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TRANSCRIPT
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
yyyâââ+++���XXX»»»LLL§§§êêê���[[[*
A† gÊ �ï#
( IEÆÊUá�ó§Æ�, p(ÀØuÄÅEâ:¢�¿, â 410073 )
( 2012 c 3 � 3 F�; 2012 c 4 � 26 F�?Uv )
ïáyâ+X»��kKN�., ê�[â+¥yâ�X»L§. ïÄL², �yâL¡A\ì�, â§Ý:ìþ,, ×�X», Ù±í�§,Ç%��uâ�§,Ç; 3X»L§¥í§Ý3âL¡NC,p'�²w, �N§Ý,pØ. ©Ûâ+SÜëêÚ¸ëêéyâ+X»�K. âßÝ�O\, â+C�´uX», ÙX»mCá, �âßÝO�½§Ý�, UYOTòéâ+�X»å4^. ¸Øåéâ+X»�K'��, 3 1—5 atm Sâ+�X»5UÄ�ØC. í¥�íßÝéâ+�X»5UKØwÍ, ���íßÝL�, éX»L§�KòOr. ââ»!í/âЧ!Ë�§Ýéâ+X»�Kã, �â»!p§Ýr¦â+¯X».ê�[©z¥Á�(J�Czª³.
'c: ®"-�ÀØuÄÅ, yâX», â+
PACS: 47.70.−n, 47.40.pq, 82.60.cx
1 Ú ó
®"-�ÀØuÄÅ´«#VguÄÅ, §¦^pUþ�7á®"-�, ®"-�36zí�^e±ü6�/ª?\ý-¿S, �ÀØí-�A [1]. ÙDÚ��N»ÀØuÄÅ-�A5k¤ØÓ, í�ü6±½�Ý�\ý-¿, Ø�3®"-�øAXÚÑé«S/¤ßÝ�â+, 3�ý-¿SâßÝÑ�, ¤±®"-�ÀØuÄÅý-¿S�-�aqu®��-�.
þ�ïÄL², +â-�üâ-�'¬Ñy-:eü!X»ò´ÏCá�y, ¡ “Ü�A [2] (cooperative effect)”(u®-�¥¡ “ßÝ�A”)[3]. ÊH@â+�-�´E,L§, Ïâ+¥â¬u)pZ6,�âÓ-�òk9þ�, ò~�z-�â�9þ, r?â�-�; �Ó, §pq�ö�z5íN, N�z5íN§
�»�¡*Ñ, ~â+�-�. âm�pK)éõ¡: UC6|ÚX»1!ÏâßÝCzò½ áX»m!é9þÚ�þ�¿�!UCâ±�íN©Ù!¦â±�6|Ú-�ÆC�. Ïdâ+-�Ø´üâ-��{üU\, �8céâmp^)�éØÙ.
IÆö [4] ÏLé�êAâ3AÏAÛ©Ù^e�-�ïÄuy, âmåéâ-�L§¥p^�Kã. Nagata � [5] ÏL¢�ïÄuyâmåéâ�»�/G9»��$ÄKé, ¿Xâmå�O, â-�mÅì~�, »�ål~�. ¦¦^» 1.25 mm �¥/â-�3âål 4, 14,20, 30 mm �ØÓ�¹e?1-�, uy3må�¹e, âÄkÑyN»�, �â�»��U\, /¤oN�Ü-�; 3�må�¹elm©ÒLyÜ+-�. Brzus-towski � [6] ÏLnØ¢�ïÄuy, â�-�Çâmå�C�~�, �â�>, Ù
* I[g,ÆÄ7 (1OÒ: 51006118) ]Ï�K.† E-mail: [email protected]
c© 2012 ¥¥¥IIIÔÔÔnnnÆÆƬ¬¬ Chinese Physical Society http://wulixb.iphy.ac.cn
164702-1
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
-�Ç�, ¿nØOüâ3â»ØÓ9måØÓ�¹e»�ÆC�/G, ¿ÏL^e�¢��yÙnØ.
