29 h ICDERS July 23–28, 2023 SNU Siheung, Ko ea
E ec o inle condi ions in hyd ogen–ai supe sonic eac i e
mixing laye s
C´
esa Hue e1, Ped o J. Ma inez-Fe e 2,4, Daniel Ma ´
ınez-Ruiz3, Daniel Mi a4
1Uni e sidad Ca los III de Mad id, Legan´
es, Mad id, Spain
2Uni e si a Poli ´
ecnica de Ca alunya, Ba celona, Spain
3Uni e sidad Poli ´
ecnica de Mad id, Mad id, Spain
4Ba celona Supe compu ing Cen e , Ba celona, Spain
1 In oduc ion
The chemical eac ion o wo supe sonic low s eams o uel and oxidize is o g ea in e es o he
de elopmen o ad anced hype sonic sys ems o ai c a p opulsion such as sc amje s. A la ge numbe
o nume ical s udies ha e p o ided undamen al insigh s and aluable explana ions o he dynamics and
low s uc u e o supe sonic mixing laye s [1–3] and o hei eac i e ex ension [4–6]. I is well known
ha he inle condi ion can ha e s ong in luence on he g ow h a e o he mixing laye , he o ma ion
o cohe en s uc u es and he oll-up cha ac e is ics [7]. Howe e , o he bes o he au ho s knowledge,
li le deba e has been p esen ed on he i ual o igin o canonical comp essible mixing laye s. In pa -
icula , Sandham and Reynolds [8] explo ed some o he nume ical modi ica ions o he inle plane in
incomp essible mixing laye s by compa ing ypical hype bolic angen and wake- ype modi ied eloci y
p o iles. Ko e al. [9] explo ed he e ec o pe u bing he in low o he incomp essible mixing laye . On
he o he hand, he as majo i y o nume ical s udies ha e ocused on he empo al e olu ion o shea
and mixing laye s due o compu a ional cos s and because hey p o ide a sa is ac o y app oxima ion o
he labo a o y spa ially-de eloping mixing laye s; howe e , his co ela ion is only alid when he slip
eloci y be ween he wo s eams is smalle han he con ec i e eloci y [10]. Fo high-speed lows such
as he ones add essed he ein, his assump ion is inaccu a e and needs o be e isi ed.
In pa icula , he nume ical s udy o supe sonic co lows demands he choice o app op ia e inle con-
di ions ha desc ibe he inne s uc u e o he mixing laye . Typically, his is ca ied ou by assuming
a smoo h hype bolic unc ion in he o m: U(y)∼ anh−1(y/δ), whe e yis he ans e se coo di-
na e, δis a cha ac e is ic mixing laye hickness ( ypically, he ini ial o ici y hickness δω,0), and U
is he s eamwise eloci y unc ion [8, 11]. This o mula ion su ices o desc ibe mos o he canonical
shea laye s. Mixing laye s, on he o he hand, demand he de ini ion o inne p o iles o each o he
species in he mix u e Yi(y), wi h he alues de e mined by a - ield condi ions: [U1,Yi,1] o he uppe
s eam and [U2,Yi,2] o he lowe one. In addi ion, empe a u e has a majo ele ance as i a ec s
he densi y and, he e o e, he ine ia o he low. Mo eo e , empe a u e is also in ol ed in he de ini-
ion o he uppe and lowe s eam Mach numbe s, M1=U1/c1and M2=U2/c2, espec i ely, wi h
c=pγp/ρ =pγRgTs anding o he sound speed, γ=cp/c and Rgbeing he a io o speci ic
hea s and he gas cons an , espec i ely, and pand ρ e e ing o p essu e mix u e and densi y. The la e
is di ec ly ela ed o he mass ac ion o he species in ol ed h ough Yi=ρi/ρ. The e o e, as long as
he mal di usion is o he same o de as species di usion in gases, ha is Lewis numbe Le ∼O(1),
empe a u e p o iles a e key o desc ibe he mixing laye de eloping hickness.
Co espondence o: chue [email protected] 1
Hue e, C. Inle Condi ions o H2-ai supe sonic mixing laye s
i ual domain
ull-p oblem domain
inle b.c.
