Peter V. Gordon

University of Akron

39Publications

8H-index

212Citations

Publications 39

Newest

#1Peter V. GordonH-Index: 8

#2Uday G. HegdeH-Index: 5

Last.Michael C. HicksH-Index: 8

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This paper is concerned with the study of autoignition of fully developed free round turbulent jets consisting of oxidizing and chemically reacting components. We derive an elementary, still experimentally feasible, model for autoignition of such jets and present analysis of this model. The derivation of the model is based on the well-established experimental fact that the fully developed free round turbulent jets, in a first approximation, have the shape of a conical frustum. Moreover, the velo...

Strongly Nonlinear Asymptotic Model of Cellular Instabilities in Premixed Flames with Stepwise Ignition-Temperature Kinetics

#1Nathan KilkerH-Index: 1

#2Dmitry GolovatyH-Index: 10

Last.Gregory I. SivashinskyH-Index: 29

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In this paper we consider an ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising, for example, in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These flames often assume the shape of propagating curved interfaces that can be identified with level sets corresponding to a prescribed ignition temperature. The present paper is concerned with the analysis of such interfaces in two spatial dimensions ...

#1Peter V. Gordon (University of Akron)H-Index: 8

#2Thomas Ian Hill (University of Akron)

Last.Gregory I. Sivashinsky (TAU: Tel Aviv University)H-Index: 29

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#1Claude-Michel Brauner (University of Bordeaux)H-Index: 9

#2Peter V. Gordon (University of Akron)H-Index: 8

Last.Wen Zhang (Ha Tai: Xiamen University)H-Index: 1

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In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has...

#1Peter V. GordonH-Index: 8

#2Uday G. HegdeH-Index: 5

Last.Michael J. KulisH-Index: 4

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This paper is concerned with the derivation and mathematical analysis of a model for autoignition of laminar co-flow jets. Such jets consist of two parts: an inner part with oxidizer that is surrounded by an outer part with fuel, or the reverse. To derive a model we use a combination of Burke--Schumann theory of diffusion flames and Semenov--Frank-Kamenerskii theory of thermal explosion. The main advantage of our model is that it gives a well-defined condition for autoignition of a jet. We provi...

#1Peter V. Gordon (University of Akron)H-Index: 8

#2Daniel J. Gotti (USRA: Universities Space Research Association)H-Index: 1

Last.Gregory I. Sivashinsky (TAU: Tel Aviv University)H-Index: 29

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In this paper, we formulate and analyse an elementary model for autoignition of cylindrical laminar jets of fuel injected into an oxidizing ambient at rest. This study is motivated by renewed interest in analysis of hydrothermal flames for which such configuration is common. As a result of our analysis, we obtain a sharp characterization of the autoignition position in terms of the principal physical and geometrical parameters of the problem.

#1I. Brailovsky (TAU: Tel Aviv University)H-Index: 10

#2Peter V. Gordon (University of Akron)H-Index: 8

Last.Gregory I. Sivashinsky (TAU: Tel Aviv University)H-Index: 29

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Abstract This study is motivated by the observation that in combustion of hydrogen–oxygen/air and ethylene–oxygen mixtures the global activation energy appears to be high at low enough temperatures and low at high enough temperatures, reflecting the complex nature of the underlying chemistry. Stability analysis of a uniformly propagating planar premixed flame controlled by a stepwise ignition-temperature kinetics (representing the activation energy temperature-dependence) is carried out. It is s...

EVENTUAL SELF-SIMILARITY OF SOLUTIONS FOR THE DIFFUSION EQUATION WITH NONLINEAR ABSORPTION AND A POINT SOURCE ∗

#1Peter V. Gordon (University of Akron)H-Index: 8

#2Cyrill B. MuratovH-Index: 25

This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point source. In one space dimension, solutions of these problems with zero initial data are known to approach the stationary solution in an asymptotically self-similar manner. Here we show that this conclusion remains true in two space dimensions, while in three and hig...

#1L. Kagan (TAU: Tel Aviv University)H-Index: 11

#2Peter V. Gordon (University of Akron)H-Index: 8

Last.Gregory I. Sivashinsky (TAU: Tel Aviv University)H-Index: 29

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Abstract Motivated by recent theoretical developments in the dynamics of slow isobaric flames evolving in narrow channels (thick flames), the present study is concerned with non-isobaric flames. A reduced Darcy-like one-dimensional model capable of capturing an abrupt transition from slow conduction-driven to fast compression-driven burning is derived through an appropriate asymptotic procedure. Specifically, the adopted approach is based on the distinguished limit where the scaled width of the ...

#1Peter V. Gordon (University of Akron)H-Index: 8

#2Vitaly Moroz (Swansea University)H-Index: 15

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classical Gelfand problem the thermal explosion occurs exclusively owing to the absence of stationary temperat...

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