c
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
3 �.�Ä�§
3.1 ííí§§§
þ§∂ρg∂t
+1r2
∂
∂r(ρgur2) = ϕ̇m rp < r < RL; (1)
Ô|©§∂ρgYi
∂t+
1r2
∂
∂r(ρguYir2)
=1r2
∂
∂r
(ρgDr
2 ∂Yi∂r
)+ ϕ̇i
rp < r < RL, (i = O2, N2); (2)
Uþ§∂ρgcpTg
∂t+
1r2
∂
∂r(ρgucpTgr2)
=1r2
∂
∂r
(ρgDcpr
2 ∂Tg∂r
)+ ϕ̇e
rp < r < RL; (3)
ª¥, u ·ÜíN»Ý, r åkKN¥%�ål, Yi |©þ©ê, cp í½Ø'9,Tg í§Ý, ϕ̇m, ϕ̇i, ϕ̇e ©Oíþ!Ô|©ÚUþ�, du3X»�ã, Au)3âL¡, ¤±±þn 0.
3.2 ââ⧧§
1) ⻧3X»L§¥âþO\Ç ṁp ÚXyþ
~�Ç ṁMg þdL¡A�íÑÇ ṁO2 û½,=
ṁp = −ṁO2 , ṁMg = βṁO2 .
b�â3L¡AL§¥, ÕtG�z��L*Ý�u Mg �Ý
dRpdt
= − ṁO24πR2pρp
, (4)
drpdt
=βṁO24πr2pρp
, (5)
Rp âØ», =�z�C�â�»;rp âSØ», =Ø��z��â�»; βzÆA�þ', =ü þ��íAÑy�þ.
2) âUþ§43πR3pρpc
dTpdt
= Qsurf − Qconv + Qrad, (6)
Ù¥, c yâ�'9, Qrad = Apεσ0(T 4B − T 4p )Ë�9, Ap yâL¡È, ε y�çÝ,σ0 Stephan-Boltzmann ~ê, TB Ú Tp ©OË�Úâ§Ý; Qconv = Aph(Tp − Tg) âíé69, 9Xê h = Nu · λ/dp, λ í�9Xê, âívké$Ä, Nu = 2;Qsurf = β · q · 4πr2p · ω L¡Aº�9þ, q y�-�9.
3.3 GGG���§§§
P =ρgRMTg,
dPdt
=dρgdt
RMTg +dRMdt
ρgTg
+dTgdt
ρgRM = 0.
(7)
Ù¥ P Ør, RM = R ·n∑
i=1
YiMi
í�íN~
ê, M ��þ.
3.4 yyyLLL¡¡¡zzzÆÆÆAAAÄÄÄåååÆÆÆ
'uy�L¡�zA, c
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
L 1 ØÓ�ãL¡AÇ
L¡A�íÑÇ/kg·m−2·s−1
ú�z�ã (< 873 K) ω1 = 1.7 × 1012(ρYO,s)0.5 exp(−34000/Tp) [10]
¥§LÞ�ã (873—923 K) ω̃ = 3.4 × 1010YO,s exp(−200000/RTp) [14]
p§�z�ã (> 923 K) ω2 = 1.7 × 1012(ρYO,s)0.5 exp(−15000/Tp) [10]
3.5 ÐÐÐ^̂̂!!!>>>...^̂̂ÚÚÚ{{{
� t = 0 , YO2 = 0.232, Tg = Tp = T0;� t = τ , 3 r = rp ?, G = GO2 = ω L«âL¡þ6þAÑ��íþ; H = h(Tp − Tg)L « â L ¡ U þ 6 þ â/ í N 9 þ;3 r = RL ?,
∂Yi∂r
= 0,∂Tg∂r
= 0.
ã 2 O��y©
§ (1)—(7) ¥, ρg, u, Yi, Tg pÍÜ, =Uê¦). �y©Xã 2 ¤«, 3âL¡NC�\, ¦^��!wªþºªlѦ).mÚ� 1 × 10−8 s. ±�CuÄÅó�êâÄ�ó¹ëê, XL 2 ¤«.
