D2 Law Research Articles

Axisymmetric phase-field-based lattice Boltzmann model for incompressible two-phase flow with phase change

In this work, a phase-field-based lattice Boltzmann equation (LBE) model for axisymmetric two-phase flow with phase change is proposed. Two sets of discrete particle distribution functions are employed to match the conserved Allen–Cahn equation and the hydrodynamic equations with phase change effect, respectively. Since phase change occurs at the interface, the divergence-free condition of the velocity field is no longer satisfied due to mass transfer, and the conserved Allen–Cahn equation needs to be equipped with a source term dependent on the phase change model. To deal with these, a novel source term in the hydrodynamic LBE is delicately designed to recover the correct target governing equations. Meanwhile, the LBE for the Allen–Cahn equation is modified with a discrete force term to model mass transfer. In particular, an additional correction term is added into the hydrodynamic LBE to reduce the spurious velocity and improve numerical stability. Several axisymmetric benchmark multiphase problems with phase change, including bubble growing in superheated liquid, D2 law, film boiling, bubble rising in superheated liquid under gravity, and droplet impact on a hot surface, have been conducted to test the performance of the proposed model. Numerical results agree well with analytical solutions and available published data in the literature.

Exploring the impact of pillar edge effects on water drop evaporation

A water drop placed on a small pillar unveils an edge effect, which amplifies volume accumulation within the same contact area. This effect stems from an increased apparent contact angle, resembling hydrophobic surfaces. This emphasizes the influence of surface geometry beyond chemical properties.This study explores the characteristics of the drop by dissecting the interplay between surface forces, geometric attributes, and the evaporation process, enabling a comprehensive understanding of their combined impact on drop behavior.Two distinct evaporation stages were identified: the first stage, characterized by a constant contact line along the pillar edge, and the second stage, involving the detachment of edges and shape alterations influenced by surface roughness.The evaporation rate from the pillar is determined by applying the D2 law and empirical observations. Moreover, the interplay among the key parameters in the process—namely, the evaporation rate, contact angle, volume, and pillar diameter—has been elucidated.

Explosions of nanodroplets studied with molecular dynamics simulations

Explosions of droplets that are caused by superheating of the liquid phase occur in many combustion processes but are difficult to investigate experimentally. We have studied this process for nanodroplets using non-equilibrium molecular dynamics simulations. Starting from an equilibrium state in which a spherical droplet is surrounded by a vapor phase, a local thermostat is used to impose a high temperature in a small control volume in the droplet center and the following process is studied for varying set temperatures. The fluid is modeled using the Lennard–Jones truncated and shifted potential. Depending on the set temperature, three different system responses were observed: (i) Low set temperatures lead to a shrinking of the droplet due to evaporation that follows the well-known d2 law. (ii) At intermediate set temperatures, a vapor bubble emerges in the droplet center and the liquid phase is formed into spherical shell that expands as the bubble inside of it grows. However, that spherical shell is only temporarily stable and eventually breaks apart. (iii) For high set temperatures, the abrupt and violent formation of the vapor bubble leads to an immediate breakup of the droplet. For case (ii), unexpected phenomena were observed. Oscillations in the diameter of the vapor bubble surrounded by the liquid film occurred. In some simulations, small holes formed temporarily in the liquid shell during its expansion, which closed again over the course of the simulation. Moreover, for one specific set temperature, a transition of the spherical droplet shell into a torus-like object was observed.

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid–vapor phase change

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change.

Microgravity Spherical Droplet Evaporation and Entropy Effects.

Recent efforts to understand low-temperature combustion (LTC) in internal combustion engines highlight the need to improve chemical kinetic mechanisms involved in the negative temperature coefficient (aka cool flame) regime. Interestingly, microgravity droplet combustion experiments demonstrate this cool flame behavior, allowing a greater focus on chemistry after buoyancy, and the corresponding influence of the conservation of momentum is removed. In Experimental terms, the LTC regime is often characterized by a reduction in heat transfer losses. Novel findings in this area demonstrate that lower entropy generation, in conjunction with diminished heat transfer losses, could more definitively define the LTC regime. As a result, the simulation of the entropy equation for spherical droplet combustion under microgravity could help us to investigate fundamental LTC chemical kinetic pathways. To provide a starting point for researchers who are new to this field, this effort first provides a comprehensive and detailed derivation of the conservation of entropy equation using spherical coordinates and gathers all relevant information under one cohesive framework, which is a resource not readily available in the literature. Subsequently, the well-known d2 law analytical model is determined and compared to experimental data that highlight shortcomings of the law. The potential improvements in the d2 law are then discussed, and a numerical model is presented that includes entropy. The resulting codes are available in an online repository to ensure that other researchers interested in expanding this field of work have a fundamental starting point.

