in jet engines, the necessity for robust models to enhance the capabilities of spray models has become imperative. Existing approaches often rely on ad hoc determinations or simplifications, resulting in information loss and potentially inaccurate predictions for critical spray characteristics, such as droplet diameters, velocities, and positions, especially under extreme operating conditions or temporal fluctuations. In this study, we introduce a novel approach to modeling multivariate spray characteristics using Gaussian mixture models (GMM). By applying this approach to spray data obtained from numerical simulations of the primary atomization in air-blast atomizers, we demonstrate that GMMs effectively capture the spray characteristics across a wide range of operating conditions. Importantly, our investigation reveals that GMMs can handle complex non-linear dependencies by increasing the number of components, thereby enabling the modeling of more complex spray statistics. This adaptability makes GMMs a versatile tool for accurately representing spray characteristics even under extreme operating conditions. The presented approach holds promise for enhancing the accuracy of spray combustion modeling, offering an improved injection model that accurately captures the underlying droplet distribution. Additionally, GMMs can serve as a foundation for constructing meta models, striking a balance between the efficiency of low-order approaches and the accuracy of high-fidelity simulations.

Heat transfer of single-phase spray cooling on heated vibrating surfaces

Effective vibration control has potential to enhance convective heat transfer. However, the precise heat transfer mechanism of single-phase spray cooling under vibration remains elusive. This study aims to elucidate this mechanism by establishing a closed-loop system for vibrating surface spray cooling. Various vibration parameters, including vibration Reynolds number (Rev), dimensionless acceleration number (Ac), amplitude, and frequency, were investigated experimentally to determine their impact on heat transfer. The research findings demonstrate that the heat flux, heat transfer coefficient, cooling efficiency, and vibration enhancement factor all decrease with an increase in Rev and amplitude. At a heating power of 200 W and Rev of 4947, the spray cooling performance on the vibrating surface is inhibited by 22%. However, as the heating power increases, the inhibitory effects of Rev and amplitude on the spray cooling heat transfer performance are weakened. Conversely, the amplitude and frequency enhance the heat flux, heat transfer coefficient, cooling efficiency, and vibration enhancement factor. At a heating power of 200 W and an Ac of 3.6, the spray cooling heat transfer performance on the vibrating surface is enhanced by 17%. Finally, a dimensionless correlation equation and a Nusselt number (Nu) prediction model for single-phase spray cooling under vibrating conditions are derived and fitted with an error of ±13.2%.

Simulation on Evaporation and Cooling Characteristics of Spray System

This study explored the evaporation and cooling characteristics of air pipeline spray based on computational fluid dynamics method. A geometric model of the pipeline air spray was constructed and meshed, and the Euler-Lagrange research method of the discrete phase model (DPM) was used to study the evaporation and cooling characteristics of the spray system. It was found that the length required for complete evaporation of droplets increased with the relative humidity. When the inlet temperature was 308K and the relative humidity was 40%, the evaporation length increased by 43.71% compared to when it was 20%. There was a negative correlation between the inlet temperature and the evaporation length, and when the relative humidity was 30%, the evaporation length at an inlet temperature of 323K decreased by 1.55m compared to when it was 313K. After spraying, the air temperature gradually decreased along the length of the pipe, and the cooling effect decreased as the relative humidity of the inlet air increased. When the inlet temperature was 308K and the relative humidity was 40%, the outlet temperature was 4.39K higher than when it was 20%, and the cooling effect increased as the inlet air temperature increased. When the relative humidity of the inlet air was 30%, the temperature drop at the outlet at an inlet temperature of 323K was 1.93K higher than when it was 313K.

Extended Coherent Flame Model applied to an optical single-cylinder engine fueled with ethanol

One way to achieve a fast track for the decarbonization of the transportation sector is through the usage of biofuels. Among the many biofuels available for transportation, ethanol is one of the most promising, especially when combined with direct-injection spark-ignited engine technologies. The present work aims to validate 3D Computation Fluid Dynamics (CFD) ethanol spray and combustion models with the calibration of specific model parameters using experimental data obtained with optical measurements. Focus is given on the investigation and determination of the Extended Coherent Flame Model parameters for hydrous ethanol turbulent spray combustion. To characterize the spray produced by the injector, measurements obtained with a Phase Doppler Interferometer system are used. Natural luminosity and in-cylinder pressure are acquired on a single-cylinder research engine with optical access. The work also considers results obtained from 1D and 3D CFD models to supplement the acquired experimental setup. From the comparison between experimental and numerical results, it comes out that a correction of the Extended Coherent Flame Model turbulence stretch parameter can be done according to a ratio of flow and combustion length scales obtained at the spark time. In this sense, an expression is proposed to allow the correction of such a parameter in different engine operating conditions. Accordingly, in-cylinder mean effective pressure calculated with 3D CFD simulations show a good agreement with the experimental data for all studied cases.