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U2
<la exi sha1_base64="FD2zudkGQ A7kHJYUmG iBPx mE=">AAAB5HicbZDNTsJAFIV 8Q/xD3XpZiIxcUVa49+SxI1LjBZIoCHT4RYmTD NzNSENLyB oy684l8Ad/GAb Q8Ky+uedMcs8NU8G1cd0 p7Syu a+Ud6sbG3 7O5V9w9aWmaKoc+kkKoTUo2CJ+gbbgR2UoU0DgW2w/HNzG8/o JcJg9mkmIQ02HCI86osaN7 +/1qzW37s5FlsE oAaFm 3qZ28gWRZjYpigWnc9NzVBTpXhTOC00ss0ppSN6RC7FhMaow7y+apTchJJRcwIy z9O5 TWO JHNpMTM1IL3qz4X9eNzPRdZDzJM0MJsxG BdlghhJZo3JgC kRkwsUKa43ZKwEVWUGXuXiq3 LZZdh ZZ3busX9yd1xpucYgyHMExnIIHV9CAW2iCDwyG8Ax 8O5EzpPz4 z+RE O8ecQ/sj5+AbGi4sK</la exi >
U1
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Y1
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T1
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T2
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Y2
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x
<la exi sha1_base64="oDSCmEF VcA0DlMLuEUNoxXokDE=">AAAB4nicbZDLSsNAFIZP6q3WW9Wlm8EiuCqJeFsW3LhswV6gDWUyPWmHTiZhZiKE0B Qlag7H8kX8G2c1iy09V99c/5/4PwnSATXxnW/nNLa+sbmVnm7s O7 39QPTzq6DhVDNssF HqBVSj4BLbhhuB UQhjQKB3WB6N/e7j6g0j+WDyRL0IzqWPOSMGj qZcNqza27C5FV8AqoQaHmsPo5GMUsjVAaJqjW c9NjJ9TZTgTOKsMUo0JZVM6x 5FSSPU 5YdEbOwlgRM0GyeP/O5jTSOosCm4momehlbz78z+unJ z1cy6T1KBkNmK9MBXExGTel4y4QmZEZoEyxe2WhE2ooszYq1Rs W+57Cp0Lu ed 2qdVl uMUhynACp3AOH xAA+6hCW1ggPAMb/DujJwn58V5/YmWnOLPM yR8/EN2o2Kig==</la exi >
y
<la exi sha1_base64="U1o WOon7DRdiRVjI8WYFok2uWg=">AAAB53icbZDLTgJBEEV 8IX4Ql266UhMXJEZ42 J4sYlJ JIYEJ6mgJaeh7p jEhE75BV0bd+T/+gH9jg7NQ8K5O172d1K0gUdKQ6345hZXV WN4mZpa3 nd6+8 9A0caoFNkSsY 0OuEElI2yQJIX RCMPA4W YHwz81uPqI2Mo3uaJOiH BjJgRSc7KjZ7aMi3i X3Ko7F1sGL4cK5K 3yp/d izSECMSih T8dyE/Ix kkLh NRNDSZcjPkQOxYjHqLxs/m2U3YyiDWjEbL5+3c246ExkzCwmZDTyCx6s+F/XielwbW yShJCSNhI9YbpIpRzGalWV9qFKQmF jQ0m7JxIh LsiepmT e4 ll6F5V Uuqxd355Wamx+iCEdwDK gwRXU4Bbq0AABD/AMb/DuSO JeXFe 6IFJ/9zCH/k HwDeLCMqQ==</la exi >
inle bounda y condi ion
spli e
pla e
uppe s eam (ai )
lowe s eam (H2)
hype bolic
sel -simila
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M(y)