4 O(J9?Ø
4.1 âââ+++���XXX»»»LLL§§§
7áâ+¥â�X»´E,�L§,Ø�Éâ§Ý�, É+¥�¹þ�.
Annamalai Ú Ryan[15] �X»�â: �â§ÝÑyâ�, =@X»u). Roberts � [16]
@yX»u)3õA=CíA, �½y�£:X»:. �©(Üâ+�A:, ½Ââ+�X»Xe: �â§ÝÑyâ�, @X»u), �â§Ý�£:�â@X»¤õ, XJâ§ÝØU�£:, @X»u)�¤õ. X»mâ+lm©É9�â§ÝÑyâ�¤²{�m.
ã 3 ÄOó¹eØÓkKN§Ý«¿ã, ã 4 ØÓkKNS§Ý�m©Ùã. ±wÑ, 3 24 ms c, â§ÝOÇ´ú�, 24 ms �, â§Ý×Jp, éámS�£:, X»¤õ. X»L§¥í§Ý�NJpØ, ´âL¡NCé�«S�íN§,'�²w. ùÌ´Ï7áy-�ØÓuu!%�, §vku°�ÛÑ, 3X»cí¥vkzÆA, í,§´âéí�L¡é69, í�N�,§díN�9XêÚâ-íL¡D9Xê, ¤±=âL¡?íN§,�²w, �lâL¡?íN§,Ø. â,§3âú�z�ãÌáÂË�9, �½§Ý�ÙL¡A�)�9þâÌ�Ù,§, ¤±X»mÌÑ3ú�z�ã. â�§,'í¯, AO´X»�ã��Ï, duL¡Aì�, Ù§,Ç'í�§,ÇNõ.
L 2 ÄOó¹êâ
íЧ Tg,0 = 673 K íЩ�þ©ê YO2,0 = 0.232
âЧ Tp,0 = 673 K Щ⻠rp,0 = 30 µm
Ë�§Ý TB = 1600 K ��y'9N c(s) = 1092 J/(kg·K)
âßÝ µ = 1/3 �y'9N c(l) = 1411 J/(kg·K)
DXê ρD = 5 × 10−5 kg/(m·s) ��yÝ ρp(s) = 1738 kg/m3
¸Øå P = 3.03 × 105 Pa �yÝ ρp(l) = 1580 kg/m3
-�9 q = 25000 kJ/kg y�çÝ ε = 0.8
164702-4
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
t=24.0 ms t=24.75 ms t=24.85 ms
T/K
t=25.0 ms t=25.03 ms t=25.09 ms
673
886
1099
1312
1525
ã 3 ØÓíÚâ�§ÝCzã µ = 1/3, Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K,rp0 = 30 µm, YO2,0 = 0.232
0 4 8 12600
800
1000
1200
1400
r/rp0
/K
t=2 ms
t=12 ms
t=24 ms
t=25 ms
ã 4 ØÓkKNS§Ým©Ù µ = 1/3,Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K,rp,0 = 30 µm, YO2,0 = 0.232
4.2 âââßßßÝÝÝéééâââ+++XXX»»»���KKK
ã 5 Úã 6 ©OâßÝØÓkKN§ÝÚ�í|©©Ù«¿ã, ã 7 ØÓ!ØÓâßÝ^ekKNS�í§Ý!�í|©ßÝ�m©Ùã. dã 5—7 ¥, âßÝ�, kKN�NÈ, kKNS�í§Ý,pú, A/KNS��í|©ßÝ~�ú, X»m, �X»í�§Ý$!�í|©ßÝ; âßÝ, Cz5ÆKfÐ.
