Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

Large Eddy Simulation of a swirl stabilized spray flame

Large Eddy Simulations (LES) of kerosene spray combustion in an axial-swirl combustor have been carried out focusing on the effect of the evaporating droplets on the flame temperature and species concentrations. The LES-PDF methodology is used for both dispersed (liquid) and gas phases. The liquid phase is described using a Lagrangian formulation whilst an Eulerian approach is employed for the gas phase. The predictive capability of LES with sub-grid scale models for spray dispersion and evaporation is assessed placing emphasis on the effect of the unresolved velocity and temperature fields on the droplet evaporation rate. The results of the fully coupled LES formulation exhibit good agreement between the measured and simulated mean velocity fields. The global behaviour of the spray combustion, such as droplet dispersion and evaporation, are captured reasonably well in the simulations. It was found that the large velocity fluctuations observed in the shear layer strongly affect the evaporation rate and thus the temperature distributions. The present work also demonstrated the feasibility of LES to study complex flow features which are typical of gas-turbine combustion chambers.     

Large-eddy simulation of evaporating spray in a coaxial combustor

Large-eddy simulation of an evaporating isopropyl alcohol spray in a coaxial combustor is performed. The Favre-averaged, variable density, low-Mach number Navier-Stokes equations are solved on unstructured grids with dynamic subgrid scale model to compute the turbulent gas-phase. The original incompressible flow algorithm for LES on unstructured grids by [Mahesh et al., J. Comp. Phys. 197 (2004) 215–240] is extended to include density variations and droplet evaporation. An efficient particle-tracking scheme on unstructured meshes is developed to compute the dispersed phase. Experimentally measured droplet size distribution and size-velocity correlation near the nozzle exit are used as the inlet conditions for the spray. The predictive capability of the LES approach on unstructured grids together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail. The mean and turbulent quantities for the gas and particle phases are compared to experimental data to show good agreement. It is shown that for low evaporation rates considered in the present study, a well resolved large-eddy simulation together with simple subgrid models for droplet evaporation and motion provides good agreement of the mean and turbulent quantities for the gas and droplet phases compared to the experimental data. This work represents an important first step to assess the predictive capability of the unstructured grid LES approach applied to spray vaporization. The novelty of the results presented is that they establish a baseline fidelity in the ability to simulate complex flows on unstructured grids at conditions representative of gas-turbine combustors.     

Polydisperse effects in jet spray flames

A laminar jet polydisperse spray diffusion flame is analysed mathematically for the first time using an extension of classical similarity solutions for gaseous jet flames. The analysis enables a comparison to be drawn between conditions for flame stability or flame blow-out for purely gaseous flames and for spray flames. It is found that, in contrast to the Schmidt number criteria relevant to gas flames, droplet size and initial spray polydispersity play a critical role in determining potential flame scenarios. Some qualitative agreement for lift-off height is found when comparing predictions of the theory and sparse independent experimental evidence from the literature.     

液体火箭有机凝胶喷雾液滴蒸发模型及仿真研究

凝胶推进剂虽然兼具有液体推进剂流量可控和固体推进剂长期可储存等优点, 但凝胶喷雾液滴蒸发燃烧问题却一直困扰着凝胶推进剂研制及燃烧室设计工作, 阻碍了凝胶推进剂实际工程应用.设计实现了凝胶单液滴蒸发燃烧实验系统, 通过某型有机凝胶偏二甲肼(UDMH)单液滴在四氧化二氮蒸气中的蒸发燃烧实验现象, 进一步深入分析了凝胶液滴蒸发燃烧机理.根据实验中凝胶单液滴在不同阶段的蒸发特性, 建立了有机凝胶喷雾液滴在胶凝剂膜形成、膨胀、破裂三个不同蒸发阶段的多组分蒸发模型, 采用初步选定的模型参数及物性参数对凝胶单液滴在高温气体环境中的蒸发全过程进行了仿真计算, 并与常规液体液滴的仿真结果进行了对比分析.结果表明,凝胶喷雾液滴表面胶凝剂含量在蒸发初期增加比较缓慢, 但在某临界时刻后的极短时间内迅速升高至形成胶凝剂膜的质量分数95%, 导致表面质量流率迅速下降至0,表面温度则快速上升至UDMH推进剂沸点.胶凝剂膜形成后, 液滴半径及表面UDMH蒸气质量分数出现了实验现象中凝胶液滴反复膨胀-破裂的震荡现象, 液滴表面温度维持在略高于沸点的某温度范围内,凝胶液滴内部的沸腾蒸发明显强于液体液滴表面稳态蒸发流率, 使得凝胶喷雾液滴生存时间小于常规液体液滴.     

