The e ec o ans e sal eloci y
luc ua ions on he he moacous ic
esponse o ehea 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.: 77
©The Au ho (s) 2025
Simon M. Heinzmann1,2,†, Nino A. Lede 1,†and Mi ko R. Bo hien1,3
Abs ac
The moacous ic analysis emains a key componen du ing he de elopmen p ocess o new combus ion chambe s.
Especially wi h he cu en challenges o c ea ing uel lexible combus ion chambe s, exis ing he moacous ic models
ha e o be imp o ed and new ones c ea ed. The e is a g ea deal o li e a u e on he e ec o longi udinal/plana acous ic
wa es on p opaga ion-s abilized lames. Rehea lames only ecen ly shi ed in o he scope o esea ch, especially
wi h ega d o he moacous ic modeling o he in luence ha ans e se combus ion chambe eigenmodes ha e on
au oigni ion lames. In wo p e ious publica ions, we showed how ans e se eigenmodes in luence he au oigni ion
p ocess. F om his, he dynamic lame esponse was deduced, and s abili y p edic ions we e made o wo combus o s
and di e en ope a ing poin s. In bo h s udies, he assump ion was made ha ans e se eloci y pe u ba ions ha e no
e ec on a one-dimensional au oigni ion lame. Wi h he s udy p esen ed he e, we show he isola ed e ec o ans e sal
eloci y pe u ba ions on he lame. This is done o wo dis inc lame s abiliza ion cases occu ing in a lab-scale ehea
combus o . Fo he i s , he lame is pa ly au oigni ion-s abilized bu also has p opaga ion-s abilized egions in he
shea laye because o eci cula ion zones induced by a backwa d acing s ep. The second ea u es only a minimal s ep
heigh and he e o e only mino eci cula ion zones, leading o an almos pu ely au oigni ion-s abilized lame. The wo
di e en lame s abiliza ion cases a e in es iga ed using Reynolds-a e aged Na ie -S okes simula ions in eg a ing an
in-house ehea combus ion model. The analysis shows ha ans e se eloci y pe u ba ions ha e no e ec on lames
ha a e pu ely s abilized by au oigni ion. In he p esence o p opaga ion-s abilized lame egions wi hin he shea laye ,
ans e se eloci y pe u ba ions do induce hea elease a e luc ua ions, as expec ed.
Keywo ds
he moacous ic, au oigni ion, CFD, ans e se eigenmodes, high- equency
No el y and Signi icance S a emen
To da e h ee app oaches (1–3) exis o model he
dynamic esponse o one-dimensional au oigni ion lames
o longi udinal/plane acous ic wa es. Recen s udies (4;5)
showed o one o hese models an adap ion and in eg a ion
in an FEM based amewo k o cap u e he he moacous ic
e ec s ha he ans e se acous ic eigenmodes o he
combus ion chambe ha e on non-compac au oigni ion
lames. In his wo k, he dynamic hea elease a e
esponse o ehea lames pe u bed by ans e sal eloci y
luc ua ions was neglec ed. The p esen ed pape aims o
ill his gap by showing no el insigh s o how au oigni ion
lames beha e when pe u bed by ans e sal eloci y
luc ua ions. The signi icance o his wo k is wo old: i s ly,
i p o ides a mo e p o ound unde s anding on he in luence
ha ans e se eigenmodes ha e on au oigni ion lames.
Secondly, i cons i u es a aluable con ibu ion o esea ch
in his ield. These indings can suppo he indus ial
de elopmen o no el low-emissions gas u bine combus ion
chambe s.
Nomencla u e
Abb e ia ions
PV P og ess Va iable
CFD Compu a ional Fluid Dynamics
FEM Fini e-Elemen -Me hod
FTF Flame T ans e Func ion
HRR Hea Release Ra e
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 PV
γRa io o speci ic hea s
ΩEigen equency
ωAngula equency in ad/s
ψModeshape
ρDensi y
Roman
(·)′Pe u ba ion in ime domain
(·)0Time-a e aged quan i y
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 Z¨
u ich, Depa men o Mechanical and P ocess Enginee ing,
Z¨
u ich
3Depa men o Ene gy and P ocess Enginee ing, NTNU, No way
†These au ho s con ibu ed equally o his wo k
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.(77)
(·)ini Ini ial
(·)eq A equilib ium
ˆ
(·)Fou ie ans o m o a luc ua ing quan i y
ˆ
˙qa,ψΩ(z)Fluc ua ing ins an aneous HRR
c0Speed o sound
iMass ac ions e.g. uel, ho gas, ca ie ai
FψΩModeshape dependen FTF
pP essu e
P(·)P obabili y
p e P essu e a e e ence loca ion
TTempe a u e
Time
TiTempe a u e o mass ac ion i
x, y, z x-,y- and z-coo dina es
YiMass ac ion o species i
Yi,0Ini ial mix u e composi ion
In oduc ion
In o de o comply wi h he Pa is ag eemen (6), he u u e
ene gy landscape mus be based on enewable ene gy
sys ems o ensu e low emissions (7–9). Gas u bines
i ing al e na i e ca bon- ee uels can be an ideal asse o
balance and s abilize he powe g id (8;10–14). To i e a
a ie y o uels wi h e y di e en combus ion p ope ies,
ex ensi e combus ion chambe de elopmen is needed.
