Calculation of the Admittance Function for a Burning Surface

Abstract

Calculation of the Admittance Function for a Burning Surface. A thorough analysis of pressure oscillations in a solid propellant rocket requires specification of the response of the burning solid. Indeed, for the case of small amplitude waves, this is the most crucial aspect of the problem; unfortunately, it is also poorly understood. The admittance function is merely a convenient expression of the response which contains the primary mechanism for driving waves. In the work reported here, the usual one-dimensional approximation is made, and three main regions are distinguished: the solid phase being heated, the solid phase involving decomposition (a thin region near the surface), and the gas phase. The problem reduces simply to the solution of appropriate ordinary differential equations and satisfaction of boundary conditions, which include matching at interfaces. The most significant differences from previous work are incorporation of a decomposition region and the treatment of the gas phase. A greatly simplified analysis of the latter leads essentially to the same results found elsewhere, but with substantially less labor. Only a quasistatic analysis, valid for frequencies less than a few thousand cycles per second, is covered, but it can be extended to higher frequencies. Laboratory measurements have shown that the response consists generally of a single peak in the range of frequency for which the quasi static approximation appears to be accurate. The qualitative aspects of such peaks, and their connection with 'self-excited' oscillations, are discussed. In particular, the influence of decomposition and pressure sensitivity of the various chemical reactions is examined. Limited numerical results are included. Eventually, the aim of calculations is principally to gain some understanding of the unsteady combustion process and to aid in classifying propellants. The regions involved in the burning are separately characterized by a small number of dimensionless groups. It appears that the effects represented by these parameters may be distinguished in the response function; one may therefore be able, by use of experimental results, to determine at least qualitative connections between the response to pressure oscillations and changes of composition. In this regard, observations made in both T -burners and L * burners should prove useful.