T/K
673
µ=10/3,t=19.08 ms
µ=1,t=22.1 ms
µ=1/3,t=25.09 ms
886
1099
1312
1525
ã 5 â+X»kKNS§Ý©Ù«¿ã Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K, rp0 = 30 µm,YO2,0 = 0.232
164702-5
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
µ=10/3,t=19.08 ms
µ=1,t=22.1 ms
µ=1/3,t=25.09 ms
0
YO2
0.058
0.116
0.174
0.232
ã 6 â+X»kKNS�í|© YO2 ©Ù«¿ã Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K,rp0 = 30 µm, YO2,0 = 0.232
0 2 4 6 8 10 12 14
720
770
820
870
920
970
1020
1070
1120
0
0.05
0.10
0.15
0.20
0.232
YO
2
YO
2
Tg ↼µ//↽
YO2 ↼µ//↽
t=25 ms
Tg ↼µ//↽
Tg ↼µ/↽
YO2 ↼µ//↽
YO2 ↼µ/↽
Tg ↼µ//↽
Tg ↼µ/↽
YO2 ↼µ//↽
YO2 ↼µ/↽
Tg ↼µ//↽
YO2 ↼µ//↽
t=22 mst=19 ms
0 2 4 6 8 10 12 140.2319978
0.2319980
0.2319985
0.2319990
0.2319995
0.232
/K
r/rp0
r/rp0
ã 7 ØÓ!ØÓâßÝ!kKNSí§ÝÚ|©m©Ù Tp,0 = Tg,0 = 673 K, P = 3 atm,TB = 1600 K, rp0 = 30 µm, YO2,0 = 0.232
ã 8 ØÓâßÝâ+§Ý - mã. dã 8 ±wÑ, â+�X»mâßÝ�~�O, �ù«'XØ´5'X, µ ∈ [0.1, 1] X»méâßÝ�¯aÝ' µ ∈ [1, 10] �õ. ù´ÏâßÝ, Kí'~é�, âDí�9þU�¯J,í§Ý, í§Ý�,pK¿Xâí�Ñ9ò~�, 3âáÂ9Ë�9L¡Aº9þØC�¹e, ÙÑ9þ�~�ÃÉ¿XÙg�§Ý�×J,, ÒLyÙX»m
Cá. ��âßÝO�½§Ý, â+¥�þòé�, âmé�í�¿�ì�, ò�,«/�Ñy, Xã 8 ¥ µ = 10 �, â§Ýé@Ñyâ�: (A :), �3 B :�%Ñyâ§ÝJ±þ,�¹. ù´Ï3X»�ÐÏ, âé�í�-�¿�¦�â+§Ý×þ,, ���Ï�í¹þ:ìeü, âL¡AÊ¢, â�9ØE3, ¤±Ù§ÝØUUY¯þ,, ±uX»¤õ. ¤±3âßÝ�¹e, �¹þò¤û½â+X»¤
164702-6
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
õÄ�!. 3âßÝ��¹e, í¥��¹þéâX»ó´¿ü�, ââm��þ!9þ�«¿�Ñ~�, ¿âßÝ��, â��CuüâX», ã 8 ¥ µ l 0.2� 0.1, X»mCzØ�, µ < 0.1 �X»ò´Cz�ÒéÐ/`²ù:.
0 5 10 15 20 25650
850
1050
1250
1450
时间/ms
Tp/K
µ=10µ=5µ=10/3µ=2µ=4/3µ=1µ=0.5µ=1/3µ=0.2µ=0.1
A
B
ã 8 µ Ø Ó â § Ý m C z Tp,0 =Tg,0 = 673 K, P = 3 atm, TB = 1600 K, rp,0 = 30 µm,YO2,0 = 0.232
0 10 20 30 40650
850
1050
1250
1450 rp0=10
rp0=30
rp0=50
rp0=70
Tp/K
ã 9 rp,0 ØÓâ§ÝmCz µ = 1/3,Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K,YO2,0 = 0.232
4.3 âââÐÐЩ©©»»»éééâââ+++XXX»»»���KKK
dã 9 , Xââ»�~�, â+�X»m á. d(Ø3u®ó9®�¿�+¥�2@. Ïâ��, Ù'L¡È�,3Ù¦^ÑØC�¹e, ü þ-�âáÂË�9þÚAº�9þÒ�õ, �,§,Ý'�¯, rp0 = 10 µm ��â§Ý$ëLz²�Ñ®. ¤±[â�®�ÙX
»m4á, �¿�x54.
