JP2005048638A - Combustion vibration analysis method and its device, and analysis program using the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a combustion vibration analysis method and its device relating to combustion vibration control to be induced with pressure fluctuation in a combustion process in a combustor, and to provide a medium on which an analysis program is recorded for executing a computer using the analysis method. <P>SOLUTION: The combustion chamber 13 is divided into a plurality of cavities which are connected together via communication pipes 29. A flame as a vibration exciting source is placed in at least one cavity 27 of the cavities to serve as a pressure source to be fluctuated in a vibration exciting frequency. A resonator 22 is installed via a throat in one cavity of the combustion chamber 13 divided into the plurality of cavities 27, 28. Combustion vibration to be excited as acoustic vibration in the combustion chamber 13 is represented by Helmholz vibration where pressure in the cavity and the resonator 22 and flow rates in the connection pipes and the throat are fluctuated in a certain frequency. In accordance with the sizes of the cavities 27, 28, the resonator 22, the communication pipes 29 and the throat, the frequency response property of the Helmholz vibration to the vibration exciting frequency of the pressure source is calculated to evaluate the vibration damping effect of the resonator 22 and derive the frequency response property of the pressure and the flow rates from numeric calculation. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【００５５】
共鳴器２２は、共鳴器空洞２４とスロート２５から構成され、燃焼室１３と共鳴器２２はスロート２５により連結されている。燃焼室１３と共鳴器空洞２４の間でスロート２５を介して励振されるヘルムホルツ振動２６は、燃焼室１３内に励振されている音響共鳴振動２３と相互作用することにより音響共鳴振動２３を制振する効果を備えている。このような音響共鳴振動２３に対する制振については、従来の波動方程式または流体方程式を支配方程式とした燃焼振動解析方法により定性的な評価を可能にしていた。
【００５６】
しかし、実際の燃焼室１３内に励振される音響共鳴振動２３については、その計算精度に問題があり、あるいは実測による補正が必要となる。例えば、式（１）に示した音響共鳴周波数ω_ｍは、そもそも密封された筐体内における微少圧力変動による音響波の共鳴特性を示すものであるが、実際には燃焼室１３内では燃料９の燃焼反応による温度分布、流速分布の影響を考慮しなければならず、音速ａについても燃焼室１３内で一定ではなくなるなどの事情を抱えている。
【００５７】
そこで本発明では、波動方程式や流体方程式を支配方程式とする従来の燃焼振動解析方法に代わって、より簡便で振動制御に適しているヘルムホルツ振動方程式に基づく燃焼振動解析方法、燃焼振動解析装置、およびこれらの解析手法を用いた解析プログラムを提供するものである。
【００５８】
図４は、本発明に係る共鳴器による燃焼振動の制振に関する計算モデルの一例を示す概念図である。
【００５９】
本実施形態では、図３で示した燃焼室１３内で両端が腹で、中央が節となる音響共鳴振動２３を、燃焼室１３を仮想的に分割した燃焼室空洞２７、２８の間で、それらを連結する連通管２９を介して一定の周波数で圧力、流量が変動するヘルムホルツ振動３０として扱っている。そして、本実施形態では、励振源である火炎１９を燃焼室空洞２８内の音源として設置し、燃焼室１３内のヘルムホルツ振動３０と、燃焼室１３と共鳴器空洞２４の間で励振される上述のヘルムホルツ振動２６とを二自由度ヘルムホルツ振動系として取り扱い、ヘルムホルツ振動方程式を支配方程式とする燃焼振動解析方法による圧力、流量の周波数応答特性をコンピュータ等の計算機で導き出すことができるようにしている。
【００６０】
図４の概略的に示した二自由度ヘルムホルツ振動系において、燃焼室１３内に励振された音響共鳴振動２３（図３参照）に対して、共鳴器２２は、どのように効果的な制振を備えているかを、以下に詳しく説明する。
【００６１】
まず、一般にヘルムホルツ振動では、（１）同位相近似、（２）等エントロピー近似、（３）線形近似の３つの前提条件を仮定している。
【００６２】
ここで、
（１）同位相近似は、共鳴器空洞２４などの要素寸法が音響波の波長に較べて充分に小さく、各要素が集中定数として扱えるもので、要素内において音響振動のようなモードは励振されず、変動は同位相となるものである。
【００６３】
（２）等エントロピー近似は、作動流体の熱力学的変化が準静的な断熱過程として等エントロピー過程とするものである。
【００６４】
（３）線形近似は、流体振動に伴う変動値が定常値に較べて充分小さいとしたものを適用するものである。
【００６５】
上述の同位相近似により、共鳴器空洞２４、スロート２５、燃焼室空洞２７，２８、および連通管２９内の状態変数は均一と仮定すると、式（２）により、連通管２９およびスロート２５内の作動流体に関する運動方程式を得る。
【００６６】
ここで、Ａは断面積［ｍ^２］、Ｌは長さ［ｍ］、ｐは圧力［ｐａ］、Ｒは抵抗［ｍ^−１ｓ^−１］、ｔは時間［ｓ］、ｆは流量流束［ｋｇ／ｓ］であり、変数に対する下付き添え字Ａ，Ｂ，Ｃ，Ｆ，Ｓはそれぞれ燃焼室空洞２７，２８、共鳴器空洞２４、連通管２９、スロート２５の各変数に対して付すものとし、以下においてもそれに準じるものとする。なお、質量流束ｆ_Ｆ、ｆ_Ｓの方向は、それぞれ燃焼室空洞２８から燃焼室空洞２７へ、あるいは共鳴器空洞２４から燃焼室空洞２８への方向を正方向とする。
【００６７】
【数２】

【００６８】
【数３】

【００６９】
【数４】

【００７０】
次に、燃焼室空洞２８内にＰ_ｆ（ｔ）＝Ｆ・_ｓｉｎωｔなる励振源が存在したとし、式（３）は式（５）により式（６）のように近似してあらわすことができる。これは、燃焼室空洞２７，２８および共鳴器空洞２４内の圧力ｐ_Ａ、ｐ_Ｂ、ｐ_Ｃと、連通管２９およびスロート２５内の質量流束ｆ_Ｆ、ｆ_Ｓの関係を示すものである。
【００７１】
【数５】

【００７２】
【数６】

【００７３】
式（７）の一般解のうち、固有振動項を除外した外力（励振源）による応答振動項のみを式（８）に示す。固有振動項はｔ→∞と共に減衰するが、応答振動項は励振源が存続する限り持続的な振動を継続する。式（９）は、式（６）、式（８）から得られた燃焼室空洞２８および共鳴器空洞２４内の圧力ｐ_Ｂ、ｐ_Ｃを示す。
【００７４】
【数７】

【００７５】
式（８）、式（９）における係数Ｃ_１、Ｃ_２、Ｄ_１、Ｄ_２については、式（８）を式（７）に代入して得られる式（１０）を解いて与えられる。式（１１）は、燃焼室空洞２７，２８の間の連通管２９を介したヘルムホルツ周波数ω_ＡＢ、共鳴器空洞２４と燃焼室空洞２８との間のスロート２５を介したヘルムホルツ周波数ω_ＢＣ、燃焼室空洞２８から連通管２９を介して無限大気に自由開放されるときのヘルムホルツ周波数ω_Ｂ，Ｆ、燃焼室空洞２８からスロート２５を介して無限大気に自由開放されるときのヘルムホルツ周波数ω_Ｂ，Ｓをそれぞれ定義する。式（１２）は、燃焼室空洞２７，２８、および共鳴器空洞２４それぞれの温度Ｔ_Ａ、Ｔ_Ｂ、Ｔ_Ｃが異なる場合について定義した音速ａ_ＡＢ、ａ_ＢＣ、ａ_Ｂである。特に、燃焼室空洞２７，２８、共鳴器空洞２４との間に温度差が存在する場合、式（１２）に示すような音速の補正を要するが、これらの温度が全て等しい場合、式（１２）に定義した各音速は全て等しくなる。
【００７６】
【数８】

【００７７】
いま、式（８）〜式（１２）において、スロート２５の断面積Ａ_Ｓをゼロと設定し、式（１３）〜式（１５）にそれぞれ連通管２９内の質量流束ｆ_Ｆ、燃焼室空洞２８内の圧力ｐ_Ｂ、および励振源からの応答位相遅れψを得る。これらは、共鳴器２２を設置しない場合における燃焼室１３の燃焼室空洞２７，２８の間の連通管２９を介したヘルムホルツ振動３０に対して、励振周波数ωに対する周波数応答特性をあらわすものである。
【００７８】
【数９】

【００７９】
図５は、式（１３）に示した質量流束ｆ_Ｆ［ｋｇ／ｓ］の周波数応答特性を示し、言わば単自由度ヘルムホルツ振動系の周波数応答特性を概念的に示したものである。
【００８０】
図５に示すとおり、励振周波数ωがヘルムホルツ周波数ω_ＡＢに等しいときに周波数応答特性は、共鳴ピークを有し、流体抵抗Ｒ_Ｆ＝０のとき共鳴ピークは発散するが、逆に流体抵抗Ｒ_Ｆが過大のときは共鳴ピークは出現しない。また、流体抵抗Ｒ_Ｆ＝０のとき応答位相差はゼロであるが、流体抵抗Ｒ_Ｆ＞０のときはある位相差を有する。そして、燃焼室空洞２７、２８の間の連通管２９を介したヘルムホルツ振動３０は、ヘルムホルツ周波数ω_ＡＢが励振周波数ωと合致したときに共鳴する。
【００８１】
また、共鳴器２２による効果的な制振は、既に式（８）を導出しているとおり、実際の体系に対して周波数応答特性を解析的に評価することが可能である。
【００８２】
本実施形態では、燃焼室空洞２７、２８の間の連通管２９を介したヘルムホルツ振動３０が励振周波数ωと共鳴して激しく振動している場合、共鳴器２２を設置することにより、燃焼室１３と共鳴器２２からなる二自由度ヘルムホルツ振動系の周波数応答特性を励振周波数ωから離調（非共鳴化）させることにより制振するのが狙いである。
【００８３】
以下に、本実施形態で導出した式（８）〜式（１２）に基づき、コンピュータ等の計算機により燃焼室１３と共鳴器２２からなる二自由度ヘルムホルツ振動系の周波数応答特性における、ヘルムホルツ周波数ω_ＡＢからの離調について検証する。
【００８４】
まず、式（１６）は、式（８）において、流体抵抗Ｒ_Ｆ、Ｒ_Ｓを無視した場合の質量流束である。
【００８５】
【数１０】

【００８６】
図６のうち（Ａ）は、図４における共鳴器２２による燃焼振動の制振原理と二自由度ヘルムホルツ振動系の周波数応答特性を示す概念図である。共鳴器２２が設置されていない燃焼室１３のみの単自由度ヘルムホルツ振動系の状態では、例えば、図５に示すように、単一の共鳴周波数ω_ＡＢであるが、これに対して図６のうち、（Ｂ）では燃焼室１３と共鳴器２２からなる二自由度ヘルムホルツ振動系が形成され、式（１７）に示す２つの共鳴周波数ω_１、ω_２になる。
【００８７】
【数１１】

