Droplets and Sprays

Spray characteristics play an important role in determining efficiency of gas turbine, rocket combustors and internal combustion engines. Droplet atomization and break-up forms the fundamental building block in many spray-based applications. Detailed analysis of the internal and the near-nozzle flow of fuel injectors is a necessity for a comprehensive understanding of any internal combustion engine performance. Understanding turbulence is one of the most difficult topics in science and engineering. In liquid fuelled combustion, the interaction of spray droplets with surrounding turbulent air flow is crucial since it influences the evaporation rate of the fuel droplets and the process of air and fuel vapour mixture preparation. For detail understanding on the droplet–turbulence interaction mechanisms as well as to validate numerical simulations of sprays, simultaneous measurement of both dispersed and carrier phases of the spray is essential. Turbulent spray combustion involves many areas of physics and chemistry, which accompany a variety of mathematical challenges. This monograph deals with all above aspects to enhance the understanding of spray characteristics involved with different applications.

The goal of modeling dispersed multiphase flows is to predict spatial distributions of the volume fraction, velocities and other properties of interest of the dispersed and continuous phases in geometries of practical interest. In this chapter we summarize key advances that have enabled progress towards this goal by starting with the development of interphase momentum transfer models for flow past single particles with a view to extending them to multiparticle systems. Particle-resolved direct numerical simulation of microscale (particle scale) phenomena has emerged as a powerful tool to propose statistical models for mesoscale and macroscale simulations of dispersed multiphase flow. Key advances in modeling of interphase momentum as well as particle and fluid velocity fluctuations are briefly reviewed. Building on this foundation we examine deterministic models for multiparticle effects that are based on the generalized Faxén theorem which provides a rigorous theoretical foundation for their development. In particular, the recently proposed pairwise interaction extended point-particle (PIEP) model is presented as a means of systematically including fluid-mediated particle-particle interactions in a deterministic framework. The performance of the PIEP model is assessed in different validation tests. Although the deterministic modeling approach provides physical insight and mechanistic interpretation of model terms, its limitation is it does not fully account for all the fluctuations that occur at the microscale. Therefore it is important to complement the deterministic model with a stochastic component to properly account for the statistical variability that is naturally present in all dispersed multiphase flows. We review key advances in statistical modeling of dispersed multiphase flows in terms of both the two-fluid theory as well as the Euler-Lagrange approach, with an emphasis on the latter, where we consider both Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) descriptions of the carrier phase. Finally, we propose a new paradigm for modeling dispersed multiphase flows that effectively combines the best elements of the deterministic and statistical modeling approaches as the most promising direction for development of predictive models.

The modelling of droplet heating and evaporation has been extensively studied since the beginning of the last century, and the results have been summarised in numerous reviews and monographs including. These studies have been mainly motivated by engineering, environmental and pharmaceutical applications of the results of this modelling.

This chapter provides a brief review of primary atomization mechanisms in spray nozzle relevant to the propulsive devices. Attention which focused on experimental efforts has been made in understanding the primary atomization. Primary atomization involved in two widely used class of nozzles namely, pressure jet and twin-fluid (air-assist) atomizer is explicitly considered.

Spray characteristics play an important role in determining efficiency of gas turbine or rocket combustors. The breakup of liquid jet is a complex nonlinear process governed by the fundamentals of well-known instabilities like Rayleigh instability and Kelvin–Helmholtz instability. Current availability of powerful computing tools has made computational fluid dynamics (CFD) along with other analytical and numerical techniques a viable tool for the design of combustors which reduced the requirement of expensive experimental studies in the design process. In this chapter, we demonstrate a system which incorporates a liquid jet that breaks up in the presence of a strong swirling field and sandwiched between two swirling air flow streams. Our work includes computational fluid dynamics, analytical technique (linear stability), and statistical tool (entropy formulation) to model the spray characteristics in the form of breakup length and droplet distribution from nozzle geometry and inlet kinematic conditions. The internal hydrodynamics of the nozzle is modeled in commercial software named Ansys. The output of this simulation in the form of flow kinematics is used to estimate the growth rate of instability associated with atomization using a linear stability analysis. The breakup length which is a function of this growth rate is found to closely match with experimental values. A statistical method known as maximum entropy formulation (MEF) is further used with inputs as the breakup length and a mean diameter value (obtained from linear stability analysis) to estimate the droplet diameter distribution. Thus, a comprehensive model is described in this chapter which is a useful prediction tool for spray characteristics and hence is a significant contribution to the spray and droplet community.

