考虑周向平均流动影响的环形燃烧室燃烧不稳定性模型研究

Accurate determination of unstable circumferential modal waveform has been a longstanding challenge in the research of combustion instabilities within annular combustors. The circumferential mean flow has a strong impact on the circumferential modal waveform. However, there are still very few relevant researches and theoretical models under complicate operating conditions. The interaction of acoustic waves, entropy waves and vorticity waves has a strong impact on the combustion instability in the annular combustor, and this will be firstly studied based on numerical methods. Based on reasonable assumptions, the linearized Euler equations of annular chambers in the presence of circumferential mean flow, axial mean flow, mean temperature distribution or cross-sectional surface area distribution will be combined to an ordinary differential equation (ODE) as a function of pressure perturbation. This ODE will be solved using the WKB approximation method to get the analytical solutions of acoustic, entropy and vorticity waves. These solutions will be validated by comparing them to numerical solutions. Due to the presence of circumferential mean flow, the acoustic boundary conditions at the exit of annular combustion chambers also change, and current models are no longer suitable for this situation. In this study, the acoustic boundary conditions of annular nozzle with circumferential mean flow will be deduced by the perturbation method, effective length method and WKB approximation method. The results will be verified by comparing them to numerical results. Finally, the influence of the mean circumferential flow on the unstable circumferential modal waveform in the annular combustor will be studied based on these derived analytical solutions or theoretical models.

环形燃烧室燃烧不稳定周向模态波形的准确判定一直是燃烧不稳定性研究的难题。周向平均流动能够对周向模态波形产生很大影响，然而相关的研究尤其是复杂工况下的理论模型还非常少。声波、熵波和涡波的相互作用能够影响燃烧不稳定性。本申请首先采用数值方法研究了周向平均流动对三种波相互作用的影响规律。然后通过合理假设将存在周向和轴向平均流动、平均温度分布或管截面变化的环形燃烧室的线性化欧拉方程组合并为声波的常微分方程，通过WKB近似法求解了管内声波、熵波和涡波的解析解,并通过对比数值结果进行验证。由于存在周向平均流动，环形燃烧室的出口声学边界条件也发生了变化，现有的模型不再适用。本研究结合摄动法、有效长度法和WKB近似法推导了存在周向平均流动的环形喷管声学边界条件，并通过对比数值结果进行验证。最后结合推导出的解析解或理论模型，研究了周向平均流动对环形燃烧室燃烧不稳定周向模态波形的影响规律。

环形燃烧室内燃烧热释放脉动和声学扰动极易相互耦合导致燃烧不稳定的发生，其中周向模态稳定性和波形的准确预测是发动机设计与优化的重大技术关键。本项目针对周向平均流动，轴向平均流，温度梯度或截面积变化这些燃烧室普遍存在的复杂工况，依据线性理论和线性欧拉方程，发展出了一系列环形燃烧室中声波、熵波和涡波的解析解；通过WKB近似，渐进理论和有效长度等理论方法获得了存在周向平均流动的喷管声学特性并修正了喷管边界条件；结合得到的理论方法获得了变截面燃烧室和喷管中声波、熵波和涡波相互耦合作用和复杂工况中的产生、传播和发展的规律；通过对比数值计算结果进行理论模型的验证环形燃烧室各个参数变化对周向模态的影响。通过相关成果在实际型号中的实践，成功实现了相关燃烧稳定性快速预测理论模型在工程实际中的应用。本项目围绕环形燃烧室中燃烧稳定性和周向平均流动影响规律所建立的一系列理论模型和研究方法，为理解环形燃烧室中燃烧不稳定的物理机制与控制发动机中的燃烧不稳定提供量化工具，可以有效节省高精度数值仿真带来的时间和经济成本。