Numerical simulation of conduction problem with evaporation based on a SPH model improved by a fractional order convection-diffusion equation

Smoothed particle hydrodynamics (SPH) simulations of phase transitions are not accurate because of the decrease in liquid particles at the end of the evaporation phase transition. In this paper, we establish a numerical model of droplet evaporation suitable for SPH by introducing a time fractional-order convection–diffusion equation. This model was used to study the evaporation process of droplets under different environments, and the stationary evaporation of droplets was simulated by combining convection–diffusion equations of different orders to determine the optimal order. The results conformed to the “D2 Law,” confirming the effectiveness and accuracy of our method. The model was then used to study the phase transition process of droplets impacting flat and curved surfaces. Among the tested equations, the 0.1-order convection–diffusion equation had the best correction effect on the evaporation model. This equation improved the accuracy of the calculation and had a good corrective effect for both static evaporation and the evaporation of droplets impacting flat and curved surfaces.

Experimental and numerical investigation of aluminum particle combustion driven instability in solid rocket motors

Aluminum particles are extensively employed to enhance the energetic properties of propellants. However, the heat release rate (HRR) fluctuations resulting from aluminum combustion can potentially affect the stability of solid rocket motors (SRMs). Using a self-made high-pressure combustion diagnostics system and laser ignition system, this work investigates the combustion behavior of single aluminum particle under propellant atmosphere and acoustic excitation. An unsteady aluminum combustion model using Ranz-Marshall correlation and involving the heat and mass transfer equation was developed. The D2 law of aluminum particle combustion in a real propellant under 0.5 MPa was fitted as t = D2/0.31. The measured combustion rate of laser-ignited aluminum particles was found to increase from 0.381mm2/s to 0.465 mm2/s when an acoustic excitation of sine wave(200 Hz, 20Pa) was applied to the propellant, which agreed well with the prediction of the proposed unsteady combustion model whose error was 4.7%. Then, the verified correlation was included in the SRM to calculate the HRR fluctuation of the aluminum on acoustic boundary near the propellant burning surface. The effects of particle diameter, gas velocity, oscillation amplitude and frequency on the HRR fluctuation were obtained. It was found that the HRR fluctuation increases with the increasing particle diameter, gas velocity, and oscillation amplitude, and that due to the acoustic boundary effect, the HRR fluctuation is more sensitive under low-frequency oscillation. Based on the HRR fluctuation of aluminum combustion and particle damping, the growth rate of instability resulting from aluminum combustion in an SRM was investigated. The results showed that the growth rate of instability resulting from aluminum combustion were 9.38s-1 and 24.06s-1, while the particle damping (−25.8s-1) caused by combustion residuals, which suggests the aluminum particles play a critical role in SRMs combustion instability.

Numerical simulation of droplet evaporation based on the smoothed particle hydrodynamics method

Based on the smoothed particle hydrodynamics method, a numerical model of smoothed particle hydrodynamics in multi-phase flow evaporation accompanied with heat and mass transfer has been established, and phase transition of droplet evaporation is simulated. In this paper, an smoothed particle hydrodynamics mass transfer equation of gas phase in evaporation are proposed based on Fick?s law. In order to solve the problem of large mass difference of particles at the phase interface during evaporation, the particle splitting and merging techniques are introduced, and the tensile instability of particles during the splitting and merging is weakened by artificial stress. Besides, by adding the surface tension model, the mutual penetration of particles at the gas-liquid interface is effectively prevented. On this basis, the evaporation of single droplet and interacting droplets without gravity is simulated. The results show that the evaporation time of single droplet in this study conforms to D2 law and is within the theoretical range. There is a great influence between interacting droplets in the process of evaporation. Only when dimensionless number C (droplet spacing/droplet diameter) is larger than eight, the influence between droplets can be approximately ignored.