Detailed analysis of the internal and the near-nozzle flow of fuel injectors is a necessity for a comprehensive understanding of any internal combustion engine performance. For gasoline direct injection engines, under part-load conditions, the in-cylinder pressure can be subatmospheric when the high-temperature fuel is injected, resulting in flash boiling. Detailed experimental characterization of such complex phenomena is extremely difficult. Three-dimensional computational fluid dynamics (CFD) simulations provide key insights into the flash boiling phenomena. The Spray G injector from Engine Combustion Network (ECN) has been considered for this study, which has eight counter-bored holes. Homogeneous relaxation model is used to capture the rate of phase change. Standard and RNG \(k-\epsilon \) turbulence models have been employed for modeling turbulence effects. Based on apriori thermodynamic estimates, three types of thermodynamic conditions have been explored: non-flashing, moderate flashing, and intense flashing. Numerical analyses showed that with more flashing the spray plumes grow wider due to the volume expansion of the rapidly forming fuel vapor. Mainly single-component fuel is studied in this work. Iso-octane is considered as the gasoline surrogate for this study. Binary component blends of isooctane and ethanol were also tested for blended fuel flashing predictions using the existing numerical setup. After careful estimation of blended fuel saturation properties, the simulations indicated that blended fuels can be more volatile than the individual components and thus exhibit more flashing compared to the cases with single-component fuels.

A spray nozzle which can produce extremely small droplet size (≤10 μm) finds relevance in drying, liquid-fueled engines, etc. In addition to the droplet size, its momentum too has equal importance in high-speed combustion systems like scramjets, pulse detonation engines for rapid mixing. Many of the nozzles which adopt standalone techniques (pressure, air-assist) fail to produce finer size droplets. Efforts have been made to hybridize two or more techniques to achieve the finer atomization. For instance, standard air-assist atomizer can be combined with effervescent/ultrasonic means to achieve further reduction in droplet size. This chapter presents the comprehensive aspects of such type of hybrid atomizers. Features such as mode of operation, benefits, shortcomings, areas of application are discussed in greater details.

Gas turbines have wide applications as prime movers in transportation and power-generating sectors, most of which are currently driven by fossil fuels. The problem of air pollution can be associated with the use of conventional fuels, and their prolonged use has caused the fuel reserves to get depleted gradually. The addition of ethanol in conventional fossil fuel leads to better spraying characteristics and decreases air pollution as well. The present work is done for knowing the spray characteristics of pure kerosene, pure ethanol, and ethanol-blended kerosene (10 and 20% ethanol-blended kerosene by volume) by using a hybrid atomizer. The novelty of the hybrid atomizer lies in the fact that the fuel stream is sandwiched between two annular air streams. Tangential inlets are used for both fuel and air stream; however, the inner air stream can be used in axial configuration. A high swirling effect is produced outside the nozzle due to the tangential inlet of the flow direction. The direction of the fuel flow and both the air streams in the atomizer may be configured in the same direction or in opposite directions, respectively. The inner and outer air flow rates are varied continuously. Here, backlight imaging technique is used for capturing the spray images. Various spray breakup regimes like distorted pencil, onion, tulip, and fully developed spray regimes have been observed. The breakup length, cone angle, and sheet width of the fuel stream are analyzed from the images for different fuels and air flow rates. It is observed that breakup length decreases for ethanol-blended kerosene due to low viscosity of ethanol. It is also observed that at higher air flow rate, breakup length decreases due to turbulent nature of the fuel stream.