Atmospheric Sea Spray Modeling in the North‐East Atlantic Ocean Using Tunnel‐Derived Generation Functions and the SUMOS Cruise Data Set

AbstractThis study contributes to the communal effort to improve understanding of sea spray generation and transport. For the first time, laboratory‐derived sea spray generation functions (SSGFs) are parameterized in the Meso‐NH mesoscale atmospheric model and are field tested. Formulated from the MATE19 laboratory experiments (Bruch et al., 2021, https://doi.org/10.1007/s10546-021-00636-y) the two SSGFs are driven by the upwind component of the wave‐slope variance (herein B21A), or both and the wind friction velocity cubed (herein B21B). In this first attempt to incorporate the SSGFs in Meso‐NH, the simulations are run without a wave model, and the wave‐wind SSGFs are assumed wind‐dependent. Model evaluation is achieved with a new set of sea spray and meteorological measurements acquired over the 0.1–22.75 μm radius range and U10 1–20 m s−1 wind speeds onboard R/V Atalante during the 25 day SUMOS field campaign in the Bay of Biscay. The B21B SSGF offers particularly good sensitivity to a wide range of environmental conditions over the size range, with an average overestimation by a factor 1.5 compared with measurements, well below the deviations reported elsewhere. B21A also performs well for larger droplets at wind speeds above 15 m s−1. Associated with airflow separation and wave breaking, wave‐slope variance allows to represent multiple wave scales and to scale sea spray generation in the laboratory and the field. Using Meso‐NH simulations we find that sea spray may be transported inland and to altitudes well above the marine atmospheric boundary layer.

A parametric distribution model of electrostatic spray rotating bell and application for automobile painting

A parametric distribution model of electrostatic spray rotating bell and application for automobile painting

Modeling of the SNCR process – Based on a semianalytical spray model approach

Modeling of the SNCR process – Based on a semianalytical spray model approach

Two-way Eulerian-Lagrangian coupling approach in GASFLOW code for containment spray modelling

Spray droplets are considered to have significant effects on the gas mixing and depressurization in the containment of nuclear power plants during hypothetical accident scenarios. The Eulerian-Lagrangian approach, which enables the two-way mass, momentum, and energy coupling of the continuous gas and the dispersed spray droplets, is promising to model the behaviours of spray droplets in 3D simulations of the full-scale containment. Two-way heat and mass transfer models have been developed in the 3D CFD code GASFLOW. The particle group method is applied in the Lagrangian approach to track the droplets. The ordinary differential equations which couple the local heat and mass exchanges between each droplet group and the surrounding gas mixtures have been solved using the Runge-Kutta method. The GASFLOW coupling this new approach is validated by TOSQAN water spray experiments, which demonstrate the good feasibility of implementing the approach. The analysis of the impact of the spray on containment atmosphere indicates that: 1) the droplet swarm entrains and mixes the surrounding gas, breaking up the gas stratification, with turbulent diffusion dominating momentum mixing in dead zones; 2) the thermal and mass exchanges between the spray droplet swarm and gas jointly determine the atmosphere depressurization, with the evaporation of the spray-formed film/sump on heat structures of great importance for the containment pressure development; and 3) these spray thermodynamic and dynamic effects highly depend on the droplet size distribution and the spray shape.

Evaluation of Spray and Combustion Models for Simulating Dilute Combustion in a Direct-Injection Spark-Ignition Engine

