On spray formation
TL;DR: In this paper, the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface are depicted and analyzed, showing that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid.
Abstract: We depict and analyse the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface. Experiments performed with various liquids in a fast air flow show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh–Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets.
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TL;DR: A review of the fundamental and technological aspects of these subjects can be found in this article, where the focus is mainly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science.
Abstract: Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects
1,583 citations
TL;DR: In this article, Zhou et al. presented the initial condition dependence of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) mixing layers, and introduced parameters that are used to evaluate the level of mixedness and mixed mass within the layers.
606 citations
TL;DR: In this article, a simulation of primary atomization of liquid injected at high speed into still air is investigated to elucidate physical processes by direct numerical simulation, where ligament and droplet formation can be captured in a physically sound way.
392 citations
TL;DR: Stochastic simulation of the liquid jet depletion in the framework of fragmentation under scaling symmetry and primary atomization in terms of Reynolds-averaged Navier-Stokes (RANS) mixing with a strong variation of density are highlighted.
Abstract: This review concerns recent progress in primary atomization modeling. The numerical approaches based on direct simulation are described first. Although direct numerical simulation (DNS) offers the potential to study the physical processes during primary atomization in detail, thereby supplementing experimental diagnostics, it also introduces severe numerical challenges. We outline these challenges and the numerical methods to address them, highlighting some recent efforts in performing detailed simulation of the primary atomization process. The second part is devoted to phenomenological models of primary atomization. Because earlier conventional models of breakup are well reported in the available literature, we highlight only two recent developments: (a) stochastic simulation of the liquid jet depletion in the framework of fragmentation under scaling symmetry and (b) primary atomization in terms of Reynolds-averaged Navier-Stokes (RANS) mixing with a strong variation of density.
384 citations
TL;DR: In this paper, a review of the early atomization step of liquid spray can be found, where the main instability mechanisms, which control primary breakup processes, are rather well described, as well as the significant parameters they depend on.
Abstract: The production of a liquid spray can be summarized as the succession of the following three steps; the liquid flow ejection, the primary breakup mechanism and the secondary breakup mechanism. The intermediate step—the primary breakup mechanism—covers the early liquid flow deformation down to the production of the first isolated liquid fragments. This step is very important and requires to be fully understood since it constitutes the link between the flow issuing from the atomizer and the final spray. This paper reviews the experimental investigations dedicated to this early atomization step. Several situations are considered: cylindrical liquid jets, flat liquid sheets, air-assisted cylindrical liquid jets and air-assisted flat liquid sheets. Each fluid stream adopts several atomization regimes according to the operating conditions. These regimes as well as the significant parameters they depend on are listed. The main instability mechanisms, which control primary breakup processes, are rather well described. This review points out the internal geometrical nozzle characteristics and internal flow details that influence the atomization mechanisms. The contributions of these characteristics, which require further investigations to be fully identified and quantified, are believed to be the main reason of experimental discrepancies and explain a lack of universal primary breakup regime categorizations.
350 citations
References
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01 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Abstract: Office hours: MWF, immediately after class or early afternoon (time TBA). We will cover the mathematical foundations of probability theory. The basic terminology and concepts of probability theory include: random experiments, sample or outcome spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in statistics. Theoretical concepts are introduced via interesting concrete examples. In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications in Chapter 2. I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in lectures that are not treated in Ross. You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any.
10,221 citations
"On spray formation" refers background in this paper
...This final distribution is a gamma distribution (Feller 1971) pB(x) = nn (n) xn−1 e−nx, (5.3) with x = d/〈d〉, and 〈d〉 = nξb....
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...This final distribution is a gamma distribution (Feller 1971)...
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TL;DR: In this article, it was shown that when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa.
Abstract: It is shown that, when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa. The relationship between the rate of development of the instability and the length of wave-like disturbances, the acceleration and the densities is found, and similar calculations are made for the case when a sheet of liquid of uniform depth is accelerated.
2,839 citations
TL;DR: In this paper, Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of an air stream, and (c) emulsification in a turbulent flow are studied.
Abstract: The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished.
The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group NWe and a viscosity group NVi. Breakup occurs when NWe exceeds a critical value (NWe)crit. Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow.
It is shown that (NWe)crit depends on the type of deformation and on the flow pattern around the globule. For case (a) (NWe)crit shows a minimum value ∼ 0.5 at a certain value of (NVi) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) (NWe)crit varies between 13 and ∞, depending on NVi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and Nvi→0. For case (c) (NWe)crit, which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of NVi appear to be small. A formula is derived for the maximum drop size.
2,196 citations
"On spray formation" refers background in this paper
...The critical Weber number above which the droplet disintegrates is about 10 (Hanson, Domich & Adams 1963) and somewhat smaller when the destabilizing flow is turbulent (Hinze 1955)....
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