scholarly journals The Mathematical Model for the Secondary Breakup of Dropping Liquid

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6078
Author(s):  
Ivan Pavlenko ◽  
Vsevolod Sklabinskyi ◽  
Michał Doligalski ◽  
Marek Ochowiak ◽  
Marcin Mrugalski ◽  
...  
Keyword(s):  
Practical Problem ◽  
Heterogeneous Systems ◽  
Critical Diameter ◽  
Nonstationary Process ◽  
Critical Value ◽  
Simultaneous Action ◽  
Liquid Droplets ◽  
Secondary Breakup ◽  
Spray Granulation ◽  
Breakup Time

Investigating characteristics for the secondary breakup of dropping liquid is a fundamental scientific and practical problem in multiphase flow. For its solving, it is necessary to consider the features of both the main hydrodynamic and secondary processes during spray granulation and vibration separation of heterogeneous systems. A significant difficulty in modeling the secondary breakup process is that in most technological processes, the breakup of droplets and bubbles occurs through the simultaneous action of several dispersion mechanisms. In this case, the existing mathematical models based on criterion equations do not allow establishing the change over time of the process’s main characteristics. Therefore, the present article aims to solve an urgent scientific and practical problem of studying the nonstationary process of the secondary breakup of liquid droplets under the condition of the vibrational impact of oscillatory elements. Methods of mathematical modeling were used to achieve this goal. This modeling allows obtaining analytical expressions to describe the breakup characteristics. As a result of modeling, the droplet size’s critical value was evaluated depending on the oscillation frequency. Additionally, the analytical expression for the critical frequency was obtained. The proposed methodology was derived for a range of droplet diameters of 1.6–2.6 mm. The critical value of the diameter for unstable droplets was also determined, and the dependence for breakup time was established. Notably, for the critical diameter in a range of 1.90–2.05 mm, the breakup time was about 0.017 s. The reliability of the proposed methodology was confirmed experimentally by the dependencies between the Ohnesorge and Reynolds numbers for different prilling process modes.

Simulation of Impaction Between Liquid Droplet and Solid Particles Based on SPH Method

2014 ◽  
Author(s):  
Shuai Meng ◽  
Qian Wang ◽  
Rui Yang
Keyword(s):  
Surface Tension ◽  
Solid Particle ◽  
Liquid Droplet ◽  
Particle Interaction ◽  
Solid Particles ◽  
Seed Particle ◽  
Liquid Droplets ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Spray Granulation

The phenomenon of impaction between liquid droplets and solid particles is involved in many scientific problems and engineering applications, such as impaction between sprayed droplet and solid particles in limestone injection desulfurization system and the collision between a droplet of the liquid to be granulated and a seed particle in fluidized bed spray granulation process. There are a lot of factors affected this phenomenon: droplet and particle size, momentum of both liquid droplet and solid particles, materials, surface conditions of the solid particles and so on. However the experimental or numerical researches have been done mostly pay attention to Specific application or process, so the impaction phenomenon has not been through studied, for example how different factors affected the impaction process with its effect on different applications. This paper focuses on the basic issue of interaction between droplet and solid particles. Three main factors were considered: ratio of diameter between the droplet and solid particle, relative velocity and the surface tension (including the contact angle between droplet and solid particle). All the study is based on simulation using SPH (smoothed particle hydrodynamics) method, and the surface tension is simulated by particle-particle interaction.

Experimental Study of Spray Penetration under High Pressure Common Rail Condition

2011 ◽  
Vol 347-353 ◽  
pp. 66-69
Author(s):  
Jian Xin Liu ◽  
Song Liu ◽  
Hui Yong Du ◽  
Zhan Cheng Wang ◽  
Bin Xu
Keyword(s):  
High Pressure ◽  
High Speed ◽  
Injection Pressure ◽  
Electronic System ◽  
Common Rail ◽  
Spray Penetration ◽  
Jet Breakup ◽  
Secondary Breakup ◽  
Breakup Time ◽  
High Pressure Common Rail

The fuel spray images were taken with an equipment (camera-flash-injection) which has been synchronized with a purpose made electronic system under the condition of the high pressure common rail in two injection pressure has been expressed in this paper. It is discovered when fitting spray tip penetration that after jet breakup for a period of time, the spray tip begin to slow down rapidly, and the speed of spray tip running becomes smooth. Hiroyasu and other traditional tip penetration fitting formula are fitting larger to this phase. This is because that after jet breakup, the secondary breakup of striker particles will occur under the influence of the aerodynamic, surface tension and viscosity force. Therefore, a spray penetration fitting formula containing secondary breakup time to fit penetration in three sections was proposed in this paper. Results show that when pressure difference increase, both first and second breakup time become earlier. The former is because of gas-liquid relative velocity increasing, while the latter is due to high speed interface movement acceleration increasing.