When de eloping a new combus o , a c i ical challenge is
a de ailed he moacous ic analysis o mi iga e combus ion
ins abili ies (15). Thus, he need o mo e de ailed and
sophis ica ed he moacous ic analysis ools is appa en .
The he moacous ic analysis o longi udinal/plana
acous ic wa es on p opaga ion s abilized lames has been
ex ensi ely s udied in he pas (16–24). Nicoud e al. (16)
showed how he he moacous ic s abili y o combus ion
chambe s wi h p opaga ion-s abilized lames can be
assessed using he ini e elemen me hod (FEM) and a n−τ
model, i s in oduced by C occo (25). Schue mans (18)
showed how he acous ics o complex geome ies can be
segmen ed in o simple subdomains desc ibed by a s a e-
space ep esen a ion and hen conca ena ed in a ne wo k
model o pe o m he moacous ic analysis o acous ically
compac lames wi h high accu acy. In he con as o
his, ehea lames only ecen ly shi ed in o he scope o
esea ch (1;3;26–31). Bo hien e al. (28) econs uc ed
he acous ic ans e ma ix om a LES simula ion o
a backwa d- acing-s ep ehea combus o . Zellhube e
al (26), Gan e al. (1) and Gopalak ishnan e al. (3)
de i ed amewo ks o cha ac e ize he HRR esponse o
1D ehea lames pe u bed by plana wa es. Heinzmann e
al. (4;32) ex ended he nume ical Lag angian amewo k o
Gopalak ishnan o compu e modeshape dependen FTFs o
ans e se modes accu a ely.
In gene al, p opaga ion-s abilized lames and au oigni ion
lames eac e y di e en ly o acous ic pe u ba ions.
Howe e , he di e en ia ion he eo is no i ial. Rehea
lames in indus ial gas u bine combus ion chambe s
a e usually composed o di e en hea elease a e (HRR)
egions. Ce ain egions o a ehea lame a e solely s abilized
by au oigni ion, o he s a e s abilized by p opaga ion. The
p opaga ion-s abilized HRR egions o ehea lames a e
ypically loca ed in he shea laye s, which o m due o
eci cula ion zones a geome ical a ea jumps o a ound blu
bodies. The co e o he ehea lame is au oigni ion s abilized
wi hin he bulk low. The o e all HRR dis ibu ion be ween
he di e en zones is no ixed and can a y. Wi h highe
inle empe a u es in a sequen ial combus ion chambe he
o e all HRR zone becomes mo e au oigni ion d i en wi h
cha ac e is ic sho e igni ion delay imes; and ice e sa o
colde condi ions. While he p opaga ion-s abilized HRR
egions a e go e ned by he balance o lame consump ion
speed and local low eloci y, he au oigni ion is go e ned
by he balance be ween chemical and esidence ime scales.
Acous ic luc ua ions can ha e a la ge impac on bo h lame
zones.
Wi h espec o pe u ba ions in ans e se di ec ion,
ans e sal acous ic wa es can signi ican ly a ec he lame
shape and HRR. Close o geome ic discon inui ies, such
as a ea jumps, ans e sal acous ic eigenmodes can induce
o ex shedding and modula e he eac i e shea laye s. This
leads o HRR luc ua ions locally wi hin he p opaga ion-
s abilized pa o he lame (33). The au oigni ion-s abilized
HRR egions a e sensi i e o acous ic p essu e and isen opic
empe a u e luc ua ions, which modi y he local igni ion
delay ime and he e o e shi he lame back and o h (3;
4). Heinzmann e al. (4;5) de eloped a amewo k o
model he dynamic e ec ha such modes ha e on
ehea lames. They assessed ans e se eigenmode s abili y
and alida ed i wi h expe imen s. An assump ion o he
amewo k is, ha ans e se eloci y pe u ba ions ha e
negligible e ec on a one-dimensional (1D) au oigni ion
lame. This assump ion is based on he ac ha ehea
lames eac signi ican ly weake o eloci y luc ua ions in
low di ec ion when compa ed o empe a u e and p essu e
luc ua ions. This can be seen by he low alue o he FTF
wi h espec o eloci y pe u ba ions in Re . (28). The
mechanism esponsible o he HRR esponse due o in
low o ien ed eloci y pe u ba ion is he modula ion o he
equi alence a io (1;2;26;34). Howe e , no equi alence
a io luc ua ions a e p esen in he case o ans e se eloci y
pe u ba ions in ully p emixed condi ions. A homogeneous
p emixed mix u e upon en y in o he combus ion chambe
was con i med by a p io s udy o he in es iga ed
combus o (35). In-house CFD simula ions also concluded
a good mixing o uel and ai be o e en e ing he combus o .
