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Analytical Investigation of Thermoacoustic Instabilities in Premixed Combustion Systems.

机译:预混燃烧系统中热声不稳定性的分析研究。

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摘要

The primary objective of this dissertation is to develop and investigate various analytical methods to predict thermoacoustic instabilities in premixed combustion systems. The analytical models derived as part of this study are of four main types: (1) Acoustically consistent, linear modal analysis method to predict the longitudinal and transverse combustion instabilities in a dump combustor; (2) Novel level set method for deriving flame surface-area response to incident acoustic fluctuations; (3) Novel approximate analytical solutions to acoustic waves in inhomogeneous media; and (4) Investigation of the limit-cycle behavior of nonlinear acoustic wave equation with combustion source term.;The linear modal analysis method that was developed in this study, has a number of novel and distinguishing features when compared to prior works on combustion instability. (i) Combustion instabilities are a thermoacoustic phenomenon, i.e.~they are manifested as self-excited acoustic oscillations that are sustained by a feedback loop between the acoustic perturbations and the flame heat-release fluctuations. Therefore, first and foremost, an instability model must be able to predict the natural acoustic modes of the combustor in the absence of combustion. Our model satisfies this criterion by successfully predicting the acoustic modes of ducts with multiple discontinuities in cross-sectional area. Such a consistency testing of an instability model had not been performed previously. (ii) New acoustically consistent matching conditions with distinct forms for the purely axial and non-axial modes were developed and applied at the zonal interfaces of a duct, whereas prior studies employed the conventional mass, momentum, and energy balances at the interfaces. For the purely axial modes, acoustic mass velocity and total pressure are mathced across the interface while for non-axial modes, the continuity of acoustic velocity and pressure fluctuations is applied. The new matching conditions are essential to accurately predict the duct acoustic modes. (iii) Effects of edge conditions on the linear modal analysis of ducts with area discontinuities are analyzed in great detail. Edge conditions are constraints that need to be satisfied in addition to the matching conditions at an area discontinuity. (iv) Through a novel approach, the effects of the fluctuating heat-release source term in the acoustic wave equation are directly incorporated into the modified axial wavenumbers in the combustion region. This approach obviates the need for applying a separate matching condition across the flame. (v) The analytical model presented in this work, is the first to account for realistic mean flame shapes in combustion instability analysis, whereas prior models assumed that combustion occurred in a cross-sectional plane of zero thickness.;A new G-equation level-set method was developed that describes flame surface-area response to acoustic oscillations incident on the flame. This method presents a different paradigm when compared to an approach that has existed for at least two decades. In this method, we directly solve for the level set fluctuations G' in terms of velocity fluctuations, and relate the flame surface-area oscillations to G', whereas in the conventional f-approach, the level-set G is expressed as G(x,y,t) = x -- f(y,t) and a solution for f is sought. In the absence of turbulent flame-speed