【００８８】
図７（Ａ），（Ｂ）は、図４における燃焼室１３と共鳴器２２の圧力振動モードの位相関係を示す概念図である。
【００８９】
図７（Ａ），（Ｂ）に示すように、これらの共鳴周波数は共鳴器空洞２４と燃焼室空洞２８が同位相モードで振動するω_１と、逆位相モードで振動するω_２の２つのモードに対応する。すなわち、共鳴器２２を設置することにより、ヘルムホルツ周波数ω_ＡＢに近い励振周波数ωで脈動燃焼する火炎１９と燃焼室１３が共鳴して激しく振動することが抑制される。
【００９０】
例えば、式（１３）でＲ_Ｆ＝０、ω＝ω_ＡＢのときはｆ_Ｆ→∞となって発散していたが、式（１６）ではｆ_Ｆは有限な値に落ち着いている。これは共鳴器２２の設置による周波数応答特性の離調によるものである。
【００９１】
一方、式（１６）でＲ_Ｆ＝０、ω＝ω_１またはω＝ω_２のときはｆ_Ｆ→∞となって発散し、共鳴ピークが二極化したことを意味する。
【００９２】
図８は、図４における共鳴器諸元が燃焼振動の制振に与える影響を概念的に示し、共鳴器２２のヘルムホルツ周波数ω_ＢＣと振動強度の関係において、スロート２５の抵抗Ｒ_Ｓに対する依存性を示す概念図である。
【００９３】
ω_ＡＢ＝ω_ＢＣときに燃焼室１３と共鳴器２２が共鳴状態となり、上述のような効果的な制振が最も期待できるが、そのような条件下でも抵抗Ｒ_Ｓが大きければ制振は低減する。
【００９４】
以上述べたように、燃焼室１３に対して共鳴器２２を設置してω_ＡＢ＝ω_ＢＣとなるように調節することにより、系の共鳴周波数をω_ＡＢから離調させることができる。その一方、燃焼室１３内に実際に励振されている音響共鳴振動２３は、燃焼室形状から規定される特定の共鳴周波数以外の自由度は許容されない。
【００９５】
したがって、本実施形態では、共鳴器２２を設置することにより、系の共鳴周波数をω_ＡＢから離れた周波数領域に移動させ、システム的には非共鳴の状態に遷移させることを以って、音響共鳴振動２３を制振させたものである。なお、燃焼室１３のさらなる静音化のためには、燃焼室１３内に定在化する音響エネルギを吸収できる充分な大きさを有する共鳴器２２を設置することが必要であり、共鳴器２２の形状等の諸元の最適化を図ることも大切である。
【００９６】
次に、本発明に係る燃焼振動解析方法、燃焼振動解析装置およびこれらの解析手法を用いてた解析プログラムの別の実施形態を、以下に示す図面および図面に付した符号を引用して説明する。
【００９７】
なお、図１８に示した従来技術の構成部分と同一構成部分には同一符号を付し、重複説明を省略する。
【００９８】
図９は、本発明に係る燃焼振動解析方法の手順を示すフロー図である。
【００９９】
まず、手順１で燃焼室１３と共鳴器２２の形状をコンピュータ等の計算機に入力し、次に手順２で火炎１９による励振源を設定する。
【０１００】
例えば、Ｐｆ（ｔ）＝Ｆ・ｓｉｎωｔなる励振源が存在した場合、音響振幅Ｆと励振周波数ωを設定する。
【０１０１】
さらに、手順３では、手順１で入力した燃焼室１３等の形状に基づき、二自由度ヘルムホルツ振動系の各要素条件を設定する。
【０１０２】
例えば、燃焼室空洞２７，２８、共鳴器空洞２４の質量Ｍ、圧力Ｐ、容積Ｖおよび連通管２９、スロート２５の断面積Ａ、長さＬ、抵抗Ｒを設定する。
【０１０３】
手順４では、手順３で設定された各要素条件に基づき、式（１０）を実際に数値計算を行って解くことにより係数Ｃ_１，Ｃ_２，Ｄ_１，Ｄ_２を求める。
【０１０４】
手順５では、手順４で求められた係数Ｃ_１，Ｃ_２，Ｄ_１，Ｄ_２を式（８）、式（９）に代入し、質量流束φ、圧力Ｐの周波数応答特性を評価する。
【０１０５】
手順６では、実際の測定によって得られた燃焼振動の音響共鳴周波数に対して周波数分析を行い、大きな圧力変動の振幅を有する音響共鳴周波数をリアルタイムに探索する。測定された音響共鳴周波数が、コンピュータ等の計算機で数値計算によって導出されたヘルムホルツ振動の周波数と偏差が生じた場合は、手順４に戻され振動要素の条件設定を見直した後に、再び計算が行なわれる。
【０１０６】
また、手順７も、手順６と同様に、実際の測定によって得られた共鳴器機内の圧力変動データに基づき、測定された圧力変動とコンピュータ等の計算機で数値計算による圧力変動の周波数や振幅を比較分析する。測定された圧力変動と数値計算による圧力変動の周波数や振幅で偏差が生じた場合は、数値計算に用いる前記燃焼室と前記共鳴器を連結するスロート流体抵抗の値を実態に即応する様に調整し、手順３に再び戻される。
【０１０７】
このように、本実施形態は、手順１〜手順７をプログラム化する記録媒体としてコンピュータなどの燃焼振動解析装置に格納したので、燃焼室１３および共鳴器２２内の圧力、流量の時間変化を連成して解析するとともに、圧力、流量の周波数応答特性を数値計算で導出でき、その数値計算を基に制振の良否を評価することができる。
【０１０８】
図１０は、図９のフロー図で示した燃焼振動のデータ処理系および演算処理系の実施形態を今少し詳しく説明するために用いたブロック図である。
【０１０９】
なお、図４に示した構成部分と同一構成部分には同一符号を付す。
【０１１０】
本実施形態は、燃焼室１３に設置されたセンサ１７によって測定された圧力変動を、データ処理系３１で周波数分析し、特に大きな圧力変動の振幅を有する音響共鳴周波数をリアルタイムに探索するとともに、その結果を演算処理系３２に反映させる。
【０１１１】
すなわち、図９に示した手順６においては、実際に得られた音響共鳴周波数の測定値を、周波数の手順４までの計算手続により得られたヘルムホルツ周波数Ω_ＡＢの計算値と比較し、両者の乖離を解消してより実際の音響共鳴モードを模擬し、二自由度ヘルムホルツ振動系の各要素条件を修正する。
【０１１２】
このように、本実施形態は、燃焼室１３等の装置形状の入力（手順１）、励振源の設定（手順２）、振動系要素の条件設定（手順３）、ヘルムホルツ振動方程式による数値計算（手順４）、周波数応答特性の評価（手順５）、振動系要素条件の補正（手順６）、スロート抵抗の補正（手順７）を経て、燃焼室１３に共鳴器２２を設置した場合における音響共鳴振動２３の制振をコンピュータ等の計算機で数値計算により評価することができる。
【０１１３】
このような有用性に対し、以下に具体的な計算例を用いて説明する。
【０１１４】
図４に示す計算モデルにおいて、特に重要な計算パラメータが共鳴器空洞２４の容積Ｖ_Ｃ、火炎１９の励振周波数ω、スロート２５の抵抗Ｒ_Ｓである。一番目の計算パラメータである共鳴器空洞２４の容積Ｖ_Ｃは、共鳴器２２のヘルムホルツ周波数ω_ＢＣ、すなわち燃焼室１３と共鳴器２２との共鳴状態を決める。これに対して、二番目の計算パラメータである励振周波数ωは、燃焼室１３と火炎１９との共鳴状態を決める。燃焼室１３と火炎１９が共鳴状態にあるとき、通常は燃焼室１３内に大きな音響共鳴振動２３が励振されるが、燃焼室１３と共鳴状態にある共鳴器２２を付加することにより、燃焼室１３内の音響共鳴振動２３は逆に制振される。三番目の計算パラメータであるスロート２５の抵抗Ｒ_Ｓは、既に図８に示したように、この制振効果がどの程度期待できるかを与えるパラメータである。
【０１１５】
まず、計算条件として、作動流体は平均分子量が２８．３４ｋｇ／ｋｍｏｌ、比熱比が１．２７８、圧力が１．０１３×１０^５Ｐａ（１気圧）の燃焼ガスとした。燃焼室空洞２７、２８はともに直径２２４ｍｍ、長さ５００ｍｍ、温度１８００Ｋ、連通管２９は直径２２４ｍｍ、長さ５００ｍｍ、温度１８００Ｋとした。また、共鳴器空洞２４は直径１５２ｍｍ、長さ４０ｍｍ、温度４６０Ｋ、スロート２５は直径２７ｍｍ、長さ５５ｍｍ、温度８００Ｋとした。
【０１１６】
スロート２５の抵抗Ｒ_Ｓ、および連通管２９の抵抗Ｒ_Ｆについては、下記により概算した数値を基準に算定した。
【０１１７】
まず、スロート２５の抵抗と質量流束φｓの積は、スロート２５の圧力損失に相当する。ヘルムホルツ振動２６のような流体振動を伴う流動変動の振幅は、基本的には線形近似が適用できる程に小さな値であるため、変動流速による摩擦損失係数ζ_Ｆは層流の式を適用して式（１８）が与えられる。
【０１１８】
なお、Ｄｓはスロート２５の直径［ｍ］、Ｌｓは長さ［ｍ］であり、Ｒｅはスロート２５内の作動流体のレイノルズ数［−］、μｓは流速［ｍ／ｓ］、μは粘性率［ｍ^２／ｓ］、ρは質量密度［ｋｇ／ｍ^３］である。
【０１１９】
【数１２】

【０１２０】
したがって、Ｍをスロート２５内の流体の平均分子量［ｋｇ／ｍｏｌ］、Ｐ_０を圧力［Ｐａ］、Ｒ，を気体定数［Ｊ／ｍｏｌ＊Ｋ］、Ｔ_Ｓを温度［Ｋ］とし、前記の計算条件を代入すれば、抵抗Ｒ_Ｓとして式（１９）を導き出することができる。
【０１２１】
一方、連通管２９の抵抗Ｒ_Ｆに関し、連通管２９の直径Ｄ_Ｆは、ヘルムホルツ周波数ω_ＡＢを与えるためのものであり、抵抗Ｒ_Ｆを与えるためのものではない。抵抗Ｒ_Ｆは制振対象である燃焼室１３の抵抗を代表しており、制振手段であるスロート２５の抵抗Ｒ_Ｓと同等の数値を仮定する。なお、式（１９）は滑らかな管内の壁面摩擦損失による抵抗Ｒ_Ｓを示しており、スロート２５における内壁面の表面粗さや両端での流れの縮流・拡大損失などの影響により、実際の抵抗Ｒ_Ｓは式（１９）に示す値を下限として、これを上回る値となる。
【０１２２】
【数１３】