Thus, he modeshape-dependen FTF FψΩ(ω) o a ce ain
eigenmode Ω o compu e he luc ua ing ins an aneous hea
elease a e (HRR) ˆ
˙qa,ψΩo Eq. 1is assumed o emain
una ec ed by ans e se eloci y pe u ba ions (4).
ˆ
˙qa,ψΩ(z) = ˙q0,a(z)FψΩ(ω)ˆp(x e , z)
p0
(1)
To he bes o ou knowledge, he e is no li e a u e o
da e s a ing whe he ans e se eloci y pe u ba ions ha e
an e ec on 1D ehea lames. In his pape , we iden i y he
dynamic HRR esponse o wo dis inc c oss-sec ions o a
ec angula lab-scale ehea combus ion chambe (36). This
is done by acous ically exci ing he i s ans e se modes o
bo h dimensions o a ec angula combus ion chambe (i.e.
in xy- and xz-di ec ion) in uns eady comp essible RANS
Heinzmann e al. 3
Figu e 1. Geome y o he ehea combus ion chambe a TUM. The xy-c oss-sec ion is shown on he op, and he
xz-c oss-sec ion on he bo om. Quali a i e expe imen al lame images a e shown solely o he isualiza ion pu pose (di e en
ope a ing poin ).
simula ions. To iden i y and isola e whe he ans e se
eloci y luc ua ions ha e negligible e ec on a pu e ehea
lame, wo di e en simula ions a e pe o med o each
o he dimensions ( ou in o al). Non-compac Fou ie
decomposi ion is done o he esul s o iden i y he lame
esponse o bo h he au oigni ion s abilized lame pa s as
well as he p opaga ion-s abilized assis ed lame egions.
Me hodology
The me hodology sec ion desc ibes how he RANS
compu a ion is se up. Fi s , he geome y is shown. Second,
he combus ion model is in oduced. Thi d, he nume ical
se up is discussed. Fou h, he mean ields a e shown
and las ly, he implemen a ion o he ans e se o cing is
discussed.
Combus o geome y
The a mosphe ic combus o o he Technical Uni e si y o
Munich (TUM) (36) shown in Fig. 1consis s o a i ia o
ollowed by a ehea combus o . The i ia o is ope a ed
wi h a lean, pe ec ly p emixed, p ehea ed and wi h a
mix u e o hyd ogen and me hane. The i ia ed ai en e s
he ehea combus o and passes h ough a mixing sec ion
whe e he uel is injec ed in o he ho gas in a je -in-c oss-
low a angemen . To imp o e mixing, del a wing-shaped
o ex gene a o s a e placed ups eam o he uel injec ion.
The mix u e hen passes h ough a con e gen sec ion be o e
en e ing he ehea combus ion chambe h ough a di use -
shaped ou le . The ec angula combus ion chambe mainly
expands in y-di ec ion, which leads o s ong uppe and
lowe eci cula ion zones downs eam o he a ea jump.
In z-di ec ion, he combus ion chambe does no expand
signi ican ly, and hus no signi ican eci cula ion zones a e
obse ed. Fo mo e de ails on he sequen ial combus o , he
eade is e e ed o Re s. (4;33;36;37).
RANS compu a ion
The RANS CFD compu a ions a e pe o med o he
p esen ed ec angula ehea combus ion chambe (Fig. 1)
bu ning a mix u e o 50% me hane and 50% hyd ogen by
weigh a lean and au oigni i e condi ions. The CFD is done
using ANSYS Fluen 2024 R1 (38) using he ealizable
k−ϵmodel o u bulence wi h an adap i e Schmid numbe
o ob ain be e mixing esul s a he je -in-c oss low uel
injec ion. A RANS e sion o he combus ion model de i ed
by Kulka ni e al. (39;40) was implemen ed and ex ended o
cap u e he e ec s o acous ic wa es.