Abstract Dilute combustion in spark-ignition engines has the potential to improve thermal efficiency by mitigating knock and by reducing throttling and wall heat losses. However, ignition and combustion processes can become unstable for dilute operation due to a lowered laminar flame speed, resulting in excessive cycle-to-cycle variability (CCV) of the combustion process. To compensate for the slower combustion in less reactive mixtures, a modified intake port geometry can be employed to generate a strong tumble flow in the cylinder and elevate turbulence levels around the spark plug, thereby promoting a faster transition to turbulent deflagration. Consequently, optimizing combustion chamber geometry and operating strategy is crucial to maximizing the benefits of using dilute combustion with enhanced in-cylinder turbulence across a wide range of operating conditions. Computational fluid dynamics (CFD) simulations can be utilized for virtual engine optimization tasks, but this would require the models to be truly predictive regarding the impact of changes to the engine design and operational parameters. In this study, multicycle large-eddy simulations (LES) are performed for a direct-injection spark-ignition engine to investigate the model performance in predicting engine combustion characteristics with respect to changes in the intake configuration. A tumble plate that blocks the lower part of the intake port inlet is used to vary the tumble. A set of CFD models that have been recently developed are employed, which takes into account the drag of nonspherical droplets, flash-boiling behavior of liquid sprays, spray-wall interaction, surrogate formulation of a research-grade E10 gasoline, and fast chemical kinetic solvers. Simulation results are compared to experimental engine data in terms of cylinder pressure, apparent heat release rate, mass fraction burned timing, and flame images. It is found that LES employing the state-of-the-art CFD models are capable of properly predicting the spray processes and reproducing the measured mean cylinder pressure for the case with the tumble plate. On the other hand, the LES over-predicts the combustion rate during the early combustion stage and under-estimates the CCV, and these discrepancies become larger when the tumble plate is removed.

Model predictive temperature control of a closed-loop spray cooling system

A dynamic model of a closed-loop spray cooling system was proposed, and a model predictive temperature control algorithm was presented. The presented algorithm could quantitively estimate sudden changes in heat load, and then plan an optimized control path along which the temperature trajectory was numerically predicted to be the most stable. Then, the presented algorithm was integrated into a closed-loop spray cooling system, and its control performance was numerically studied. The results showed that, following a 20 W downward step change in heat load, the temperature was re-stabilized in 4 s, with its oscillation less than 0.14 K. Under identical conditions, the presented algorithm outperformed PID in terms of temperature stability, with its peak time shorter by 25–55%, settling time shorter by 38–51%, and average temperature offset smaller by 50–60%. This advantage was mainly because the presented algorithm compensated for hydraulic and thermal lags, two sources of control nonlinearity, by excessive regulation in advance. Unexpectedly, temperature overshoots of the presented algorithm and PID did not differ significantly, seemingly due to the algorithm-inherent estimation lag. From a system design perspective, the length of pump pipeline should be as short as possible, which proved to help reduce overshoot and settling time. Similarly, addition in heat load’s mass also helped reduce overshoot, but would result in an unfavorable long settling time, and vice versa. The simulation results were validated by experimental data, with error less than 10%.

Mathematical model and numerical investigation of the influence of spray drying parameters on granule sizes of mold powder

In this work, the formation mechanism of the droplet-to-granule was investigated in detail based on mold powder manufacturing. A specific mathematical model of two-stage spray drying was established to describe droplet and granule motion, heat and mass transfer, and granule morphology during spray drying. Then, the relationships between spray drying parameters (inlet temperature, atomization pressure, slurry mass flow rate) and the properties of the drying tower (temperature and velocity fields) and mold powder granules (temperature, evaporation rates, moisture content, and diameter) were simulated and calculated using ANSYS/Fluent software. To ensure that the granule size of mold powder was controlled within the ideal range (0.2–0.6 mm) for producing granules with appropriate mechanical and metallurgical properties, the following optimum spray drying parameters were chosen based on the results of the numerical simulation: inlet temperatures, 873 K; slurry atomization pressure, 1.8 MPa; slurry mass flow rate, 0.05 kg s−1. Among these parameters, the slurry mass flow rate has the most significant effect on granule size.

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.

Comparative Spray Atomization and Evaporation Characteristics of Dimethyl Ether and Mineral Diesel

Abstract Dimethyl ether is a new-generation alternative fuel to mitigate cold-start issues in compression ignition engines. It has a higher cetane number and can efficiently lead to superior atomization and evaporation characteristics. This computational study compares Dimethyl ether and baseline diesel sprays in a constant-volume spray chamber. This simulation study compares spray and evaporation characteristics en-hancement due to Dimethyl ether adaptation. Fuel properties greatly influence spray atomization and evaporation characteristics. This study is based on the Eu-lerian-Lagrangian approach adopted in the Reynolds-averaged Navier-Stokes framework. The liquid spray penetration obtained by simulations matched well with the experimental results of Dimethyl ether and baseline diesel. Spray model con-stants were tuned for diesel and Dimethyl ether separately, as the fuel properties of both test fuels are completely different. These tuned models were used to simulate Dimethyl ether and diesel sprays at fixed fuel injection timings and ambient condi-tions. Results showed a lower spray penetration length for Dimethyl ether than die-sel because of the flash boiling of Dimethyl ether. Smaller diameter droplets formed due to Dimethyl ether's lower viscosity, density, surface tension, and higher evapora-tion rate. The reduction in Sauter mean diameter was quite sharp after the start of injection for the Dimethyl ether. Diesel spray showed retarded atomization and evaporation compared to Dimethyl ether. The vapour penetration length of both fuels was almost the same; however, the vapor mass fraction was higher for Dime-thyl ether than baseline diesel. Dimethyl ether spray showed superior spray atomi-zation and improved evaporation of Dimethyl ether droplets.