【０１２３】
図１１は、図６に対応して、共鳴器のスロート抵抗を１×１０^４ｍ^−１ｓ^−１としたとき、燃焼室１３内および共鳴器２２の内圧力と励振周波数の関係に対する計算結果の一例を示す図である。
【０１２４】
上述のように、図１０で示した二自由度ヘルムホルツ振動系の各要素条件では、ヘルムホルツ振動２６、３０のヘルムホルツ周波数が共に同じくω_ＡＢ＝ω_{Ｂ Ｃ}＝２７０Ｈｚとなるように調整されている。励振源は、燃焼室空洞２８内に置かれた圧力変動の振幅１．０Ｐａの音源であり、共鳴器２２が「ない」ときの燃焼室空洞２８内の圧力ｐ_Ｂ、および共鳴器２２が「ある」ときの燃焼室空洞２８内の圧力ｐ_Ｂと共鳴器空洞２４内の圧力ｐ_Ｃの周波数応答特性を示している。
【０１２５】
共鳴器２２が「ない」とき、燃焼室空洞２８内の周波数応答特性は２７０Ｈｚの箇所に共鳴ピークを有する。すなわち、火炎１９の励振周波数がω＝２７０Ｈｚである場合、燃焼室１３は火炎１９と共鳴して激しく振動する。これに対して、共鳴器２２が「ある」とき、燃焼室空洞２８内の周波数応答特性はω＝２７０Ｈｚの箇所にはもはや共鳴ピークを有さず、共鳴ピークは高周波数側と低周波数側に二極化している。その結果として、ω＝２７０Ｈｚの励振周波数を有する火炎１９に対しては、共鳴器２２の効果により燃焼室空洞２８はもはや共鳴しなくなったことが分かった。
【０１２６】
以上の通り、センサ１７によって収集された燃焼室１３内の圧力変動をデータ処理系３１において周波数分析し、特に大きな圧力変動の振幅を有する音響共鳴周波数が確認され、例えばそれが２７０Ｈｚであった場合、演算処理系３２においてヘルムホルツ周波数ω_ＢＣ＝２７０Ｈｚとなるように、ヘルムホルツ振動３０の各要素条件を調整する。
【０１２７】
このような手段を採ることによって、燃焼室１３内で絶えず変動する音響共鳴周波数をリアルタイム、かつ的確に把握し、より実際の音響共鳴モードを制振することができる。
【０１２８】
次に、本発明に係る燃焼振動解析方法、燃焼振動解析装置およびこれらの解析手法を用いてコンピュータで実行させる解析プログラムを記録した媒体の、さらに別の実施形態を、以下に示す図面および図面に付した符号を引用して説明する。
【０１２９】
なお、図１８に示した従来技術の構成部分および図１０に示した本発明に係る構成部分と同一構成部分には同一符号を付し、重複説明を省略する。
【０１３０】
図１２は、本発明に係る燃焼振動のデータ処理系、演算処理系、共鳴器のデータ処理系および制御駆動系の実施形態を示す概念図である。
【０１３１】
既に、図１０に示した実施形態では、図９に示す手順６までの手続により、センサ１７によって収集された燃焼室１３内の圧力変動をデータ処理系３１において、リアルタイムで周波数分析し、その結果を演算処系３２に反映させ、時々刻々変動する燃焼振動の態様に則した数値計算がコンピュータ等でできるようになった。燃焼振動の態様に則した数値計算ができるようになった結果、燃焼室１３内の音響共鳴振動２３が充分に制振されているかの有無の確認作業が実施できる。
【０１３２】
その一方で、図１２に示す本実施形態では、共鳴器２２にデータ処理系３３が設けられており、共鳴器空洞２４内の圧力Ｐｃの測定結果と、演算処理系３２で導出された共鳴器空洞２４内の圧力Ｐｃの計算結果とを比較分析する。
【０１３３】
この比較作業に基づき、図９に示した手順７として演算処理系３２におけるコンピュータ等で行う数値計算により使用するスロート２５の抵抗Ｒｓをより真値に近い値に補正し、適正な予測精度をもって共鳴器２２による制振を数値計算で導き出すことができるようになった。
【０１３４】
また、制御駆動系３４は、演算処理系３２からの出力情報が常時入力され、駆動ロッド３５を制御駆動する機能を備えている。駆動ロッド３５の先端にはピストン３６が取り付けられている。また、共鳴器空洞２４の長さは、ピストン３６の位置により調整することができるようになっている。
【０１３５】
仮に、燃焼室１３と共鳴器２２が非共鳴状態であって、音響共鳴振動２３の制振が充分でない場合、図９に示すフロー図には、制御駆動系３４が共鳴器空洞２４の容積を最適化するために、駆動ロッド３５の制御駆動がなされることが新たに手順８として加えられる。
【０１３６】
以下、本実施形態の有用性について具体的な計算例を例示しながら説明する。
【０１３７】
図１３は、図８に対応するものであり、共鳴器２２のスロート抵抗が燃焼室１３の内圧と共鳴器２２のヘルムホルツ周波数の関係に及ぼす影響に対する計算結果の一例を示す図である。計算条件は、図１１に示した計算結果を導出する際に使用した各要素条件に準拠する。図１３に示す縦軸は、燃焼室空洞２８内の圧力ｐ_ＢのＳＰＬ値［ｄＢ］（ＳＰＬ：Ｓｏｕｎｄ Ｐｒｅｓｓｕｒｅ Ｌｅｖｅｌ）、横軸は共鳴器２２のヘルムホルツ周波数ω_ＢＣ、パラメータはスロート２５の抵抗Ｒ_Ｓである。ＳＰＬ値は式（２０）に示すとおり［ｄＢ］表示で定義されるが、通常のＳＰＬ値は定常的な大気圧に比べて非常に微小な変動量であり、日常における人の会話の音圧は約６０ｄＢという値である。図１３に示す本実施形態では、燃焼室１３内のヘルムホルツ振動３０が励振周波数ω＝２７０Ｈｚと共鳴して激しく振動している場合（ω＝ω_ＡＢ）、共鳴器２２のヘルムホルツ周波数ω_ＢＣをω_ＡＢ近傍に調整したときにほぼ制振効果が現れるが、本実施形態による数値計算によると、制振効果最大の箇所は２７０Ｈｚよりやや高周波数側にシフトしていることが分かった。
【０１３８】
【数１４】

