The moacous ic FEM modeling o pa ly
au oigni ion and p opaga ion-s abilized
lames
Symposium on The moacous ics in
Combus ion: Indus y mee s Academia
(SoTiC 2025)
Sep . 8 - Sep . 11, 2025
T ondheim, No way
Pape No.: 52
©The Au ho (s) 2025
Simon M. Heinzmann1,2 , Nino A. Lede 1, Ha ish S. Gopalak ishnan1and Mi ko R. Bo hien1,3
Abs ac
This pape desc ibes a me hodology o he moacous ically accoun o di e en lame ypes in a single Fini e-Elemen -
compu a ion. To do so, he lame segmen a ion mechanism p esen ed in p e ious s udies is used o cha ac e ize he
di e en lame zones. Di e en ia ion is done be ween p opaga ion-s abilized shea -laye lames and au oigni ion lames
ha espond o acous ic pe u ba ions e y di e en ly. While au oigni ion lames mainly espond o acous ic p essu e
and empe a u e luc ua ions, p opaga ion-s abilized lames espond o acous ic eloci y pe u ba ions. Thus, lame
ans e unc ions speci ic o each lame ype a e analy ically implemen ed wi hin he equency domain Fini e-Elemen -
compu a ion. Using he no el amewo k, i is shown ha he global FTF ob ained om Compu a ional-Fluid-Dynamics
(CFD) simula ions o a backwa d acing s ep ehea combus o can be ep oduced accu a ely in he low- equency
egime o an ope a ing poin whe e he lame is o ced in a plana manne . The in es iga ed ope a ing poin ope a es
on hyd ogen ully p emixed a lean and au oigni i e condi ions. The au oigni ion amewo k is alida ed by compa ison
o one-dimensional di ec -nume ical-simula ion (DNS). The ime a e aged CFD hea elease a e esul is alida ed wi h
la ge eddy simula ion (LES) da a.
Keywo ds
he moacous ic, au oigni ion, ehea -combus o , FEM
No el y and Signi icance S a emen
The no el y o his wo k lies in he inco po a ion o wo
di e en ypes o lame in a single he moacous ic FEM
calcula ion. To he bes o ou knowledge, his has no ye
been shown in he li e a u e be o e. The signi icance o his
wo k lies wi hin indus ial applica ions. In indus ial ehea
combus ion chambe s, he au oigni ion lame is ypically no
pu ely au oigni ion s abilized, and lame ancho ing egions
a e p esen which con ibu e o he s abili y o he lame.
Nomencla u e
Abb e ia ions
PV P og ess Va iable
CFD Compu a ional Fluid Dynamics
CFL Cou an -F ied ichs-Lewy
FEM Fini e-Elemen -Me hod
FTF Flame T ans e Func ion
HRR Hea Release Ra e
LES La ge eddy simula ion
RANS Reynolds A e aged Na ie -S okes
G eek
¯
˙ωP V A e aged u bulen sou ce e m o PV
˙ωP V Sou ce e m o P V
γRa io o speci ic hea s
ωAngula equency in ad/s
ρDensi y
σSp ead o ime delay
σ˙q,ai HRR wid h o au oigni ion lame
σ˙q,ps HRR wid h o p opaga ion-s abilized lame
τTime delay
Yi,0Ini ial mix u e composi ion
Roman
(·)′Pe u ba ion in ime domain
(·)0Time-a e aged quan i y
(·)ini Ini ial
(·)ai Au oigni ion
(·)ps P opaga ion-s abilized
˙qIns an aneous o al HRR
˙q0,a,ai Volume ic HRR in eg a ed along he s eam-
wise di ec ion o he au oigni ion lame
[W/m2]
˙q0,a,ps Volume ic HRR in eg a ed along he s eam-
wise di ec ion o he p opaga ion-s abilized
lame [W/m2]
ˆ
(·)Fou ie ans o m o a luc ua ing quan i y
ˆ
˙qVolume ic HRR pe u ba ion o en i e com-
bus ion chambe
ˆ
˙qa,ai Au oigni ion lame in eg a ed HRR pe u ba-
ion
1ZHAW Zu ich Uni e si y o Applied Sciences, Ins i u e o Ene gy
Sys ems and Fluid-Enginee ing, Win e hu , Swi ze land
2ETH Zü ich, Depa men o Mechanical and P ocess Enginee ing,
Zü ich
3Depa men o Ene gy and P ocess Enginee ing, NTNU, No way
Co esponding au ho :
S. M. Heinzmann, ZHAW Zu ich Uni e si y o Applied Sciences, Ins i u e
o Ene gy Sys ems and Fluid-Enginee ing, Win e hu , Swi ze land
Email: [email protected]
2Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(52)
ˆ
˙qa,ps P opaga ion-s abilized lame in eg a ed HRR
pe u ba ion
ˆ
1Downs eam a eling acous ic wa e
ˆg1Ups eam a eling acous ic wa e
ˆ
h1En opic wa e
ˆxig Au oigni ion lame mo emen pe u ba ion
c0Speed o sound
F1, F2, F3Au oigni ion lame HRR FTFs