This combus ion model is based on a anspo ed
no malized p og ess a iable (P V ) which ep esen s
in e media e species eac ions ha go e n he igni ion delay.
In con a y o using a linea PV , eac ion species om
he adicals (CH2O,CO,HO2) and p oduc pool (CO2,
H2O) a e used o p ope ly cap u e he igni ion p ocess.
The ad an age o including he (ho ) p oduc s is ha
he p opaga ion-s abilized lames in he shea laye o
he eci cula ion zones a e cap u ed mo e accu a ely. The
no malized PV is ob ained by di iding he sum o he
included species mass ac ions by i s sum a equilib ium:
PV =PYi
PYi,eq
(2)
The PV sou ce e m can be compu ed using ini e
di e encing. Fo he model o wo k, he sou ce e m mus
be s ic ly posi i e and only depend on known pa ame e s
like he local uel mass ac ion F, ho gas mass ac ion
H, empe a u e, p essu e and he alue o he PV i sel .
By spli ing he empe a u e and p essu e in o i s mean and
luc ua ing pa , and unde he assump ion ha he mean
alue o he empe a u e and p essu e a e cons an du ing he
adical buildup, he P V sou ce can be exp essed as:
˙ωP V = ˙ωP V ( i, T0,ini , T′, p0, p′, PV )(3)
In hei combus ion models, B and (41) and Kulka ni (39)
assumed ha he anspo o ene gy scales he same as
4Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(77)
he anspo o mass, and ha he change o speci ic hea
capaci y cpups eam o he lame is negligible. The e o e,
he ini ial empe a u e can be exp essed h ough he mass
ac ions iand he known ini ial empe a u es Ti,ini :
T0,ini =XTi,ini i(4)
Assuming an isen opic co ela ion o p essu e and
empe a u e o acous ic wa es, T′can be exp essed h ough
p′, and as he ope a ing p essu e p0is known, he PV sou ce
can be simpli ied o:
˙ωP V = ˙ωP V ( i, p′, PV )(5)
To model he Tu bulence Chemis y In e ac ion (TCI) a
PDF app oach o he mass ac ions iand he PV is used.
The mean u bulen sou ce e m is ob ained by olding he
sou ces o e a p obabili y dis ibu ion:
˙ωP V =Z1
0Z1
0
˙ωP V ( i, p′, PV )P( i)d iP(PV )dPV
(6)
The HRR is hen ob ained by using he mixed is bu ned
app oxima ion and delaying i by mul iplying he eac ion
a e wi h he PV.
The majo ad an age o his app oach is ha i is
compu a ionally cheap. The sou ce e ms, which can be
compu ed using 0D eac o s, and he in eg a ion can be done
a p io i and s o ed. The e o e, only he educ s, p oduc s,
PV , i s a iance and he mass ac ions wi h hei a iances
need o be anspo ed, and no expensi e eac ion a e
compu a ions a e necessa y. Using his app oach, i is
assumed ha he e is no in e ac ion be ween he indi idual
eac o s du ing compu a ions. Pe o ming 0D eac o mixing
s udies, B and (41) e i ied his assump ion and ob ained an
o e all e o below 10%.
In his pape , he PV sou ce e ms we e compu ed using
he GRI30 (42) mechanism and he p obabili y dis ibu ions
o in eg a ion we e c ea ed using modi ied cu l mixing o
pa icles (43). To educe PV sou ce lookup ime du ing
he simula ion, a Residual Ne wo k is used o e ie e he
sou ces. Residual Ne wo ks a e neu al ne wo ks whe e each
block adds a skip connec ion. The skip connec ion helps
wi h he aining s abili y and accu acy o deepe ne wo ks
by mi iga ing anishing g adien s and o e i ing. The
ne wo k used he e consis s o an inpu block ollowed by
h ee esidual blocks, each consis ing o wo ully connec ed
laye s wi h a skip connec ion, and an ou pu laye (44).
Fi s ans e se
eigenmode
Simula ion nomencla u e
all e ec s wi hou p’
and T’ e ec s
y-di ec ion T1y T1yNPE
z-di ec ion T1z T1zNPE
Table 1. Simula ion nomencla u e depending on eigenmode
and accoun ed HRR e ec s.
Figu e 2. Po ous zones and momen um sou ce e ms.
