Quasi-steady combustion modeling of homogeneous solid propellants

Classical, linearized quasi-steady (QS) theory of unsteady combustion of homogeneous solid propellants (both pressure- and radiation-driven) is reexamined. Zeroth order, high activation energy (E/RT ≫ 1), decomposition is assumed. Many prevailing ideas about condensed-phase pyrolsis are challenged and several misconceptions are corrected. The results show the following: (1) the inadequacy of simple Arrhenius surface pyrolysis; (2) that the common assumption of zero Jacobian (δ or n_s) parameter is physically unrealistic for pressure-driven combustion except perhaps in plateau regions; (3) that classical quasi-steady theory is not necessarily incompatible with observed pressure instability [Re{R_p} > 0] in mesa propellants; (4) that measured steady-state combustion parameters (e.g., E_c = 2E_s = 40 kcal/mol for double base propellant) and quasi-steady theory can model T-burner data reasonably well; (5) that the preexponential parameters in the pyrolysis expression play a critical role in the dynamic response (particularly T₀ and Q_c); (6) that thermal radiation also plays an important role through its effect on the steady state sensitivity parameters, particularly the k (or σ_p) parameter. An approach is outlined for modeling dynamic combustion response based on zeroth order pyrolysis which allows difficult parameters, such as r and δ (or A and n_s) to be obtained from relatively easily measured ones, k and ν (or B and n), E_c, Q_c, and T_s. An approach for determining these fundamental combustion parameters using radiation-driven unsteady burning tests is described.