【０１３９】
次に、図１３において計算パラメータとしたスロート２５の抵抗Ｒ_Ｓが、周波数応答特性に与える影響を以下に説明する。
【０１４０】
図１４および図１５は、燃焼室１３内および共鳴器２２内圧と励振周波数の関係に対する計算結果の一例を示した図１１において、共鳴器２２のスロート２５の抵抗Ｒ_Ｓをそれぞれ１×１０^５ｍ^−１ｓ^−１、１×１０^６ｍ^−１ｓ^−１としたときの計算結果の一例を示す。既に図１１で示したように、スロート２５の抵抗Ｒ_Ｓ＝１×１０^４ｍ^−１ｓ^−１の共鳴器２２を設置した場合、燃焼室空洞２８内の周波数応答特性は励振周波数ω＝２７０Ｈｚの高周波数側と低周波数側に２つの共鳴ピークを備え、励振周波数ω＝２７０Ｈｚに対して燃焼室空洞２８は共鳴しなくなった。
【０１４１】
しかし、図１４および図１５に示すように、スロート２５の抵抗Ｒ_Ｓが増加するに伴い、共鳴ピークの二極化傾向は認められなくなる。すなわち、共鳴器２２がないときと同様に、燃焼室空洞２８内の周波数応答特性は励振周波数ω＝２７０Ｈｚの箇所に共鳴ピークがくる。特に、スロート２５の抵抗Ｒ_Ｓが十分に大きな状態では、共鳴器２２がないときとほぼ等価の状態であるため、励振周波数ω＝２７０Ｈｚに対して燃焼室１３は共鳴して激しく振動する。
【０１４２】
図１６は、上述の計算結果を含めた、共鳴器２２のスロート抵抗Ｒｓが燃焼室１３の内圧力と励振周波数の関係に及ぼす影響に対する計算結果の一例を示す図である。
【０１４３】
また、図１７は、抵抗Ｒ_Ｓ＝１．×１０^３ｍ^−１ｓ^−１のときの共鳴器２２のヘルムホルツ周波数が燃焼室１３の内圧力と励振周波数の関係に及ぼす影響に対する計算結果の一例を示す図である。
【０１４４】
共鳴器２２のヘルムホルツ周波数ω_ＢＣ＝２７０Ｈｚの場合、図中の破線で示すように、ω＝２７０Ｈｚでは燃焼室空洞２８内の圧力変動の振幅が充分に小さく、制振されている。これに対して、ω_ＢＣが２７０Ｈｚから外れている場合、圧力変動の振幅はもはや小さな値ではない。
【０１４５】
本実施形態では、図９に示す手順７においては、上述のデータ処理系３３による共鳴器２２内の圧力変動の測定値と、既に演算処理系３２により数値計算されている圧力変動の計算値とを比較分析する。この比較分析作業を通して、本実施形態では、上述演算処理系３２での数値計算で使用しているスロート２５の抵抗Ｒ_Ｓをより真値に近い方向で補正し、より良好な予測精度をもって共鳴器２２による制振を数値計算により導出できるように調整する。この操作を繰り返し実施することで、ほぼ最適な予測精度を確保することができる。
【０１４６】
次に、手順８では、共鳴器２２の制振効果を最大限に発揮させるため、ピストン３６の位置を可変として共鳴器空洞２４の容積Ｖ_Ｃを調整し、共鳴器２２のヘルムホルツ周波数ω_ＢＣを最適化する。さらに、これらを踏まえて手順３に再び戻り、最適化された新たな要素条件に基づき、励振源に対する周波数応答特性を数値計算により再確認する。
【０１４７】
以上のとおり本実施形態では、スロート抵抗の調整（手順７）、共鳴器空洞容積の最適化（手順８）を経て、燃焼室１３に共鳴器２２を設置した場合における、音響共鳴振動２３の制振に対する予測精度を高く維持しながら、制振を数値計算によりリアルタイムで評価することができる。また、本実施形態において、ヘルムホルツ振動方程式による数値計算は計算負荷も小さく、アクティブ制御などへの技術適用も含め、共鳴器諸元の最適化も含めた制振手段を講じることが直ちに可能となる。
【０１４８】
【発明の効果】
以上の説明のとおり、本発明によれば、ガスタービン燃焼器などの燃焼装置内に誘起される燃焼振動を解析し、その実状を把握した上で、それに起因する各種振動レベルを低減する対策を的確に講じることができるので、燃焼装置自身の長寿命化をはじめ、ガスタービンまたはガスタービンプラントの信頼性を高め、プラントの運用率や補修点検費の節減に寄与し、その効果は非常に大きい。
【図面の簡単な説明】
【図１】本発明に係る燃焼振動解析方法における燃焼振動の態様を示す概念図。
【図２】図１における燃焼振動の態様に対しての相互の関係を示す簡易ブロック図。
【図３】従来の共鳴器による燃焼振動の制振に関する計算モデルの一例を示す概念図。
【図４】本発明に係る共鳴器による燃焼振動の制振に関する計算モデルの一例を示す概念図。
【図５】単自由度ヘルムホルツ振動系の周波数応答特性を概念的に示す図。
【図６】図４における共鳴器による燃焼振動の制振原理と二自由度ヘルムホルツ振動系の周波数応答特性を示す概念図で、（Ａ）は二自由度ヘルムホルツ振動系の概念図、（Ｂ）は二自由度ヘルムホルツ振動系の上述応答特性を概念的に示す図。
【図７】図４における燃焼室と共鳴器の圧力振動モードの位相関係を示す概念図で、（Ａ）は同位相モードを示す概念図、（Ｂ）は逆位相モードを示す概念図。
【図８】図４における共鳴器諸元が燃焼振動の制振効果に与える影響を模式的に示す概念図。
【図９】本発明に係る燃焼振動解析方法の手順を示すフロー図。
【図１０】本発明に係る燃焼振動のデータ処理系および演算処理系の実施形態を示すブロック図。
【図１１】燃焼室内および共鳴器内圧力と励振周波数の関係に対する計算結果の一例を示す図（共鳴器のスロート抵抗を１×１０^４ｍ^−１ｓ^−１としたとき）。
【図１２】本発明に係る燃焼振動のデータ処理系、演算処理系、共鳴器のデータ処理系および制御駆動系の実施形態を示す概念図。
【図１３】共鳴器のスロート抵抗が燃焼室内圧力と共鳴器のヘルムホルツ周波数の関係に及ぼす影響に対する計算結果の一例を示す図。
【図１４】図１１において共鳴器のスロート抵抗を１×１０^５ｍ^−１ｓ^−１としたときの燃焼室内および共鳴器内圧力と励振周波数の関係に対する計算結果の一例を示す図。
【図１５】図１１において共鳴器のスロート抵抗を１×１０^６ｍ^−１ｓ^−１としたときの燃焼室内および共鳴器内圧力と励振周波数の関係に対する計算結果の一例を示す図。
【図１６】共鳴器のスロート抵抗が燃焼室内圧力と励振周波数の関係に及ぼす影響に対する計算結果の一例を示す図。
【図１７】共鳴器のヘルムホルツ周波数が燃焼室内圧力と励振周波数の関係に及ぼす影響に対する計算結果の一例を示す図。
【図１８】従来のガスタービン燃焼器の構造および周辺構成を示す概略図。
【図１９】従来のガスタービン燃焼器内に発生する燃焼振動強度の一例を示すグラフ。
【符号の説明】
１ ロータ
２ 圧縮機
３ ガスタービン
４ 空気
５ 高圧空気
６ ガスタービン燃焼器
７ 燃料配管
８ 燃料弁
９ 燃料
１０ 燃焼ガス
１１ 排気ガス
１２ 燃焼器ケーシング
１３ 燃焼室
１４ 燃料噴射部
１５ 点火プラグ
１６ 燃焼域
１７ センサ
１８ 尾筒
１９ 火炎
２０ 入口端
２１ 出口端
２２ 共鳴器
２３ 音響共鳴振動
２４ 共鳴器空洞
２５ スロート
２６ ヘルムホルツ振動
２７，２８ 燃焼室空洞
２９ 連通管
３０ ヘルムホルツ振動
３１ データ処理系
３２ 演算処理系
３３ データ処理系
３４ 制御駆動系
３５ 駆動ロッド
３６ ピストン[0001]
BACKGROUND OF THE INVENTION
In the present invention, when a combustion gas is generated by mixing fuel and air, the combustion vibration phenomenon induced by the generated combustion gas is grasped by numerical analysis in advance, and the combustion vibration is suppressed based on the grasped numerical analysis. The present invention relates to a combustion vibration analysis method, a combustion vibration analysis apparatus, and an analysis program using these analysis techniques.
[0002]
[Prior art]
Recently, in a combustion apparatus, for example, a gas turbine combustor, stable operation is required over a wide range from start operation to rated load operation or stop operation as part of improving reliability.
[0003]
Furthermore, in gas turbine combustors, as part of efforts to improve performance and prevent environmental destruction, the output (load) is further increased as the gas turbine inlet combustion gas temperature is increased, or the NOx concentration is further reduced. Enhancements have been made.
[0004]
As countermeasures for these problems, in gas turbine combustors, low NOx using premixed combustion, cooling of components using air or steam, increase of internal energy by heating fuel in advance, etc. .
[0005]
Gas turbine combustors are required to diversify fuel such as conversion from expensive fuels such as liquefied natural gas (LNG) to inexpensive fuels such as kerosene and light oil. Although measures to cope with these high temperatures, low NOx, and diversification of fuels are being performed as appropriate, the operating conditions are still quite severe with respect to stabilization of combustion and the life of components in application. In particular, NOx reduction by premixed combustion, steam, and water injection sacrifices the combustion stability of the combustion gas in the combustion chamber, and as a result, durability due to wear of components due to increased combustion vibration, etc. It has a great influence on life reliability.
[0006]
FIG. 18 is a schematic system diagram illustrating conventional gas turbine combustion as an example.
[0007]
The gas turbine rotor 1 is provided with a compressor 2 and a gas turbine 3. The compressor 2 sucks in atmospheric air 4, turns the sucked air 4 into high-pressure air 5, and supplies it to the gas turbine combustor 6.
[0008]
In the gas turbine combustor 6, the fuel 9 sent through the fuel valve 8 of the fuel pipe 7 is added to the high-pressure air 5 from the compressor 2, and both are mixed to generate the combustion gas 10. The combustion gas 10 is supplied to the gas turbine 3 as a working fluid.
[0009]
The gas turbine 3 performs an expansion work on the combustion gas 10 as a working fluid supplied from the gas turbine combustor 6 to obtain power (rotational torque), and then drives a generator (not shown) to output electric power. The gas turbine exhaust that has finished the expansion work is discharged as the exhaust gas 11 into the atmosphere.
[0010]
In addition, the gas turbine combustor 6 includes a cylindrical combustion chamber 13 surrounded by a combustor casing 12, and a fuel injection unit 14 for injecting fuel 9 in a mist form is installed on the head side, thereby injecting fuel. The high-pressure air 5 from the compressor 2 is added to the fuel 9 injected from the section 14 to diffuse and turn.
[0011]
The combustion chamber 13 includes an ignition plug 15 that ignites the fuel 9 injected from the fuel injection unit 14, a sensor 17 that detects pressure fluctuations of the combustion gas 10 generated in the combustion region 16 by ignition, and the combustion gas 10. Are respectively provided to the gas turbine 3.
[0012]
On the other hand, the fuel 9 continues to burn while being mixed and diffused with the swirling high-pressure air 5, and at that time, combustion vibration having a frequency ranging from about several tens Hz to about several tens kHz may be accompanied. In particular, this combustion vibration grows in resonance with the acoustic characteristics of the combustion chamber 13 using a pulsating flame generated in the fuel region 16 as an excitation source, and a high vibration intensity appears in a relatively low frequency range up to several hundred Hz. There are many. Sometimes, it resonates with the casing vibration and acoustic vibration of the gas turbine combustor itself, and a large abnormal vibration or abnormal internal pressure appears, which is one of the factors that impair the reliability of the gas turbine combustor 6.
[0013]
FIG. 19 shows an example of the result of frequency analysis of the pressure fluctuation detected by the sensor 17 (see FIG. 18) provided in the combustion chamber 13 and shows the combustion vibration intensity generated in the gas turbine combustor 6. It is a graph. Such combustion vibrations are considered to be unavoidable to some extent during the combustion process of the fuel 9, although there are differences in level.
[0014]
As described above, the elucidation and vibration suppression of the combustion vibration of the gas turbine combustor 5 is one of the important technical issues along with the high temperature of the gas turbine inlet combustion gas, low NOx, and fuel diversification. On the other hand, however, the vibration mechanism and vibration characteristics of the combustion reaction flow with complicated behavior have not been clarified yet, and there are no successful examples of numerical simulation prediction of combustion vibration. Met.
[0015]
[Problems to be solved by the invention]
As described above, it is considered that predicting combustion vibration characteristics and establishing the vibration control technology have great significance for improving the operational reliability of the gas turbine combustor and extending the service life of components. In particular, in combined cycle power plants and coal gasification combined power plants, which are expected to be installed more and more in the future, high temperatures and low NO as described above._XTherefore, the importance of combustion vibration suppression technology is expected to increase more and more.
[0016]
By the way, in recent gas turbine combustors, high output is demanded, and accordingly, the gas turbine inlet combustion gas temperature is 1500 ° C. or more. For this reason, the combustion chamber is generated by a high combustion gas temperature while selecting a high-strength heat-resistant steel to cope with excessive thermal stress that occurs due to a sudden rise in temperature of the combustion gas or gas turbine load fluctuations, etc. In consideration of thermal expansion, the joint portions of the combustion chamber nodes are loosely connected. In recent combustion chambers, a relatively thin material is used for a high strength ratio in order to reduce labor for carrying-in, installation, inspection and the like.
[0017]
However, if the combustion chamber is made of a thin material and the joints of the combustion chamber nodes have the above-described loose-fitting connection configuration, if an unexpected excessive combustion vibration is excited, or the combustion vibration If the acoustic characteristics of the combustion chamber and the combustion chamber resonate, the combustion chamber may vibrate vigorously, resulting in excessive damage. Further, even when the combustion vibration does not become apparent, the combustion chamber itself is accompanied by a slight vibration, which may cause a crack due to high cycle fatigue in the support member constituting the gas turbine combustor. For this reason, suppressing combustion vibration is an important technical matter that leads to not only stable operation of the gas turbine combustor, but also stabilization of the component member life.
[0018]
In addition, high temperature and low NO required for gas turbine combustors_XCombustion conditions accompanying fuel conversion, fuel diversification, etc. cultivate conditions that facilitate and induce combustion vibrations. These demands have a trade-off relationship with the combustion stability in the combustion chamber, and while responding to these demands, there is a possibility of inducing the result of impairing reliability due to equipment wear due to increased vibration. .
[0019]
In this way, it is urgently required to improve the reliability by suppressing the combustion vibration in the entire operation range of the gas turbine combustor, and the excitation source generated in the combustion process and the excitation mechanism of the combustion vibration are clarified. In addition, there has been a demand for the establishment of effective damping technology against combustion vibration.
[0020]
The present invention has been made on the basis of such circumstances, and the combustion gas required for the combustion apparatus has a high temperature and low NO._XCombustion vibration analysis method, combustion vibration analysis apparatus, and analysis methods for reducing combustion vibration in the entire operating range of the combustion apparatus and improving reliability while responding to demands for fuel conversion and fuel diversification An object is to provide an analysis program using the.
[0021]
[Means for Solving the Problems]
In order to achieve the above object, a combustion vibration analyzing method according to the present invention divides a combustion chamber into a plurality of cavities and connects them through a communication pipe as described in claim 1. A flame as an excitation source is placed in at least one of the cavities as a pressure source that fluctuates with the number of excitation cycles, and a resonator is installed in one of the combustion chambers divided into a plurality of cavities via a throat. The combustion vibration excited as acoustic vibration in the combustion chamber is represented as Helmholtz vibration in which the pressure in the cavity and the resonator, the flow rate in the connecting pipe and the throat fluctuates at a constant frequency, and the cavity The frequency response characteristics of the Helmholtz vibration with respect to the excitation frequency of the pressure source are calculated on the basis of the dimensions of the resonator, the communication tube, and the throat, thereby evaluating the vibration damping effect of the resonator. And a method of deriving by numerical calculation pressure, the frequency response characteristic of the flow rate.
[0022]
Moreover, in order to achieve the above-mentioned object, the combustion vibration analysis method according to the present invention divides the combustion chamber into a plurality of cavities as described in claim 2, and connects them through a communication pipe. The combustion vibration excited as acoustic vibration in the combustion chamber is represented as Helmholtz vibration in which the pressure in the cavity and the flow rate in the connecting pipe fluctuate at a constant frequency, and the acoustic resonance frequency of the actually measured combustion vibration is Method of deriving the frequency response characteristics of pressure and flow rate corresponding to the actual combustion vibration form by numerical calculation by adjusting the volume of the cavity and the cross-sectional area and length of the communication pipe so as to be equal to the frequency of Helmholtz vibration It is.
[0023]
Moreover, in order to achieve the above-mentioned object, the combustion vibration analyzing method according to the present invention divides the combustion chamber into a plurality of cavities as described in claim 3, and connects them through a communication pipe. The combustion vibration excited as acoustic vibration in the combustion chamber is represented as Helmholtz vibration in which the pressure in the cavity and the flow rate in the connecting pipe fluctuate at a constant frequency, and the frequency is relative to the acoustic resonance frequency of the actual combustion vibration. Analysis is performed to search for an acoustic resonance frequency having a large pressure fluctuation amplitude in real time, so that the measured acoustic resonance frequency is equal to the frequency of the Helmholtz oscillation, the volume of the cavity, the cross-sectional area of the communication pipe, and This is a method of adjusting the length and deriving the frequency response characteristics of pressure and flow rate that respond quickly to combustion vibrations that change from moment to moment by numerical calculation.
[0024]
Moreover, in order to achieve the above-mentioned object, the combustion vibration analyzing method according to the present invention includes a combustion chamber and a resonator installed in the combustion chamber via a throat as described above. Resonator specifications such as the length of the resonator and the throat length are adjusted by a control drive system so that the frequency response characteristics of pressure and flow rate corresponding to the combustion vibration that varies from time to time are derived by numerical calculation. Is the method.
[0025]
Further, in order to achieve the above-mentioned object, the combustion vibration analyzing method according to the present invention was actually measured by measuring the pressure fluctuation in the resonator installed in the combustion chamber as described in claim 5. Comparing and analyzing the frequency and amplitude of the pressure fluctuation by the pressure fluctuation and the numerical calculation, the combustion chamber and the resonator used for the numerical calculation are matched so that the measured pressure fluctuation matches the frequency and the amplitude of the pressure fluctuation by the numerical calculation. In this method, the value of the connected throat fluid resistance is adjusted so as to immediately respond to the actual situation, and the vibration damping effect is derived by numerical calculation with optimum prediction accuracy with respect to the combustion vibration that fluctuates every moment.
[0026]
Moreover, in order to achieve the above-mentioned object, the combustion vibration analyzing apparatus according to the present invention divides the combustion chamber into a plurality of cavities as described in claim 6, and connects them through a communication pipe, A flame as an excitation source is placed in at least one of the cavities as a pressure source that fluctuates with the number of excitation periods, and a resonator is provided via a throat in any one of the combustion chambers divided into a plurality of cavities. The combustion vibration excited as acoustic vibration in the combustion chamber is represented as Helmholtz vibration in which the pressure in the cavity and the resonator, the flow rate in the connecting pipe and the throat fluctuates at a constant frequency, and By calculating the frequency response characteristics of the Helmholtz vibration with respect to the excitation frequency of the pressure source based on the dimensions of the cavity, the resonator, the communication pipe, and the throat, Evaluated, those having an analysis means for performing pressure, Starring processing and data processing the frequency response characteristic of the flow rate is derived by numerical calculations.
[0027]
Moreover, in order to achieve the above-mentioned object, the combustion vibration analyzing apparatus according to the present invention comprises means for actually measuring an acoustic resonance frequency of combustion vibration, and the measured acoustic resonance as described in claim 7. Adjust the calculation conditions such as the volume of the cavity that divides the combustion chamber into multiple parts and the dimensions of the connecting pipe to connect the frequency so that the frequency matches the Helmholtz frequency, and the frequency response of the pressure and flow rate corresponding to the actual combustion vibration mode And an analyzing means for deriving the characteristic by numerical calculation.
[0028]
In order to achieve the above-mentioned object, the combustion vibration analyzing apparatus according to the present invention performs frequency analysis on the acoustic resonance frequency of the combustion vibration to achieve a large pressure fluctuation amplitude. Means for searching the acoustic resonance frequency in real time, and calculation conditions such as the volume of the cavity divided into a plurality of combustion chambers so that the measured acoustic resonance frequency matches the Helmholtz frequency, the dimensions of the communication pipe connecting them And analyzing means for deriving the frequency response characteristics of the pressure and flow rate corresponding to the combustion vibration that varies from time to time by numerical calculation.
[0029]
Further, in order to achieve the above-mentioned object, the combustion vibration analyzing apparatus according to the present invention has a resonance cavity volume, a throat dimension for connecting the combustion chamber and the resonator, etc. The apparatus is equipped with means for adjusting the specifications of the chamber so that the combustion chamber and the resonator are constantly in resonance, and analysis means for deriving optimal vibration suppression with respect to combustion vibration that varies from time to time by numerical calculation.
[0030]
In order to achieve the above-mentioned object, the combustion vibration analyzing apparatus according to the present invention measures the pressure fluctuation in the resonator as described in claim 10, and the measured pressure fluctuation and the pressure by numerical calculation are measured. By means of comparative analysis of fluctuations, the throat resistance connecting the combustion chamber and the resonator is corrected to a value closer to the true value based on the comparative analysis results, and the vibration is controlled with optimal prediction accuracy against the fluctuation of the combustion fluctuations from moment to moment. And an analysis means for deriving by numerical calculation.
[0031]
In order to achieve the above object, an analysis program according to the present invention is a medium in which a program for analyzing combustion vibrations in a combustion chamber by a computer is recorded. And time variation of pressure and flow rate in the combustion chamber and the resonator using the Helmholtz oscillation equation for the combustion chamber and the medium fluid in the resonator. Are coupled and analyzed, and a procedure for deriving frequency response characteristics of pressure and flow rate by numerical calculation is executed.
[0032]
Further, in order to achieve the above object, an analysis program according to the present invention is based on measurement and analysis results such as an acoustic resonance frequency in a combustion chamber and a pressure fluctuation in a resonator. Adjust the calculation conditions such as the volume of the cavity that divides the combustion chamber into multiple parts and the dimensions of the communication pipe that connects them, and correct the throat resistance that connects the combustion chamber and the resonator to a value closer to the true value. These data are reflected as calculation conditions when the Helmholtz oscillation equation is analyzed.
[0033]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of a combustion vibration analysis method, a combustion vibration analysis apparatus, and an analysis program using these analysis techniques according to the present invention will be described with reference to the drawings and the reference numerals attached to the drawings.
[0034]
In addition, the same code | symbol is attached | subjected to the same component as the component of the prior art shown in FIG. 18 and FIG. 19, and duplication description is abbreviate | omitted.
[0035]
FIG. 1 is a conceptual diagram showing an embodiment of combustion vibration in the combustion vibration analysis method according to the present invention.
[0036]
In the combustion vibration analysis method according to the present embodiment, the combustion vibration is classified into three types: (a) natural vibration, (b) acoustic vibration, and (c) system vibration.
[0037]
These three types of vibrations are classified as follows.
[0038]
(A) The natural vibration is a vibration derived from microscopic instability or fluctuation held in the reactivity of the fuel 9 in the flame 19 generated in the combustion region 16 on the head side of the combustion chamber 13.
[0039]
The existence of this natural vibration is theoretically predicted and there are few examples of academic practical research, but there are few reports on practical use in engineering.
[0040]
(B) The acoustic vibration is one in which a specific acoustic resonance frequency is induced using the natural vibration of the flame 19 as a white sound source including various frequency components as an excitation source and the combustion chamber 13 as an acoustic resonator. In addition, the shape of the combustion chamber 13 is not a little affected.
[0041]
(C) In the system vibration, the combustion chamber 13 forms a single fluid vibration system with a peripheral system such as a fuel supply system, an air supply system or an exhaust gas system, and the natural vibration and acoustic vibration of the flame 19 serve as an excitation source. Resonance occurs.
[0042]
FIG. 2 is a simple block diagram showing the relationship between the three types of combustion vibration modes (a) natural vibration, (b) acoustic vibration, and (c) system vibration classified in FIG. is there.
[0043]
In FIG. 2, the fuel 9 injected from the fuel injection section 14 into the combustion zone 16 forms a flame 19 as an excitation source of natural vibration. The acoustic waves of various frequencies generated by this natural vibration reciprocate in the space between the inlet end 20 and the outlet end 21 of the combustion chamber 13 using the combustion gas 10 as a medium.
[0044]
The acoustic field in the combustion chamber 13 resonates by such reciprocation of the acoustic wave, and acoustic vibration of a specific frequency is induced. Further, due to the interference between the fuel injection unit 14 and the flame 19, the pulsation change of the flame 19 is negatively fed back to the fuel valve 8, and system vibration such as Helmholtz vibration accompanied by pulsation of fuel supply may occur.
[0045]
On the other hand, regarding combustion vibration, from the viewpoint of both resonance instability and system instability, analysis by Rayleigh has long been used (for example, see Rayleigh, L., “The Theory of Sound”, Dover-Press (1945)). Since then, various elucidations have been made on the generation mechanism of combustion vibration. Many of them are wave equations, and numerical calculations using the wave equations (e.g., Bruno B. H. Schuermans, et.al, “Prediction and Acoustic-Pres- -0105, Proceedings of IGTITE 2000, ASME International Gas Turbine and Aeroengine Congress and Exhibition, May 13-16, 2000 Munich, Bavaria, and vibrations) The analysis method is also disclosed in Japanese Patent Application Laid-Open No. 11-132458.
[0046]
However, the wave equation expresses the behavior of acoustic waves in a stationary medium with a constant temperature as a linear approximation, and changes in temperature distribution and flow velocity distribution due to combustion, such as combustion oscillations in the combustion chamber 13. Not applicable when accompanied. Therefore, in the numerical calculation using the wave equation, the actual situation is that it has not always been successful enough to describe the combustion vibration.
[0047]
On the other hand, numerical fluid dynamics using a fluid equation (for example, Steven J. Brookes, et.al, “Computational Modeling of Self-Excited Combustion Institutes”, 2000-GT-0104, Proceedings of TURBO EP Unlike May 8-11, 2000, Munich Germany), the flow phenomenon can be described more precisely unlike the numerical calculation by the wave equation described above.
[0048]
On the other hand, however, there is a problem that the calculation amount is enormous, and for the complex interaction between the combustion flame and the acoustic field, although it is possible to interpret the experimental results to some extent, the prior prediction of vibration generation is not possible. It is still a difficult situation.
[0049]
FIG. 3 is a conceptual diagram showing an example of a calculation model related to damping of combustion vibration by a conventional resonator.
[0050]
This example is a calculation model in which a Helmholtz vibration system including a resonator 22 installed for vibration suppression is added to an acoustic vibration system including a combustion chamber 13, and a conventional combustion vibration having a wave equation or a fluid equation as a governing equation. An acoustic damping model of combustion vibration by an analysis method is schematically shown.
[0051]
As shown in FIG. 3, in order to enhance the vibration damping effect, the resonator 22 is installed at a position close to the inlet end 20 of the combustion chamber 13 which is the abdomen of the pressure fluctuation portion. Here, the flow in the combustion chamber 13 is treated as a one-dimensional flow from the inlet end 20 to the outlet end 21, and the normal temperature fuel 9 is supplied from the inlet end 20 of the combustion chamber 13 at a predetermined inlet flow velocity, and combustion is performed. A combustion reaction is caused in the region to form a flame 19.
[0052]
Further, the combustion gas 10 generated on the downstream side is exhausted from the outlet end 21 of the combustion chamber 13. At this time, if the combustion chamber 13 is considered as an acoustic housing, as shown in FIG. 3, the acoustics having an inlet end 20 and an outlet end 21 as the pressure fluctuation abdomen and the center of the combustion chamber 13 as the pressure fluctuation node are shown. Resonant vibration 23 is excited.
[0053]
Equation (1) is the acoustic resonance frequency ω of the acoustic m-order mode excited in the housing._m[Rad / s] is given. The acoustic resonance vibration 23 shown in FIG. 3 corresponds to the case of the primary acoustic mode in which m = 1 in Equation (1). Here, a is the speed of sound [m / s], L is the effective length [m] of the combustion chamber 13, M is the average molecular weight [kg / mol] of the combustion gas 10, and m is the order of the acoustic mode [−], p Is the pressure [Pa], R is the gas constant [J / mol * K], T is the temperature [K], g is the specific heat ratio [−], and r is the mass density [kg / m.³]. Note that the phase relationship (the relationship between the antinode and the node) of the flow velocity fluctuation is reversed from the pressure fluctuation acoustic mode, the inlet end 20 and the outlet end 21 become nodes, and the center of the combustion chamber 13a becomes antinode.
[0054]
[Expression 1]