<la exi sha1_base64="oDSCmEF VcA0DlMLuEUNoxXokDE=">AAAB4nicbZDLSsNAFIZP6q3WW9Wlm8EiuCqJeFsW3LhswV6gDWUyPWmHTiZhZiKE0B Qlag7H8kX8G2c1iy09V99c/5/4PwnSATXxnW/nNLa+sbmVnm7s O7 39QPTzq6DhVDNssF HqBVSj4BLbhhuB UQhjQKB3WB6N/e7j6g0j+WDyRL0IzqWPOSMGj qZcNqza27C5FV8AqoQaHmsPo5GMUsjVAaJqjW c9NjJ9TZTgTOKsMUo0JZVM6x 5FSSPU 5YdEbOwlgRM0GyeP/O5jTSOosCm4momehlbz78z+unJ z1cy6T1KBkNmK9MBXExGTel4y4QmZEZoEyxe2WhE2ooszYq1Rs W+57Cp0Lu ed 2qdVl uMUhynACp3AOH xAA+6hCW1ggPAMb/DujJwn58V5/YmWnOLPM yR8/EN2o2Kig==</la exi >
y
hype bolic
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u(y),T(y),Y
i(y)
<la exi sha1_base64="x4Xz2yP/C9/ oOEM/exKb MAn 4=">AAAB5XicdVDLSsNAFL3xWeu 6 LNYBHqJiRVq90V3LgRK gH KFMpj 0MmDmYkQQj9BV6Lu/CF/wL8xqRV8n W595wL51w3Elxpy3ozFhaXlldWC2 F9Y3N e3Szm5bhbFk2GKhCGXXpQoFD7CluRbYjSRS3xXYcScXud65Ral4GNzoJELHp6OAe5xRna+uKsnRoFS2zGq9Vj2uk9/ENq0ZyjBHc1B67Q9DF sYaCaoUj3bi STUqk5Ezg 9mOFEWUTOsJeRgPqo3LSWdYpO RCS QYyWz+6k2p 1Tiu5nHp3qs m 58i+ F2 3El5EMUaA5ZZMs2LBdEhySuTIZ I EgyQpnkWU CxlRSp PHFLP6nx3J/6RdNe2aeXp9Um5Y80cUYB8OoAI2nEEDLqEJLWAwhn 4gmdjZNwZD8bjh3XBmN/swTcYL++7Fouj</la exi >
M(y)
(no o scale)
au o-igni ion
<la exi sha1_base64="yN8BB41dWNRQu mwBXhJhQls3Z8=">AAAB4nicbZC7TsMwFIZPyq2UW4GRxaJCYqoSxG2sYGFgaCV6kdqoc yT1qqdRLaDVEV9AZgQsPFI AB g1syQMs/ T7/b+n8J0gE18Z1 5zCyu a+kZxs7S1 bO7V94/aOk4VQybLBax6gRUo+ARNg03AjuJQioDge1g D z24+oNI+jBzNJ0Jd0GPGQM2 sqHH L1 cqjsXWQY hw kq Ln71BzFKJkWGCa 313MT4GVWGM4HTUi/VmFA2pkPsWoyoRO1n80Wn5CSMFTEjJPP372xGpdYTGdiMpGakF73Z8D+ m5 w2s94lKQGI2Yj1g TQUxMZn3JgC kRkwsUKa43ZKwEVWUGXuVkq3 LZZdh ZZ1busXjTOK7Wb/BBFOIJjOAUP qAGd1CHJjBAeIY3eHcGzpPz4 z+RA O/ucQ/sj5+Aac0Yp </la exi >
L
<la exi sha1_base64="7o0BhmcRCF2L+DXjOJXbsZlPBk0=">AAAB5HicbZC7TsMwFIZPyq2UW4GRxaJCYqoSxG2sYGFgKIJepDaqHPek e Eke0gVVH ACYEbDwRL8Db4JYM0PJPn8//Wz /CRLB XHdL6ew LyyulZcL21sbm3 lH 3mlqmimGDSSFVO6AaBY+xYbgR2E4U0igQ2ApG11O/9YhKcxk/mHGC kQHMQ85o8aO7m97sleuuFV3J IIXg4VyFX lT+7 cnSCGPDBNW647mJ8TOqDGcCJ6VuqjGhbEQH2LEY0wi1n81WnZCjUCpihkhm79/ZjEZaj6PAZiJqhn emw7/8zqpCS/9jMdJajBmNmK9MBXESDJ TPpcITNibIEyxe2WhA2poszYu5Rs W++7CI0T6 ee Xs7 RSu8oPUYQDOIRj8OACanADdWgAgwE8wxu8O6Hz5Lw4 z/RgpP/2Yc/cj6+ARsIi1E=</la exi >
Lo
<la exi sha1_base64="lT88kS/RAFyYHOp68dSAl3EOkco=">AAAB5HicbZDLTsMwEEUn5VXKq8CSjUWFxKpKEK9lBRuWRdCH1EaV405aq04c2Q6ii oHsELAji/iB/gb3JIF NzV8dx ae4EieDauO6XU1haXlldK66XNja3 n Ku3 NLVPFsMGkkKodUI2Cx9gw3AhsJwppFAhsBaP qd96QKW5jO/NOEE/ooOYh5xRY0d3jz3ZK1 cqjsTWQQ hw kq Kn92+ZGmEsWGCa 3x3MT4GVWGM4GTUj VmFA2ogPsWIxphN PZq OyFEoFTFDJLP372xGI63HUWAzETVDPe9Nh/95ndSEl37G4yQ1GDMbsV6YCmIkmTYm a6QGTG2QJnidk ChlRRZuxdS a+N192EZonVe+8enZ7Wqld5YcowgEcwjF4cAE1uIE6NIDBAJ7hDd6d0HlyXpzXn2jBy /swx85H99dCI 9</la exi >
