Modelling of unsteady combustion regimes for polydisperse fuels—I. Instability and auto-oscillations

Buyevich, Yu.A.; Korolyova, N.A.; Natalukha, I. A.

doi:10.1016/s0017-9310(05)80153-x

Cited by 17 publications

(9 citation statements)

References 3 publications

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“…When considering different industrial applications of the aforementioned processes, an important question arises about the stability of solutions. Therefore, the dynamical and/or morphological stability analysis should be carried out in the spirit of works [27][28][29][30]. Such a theory represents a challenging problem for future investigations in different applications of the phase transformation phenomena.…”

Section: Resultsmentioning

confidence: 99%

Phase transformations in metastable liquids combined with polymerization

Ivanov

Аlexandrova

Alexandrov

2019

Phil. Trans. R. Soc. A.

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This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space–time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

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Section: Resultsmentioning

confidence: 99%

Phase transformations in metastable liquids combined with polymerization

Ivanov

Аlexandrova

Alexandrov

2019

Phil. Trans. R. Soc. A.

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“…By analogy, when dealing with the crystallization of a supersaturated solution, we have w = ∆C/∆C 0 , where ∆C and ∆C 0 stand for the current and initial supersaturations. Note that in the case of boiling of a superheated liquid and combustion of a polydispersed fuel, w can be defined as the dimensionless superheating of the medium [25,26,30,46,47], and in the case of dissolution of dispersed solids, w is described by the dimensionless undersaturation of the liquid [31][32][33].…”

Section: The Modelmentioning

confidence: 99%

“…Then the boundary conditions (46) become Z(0) − v 0 Z (0) = 0 and Z(z 0 ) = 0. Taking this into account and using the method of variables separation, we get the eigenfunctions Z j (z) and equation for eigenvalues m j as follows Z j (z) = 2m j v 0 cos(m j z) + sin(m j z) exp z 2v 0 , 2m j v 0 cos(m j z 0 ) + sin(m j z 0 ) = 0, j = 0, 1, 2, .…”

Section: Kinetic Equation Of the Second Order With A Sink Of Crystalsmentioning

confidence: 99%

Evolution of a Polydisperse Ensemble of Spherical Particles in a Metastable Medium with Allowance for Heat and Mass Exchange with the Environment

et al. 2022

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Motivated by a wide range of applications in various fields of physics and materials science, we consider a generalized approach to the evolution of a polydisperse ensemble of spherical particles in metastable media. An integrodifferential system of governing equations, consisting of a kinetic equation for the particle-size distribution function (Fokker–Planck type equation) and a balance equation for the temperature (concentration) of a metastable medium, is formulated. The kinetic equation takes into account fluctuations in the growth/reduction rates of individual particles, the velocity of particles in a spatial direction, the withdrawal of particles of a given size from the metastable medium, and their source/sink term. The heat (mass) balance equation takes into account the growth/reduction of particles in a metastable system as well as heat (mass) exchange with the environment. A generalized system of equations describes various physical and chemical processes of phase transformations, such as the growth and dissolution of crystals, the evaporation of droplets, the boiling of liquids and the combustion of a polydisperse fuel. The ways of analytical solution of the formulated integrodifferential system of equations based on the saddle-point technique and the separation of variables method are considered. The theory can be applied when describing the evolution of an ensemble of particles at the initial and intermediate stages of phase transformation when the distances between the particles are large enough, and interactions between them can be neglected.

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“…While several products such as asphalt, lubricating oil base stock (LOBS), etc are all derived from crude oil residue, decant oil from FCCU is mostly used as fuel oil. Carbon black is produced by similar high temperature combustion processes (Buyevich et al, 1993a), thereby becoming a ready product of it. There is a high demand for carbon black for applications such as production of tyres, reenforcement of natural as well as synthetic rubbers for different uses, high performance coatings, manufacture of graphite and also in plastics manufacture to mention a few.…”

Section: Figure 1 Carbon Black Furnace Reactor (Verlags 1986)mentioning

confidence: 99%

Simulation of an Industrial Carbon Black Reactor Using Collision Kinetics

Igbagara¹

2021

EJPS

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Purpose: Objective of the work was to test efficacy of the proposed flame chemistry and collision kinetics for prediction of process parametres through determination of the effect of basic process parameters on yield (which includes but not limited to grade of carbon black produced). Methodology: The research methodology in this work was simulation of an industrial Carbon Black Reactor based on reaction kinetics from flame chemistry which assumes that primary particle formation and particle growth is strictly by collision of molecular nuclei with gas molecule as proposed by the collision theory. Decant oil from the Fluid Catalytic Cracking Unit (FCCU) of the Warri Refinery and Petrochemical Company Limited of Nigeria represented by naphthalene was used as feedstock in the simulation while methane gas is the fuel for combustion needed to attain the reaction temperature. Findings: Results showed an excellent quantitative prediction of trends by models. Qualitative predictions gave far higher parameter values, something easily attributable to the excessively high values of kinetic data used for model testing. Recommendation: The simplifying assumptions of these models completely ignored microscopic phenomena such as interface mass and heat transfer and other similar processes. Consequently, the model can be improved upon by introducing some of these processes as identified.

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Modelling of unsteady combustion regimes for polydisperse fuels—I. Instability and auto-oscillations

Cited by 17 publications

References 3 publications

Phase transformations in metastable liquids combined with polymerization

Phase transformations in metastable liquids combined with polymerization

Evolution of a Polydisperse Ensemble of Spherical Particles in a Metastable Medium with Allowance for Heat and Mass Exchange with the Environment

Simulation of an Industrial Carbon Black Reactor Using Collision Kinetics

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