Ther­moa­cous­tics

What are the caus­es of acous­tic feed­back?

Acous­tic feed­back is char­ac­ter­ized by eigen­fre­quen­cies and eigen­modes. With most self-ex­cit­ed com­bus­tion in­sta­bil­i­ties, feed­back is pro­vid­ed by acous­tics. To un­der­stand the caus­es lead­ing to self-ex­cit­ed com­bus­tion in­sta­bil­i­ties, it is thus in­dis­pens­able to first con­sid­er in de­tail the acous­tics of a com­bus­tion sys­tem. In this con­text, po­ten­tial­ly res­o­nant acous­tic fre­quen­cies (eigen­fre­quen­cies) and the as­so­ci­at­ed eigen­modes of sound pres­sure and par­ti­cle ve­loc­i­ty are of major im­por­tance. Ei­gen­modes are de­fined as the stand­ing waves of sound pres­sure and par­ti­cle ve­loc­i­ty pro­duced by res­o­nance.

The fol­low­ing il­lus­tra­tion demon­strates, for a sim­ple tube closed at one end and open at the other, the eigen­modes cor­re­spond­ing to the first, sec­ond and third har­mon­ic along the lon­gi­tu­di­nal axis of the tube. The bound­ary con­di­tions are ide­al­ized and as­sumed to be acous­ti­cal­ly closed for the left end and acous­ti­cal­ly open for the right one.

In con­trast to this sim­ple ex­am­ple, eigen­modes in a real com­bus­tion sys­tem look sig­nif­i­cant­ly dif­fer­ent owing to changes in cross-sec­tion, to the in­flu­ence ex­ert­ed by flow con­di­tions, to tem­per­a­ture fluc­tu­a­tions with­in the com­bus­tion zone and to the com­plex bound­ary con­di­tions at the in­lets and out­lets of the sys­tem.

Premix flames are fa­vored in mod­ern com­bus­tion sys­tems to re­duce emis­sions, be­cause they have low NOx emis­sions due to their low flame tem­per­a­tures. Un­for­tu­nate­ly, with this type of com­bus­tion, and in con­junc­tion with com­bus­tion-cham­ber acous­tics, so-called self-ex­cit­ed com­bus­tion dy­nam­ics emerge very quick­ly. These are often also re­ferred to as com­bus­tion in­sta­bil­i­ties, ther­moa­cous­tic in­sta­bil­i­ties, or, in ac­cor­dance with the au­di­ble fre­quen­cies, also known as rum­bling, hum­ming, screech­ing or pul­sa­tion.

Strong pres­sure fluc­tu­a­tions at one or more fre­quen­cies are the un­der­ly­ing cause of such vi­bra­tions. Pres­sure fluc­tu­a­tions can achieve such high am­pli­tudes that the com­bus­tion sys­tem it­self or com­po­nents con­nect­ed up­stream and down­stream are de­stroyed. These vi­bra­tions can be ob­served in a range of sit­u­a­tions from house­hold heat­ing sys­tems to large-scale fir­ings and from sta­tion­ary gas tur­bines to rock­et en­gines.

The IFTA PreCur­sor is a method for early de­tec­tion of com­bus­tion dy­nam­ics- even be­fore high am­pli­tudes occur which can lead to dam­age.

How does the nu­mer­i­cal modal anal­y­sis work?

For com­put­ing pur­pos­es, any ge­om­e­try to be an­a­lyzed is ren­dered dis­crete by means of cylin­dri­cal and con­i­cal el­e­ments that per­mit the mod­el­ing of ac­tu­al cross-sec­tions to any de­gree of pre­ci­sion re­quired. This dis­cretiz­ing pro­ce­dure is backed by com­pre­hen­sive ex­per­i­men­tal know-how; after all, the qual­i­ty of any re­sults ob­tained is de­ter­mined to a large ex­tent by ap­pro­pri­ate par­ti­tion­ing of the do­main to be an­a­lyzed. Dis­cretized ge­om­e­try, to­geth­er with fur­ther pa­ram­e­ters - tem­per­a­ture, flow ve­loc­i­ty and acous­tic bound­ary con­di­tions - con­sti­tute the basic data for a spe­cial nu­mer­i­cal code. Acous­tic bound­ary con­di­tions, in­clud­ing fre­quen­cy-de­pen­dent ones, can be im­posed at will. In the event that com­pli­cat­ed bound­ary con­di­tions can­not be suf­fi­cient­ly for­mal­ized by the­o­ret­i­cal ap­proach­es, we offer ex­per­i­men­tal stud­ies per­formed ac­cord­ing to the n mi­cro­phone method. The pro­gram code used was writ­ten at IFTA; new fea­tures are being added con­tin­u­ous­ly.