fluctuations, the response functions from the present G-equation approach are in good agreement with those from the conventional f-equation approach. However, when turbulent flame-speed fluctuations are included, the two approaches differ, principally in the flame response to axial velocity fluctuations. This G-equation approach is more generalized since the effects of flame-speed fluctuations are reflected in both the axial and tranverse velocity response functions; whereas in the f-equation approach, this inclusion predominantly affects the axial velocity fluctuations.;As part of this work, an analytical Wentzel-Kramers-Brillouin (WKB)-type approximation for a 2-D acoustic duct with axial gradients in temperature, axial mean flow and duct cross-sectional area has been developed. Standard WKB method uses two principal approximations: (i) the amplitude of the wave varies slowly compared to its frequency and (ii) the mean properties vary slowly in space. The modified WKB method developed in this study relaxes the latter assumption of slowly varying mean properties. Using this novel WKB-type solutions along with the acoustically consistent modal analysis framework that was developed earlier, we are able to compute acoustic resonant frequencies as well as predict lonigtudinal unstable modes of a duct with discontinuities, which has not been done before.;The effects of nonlinear acoustic and combustion source terms on the limit-cycle behavior of thermoacoustic instabilities in a Rijke tube has also been investigated. First, the relevant parameters that dictate the linear instbility viz., convective time-lag and mean heat-release rate are identified. And in the linearly unstable regime, the limit-cycle amplitudes for the first two longitudinal modes of a duct are computed. (Abstract shortened by ProQuest.).
机译:本文的主要目的是开发和研究各种分析方法来预测预混燃烧系统中的热声不稳定性。作为本研究的一部分而得出的分析模型有四种主要类型:(1)声场一致的线性模态分析方法,用于预测排料燃烧室的纵向和横向燃烧不稳定性; (2)推导对入射声波起伏的火焰表面积的新的水平集方法; (3)非均匀介质中声波的新型近似解析解; (4)研究带有燃烧源项的非线性声波方程的极限循环行为。;本研究开发的线性模态分析方法,与现有的关于燃烧不稳定性的研究相比,具有许多新颖而独特的特征。 (i)燃烧不稳定性是一种热声现象,即表现为自激声振荡,该振荡由声扰动与火焰放热波动之间的反馈回路维持。因此,首先,一个不稳定性模型必须能够在没有燃烧的情况下预测燃烧室的自然声模。我们的模型通过成功地预测横截面积具有多个不连续性的管道的声模来满足该标准。之前尚未进行过这种不稳定性模型的一致性测试。 (ii)开发了新的声学上一致的匹配条件,其具有纯形式的纯轴向模式和非轴向模式,并应用于管道的区域界面,而先前的研究在界面处采用了常规的质量,动量和能量平衡。对于纯轴向模式,通过界面计算声速和总压力,而对于非轴向模式,则应用声速和压力波动的连续性。新的匹配条件对于准确预测管道声学模式至关重要。 (iii)详细分析了边缘条件对具有区域不连续性的管道的线性模态分析的影响。边缘条件是除了区域不连续处的匹配条件之外还需要满足的约束条件。 (iv)通过一种新颖的方法,将声波方程中波动的放热源项的影响直接并入燃烧区域的修正轴向波数中。这种方法消除了在火焰上施加单独的匹配条件的需要。 (v)这项工作中提出的分析模型是第一个在燃烧不稳定性分析中考虑实际平均火焰形状的模型,而先前的模型则假定燃烧发生在零厚度的横截面上;新的G方程级开发了一种设定方法,该方法描述了火焰表面积对入射在火焰上的声波振荡的响应。与已经存在至少二十年的方法相比,该方法呈现出不同的范例。在这种方法中,我们直接根据速度波动来求解水平集波动G',并将火焰表面积波动与G'相关联,而在传统的f方法中,水平集G表示为G( x,y,t)= x-f(y,t)并寻求f的解。在没有湍流的火焰速度波动的情况下,当前G方程方法的响应函数与常规f方程方法的响应函数非常吻合。但是,当包括湍流的火焰速度波动时,两种方法有所不同,主要在于火焰对轴向速度波动的响应。由于火焰速度波动的影响反映在轴向和横向速度响应函数中,因此这种G方程方法更为通用。 ;在f方程法中,这种包含主要影响轴向速度波动。作为这项工作的一部分,对具有轴向轴向温度梯度的二维声波导管,进行了Wentzel-Kramers-Brillouin(WKB)型解析近似,已经开发出轴向平均流量和管道横截面积。标准WKB方法使用两个主要近似值:(i)波的振幅与频率相比变化缓慢,并且(ii)在空间中的平均特性变化缓慢。在这项研究中开发的改进的WKB方法放宽了缓慢变化的平均特性的后一种假设。使用这种新颖的WKB型解决方案以及较早开发的声学上一致的模态分析框架,我们能够计算出声共振频率并预测具有不连续性的管道的纵向不稳定模态,这是以前从未做过的。还研究了非线性声学和燃烧源项对Rijke管中热声不稳定性极限循环行为的影响。第一确定了指示线性不稳定性的相关参数,即对流时滞和平均放热率。在线性不稳定状态下,计算出管道的前两个纵向模式的极限循环幅度。 (摘要由ProQuest缩短。)。

著录项

  • 作者

    Rani, Vijaya Krishna.;

  • 作者单位

    The University of Alabama in Huntsville.;

  • 授予单位 The University of Alabama in Huntsville.;
  • 学科 Mechanical engineering.;Fluid mechanics.;Acoustics.
  • 学位 Ph.D.
  • 年度 2017
  • 页码 224 p.
  • 总页数 224
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 TS97-4;
  • 关键词

  • 入库时间 2022-08-17 11:54:16

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