Relationship between empirical laws of turbulent combustion of dust/air mixtures

Introduction. An array of known experimental data, mainly obtained in a standard 1 m³ chamber, is considered in the article. It allowed to identify the nature of three dependences of the turbulent combustion of dust, including the dependences of limited oxygen concentration (LOC) and explosive index Kst on the energy of ignition source E_ig (on a logarithmic scale) and the dependence of K_st on the initial oxygen content in the air C_ox.
Empirical dependencies. The analysis showed that all considered dependences, having a relative accuracy of about 20 % can be represented as linear functions of an argument varying within the following limits: E_ig varies from minimum ignition energy E_min to 10 kJ; C_ox ranges from LOC to 21 % vol. According to the nature of dependence of K_st on E_ig, all dusts are divided into two types. For the first type of dust, K_st does not depend on E_ig. For the dust of the second type, K_st ^∝ (E_ig – E_min).
Relationship of empirical dependencies. It is shown that the considered empirical dependences should be interrelated for the dust of the second kind. Namely, slopes C_n (n = 1, 2 or 3 as the number of the dependence) of linear functions, approximating the empirical dependences for a particular dust sample, satisfy the relationship: С₂(21 vol. %) = –С₁∙С₃(10 kJ). Due to the absence of a dust sample, for which data on all three dependences are available, the obtained relationship was confirmed for the average values of parameters: <С₂(21 vol. %)> = =–<С₁>∙<С₃(10 kJ)>.
Discussion of the result. The satisfactory accuracy of the relationship between C₁, C₂ и C₃ gives rise to the confidence in the objectivity and relationship of the considered empirical dependences of the turbulent combustion of dust.

Conclusions. It is shown that the considered empirical dependences of the turbulent combustion of dust in a 1 m³ chamber are interrelated and the form of this relationship is identified.

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