iMass ac ions e.g. uel, ho gas, ca ie ai
FTFps P opaga ion-s abilized lame HRR FTF
G1, G2, G3Au oigni ion lame mo emen FTFs
pP essu e
P(·)P obabili y
pop Ope a ing p essu e
p e P essu e a e e ence loca ion
TTempe a u e
Time
uVeloci y
x, y, z x-,y- and z-coo dina es
xig,0Mean igni ion leng h
In oduc ion
To ul ill he Pa is ag eemen (1), a la ge-scale in eg a ion
o enewable ene gy sys ems in he ene gy landscape is
essen ial (2–4). To s abilize and balance he g id, gas u bines
unning on ca bon- ee uels can be an ideal asse (3;5–9).
Howe e , hese non-con en ional uels possess e y di e en
combus ion p ope ies when compa ed o na u al gas. Thus,
no el gas u bine combus o de elopmen is aced wi h new
challenges o enable he uel lexible i ing capabili y o an
engine. The he moacous ic analysis o aid he mi iga ion
o combus ion ins abili ies emains a key componen in he
de elopmen phase (10).
The e a e a a ie y o me hods o pe o m he moacous ic
analysis o combus ion chambe s. Di ec nume ical
simula ion (DNS) (11;12) and la ge eddy simula ion
(LES) (13) a e conside ed high- ideli y analysis ools,
which a e capable o analyzing ce ain he moacous ic
e ec s in he highes de ail. Howe e , hey come wi h
a high compu a ional cos and a e un easible o en i e
indus ial combus o geome ies. Al e na i ely, Helmhol z
sol e s in combina ion wi h lame ans e /desc ibing
unc ions ex ac ed om compu a ions o expe imen s
ha e been shown o accu a ely cap u e he he moacous ics
o combus ion chambe s (14–20). Nicoud e al. (14)
showed ha using a FEM Helmhol z sol e he s abili y o
combus ion chambe s wi h p opaga ion-s abilized lames
could be cap u ed accu a ely. To do so, he lame ans e
unc ion (FTF) was desc ibed by an n−τmodel (21).
Lae a e al. (15) also used a Helmhol z sol e oge he
wi h a lame desc ibing unc ion o co ec ly cap u e he
s abili y o a labo a o y scale annula combus ion chambe
comp ised o mul iple ma ix bu ne s. Sil a e al. (19)
combined a Helmhol z sol e wi h a lame desc ibing
unc ion o a swi l-s abilized combus ion chambe o
p edic he acous ic p essu e ampli udes o limi -cycles.
Gene ally, he applica ion o Helmhol z sol e s o pe o m
he moacous ic analysis signi ican ly educes compu a ional
ime compa ed o DNS and LES. Al e na i ely, ne wo k-
models ha e shown o be able o ep oduce he combus ion
chambe acous ics and lame in e ac ion wi h he highes
compu a ional e iciency (22–26).
In his pape , we p esen an FEM based app oach o
he moacous ically model lames ha a e pa ly s abilized
by au oigni ion. The o e all lame, which consis s o
a p opaga ion- and an au oigni ion pa , is analy ically
desc ibed in FEM. The segmen a ion mechanism om
p io s udies (17;18) is le e aged o de ine he di e en
lame ypes. The segmen a ion mechanism (17;27) was
ini ially designed o he moacous ically model non-compac
ehea lames unde he in luence o ans e se combus o
eigenmodes. In he case o ans e se eigenmodes, he
acous ic wa eleng h is o simila leng h as he lame, hus,
esul ing in an acous ically non-compac lame. To deal
wi h his, he segmen a ion mechanism di ides he lame
in o mul iple sub lames in ans e se di ec ion. Each o he
e y hin sub lames is hen conside ed acous ically compac
wi hou a ia ion o he luc ua ion quan i ies ac oss i s
heigh . Thus, single alues o he p essu e, empe a u e
and eloci y luc ua ions ac on each sub lame. Fo each
o he sub lames, a ans e unc ion can be assigned. In
he s udy p esen ed he e, he lame is acous ically compac
and as such no segmen a ion is needed. Howe e , he
segmen a ion mechanism is le e aged o assign a speci ic
FTF o each hea elease a e (HRR) egion depending on i s
lame s abiliza ion ype. To ob ain he lame cha ac e iza ion
pa ame e s, RANS simula ions a e done using Fluen wi h
an in-house ehea lame model, which is an adap a ion and
ex ension o he model de i ed by Kulka ni e al. (28;29).