Numerical Investigations of Pseudo-Boiling and Multi-Component Mixing Under Trans-/supercritical Conditions for Engine Applications

ABSTRACT The fuel injection and mixing process are often carried out under trans-/supercritical conditions for engine applications; however, the process is still unclear. In this study, based on OpenFOAM, a multi-component trans-/supercritical spray model based on the KT/KNP scheme is developed, which covers the special real fluid equation of state, various mixing rules and modified thermodynamic properties. In addition, the PIMPLE algorithm is extended to deal with the high nonlinearity. First, a one-dimensional advection case is applied to evaluate the performance of the model. Then, the effect of various mixing rules and pseudo-boiling phenomenon on n-heptane/nitrogen jet are thoroughly analyzed under trans-/supercritical conditions. The results show that the jet is extremely sensitive to the changes of the initial jet temperature and chamber pressure, and the “heat shield” effect of pseudo-boiling delays the breakup and mixing in the transcritical jet. With the mixing of different components, unlike the single-component condition, the pseudo-boiling intensity will increase. The increase of pressure and occurrence of mixing will lead to the decrease of pseudo-boiling temperature, and the pseudo-boiling will end earlier, which is obviously different from the single-component fluid case. For the n-heptane/nitrogen mixture, when the mole fraction of n-heptane in the mixture changes from 1.0 to 0.7, and the pseudo-boiling temperature decreases from 571 K to 465 K. With increasing injection temperature or chamber pressure, the pseudo-boiling intensity gradually decreases, and the potential core shortens, the difference among various mixing rules decreases. When the injection temperature is higher than 571 K, the pseudo-boiling phenomenon no longer exists. When the chamber pressure reaches 9 MPa, the pseudo-boiling strength is very low. Therefore, the spray mixing under supercritical conditions will be more sufficient. With the occurrence of mixing, the critical parameter gradually transitions from the critical value of n-heptane to the critical value of nitrogen, which strongly depends on the mixing rule.

An improved SPH scheme for the 3D FEI (Fluid-Elastomer Interaction) problem of aircraft tire spray

The problem of aircraft tire spray produced by taking off or landing on wet runways is widely concerned. When simulating this kind of FEI(Fluid-Elastomer Interaction) problem with traditional SPH((Smoothed Particle Hydrodynamics) method, there are some drawbacks in both fluid and elastomer calculation. For the elastomer simulation, the TL-SPH(Total Lagrangian-SPH) is used to deal with the deformation of tire under complicated motion and load. For the fluid simulation, a new SPH scheme of Riemann solver combined with transport velocity is proposed to solve the problem of particle clumping when the free surface is suffering from violent splash. Then the tire spray model by unified SPH is established, in which both the tire deformation and the spray pattern are validated by experiments. Finally, based on the large-scale tire spray simulation, the phenomenon of tire hydroplaning is studied.

Mechanism study on the influence of combustion models and spray gun geometric parameters on high-velocity oxygen-fuel (HVOF) thermal spraying

HVOF thermal spraying technology has unique advantages for spraying WC-12Co ceramic powder. The spraying process is complex, involving the gas-liquid-solid multiphase flow, chemistry, heat transfer and intelligent control. It is vital to quantitatively reveal the reaction mechanism of combustion components, which optimizes the thermal spraying process and improves the coating quality. A numerical model of HVOF thermal spraying was established, including the gas dynamics model, chemical thermodynamics model and discrete phase model for spraying particle. The difference between the eddy dissipation model (EDM) and EDC model in the traditional calculation was compared. The results show that the EDC model reveal the chemical reaction mechanism of the combustion in detail step by step, and quantitatively display the exothermic phenomenon during whole spraying. The exothermic reaction predicted by the EDC model continues into the air domain with the flame flow. The geometric structure of spray gun was analyzed based on the EDM model. The results show that the diameter of the combustion chamber is 30.2 mm, the diameter of the parallel nozzle is 10.5 mm, and the length from the particle inlet to the nozzle starting point is 13.3 mm, the flight temperature and velocity for particles are relatively high.