Effect of Non-Isothermal Conditions on Liquid Breakup Mechanisms

2010 ◽  
Author(s):  
Ilai Sher
Keyword(s):  
Physical Properties ◽  
Fuel Injection ◽  
Thermal Exposure ◽  
Ambient Air ◽  
Combustible Mixture ◽  
Liquid Droplets ◽  
Gas Temperature ◽  
Fuel Droplets ◽  
Breakup Mechanism ◽  
Secondary Breakup

Liquid breakup mechanism utilization is prevalent in numerous applications. One of the most common uses of this phenomenon is in fuel injection systems. Liquid fuel is injected into an ambient air, to prepare a combustible mixture. Generally, evenly spread tiny fuel droplets are desirable. This is usually achieved through multiple liquid breaking mechanisms: Primary breakup of liquid jet, Secondary breakup of travelling liquid droplets, and Secondary breakup of wall-impinging liquid droplets. Indeed, many studies are devoted to the modelling of those phenomena. However, the absolute majority of those studies are limitedly focused on the isothermal case, where liquid is assumed to be of ambient gas’ temperature. Conversely, practical conditions, under which rather cold fuel is normally injected into hot ambient air, suggest the real case to be non-isothermal. Moreover, the non-isothermal nature of that process seems to have its effect at the most relevant to breakup regions, i.e. the breaking interfacial surfaces. It is shown that as these surfaces can be in instant contact with a hot ambient, breakup can be greatly altered by the extent of this sudden thermal exposure, through its mostly transient and even spatial effect on physical properties of breaking interfaces. This is shown to be of significant effect on all breakup mechanisms: primary and secondary. New models are suggested for these non-isothermal phenomena, which combine transient heat-transfer with inter-phase hydrodynamic breakup, through physical properties’ dependency on temperature. Results are discussed in terms of effect on spray breakup products, and a careful comparison with the trend of a limited number of so-far available experimental results is presented.

Secondary Breakup of Electrically Charged Newtonian Drops

2007 ◽  
Author(s):  
Daniel R. Guildenbecher ◽  
Paul E. Sojka
Keyword(s):  
Experimental Investigation ◽  
Relaxation Time ◽  
Surface Stress ◽  
Weber Number ◽  
High Speed ◽  
Drop Breakup ◽  
Air Stream ◽  
Secondary Breakup ◽  
Breakup Time ◽  
Electrically Charged

An experimental investigation was conducted to determine the secondary breakup morphology of electrically charged drops. Movies of drop breakup in a high speed air stream were recorded for drops charged between 0 and 60% of the Rayleigh charge limit. The conventional Weber number was found to be insufficient to classify the breakup morphology of charged drops. Rather an electrostatic Weber number was defined to account for the presence of the electrostatic surface stress. When the electrostatic Weber number was used in place of the classical Weber number, the observed breakup morphology was found to be similar to that proposed by previous researchers for uncharged drops. It is therefore concluded that secondary breakup of electrically charged drops can be characterized using the wealth of available literature on uncharged Newtonian drops, provided the electrostatic Weber number is used, and that the charge relaxation time is much smaller than the breakup time.

Gravitationsinstabilitäten eines Plasmas bei differentieller Rotation

1967 ◽  
Vol 22 (4) ◽  
pp. 431-437
Author(s):  
R. Ebert
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Wave Length ◽  
Critical Value ◽  
Unstable Wave ◽  
Simultaneous Action ◽  
Axially Symmetric ◽  
Gas Density ◽  
Axis Of Rotation ◽  
The Magnetic Field

In this paper an instability calculation is given for an axially symmetric gas distribution which has a differential rotation and in which a magnetic field is present. It is a generalization of similar calculations given by CHANDRASEKHAR and BEL and SCHATZMAN. The generalization becomes necessary for the study of problems of the formation of planetary systems, and star formation.The instability conditions and the critical wave lengths are calculated for plane-wave-like disturbances. For disturbances running perpendicularly to the axis of rotation instability can occur only if the gas density exceeds a critical value which depends on the differential rotation at the considered distance only as long as pressure gradients and gradients of the magnetic field strength are negligible. If the gas density exceeds this critical value the shortest unstable wave length is proportional to the square root of vT2+vB2, where vT means the velocity of sound and vB the ALFVÉN-velocity.For disturbances running parallel to the axis of rotation in addition to the JEANS instability a new type of instability occurs due to the simultaneous action of the magnetic field and the differential rotation; for rigid rotation this instability vanishes.

