The Convective–Conductive Theory of Combustion of Condensed Substances

  • Nickolai M. RubtsovEmail author
  • Boris S. Seplyarskii
  • Michail I. Alymov
Part of the Heat and Mass Transfer book series (HMT)


The convective mechanism of combustion is suggested for the explanation of an abnormally high combustion velocity found in combustion of the systems, which are considered “gasless”, titanium + soot, and also titanium + soot + polystyrene under conditions of one-dimensional filtration of impurity gases. The analysis of the available experimental and theoretical data showed that under conditions of impurity gas emission, a convective combustion mechanism can be provided by the movement of a melted layer of one of reagents under the influence of pressure difference of impurity gases. Physical and mathematical models of convective combustion of “gasless” systems are formulated. It is established that realization of the accelerating combustion mode requires presence of the free volume, which is not occupied with a sample. It is shown that at an initial stage of combustion as well as at the value of free volume exceeding the sample volume, the velocity of the front and the pressure of gas increase following the exponential law. Analytical expressions for calculation of the average velocity of convective combustion are obtained. The examination of the model formulated in the chapter allowed explaining the distinctions in regularities of combustion of “gasless” systems under conditions of counter, cocurrent, and bilateral filtration of impurity gases. It is shown that depending on the organization of combustion process, the pressure difference of impurity gases can both accelerate, and slow down the penetration of the melt into an initial sample, thereby changing a combustion velocity. The estimates of the width of a warming up zone show that impurity gas emission in the warming up zone occurs, first of all, at the expense of a desorption of gases and vapors, which are adsorbed on a surface of the particles of a fine component. By means of the new combustion model, the explanation of an increase in combustion velocity of “gasless” systems observed at thermal vacuum processing and reduction of diameter of initial samples is given. Based on the grounds of the convective–conductive theory of combustion (CCTC) of heterogeneous condensed systems, it is offered to apply a method of pumping out a sample to control the synthesis. The regularities of combustion by the example of Ti–C powders under conditions of artificially created pressure difference along the sample are investigated. It is shown that the removal of impurity gases in a warming up zone of the reaction front provides significant increase in the combustion velocity. It is established that preliminary thermal vacuum processing (TVP) of initial mixes leads to an increase in combustion velocity for samples of bulk density. It is established that the presence of moisture does not practically influence combustion regularities and phase structure of products of granulated Ti + 0.5C samples. It is found out that under conditions of Ar coflow, the influence of humidity on the phase structure of reaction products decreases, and combustion velocity of the powder sample increases. It is shown that the presence of moisture in the Ti + 0.5C powder sample has an impact on the phase structure of combustion products and practically has no influence on the combustion velocity of the sample without a gas flow. It was revealed that the thermovacuum processing of Ti + 0.5C mixtures leads to an increase in combustion velocity (twofold) and sample shrinkage. Mechanical alloying decreases combustion velocity and enlarges (threefold) sample elongation. The results provide a strong argument in favor of conduction–convection combustion theory (CCTC). Thus, the available literature and experimental data confirm the applicability of the convective–conductive mechanism of combustion wave propagation in the fast-burning “gasless” systems containing a fusible reagent.


SHS Heat transfer Convective Conductive Penetration Melted layer Impurity gases Darcy’s law Combustion Velocity Thickness Porosity Thermovacuum processing Mechanical activation 


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© Springer International Publishing AG 2017

Authors and Affiliations

  • Nickolai M. Rubtsov
    • 1
    Email author
  • Boris S. Seplyarskii
    • 1
  • Michail I. Alymov
    • 1
  1. 1.Institute of Structural Macrokinetics and Materials ScienceRussian Academy of SciencesMoscowRussia

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