In liquid-fueled combustion, the interaction of spray droplets with surrounding turbulent air flow is crucial since it influences the evaporation rate of the fuel droplets and the process of air and fuel vapor mixture preparation. For detail understanding on the droplet-turbulence interaction mechanisms as well as to validate numerical simulations of sprays, simultaneous measurement of both dispersed and carrier phases of the spray is essential. This way the vortical interaction of droplets can be fully characterized such that important issues such as local spray unsteadiness and spatiotemporal inhomogeneity of droplet concentration due to droplet clustering and group evaporation of droplets can be addressed. This review focuses on the advances in the optical diagnostics (especially the planar techniques) in the last few decades to meet these requirements. Due to broad size and velocity distributions of spray droplets, the application of the two-phase measurement techniques to sprays encounters challenges especially in phase discrimination. Additionally, for sprays, it is not sufficient to simultaneously measure two-phase velocities but the droplet size is also important since the dynamic drag on droplets is according to their size and velocity relative to the surrounding gas flow. The techniques with such capability are explored. The sources of uncertainty and advantages and limitations of different two-phase measurement approaches are analyzed according to their application to dense and dilute sprays.

Understanding turbulence is one of the most difficult topics in science and engineering. This is because turbulent spray combustion involves many areas of physics and chemistry which accompany a variety of mathematical challenges. Defining the various length and timescales existing in turbulent flow provides a better way to understand and characterize this chaotic phenomenon. However, the degree of complexity increases when there is a strong interaction between turbulence flow and chemistry. Here, characteristic times of chemical reaction in a molecular level (chemical) and fluid-mechanic level (physical) determine which of these are more dominant. This interaction remains as one of the most important and challenging aspects of turbulent reacting spray. In the present chapter, we begin with a general discussion on turbulence. The following section covers description of key features involved in a spray combustion scenario. Concepts involving higher fidelity in description of turbulent combustion are covered by discussion of interaction of turbulence and combustion. In most actual spray combustion applications, the combustion is dominantly non-premixed. There is a minor aspect of premixed combustion too which are discussed in this chapter. New advanced combustion modes such as partially premixed combustion (PPC) and multiple injections, topics with growing interests, are introduced and discussed later. Finally, numerically simulating these aspects is a key area of combustion research. It is of utmost important to optimize the combustion system using computer-based simulations to avoid higher cost for experimentally parametric study. Reynolds-averaged Navier–Stokes (RANS) models are mostly used in commercial sector for computationally tractable simulation time. Large-eddy simulation (LES) offers a higher fidelity approach. With the advent of higher computational resources, LES approaches are becoming more popular for obtaining solutions of turbulent combustion. Aspects of both RANS and LES relevant to spray combustion scenarios are discussed. Although usually requiring very high computational power, direct numerical simulation (DNS) can provide an actual representative of many chemical and physical aspects of spray combustion such as evaporation and auto-ignition, which are discussed at the end of this chapter.