P ope y Ho Gas Fuel p emixed wi h
addi ional ai
˙m[g/s] 366.46 8.55
T[K] 967 283.15
YO20.168 0.123
YN20.76 0.461
YCO20.039 -
YH2O0.032 -
YCH4- 0.208
YH2- 0.208
Table 2. Gas p ope ies
Fou simula ions a e compu ed in o al. Table 1displays
he naming con en ion, depending on he o ien a ion o
he i s eigenmode as well as he HRR e ec s accoun ed
o . The T1y- and T1z-simula ions a e compu ed o he
i s ans e se eigenmode in y- and z-di ec ion (Fig. 1),
espec i ely, wi h he inclusion o local acous ic p essu e and
empe a u e luc ua ions e ec s. The T1yNPE- and T1zNPE-
simula ions (NPE: No P essu e E ec s) do no accoun o
a change in HRR due o local p essu e and empe a u e
luc ua ions in he CFD p og ess a iable. Thus, he lame
only eac s o eloci y and equi alence a io luc ua ions. Fo
he NPE cases, p′is se o ze o o he sou ce e m lookup.
The e o e, he e ec o he p essu e and empe a u e change
induced by acous ic wa es is igno ed du ing he simula ion.
The compu a ional domain (Fig. 3) is hal o he ehea
combus o (36) making use o he symme y planes xz and
xy o e iciency. The mesh is made up o app oxima ely
1.3*106cells wi h e inemen s a he walls, he a ea
changes and he uel injec ion. A mesh independence s udy
compa ing he uel mix u e ac ions a he dump plane as
well as he magni ude and posi ion o he HR shows no
a ia ion o a ine mesh. Time and space a e disc e ized
in second o de and he imes ep is se o 4e-7s o ob ain
an acous ic CFL below one. The ope a ing poin , which is
shown in Tab. 2, is equal o he NG50med ope a ing poin
om F anke e al. (36).
The exci a ion is achie ed in a simila way as was
shown by Zellhube e al. (45). On he combus o walls,
which coincide wi h he an inodes o he i s ans e sal
eigenmode, small po ous zones wi h high esis ance a e
added, Fig. 2and Fig. 3. Wi hin hese zones, momen um
sou ce e ms a e applied o o ce o he luid domain. The
p ecise o cing equencies o he T1y-and T1z modes a e
calcula ed by sol ing he homogeneous Helmhol z equa ion
Eq. 7in COMSOL 6.2.
Heinzmann e al. 5
Figu e 3. Hal o he CFD mesh and compu a ional domain.
Figu e 4. CFD mean ields o he xz-c oss-sec ion: a) empe a u e ield, b) x- eloci y ield and c) p og ess a iable (PV).
∇ · 1
ρ0
∇ˆp+ω2
γp0
ˆp= 0 (7)
The ime a e aged lame is accoun ed o in he FEM s udy
by inclusion o he ime a e aged empe a u e ield in he
combus ion chambe , which is aken om he s eady CFD
compu a ion.
Resul s
Fi s he CFD mean ield esul s a e shown and he
ime a e aged HRR ield is alida ed o he xy-c oss-
sec ion using expe imen al da a om (36). Subsequen ly,
obse a ions a e made o wo dis inc geome ical planes
o he combus ion chambe . Then, he xy-plane (z= 0)
is analyzed whe e he lame esponse is composed o
au oigni ion and p opaga ion-s abilized lame egions o
bo h he T1y and T1yNPE simula ions. The subsequen
sec ion p esen s he esul s o he analysis o he xz-plane
(y= 0). He e, he lame is p edominan ly au oigni ion
s abilized (4;29), and compa isons a e d awn be ween he
T1z- and T1zNPE simula ions.
6Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(77)
Figu e 5. a) Time a e aged HRR mean ield on he xy-plane o
he expe imen al line-o -sigh -in eg a ed chemiluminescence
imaging (36), b) ime a e aged HRR mean ield on he xy-plane
o he RANS compu a ion, c) he ime a e aged HRR mean ield
on he xz-plane o he RANS compu a ion.
CFD s eady HRR mean ield alida ion
Fig. 4shows he empe a u e, x- eloci y and PV con ou s
om he RANS compu a ion o he xz-c oss-sec ion.
Fig. 4a) shows a uni o m empe a u e dis ibu ion a he
inle o he combus ion chambe . Fig. 4b) indica es ha he
eci cula ion zones induced by he s ep a e small. Fig. 4c)
shows he esul o he in-house combus ion model. The
ea lie imed igni ion a he co ne o he a ea jump is
cap u ed because o he inclusion o ( eci cula ing) ho
p oduc s. On he x-axis he lame is pu ely au oigni ion-
d i en and he posi ion ma ches wi h he analy ical mean
igni ion delay ime also epo ed in Re . (36).