A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments

The distribution of sizes and velocities of droplets initially formed in sprays is an important piece of information needed in the spray modelling, because it defines the initial condition of the spray droplets in the predictive calculations of the downstream two‐phase flow fields. A predictive model for the initial droplet size and velocity distributions in sprays is formulated in this study. The present model incorporates both the deterministic and the stochastic aspect of spray formation process. The deterministic aspect takes into account of the unstable wave motion before the liquid bulk breakup through the linear and nonlinear instability analysis, which provides information for the liquid bulk breakup length, the mass‐mean diameter and a prior distribution for the droplet sizes corresponding to the unstable wave growth of various wavelengths. The stochastic aspect deals with the final stage of droplet formation after the liquid bulk breakup by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub‐models are coupled together by the various source terms signifying the liquid‐gas interaction, the mass mean diameter and the prior distribution based on the instability analysis. The initial droplet size and velocity distributions are measured experimentally by phase‐Doppler interferometry for sprays generated by a planar research nozzle and a practical gas turbine airblast nozzle. For the two nozzles, the liquid bulk sheet is formed before its breakup in a coflowing air stream. It is found that the model predictions are in satisfactory agreement with the experimental data for all the cases measured. Hence the present model may be applied to a variety of practical sprays to specify the initial conditions for the spray droplets formed in practical spray systems.     

Identification of droplet burning modes in lean, partially prevaporized swirl-stabilized spray flames

Experimental and numerical investigations of single droplet burning modes in a lean, partially prevaporized swirl-stabilized spray flame are reported. In the experiment single droplet flames have been visualized by CH-PLIF and simultaneous recording of the Mie signal. Two single droplet burning modes were identified: the envelope flame is a spherical diffusion flame burning at near-stoichiometric conditions. The wake flame is a potentially lean, partially premixed flame located downstream of the droplet. The droplet burning mode is of practical relevance, since it has significant impact on NO formation due to incomplete prevaporization.The droplet burning mode is determined by the ratio of chemical and convective time scales. The convective time scale is related to the droplet slip velocity. The impact of turbulent gas phase velocity fluctuations on droplet mechanics and droplet burning is discussed, based on a previous numerical investigation. In the present study the droplet slip velocity was measured with the 3D Phase Doppler (3D-PD) technique. For the measured slip velocities and ambient conditions in the hot gas region of the spray flame, simulations of single droplet burning were performed utilizing detailed models for chemical reaction, diffusive transport and vaporization. An agreement between the droplet burning modes predicted by the simulation and the droplet burning modes observed in the experiments was found.     

Polydisperse spray diffusion flames in oscillating flow

The phenomenon of droplet clustering or grouping found when a spray of droplets is moving in an oscillating host flow field is investigated for the case of a polydisperse spray that fuels a laminar co-flow diffusion flame. A mathematical solution is developed for the liquid phase based on use of small Stokes numbers for size sections into which the polydisperse spray size distribution is divided. Droplet clustering in the oscillatory flow field is accounted for by constructing a special model for the sectional vaporization Damkohler numbers in accordance with droplet size. Combining this with a formal solution for a gas phase Schvab-Zel'dovich variable yields the means whereby flame dynamics can be described. Results calculated from this solution demonstrate that preferential droplet size behaviour (with smaller droplets tending to cluster to a greater extent and reduce the vaporization Damkohler number more than larger ones) can have a major impact on the flame dynamics through local droplet enrichment with attendant consequences on the production of fuel vapour. The dynamics of the sort of flame (over- or under-ventilated) and the occurrence of flame pinching leading to multiple flame sheets are altered under these circumstances. However, potential control of the actual initial spray polydispersity may reduce the intensity of such effects.     

Interaction between phases in the liquid–gas system

This work analyzes the equilibrium between a liquid and a gas over this liquid separated by an interface. Various gas forms exist inside the liquid: dissolved gas molecules attached to solvent molecules, free gas molecules, and gaseous bubbles. Thermodynamic equilibrium is maintained between two phases; the first phase is the liquid containing dissolved and free molecules, and the second phase is the gas over the liquid and bubbles inside it. Kinetics of gas transition between the internal and external gas proceeds through bubbles and includes the processes of bubbles floating up and bubble growth as a result of association due to the Smoluchowski mechanism. Evolution of a gas in the liquid is considered using the example of oxygen in water, and numerical parameters of this system are given. In the regime under consideration for an oxygen–water system, transport of oxygen into the surrounding air proceeds through micron-size bubbles with lifetimes of hours. This regime is realized if the total number of oxygen molecules in water is small compared with the numbers of solvated and free molecules in the liquid.     

Design and Performance of an Ultrasonic Atomization System for experimental combustion applications

Although common atomizing systems efficiently produce sprays, a range of droplet sizes is generally obtained and the distribution is often difficult to control in terms of liquid or gaseous flow rates. It is shown that an alternative system, based on ultrasonic surface instabilities, is well suited for experimental applications where all parameters have to be controlled. Technological aspects of ultrasonic atomization are described and the droplet spray produced by an ultrasonic atomizer is characterized experimentally.     

