非预混火焰热声耦合机理的理论和计算分析
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摘要
非预混燃烧广泛存在于动力推进系统中。本论文通过理论分析和数值计算，辅以相关实验数据，研究了非预混燃烧过程中的热声耦合问题。对于燃气轮机燃烧室内的燃烧过程，产生热声耦合需要两个条件：第一，流场中需要存在一个初始的扰动，也就是热声耦合产生的诱因，燃烧过程的直接燃烧噪音便是产生这种流场内初始扰动的重要因素；第二，燃烧室的声学边界条件需要满足相关条件，使得流场中的初始扰动可以通过声学反馈，和燃烧过程耦合，产生自维持的热声耦合振荡燃烧。全文围绕热声耦合问题的两个重要分支：燃烧过程的直接噪音和间接噪音展开，研究其产生机理和相关特性，并对其内在联系做了相关讨论。
首先，利用低阶模型的数学思想，理论推导了低阶燃烧动力学模型以及一维分布式火焰传递函数的表达式。这些结果从守恒方程组出发，描述了燃烧动力学过程中放热率脉动和流场扰动之间的关系，它们的成立并不依赖于具体的燃料组织方式或燃烧模型，对于预混、非预混、以及部分预混燃烧都是成立的。接着，论文以一个理想的二维平板非预混火焰作为研究对象，通过格林函数法，解析计算了这个典型非预混燃烧过程的一维分布式火焰传递函数，研究了非预混火焰不稳定燃烧过程中的一类重要问题：热斑的产生及其演化过程，分析其影响因素。
接下来，通过分析直接数值模拟的计算结果，得到了非预混火焰放热率脉动时间变化率的空间相关函数表达式，从而简化了非预混燃烧过程中直接燃烧噪音的计算方法。通过燃烧过程中特征量对直接数值模拟结果的无量纲化，使得分析计算的结果表征了非预混燃烧过程中直接燃烧噪音的本质，使结果具有一般性。
在第五章，以一个真实的燃气轮机模型燃烧室为例，通过数值计算，预测了模型燃烧室的自激振荡燃烧状况。通过线性声学的理论推导，得到了描述燃烧室上下游声学边界条件的声阻抗表达式，使得数值计算的区域可以只考虑燃烧区。
最后，讨论了非预混火焰热声耦合振荡燃烧对于宽频扰动的激发模态。通过结合数值计算和系统辨识得到宽频分布式火焰传递函数，通过形状因子在低阶模型中考虑流动的不均匀性，通过声阻抗描述自激振荡声学边界条件，得到了可以准确预测整个燃烧系统热声耦合振荡燃烧的特征频率簇以及相应的初始增长率的研究方法，刻画了从宽频的燃烧直接噪音到特定频率自激振荡燃烧的激发模态。
Non-premixed combustion widely exists in industrial equipments and propulsionsystems. Through theoretical analysis and numerical simulation, supported by relevantexperimental data, the thermoacoustic coupling relationships in non-premixed combus-tion are investigated. For the combustion in gas turbines, there are two preconditions forthermoacoustic oscillation occurrence. First, there should be initial disturbances in theflow field which could induce the thermoacoustic oscillations. Direct combustion noiseplays a significant role in it. And second, the corresponding acoustic boundary condi-tions should be satisfied to couple the acoustic wave propagation process with unsteadycombustion. This research includes two major branches of thermoacoustic oscillations ofnon-premixed combustion: the direct combustion noise and indirect combustion noise.The generation mechanisms, main characteristics and their internal relationships are in-vestigated in diferent chapters.
First of all, based on theoretical analysis, the low order model of combustion dynam-ics and one-dimensional distributed flame transfer functions are obtained. These resultsare based on conservation equations and don’t depend on the combustion type and com-bustion modelling. They are established in premixed combustion, non-premixed com-bustion and partially premixed combustion. To demonstrate the implementation of aboveanalytical models, an idealized two-dimensional flat non-premixed flame with three slotsis employed. Based on Green’s function method, the one-dimensional distributed flametransfer function is calculated and the generation and evolution of hot spots are investi-gated.
And then, based on the direct numerical simulation results, the two-point correlationfunctions of the rate of change of fluctuating heat release rate are investigated. Afternormalized by characteristic quantities, the correlation functions can be represented ingeneral form and independent with local turbulence and chemical reactions. These resultscan simplify the calculation of sound pressure level of direct combustion noise.
In chapter5, by using a modelling gas turbine type burner for research, the ther-moacoustic combustion oscillations are investigated by numerical simulation. Based onlinear acoustic analysis, the acoustic impendence boundary conditions of the combustor’supstream and downstream are obtained and the CFD calculation can be limited only in the combustion zone.