[0055]
The resonator 22 includes a resonator cavity 24 and a throat 25, and the combustion chamber 13 and the resonator 22 are connected by a throat 25. The Helmholtz vibration 26 excited between the combustion chamber 13 and the resonator cavity 24 via the throat 25 interacts with the acoustic resonance vibration 23 excited in the combustion chamber 13 to thereby suppress the acoustic resonance vibration 23. Has the effect of. The vibration suppression for the acoustic resonance vibration 23 can be qualitatively evaluated by a combustion vibration analysis method using a conventional wave equation or fluid equation as a governing equation.
[0056]
However, the acoustic resonance vibration 23 excited in the actual combustion chamber 13 has a problem in its calculation accuracy or needs to be corrected by actual measurement. For example, the acoustic resonance frequency ω shown in Equation (1)_mShows the resonance characteristics of acoustic waves due to minute pressure fluctuations in the sealed casing in the first place. Actually, however, the influence of the temperature distribution and flow velocity distribution due to the combustion reaction of the fuel 9 must be considered in the combustion chamber 13. In other words, the speed of sound a is not constant in the combustion chamber 13.
[0057]
Therefore, in the present invention, instead of the conventional combustion vibration analysis method using the wave equation or the fluid equation as a governing equation, a combustion vibration analysis method based on the Helmholtz vibration equation, a combustion vibration analysis device, which is more suitable for vibration control, and An analysis program using these analysis methods is provided.
[0058]
FIG. 4 is a conceptual diagram showing an example of a calculation model related to damping of combustion vibration by the resonator according to the present invention.
[0059]
In the present embodiment, the acoustic resonance vibration 23 whose both ends are antinodes and the center is a node in the combustion chamber 13 shown in FIG. 3 is formed between the combustion chamber cavities 27 and 28 in which the combustion chamber 13 is virtually divided, It is handled as Helmholtz vibration 30 in which pressure and flow rate fluctuate at a constant frequency through a communication pipe 29 connecting them. In this embodiment, the flame 19 as an excitation source is installed as a sound source in the combustion chamber cavity 28, and the Helmholtz vibration 30 in the combustion chamber 13 is excited between the combustion chamber 13 and the resonator cavity 24. The Helmholtz vibration 26 is treated as a two-degree-of-freedom Helmholtz vibration system, and the frequency response characteristics of pressure and flow rate by a combustion vibration analysis method using the Helmholtz vibration equation as a governing equation can be derived by a computer or the like.
[0060]
In the two-degree-of-freedom Helmholtz vibration system schematically shown in FIG. 4, how effective is the resonator 22 against the acoustic resonance vibration 23 (see FIG. 3) excited in the combustion chamber 13. Whether it is provided will be described in detail below.
[0061]
First, in general, three preconditions are assumed for Helmholtz oscillation: (1) in-phase approximation, (2) isentropic approximation, and (3) linear approximation.
[0062]
here,
(1) In the in-phase approximation, the element size of the resonator cavity 24 or the like is sufficiently smaller than the wavelength of the acoustic wave, and each element can be treated as a lumped constant, and a mode such as acoustic vibration is excited in the element. Instead, the fluctuations are in phase.
[0063]
(2) The isentropic approximation is an isentropic process in which the thermodynamic change of the working fluid is a quasi-static adiabatic process.
[0064]
(3) The linear approximation applies a value in which the fluctuation value associated with the fluid vibration is sufficiently smaller than the steady value.
[0065]
Assuming that the state variables in the resonator cavity 24, the throat 25, the combustion chamber cavities 27 and 28, and the communication pipe 29 are uniform by the above-mentioned in-phase approximation, the equation (2) Obtain the equation of motion for the working fluid.
[0066]
Where A is the cross-sectional area [m²], L is length [m], p is pressure [pa], R is resistance [m]^-1s^-1], T is the time [s], f is the flow flux [kg / s], and the subscripts A, B, C, F, and S for the variables are the combustion chamber cavities 27 and 28 and the resonator cavity 24, respectively. In addition, it shall be attached | subjected with respect to each variable of the communication pipe | tube 29 and the throat 25, and it shall be based on it also below. The mass flux f_F, F_SThe positive direction is the direction from the combustion chamber cavity 28 to the combustion chamber cavity 27, or from the resonator cavity 24 to the combustion chamber cavity 28, respectively.
[0067]
[Expression 2]