Dynamic modelling and simulation of 15N separation by chemical exchange in NO,NO2–HNO3 system

The dynamic behaviour of a ¹⁵N separation process by chemical exchange in a NO, NO₂–HNO₃ system has been analysed based on an accurate mathematical model. A nonlinear system of first-order partial differential equations was determined by considering the multiple exchange reactions between the components of the gaseous mixture and the liquid phase constituents. The mathematical model of the process describes the space–time variation of the ¹⁵N mole fraction in gas and liquid phases and provides a better understanding of operating limits and decision support in process design and optimisation.     

Auto-ignition of a polydisperse fuel spray

In the present paper, the effect of fuel spray polydispersity on the auto-ignition process in a fuel cloud is considered. In many engineering applications it is common practice to relate to the actual polydisperse spray as being equivalent to a monodisperse spray with all droplets therein having some average diameter. In combustion systems, the Sauter mean diameter (SMD) is frequently used for this purpose; it is based on the ratio between the total droplet volume and the total droplet surface area of all the droplets in the polydisperse spray. The main purpose of the current work is to examine qualitatively the dynamics of ignition of a truly polydisperse spray in a combustible gas medium and compare it with the dynamics of an equivalent monodisperse spray based on the SMD. Since the system of governing equations represents a multi-scale problem the method of integral manifolds is applied in order to extract the dynamical behavior. Preliminary computed results suggest that the use of the usual SMD-based monodisperse spray leads to quite a significant over-estimate of the ignition time. An alternative modified definition of the SMD, in which the overall liquid fuel volume is also conserved in the averaging process, reduces the discrepancy between the ignition time for the polydisperse spray and that of the equivalent monodisperse spray. However, it seems that some other sort of average droplet size needs to be determined to minimize the aforementioned discrepancy. These results highlight the care that must be exercised before dispensing with the behavior of the actual polydisperse spray in favor of that of an equivalent monodisperse spray, even at the expense of complexity.     

Analysis of combustion regimes and conditional statistics of autoigniting turbulent n-heptane sprays

DNS is performed for a statistically one dimensional layer of a spray region resembling diesel engine conditions. The group and collective combustion regimes are identified according to the ratio of the chemical and transport time scales for a single droplet. The statistics in group combustion are similar with those in gas phase combustion. The collective combustion regime involves interspersed rich regions with different dissipation characteristics. Reasonable agreements are shown with the scaled AMC model and the linear evaporation model in the ranges of meaningful probability. Initially the evaporation terms are dominant in the budgets of the conditional enthalpy equation. After ignition the chemical reaction term becomes dominant to be balanced by the time rate of change term. For modeling turbulent spray combustion it may not be essential to consider detailed micro structures around each droplet, unless in the droplet combustion regime.     

Influence of nitrogen in aluminum droplet combustion

The influence of nitrogen on the aluminum droplet combustion under forced convection conditions has been studied. An aerodynamic levitation technique of millimetric size liquid droplets heated with a CO₂ laser has been adopted to characterize the combustion of aluminum droplets and, in particular, to observe the surface phenomena. The determination of the burning rate and of the droplet temperature in several atmospheres (H₂O/O₂, H₂O/Ar, H₂O/N₂, and air) has shown that they depend only on the nature and concentration of the oxidizers (O₂ and H₂O); a comparison of experiments in nitrogen and in argon containing mixtures demonstrated that N₂ did not influence the gas phase combustion. However, for nitrogen containing atmospheres we observed the formation of solid aluminum nitride (AlN) at the droplet surface after a latency time depending on the nitrogen pressure. AlN first interacts with the oxide cap producing an aluminum oxynitride, then completely covers the droplet, and finally prevents combustion. The existence of a latency time varying with the nitrogen pressure suggests that the AlN formation is controlled by heterogeneous kinetics. The phenomenon of oxide cap regression during combustion was also observed in all gases, and it is attributed to a chemical decomposition process of alumina by aluminum forming gaseous Al_xO_y species. Therefore, nitrogen effects are significant at the droplet surface rather than in the gas phase, and it is suggested that N₂ is probably one of the main species causing the manifestation of unsteady processes during aluminum droplet burning.     