4.4 ¸̧̧ØØØåååéééâââ+++XXX»»»���KKK
ã 10 ¸ØåØÓéâ+X»�K.dã 10 , Øåéâ+X»�K¿Ø, Øå�O, â+�X»mÑkJc. ¤m [17] 3Y�í¸¥?1y�X»¢�ïÄ,¦©O3 0.1, 0.5, 1.0, 1.5, 2.0 MPa �ØÓ�Øåe*y�X»5U, uyy�X»§ÝÚX»mØå�ØÓCzé�, �ѸØåéyâ�X»KØ�(Ø, ù��.�(Ø´�. ù´Ïyâ�X»L§Ì´dâ�\9Ý�, â�É93éãmS´Ë��9Ë�ÓÌ�/ , ØåTTØé9Ë�å^, ¤±Øåéâ+�X»L§KØ.âd(Ø, 3~Øe?1â+:»¢����(Ø95ƱA^u®"-�ÀØuÄÅ-�¿�pØ^e (®"-�ÀØuÄÅ-�¿Øå3 0.3—0.5 MPa m).
ã 10 Ø r P é â + X » � K µ = 1/3,Tp,0 = Tg,0 = 673 K, TB = 1600 K, rp,0 = 30 µm,YO2,0 = 0.232
4.5 ���íííßßßÝÝÝéééâââ+++XXX»»»���KKK
ã 11 í¥�íßÝéâ+X»�K. dã 11 , 3½S, �íßÝéâ+X»�KØ, í¥�í�þ©êl 0.2Cz� 0.5, �â�§ÝCz¿Ø´é²w. Cassel Ú Liebman[18] ïÄuy, �íßÝ©O 23%Ú 100%, y�X»§Ý%vk²wCz.
¤m [17] ÏLy3Y�í¸¥�¢�ïÄuy�zJßÝéy�X»§ÝÚX»mÑvk�K. ù¢�(JÑ�y��.��(5.
164702-7
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
©ÛÙ�ÏÌ´Ï3y�X»L§¥, �zJ*ÑØ´AÇ�!, Ïd�zJßÝéâA9�K��, léyâ+X»mK¿Ø´éwÍ. ���.uy, �íßÝ�v��§Ý�, éâ+X»�Km©wÍ, ã¥��í�þ©êl 0.2 C� 0.1 , â�§Ý�)��Cz, ùÌ´Ïí¥�þ~��½§Ý�, �þéAÇ�!C�â,å5.
0 5 10 15 20 25 29650
850
1050
1250
1450YO2,0=0.1
YO2,0=0.2
YO2,0=0.232
YO2,0=0.35
YO2,0=0.5
Tp/K
ã 11 YO2 ØÓâ§ÝmCz µ = 1/3,Tp,0 = Tg,0 = 673 K, P = 3 atm, TB = 1600 K,rp0 = 30 µm
0 10 20 30 40 50 60650
850
1050
1250
1450
0.12
0.16
0.20
0.24
Tp(TB=1800 K)
Tp(TB=1600 K)
Tp(TB=1400 K)
Tp/K
YO
2
ã 12 Ë�§Ý TB éâ+X»�K, µ = 1/3,Tp,0 = Tg,0 = 673 K, P = 3 atm, rp,0 = 30 µm,YO2,0 = 0.232
4.6 ËËË���
§§§ÝÝÝ999ííí!!!âââÐÐЧ§§éééâââ+++XXX»»»���KKK
ã 12 Ë�§Ýéâ+X»�K. dã 12 , Ë�§Ýéâ+X»�Kã,Ë�§Ý�p, X»m�á, TB = 1800 K X»m ~ TB = 1400 K � 1/6. JpË�§Ý´ áâ+X»m�k�å».
ã 13 íÚâЧéâ+X»�K. dã 13 , íÚâЧéâ+X»�K©wÍ, XíÚâЧ�,p,X»²w\¯. Ï7áy3X»c´vku°ÛÑ�, §�,§3cϱáÂË�9Ì, �ϱL¡Aº9Ì, ÙX»¤Ñ¤�mÌ8¥3ì�L¡Ac; L¡A\ì�duA9þ, Ù,§³Þé×, éámSÒ¢yX». ¤±JpíÚâ�Ч, ¢Sþ´�/ áÙú�z�ã�m, ?4/ áX»�m.
