环形燃烧室热声非线性特征值问题的稳定性分析。第一部分.灵敏度
Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity
摘要：
本文提出了一种基于伴随的方法来计算非线性、退化和非自伴特征值问题的特征值摄动。该方法被应用到热声环形燃烧室网络，其稳定性是由一个非线性特征值问题。我们计算的一阶和二阶灵敏度的增长率和频率的几何，流量和火焰参数。三种不同的配置进行了分析。基准灵敏度是通过有限差分法得到的，这涉及到求解非线性特征值问题至少与参数数目一样多的次数。通过只求解一个伴随特征值问题，我们得到了对任何热声参数的灵敏度，它匹配的有限差分解决方案，在更低的计算成本。
英文摘要：
We present an adjoint-based method for the calculation of eigenvalue perturbations in nonlinear, degenerate and non self-adjoint eigenproblems. This method is applied to a thermo-acoustic annular combustor network, the stability of which is governed by a nonlinear eigenproblem. We calculate the first- and second-order sensitivities of the growth rate and frequency to geometric, flow and flame parameters. Three different configurations are analysed. The benchmark sensitivities are obtained by finite difference, which involves solving the nonlinear eigenproblem at least as many times as the number of parameters. By solving only one adjoint eigenproblem, we obtain the sensitivities to any thermo-acoustic parameter, which match the finite-difference solutions at much lower computational cost.
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