xo
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yo
<la exi sha1_base64="V9VKaaO 20kl Ku h G9Q Yemes=">AAAB6XicbZDLTsJAFIZP8YZ4Q126aSQm kh C2JblxiIpcEGjIdDjBh2mlmTk1Iw0Poyqg7X8cX8G0csAsF/9U35/8nO 8JEykMed6XU1hZXV KG6W Z3d K+wdNo1LNscGVVLodMoNSxNggQRLbiUYWhRJb4 h25 ceURuh4geaJBhEbBiLgeCM7Kjd7aMk1lO9csW enO5y+DnUIFc9V75s9 XPI0wJi6ZMR3 SyjImCbBJU5L3dRgw iYDbFjMWYRmiCb7z 1TwZKuzRCd/7+nc1YZMwkCm0mYjQyi95s+J/XSWlwHWQiTlLCmNuI9QapdEm5s9puX2jkJCcWGN CbunyEdOMkz1Oydb3F8suQ/Os6l9WL+7PK7Wb/BBFOIJjOAU qAGd1CHBnCQ8Ax 8O6MnS nxXn9iRac/M8h/JHz8Q0AmY2d</la exi >
o
Figu e 1: Ske ch o he lamina mixing laye domains and he a bi a y choice o he inle condi ions in
he i ual compu a ional domain.
The e ec o imposing di e en inne p o iles o he s a e a iables on he igni ion dis ance o a supe -
sonic mixing laye p oblem is explo ed he e. In pa icula , he p oblem o a supe sonic hyd ogen–ai
mixing laye , simila o he expe imen conduc ed by Cheng e al. [12], is in es iga ed using di ec
nume ical simula ions. A ske ch o he se up wi h he compu a ional domain used o nume ical simu-
la ions and he a bi a y choice o he inle condi ions is shown in Fig. 1. I can be seen ha bounda y
condi ions o U,Yi, and T o each s eam mus be p o ided o de ine a well-posed ma hema ical p ob-
lem. The choice o he inle condi ion may ha e a po en ial impac in he p edic ion o he au oigni ion
dis ance, pa icula ly in high-speed eac i e mixing laye s whe e a a ia ion o he o de o milliseconds
in he au oigni ion ime, owing o a miss-calcula ion o he mixing laye s a e, is ansla ed in o dis ances
o he o de o me e s, he cha ac e is ic leng h o a supe sonic combus ion chambe . In he ollowing,
he ideal gas law is assumed o bo h s eams and, since he mix u e is mos ly made o dia omic gases
a condi ions o in e es , he adiaba ic index is aken cons an , γ1=γ2=γ= 7/5. Besides, p es-
su e is assumed o be uni o m a he inle , so he ollowing ela ionships apply o molecula weigh s,
W1ρ2T2=W2ρ1T1, and Mach numbe s, M1U2√ρ1=M2U1√ρ1ou side o he mixing laye .
