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Combustion of titanium alloy is a typical catastrophic failure of modern aeroengine. The abnormal friction between compressor rotor and stator is the main ignition source. A thermal theory model with friction heat source of titanium alloy is established based on the theory of heterogeneous ignition. The corresponding equation of critical temperature and ignition delay time are derived. The difference between the frictional ignition model and the classic model is discussed. The concept of critical heat generation temperature is proposed. The difference from the heterogeneous ignition model, and the effects of friction coefficient, oxygen concentration, flow velocity, contact radius and flame retardant layer thickness on the ignition parameters are analyzed. The research result shows that when the instantaneous temperature of the contact surface is lower than the critical heat temperature, the heat generation process is dominated by frictional heat, and when the temperature is higher than the critical heat temperature, the heat generation process is dominated by chemical reaction heat, that reducing the coefficient of friction can dramatically increase the critical temperature, but the change of friction coefficient has very little effect on the ignition delay time which can be ignored, that the critical temperature decreases significantly with the increase of oxygen concentration and the decrease of flow velocity. When the oxygen concentration increases from 21% to 42% and the flow velocity decreases from 310 m/s to 50 m/s, the critical temperature decreases by about 213 K and 197 K, respectively. The relative error between the experimental result and the theoretical result is 8.3%, which verifies the reliability of the model. The contact area has an effect on friction heat generation, reaction heat generation, and surface heat dissipation, and has a great influence on the critical temperature. The critical temperature decreases exponentially with contact radius increasing. When the contact radius increases to 0.007 m, the ignition temperature of the titanium alloy and its flame retardant layer are 899 K and 988 K, respectively. The increase of the thickness of flame retardant layer can effectively improve the critical temperature and ignition delay time. The critical temperature of titanium alloy with flame retardant layer is increased by about 172 K, and the ignition delay time is increased by about 3 s.
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Keywords:
- titanium alloy /
- ignition model with friction /
- heterogeneous reaction /
- fireproof
[1] Borisova E A, Sklyarov N M 2007 Aviation Materials and Technologists: Production Combustion and Fire Safety of Titanium Alloys (Moscow: VIAM) p21
[2] 弭光宝, 黄旭, 曹京霞, 王宝, 曹春晓 2016 物理学报 65 056103
Google Scholar
Mi G B, Huang X, Cao J X, Wang B, Cao C X 2016 Acta Phys. Sin. 65 056103
Google Scholar
[3] Frank-Kamenetskii D A 1955 Diffusion and Heat Exchange in Chemical Kinetics (Princeton: Princeton University Press) p288
[4] Merzhanov A G 1975 AIAA J. 13 209
Google Scholar
[5] Elsayed S A 1996 J. Loss Prevent Proc. 9 393
Google Scholar
[6] Khaikin B I, Bloshenko V N 1970 Combust. Explos. Shock Waves 6 412
Google Scholar
[7] Aldushin A P, Bloshenko V N, Seplyarskii B S 1973 Combust. Explos. Shock Waves 9 423