0 10 20 30 40550
750
950
1150
1350
1550
Tg,0=
673 K
, T
p,0=
673 K
Tg,0=
673 K
, T
p,0=
573 K
Tg,0=
673 K
, T
p,0=
773 K
Tg,0=
673 K
, T
p,0=
873 K
Tg,0=
573 K
, T
p,0=
673 K
Tg,0=
773 K
, T
p,0=
673 K
Tg,0=
873 K
, T
p,0=
673 K
Tp/K
ã 13 Tg,0, Tp,0 Ø Ó â § Ý m C z µ = 1/3, P = 3 atm, TB = 1600 K, rp,0 = 30 µm,YO2,0 = 0.232
5 ( Ø
�©ïáyâ+X»��kKN�., ê�[yâ+�X»L§, ¼�âX»��)L§Úí§Ý!|©3kKNS�©Ù. ïÄL², â+X»�mÌÑ3ú�z�ã, 3X»L§¥í§Ý�NJpØ, ´âNCé�«S§,'�²w; �yâL¡A\ì�, §Ý:ìþ,,×�X», Ù±�í§Ýþ,Ý%��uâ�§,Ç.
XâßÝ�O, X»C�N´, �TO�½§Ý�, qØ|uX»u). ââ»éâ+X»�Ké²w, â»��, X»�N´, À��â»âòwÍJpâ+�X»5U.¸Øåéâ+X»Ké�. í¥�íßÝ3½Séâ+X»�KØ, ��í¥�íßÝv$�ÿ, ÙéX»�K^òØ
164702-8
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
�À. í!âЧÚË�§Ýéâ+X»�K´ã�, Jpùnö�§Ýò4 áX»m.
��.��¡/Nyâ+X»�Ån,
¢S¹Î, ¿UòüâX»+NX»éXå5, äk½�¢^d, ±^5�®"-�ÀØuÄÅý-¿g-'��O.
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164702-9
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Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 164702
Numerical studies of unsteady ignition of pulverizedmagnesium particle cloud∗
Yang Jin-Zhao† Xia Zhi-Xun Hu Jian-Xin
( Science and Technology on Scramjet Laboratory, College of Aerospace and Material Engineering, National University of Defense Technology,
Changsha 410073, China )
( Received 3 March 2012; revised manuscript received 26 April 2012 )
Abstract
A one-dimensional unsteady magnesium particle cloud ignition model with finite influencing sphere is established. The behavior
of ignition of magnesium particle cloud is numerically simulated. The result shows that when the reaction is speeded up on the
surface of magnesium particle, the temperature of the particle phase rises rapidly up to ignition temperature, while the surrounding air
is much slower in temperature rising than particles; the gas temperature rising is unconspicuous in the whole sphere in the ignition
process, albeit it is significant near the particle surface. The effects of the interior parameters and the environmental parameters on
the ignition of the magnesium particle cloud are analyzed. With the increase of particle concentration, the particle cloud becomes
easier to be ignited, and reduction in its ignition time delay can be seen. However, when the particle concentration has increased to
some specific extent and its further increase will be adverse to the ignition of the particle cloud. The influence of the environmental
pressure on the ignition of particle cloud is insignificant, and the ignition performance of the particle cloud almost keeps constant in
a range of 1–5 atm. The oxygen concentration in the gas phase also has a weak effect on the ignition performance of particle cloud,
but when the oxygen concentration is very low, the effect will significantly increase. The particle size, the initial temperature of the
gas/particle and the radiant source have all great influences on the ignition performance of the particle cloud. Small particle and high
temperature are helpful for speeding up the ignition process. The tendency obtained by numerical simulation coincides well with that
of the experimental results from the literature.
Keywords: powdered fuel ramjet, ignition of magnesium particle, particle cloudPACS: 47.70.−n, 47.40.pq, 82.60.cx
* Project supported by the National Natural Science Foundation of China (Grant No. 51006118).
† E-mail: [email protected]
164702-10