1.1 Hype bolic unc ions o he inle a iables
The a bi a iness in he inle condi ion elies in he choice o he inne p o iles o he mixing laye . Fo
example, Fig. 1 depic s he lamina mixing laye domains and he a bi a y choice o he inle condi ions
in he compu a ional domain. Be o ehand, we could make use o he hype bolic inle condi ion o ei he
o he independen a iables, namely
ϕ(¯y) = ϕ1+ϕ2
2+ϕ1−ϕ2
2 anh−1(¯y),(1)
whe e ¯y=y/δ is he scaled o de -o -uni y ans e se coo dina e and ϕ ep esen s any sui able inle
condi ions o he s eamwise eloci y ( ans e se eloci y is se o a ze o alue), empe a u e, and N−1
species mass ac ions. On condi ion ha p essu e is uni o m and known, PN
1Yi= 1 and he equa ion
o s a e a e used o compu e he N h species and he densi y ield. In ou case, he mix u e composi ion
in he uppe and lowe s eams is gi en by YH2,1= 0,YO2,1= 0.233, and YN2,1= 0.767, and YH2,2= 1
and YO2,2=YN2,2= 0, espec i ely. By choosing also he eloci y and he empe a u e o he ou e
s eams [U1,T1] and [U2,T2], he es o he low a iables can be de i ed, as s a ed abo e. A widely-
used app oach o p esc ibe hese quan i ies is he Buseman–C occo eloci y– empe a u e ela ion [3,5],
a e y pa icula choice a om alidi y in gene al applica ions.
29 h ICDERS – July 23–28, 2023 – SNU Siheung, Ko ea 2
Hue e, C. Inle Condi ions o H2-ai supe sonic mixing laye s
Al e na i ely, he Mach numbe p o ile could be imposed o ollow he hype bolic ela ion gi en by
Eq. (1) so ha Umus be ans o med in o a dependen a iable. This inle condi ion o M(¯y)is
appealing as i di ec ly p o ides he con ec i e Mach numbe Mc=M1−M2as an inpu pa ame e ,
which is known o play a dominan ole in he desc ip ion o he lamina – u bulen low ansi ion in
high-speed condi ions. Ne e heless, o hyd ogen–ai mixing laye s, he s eam con aining hyd ogen
is much ligh e han he oxidize s eam, and he modi usi e e ec s can play an impo an ole on he
composi ion and he mal ield along he mixing laye de elopmen . In ac , none o he abo e-p esc ibed
hype bolic inle condi ions occu s as he na u al solu ion o a uly e ol ing mixing laye .
1.2 Sel -simila mixing laye o he inle a iables
A mo e app op ia e de ini ion o he inle condi ion is based on he assump ion ha he low e ol es
lamina ly om he leading edge o he hin spli e pla e. He e, he ele an Reynolds numbe o he
low Re =ρ1U1Lo/µ1, is based on he eloci y U1, densi y ρ1, and shea iscosi y µ1o he up-
pe s eam. I esul s in a slende mixing laye , whose cha ac e is ic hickness inc eases acco ding o
[(µ1/ρ1)xo/U1]1/2, eaching a alue o δo∼O(Re−1/2Lo)≪Loa xo=Lo. Since ni ogen and oxy-
gen ha e simila molecula weigh s, he a io o he species along he mixing laye can be assumed o be
cons an un il he au oigni ion poin . Consequen ly, i can be assumed ha he mixing p ocess is equi -
alen o ha o a bina y mix u e be ween uel and ai . The e o e, he co esponding uel di usion lux,
non-dimensionalized by [ρ1µ1U1/Lo]1/2, can be compu ed wi h an explici o m [13,14], as gi en by he
second equali y in (5). I accoun s o mass and he mal di usion, he la e ha ing a signi ican e ec
o hyd ogen. He e, ¯
T=T/T1and ¯ρ=ρ/ρ1co espond o he dimensionless empe a u e and densi y
unc ions, espec i ely, and η=y/[(µ1/ρ1)x/U1]1/2 ep esen s he o de -o -uni y sel -simila a iable.