The advancement of high-performance computing has made computational fluid dynamics (CFD) simulations a viable alternative to expensive experimentation. Most industrial flows are innately turbulent, and the modelling of turbulent flow remains a challenging task. This complexity is augmented in turbulent droplet combustion simulations by the complex interaction of heat and mass transfer associated with evaporation, fluid dynamics, combustion and heat release. As a result of this, the fidelity of CFD simulations of turbulent reacting flows remains sensitive to the accuracy of the combustion modelling, which principally focuses on the prediction of mean chemical reaction and heat release rates. The closure of the mean reaction rate in the context of Reynolds-averaged Navier–Stokes (RANS) simulations in the combustion of turbulent droplet-laden mixtures often requires the knowledge of the variances of the fuel mass fraction \( {\text{Y}}_{\text{F}} \) fluctuations \( \left( {\widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }}} \right) \), the mixture fraction \( \upxi \) fluctuations \( \left( {\widetilde{{\upxi^{{{\prime \prime }\,2}} }}} \right) \) and co-variance \( \left( {\widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }}} \right) \), where \( {\bar{\text{q}}} \), \( {\tilde{\text{q}}} = \overline{{\uprho{\text{q}}}} /{\bar{\uprho }} \) and \( {\text{q}}^{{\prime \prime }} = {\text{q}} - {\tilde{\text{q}}} \) are Reynolds average, Favre mean and Favre fluctuation of a general quantity q and \( \uprho \) is the gas density. Algebraic and transport equation-based closures of \( \widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }} \), \( \widetilde{{\upxi^{{{\prime \prime }\,2}} }} \) and \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) have previously been considered in the context of purely gaseous phase combustion where variations in equivalence ratio exist. Whilst limited effort has been directed to the modelling of the fuel mass fraction variance \( \widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }} \) and mixture fraction variance \( \widetilde{{\upxi^{{{\prime \prime }\,2}} }} \) for turbulent combustion in droplet-laden mixtures, the statistical behaviour of \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) and its transport in turbulent spray flames are yet to be considered in detail. Furthermore, the validity of existing closures for \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) and the unclosed terms of its transport equation, which were originally proposed for purely gaseous phase combustion, are yet to be assessed for turbulent spray flames. These gaps in the existing literature are addressed by analysing the statistical behaviours of \( \widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }} \), \( \widetilde{{\upxi^{{{\prime \prime }\,2}} }} \) and \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) as well as the terms of their transport equations using a three-dimensional compressible Direct Numerical Simulation (DNS) database of statistically planar turbulent flames propagating into droplet-laden mixtures where the fuel is supplied in the form of monodisperse droplets ahead of the flame. This chapter focuses on the effects of droplet diameter \( {\text{a}}_{\text{d}} \) and droplet equivalence ratio \( \phi_{\text{d}} \) (i.e. fuel in liquid droplets to air ratio by mass, normalized by fuel-to-air ratio by mass under stoichiometric conditions) on the statistical behaviours of \( \widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }} \), \( \widetilde{{\upxi^{{{\prime \prime }\,2}} }} \) and \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) and their transport in detail. Furthermore, the validity of the existing models for the unclosed terms of \( \widetilde{{{\text{Y}}_{\text{F}}^{{{\prime \prime }\,2}} }} \), \( \widetilde{{\upxi^{{{\prime \prime }\,2}} }} \) and \( \widetilde{{{\text{Y}}_{\text{F}}^{{\prime \prime }}\upxi^{{\prime \prime }} }} \) transport equations, which were originally proposed for gaseous stratified mixture combustion, has been assessed for turbulent combustion in droplet-laden mixtures. Based on this exercise, either the modification of existing models has been suggested or new models are proposed, wherever necessary, based on the physical insights extracted from DNS data.

Droplet break-up and atomization is ubiquitous in a plethora of industrial applications. Typical spray-based industrial processes such as surface coating, drying, ink-jet printing, powder and food processing involve a cluster of droplets or sprays exposed to specific environmental conditions (James et al. 2003; Basu et al. 2012). The fate of each drop is determined by various forces acting upon it which usually causes severe deformation and disintegration of the droplets. Interactions between multiple drops with the gas phase lead to drop collision, coalescence, and break-up, which determine the final drop size distribution in the spray.

Thermoacoustic instability is a plaguing problem in confined combustion systems, where self-sustained periodic oscillations of ruinous amplitudes that cause serious damage and performance loss to propulsive and power generating systems occur. In this chapter, we review the recent developments in understanding the transition route to thermoacoustic instability in gaseous combustion systems and describe a detailed methodology to detect this route in a two-phase flow combustion system. Until now, in these combustion systems, the transition to such instabilities has been reported as Hopf bifurcation, wherein the system dynamics change from a state of fixed point to limit cycle oscillations. However, a recent observation in turbulent gaseous combustion system has shown the presence of intermittency that precedes the onset of thermoacoustic instability. Intermittency is a dynamical state of combustion dynamics consisting of a sequence of high amplitude bursts of periodic oscillations amidst regions of relatively low amplitude aperiodic oscillations. Here, we discuss the process of transition to thermoacoustic instability in the two-phase flow system due to change in the control parameter, a location of flame inside the duct. As the flame location is varied, the system dynamics is observed to change from a region of low amplitude aperiodic oscillations to high amplitude self-sustained limit cycle oscillations through intermittency. The maximum amplitude of such intermittent oscillations witnessed during the onset of intermittency is much higher than that of limit cycle oscillations. We further describe the use of various tools from dynamical systems theory in identifying the type of intermittency in combustion systems.