A Novel Surrogate Fuel Approach for the Numerical Simulation of Renewable Fuels for the Transport Sector

The use of fuels made from renewable resources can be beneficial in reducing the CO2 emission balance of the existing vehicle fleet. These fuels should be drop-in-capable, i.e., their properties should correspond as far as possible to those of fossil fuels. In addition, they should be able to be blended with conventional fuels. In order to determine the full potential of new renewable drop-in fuels, numerical investigations can make a significant contribution.A novel Surrogate Fuel Approach (SFA) was proposed to perform the numerical simulations for blends of paraffinic diesel fuel and alcohols. A set of modeling and mixing rules were used to estimate and extrapolate the required thermo-physical and physicochemical properties of renewable fuels. The detailed chemical mechanisms for n-dodecane and n-octanol were merged. A systematic reduction of the detailed chemical mechanisms was performed using the Directed Relation Graph with Error Propagation (DRGEP) method. For the selected target species, the reduced mechanism from the DRGEP and lumping method contains ∼31% species and ∼40% reactions as of the merged reaction mechanism. The blended fuel properties and the reduced reaction mechanism were incorporated into the numerical simulations. The surrogate fuel approach was validated for steady-state as well as transient operating conditions using the experimental results obtained from the optical high-pressure chamber (HPC) and a heavy-duty single-cylinder engine (HD-SCE). The HD-SCE testing shows that the 60% B0-Di/40% RF blend increases ITE by ∼2% in absolute values and lower ISCO2, ISCO, ISHC and smoke emissions as compared to Diesel fuel. This is due to the paraffinic fuel structure, the fuel-borne oxygen, the high calorific value, and the high cetane number. The calibrated 3D-CFD spray models show an excellent agreement with experimental data from the optical investigations of different spray characteristic values — Liquid and Gaseous penetration Length, Lift of Length and ignition delay for the 60% B0-Di/40% RF fuel. Further, the pressure traces, heat release rates, and nitrogen oxides (NOX) emissions from the numerical 3D-CFD simulations showed a good agreement with the results from the HD-SCE experiments. Overall, these results support the suitability of the proposed novel surrogate fuel approach for simulating different blends of renewable drop-in fuels.

Sea spray induced air-sea heat and salt fluxes based on the wave-steepness-dependent sea spray model

Sea spray induced air-sea heat and salt fluxes based on the wave-steepness-dependent sea spray model

Primary spray breakup from a nasal spray atomizer using volume of fluid to discrete phase model

Spray atomization process involves complex multi-phase phenomena. Abundant literature and validation of spray modeling for industrial applications like fuel injection in internal combustion and turbine jet engines are available. However, only a handful of studies, primarily limited to discrete phase modeling, of low-pressure applications, such as nasal spray exists. This study aims to provide insight into the external and near-nozzle spray characterization of a continuous spray and establishes good validation against the experiment. A three-dimensional (3D) x-ray scanner was used to extract the internal nasal spray nozzle geometry which was reconstructed to build a 3D computational model. A novel volume-of-fluid to discrete phase transition model was used to track the liquid phase and its transition to droplets, which was based on the shape and size of the liquid lumps. In this study, an early pre-stable and stable phase of spray plume development was investigated. Qualitative and quantitative analyses were carried out to validate the computational model. A liquid column exited a nozzle which distorted at its base with advancement in time and eventually formed a hollow-cone liquid sheet. It then disintegrated due to instability that produced fluctuations to form ligaments resulting in secondary breakup. This study provides in-depth understanding of liquid jet disintegration and droplet formation, which adds value to future nasal spray device designs and techniques to facilitate more effective targeted nasal drug delivery.

Review of physicochemical properties and spray characteristics of biodiesel.

The United Nations Sustainable Development Goals by 2030 deal with seventeen goals for the planet's sustainability. The present review focuses on affordable and clean energy through the effective combustion of fuels with minimal pollution. Effective fuel spray characteristics are essential for combustion among various parameters and fuel properties. The inherent nature of the fuel has a functional relationship with the injection and injectors' conditions. Therefore, the study of fuels' physicochemical properties is essential. This review deals with the spray characteristics of biodiesel. Biodiesels in its purest form and blended with diesel, di-n-butyl ether, dimethyl ether, diethyl ether, ethanol, and butanol are considered for the study. The physicochemical properties of biodiesels, injection conditions, and injector constraints are analyzed to understand the spray process. The atomization features such as spray tip penetration, Sauter mean diameter, spray cone angle, spray area, and spray volume are analyzed. The chemical properties of biodiesel are utilized to describe the spray's transient behavior. In addition, supporting systems for spray diagnostics and models are also discussed. The highlighted significant spray challenges features and future research direction benefit the fuel and combustion community.