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钛合金高温摩擦着火理论研究

梁贤烨 弭光宝 李培杰 黄旭 曹春晓

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钛合金高温摩擦着火理论研究

梁贤烨, 弭光宝, 李培杰, 黄旭, 曹春晓

Theoretical study on ignition of titanium alloy under high temperature friction condition

Liang Xian-Ye, Mi Guang-Bao, Li Pei-Jie, Huang Xu, Cao Chun-Xiao
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  • 钛合金燃烧是现代航空发动机的典型灾难性事故, 压气机转子与静子的异常摩擦是主要的着火源. 本文基于非均相着火理论建立了考虑摩擦热源的钛合金着火模型, 推导了着火温度和着火延迟时间的理论计算公式, 进而分析摩擦系数、氧浓度、流速、接触半径以及阻燃层等因素对着火参数的影响规律. 结果表明: 当摩擦接触区的瞬时温度低于临界生热温度时, 生热过程由摩擦热主导; 当高于临界生热温度时, 生热过程由化学反应热主导. 降低摩擦系数可以显著提高着火温度, 而摩擦系数的变化对着火延迟时间影响很小. 着火温度随着氧浓度的增大和流速的减小均呈明显下降趋势. 当氧浓度从21%增加至42%、流速从310 m/s下降至50 m/s时, 着火温度分别降低约213 K和197 K. 实验结果与理论计算值的相对误差为8.3%, 验证了模型的可靠性. 阻燃层可以明显提高钛合金的着火温度和着火延迟时间, 带阻燃层的钛合金的着火温度提高约172 K, 着火延迟时间提高约3 s.
    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.
      通信作者: 弭光宝, miguangbao@163.com
    • 基金项目: 国家科技重大专项(批准号: 2017-VII-0012109, j2019-VIII-0003)、国家自然科学基金(批准号: 51471155)和中国航发创新基金(批准号: CXPT-2018-36)资助的课题
      Corresponding author: Mi Guang-Bao, miguangbao@163.com
    • Funds: Project supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant Nos. 2017-VII-0012109, j2019-VIII-0003), the National Natural Science Foundation of China (Grant No. 51471155), and the Innovation Fund of AECC, China (Grant No. CXPT-2018-36)
    [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 056103Google Scholar

    Mi G B, Huang X, Cao J X, Wang B, Cao C X 2016 Acta Phys. Sin. 65 056103Google 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 209Google Scholar

    [5]

    Elsayed S A 1996 J. Loss Prevent Proc. 9 393Google Scholar

    [6]

    Khaikin B I, Bloshenko V N 1970 Combust. Explos. Shock Waves 6 412Google 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 513Google Scholar

    [9]

    Shafirovich E, Teoh S K, Varma A 2008 Combust. Flame 152 262Google Scholar

    [10]

    Yuan C M, Amyotte P R, Hossain M N, Li C 2014 J. Hazard. Mater. 274 322Google Scholar

    [11]

    Breiter A L, Maltsev V M, Popov E I 1977 Phys. Combust. Explos. 13 558Google Scholar

    [12]

    Bolobov V I 2012 Phys. Combust. Explos. 48 35Google Scholar

    [13]

    Bolobov V I 2003 Combust. Explos. Shock Waves 39 677Google Scholar

    [14]

    Bolobov V I 2016 Phys. Combust. Explos. 52 54Google Scholar

    [15]

    Ouyang P X, Mi G B, Cao J X, Huang X, He L J, Li P J 2018 Mater. Today Commun. 16 364Google 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 94Google Scholar

    Mi G B, Ouyang P X, Li P J, Cao J X, Huang X, Cao C X 2019 J. Aeron. Mater. 39 94Google Scholar

    [17]

    弭光宝, 黄旭, 曹京霞, 曹春晓 2014 金属学报 50 575Google Scholar

    Mi G B, Huang X, Cao J X, Cao C X 2014 Acta Metall. Sinica 50 575Google Scholar

    [18]

    Li W Y, Ma T, Li J 2010 Mater. Des. 31 1497Google Scholar

    [19]

    Darvazi A R, Iranmanesh M 2014 Int. J. Adv. Manuf. Technol. 75 1299Google 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 833Google 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 269Google Scholar

    [24]

    弭光宝, 曹春晓, 黄旭, 曹京霞, 王宝 2014 航空材料学报 34 83Google Scholar

    Mi G B, Cao C X, Huang X, Cao J X, Wang B 2014 J. Aeron. Mater. 34 83Google 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 2284Google Scholar

    [27]

    Chen K M, Zhang Q Y, Li X X, Wang L, Cui X H, Wang S Q 2014 Tribo. Trans. 57 838Google 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

  • 图 1  转子与静子摩擦模型示意图

    Fig. 1.  Schematic diagram of the model of friction between rotor and stator.