This ver­sion makes it pos­si­ble to eas­i­ly vary the length or cross-sec­tion of any given tube el­e­ment to tar­get re­search on spe­cif­ic shifts in mode or fre­quen­cy.

What de­fines the Rayleigh cri­te­ri­on?

The Rayleigh cri­te­ri­on is an im­por­tant sta­bil­i­ty cri­te­ri­on for self-ex­cit­ed com­bus­tion os­cil­la­tions

If any res­o­nant fre­quen­cy is to be ex­cit­ed with­in a com­bus­tion cham­ber, a source of sound is re­quired that con­stant­ly feeds en­er­gy into the sys­tem at the cor­rect os­cil­la­to­ry fre­quen­cy. With any com­bus­tion sys­tem, en­er­gy is sup­plied by heat re­lease rates os­cil­lat­ing around their mean value.

How­ev­er, any such ther­mal power os­cil­la­tion must not only have the cor­rect fre­quen­cy to trig­ger self-ex­cit­ed com­bus­tion in­sta­bil­i­ties but also the cor­rect phase angle suit­able for re­in­forc­ing the sound pres­sure fluc­tu­a­tions aris­ing with­in the sys­tem. In 1878, Lord Rayleigh first de­ter­mined the cri­te­ri­on that now bears his name. Ac­cord­ing to it, com­bus­tion in­sta­bil­i­ties are ex­cit­ed if the os­cil­la­tion of sound-pres­sure and a flame's heat re­lease rate are in-phase, or damped down, if they are anti-phase. Put­nam and Den­nis took up this idea and pro­vid­ed a for­mal math­e­mat­i­cal rep­re­sen­ta­tion of Rayleigh's cri­te­ri­on, the so-called "Rayleigh in­te­gral":

This in­te­gral means that the prod­uct of ther­mal power Q(t) and sound pres­sure os­cil­la­tion p(t), in­te­grat­ed over the pe­ri­od of os­cil­la­tion T (=1/f [s]), must be pos­i­tive for any com­bus­tion os­cil­la­tion to be ex­cit­ed. When­ev­er it is neg­a­tive, os­cil­la­tions are damped.

Ap­ply­ing this equa­tion to any har­mon­ic os­cil­la­tion, the con­di­tion is met if the ab­so­lute value for the phase dif­fer­ence be­tween the os­cil­la­tions of heat re­lease and of sound pres­sure is less than or equal to 90°.

The re­search tools now avail­able from us for the one and two-di­men­sion­al Rayleigh in­dex­es con­sti­tute a log­i­cal­ly con­sis­tent ap­pli­ca­tion of this cri­te­ri­on. The Rayleigh index is a local ver­sion of the glob­al­ly ex­pressed in­equal­i­ty above al­low­ing to iden­ti­fy areas sub­ject to ex­ci­ta­tion and damp­ing with­in any com­bus­tion zone. With this in­for­ma­tion, the in­ter­ac­tions be­tween ther­mal and acous­tic os­cil­la­tions can be in­flu­enced de­lib­er­ate­ly.

The above il­lus­tra­tion shows the one and two-di­men­sion­al Rayleigh in­dex­es com­put­ed from ex­per­i­men­tal data ob­tained for a liq­uid fu­eled com­bus­tor. The one-di­men­sion­al Rayleigh index is plot­ted ver­sus burn­er length (bot­tom), the two-di­men­sion­al one as an in­ten­si­ty plot to­geth­er with the burn­er ge­om­e­try (top). It is ob­vi­ous that flame sec­tions sub­ject to ex­ci­ta­tion and damp­ing al­ter­nate along the com­bus­tion cham­ber and that ex­cit­ing do­mains pre­dom­i­nate, a fact which leads to the ob­served com­bus­tion in­sta­bil­i­ties.

