Electric pulse heating of reactive compositions by thin-walled conductors-heaters in the modes of multi-point ignition of propellant charges

S. I. Volodchenkov ; A. A. Glazunov ; S. V. Sinyaev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 70 (2021), pp. 24-36

Résumé

The problem of electric pulse heating of a medium by the heater made of metal foil with an ideal thermal contact with the medium is solved. The solution is obtained in the form of rapidly converging series for ohmic heating power, which is given as an arbitrary function of time. Using the obtained solution, a dimensionless criterion is introduced for quasi-homogeneous heating of the heater up to a melting point with intensive heat transfer to environment. It is shown that with a fixed heating duration, the criterion value depends weakly on the type of a heating power function, which allows ignoring parameters of the external electrical circuit of the device while choosing the heater thickness. The definition of a “thin” heater is introduced, which admits of bulk droplet destruction during heating of a reactive medium. In the “thin” heater approximation, quadrature solutions to the thermal problem are obtained under heat exchange according to Newton's law and ideal thermal contact, when the heater power is an arbitrary function of time. Dimensionless similarity parameters of the simulated processes are identified in all solutions, which include thermal and physical characteristics of the heater and medium, as well as the thickness of the heater and the time of its heating up to the melting point. The applicability of the “thin” heater model for calculating the thermal state of a high-energy pyrotechnic coating is shown. As an example, the permissible values of the thickness of the magnesium foil heater are determined, which ensure its uniform heating up to the melting point in 1 and 5 milliseconds under the ideal thermal contact with ignited coating. The obtained quadrature solutions to the thermal problems and the calculated results are applicable in the design of compact electric pulse devices for contact multi-point ignition of various reactive compositions with efficient consumption of electric energy.

Détail

Keywords: electric discharge, pulse heating, conductor-heater, heated medium, heat exchange, “uniformity” condition, conjugate problem.