The he moacous ic analysis is done o a plana ly o ced
backwa d acing s ep (BFS) bu ning hyd ogen a ele a ed
p essu e.
The p esen ed esea ch is ele an , because in indus ial
ehea combus o s he au oigni ion lame is ne e only s a-
bilized by au oigni ion. Typically, he ehea lame consis s
o p opaga ion-s abilized HRR egions as well as egions
p edominan ly s abilized by au oigni ion. P opaga ion-
s abilized lames occu wi hin he shea laye s o eci cu-
la ion zones. Thei s abiliza ion is go e ned by he balance
o he lame consump ion speed and he low eloci y.
Wi h espec o he moacous ics, he acous ic wa es a ec
he p opaga ion-s abilized lame egions by eloci y luc u-
a ions, which modula e he equi alence a io. In con as ,
au oigni ion s abilized lames a e go e ned by he balance
o he au oigni ion ime scale and he low esidence ime
scale. The luc ua ing p essu e and especially he isen opic
empe a u e luc ua ions induced by acous ic wa es a ec
he local eac ion a es and hus he igni ion chemis y.
This can s ongly al e he igni ion ime and he e o e he
igni ion leng h, which esul s in HRR luc ua ions. The eby,
he his o y e ec o he luc ua ions du ing he igni ion phase
ma e s o ehea lames and is accoun ed o in cu en
s a e-o - he-a lame esponse modeling ools, as p esen ed
in Re s. (17;27;30–33).
Heinzmann e al. 3
Valida ion da a
The segmen a ion mechanism de eloped by Heinzmann e
al. (17;18) was al eady alida ed in p io s udies and ini ially
designed o nume ically deal wi h acous ically non-compac
lames. This segmen a ion mechanism can also be e icien ly
used o he plana wa e case o inco po a e di e en lame
ypes. The model is compa ed o 1D DNS (32) o a lame
solely s abilized by au oigni ion, and o RANS compu a ions
o he pa ly au oigni ion- and p opaga ion-s abilized lame
in a BFS combus ion chambe .
1D DNS simula ion
The CFD s udy used o alida ion in Re . (34) is a
comp essible 1D DNS compu a ion bu ning hyd ogen ully
p emixed a lean condi ions. The ope a ing p essu e is
a mosphe ic wi h an inle empe a u e o 1100 K and an inle
low speed o 200 m/s. The duc o leng h 0.3 m wi h non-
e lec ing bounda y condi ions was o ced wi h acous ic and
en opic wa es a he inle . Fo mo e de ails on he nume ical
se up he eade is e e ed o Re . (34). The duc is modeled
in 2D in FEM wi h a leng h o 0.3 m and a heigh o 0.05 m.
The bounda y condi ions we e se o non- e lec ing and he
ˆ
1and ˆg1acous ic o cing s a e om he CFD ini ialized
by o cing wi h ˆ
1,b,ˆ
h1,b and ˆg2,b wa es (Fig. 1), whe e
he subsc ip bs ands o bounda y. Because he Helmhol z
equa ion does no accoun o any mean low e ec s, en opic
wa es inciden a he inle we e o ced di ec ly wi hin he
ma hema ical lame o mula ion ia a ha monic sou ce e m.