[8] Chernenko E V, Griva V A, Rozenband V I 1982 Combust. Explos. Shock Waves 18 513
Google Scholar
[9] Shafirovich E, Teoh S K, Varma A 2008 Combust. Flame 152 262
Google Scholar
[10] Yuan C M, Amyotte P R, Hossain M N, Li C 2014 J. Hazard. Mater. 274 322
Google Scholar
[11] Breiter A L, Maltsev V M, Popov E I 1977 Phys. Combust. Explos. 13 558
Google Scholar
[12] Bolobov V I 2012 Phys. Combust. Explos. 48 35
Google Scholar
[13] Bolobov V I 2003 Combust. Explos. Shock Waves 39 677
Google Scholar
[14] Bolobov V I 2016 Phys. Combust. Explos. 52 54
Google Scholar
[15] Ouyang P X, Mi G B, Cao J X, Huang X, He L J, Li P J 2018 Mater. Today Commun. 16 364
Google Scholar
[16] 弭光宝, 欧阳佩旋, 李培杰, 曹京霞, 黄旭, 曹春晓 2019 航空材料学报 39 94
Google Scholar
Mi G B, Ouyang P X, Li P J, Cao J X, Huang X, Cao C X 2019 J. Aeron. Mater. 39 94
Google Scholar
[17] 弭光宝, 黄旭, 曹京霞, 曹春晓 2014 金属学报 50 575
Google Scholar
Mi G B, Huang X, Cao J X, Cao C X 2014 Acta Metall. Sinica 50 575
Google Scholar
[18] Li W Y, Ma T, Li J 2010 Mater. Des. 31 1497
Google Scholar
[19] Darvazi A R, Iranmanesh M 2014 Int. J. Adv. Manuf. Technol. 75 1299
Google Scholar
[20] Bohle M, Etling D, Muller U, Sreenivasan K R S, Riedel U, Warnatz J 2004 Prandtl’s Essentials of Fluid Mechanics (Heidelberg: Springer) (2nd Ed.) p428
[21] Thomas P H 1960 Trans. Faraday Soc. 56 833
Google Scholar
[22] Gray P, Harper M J 1958 Sixth Symposium on Combustion New Haven, America, August 19–24, 1958 p425
[23] Boddington T, Feng C G, Gray P 1984 Proc. Roy. Soc. London 391 269
Google Scholar
[24] 弭光宝, 曹春晓, 黄旭, 曹京霞, 王宝 2014 航空材料学报 34 83
Google Scholar
Mi G B, Cao C X, Huang X, Cao J X, Wang B 2014 J. Aeron. Mater. 34 83
Google Scholar
[25] 中国航空材料手册编辑委员会 2001 中国航空材料手册(第4卷) (北京: 中国标准出版社) p147
China Aeronautical Materials Handbook Editorial Committee 2001 China Aeronautical Materials Handbook (Volume 4) (Beijing: China Standards Press) p147 (in Chinese)
[26] Wang L, Zhang Q Y, Li X X, Cui X H, Wang S Q 2014 Metall. Mater. Trans. A 45 2284
Google Scholar
[27] Chen K M, Zhang Q Y, Li X X, Wang L, Cui X H, Wang S Q 2014 Tribo. Trans. 57 838
Google Scholar
[28] Elrod C W 1980 Proceedings of the Tri-Service Conference on Corrosion Boulder, America, November 5–7, 1980 p54
[29] 梁贤烨, 弭光宝, 李培杰, 曹京霞, 黄旭 2019 钛工业进展 36 1
Liang X Y, Mi G B, Li P J, Cao J X, Huang X 2019 Titanium Ind. Prog. 36 1
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图 1 转子与静子摩擦模型示意图
Figure 1. Schematic diagram of the model of friction between rotor and stator.
图 2 生热项T-Q曲线
Figure 2. Curves of heat generation in T-Q diagram.
图 3 θ在0—2区间内的变化 (a)数值解与近似解的对比; (b)解析解与数值解的误差
Figure 3. Variations of θ within the 0−2 interval: (a) Comparison of numerical and approximate solutions; (b) errors between analytical and numerical solutions.
图 4 临界条件下摩擦着火过程的原位观察(I为静子背面反应区着火的镜像; II为反应区中心着火的放射状火花), 各子图分别对应摩擦结束后的不同时间 (a) 0.05 s; (b) 0.10 s; (c) 0.15 s; (d) 0.20 s; (e) 0.25 s; (f) 0.5 s
Figure 4. In-situ observation of friction ignition process under critical condition (I, mirror image of ignition of reaction zone; II, spark of micro-bump near the centre hole of reaction zone): (a) 0.05 s, (b) 0.10 s, (c) 0.15 s, (d) 0.20 s, (e) 0.25 s, (f) 0.5 s after the rubbing ends.
图 5 (a) 温度系数B对Tg的影响; (b) 温度系数B对T-QG曲线的影响
Figure 5. (a) Effect of B on Tg; (b) effect of B on T-QG diagram.