How do self-ex­cit­ed or self-in­duced com­bus­tion os­cil­la­tions de­vel­op?

Given cer­tain op­er­at­ing con­di­tions, in­dus­tri­al-type com­bus­tion and propul­sion sys­tems may be sub­ject to self-ex­cit­ed com­bus­tion in­sta­bil­i­ties, some­times des­ig­nat­ed flame pul­sa­tions or os­cil­la­tions, which are char­ac­ter­ized by pres­sure os­cil­la­tions aris­ing at dis­crete fre­quen­cies. With low-power sys­tems, such as do­mes­tic or aux­il­iary ve­hi­cle heat­ing sys­tems, com­bus­tion in­sta­bil­i­ties nor­mal­ly only pro­duce high lev­els of noise.

With high­er-power sys­tems, such as re­gen­er­at­ing air heat­ing units, process gas heaters, gas tur­bines or rock­et en­gines, the pres­sure am­pli­tudes reached are some­times so high that the al­ter­nat­ing loads en­tailed by them may re­sult in me­chan­i­cal sys­tem fail­ure of the com­bus­tion cham­bers as well as the up­stream and down­stream com­po­nents. For in­stance, pres­sure am­pli­tudes mea­sured for process gas heaters reached 0.5 bar, and even 5 bars for a rock­et com­bus­tion cham­ber.

In ad­di­tion to pres­sure fluc­tu­a­tions, self-ex­cit­ed com­bus­tion in­sta­bil­i­ties in­vari­ably in­duce, via sound par­ti­cle ve­loc­i­ties, equiv­a­lent fluc­tu­a­tions of flow ve­loc­i­ties that lead, in their turn, to sub­stan­tial­ly in­creased amounts of heat being trans­ferred to com­bus­tion cham­ber walls. Thus, ther­mal loads will in­crease, in ad­di­tion to me­chan­i­cal ones, so that there are def­i­nite ther­mal haz­ards that might even de­stroy the com­bus­tion cham­ber. When am­pli­tudes reach sub­stan­tial val­ues, burn­er flames can often no longer be sta­bi­lized so that they may flash back or be ex­tin­guished.

Ba­si­cal­ly, any self-ex­cit­ed com­bus­tion in­sta­bil­i­ty is due to sev­er­al quan­ti­ties in­ter­act­ing phys­i­cal­ly and lead­ing, given ap­pro­pri­ate pre­con­di­tions, to res­o­nance. In order to allow any such os­cil­la­tion to arise in a self-ex­cit­ed man­ner, sound-pres­sure and heat-re­lease os­cil­la­tions have to re­in­force each other. For this to hap­pen, there must be a feed­back mech­a­nism in­duc­ing heat re­lease fluc­tu­a­tions strong enough to re­in­force sound pres­sure os­cil­la­tions. In most cases, feed­back is caused by the acous­tics of the com­bus­tion sys­tem con­cerned. How­ev­er, other mech­a­nisms have like­wise been ob­served.

For in­stance, struc­tural vi­bra­tions in rock­et drives may mod­u­late fuel flows sup­ply­ing the com­bus­tion cham­ber and thus pro­duce os­cil­la­tions of the heat re­lease rate of the flame. The vi­bra­tions caused by these pe­ri­od­ic changes of the heat re­lease rate in turn re­in­force the struc­tural os­cil­la­tions, thus clos­ing the loop.

Self-ex­cit­ed com­bus­tion dy­nam­ics are also often re­ferred to as com­bus­tion in­sta­bil­i­ties, ther­moa­cous­tic in­sta­bil­i­ties, or, in ac­cor­dance with the au­di­ble fre­quen­cies, also known as rum­bling, hum­ming, screech­ing or pul­sa­tion.