Au oigni ion lame RANS compu a ion
The 2D RANS CFD compu a ions a e pe o med o a BFS
Fig. 2wi h a o al leng h o 0.3 m. The BFS is loca ed a
0.15 m, wi h a symme ic a ea expansion om 0.01 m o
0.02 m. The in es iga ed ope a ing poin bu ns hyd ogen
and ai ully p emixed a lean and au oigni i e condi ions
(mass ac ions: H2(0.0053), O2(0.1842), H2O(0.0521),
N2(0.7584)). The inle eloci y measu es 150 m/s, he mean
ope a ing p essu e is 12.9 ba , and he inle empe a u e is
1143 K. The simula ion is done using ANSYS Fluen 2024
R1 (35) wi h an in-house combus ion model which is based
on he wo k o Kulka ni e al. (28;29). In he combus ion
model, he adical buildup du ing he induc ion phase is
ep esen ed by a no malized p og ess a iable (PV ). The
PV and i s sou ce e m is ob ained by acking ep esen a i e
in e media e and p oduc species (he e HO2and H2O) in 0D
eac o s. Fo no maliza ion, he sum o he acked species
Figu e 1. 1D DNS con igu a ion schema ic o he modeled duc
in he FE-sol e . The bounda ies a e o ced wi h ˆ
1,b,ˆ
h1,b and
ˆg2,b wa es.
mass ac ions is hen di ided by i s sum a equilib ium. I
can be shown, ha o ully p emixed condi ions, he PV
sou ce e m only depends on he empe a u e, p essu e and
he cu en igni ion p og ess (36).
˙ωPV = ˙ωPV(T, p, PV )(1)
Assuming, ha he empe a u e does no change signi -
ican ly du ing he adical build up, i can be di ided in o
wo pa s: The ini ial empe a u e T0,ini and he luc ua ing
empe a u e T′due o he acous ic o cing. Simila ly, he
p essu e is di ided in o he ope a ing p essu e pop and he
luc ua ing pa p′.
˙ωPV = ˙ωPV(T0,ini , T′, pop, p′, PV )(2)
By assuming isen opic co ela ion o p essu e and
empe a u e o acous ic wa es, T′can be exp essed using
p′,pop and T0,ini :
T′=T0,ini p′
pop
+ 1γ−1
γ
+T0,ini (3)
As pop and T0,ini a e cons an and known a p io i, he
PV sou ce e m is de ined by:
˙ωPV = ˙ωPV(p′, PV )(4)
Fo he u bulence chemis y in e ac ion (TCI) a p esumed
be a PDF (37) app oach is used. The mean u bulen PV
sou ce e m is hen ob ained by olding he sou ce e m o e
a p obabili y dis ibu ion P(PV )which is de ined by he
PV ’s mean and a iance:
˙ωPV =Z1
0
˙ωPV(p′, PV )P(PV )dPV (5)
The eac ion a e is hen compu ed by mul iplying he
Eddy Dissipa ion Model’s (38) eac ion a e wi h he alue
o he PV in o de o delay i un il he esidence ime o a
luid pa icle is equal o he igni ion delay ime.
The ad an age o his app oach is ha he co ec igni ion
delay ime can be achie ed wi hou anspo ing all he
in e media e species and compu ing hei eac ion a es.
Ins ead, he PV sou ce e ms a e compu ed a p io i using a
de ailed mechanism (SanDiego (39)) and s o ed in a lookup
able.
Fo he CFD simula ions he ealizable k−ϵ u bulence
model and second o de empo al and spa ial disc e iza ion
is used wi h a imes ep o 6e-6 s o ob ain an acous ic CFL
o 0.96. The s uc u ed uni o m mesh consis s o hexahed al
elemen s wi h a size o 0.5 mm. A mesh independence s udy
has been made compa ing elemen sizes o 0.2 mm and
0.125 mm. The RANS mean ield is alida ed by compa ison
o da a om a comp essible LES compu a ion o he same
geome y and a he same ope a ing poin . The OpenFoam
code (40) is used o sol e he Na ie -S okes equa ions. The
pa ially-s i ed eac o (PaSR) u bulen combus ion model
is employed. The LES simula ion is se up iden ically o he
sho e BFS shown in Gopalak ishnan e al. (33).
4Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(52)
Figu e 2. Schema ic o he backwa d acing s ep (BFS) geome y.
Me hodology
Flame esponse and segmen a ion
The lame esponse o plana acous ic wa es is cha ac e ized
di e en ly o he p opaga ion-s abilized shea laye lames
and he au oigni ion lame. Fo he shea laye lame,
an n−τ−σmodel is implemen ed, simila ly o (41),
using Eq. 6. The FTF he eo (FTFps Eq. 7) ela es he
HRR pe u ba ions o he eloci y luc ua ions a he dump
plane, and is de i ed om he ini ial n−τmodel om
C occo (21). The magni ude nhas been chosen equal o 1
o sa is y he low equency FTF limi o ully p emixed
p opaga ion-s abilized lames (gain equal o 1) (42). The
second exponen ial e m exp(−σ2
psτ2
ps/2) is a measu e o
he delay sp ead ac oss he lame and ac s as a low-pass il e
a highe equencies. They a e calcula ed by i ing Gaussian
ke nels o he imely a e aged HRR ield and e alua ing he
loca ion and sp ead o igni ion leng hs.
