A Phenomenological Model for the Unsteady Combustion of Solid Propellants from a Zel’dovich-Novzhilov Approach

Abstract

Solid rocket motors are prone to combustion instabilities, which may lead to various problems for the rockets, from unexpected oscillations, precision decreasing, to explosion. The unsteady combustion dynamics of the propellants play a crucial role in most solid rocket motors experiencing combustion instabilities. A modeling framework for the unsteady combustion of the solid propellant is constructed via the Zel’dovich-Novozhilov (ZN) phenomenological perspective. The overall unsteady combustion features of a quasi-steady homogeneous one-dimensional (QSHOD) model are investigated. The phenomenological ZN parameters are then calculated. Compared with the traditional ZN-QSHOD linear equivalence relation, the new calculated system yields better results for the pressure coupling response, especially in the non-linear regime. The proposed phenomenological modeling provides a new methodology for the model reduction of the complex flame models.

A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

“…The PDE (1) and the boundary condition (2) define a coupled problem of the unsteady temperature field and its regressing boundary. It should be remarked that the infinity boundary condition θ(+∞, t) = 0 can only be exactly fulfilled by the spectral method, as discussed in [7,8]. In the FDM or the DG-FEM in the present paper, an approximate Dirichlet boundary condition θ(x R , t) = 0 is used, which has little influence on the key region as the temperature will decay exponentially away from the burning surface in the manner of e −x .…”

“…As discussed in a previous work [8], the unsteady behavior of the combustion models can be unified by a phenomenological approach. Thus, the phenomenological ZN model is used in the present paper as the benchmark.…”

“…The algorithm used here is based on [7,8], where the temperature is expanded by the Laguerre polynomials L i (x) as…”

“…It has been found that the ZN model yields chaotic behavior in some specific parameter ranges [2,8]. The chaotic motion, determined by some strange attractor, is known to be an extremely subtle structure.…”

“…The two categories of models were compared in detail in a previous work [7,8]. It was shown that the two models behave differently in nonlinear regions despite their linear equivalency.…”