Stochastic modeling of atomizing spray in a complex swirl injector using large eddy simulation

Large-eddy simulation of an atomizing spray issuing from a gas-turbine injector is performed. The filtered Navier–Stokes equations with dynamic subgrid scale model are solved on unstructured grids to compute the swirling turbulent flow through complex passages of the injector. The collocated grid, incompressible flow algorithm on arbitrary shaped unstructured grids developed by Mahesh et al. (J. Comp. Phys. 197 (2004) 215–240) is used in this work. A Lagrangian point-particle formulation with a stochastic model for droplet breakup is used for the liquid phase. Following Kolmogorov’s concept of viewing solid particle-breakup as a discrete random process, the droplet breakup is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. The size and number density of the newly produced droplets is governed by the Fokker–Planck equation for the evolution of the pdf of droplet radii. The parameters of the model are obtained dynamically by relating them to the local Weber number and resolved scale turbulence properties. A hybrid particle-parcel is used to represent the large number of spray droplets. The predictive capability of the LES together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail by comparing it with the spray patternation study for the gas-turbine injector. The present approach is computationally efficient and captures the global features of the fragmentary process of liquid atomization in complex configurations.     

Structure of Liquid‐Sheet Sprays

Spray characteristics and their spatial distribution have been investigated experimentally for sprays generated by the breakup of thin liquid sheets in co‐flowing air streams. The spray characteristics such as droplet mean and fluctuation velocity and Sauter mean diameter have been measured by using phase Doppler anemometry under various liquid and air flow conditions at the nozzle exit. The results show that at a given spray cross section the droplet axial mean velocity has a maximum value at the spray center, and decreases towards the edge of the spray; whereas the Sauter mean diameter has a minimum value at the center and increases monotonically towards the spray periphery. Data analysis indicates that sufficiently downstream of the nozzle exit the droplet mean velocity attains a jet‐like self‐similar distribution in the transverse direction, and such universal distribution is also observed for the turbulent fluctuation velocity and turbulent intensity, although it is achieved further downstream compared to the mean velocity profile. The Sauter mean diameter at the spray center has a complex variation in the downstream direction due to secondary atomization at high air velocity near the nozzle exit and droplet entrainment, migration and possible coalescence farther downstream.     

Coupling of turbulence on the ignition of multicomponent sprays

This study examines the effect of turbulence on the ignition of multicomponent surrogate fuels and its role in modifying preferential evaporation in multiphase turbulent spray environments. To this end, two zero-dimensional droplet models are considered that are representative of asymptotic conditions of diffusion limit and the distillation limit are considered. The coupling between diffusion, evaporation and combustion is first identified using a scale analysis of 0D homogeneous batch reactor simulations. Subsequently, direct numerical simulations of homogeneously dispersed multicomponent droplets are performed for both droplet models, in decaying isotropic turbulence and at quiescent conditions to examine competing time scale effects arising from evaporation, ignition and turbulence. Results related to intra-droplet transport and effects of turbulence on autoignition and overall combustion are studied using an aviation fuel surrogate. Depending on the characteristic scale, it is shown that turbulence can couple through modulation of evaporation time or defer the ignition phase as a result of droplet cooling or gas-phase homogenization. Both preferential evaporation and turbulence are found to modify the ignition delay time, up to a factor of two. More importantly, identical droplet ignition behavior in homogeneous gas phase can imply fundamentally different combustion modes in heterogeneous environments.     

A discrete droplet transport model for predicting spray coating patterns of an electrostatic rotary atomizer

Electrostatic spray (E-spray) coating is widely used for coating conductive substrates. The combination of a high-velocity shaping air, an imposed electric field and charged droplets, leads to higher transfer efficiency than conventional spray coating. In this paper, a mathematical model of droplet transport in E-spray is presented which enables simulating the coating deposition rate profile. A dilute spray assumption (no particle–particle interactions) allows modeling single-droplet trajectories resulting from a balance of electrostatic force, drag and inertia. Atomization of liquid droplets is not modeled explicitly—rather an empirical correlation is used for the mean droplet size while individual droplet sizes and starting locations are determined using random distributions. Strong coupling requires the electrostatic field and droplet trajectories be determined iteratively by successive substitution with relaxation. The influences of bell-cup voltage and atomization constant on the coating deposition rate profile, mass transfer efficiency and droplet trajectories are also shown. Using individually predicted droplet trajectories and impact locations, a static coating deposition rate profiles is determined. For the parametric values considered in this paper, the predicted spray is a cone hollow with no deposition in the center, a heavy ring near the center, and a tapering of thickness toward the outer edge.     

Dynamic modelling and simulation of ¹⁵N separation by chemical exchange in NO, NO₂-HNO₃ system

The dynamic behaviour of a 1?N separation process by chemical exchange in a NO, NO?-HNO? system has been analysed based on an accurate mathematical model. A nonlinear system of first-order partial differential equations was determined by considering the multiple exchange reactions between the components of the gaseous mixture and the liquid phase constituents. The mathematical model of the process describes the space-time variation of the 1?N mole fraction in gas and liquid phases and provides a better understanding of operating limits and decision support in process design and optimisation.