ˆ
˙qa,ps
˙q0,a,ps
=exp(iωτps)exp(−σ2
psτ2
ps/2) ˆux(x e ,y)
¯u0
(6)
FTFps =
ˆ
˙qa,ps
˙q0,a,ps
ˆux(x e ,y )
¯u0
(7)
Fo he au oigni ion lame, he amewo k om Gopalak -
ishnan e al. (32) is used o quan i y he lame esponse. The
o al au oigni ion HRR esponse o he lame is assumed o
be a linea supe posi ion o he indi idual lame esponses
(FTFs) o he acous ic and en opic wa es (31). Eq. 8
ep esen s he HRR FTFs Fi(ω)and Eq. 9cha ac e izes
he lame mo emen using he Gi(ω)FTFs. ˆ
˙qa,ai/˙q0,a,ai
is he no malized hea elease a e pe u ba ion, ˆxig/xig,0
he no malized lame mo emen , ˙q0,a,ai (W/m2) is he mean
hea elease a e pe uni a ea and xig,0 he mean igni ion
leng h (32). ˆ
1is he downs eam a eling acous ic wa e,
ˆg1 he ups eam a eling acous ic wa e and ˆ
h1 he wi h he
low anspo ed en opic wa e (32).
ˆ
˙qa,ai
˙q0,a,ai
=F1(ω)ˆ
1
p0
+F2(ω)ˆg1
p0
+F3(ω)ˆ
h1
p0
(8)
ˆxig
xig,0
=G1(ω)ˆ
1
p0
+G2(ω)ˆg1
p0
+G3(ω)ˆ
h1
p0
(9)
FEM implemen a ion
To cha ac e ize he lame in he FEM simula ion and
sol e he inhomogeneous Helmhol z equa ion (Helmhol z
equa ion wi h sou ce e ms), he nume ical segmen a ion
mechanism de i ed by (17;18) is used. A main bene i
o he segmen a ion is, ha simula ions can be done o
non-compac lames, i.e. lames ha a e unde he in luence
o ans e se eigenmodes. Fig. 3schema ically isualizes he
segmen a ion mechanism. Di e en ia ion is made be ween
p opaga ion-s abilized sub lames (blue ci cles) and he
au oigni ion sub lames (magen a ci cles). Due o he ine
segmen a ion, i can be assumed ha o each sub lame
a single alue o he p essu e and eloci y pe u ba ion
is p esen . Thus, he lame also eac s wi h a single alue
o he HRR and he lame mo emen . Fo each o he
sub lames, speci ic FTFs can be implemen ed o cap u e
he di e en lame esponses o p opaga ion-s abilized and
au oigni ion lames. Hence, he segmen a ion mechanism
allows di e en lame ypes in he same FEM compu a ion.
Fo he p opaga ion-s abilized lame pa s (Eq. 10) as
well as he au oigni ion lame egions (Eq. 11), Gaussian
ke nels a e used o analy ically posi ion he lame in he
compu a ional domain. σ˙q,ps and σ˙q,ai a e measu es o he
HRR wid h, x ,ps(y)and xig,0(y) he mean lame posi ions.
˙qps(x, y) = ˙q0,a,ps(y)
σ˙q,ps(y)√2πexp −1
2x−x ,ps(y)
σ˙q,ps(y)2!
(10)
˙qai(x, y) = ˙q0,a,ai(y)
σ˙q,ai(y)√2πexp −1
2x−xig,0(y)
σ˙q,ai(y)2!
(11)
The pa ame e s o he HRR wid h, he mean lame
posi ion and he in eg a ed HRR can be calcula ed
om ei he CFD mean ield solu ions o expe imen al
chemiluminescence imaging i a ailable. Using
hese quan i ies and he assump ion o he Gaussian
ke nel in x-di ec ion (mul iple s udies used Gaussian
dis ibu ions (17;30;31;34;43)), he a e age lame can
be ebuil ully in FEM. Whils he p ocedu e he e is done
in 2D on he xy-plane, he p e ious s udy (27) de i ed he
iden ical p ocedu e in 3D. Hence, he new me hod shown
he e can also be used in 3D.