[0068]
[Equation 3]

[0069]
[Expression 4]

[0070]
Next, P in the combustion chamber cavity 28_f(T) = F ·_sinAssuming that an excitation source ωt exists, Equation (3) can be approximated by Equation (5) as Equation (6). This is due to the pressure p in the combustion chamber cavities 27, 28 and the resonator cavity 24._A, P_B, P_CAnd the mass flux f in the communication pipe 29 and the throat 25_F, F_SThis shows the relationship.
[0071]
[Equation 5]

[0072]
[Formula 6]

[0073]
Of the general solution of Equation (7), only the response vibration term due to the external force (excitation source) excluding the natural vibration term is shown in Equation (8). The natural vibration term decays with t → ∞, but the response vibration term continues to vibrate as long as the excitation source persists. Equation (9) represents the pressure p in the combustion chamber cavity 28 and resonator cavity 24 obtained from equations (6) and (8)._B, P_CIndicates.
[0074]
[Expression 7]

[0075]
Coefficient C in Equation (8) and Equation (9)₁, C₂, D₁, D₂Is obtained by solving equation (10) obtained by substituting equation (8) into equation (7). Equation (11) is the Helmholtz frequency ω via the communication pipe 29 between the combustion chamber cavities 27, 28._ABThe Helmholtz frequency ω through the throat 25 between the resonator cavity 24 and the combustion chamber cavity 28._BC, Helmholtz frequency ω when freely released from the combustion chamber cavity 28 to the infinite atmosphere through the communication pipe 29_{B, F}, Helmholtz frequency ω when free from the combustion chamber cavity 28 to the infinite atmosphere through the throat 25_{B, S}Define each. Equation (12) shows the temperature T of each of the combustion chamber cavities 27 and 28 and the resonator cavity 24._A, T_B, T_CSpeed of sound a defined for different_AB, A_BC, A_BIt is. In particular, when there is a temperature difference between the combustion chamber cavities 27 and 28 and the resonator cavity 24, the correction of the sound velocity as shown in the equation (12) is required, but when these temperatures are all equal, the equation (12 All sound velocities defined in) are equal.
[0076]
[Equation 8]

[0077]
Now, in the equations (8) to (12), the cross-sectional area A of the throat 25_SIs set to zero, and the mass flux f in the communication pipe 29 is expressed by the equations (13) to (15), respectively._F, Pressure p in the combustion chamber cavity 28_B, And the response phase delay ψ from the excitation source. These represent frequency response characteristics with respect to the excitation frequency ω with respect to the Helmholtz vibration 30 through the communication pipe 29 between the combustion chamber cavities 27 and 28 of the combustion chamber 13 when the resonator 22 is not installed.
[0078]
[Equation 9]

[0079]
FIG. 5 shows the mass flux f shown in equation (13)._FThe frequency response characteristic of [kg / s] is shown. In other words, the frequency response characteristic of a single degree of freedom Helmholtz vibration system is conceptually shown.
[0080]
As shown in FIG. 5, the excitation frequency ω is the Helmholtz frequency ω._ABThe frequency response characteristic has a resonance peak and the fluid resistance R_FWhen = 0, the resonance peak diverges, but conversely, the fluid resistance R_FWhen is too large, no resonance peak appears. Also, fluid resistance R_F= 0, the response phase difference is zero, but the fluid resistance R_FWhen> 0, there is a certain phase difference. The Helmholtz vibration 30 via the communication pipe 29 between the combustion chamber cavities 27 and 28 is expressed by the Helmholtz frequency ω._ABResonates when it matches the excitation frequency ω.
[0081]
In addition, effective vibration suppression by the resonator 22 can analytically evaluate the frequency response characteristic with respect to the actual system, as already derived from the equation (8).
[0082]
In the present embodiment, when the Helmholtz vibration 30 via the communication pipe 29 between the combustion chamber cavities 27 and 28 vibrates violently in resonance with the excitation frequency ω, the resonator 22 is provided to install the combustion chamber 13. The objective is to dampen the frequency response characteristic of the two-degree-of-freedom Helmholtz vibration system comprising the resonator 22 by detuning (non-resonating) from the excitation frequency ω.
[0083]
The Helmholtz frequency ω in the frequency response characteristic of the two-degree-of-freedom Helmholtz vibration system including the combustion chamber 13 and the resonator 22 based on the equations (8) to (12) derived in this embodiment will be described below._ABVerify the detuning from.
[0084]
First, the equation (16) is expressed by the equation of the equation (8) in which the fluid resistance R_F, R_SIs the mass flux when ignoring.
[0085]
[Expression 10]

[0086]
FIG. 6A is a conceptual diagram illustrating the vibration vibration suppression principle of the resonator 22 in FIG. 4 and the frequency response characteristics of the two-degree-of-freedom Helmholtz vibration system. In the state of the single-degree-of-freedom Helmholtz vibration system having only the combustion chamber 13 in which the resonator 22 is not installed, for example, as shown in FIG._ABHowever, in FIG. 6, in FIG. 6B, a two-degree-of-freedom Helmholtz vibration system composed of the combustion chamber 13 and the resonator 22 is formed, and the two resonance frequencies ω shown in the equation (17) are formed.₁, Ω₂become.
[0087]
## EQU11 ##

[0088]
7A and 7B are conceptual diagrams showing the phase relationship between the pressure oscillation modes of the combustion chamber 13 and the resonator 22 in FIG.
[0089]
As shown in FIGS. 7A and 7B, these resonance frequencies are equal to ω at which the resonator cavity 24 and the combustion chamber cavity 28 vibrate in the same phase mode.₁And oscillating in antiphase mode₂Corresponds to the two modes. That is, by installing the resonator 22, the Helmholtz frequency ω_ABIt is suppressed that the flame 19 and the combustion chamber 13 that pulsately burn at an excitation frequency ω close to 1 and the combustion chamber 13 vibrate in resonance.
[0090]
For example, R in equation (13)_F= 0, ω = ω_ABIs f_F→ ∞ diverged, but in equation (16) f_FIs settled to a finite value. This is due to the detuning of the frequency response characteristics due to the installation of the resonator 22.
[0091]
On the other hand, R in equation (16)_F= 0, ω = ω₁Or ω = ω₂Is f_F→ ∞ diverges, meaning that the resonance peak is dipolarized.
[0092]
FIG. 8 conceptually shows the influence of the resonator specifications in FIG. 4 on the suppression of combustion vibration, and shows the Helmholtz frequency ω of the resonator 22._BCAnd the vibration strength, the resistance R of the throat 25_SIt is a conceptual diagram which shows the dependence with respect to.
[0093]
ω_AB= Ω_BCSometimes the combustion chamber 13 and the resonator 22 are in resonance, and the most effective vibration suppression as described above can be expected, but even under such conditions, the resistance R_SIf is large, vibration control is reduced.
[0094]
As described above, the resonator 22 is installed in the combustion chamber 13 and the ω_AB= Ω_BCBy adjusting so that the resonance frequency of the system becomes ω_ABCan be detuned. On the other hand, the acoustic resonance vibration 23 actually excited in the combustion chamber 13 does not allow a degree of freedom other than a specific resonance frequency defined by the shape of the combustion chamber.
[0095]
Therefore, in this embodiment, the resonance frequency of the system is set to ω by installing the resonator 22._ABThe acoustic resonance vibration 23 is damped by moving to a frequency region away from the system and transitioning to a non-resonant state in terms of the system. In order to further reduce the noise of the combustion chamber 13, it is necessary to install a resonator 22 having a sufficient size that can absorb acoustic energy that is localized in the combustion chamber 13. It is also important to optimize specifications such as shape.
[0096]
Next, another embodiment of a combustion vibration analysis method, a combustion vibration analysis apparatus, and an analysis program using these analysis techniques according to the present invention will be described with reference to the drawings shown below and the reference numerals attached to the drawings. .
[0097]
In addition, the same code | symbol is attached | subjected to the same component as the component of the prior art shown in FIG. 18, and duplication description is abbreviate | omitted.
[0098]
FIG. 9 is a flowchart showing the procedure of the combustion vibration analyzing method according to the present invention.
[0099]
First, in step 1, the shapes of the combustion chamber 13 and the resonator 22 are input to a computer such as a computer. Next, in step 2, an excitation source by the flame 19 is set.
[0100]
For example, when an excitation source of Pf (t) = F · sin ωt exists, the acoustic amplitude F and the excitation frequency ω are set.
[0101]
Further, in step 3, each element condition of the two-degree-of-freedom Helmholtz vibration system is set based on the shape of the combustion chamber 13 and the like input in step 1.
[0102]
For example, the mass M of the combustion chamber cavities 27 and 28, the resonator cavity 24, the pressure P, the volume V, the communication pipe 29, the cross-sectional area A, the length L, and the resistance R of the throat 25 are set.
[0103]
In the procedure 4, the coefficient C is obtained by solving the equation (10) by actually performing numerical calculation based on each element condition set in the procedure 3.₁, C₂, D₁, D₂Ask for.
[0104]
In step 5, the coefficient C obtained in step 4₁, C₂, D₁, D₂Is substituted into equations (8) and (9), and the frequency response characteristics of mass flux φ and pressure P are evaluated.
[0105]
In step 6, frequency analysis is performed on the acoustic resonance frequency of the combustion vibration obtained by actual measurement, and an acoustic resonance frequency having a large pressure fluctuation amplitude is searched in real time. If the measured acoustic resonance frequency deviates from the frequency of Helmholtz vibration derived by numerical calculation with a computer such as a computer, the calculation is performed again after returning to step 4 and reviewing the condition setting of the vibration element. It is.
[0106]
Similarly to step 6, in step 7, based on the pressure fluctuation data in the resonator obtained by actual measurement, the measured pressure fluctuation and the frequency and amplitude of the pressure fluctuation by numerical calculation by a computer such as a computer are calculated. Perform comparative analysis. If there is a deviation between the measured pressure fluctuation and the frequency or amplitude of the pressure fluctuation by numerical calculation, adjust the value of the throat fluid resistance connecting the combustion chamber and the resonator used for numerical calculation so as to respond to the actual situation. Then, the procedure returns to the procedure 3 again.
[0107]
As described above, in the present embodiment, since the combustion vibration analysis apparatus such as a computer is stored as a recording medium for programming the procedures 1 to 7, the temporal changes in the pressure and flow rate in the combustion chamber 13 and the resonator 22 are linked. The frequency response characteristics of pressure and flow rate can be derived by numerical calculation, and the quality of damping can be evaluated based on the numerical calculation.
[0108]
FIG. 10 is a block diagram used to describe the embodiment of the combustion vibration data processing system and arithmetic processing system shown in the flowchart of FIG. 9 in more detail.
[0109]
In addition, the same code | symbol is attached | subjected to the same component as the component shown in FIG.
[0110]
In the present embodiment, the pressure fluctuation measured by the sensor 17 installed in the combustion chamber 13 is frequency-analyzed by the data processing system 31, and an acoustic resonance frequency having a particularly large pressure fluctuation amplitude is searched in real time. The result is reflected in the arithmetic processing system 32.
[0111]
That is, in the procedure 6 shown in FIG. 9, the actually obtained measurement value of the acoustic resonance frequency is converted into the Helmholtz frequency Ω obtained by the calculation procedure up to the frequency procedure 4._ABCompared with the calculated value, the difference between the two is eliminated to simulate the actual acoustic resonance mode, and each element condition of the two-degree-of-freedom Helmholtz vibration system is corrected.
[0112]
As described above, in this embodiment, the apparatus shape such as the combustion chamber 13 is input (procedure 1), the excitation source is set (procedure 2), the vibration system element condition is set (procedure 3), and the numerical calculation is performed by the Helmholtz vibration equation ( The acoustic resonance in the case where the resonator 22 is installed in the combustion chamber 13 through the procedure 4), the evaluation of the frequency response characteristics (procedure 5), the correction of the vibration system element condition (procedure 6), and the correction of the throat resistance (procedure 7). The vibration suppression of the vibration 23 can be evaluated by numerical calculation with a computer such as a computer.
[0113]
Such usefulness will be described below using a specific calculation example.
[0114]
In the calculation model shown in FIG. 4, a particularly important calculation parameter is the volume V of the resonator cavity 24._C, Flame 19 excitation frequency ω, throat 25 resistance R_SIt is. The volume V of the resonator cavity 24, which is the first calculation parameter_CIs the Helmholtz frequency ω of the resonator 22_BCThat is, the resonance state between the combustion chamber 13 and the resonator 22 is determined. On the other hand, the excitation frequency ω, which is the second calculation parameter, determines the resonance state between the combustion chamber 13 and the flame 19. When the combustion chamber 13 and the flame 19 are in resonance, a large acoustic resonance vibration 23 is normally excited in the combustion chamber 13, but by adding a resonator 22 in resonance with the combustion chamber 13, the combustion chamber On the contrary, the acoustic resonance vibration 23 in 13 is damped. The third calculation parameter, the resistance R of the throat 25_SAs already shown in FIG. 8, is a parameter that gives how much this damping effect can be expected.
[0115]
First, as calculation conditions, the working fluid has an average molecular weight of 28.34 kg / kmol, a specific heat ratio of 1.278, and a pressure of 1.013 × 10 6.⁵The combustion gas was Pa (1 atm). Both the combustion chamber cavities 27 and 28 had a diameter of 224 mm, a length of 500 mm, and a temperature of 1800 K, and the communication pipe 29 had a diameter of 224 mm, a length of 500 mm, and a temperature of 1800 K. The resonator cavity 24 has a diameter of 152 mm, a length of 40 mm, a temperature of 460 K, and the throat 25 has a diameter of 27 mm, a length of 55 mm, and a temperature of 800 K.
[0116]
Throat 25 resistance R_S, And resistance R of the communication pipe 29_FWas calculated on the basis of the figures estimated by the following.
[0117]
First, the product of the resistance of the throat 25 and the mass flux φs corresponds to the pressure loss of the throat 25. Since the amplitude of the flow fluctuation accompanying the fluid vibration such as the Helmholtz vibration 26 is basically a small value to which linear approximation can be applied, the friction loss coefficient ζ due to the fluctuation flow velocity_FApplies the laminar flow equation to give equation (18).
[0118]
Ds is the diameter [m] of the throat 25, Ls is the length [m], Re is the Reynolds number [−] of the working fluid in the throat 25, μs is the flow velocity [m / s], and μ is the viscosity. [M²/ S], ρ is the mass density [kg / m³].
[0119]
[Expression 12]