Cavitation bubbles with a tunable-surface-tension thermal lattice Boltzmann model

The effects of surface tension and initial input energy on cavitation properties based on a tunable-surface-tension large-density-ratio thermal lattice Boltzmann method pseudo-potential model are investigated. The validity and superiority of the proposed model in simulating the D2 law, Laplace law, and revised thermal two-dimensional Rayleigh–Plesset equation are demonstrated. Moreover, the lattice Boltzmann method was used to study the effects of varied surface tension on cavitation bubble properties for the first time, and the maximum surface tension-to-minimum surface tension ratio of 25 is utilized, which is highly improved compared with previous numerical simulations (<4) and makes our result more clear. The simulation results indicate that for an infinite liquid, the increase in the surface tension will improve the collapse intensity of cavitation bubbles, increasing the collapse pressure, velocity, and temperature and meanwhile reducing the bubble lifetime. For the cavitation bubbles collapsing near a neutral wall, with an increase in the surface tension, the collapse pressure, temperature, and cavitation bubble lifetime trends are the same as in the infinite liquid. However, the collapse velocity is affected by the neutral wall, and the micro-jet becomes wider and shorter. The maximum cavitation bubble radius in an infinite liquid is nearly linearly proportional to the input initial energy. An increase in the surface energy reduces the maximum radius of the cavitation bubbles, while increasing the pressure energy and thermal energy promotes the maximum radius of the cavitation bubbles. This series of simulations proves the feasibility of the proposed model to investigate the thermodynamic process of the cavitation bubbles with high density ratios, wide viscosity ratios, and various surface tensions.

Micro-explosion enhanced combustion of Jatropha oil/2, 5-dimethylfuran (DMF) blended fuel droplets

The present study investigated the micro-explosive combustion characteristics of Jatropha oil-2, 5-dimethylfuran (DMF) blended fuel droplets using fiber-support and high-speed backlit imaging technique. The flame temperature and soot optical thickness (KL) are measured by two-color pyrometry method. The results show that the combustion of Jatropha oil-DMF blended droplets containing four stages: ignition delay, first micro-explosive combustion, d2 law combustion and second micro-explosive combustion stage. The micro-explosion in second and fourth stage is caused by superheating of DMF and pyrolysis, respectively. The flames of DMF, diesel and Jatropha oil droplets belong to typical diffusion combustion. However, the micro-explosive flame of Jatropha oil-DMF blended droplets belongs to premixed combustion. When the DMF concentration reaches 50%vol, the ignition delay is equivalent to that of diesel. The average burning rate of Jatropha oil-DMF blended droplets increases nonlinearly with air velocity. When the DMF concentration is 75%vol, it reaches the peak, which is 66.4% higher than that of diesel. Furthermore, the effect of micro-explosion on droplet flame deformation is summarized into four modes: slight fluttering flame, local flame separation, large deformation flame, large deformation flame with local flame separation. When there is air flow in the horizontal direction, a “soot shell” forms around the droplets. This is due to the upward buoyancy interacts with the horizontal airflow force to form a rotating airflow force, which concentrates the soot particles around the droplets.

Chemically cross-linked gel storage for fuel to realize evaporation suppression

High-energy density liquid fuels are commonly used to operate combustors such as rockets, gas turbines, automotive engines, and boilers to make an energy transformation. To prevent a serious incident such as an explosion or a fire disaster, we have recognized practical issues of the liquid fuels that are safety and stability during transportation and storage, evaporation rate, and burning rate constant. In this experiment, ethanol is used as a liquid fuel and is retained on chemically cross-linked poly(N-isopropylacrylamide) (PNIPPAm) gel to use it as a polymeric gel storage for liquid fuels. In general, because the cross-linking structure of chemical gels is formed by covalent bonding, it is more stable than physical gels for a thermodynamic change such as temperature. The evaporation rate of the polymeric gel storage to suppress evaporating the ethanol is investigated. We finally demonstrate to obtain burning rate constants based on a changing mass of the polymeric gel storage during combustion. By demonstrating the polymeric gel storage combustion, we revealed existence of the d2 law in a droplet combustion.

Real-time observation and quantification of carbon black oxidation in an environmental transmission electron microscope: Impact of particle size and electron beam

Carbon black oxidation is a post-treatment method to control its properties for different applications, and its outcomes may depend on the particle size. Three different sizes of carbon blacks were oxidized in an environmental transmission electron microscope to study the size effect on their oxidation pathway and rate. The oxidation at the nanoscale has been quantified using the ASTM D3849-14a standard method for the carbon blacks and compared with the theory of solid particle burning, i.e., D2 law. This comparison confirms the validity of the diffusion-controlled burning model for all three samples oxidized at 800°C in the presence of oxygen molecules. Electron microscope images show surface burning is the governing mode under this condition. Oxidation under electron-beam irradiation shows that the oxidation rate reduces by ∼0%, 30%, and 80% for particles with 33, 112, and 356 nm in diameter, respectively. The results suggest that the electron beam is causing the atomic bonds to break and transform to the graphitic structure at relatively high temperatures (e.g., 800°C) that causes oxidation rate reduction in larger particles. Despite the reduction in oxidation rate as the initial size of carbon particles increases, observations show that surface burning is the dominant mode under electron-beam irradiation.