图 6 (a) 摩擦系数F对Tcr的影响; (b) 温度系统B对Tcr的影响
Figure 6. (a) Effect of F on Tcr; (b) effect of B on Tcr.
图 7 (a) 摩擦系数F对τ的影响; (b) 温度系数B对τ的影响
Figure 7. (a) Effects of F on τ; (b) effects of B on τ.
图 8 氧浓度对Tcr的影响
Figure 8. Effects of oxygen concentrations on Tcr.
图 9 摩擦着火反应区的原位观察, 各子图分别对应摩擦结束后不同时间 (a) 0.15 s; (b) 0.25 s; (c) 0.5 s; (d) 1.0 s
Figure 9. In-situ observation of friction ignition reaction zone: (a) 0.15 s, (b) 0.25 s, (c) 0.5 s, (d) 1.0 s after the rubbing ends.
图 10 流速对Tcr的影响
Figure 10. Effects of flow velocities on Tcr.
图 11 钛合金的氧浓度-流速着火边界图
Figure 11. Flow velocity-oxygen concentration critical condition of titanium alloy.
图 12 带阻燃层的钛合金的氧浓度-流速着火边界图
Figure 12. Flow velocity-oxygen concentration critical condition of titanium alloy with flame retardant layer.
图 13 摩擦接触半径对Tcr的影响
Figure 13. Effect of friction contact radius on Tcr.
图 14 数值计算流程图
Figure 14. Flow chart of simulation
图 15 带阻燃层的钛合金静子背面温度场
Figure 15. Temperature field of back surface of titanium alloy stator with flame retardant layer.
图 16 带阻燃层钛合金静子背面及接触面的温度变化
Figure 16. Temperature history of back surface and contact surface of titanium alloy stator with flame retardant layer.
图 17 不带阻燃层的钛合金静子背面以及接触面的温度变化
Figure 17. Temperature history of back surface and contact surface of titanium alloy stator without flame retardant layer
图 18 静子摩擦接触面与背面温差的比较
Figure 18. Difference in temperature between friction contact surface and back surface of stator.
表 A1 术语表
Table A1. Nomenclature
符号 物理意义 单位 λ 热传导系数 W·m–1·K–1 cp 比热 J·kg–1·K–1 q 单位反应热 MJ·kg–1 k 指前因子 kg·m–2·s–1 E 激活能 kJ·mol–1 f 摩擦应力 N·m–2 τ 着火延迟时间 s N 接触应力 N·m–2 φ 厚度 m d 试验舱直径 m R2 接触面内径 m R1 接触面外径 m ω 转子角速度 r·min–1 ci 氧浓度 100% v 流速 m·s QG 生热项 J·s–1 QH 反应热项 J·s–1 QC 对流散热项 J·s–1 QR 辐射散热项 J·s–1 μ 摩擦系数 / Sr 反应区面积 m2 a 吸附系数 / α 总传热系数 W·m–2·K–1 Nu 努塞尔数 / Pr 普朗特数 / Re 雷诺数 / 
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性能材料 密度
ρ/kg·m–3比热容
cp/J·kg–1·K–1反应热
q/MJ·kg–1指前因子
k/kg·m–2·s–1激活能
E/kJ·mol–1导热系数
λ/W·m–1·K–1吸附系数
a/MPa–0.5钛合金 4500 493 33 4.2 44.5 17.8 0.52 阻燃层 5600 560 — — — 0.62 —
DownLoad: CSV
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[1] Borisova E A, Sklyarov N M 2007 Aviation Materials and Technologists: Production Combustion and Fire Safety of Titanium Alloys (Moscow: VIAM) p21
[2] 弭光宝, 黄旭, 曹京霞, 王宝, 曹春晓 2016 物理学报 65 056103
Google Scholar
Mi G B, Huang X, Cao J X, Wang B, Cao C X 2016 Acta Phys. Sin. 65 056103
Google Scholar
[3] Frank-Kamenetskii D A 1955 Diffusion and Heat Exchange in Chemical Kinetics (Princeton: Princeton University Press) p288
[4] Merzhanov A G 1975 AIAA J. 13 209
Google Scholar
[5] Elsayed S A 1996 J. Loss Prevent Proc. 9 393