A his poin , he a e age lame is ully cha ac e ized in
he FEM simula ion and wha emains o be cha ac e ized
is he ep esen a ion o he luc ua ing HRR pe u ba ions.
This is achie ed by ob aining he ins an aneous HRR
a e mul iplying he mean HRR by he FTF Eq. 8( o
he p opaga ion-s abilized lame Eq. 6 espec i ely) and
accoun ing o he lame mo ion in he Gaussian dis ibu ion
using Eq. 9 o ob ain Eqs. 12. Fo he p opaga ion-s abilized
Heinzmann e al. 5
Figu e 3. Nume ical segmen a ion me hod o a pe u bed pa ly au oigni ion and p opaga ion-s abilized lame in 2D. The blue
ci cles indica e he p opaga ion-s abilized lame pa s, and he magen a ci cles ep esen he au oigni ion lame.
lame egion, no lame mo ion is in oduced due o he
ancho ed na u e o he lame.
ˆ
˙qa,ps(y) = ˙q0,a,ps(y)FTFps
ˆux(x e , y)
¯u0
ˆ
˙qa,ai(y) = ˙q0,a,ai(y) F1(ω)ˆ
1
p0
+F2(ω)ˆg1
p0
+F3(ω)ˆ
h1
p0!
(12)
Using Gaussian ke nel dis ibu ions o bo h lames he
ins an aneous olume ic HRR is ob ained (Eq. 13).
˙q(x, y) = ˙q0,a,ps(y)
σ˙q,ps(y)√2π...
exp −1
2x−x ,ps(y)
σ˙q(y)2! ˆ
˙qa,ps(y)
˙q0,a,ps(y)+ 1!+...
˙q0,a,ai(y)
σ˙q,ai(y)√2πexp −1
2x−xig,0(y)−ˆxig(y)
σ˙q,ai(y)2!...
ˆ
˙qa,ai(y)
˙q0,a,ai(y)+ 1!(13)
The luc ua ing HRR ˆ
˙q(x, y), which is he sou ce e m
o he Helmhol z equa ion, is consequen ly compu ed
by sub ac ing he mean HRR om he ins an aneous
coun e pa (Eq. 14).
ˆ
˙q(x, y) = ˙q(x, y)−( ˙qps(x, y) + ˙qai(x, y)) (14)
The equa ion o he inhomogeneous Helmhol z equa ion,
which is sol ed in FEM (in he equency domain), hus
becomes Eq. 15 by adding he sou ce e m o he igh -
hand side o he homogeneous Helmhol z equa ion. F om he
compu a ions he eigen equencies and linea g ow h a es
a e ex ac ed. In his s udy COMSOL 6.2 is used.
∇·1
ρ0∇ˆp+ω2
γp0
ˆp=−iω γ−1
γˆ
˙q(x, y)(15)
Resul s
Resul s ob ained by implemen ing he p oposed me hodol-
ogy a e shown in his ollowing sec ion.
1D DNS o ced
Fig. 4shows he in e media e esul ob ained in
compa ison wi h he DNS simula ion o alida e he
FEM implemen a ion o a lame solely s abilized by
au oigni ion. An excellen ma ch is achie ed in compa ison
wi h he DNS esul in bo h phase and magni ude. The small
de ia ion in phase could esul om neglec ing mean low
e ec s by employing he Helmhol z equa ion.
0 0.005 0.01 0.015 0.02
-0.04
-0.02
0
0.02
0.04
Figu e 4. Compa ison o he HRR luc ua ions o he 1D DNS con igu a ion o ced a 100Hz. The solid line ep esen s he DNS
da a and he dashed line he FEM esul .
6Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(52)
Figu e 5. Mean ield solu ions o he RANS simula ion: a) y- eloci y, b) x- eloci y, c) empe a u e and d) p essu e.
Figu e 6. Compa ison o he mean HRR be ween LES ( op) RANS (middle) and FEM (bo om). The backwa d acing s ep is
loca ed a x= 0.15m.
Mean ields o he BFS bu ning hyd ogen
Figu e 5shows he ime-a e aged mean ields om he
RANS simula ion. Figu e 5a) shows he y- eloci y. The
eci cula ion zone is isible by he blue and ed a eas.
Figu e 5b) displays he x- eloci y. The eci cula ion zone
can again be nicely obse ed by he nega i e eloci y a eas
in blue. The empe a u e dis ibu ion is gi en in Fig. 5c) and
ma ches well wi h he esul s om CANTERA simula ions.