The P and l numbe P =µcp/λ = 0.7 h oughou he non- eac i e zone, wi h λand cp ep esen ing
he he mal conduc i i y and he speci ic hea a cons an p essu e o he mix u e, espec i ely. The a io
o he he mal di usi i y λ/(ρcp) o he uel–ai bina y di usion coe icien Dis he so-called Lewis
numbe Le =λ1/(ρ1cp1D1) ha includes he dimensionless bina y di usion coe icien ¯
D=D/D1.
The he mal di usion ac o α, de ined as he a io o he he mal di usion coe icien o he p oduc
Y(1 −Y)ρD, is aken cons an , wi h α≈ −0.3 o hyd ogen–ai mix u es [14].
Conside ing he scaling o he quan i ies wi h he abo e dimensionless a iables, he conse a ion equa-
ions o he bounda y alue p oblem used o de ine he inle condi ions can be w i en as:
−η
2
d
dη(¯ρ¯u) + d
dη(¯ρ¯ )=0,(2)
¯ρ¯ −η
2¯ud¯u
dη=d
dη¯µd¯u
dη,(3)
¯ρ¯cp¯ −η
2¯ud¯
T
dη=1
P
d
dη¯µ¯cp
d¯
T
dη−( ¯w−1
2−1)¯
jd¯
T
dη−α(γ−1)
¯w2γ
d
dη¯w¯
j¯
T
+(γ−1)M2
1¯µd¯u
dη2
,(4)
¯ρ¯ −η
2¯udY
dη=−d¯
j
dη=1
P Le
d
dη¯ρ¯
DdY
dη+αY(1 −Y)
¯
T
d¯
T
dη ,(5)
whe e ¯u=u/U1,¯ = /U1(Lo/δo),¯µ=µ/µ1,¯cp=cp/cp1and ¯w=W/W1a e he shea iscosi y,
speci ic hea , and mean molecula weigh scaled wi h hei ai s eam alues. The abo e equa ions mus
29 h ICDERS – July 23–28, 2023 – SNU Siheung, Ko ea 3
Hue e, C. Inle Condi ions o H2-ai supe sonic mixing laye s
(a)
0
0.5
1
1.5
2
-3 -2 -1 0 1 2 3
Densi y
Tempe a u e
Veloci y
Mach
¯y[–]
(b)
0
0.2
0.4
0.6
0.8
1
-3 -2 -1 0 1 2 3
Hyd ogen
Oxygen
Wa e
Ni ogen
¯y[–]
Figu e 2: (a) Nondimensional low a iables and (b) mass ac ion inle p o iles ac oss he nondimen-
sional ans e se coo dina e: hype bolic Mach numbe (solid line), hype bolic s eamwise eloci y
(dashed line), and sel -simila solu ion (do ed line). Re e ence alues a e δω,0= 1.78 ×10−3m,
ρ e = 0.278 kg/m3,T e = 1250 K, and U e = 1429 m/s.
be supplemen ed wi h he equa ion o s a e ¯ρ¯
T= ¯w=1 + ( ¯w−1
2−1)Y−1, and wi h he exp essions
¯µ=1 + [¯µ2/¯w1/2
2−1]Y
1 + ( ¯w−1/2
2−1)Y
¯
Tσ1,¯
D=¯
T1+σ1,and ¯cp= [1 + ( ¯w−1
2−1)Y]¯
Tσ2,(6)
o accoun o he a ia ion o he anspo coe icien s and speci ic hea wi h empe a u e and compo-
si ion. The ep esen a i e alues σ1= 0.7and σ2= 0.2a e used o he empe a u e powe laws [15].