The ime a e aged low ield and lame shape o he
CFD simula ion is alida ed using expe imen al da a (36).
Fig. 5shows he a e age HRR on he xy-plane o a)
he chemiluminescence measu emen and b) he CFD
simula ion. The mean igni ion leng h (i.e. igni ion delay
ime) is compu ed by assessing Gaussian ke nel i s o he
HRR in x-di ec ion. The alue o 0.16m om he dump
plane ma ches e y well o he cen al c oss-sec ion (y=
0). This indica es ha he implemen ed in-house combus ion
model is able o accu a ely p edic he lame’s a e age
loca ion. Towa d he combus o walls, he lame is loca ed
u he ups eam as a esul o he lowe axial eloci y due o
he eci cula ion zones a e he a ea jump a he dump plane.
The implemen ed ehea model is able o cap u e he shea -
laye lames. The RANS compu a ion p edic s he s onges
zones o he shea laye lames sligh ly u he ups eam,
which is belie ed o be a nume ical a i ac o he sol e . In
addi ion, he cen e o he lame ha is solely au oigni ion
s abilized is p onounced mo e s ongly in he CFD compa ed
o he expe imen . This could be due o mul iple easons. A
main ac o could be ha in he CFD simula ion he mix u e
en e s he dump plane wi h a uni o mly sp ead uel mix u e
ac ion. The homogenei y o his pa ame e is a ec ed by
he induced o ical s uc u es o he o ex gene a o s ahead
o he uel injec o s. Thus, he e could be sligh di e ences
in he modeling o hese e ec s in ela ion o he expe imen .
Also, he je -in c oss- low uel injec ion momen um could
be sligh ly di e en in he expe imen compa ed o he
simula ion. A lowe momen um o he uel je could lead
o smalle uel mass ac ions owa ds he cen e o he
combus o . Howe e , he ime-a e aged HRR mean ield
o he CFD can cap u e he s uc u e o he expe imen ally
measu ed HRR mean ield. Wi h espec o he xz-plane
(Fig. 5c), he e a e no expe imen al measu emen s o
alida e he mean ield. Howe e , he iden ical combus ion
chambe was used in (46), whe e a simila lame shape was
de e mined o a di e en ope a ing poin bu ning me hane
and p opane. Also, o his c oss sec ion, i is belie ed ha
he HRR close o he walls is oo a ups eam in he RANS
compu a ion due o he sol e . S ill, he CFD mean ield is
accu a e and can be used o he a ge ed s udy o iden i y
he e ec ha ans e se eloci y pe u ba ions ha e on a
ehea lame.
The exci a ion equencies we e de e mined by sol ing
Eq. 7in FEM, analogously o (4). The e ec o he lame
is accoun ed o by including he ime-a e aged empe a u e
ield in he combus ion chambe . Fo he T1y-mode he
o cing equency is 1426Hz and o he T1z-mode 2660Hz.
Fig. 6a) shows he i s ans e se eigenmode o he xz-
plane ob ained by he eigen equency s udy using FEM.
Fig. 6b) shows he ins an aneous p essu e pe u ba ions o
he exci ed i s ans e se mode a an iden ical equency o
2660Hz. The compa ison shows an excellen ma ch be ween
he modeshapes. The same is he case o he T1y mode
(no shown). Thus, i is con i med ha he i s ans e se
eigenmodes a e co ec ly exci ed in he CFD simula ion.
P opaga ion-and au oigni ion s abilized lame
egions on he xy-plane
Analyzing he lame esponse on he xy-plane, dis inc
obse a ions can be made. Fig. 7a) shows he p essu e
pe u ba ions in he i s column, he ans e se eloci y
pe u ba ions in he second column, and he HRR
pe u ba ions in he hi d column o he T1y-simula ion. All
quan i ies a e plo ed o hal and oscilla ion om 90◦ o
270◦. I is isible ha he i s ans e se acous ic mode has
an e ec on he pa ly au oigni ion-s abilized ehea lame.
An al e na ing HRR pe u ba ion pa e n is clea ly isible
a a phase o 180◦. A his phase, he uppe (y > 0) HRR
pe u ba ion in he shea laye lame is a ound 180◦ou o
phase wi h he ans e se eloci y pe u ba ion. The lowe
Heinzmann e al. 7
Figu e 6. a) T1z acous ic eigenmode o he FEM compu a ion, b) T1z acous ic eigenmode o he RANS compu a ion.