Finally, the frequency response of thermoacoustic combustion oscillations on broad-band disturbances is investigated. By numerical simulation and system identification, thebroadband distributed flame transfer functions are obtained. The non-uniform of flowfield is considered by shape factors in the one-dimensional analysis model and the acous-tic boundary conditions are described by local acoustic impedances. And then, a newmethod to predict the eigenfrequencies and corresponding initial growth rates of ther-moacoustic combustion oscillations is developed. And it depicts the transitions frombroadband direct combustion noise to thermoacoustic combustion oscillations which onlyhave one or a couple of eigenfrequencies.
首先，利用低阶模型的数学思想，理论推导了低阶燃烧动力学模型以及一维分布式火焰传递函数的表达式。这些结果从守恒方程组出发，描述了燃烧动力学过程中放热率脉动和流场扰动之间的关系，它们的成立并不依赖于具体的燃料组织方式或燃烧模型，对于预混、非预混、以及部分预混燃烧都是成立的。接着，论文以一个理想的二维平板非预混火焰作为研究对象，通过格林函数法，解析计算了这个典型非预混燃烧过程的一维分布式火焰传递函数，研究了非预混火焰不稳定燃烧过程中的一类重要问题：热斑的产生及其演化过程，分析其影响因素。
接下来，通过分析直接数值模拟的计算结果，得到了非预混火焰放热率脉动时间变化率的空间相关函数表达式，从而简化了非预混燃烧过程中直接燃烧噪音的计算方法。通过燃烧过程中特征量对直接数值模拟结果的无量纲化，使得分析计算的结果表征了非预混燃烧过程中直接燃烧噪音的本质，使结果具有一般性。
在第五章，以一个真实的燃气轮机模型燃烧室为例，通过数值计算，预测了模型燃烧室的自激振荡燃烧状况。通过线性声学的理论推导，得到了描述燃烧室上下游声学边界条件的声阻抗表达式，使得数值计算的区域可以只考虑燃烧区。
最后，讨论了非预混火焰热声耦合振荡燃烧对于宽频扰动的激发模态。通过结合数值计算和系统辨识得到宽频分布式火焰传递函数，通过形状因子在低阶模型中考虑流动的不均匀性，通过声阻抗描述自激振荡声学边界条件，得到了可以准确预测整个燃烧系统热声耦合振荡燃烧的特征频率簇以及相应的初始增长率的研究方法，刻画了从宽频的燃烧直接噪音到特定频率自激振荡燃烧的激发模态。
Non-premixed combustion widely exists in industrial equipments and propulsionsystems. Through theoretical analysis and numerical simulation, supported by relevantexperimental data, the thermoacoustic coupling relationships in non-premixed combus-tion are investigated. For the combustion in gas turbines, there are two preconditions forthermoacoustic oscillation occurrence. First, there should be initial disturbances in theflow field which could induce the thermoacoustic oscillations. Direct combustion noiseplays a significant role in it. And second, the corresponding acoustic boundary condi-tions should be satisfied to couple the acoustic wave propagation process with unsteadycombustion. This research includes two major branches of thermoacoustic oscillations ofnon-premixed combustion: the direct combustion noise and indirect combustion noise.The generation mechanisms, main characteristics and their internal relationships are in-vestigated in diferent chapters.
First of all, based on theoretical analysis, the low order model of combustion dynam-ics and one-dimensional distributed flame transfer functions are obtained. These resultsare based on conservation equations and don’t depend on the combustion type and com-bustion modelling. They are established in premixed combustion, non-premixed com-bustion and partially premixed combustion. To demonstrate the implementation of aboveanalytical models, an idealized two-dimensional flat non-premixed flame with three slotsis employed. Based on Green’s function method, the one-dimensional distributed flametransfer function is calculated and the generation and evolution of hot spots are investi-gated.
And then, based on the direct numerical simulation results, the two-point correlationfunctions of the rate of change of fluctuating heat release rate are investigated. Afternormalized by characteristic quantities, the correlation functions can be represented ingeneral form and independent with local turbulence and chemical reactions. These resultscan simplify the calculation of sound pressure level of direct combustion noise.
In chapter5, by using a modelling gas turbine type burner for research, the ther-moacoustic combustion oscillations are investigated by numerical simulation. Based onlinear acoustic analysis, the acoustic impendence boundary conditions of the combustor’supstream and downstream are obtained and the CFD calculation can be limited only in the combustion zone.
Finally, the frequency response of thermoacoustic combustion oscillations on broad-band disturbances is investigated. By numerical simulation and system identification, thebroadband distributed flame transfer functions are obtained. The non-uniform of flowfield is considered by shape factors in the one-dimensional analysis model and the acous-tic boundary conditions are described by local acoustic impedances. And then, a newmethod to predict the eigenfrequencies and corresponding initial growth rates of ther-moacoustic combustion oscillations is developed. And it depicts the transitions frombroadband direct combustion noise to thermoacoustic combustion oscillations which onlyhave one or a couple of eigenfrequencies.
引文
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