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Analytical Investigation of Thermoacoustic Instabilities in Premixed Combustion Systems.

機譯：預(yù)混燃燒系統(tǒng)中熱聲不穩(wěn)定性的分析研究。

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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.).
機譯：本文的主要目的是開發(fā)和研究各種分析方法來預(yù)測預(yù)混燃燒系統(tǒng)中的熱聲不穩(wěn)定性。作為本研究的一部分而得出的分析模型有四種主要類型：（1）聲場一致的線性模態(tài)分析方法，用于預(yù)測排料燃燒室的縱向和橫向燃燒不穩(wěn)定性； （2）推導(dǎo)對入射聲波起伏的火焰表面積的新的水平集方法； （3）非均勻介質(zhì)中聲波的新型近似解析解； （4）研究帶有燃燒源項的非線性聲波方程的極限循環(huán)行為。；本研究開發(fā)的線性模態(tài)分析方法，與現(xiàn)有的關(guān)于燃燒不穩(wěn)定性的研究相比，具有許多新穎而獨特的特征。 （i）燃燒不穩(wěn)定性是一種熱聲現(xiàn)象，即表現(xiàn)為自激聲振蕩，該振蕩由聲擾動與火焰放熱波動之間的反饋回路維持。因此，首先，一個不穩(wěn)定性模型必須能夠在沒有燃燒的情況下預(yù)測燃燒室的自然聲模。我們的模型通過成功地預(yù)測橫截面積具有多個不連續(xù)性的管道的聲模來滿足該標(biāo)準(zhǔn)。之前尚未進行過這種不穩(wěn)定性模型的一致性測試。 （ii）開發(fā)了新的聲學(xué)上一致的匹配條件，其具有純形式的純軸向模式和非軸向模式，并應(yīng)用于管道的區(qū)域界面，而先前的研究在界面處采用了常規(guī)的質(zhì)量，動量和能量平衡。對于純軸向模式，通過界面計算聲速和總壓力，而對于非軸向模式，則應(yīng)用聲速和壓力波動的連續(xù)性。新的匹配條件對于準(zhǔn)確預(yù)測管道聲學(xué)模式至關(guān)重要。 （iii）詳細分析了邊緣條件對具有區(qū)域不連續(xù)性的管道的線性模態(tài)分析的影響。邊緣條件是除了區(qū)域不連續(xù)處的匹配條件之外還需要滿足的約束條件。 （iv）通過一種新穎的方法，將聲波方程中波動的放熱源項的影響直接并入燃燒區(qū)域的修正軸向波數(shù)中。這種方法消除了在火焰上施加單獨的匹配條件的需要。 （v）這項工作中提出的分析模型是第一個在燃燒不穩(wěn)定性分析中考慮實際平均火焰形狀的模型，而先前的模型則假定燃燒發(fā)生在零厚度的橫截面上;新的G方程級開發(fā)了一種設(shè)定方法，該方法描述了火焰表面積對入射在火焰上的聲波振蕩的響應(yīng)。與已經(jīng)存在至少二十年的方法相比，該方法呈現(xiàn)出不同的范例。在這種方法中，我們直接根據(jù)速度波動來求解水平集波動G'，并將火焰表面積波動與G'相關(guān)聯(lián)，而在傳統(tǒng)的f方法中，水平集G表示為G（ x，y，t）= x-f（y，t）并尋求f的解。在沒有湍流的火焰速度波動的情況下，當(dāng)前G方程方法的響應(yīng)函數(shù)與常規(guī)f方程方法的響應(yīng)函數(shù)非常吻合。但是，當(dāng)包括湍流的火焰速度波動時，兩種方法有所不同，主要在于火焰對軸向速度波動的響應(yīng)。由于火焰速度波動的影響反映在軸向和橫向速度響應(yīng)函數(shù)中，因此這種G方程方法更為通用。 ；在f方程法中，這種包含主要影響軸向速度波動。作為這項工作的一部分，對具有軸向軸向溫度梯度的二維聲波導(dǎo)管，進行了Wentzel-Kramers-Brillouin（WKB）型解析近似，已經(jīng)開發(fā)出軸向平均流量和管道橫截面積。標(biāo)準(zhǔn)WKB方法使用兩個主要近似值：（i）波的振幅與頻率相比變化緩慢，并且（ii）在空間中的平均特性變化緩慢。在這項研究中開發(fā)的改進的WKB方法放寬了緩慢變化的平均特性的后一種假設(shè)。使用這種新穎的WKB型解決方案以及較早開發(fā)的聲學(xué)上一致的模態(tài)分析框架，我們能夠計算出聲共振頻率并預(yù)測具有不連續(xù)性的管道的縱向不穩(wěn)定模態(tài)，這是以前從未做過的。還研究了非線性聲學(xué)和燃燒源項對Rijke管中熱聲不穩(wěn)定性極限循環(huán)行為的影響。第一確定了指示線性不穩(wěn)定性的相關(guān)參數(shù)，即對流時滯和平均放熱率。在線性不穩(wěn)定狀態(tài)下，計算出管道的前兩個縱向模式的極限循環(huán)幅度。 （摘要由ProQuest縮短。）。

著錄項

  • 作者

    Rani, Vijaya Krishna.;

  • 作者單位

    The University of Alabama in Huntsville.;

  • 授予單位 The University of Alabama in Huntsville.;
  • 學(xué)科 Mechanical engineering.;Fluid mechanics.;Acoustics.
  • 學(xué)位 Ph.D.
  • 年度 2017
  • 頁碼 224 p.
  • 總頁數(shù) 224
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類 TS97-4;
  • 關(guān)鍵詞

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