(y < 0) HRR pe u ba ion in he shea laye lame is in
phase wi h he eloci y pe u ba ion. The same beha io is
no obse ed o he T1yNPE-simula ion shown in Fig. 7b).
The e o e, he clea ly obse able HRR pe u ba ion pa e n
in he T1y-simula ion is belie ed o occu due o p essu e
and empe a u e e ec s. The e y local and small HRR
luc ua ions igh a e he dump plane (x= 0) a e e y
simila in bo h simula ions, and no quali a i e di e ences a e
obse ed. Mos likely, hey a e induced by o ical s uc u es
ha o igina e igh a e he dump plane. This beha io
was also obse ed in p io expe imen s o he expe imen al
se up by McClu e e al. (33). The acking o mo e/less
in ense HRR pe u ba ion pa ches e ealed ha hese o ical
s uc u es a e anspo ed wi h he mean low (33). They
a e con ained be ween he shea laye s o he eci cula ion
zones, i.e. in he p opaga ion-s abilized shea laye lames.
Wi h espec o he cen al symme y line (y= 0), no
HRR luc ua ions a e p esen in bo h simula ions. This is
in e es ing o obse e, because he cen al symme y line
is a nodal line o he p essu e modeshape and an an inode
o he eloci y pe u ba ions. Thus, on his line, a luid
pa icle expe iences no p essu e luc ua ion, bu indeed he
s onges eloci y luc ua ions. The e o e, i is ound, ha
he ans e se eloci y luc ua ions ha e no in luence on a
solely au oigni ion s abilized ehea lame segmen a (y=
0). This is u he suppo ed by he expe imen al esul s om
McClu e e al. (33) o he same combus ion chambe . In he
expe imen , he iden ical i s ans e se mode was measu ed
in he combus o and no lame modula ion was ound o he
au oigni ion co e egion.
Quan i a i e compa isons be ween he simula ions can
also be made. By in eg a ing he HRR o mul iple c oss-
sec ions pa allel o he x-axis and ela ing he in eg al
quan i y o he local eloci y pe u ba ions sligh ly ups eam
o he lame on , speci ic local FTFs can be compu ed.
Fig. 8shows he local FTFs o a) he T1y-simula ion and
b) he T1yNPE-simula ion. The in eg a ed HRR is plo ed by
he dashed black line o iden i y which loca ions co espond
o he mo e s ongly p onounced shea laye lames. The
ollowing obse a ions a e made:
• The ans e se eloci y luc ua ions induce no HRR
luc ua ion o he cen e c oss-sec ion (y= 0), which
is isible by he gain o 0. This is he case o
bo h simula ions (Fig. 8a)) and Fig. 8b). This is
pa icula ly meaning ul, as his c oss-sec ion a (y= 0)
coincides wi h he an inode o he ans e se eloci y
pe u ba ion ield. Thus, i he ans e se eloci y
had an e ec on a ehea lame, i would appea
he s onges o his c oss-sec ion. Thus, he ini ial
hypo hesis ha a ans e se eloci y does no a ec he
HRR esponse o a solely au oigni ion s abilized lame
is con i med.
• The phase o he T1y-HRR esponse in he shea laye
lames oscilla es a ound 0 o he lame loca ed on he
nega i e y-axis, and −π/2 o he lame loca ed on he
posi i e y-axis. Whils he eloci y pe u ba ion has
he same phase on he in es iga ed plane, he p essu e
and esul ing isen opic empe a u e pe u ba ions a e
ou o phase owa ds he combus o walls (an inodes
a e a he walls). This is mos -likely he eason o he
di e en phase in he HRR- esponse compa ed o he
T1yNPE-simula ion. Fo he T1yNPE-simula ion, he
phases o he HRR- esponse o he shea laye lames
appea simila a a ound −π/2.
• The peaks in he FTF gain coincide wi h he s onge
shea laye HRR lame egions.
• The gain o he HRR- esponse o he shea laye
lames is signi ican ly highe in he T1y-simula ion
compa ed o he T1yNPE-simula ion. This is due o
he ac ha no HRR- esponse due o p essu e and
isen opic empe a u e pe u ba ions is accoun ed o
in he la e . Fu he , he shea laye lames a e loca ed
closely o he p essu e an inodes, which sugges s a
p onounced HRR- esponse.
• Towa ds he combus o walls, he ans e se eloci y
ield has i s an inodes. Hence, as he y-coo dina e
app oaches he loca ion o he combus o walls, he
ans e se eloci y measu es low alues which can
esul in a high sensi i i y o he compu ed FTF.