Las ly, he p essu e is shown in Fig. 5d), whe e a p essu e
d op downs eam o he a ea jump is obse ed and a p essu e
inc ease downs eam o he lame.
The ime-a e aged lame shape is compu ed using he
in-house au oigni ion ehea lame model desc ibed in
he CFD sec ion. To alida e he mean ield quali a i ely,
compa isons o cen e -plane da a om he desc ibed LES
simula ion a e made. The compa ison be ween he esul s
om he LES and he RANS simula ions shows ha he
model can eplica e he lame o a ce ain ex en . The mean
igni ion-leng h and o e all lame shape is cap u ed well
(leng h scales a e small). The RANS simula ion howe e
p edic s he p opaga ion-s abilized shea laye lames o be
u he ups eam compa ed o he alida ion da a. Expe ience
shows, ha he occu ence o an ea lie imed igni ion is
linked o he RANS sol e used in combina ion wi h he
ehea lame model.
Fu he compa isons can be made by analyzing he
olume ic HRR o Fig. 6 o wo di e en sec ions in
Fig. 7. The h ee dash-do ed blue lines show he no malized
olume ic HRR along a sec ion (y= 0.001m) ac oss he
shea laye lame. The diamonds ep esen he LES da a,
he ci cles he RANS da a and he s a s he FEM da a,
espec i ely. As was al eady indica ed be o e, he HRR peak
o he shea laye lame occu s u he ups eam in he RANS
simula ion a 0.158m compa ed o 0.169m. The FEM alue
ma ches he one o he RANS closely wi h 0.157m. The
peak alue is o e -p edic ed by he RANS compa ed o he
LES simula ion. The solid magen a lines p o ide he same
compa ison o a sec ion a a y-coo dina e o 0.001m, close
o he symme y line. In his egion he lame is s abilized
by au oigni ion. The peak o he RANS simula ion is a an
Heinzmann e al. 7
Figu e 7. Compa ison o he olume ic HRR o di e en sec ions h ough he shea laye lame (blue dash-do ed lines.) and he
au oigni ion s abilized pa (solid lines). The compa ison is made be ween he LES (diamonds), RANS (ci cles) and he FEM (s a s).
Figu e 8. FTF Compa isons be ween he CFD esul s (diamonds) and he FEM compu a ion (ci cles). The blue dashed line
ep esen s he used n−τ−σmodel.
x-coo dina e o 0.188m. I is p edic ed u he downs eam
compa ed o he LES a a ound ∼0.18m. The mean igni ion
leng h o he FEM ma ches he RANS closely wi h 0.186m.
The HRR dis ibu ion is sp ead mo e symme ically a ound
he peak compa ed o he RANS, which is a p e equisi e
o he in oduced ma hema ical model (Eq. 13). Mo e
gene ally, he lame appea s mo e compac in he LES
compa ed o he RANS compu a ion. Due o he ma ch o
he o e all lame shape, he RANS mean ield can s ill be
used o he subsequen s udy. Simula ions wi h ha monic
acous ic o cing a he inle wi h a p essu e ampli ude o
0.5% a e pe o med using ANSYS Fluen . The alues o he
n−τ−σmodel a e compu ed o be n= 1 (low equency
limi o ully p emixed p opaga ion s abilized lames (42)),
σ= 0.099ms and τ= 0.12ms using he me hod desc ibed
in he me hodology sec ion.
The o ced FEM simula ion is se up iden ically o he
RANS compu a ion by o cing ha monically a he inle
wi h a p essu e ampli ude o 0.5%. The ou le is se o
8Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(52)
Figu e 9. FTF Compa isons be ween he n−τ−σmodel (blue dashed) and he au oigni ion FTF (magen a dash-do ed line).
The solid black line is he combina ion o bo h FTFs. The ci cles ep esen he FTF om he FEM, and he diamonds he FTF om
he RANS simula ions.
ully anechoic o mi iga e e lec ions and ups eam a eling
acous ic g-wa es.
Fig. 8shows he FTFs ( ˙q′/˙q0)/(u′/u0)o bo h he RANS
simula ions and he FEM simula ions. The FEM compu a ion
(ci cles) is able o cap u e he phase e y accu a ely. The
gain o he FTF shows sligh di e ences be ween he
CFD simula ion (diamonds) and he FEM compu a ion. The
o e all ma ch o he FTF is good, and he newly in oduced
segmen a ion model o combine di e en ly beha ing ehea
lame egions o FEM compu a ions wo ks. Fu he , he
compa ison o he dashed blue line, which ep esen s he n−
τ−σmodel, indica es ha he in es iga ed lame esponse is
domina ed by he p opaga ion-s abilized lames in he shea
laye . Consequen ly, he p oposed me hodology can be used
in a u he s ep o s abili y calcula ions o longi udinal
eigenmodes.