Comparison of evaporation rate constants of a single fuel droplet entering subcritical and supercritical environments

This work compares the evaporation rate constants of a single fuel droplet under subcritical and supercritical environments by experimental visualizations (in millimeter scale) and molecular dynamics simulations (in nanometer scale). The objection is to understand the differences of fuel droplet evaporation rate constant variations under the subcritical and supercritical environments. Firstly, an experimental apparatus is designed to study the diesel droplet evaporation under subcritical and supercritical environments. The results show that the droplet evaporation obeys the D2 law in subcritical environments, while the D2 law is no longer strictly applicable in supercritical environments and the evaporation rate constant isn’t a constant but a variable that increases with the evaporation time. Secondly, the molecular dynamics simulations are applied to investigate the evaporation of diesel surrogate n-dodecane under subcritical and supercritical environments. The results show that the droplet temperature keeps at the equilibrium temperature in subcritical environments, but keeps increasing in supercritical environments. In supercritical environments, the reason for the evaporation rate constant keeps increasing is that the droplet density keeps decreasing with the increase of droplet temperature. The droplet surface tension will rapidly vanish in supercritical environments, which implies that the formation of fuel–air mixture is no longer dominated by the surface tension, but is the turbulent diffusion in diesel trans/supercritical injection conditions. It can deduce that the evaporation rate constants of a fuel droplet in micrometer scale (that is commonly generated in engines) will follow the same trend and within the same variation scale at the same ambient pressures and temperatures.

A computational study on shock induced deformation, fragmentation and vaporization of volatile liquid fuel droplets

This study investigates the fundamental mechanisms underlying the deformation, fragmentation, and vaporization of volatile liquid fuel droplets impacted by a normal shock wave using a high-fidelity, VOF-DIM (volume of fluid - diffuse interface method)-based framework. The theoretical and mathematical formulation of this multiphase, multi-fluid problem is based on a modified 5-equation Kapila formulation with pressure-relaxation, viscous, and surface tension effects. A thermal-mechanical-chemical equilibrium relaxation procedure is implemented to simulate vaporization. The framework is first validated against measurements of shock impact on a non-vaporizing water droplet; the computations agree well with the experimental data. Next, the vaporization model is validated against the d2 law, showing excellent agreement. This is followed by a systematic investigation of the atomization and vaporization physics of a n-dodecane droplet as it interacts with a shock wave traveling at a Mach number of 6.5. To compare and contrast the effect of vaporization on breakup physics, two numerical experiments were conducted with and without the vaporization model. It is found that when the vaporization model is not enabled, the gaseous and liquid phase dynamics are similar to that of non-vaporizing water droplet-shock wave interactions. However, when vaporization is enabled, aerothermal heating from the shock impact and high temperatures in the post-shock region provide sufficient heating for volatile liquid droplets to undergo phase change and the breakup behaviors are significantly different from the non-vaporizing counterpart. Furthermore, it is found that vaporization is a strong function of the shock strength – low Mach number shock waves lead to higher vaporization.

Molecular dynamics simulations on evaporation of a suspended binary mixture nanodroplet

Mixture working fluids have the advantages of active design and adjustable physical properties, therefore it has a promising future in many power and refrigeration applications. Studies on the evaporation process of mixture nanodroplets are helpful to reveal the mechanism of heat transfer at the interface of mixture working fluids. However, at present, there are few studies on the evaporation of mixture droplet, and the conclusions on the pure fluids evaporation cannot be directly applied to the mixture working fluids, thus it is necessary to carry out specific research on the evaporation of mixtures. In this study, molecular dynamics simulation was used to study the evaporation process of R32/R1234yf nanodroplets with different compositions (xR32=0, 0.2, 0.4, 0.6, 0.8, 1) in a large space. The dynamic changes of evaporation rates of droplets with different components were compared, and the evaporation characteristics of droplet with different concentrations were analyzed in combination with the density, temperature and concentration field distribution near the liquid-vapor interface during the evaporation process. The results show that the evaporation rate of the mixture nanodroplets is lower than the linear interpolation with those of the two components, which is similar to the heat transfer deterioration of the mixture working fluids in pool or flow boiling. The prediction deviation of R32/R1234yf mixture nanodroplet evaporation by the D2 law is around 80%. Considering the scale effect and the interfacial concentration gradient, the prediction accuracy of the D2 law can be improved.