8Symposium on The moacous ics in Combus ion: Indus y mee s Academia (SoTiC 2025) Pape No.(77)
Figu e 7. a) P essu e pe u ba ions ( i s column), ans e se eloci y pe u ba ions (second column), and HRR pe u ba ions ( hi d
column) o he T1y-simula ion and hal an oscilla ion. The same a iables a e plo ed in b) o he T1yNPE-simula ion.
Figu e 8. The local FTFs o eloci y luc ua ions o a) he T1y-simula ion and b) he T1yNPE-simula ion. The in eg a ed HRR is
plo ed by he dashed black line.
Heinzmann e al. 9
Figu e 9. a) P essu e pe u ba ions ( i s column), ans e se eloci y pe u ba ions (second column), and HRR pe u ba ions ( hi d
column) o he T1z-simula ion and hal an oscilla ion. The same a iables a e plo ed in b) o he T1zNPE-simula ion.
Au oigni ion s abilized lame egions on he
xz-plane
Simila compa isons as o he xy-plane can be made o he
xz-plane. The main di e ence be ween he c oss-sec ions
is, ha he xz-HRR ield is p edominan ly s abilized by
au oigni ion. The minimal a ea jump a he dump plane
induces smalle eci cula ion zones. The e o e, only a small
po ion o he lame is p opaga ion s abilized in he shea
laye . Fig. 9a) shows he same quan i ies plo ed as in
Fig. 7a) o he xz-plane and he T1z-simula ion. A e y
dis inc pa e n o he HRR- esponse on he uppe and
lowe lame egions a e obse ed. The HRR pe u ba ions
in ensi y owa ds he ou e combus o walls and a e ou
o phase wi h he ans e se eloci y o he uppe lame
egions and in phase o he lowe lame egions. The HRR
luc ua ion pa e n looks e y simila o he nume ical
compu a ions and he expe imen al da a in (4). In con as ,
he T1zNPE-simula ion does no ep oduce he same HRR-
esponse. Wi hou inclusion o he p essu e and isen opic
empe a u e e ec s on he lame, he HRR- esponse is nea
0 o mos o he lame egion. This is o be expec ed, as he
analysis o he xy-plane al eady showed no e ec o he
ans e se eloci y on he cen al c oss-sec ion. Hence, i is
also con i med o he xz-plane ha he ans e se eloci y
luc ua ions ha e no e ec on he HRR o he lame. The
expe imen al da a shown in (4) o he same c oss-sec ion
u he suppo s his.
The local FTFs o he in eg a ed HRR (in eg a ed along
he x-axis) and he eloci y pe u ba ion ups eam o he
lame a e shown in Fig. 10a) o he T1z-simula ion, and
in Fig. 10b) o he T1zNPE-simula ion. In a) i is clea ly
obse able ha he cen al c oss-sec ion a z= 0 has a
gain close o ze o, meaning ha he lame esponse is
negligible. The same obse a ion is made o he T1zNPE-
simula ion. The small gain o 0.07 o z= 0 o he
T1zNPE-simula ion a ises om a sligh dec ease o he
T1z modeshape ampli ude o e one ha monic cycle. As a
esul , he HRR o he i s 50% o he cycle does no
a e age o ze o wi h he second 50% o he cycle, as is he
case o he o he simula ions. Fo he T1zNPE simula ion,
ob aining a close o cons an modeshape ampli ude o
mul iple cycles emained mo e challenging compa ed o
he o he simula ions. None heless, he negligible gain can
be a ibu ed o hese nume ical di icul ies, and he esul s
suppo he same indings om he o he simula ions.
The e o e, he ini ial hypo hesis o Heinzmann e al. (4;32),
ha ans e se eloci y pe u ba ions ha e no e ec on a
solely au oigni ion s abilized lame, is con i med.
Conclusion
The e ec o ans e se acous ic eigenmodes on au oigni ion
lames has been in es iga ed in ecen s udies (4;32). In
his pape , we speci ically u he analyze he e ec ha
ans e sal eloci y luc ua ions ha e on ully- and pa ly-
au oigni ion-s abilized lames. Fo his, uns eady o ced
RANS compu a ions a e pe o med in Fluen o a lab-
scale ehea combus o (29) and he mean ields alida ed
wi h expe imen al measu emen s. The analysis shows ha
ans e se eloci y pe u ba ions ha e no e ec s on lames
solely s abilized by au oigni ion. This was con i med in all
ou simula ions. The e o e, he ini ially s a ed hypo hesis is
con i med. Fo pa ly au oigni ion s abilized lames, whe e