Tensile Strength of the Aorta can be Estimated From Mechanical Parameters Which Depends on Degree of Intramural Collagen Fiber Alignment

2013 ◽  
Author(s):  
Shukei Sugita ◽  
Takeo Matsumoto
Keyword(s):  
Collagen Fiber ◽  
Critical Diameter ◽  
Critical Value ◽  
Aneurysm Rupture ◽  
Aortic Aneurysms ◽  
Reliable Prediction ◽  
Fiber Alignment ◽  
Aneurysmal Wall ◽  
Local Strength ◽  
Risk Of Rupture

Aortic aneurysms larger than a critical value, ∼50 mm for example, have high risk of rupture due to the Laplace’s law. However, aneurysms smaller than the critical diameter sometimes rupture (1, 2). Since intramural stress is relatively low in smaller aneurysms, their rupture indicates weakening of aneurysmal wall. For more reliable prediction of risk of aneurysm rupture, therefore, local strength of aneurysmal wall should be obtained.

scholarly journals The surface as a limiting factor in the slow combustion of hydrocarbons

1940 ◽  
Vol 176 (967) ◽  
pp. 429-448 ◽  
Keyword(s):  
Reaction Rate ◽  
Critical Diameter ◽  
Vessel Diameter ◽  
Critical Value ◽  
Limiting Factor ◽  
Slow Combustion ◽  
Hydrocarbon Oxidations ◽  
Reaction Vessels ◽  
Considerable Range ◽  
Effect Of Surface

With special reaction vessels, varying widely in diameter while maintaining approximately constant volume, and employing several refinements in technique, a study has been made of the effect of surface on the slow oxidation of several hydrocarbons, both saturated and unsaturated. All reactions were of the degenerate branching type, and were found to be principally homogeneous in character. When the diameter of the reaction vessel was sufficiently reduced, the reaction rate was observed to drop abruptly toward zero, while the corresponding induction period increased toward infinity. Data so obtained have demonstrated that in narrow vessels surface deactivation can predominate over other processes of deactivation, while in wider vessels surface and volume deactivation occur to a comparable extent over a considerable range of pressure. When the vessel diameter is decreased to a critical value, the surface deactivation almost alone can suppress the factors leading to chain branching, and from the reactions investigated the existence of such a critical diameter appears to be a general property of hydrocarbon oxidations in conformity with the theory of degenerate branching.

AEM analysis of solidification catalysts in atomized Fe-Ni

1986 ◽  
Vol 44 ◽  
pp. 584-585
Author(s):  
Matthew R. Libera
Keyword(s):  
Powder Particle ◽  
Alloy Composition ◽  
Particle Diameter ◽  
Metastable Phases ◽  
Liquid Droplets ◽  
Nucleation Kinetics ◽  
Ni Alloys ◽  
Nonequilibrium Solidification

The liquid droplets produced by atomization processes are believed to undergo substantial supercooling during solidification, because the catalytic heterogeneities, for statistical reasons, tend to be isolated in the larger droplets. This supercooling can lead to the nucleation of metastable phases. As part of a study on the effect of liquid supercooling on nonequilibrium solidification, three binary Fe-Ni alloys have been produced by conventional argon atomization (Fe-20Ni, Fe-30Ni, and Fe-40Ni). The primary variables in these experiments are: i) the alloy composition; and ii) the powder particle diameter (inversely proportional to supercooling). Of particular interest in this system is the competitive nucleation kinetics between the stable fee and metastable bec phases. Bcc is expected to nucleate preferentially with decreasing %Ni and decreasing particle diameter.

HREM observation of NiO growth on submicron spheres of pure nickel

1989 ◽  
Vol 47 ◽  
pp. 548-549
Author(s):  
C.M. Teng ◽  
T.F. Kelly ◽  
J.P. Zhang ◽  
H.M. Lin ◽  
Y.W. Kim
Keyword(s):  
Nickel Oxide ◽  
Grain Boundaries ◽  
Pure Nickel ◽  
Submicron Particles ◽  
Crystal Formation ◽  
Nickel Wire ◽  
Liquid Droplets ◽  
Oxide Interface ◽  
Nickel Chromium ◽  
Chromium Alloys

Spherical submicron particles of materials produced by electrohydrodynamic (EHD) atomization have been used to study a variety of materials processes including nucleation of alternative crystallization phases in iron-nickel and nickel-chromium alloys, amorphous solidification in submicron droplets of pure metals, and quasi-crystal formation in nickel-chromium alloys. Some experiments on pure nickel, nickel oxide single crystals, the nickel/nickel(II) oxide interface, and grain boundaries in nickel monoxide have been performed by STEM. For these latter studies, HREM is the most direct approach to obtain particle crystal structures at the atomic level. Grain boundaries in nickel oxide have also been investigated by HREM. In this paper, we present preliminary results of HREM observations of NiO growth on submicron spheres of pure nickel.Small particles of pure nickel were prepared by EHD atomization. For the study of pure nickel, 0.5 mm diameter pure nickel wire (99.9975%) is sprayed directly in the EHD process. The liquid droplets solidify in free-flight through a vacuum chamber operated at about 10-7 torr.

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