Fo comple eness, Fig. 9shows he used FTFs (wi h
espec o he eloci y luc ua ions ( ˙q′/˙q0)/(u′/u0)) o
a la ge equency ange. A highe equencies, he
assump ion o no mean low eloci y b eaks down in he
FEM. Howe e , he FTFs can s ill be analyzed o unde s and
he lame esponse a highe equencies. Looking a he
n−τ−σFTF (blue dashed line) o he shea laye lame
zones, he low-pass il e beha io can clea ly be obse ed.
A negligible HRR esponse con ibu ion om he shea
laye lames om 4000Hz onwa ds is indica ed. The FTF
om he solely au oigni ion s abilized cen al HRR zone is
compu ed using he Lag angian amewo k (32) and is shown
by he magen a dash do ed line. The FTF indica es ha a
highe equencies he au oigni ion lame zone con ibu es
o a la ge ex en o he o e all lame esponse. Howe e , no
low-pass il e is con ained in he model and hus he gain
is es ima ed o be sligh ly lowe in eali y. The Lag angian
amewo k (32) was alida ed wi h 1D DNS simula ions
up o 4000Hz, whe e de ia ions o +20% we e obse ed in
he gain be ween DNS and he model. The black solid line
ep esen s a supe posi ion o bo h he shea laye lame FTF
and he au oigni ion lame FTF wi h an o e all au oigni ion
weigh ing o 0.32 and a shea laye lame weigh ing o
0.68 espec i ely. This gi es an indica ion o how he
lame beha es globally a highe equencies, gi en ha
he assump ion o a supe posi ion o he HRR esponse o
a p opaga ion-s abilized lame egion and an au oigni ion
lame egion is alid.
Conclusion
Wi h ehea combus o s becoming o inc easing in e es in
indus ial gas u bines, au oigni ion lames ha e shi ed in o
he scope o cu en esea ch. Especially in indus ial ehea
combus ion chambe s, an au oigni ion lame will likely
ha e ce ain lame egions ha a e p opaga ion-s abilized
due o ei he low eci cula ion o o ex b eakdown.
So a , esea ch on he moacous ics, especially he lame
dynamics, has been pe o med sepa a ely o p opaga ion-
s abilized lames and au oigni ion-s abilized lames. In
his pape , we p opose an analy ical model o p edic
he esponse o a composi e lame pa ly s abilized by
p opaga ion and pa ly by au oigni ion. We le e age a
p e iously de eloped segmen a ion me hod o inco po a e
bo h lame ypes in he same FEM compu a ion. Using he
segmen a ion mechanism, di e en FTFs a e p esc ibed o
he p opaga ion- and au oigni ion-s abilized lame egions.
Fo he p opaga ion-s abilized HRR egions, a classical
n−τ−σmodel is used. Fo he au oigni ion-s abilized
HRR egions, he FTF ob ained om a Lag angian pa icle
acking based app oach is used. Resul s showed a e y good
Heinzmann e al. 9
i in compa ison o o ced CFD da a. Consequen ly, he
amewo k can be used o compu e longi udinal eigenmode
s abili y p edic ions o pa ly au oigni ion and p opaga ion-
s abilized lames and can aid he de elopmen o no el
emissions- ee indus ial gas u bine combus o s.
Acknowledgemen s
The esea ch wo k p esen ed in his manusc ip was ca ied ou
wi hin he FLEX4H2 p ojec . The FLEX4H2 p ojec is suppo ed
by he Clean Hyd ogen Pa ne ship and i s membe s Eu opean
Union, Hyd ogen Eu ope and Hyd ogen Eu ope Resea ch (GA
101101427), and he Swiss Fede al Depa men o Economic
A ai s, Educa ion and Resea ch, S a e Sec e a ia o Educa ion,
Resea ch and Inno a ion (SERI). Views and opinions exp essed
a e howe e hose o he au ho (s) only and do no necessa ily
e lec hose o he Eu opean Union o any o he g an ing au ho i y.
Nei he o hem is liable o any use ha may be made o he
in o ma ion con ained he ein.
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