Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion
Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion
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DOI：
10.1512/iumj.2005.54.2685
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发表时间：
2005-01-01
影响因子：
1.1
通讯作者：
Williams, M
中科院分区：
文献类型：
--
作者：
Jenssen, HK;Lyng, G;Williams, M
我们使用流体动力学稳定性理论的经典简正模方法来定义三种常用燃烧模型中多维强爆轰的稳定性决定因素（Evans函数）：全反应Navier-Stokes（RNS）模型，以及更简单的Zeldovich-von Neumann-Doring（ZND）和Chapman-jouguet（Q）模型。行列式是频率（λ，η）的函数，其中λ是时间变量的对偶复变量，η是Pd-1的元素，与横向空间变量对偶。在R lambda > 0中，这些行列式的零点对应于随时间呈指数增长的扰动。CJ行列式Delta（CJ）（lambda，eta）被证明是显式可计算的。RNS和ZND行列式是不可能明确计算的，但我们能够计算其一阶低频展开式的误差项是一致的小相对于所有可能的（λ，η）方向。有点令人惊讶的是，这个计算产生了一个等价定理：在RNS和ZND行列式的展开式中的主要系数是Delta（CJ）的常数倍！在这个意义上，所有三种模型中强爆轰的低频稳定性条件是等价的。通过计算Delta（CJ），我们能够给出对所有三种模型都有效的低频稳定性准则，这些准则是根据马赫数、Gruneisen系数、压缩比和放热等物理量确定的。等价定理及其周围的分析是CJ和ZND模型作为完整RNS模型的近似的严格理论证明的一步。
We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes (RNS) model, and the simpler Zeldovich-von Neumann-Doring (ZND) and Chapman-jouguet (Q) models. The determinants are functions of frequencies (lambda, eta), where lambda is a complex variable dual to the time variable, and eta is an element of Pd-1 is dual to the transverse spatial variables. The zeros of these determinants in R lambda > 0 correspond to perturbations that grow exponentially with time.The CJ determinant, Delta(CJ) (lambda, eta), turns out to be explicitly computable. The RNS and ZND determinants are impossible to compute explicitly, but we are able to compute their first-order low-frequency expansions with an error term that is uniformly small with respect to all possible (lambda, eta) directions. Somewhat surprisingly, this computation yields an Equivalence Theorem: the leading coefficient in the expansions of both the RNS and ZND determinants is a constant multiple of Delta(CJ)! In this sense the low-frequency stability conditions for strong detonations in all three models are equivalent. By computing Delta(CJ) we are able to give low-frequency stability criteria valid for all three models in terms of the physical quantities: Mach number, Gruneisen coefficient, compression ratio, and heat release. The Equivalence Theorem and its surrounding analysis is a step toward the rigorous theoretical justification of the CJ and ZND models as approximations to the full RNS model.