[0120]
Therefore, M is the average molecular weight of the fluid in the throat 25 [kg / mol], P₀Is the pressure [Pa], R is the gas constant [J / mol * K], T_SIs the temperature [K] and the above calculation condition is substituted, the resistance R_SEquation (19) can be derived as follows.
[0121]
On the other hand, the resistance R of the communication pipe 29_FThe diameter D of the communication pipe 29_FIs the Helmholtz frequency ω_ABResistance R_FNot for giving. Resistance R_FRepresents the resistance of the combustion chamber 13 that is the object of vibration suppression, and the resistance R of the throat 25 that is the vibration suppression means._SAssuming a numerical value equivalent to. In addition, Formula (19) is resistance R by the wall friction loss in a smooth pipe | tube._SThe actual resistance R due to the influence of the surface roughness of the inner wall surface at the throat 25 and the contraction / expansion loss of the flow at both ends is shown._SIs a value exceeding this, with the value shown in Equation (19) as the lower limit.
[0122]
[Formula 13]

[0123]
FIG. 11 corresponds to FIG. 6 with the throat resistance of the resonator being 1 × 10⁴m^-1s^-15 is a diagram showing an example of a calculation result for the relationship between the internal pressure of the combustion chamber 13 and the resonator 22 and the excitation frequency.
[0124]
As described above, in each element condition of the two degree-of-freedom Helmholtz vibration system shown in FIG._AB= Ω_{B C}Is adjusted to be 270 Hz. The excitation source is a sound source having a pressure fluctuation amplitude of 1.0 Pa placed in the combustion chamber cavity 28, and the pressure p in the combustion chamber cavity 28 when the resonator 22 is "not"._B, And the pressure p in the combustion chamber cavity 28 when the resonator 22 is “present”_BAnd the pressure p in the resonator cavity 24_CThe frequency response characteristic is shown.
[0125]
When the resonator 22 is “not present”, the frequency response characteristic in the combustion chamber cavity 28 has a resonance peak at 270 Hz. That is, when the excitation frequency of the flame 19 is ω = 270 Hz, the combustion chamber 13 vibrates vigorously in resonance with the flame 19. On the other hand, when the resonator 22 is “present”, the frequency response characteristic in the combustion chamber cavity 28 no longer has a resonance peak at the position of ω = 270 Hz, and the resonance peak is on the high frequency side and the low frequency side. Bipolarization. As a result, it has been found that for the flame 19 having an excitation frequency of ω = 270 Hz, the combustion chamber cavity 28 no longer resonates due to the effect of the resonator 22.
[0126]
As described above, the pressure fluctuation in the combustion chamber 13 collected by the sensor 17 is subjected to frequency analysis in the data processing system 31, and an acoustic resonance frequency having a particularly large pressure fluctuation amplitude is confirmed, for example, when it is 270 Hz. In the arithmetic processing system 32, the Helmholtz frequency ω_BCEach element condition of the Helmholtz vibration 30 is adjusted so that = 270 Hz.
[0127]
By adopting such means, the acoustic resonance frequency that constantly varies in the combustion chamber 13 can be accurately grasped in real time, and the actual acoustic resonance mode can be further damped.
[0128]
Next, still another embodiment of the combustion vibration analyzing method, the combustion vibration analyzing apparatus, and the medium in which the analysis program to be executed by the computer using these analysis techniques is recorded in the drawings and drawings shown below. The description will be made with reference to the attached symbols.
[0129]
Note that the same reference numerals are given to the same components as those of the related art shown in FIG. 18 and the components of the present invention shown in FIG.
[0130]
FIG. 12 is a conceptual diagram showing an embodiment of a combustion vibration data processing system, arithmetic processing system, resonator data processing system, and control drive system according to the present invention.
[0131]
In the embodiment shown in FIG. 10, the pressure fluctuation in the combustion chamber 13 collected by the sensor 17 is frequency-analyzed in real time in the data processing system 31 by the procedure up to step 6 shown in FIG. Is reflected in the arithmetic processing system 32, and a numerical calculation can be performed by a computer or the like in accordance with the mode of combustion vibration that varies from moment to moment. As a result of being able to perform numerical calculations in accordance with the mode of combustion vibration, it is possible to check whether or not the acoustic resonance vibration 23 in the combustion chamber 13 is sufficiently damped.
[0132]
On the other hand, in the present embodiment shown in FIG. 12, the data processing system 33 is provided in the resonator 22, the measurement result of the pressure Pc in the resonator cavity 24, and the resonator derived by the arithmetic processing system 32. A comparative analysis is made with the calculation result of the pressure Pc in the cavity 24.
[0133]
Based on this comparison work, the resistance Rs of the throat 25 used by the numerical calculation performed by the computer or the like in the arithmetic processing system 32 as the procedure 7 shown in FIG. 9 is corrected to a value closer to the true value, and is resonated with appropriate prediction accuracy. The vibration suppression by the device 22 can be derived by numerical calculation.
[0134]
Further, the control drive system 34 has a function of constantly driving the drive rod 35 with the output information from the arithmetic processing system 32 being constantly input. A piston 36 is attached to the tip of the drive rod 35. The length of the resonator cavity 24 can be adjusted by the position of the piston 36.
[0135]
If the combustion chamber 13 and the resonator 22 are in a non-resonant state and the vibration of the acoustic resonance vibration 23 is not sufficient, the control drive system 34 shows the volume of the resonator cavity 24 in the flowchart shown in FIG. In order to optimize, a control drive of the drive rod 35 is newly added as a procedure 8.
[0136]
Hereinafter, the usefulness of the present embodiment will be described with reference to specific calculation examples.
[0137]
FIG. 13 corresponds to FIG. 8 and is a diagram illustrating an example of a calculation result with respect to the influence of the throat resistance of the resonator 22 on the relationship between the internal pressure of the combustion chamber 13 and the Helmholtz frequency of the resonator 22. The calculation condition conforms to each element condition used when deriving the calculation result shown in FIG. The vertical axis shown in FIG. 13 indicates the pressure p in the combustion chamber cavity 28._BSPL value [dB] (SPL: Sound Pressure Level), the horizontal axis is the Helmholtz frequency ω of the resonator 22_BCThe parameter is the resistance R of the throat 25_SIt is. The SPL value is defined by [dB] display as shown in the equation (20), but the normal SPL value is a very small amount of fluctuation compared to the steady atmospheric pressure, and the sound pressure of human conversation in daily life. Is a value of about 60 dB. In this embodiment shown in FIG. 13, the Helmholtz vibration 30 in the combustion chamber 13 vibrates vigorously in resonance with the excitation frequency ω = 270 Hz (ω = ω_AB), Helmholtz frequency ω of the resonator 22_BCΩ_ABAlthough the vibration damping effect appears almost when adjusted in the vicinity, according to the numerical calculation according to the present embodiment, it has been found that the place where the vibration damping effect is maximum is shifted to a slightly higher frequency side than 270 Hz.
[0138]
[Expression 14]

