Ignition analysis of adiabatic, homogeneous systems including reactant consumption

Hermance, Clarke E.

doi:10.2514/6.1973-215

Cited by 3 publications

(7 citation statements)

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“…Physically, ofcourse, this corresponds to the effect of the vanishing quantity of fuel (a mole fraction of O(e/y) or less), making the rate of heat production very small even though the temperature is very nearly a maximum. This corresponds to a real singularity in the problem, as explicitly indicated by Kassoy (1974) and less clearly so by Hermance (1973). It occurs after the majority of chemical reaction and temperature rise is completed, and is not a consequence of the approximate methods used (by Hermance and Kassoy).…”

Section: Relationship Of Approximate and Exact Solutionsmentioning

confidence: 92%

“…which is the general form of the singularity indicated by Kassoy (1974) and Hermance (1973). (3) when combined with equation (8), and representing lo(e) as simply to, indicates that m'…”

Section: This Equation Was Developed By Expanding the Functions Havinmentioning

confidence: 96%

“…Recently Hermance (1973) and Kassoy (1974) have discussed the analysis of the ignition process of this system. In both cases, reactant consumption was explicitly taken into account with the only approximation being that of a constant mean, specific heat appropriately defined.…”

Section: Introductionmentioning

confidence: 98%

“…Kassoy (1974) used the method of matched asymptotic expansions to develop solutions over the complete temperaturetime range. The analysis given by Hermance (1973) was basically a classical ignition analysis, using a Poincare expansion technique, starting with small deviations from the initial temperature, with an extended version of the representation of the chemical reaction rate developed by Semenov (1959) and Frank-Kamenetski (1955).…”

Section: Introductionmentioning

confidence: 99%

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Implications Concerning General Ignition Processes from the Analysis of Homogeneous, Thermal Explosions

Hermance¹

1975

Combustion Science and Technology

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Two recent approximate analyses of ignition in homogeneous, adiabatic systems with fuel consumption specifically included are discussed and compared with the derived exact solution of the problem. The singularity present in both approximate solutions is shown to be the same as that found in the exact solution, and is characteristic of the time required to establish nearly complete chemical reaction. A similar situation is shown to exist for i~ition in non-adiabatic, homogeneous systems-the classical Semenov problem--causing the proposal and discussion of a thesis that a correct description of any ignition event must always include the transient behavior as quasisteady combustion is approached. Intuitively satisfying, the theoretical and experimental implications of this thesis are discussed.

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Section: Relationship Of Approximate and Exact Solutionsmentioning

confidence: 92%

“…which is the general form of the singularity indicated by Kassoy (1974) and Hermance (1973). (3) when combined with equation (8), and representing lo(e) as simply to, indicates that m'…”

Section: This Equation Was Developed By Expanding the Functions Havinmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Implications Concerning General Ignition Processes from the Analysis of Homogeneous, Thermal Explosions

Hermance¹

1975

Combustion Science and Technology

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“…Perhaps a proper description of the ignition stage can be obtained through generalizations of the promising methods of Hermance [7] and Kassoy [8] but this is unclear because as yet those methods have not been developed for problems involving partial differential equations. For procedures extending into the ignition stage or beyond, an ignition criterion different from thermal runaway will have to be developed if comparisons with previous results, such as (39) and (40), are to be made.…”

Section: Discussionmentioning

confidence: 99%

Ignition of a Reactive Solid Exposed to a Step in Surface Temperature

Liñán¹,

Williams²

1979

SIAM J. Appl. Math.

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Abstract. The title problem is classical in ignition theory. Here it is solved by an asymptotic analysis in which the nondimensional activation energy is treated as a large parameter. Inert and reactive zones are identified, and a temperature peak develops in the latter during a stage of transition to ignition. A criterion of thermal runaway yields a formally correct asymptotic expansion for the ignition time which agrees with results of numerical integrations if the activation energy is sufficiently large.

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The Subcritical Spatially Homogeneous Explosion; Initiation to Completion

Kassoy

Poland

1975

Combustion Science and Technology

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In this paper a complete solution (initiation to completion) for the sub-critical spatialIy homogeneous reaction has been developed. Complete reaction consumption is included. The solution is in two parts: (I) the rapid temperature rise (2) the subsequent decay back to initial conditions. The two parts are joined using the method of matched asymptotic expansions. The complete temperature-time history is displayed graphicalIy, to show the dependence of the temperature variation and fuel consumption on reaction order, heat loss parameter and the thermodynamic properties of the system.

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Ignition analysis of adiabatic, homogeneous systems including reactant consumption

Cited by 3 publications

References 1 publication

Implications Concerning General Ignition Processes from the Analysis of Homogeneous, Thermal Explosions

Implications Concerning General Ignition Processes from the Analysis of Homogeneous, Thermal Explosions

Ignition of a Reactive Solid Exposed to a Step in Surface Temperature

The Subcritical Spatially Homogeneous Explosion; Initiation to Completion

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