In this paper, the Heterogeneous Quasi 1-D model for steady combustion of AP–HTPB propellants is extended to the unsteady regime. The extended model is used to calculate the pressure-coupled frequency response ( ) of low-smoke (non-aluminised) multi-modal AP–HTPB propellants. The of a multi-modal propellant is expressed in terms of that of the individual binder-matrix coated AP particles constituting the statistical particle path. The weighting function, as expected from the serial burning approach, is the burn-time of particles. A closed-form expression is derived for the of the particles by perturbation analysis of the quasi 1-D burn rate model. In this equation, all except the two parameters that quantify the amplitude ( ) and phase ( ) of fluctuating heat flux on the solid side of the interface, are shown to be from the steady-state model. This result establishes a strong connection between the steady and unsteady framework as compared to earlier models, where (propellant pressure index) as was explicitly imposed. The model is used to predict for a few low-smoke compositions. Effects of AP particle size distribution, mean pressure and initial temperature are brought out. When expressed as vs (non-dimensional frequency based on conduction time scale), the peak response magnitude is of and occurs close to non-dimensional frequency ( ) value of 1. While this conclusion is in line with the earlier results, it does not explain the ubiquitous nature of acoustic instability in tactical missile rockets, which requires the peak response to be at least an order of magnitude higher than n. Burn rate oscillations associated with the binder-melt effect caused by inhibitors is brought out as the most likely mechanism for the observed instabilities. Methods to extend the theory to include this effect is outlined.

中文翻译：

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异构准一维模型的微扰分析——预测 AP-HTPB 复合固体推进剂频率响应的理论框架

在本文中，AP-HTPB 推进剂稳定燃烧的异构准一维模型扩展到非稳定状态。扩展模型用于计算低烟（非镀铝）多模态 AP-HTPB 推进剂的压力耦合频率响应 ( )。多模态推进剂的 的 表示为构成统计粒子路径的单个粘合剂基质涂覆的 AP 粒子的 。正如串行燃烧方法所预期的那样，加权函数是粒子的燃烧时间。通过准一维燃烧速率模型的微扰分析，推导出粒子 的闭式表达式。在这个方程中，除了量化界面固体侧波动热通量的幅度 ( ) 和相位 ( ) 的两个参数外，所有参数都来自稳态模型。与早期模型相比，该结果在稳态和非稳态框架之间建立了牢固的联系，其中（推进剂压力指数）是明确施加的。该模型用于预测一些低烟成分。提出了AP粒径分布、平均压力和初始温度的影响。当表示为 vs（基于传导时间尺度的无量纲频率）时，峰值响应幅度是并且接近于无量纲频率 ( ) 值 1。虽然这个结论与之前的结果一致，但并不解释战术导弹火箭中普遍存在的声学不稳定性，这要求峰值响应至少比 n 高一个数量级。与由抑制剂引起的粘合剂熔化效应相关的燃烧速率波动被认为是观察到的不稳定性的最可能机制。概述了扩展理论以包括这种效应的方法。