A step toward lifting the fog off mist explosions: Comparative study of three fuels

Gases, vapors, and dusts are all potential explosion threats; however, mists should also be taken into account. Indeed, dozens of accidents involving hydrocarbon mists were identified in incident surveys. Mist explosions continue to occur, highlighting the need to evaluate and assess the validity of present approaches for assessing mist ATEX risks and to establish reliable standardized safety parameters for fuel mists.In a modified apparatus based on the 20 L explosion sphere, three fluids of industrial interest were investigated. A new siphon injection system comprising a Venturi junction was installed, offering a wide range of dispersion performances. This system was controlled by a specifically developed program, ensuring the apparatus's versatility and adaptability to various tested liquids. It enables precise control of the gas carrier flow, liquid flow, and injection and ignition durations, allowing modification of the dilution rate of a particular droplet size distribution (DSD). The mist cloud dispersed in the 20 L sphere was characterized by determining its DSD using an in-situ laser diffraction sensor and by performing Particle Image Velocimetry (PIV). Mists of kerosene, diesel and ethanol were then subjected to tests to assess their lower explosive limit (LELmist), minimum ignition energy (MIE), maximum explosion pressure (Pmax), and rate of pressure rise (dP/dtmax). For instance, it was found that the LELmist of ethanol, kerosene Jet A1, and diesel fuel for a DSD averaged at 8–10 μm reach 77, 94, and 93 g/m3 respectively. This LELmist was also shown to increase with increasing DSD in the case of Jet A1 mists. A sensitivity study was also performed to emphasize the impact of parameters such as the fuel type, the DSD, and the mist temperature. Findings showed that the explosion severity is strongly influenced by the chemical nature and the volatility of the dispersed fuel. Moreover, controlling the sphere temperature was proven to be a crucial step when using such apparatus for the evaluation of the explosibility of mists. An evaporation model based on the d2 law was also developed to visualize the vapor-liquid ratio before ignition. These findings have already led to the development of a new procedure for determining safety standards for hydrocarbon mists, as well as tools to assess mist explosion risks. They have proven that it is possible to evaluate the ignition sensitivity and explosion severity of fuel mists using a single well-known apparatus.

D2 Law and Penetration Length of Jatropha and Camelina Bio-Synthetic Paraffinic Kerosene Spray Characteristics at Take-Off, Top of Climb and Cruise

A comparison of d2 law and penetration length of biofuels with Jet–A through the incorporation of fuel properties and actual combustor inlet data at various flight trajectories is presented. This study aims to identify fuel properties and flight operating conditions that most influence droplet characteristics accurately. The study comprises two phases involving a simulation using GSP to predict combustor inlet data for the respective flight operating conditions and a simulation using ANSYS Fluent V18.1 to obtain combustion characteristics of biofuels and Jet–A. The biofuels chosen in this study are Jatropha Bio-synthetic Paraffinic Kerosene (JSPK) and Camelina Bio-synthetic Paraffinic Kerosene (CSPK), evaluated as pure (100%) and blend (50%) with Jet–A. Thrust specific fuel consumption (TSFC) of biofuels is improved due to lower fuel consumed by the engine. The d2 law curve shows a heat-up period that takes place at the early stage of the combustion process. The penetration length of the fuels is shorter at take-off. Combusting biofuels reduce combustion temperature and the penetration length of the droplet.