Google Scholar
[6] Khaikin B I, Bloshenko V N 1970 Combust. Explos. Shock Waves 6 412
Google Scholar
[7] Aldushin A P, Bloshenko V N, Seplyarskii B S 1973 Combust. Explos. Shock Waves 9 423
[8] Chernenko E V, Griva V A, Rozenband V I 1982 Combust. Explos. Shock Waves 18 513
Google Scholar
[9] Shafirovich E, Teoh S K, Varma A 2008 Combust. Flame 152 262
Google Scholar
[10] Yuan C M, Amyotte P R, Hossain M N, Li C 2014 J. Hazard. Mater. 274 322
Google Scholar
[11] Breiter A L, Maltsev V M, Popov E I 1977 Phys. Combust. Explos. 13 558
Google Scholar
[12] Bolobov V I 2012 Phys. Combust. Explos. 48 35
Google Scholar
[13] Bolobov V I 2003 Combust. Explos. Shock Waves 39 677
Google Scholar
[14] Bolobov V I 2016 Phys. Combust. Explos. 52 54
Google Scholar
[15] Ouyang P X, Mi G B, Cao J X, Huang X, He L J, Li P J 2018 Mater. Today Commun. 16 364
Google Scholar
[16] 弭光宝, 欧阳佩旋, 李培杰, 曹京霞, 黄旭, 曹春晓 2019 航空材料学报 39 94
Google Scholar
Mi G B, Ouyang P X, Li P J, Cao J X, Huang X, Cao C X 2019 J. Aeron. Mater. 39 94
Google Scholar
[17] 弭光宝, 黄旭, 曹京霞, 曹春晓 2014 金属学报 50 575
Google Scholar
Mi G B, Huang X, Cao J X, Cao C X 2014 Acta Metall. Sinica 50 575
Google Scholar
[18] Li W Y, Ma T, Li J 2010 Mater. Des. 31 1497
Google Scholar
[19] Darvazi A R, Iranmanesh M 2014 Int. J. Adv. Manuf. Technol. 75 1299
Google Scholar
[20] Bohle M, Etling D, Muller U, Sreenivasan K R S, Riedel U, Warnatz J 2004 Prandtl’s Essentials of Fluid Mechanics (Heidelberg: Springer) (2nd Ed.) p428
[21] Thomas P H 1960 Trans. Faraday Soc. 56 833
Google Scholar
[22] Gray P, Harper M J 1958 Sixth Symposium on Combustion New Haven, America, August 19–24, 1958 p425
[23] Boddington T, Feng C G, Gray P 1984 Proc. Roy. Soc. London 391 269
Google Scholar
[24] 弭光宝, 曹春晓, 黄旭, 曹京霞, 王宝 2014 航空材料学报 34 83
Google Scholar
Mi G B, Cao C X, Huang X, Cao J X, Wang B 2014 J. Aeron. Mater. 34 83
Google Scholar
[25] 中国航空材料手册编辑委员会 2001 中国航空材料手册(第4卷) (北京: 中国标准出版社) p147
China Aeronautical Materials Handbook Editorial Committee 2001 China Aeronautical Materials Handbook (Volume 4) (Beijing: China Standards Press) p147 (in Chinese)
[26] Wang L, Zhang Q Y, Li X X, Cui X H, Wang S Q 2014 Metall. Mater. Trans. A 45 2284
Google Scholar
[27] Chen K M, Zhang Q Y, Li X X, Wang L, Cui X H, Wang S Q 2014 Tribo. Trans. 57 838
Google Scholar
[28] Elrod C W 1980 Proceedings of the Tri-Service Conference on Corrosion Boulder, America, November 5–7, 1980 p54
[29] 梁贤烨, 弭光宝, 李培杰, 曹京霞, 黄旭 2019 钛工业进展 36 1
Liang X Y, Mi G B, Li P J, Cao J X, Huang X 2019 Titanium Ind. Prog. 36 1
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