An example o how di e en inle condi ions a ec he mixing-laye p o ile, wi h he condi ions o he
expe imen o Cheng e al. [12], is shown in Fig. 2. When imposing he eloci y p o ile, he Mach num-
be is no a mono onic unc ion and a ains subsonic condi ions a an in e media e posi ion. This e ec
is o pi o al impo ance because downs eam p essu e dis u bances can each he inle plane h ough
he subsonic egion. In addi ion, i an oblique shock is conside ed o p omo e he igni ion (as occu s in
sc amje engines), he pene a ion leng h in o he mixing laye would be sho ened and he pos -shock
low co espondingly a ec ed. Fu he di e ences a e expec ed o occu o highe Mach numbe s,
whe e he hea ing associa ed wi h iscous dissipa ion, see las e m in (4), could be su icien ly in ense
o p omo e he appea ance o a local maximum inside he mixing laye [16], he eby placing he igni ion
ke nel a inside om he ho uppe s eam.
2 Di ec Nume ical Simula ions
Di ec nume ical simula ions (DNS) o he e olu ion o he eac i e mixing laye wi h di e en inle
bounda y condi ions a e o e ed in Fig. 3. I is shown h ee ins an aneous empe a u e ields associa ed
wi h he h ee condi ions employed in Fig. 2, which sha e he same low p ope ies ou side he mixing
laye . The nume ical simula ions ha e been ca ied ou wi h CREAMS [17], a comp essible eac i e
Na ie –S okes sol e ha uses a spa ial se en h-o de WENO scheme and a hi d-o de o al a ia ion
diminishing Runge–Ku a empo al scheme. The alue o he ini ial o ici y hickness, δω,0= 1.78 ×
10−3m, is calcula ed om he inle Reynolds numbe Reω,0= 3200 and he a e age and con ec i e
low p ope ies a e p o ided om expe imen al da a [12]. By di ec inspec ion o Fig. 3, i is e iden ha ,
29 h ICDERS – July 23–28, 2023 – SNU Siheung, Ko ea 4
Hue e, C. Inle Condi ions o H2-ai supe sonic mixing laye s
Figu e 3: Ins an aneous empe a u e and hea elease ields co esponding o h ee ini ial p o iles: hype -
bolic Mach numbe ( op), hype bolic s eamwise eloci y (middle), and sel -simila solu ion (bo om).
Dimensionless spa ial coo dina es scale wi h δω,0= 1.78 ×10−3m.
unde he speci ied condi ions, he u bulen s uc u es a y g ea ly based on he mixing laye p o ile.
Howe e , he sel -igni ion dis ance, measu ed a he poin o maximum eac ion a e, is oughly loca ed
a a dis ance o 3 mm om he inle condi ions and emains p ac ically unchanged. The main causes
o his ou come a e a ibu ed o h ee ac o s: (1) he empe a u e p o ile does no exhibi signi ican
a ia ions based on he selec ion o inle condi ions, (2) he ai s eam is e y ho and domina es he
he mal unway, and (3) igni ion occu s p io o he o ma ion o u bulen s uc u es. This ou come
should be analyzed u he by conside ing highe Mach numbe s and la ge con ec i e Mach numbe s,
whe e empe a u e wi hin he mixing laye may display g ea e sensi i i y o he inle condi ions.
Acknowledgemen s
The au ho s g a e ully acknowledge D . A naud Mu a, CNRS esea che a Ins i u PPRIME in F ance,
o he nume ical ool CREAMS as well as D . Alexand e E n and D . Vincen Gio angigli o
he EGLIB so wa e. C.H.and D.M.R wo k has been unded wi h p ojec s TED2021-129446B-C41
and TED2021-129446B-C43 unded by MCIN/AEI /10.13039/501100011033 and Eu opean Union
Nex Gene a ionEU/ PRTR. C.H. and D.M.R. wo k has been also suppo ed by he Mad id Go e nmen
(Comunidad de Mad id-Spain) unde he Mul iannual Ag eemen wi h UC3M (H2SFE-CM-UC3M) and
UPM (CHAC-CM-UPM). Also he p ojec s MCIN/AEI/10.13039/501100011033, ESF/10.13039/50110
0004895, RESIM-2021-3-0019, and he G an RYC2019-027592-I o P.J.M.
29 h ICDERS – July 23–28, 2023 – SNU Siheung, Ko ea 5
Hue e, C. Inle Condi ions o H2-ai supe sonic mixing laye s
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29 h ICDERS – July 23–28, 2023 – SNU Siheung, Ko ea 6