A new DNS formalism dedicated to turbulent two-phase flows with phase change

Phase change in multiphase flows occurs in many natural and industrial applications, e.g., rain formation, internal combustion engines, heat exchangers, multiphase reactors, etc. In dense two-phase flows, quantitative experimental results are scarce due to the complexity of the configuration and experimental techniques limitations. Hence, the interest in the direct numerical simulation of such flows has grown recently to better understand and access quantitative data in this kind of flows.When simulating phase change in multiphase flows, advanced numerical method are needed to consider the jump conditions at the interface, and to ensure mass, energy, momentum and species conservation. In the literature, this problem is mainly investigated with an incompressible formalism. However, this assumption is not longer suitable for simulation of multiphase flows with phase change in enclosed environment or in atomized/aerated flows.The purpose of this work is to present a numerical formalism dedicated to turbulent two phase flows, including acoustics and compressible effects with a proper treatment of the jump conditions at the interface due to phase change. To achieve this task, first, the incompressible level-set method for vaporizing two-phase flows proposed by Tanguy et al. (2007) is revisited and adapted to a mass conservative interface representation: The Coupled Level-set/Volume of Fluid method. In this context, evaporating static cylinder with a constant vaporization rate and a droplet vaporization (D2 law) have been performed as validation cases. Both cases illustrate the method accuracy and robustness in presence of velocity discontinuities at the interface due to the presence of the Stefan flow. The D2 law configuration is used as validation of the implementation of the heat and mass transfer transport equations with their jump conditions and the coupling of the evaporation rate with the flow dynamic.Then, the numerical method is extended to compressible flows using the framework dedicated to the pressure based method proposed by Duret et al. (2018). The main advantage of this framework is the ability to consider acoustics effects, variable density and multiple gas inclusions with its own thermodynamic pressure. A modified Volume of Fluid transport equation is presented, including phase change and compressibility effects. Navier–Stokes and heat and mass transfer transport equation are solved using compressible assumptions. A validation case of a static evaporating cylinder in an enclosed environment is studied to illustrate and quantify the mass conservation properties of the method and the mass transfer between the two phases. Finally, a 3D two-phase Homogeneous Isotropic Turbulence (HIT) configuration is presented to demonstrate the potential of this method in presence of breakup, gas encapsulation, coalescence and evaporation processes.

Experimental Research on the Disruptive Evaporation and the Motion Characteristics of Secondary Droplets for Emulsified Biodiesel with a Suspended Droplet Configuration.

The secondary atomization of droplets is one of the means to improve the efficiency of diesel fuel injection atomization. As a promising biomass fuel, emulsified biodiesel showed a good prospect in improving the atomization effect of diesel engines. In this study, a high-temperature and pressure-resistant evaporator was designed to simulate diesel-like conditions, and the evaporation and combustion experiments of emulsified biodiesel droplets were carried out. The morphological changes in the droplets were dynamically captured using a high-speed camera. According to the collected images, the evaporation characteristic parameters, the dynamic parameters of droplet motion, and the correlation between the original and secondary droplets were quantitatively analyzed. The gain effect of secondary atomization for droplets on the diesel engine spray was evaluated. The results showed that the emulsified biodiesel underwent nucleation, agglomeration, puffing, and explosion during the evaporation process, while the classic d2 law only meets a few cases of this fuel. The effect of high temperature was reflected in reducing the normalization time of droplet agglomeration and explosion, while the higher pressure inhibited the expansion of the droplets, thus slowing down the expansion rate and restricting the droplet volume. Driven by the water content, the time of droplet explosion was closer to the droplet lifetime. The evaporation process of the secondary droplet was similar to that of the original droplet over a reduced scale of 1–2 orders of magnitude. (Dd/Dd0)2 ≈ 1 was a necessary condition for the secondary droplets to be produced in large quantities. The average equivalent diameter of the droplets was distributed in the range of 80–140 μm, and the secondary atomization caused expansion of the spray range by 20–40%. Expansion of the range of secondary droplets was beneficial to shortening the ignition delay and increasing the combustion rate.

Study on three droplet sequential burning characteristics of coal direct liquefied diesel

Coal direct liquefied diesel (DDCL) is a new alternative fuel with high cleanliness and quality. Its hydrocarbon composition and physicochemical properties are quite different from those of petrochemical diesel. In order to study the difference in evaporative burning characteristics between DDCL and diesel during the sequential burning of multiple droplets, three fuel droplets are suspended on fibers in order by a micro-injector. The first droplet was ignited by an electrode igniter, and then the sequential burning process of three droplets was captured by a high-speed camera. An automatic processing program is written based on Matlab software to calculate the equivalent diameter of each fuel droplet. The result shows that the burning process of the DDCL droplet can be divided into three stages: initial thermal expansion, steady burning, and late micro-explosion burning. DDCL is much easier to form the burning mixture and has better flammability than diesel. The droplet spacing and fuel type have significant effects on ignition delay. The square of the normalized diameter of droplets decreases linearly with time during the steady burning period, which follows the D2 law. The reduction rates of normalized squared diameter for DDCL droplets are higher than that for diesel. The pyrolysis of macromolecular components at high temperature produces many small molecules and low boiling point components, which induce the micro-explosions in the late burning stage. The micro-explosion intensity of DDCL droplets is obviously lower than that of diesel.