[0139]
Next, the resistance R of the throat 25 as a calculation parameter in FIG._SThe effect of the frequency response characteristics on will be described below.
[0140]
14 and 15 show an example of calculation results for the relationship between the internal pressure of the combustion chamber 13 and the resonator 22 and the excitation frequency, and the resistance R of the throat 25 of the resonator 22 in FIG._S1 × 10 each⁵m^-1s^-11 × 10⁶m^-1s^-1An example of the calculation result is shown. As already shown in FIG. 11, the resistance R of the throat 25_S= 1 x 10⁴m^-1s^-1When the resonator 22 is installed, the frequency response characteristic in the combustion chamber cavity 28 has two resonance peaks on the high frequency side and the low frequency side of the excitation frequency ω = 270 Hz, and the combustion chamber corresponds to the excitation frequency ω = 270 Hz. The cavity 28 no longer resonates.
[0141]
However, as shown in FIGS. 14 and 15, the resistance R of the throat 25_SAs the value increases, the tendency of polarization of the resonance peak is not recognized. That is, as in the case where the resonator 22 is not provided, the frequency response characteristic in the combustion chamber cavity 28 has a resonance peak at a place where the excitation frequency ω = 270 Hz. In particular, the resistance R of the throat 25_SIs sufficiently equivalent to the state without the resonator 22, the combustion chamber 13 vibrates vigorously in resonance with the excitation frequency ω = 270 Hz.
[0142]
FIG. 16 is a diagram showing an example of calculation results for the influence of the throat resistance Rs of the resonator 22 on the relationship between the internal pressure of the combustion chamber 13 and the excitation frequency, including the above calculation results.
[0143]
FIG. 17 shows the resistance R_S= 1. × 10³m^-1s^-1It is a figure which shows an example of the calculation result with respect to the influence which the Helmholtz frequency of the resonator 22 at the time has on the relationship between the internal pressure of the combustion chamber 13, and an excitation frequency.
[0144]
Helmholtz frequency ω of the resonator 22_BCIn the case of = 270 Hz, as indicated by the broken line in the figure, at ω = 270 Hz, the amplitude of the pressure fluctuation in the combustion chamber cavity 28 is sufficiently small and is damped. In contrast, ω_BCIs outside of 270 Hz, the pressure fluctuation amplitude is no longer small.
[0145]
In the present embodiment, in step 7 shown in FIG. 9, the measured value of the pressure fluctuation in the resonator 22 by the data processing system 33 described above, and the calculated value of the pressure fluctuation already calculated by the arithmetic processing system 32 Compare and analyze. Through this comparative analysis work, in this embodiment, the resistance R of the throat 25 used in the numerical calculation in the arithmetic processing system 32 described above._SIs corrected in a direction closer to the true value and adjusted so that vibration suppression by the resonator 22 can be derived by numerical calculation with better prediction accuracy. By repeating this operation, almost optimal prediction accuracy can be ensured.
[0146]
Next, in step 8, in order to maximize the vibration damping effect of the resonator 22, the position of the piston 36 is variable and the volume V of the resonator cavity 24 is changed._CThe Helmholtz frequency ω of the resonator 22_BCTo optimize. Further, based on these, the procedure returns to step 3 again, and the frequency response characteristic for the excitation source is reconfirmed by numerical calculation based on the optimized new element condition.
[0147]
As described above, in the present embodiment, the acoustic resonance vibration 23 is controlled when the resonator 22 is installed in the combustion chamber 13 through adjustment of the throat resistance (procedure 7) and optimization of the resonator cavity volume (procedure 8). Vibration control can be evaluated in real time by numerical calculation while maintaining high prediction accuracy for vibration. Further, in this embodiment, the numerical calculation by the Helmholtz oscillation equation has a small calculation load, and it is possible to immediately take vibration control means including optimization of resonator specifications including application of technology to active control and the like. .
[0148]
【The invention's effect】
As described above, according to the present invention, after analyzing combustion vibrations induced in a combustion apparatus such as a gas turbine combustor and grasping the actual state, measures for reducing various vibration levels resulting therefrom are taken. Since it can be taken accurately, it contributes to the improvement of the reliability of the gas turbine or gas turbine plant, including the extension of the life of the combustion device itself, and the reduction of the operation rate and repair and inspection costs of the plant. .
[Brief description of the drawings]
FIG. 1 is a conceptual diagram showing an aspect of combustion vibration in a combustion vibration analysis method according to the present invention.
FIG. 2 is a simplified block diagram showing a mutual relationship with respect to a combustion vibration mode in FIG. 1;
FIG. 3 is a conceptual diagram showing an example of a calculation model related to damping of combustion vibration by a conventional resonator.
FIG. 4 is a conceptual diagram showing an example of a calculation model related to damping of combustion vibration by a resonator according to the present invention.
FIG. 5 is a diagram conceptually showing frequency response characteristics of a single-degree-of-freedom Helmholtz vibration system.
6 is a conceptual diagram showing the vibration damping principle of the combustion vibration by the resonator in FIG. 4 and the frequency response characteristics of the two-degree-of-freedom Helmholtz vibration system, (A) is a conceptual diagram of the two-degree-of-freedom Helmholtz vibration system; FIG. 3 is a diagram conceptually showing the above-described response characteristics of a two-degree-of-freedom Helmholtz vibration system.
7 is a conceptual diagram showing the phase relationship between the pressure oscillation modes of the combustion chamber and the resonator in FIG. 4, (A) is a conceptual diagram showing the in-phase mode, and (B) is a conceptual diagram showing the anti-phase mode.
8 is a conceptual diagram schematically showing the influence of the resonator specifications in FIG. 4 on the vibration damping effect of combustion vibration.
FIG. 9 is a flowchart showing a procedure of a combustion vibration analyzing method according to the present invention.
FIG. 10 is a block diagram showing an embodiment of a combustion vibration data processing system and an arithmetic processing system according to the present invention.
FIG. 11 is a diagram showing an example of calculation results for the relationship between the pressure in the combustion chamber and in the resonator and the excitation frequency (the throat resistance of the resonator is 1 × 10⁴m^-1s^-1)
FIG. 12 is a conceptual diagram showing an embodiment of a combustion vibration data processing system, an arithmetic processing system, a resonator data processing system, and a control drive system according to the present invention.
FIG. 13 is a diagram showing an example of a calculation result with respect to the influence of the throat resistance of the resonator on the relationship between the pressure in the combustion chamber and the Helmholtz frequency of the resonator.
14 shows the resonator throat resistance of 1 × 10 in FIG.⁵m^-1s^-1The figure which shows an example of the calculation result with respect to the relationship between the pressure in a combustion chamber and a resonator, and an excitation frequency when it is taken as.
15 shows the resonator throat resistance of 1 × 10 in FIG.⁶m^-1s^-1The figure which shows an example of the calculation result with respect to the relationship between the pressure in a combustion chamber and a resonator, and an excitation frequency when it is taken as.
FIG. 16 is a diagram showing an example of a calculation result with respect to the influence of the throat resistance of the resonator on the relationship between the pressure in the combustion chamber and the excitation frequency.
FIG. 17 is a diagram showing an example of a calculation result with respect to the influence of the Helmholtz frequency of the resonator on the relationship between the pressure in the combustion chamber and the excitation frequency.
FIG. 18 is a schematic diagram showing the structure and peripheral configuration of a conventional gas turbine combustor.
FIG. 19 is a graph showing an example of combustion vibration intensity generated in a conventional gas turbine combustor.
[Explanation of symbols]
1 rotor
2 Compressor
3 Gas turbine
4 Air
5 High pressure air
6 Gas turbine combustor
7 Fuel piping
8 Fuel valve
9 Fuel
10 Combustion gas
11 Exhaust gas
12 Combustor casing
13 Combustion chamber
14 Fuel injection part
15 Spark plug
16 Combustion zone
17 Sensor
18 tail tube
19 Flame
20 Entrance end
21 Exit
22 Resonator
23 Acoustic resonance vibration
24 Resonator cavity
25 Throat
26 Helmholtz vibration
27, 28 Combustion chamber cavity
29 Communication pipe
30 Helmholtz vibration
31 Data processing system
32 Arithmetic processing system
33 Data processing system
34 Control drive system
35 Drive rod
36 piston

Claims (12)

Dividing the combustion chamber into a plurality of cavities, connecting them through a communication pipe, placing a flame as an excitation source in at least one of the cavities as a pressure source that varies with the number of excitation cycles, A resonator is installed in any one of the combustion chambers divided into two through a throat, and combustion vibration excited as acoustic vibration in the combustion chamber is applied to the pressure in the cavity and the resonator, the connection The frequency response characteristic of Helmholtz vibration with respect to the excitation frequency of the pressure source is expressed as Helmholtz vibration in which the flow rate in the tube and the throat fluctuates at a constant frequency, and based on the dimensions of the cavity, resonator, communication tube, and throat The combustion vibration analysis method is characterized in that the vibration damping effect of the resonator is evaluated by calculating the frequency response characteristics of pressure and flow rate by numerical calculation. . The combustion chamber is divided into a plurality of cavities, and these are connected via a communication pipe. Combustion vibrations excited as acoustic vibrations in the combustion chamber are generated at a frequency at which the pressure in the cavity and the flow rate in the connection pipe are constant. The volume of the cavity, the cross-sectional area and the length of the communication pipe are adjusted so that the acoustic resonance frequency of the actually measured combustion vibration becomes equal to the frequency of the Helmholtz vibration. A combustion vibration analysis method characterized by deriving a frequency response characteristic of pressure and flow rate that immediately responds to a combustion vibration form by numerical calculation. The combustion chamber is divided into a plurality of cavities, and these are connected via a communication pipe. Combustion vibrations excited as acoustic vibrations in the combustion chamber are generated at a frequency at which the pressure in the cavity and the flow rate in the connection pipe are constant. It is expressed as a Helmholtz vibration that fluctuates in frequency, and frequency analysis is performed on the acoustic resonance frequency of the actual combustion vibration, and an acoustic resonance frequency having a large amplitude of pressure fluctuation is searched in real time, and the measured acoustic resonance frequency is the Helmholtz vibration. The volume of the cavity, the cross-sectional area and the length of the communication pipe are adjusted to be equal to the frequency of the pressure, and the frequency response characteristics of the pressure and flow rate corresponding to the combustion vibration that varies from time to time are derived by numerical calculation. A characteristic combustion vibration analysis method. The resonator parameters such as the length of the resonator and the throat length are adjusted by the control drive system so that the combustion chamber and the resonator installed in the combustion chamber via the throat are always in a resonance state. A combustion vibration analysis method characterized by deriving, by numerical calculation, frequency response characteristics of pressure and flow rate that immediately respond to fluctuating combustion vibration. Actually measure the pressure fluctuation in the resonator installed in the combustion chamber, compare and analyze the measured pressure fluctuation and the frequency and amplitude of the pressure fluctuation by numerical calculation, and the measured pressure fluctuation and the frequency of pressure fluctuation by numerical calculation The throat fluid resistance value connecting the combustion chamber and the resonator used for numerical calculation is adjusted so as to respond to the actual situation so that the amplitude and amplitude match, and the optimal prediction accuracy for the combustion vibration that changes from moment to moment A combustion vibration analysis method characterized in that the damping effect is derived by numerical calculation. Dividing the combustion chamber into a plurality of cavities, connecting them through a communication pipe, placing a flame as an excitation source in at least one of the cavities as a pressure source that varies with the number of excitation cycles, A resonator is installed in any one of the combustion chambers divided into two through a throat, and combustion vibration excited as acoustic vibration in the combustion chamber is applied to the pressure in the cavity and the resonator, the connection The frequency response characteristic of Helmholtz vibration with respect to the excitation frequency of the pressure source is expressed as Helmholtz vibration in which the flow rate in the tube and the throat fluctuates at a constant frequency, and based on the dimensions of the cavity, resonator, communication tube, and throat To evaluate the damping effect of the resonator, and to perform the performance and data processing to derive the frequency response characteristics of pressure and flow rate by numerical calculation. Combustion oscillation analysis apparatus characterized by comprising means. The means for actually measuring the acoustic resonance frequency of combustion vibration, the volume of the cavity into which the combustion chamber is divided into a plurality of parts so that the measured acoustic resonance frequency matches the Helmholtz frequency, the dimensions of the connecting pipes connecting these, etc. A combustion vibration analysis apparatus comprising: an analysis means for adjusting a calculation condition and deriving a frequency response characteristic of a pressure and a flow rate corresponding to an actual combustion vibration form by numerical calculation. A means for performing a frequency analysis on the acoustic resonance frequency of the combustion vibration and searching for an acoustic resonance frequency having a large pressure fluctuation amplitude in real time, and a combustion chamber so that the measured acoustic resonance frequency matches the Helmholtz frequency. Analyzing means that adjusts the calculation conditions such as the volume of the cavity divided into multiple parts and the dimensions of the communication pipe that connects them, and derives the frequency response characteristics of pressure and flow rate corresponding to the combustion vibration that fluctuates from time to time by numerical calculation. A combustion vibration analyzer characterized by comprising. Resonator dimensions such as resonator cavity volume, throat dimensions connecting the combustion chamber and the resonator, and other means to adjust the combustion chamber and the resonator to be in a state of continuous resonance. A combustion vibration analyzing apparatus comprising an analyzing means for deriving optimum vibration suppression by numerical calculation. A means for measuring the pressure fluctuation in the resonator and comparing and analyzing the measured pressure fluctuation and the pressure fluctuation by numerical calculation, and the throat resistance connecting the combustion chamber and the resonator is closer to the true value from the comparison analysis result. And a analyzing means for deriving vibration suppression by numerical calculation with optimal prediction accuracy with respect to combustion vibration that fluctuates every moment. A medium in which a program for analyzing combustion vibration in a combustion chamber is recorded by a computer, the data relating to the shape of the combustion chamber and the resonator, the fuel condition, the combustion condition of the flame, and the medium fluid in the combustion chamber and the resonator Using the Helmholtz oscillation equation, the pressure and flow rate changes in the combustion chamber and the resonator are coupled and analyzed, and a procedure for deriving frequency response characteristics of the pressure and flow rate by numerical calculation is executed. Analysis program. Based on the measurement and analysis results such as the acoustic resonance frequency in the combustion chamber and the pressure fluctuation in the resonator, the calculation conditions such as the volume of the cavity obtained by dividing the combustion chamber into a plurality of dimensions and the dimensions of the communication pipe connecting them are adjusted. An analysis program characterized by correcting a throat resistance connecting the combustion chamber and the resonator to a value closer to a true value and reflecting these data as calculation conditions when analyzing the Helmholtz oscillation equation.

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