    图 2  生热项T-Q曲线

    Fig. 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

    Fig. 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

    Fig. 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BTg的影响; (b) 温度系数BT-QG曲线的影响

    Fig. 5.  (a) Effect of B on Tg; (b) effect of B on T-QG diagram.

    图 6  (a) 摩擦系数FTcr的影响; (b) 温度系统BTcr的影响

    Fig. 6.  (a) Effect of F on Tcr; (b) effect of B on Tcr.

    图 7  (a) 摩擦系数Fτ的影响; (b) 温度系数Bτ的影响

    Fig. 7.  (a) Effects of F on τ; (b) effects of B on τ.

    图 8  氧浓度对Tcr的影响

    Fig. 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

    Fig. 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

    Fig. 10.  Effects of flow velocities on Tcr.

    图 11  钛合金的氧浓度-流速着火边界图

    Fig. 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

    Fig. 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

    Fig. 13.  Effect of friction contact radius on Tcr.

    图 14  数值计算流程图

    Fig. 14.  Flow chart of simulation

    图 15  带阻燃层的钛合金静子背面温度场

    Fig. 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

    Fig. 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

    Fig. 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

    Fig. 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/
    下载: 导出CSV

    表 1  材料热物性参数[13,25]

    Table 1.  Thermal property parameters of materials.

    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4500493334.244.517.80.52
    阻燃层56005600.62
    下载: 导出CSV

    表 2  模型的初始边界条件[13,16]

    Table 2.  Initial boundary conditions of the model.

    初始摩擦正应力N/kPa静子厚度φ/m特征长度d/m内半径R2/m外半径R1/m角速度ω/r·min–1氧浓度ci/%流速v/m·s–1
    2650.0020.0160.0020.00450002150
    下载: 导出CSV
  • [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 056103Google Scholar

    Mi G B, Huang X, Cao J X, Wang B, Cao C X 2016 Acta Phys. Sin. 65 056103Google 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 209Google Scholar

    [5]

    Elsayed S A 1996 J. Loss Prevent Proc. 9 393Google Scholar

    [6]

    Khaikin B I, Bloshenko V N 1970 Combust. Explos. Shock Waves 6 412Google 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 513Google Scholar

    [9]

    Shafirovich E, Teoh S K, Varma A 2008 Combust. Flame 152 262Google Scholar

    [10]

    Yuan C M, Amyotte P R, Hossain M N, Li C 2014 J. Hazard. Mater. 274 322Google Scholar

    [11]

    Breiter A L, Maltsev V M, Popov E I 1977 Phys. Combust. Explos. 13 558Google Scholar

    [12]

    Bolobov V I 2012 Phys. Combust. Explos. 48 35Google Scholar

    [13]

    Bolobov V I 2003 Combust. Explos. Shock Waves 39 677Google Scholar

    [14]

    Bolobov V I 2016 Phys. Combust. Explos. 52 54Google Scholar

    [15]

    Ouyang P X, Mi G B, Cao J X, Huang X, He L J, Li P J 2018 Mater. Today Commun. 16 364Google 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 94Google Scholar

    Mi G B, Ouyang P X, Li P J, Cao J X, Huang X, Cao C X 2019 J. Aeron. Mater. 39 94Google Scholar

    [17]

    弭光宝, 黄旭, 曹京霞, 曹春晓 2014 金属学报 50 575Google Scholar

    Mi G B, Huang X, Cao J X, Cao C X 2014 Acta Metall. Sinica 50 575Google Scholar

    [18]

    Li W Y, Ma T, Li J 2010 Mater. Des. 31 1497Google Scholar

    [19]

    Darvazi A R, Iranmanesh M 2014 Int. J. Adv. Manuf. Technol. 75 1299Google 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 833Google 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 269Google Scholar

    [24]

    弭光宝, 曹春晓, 黄旭, 曹京霞, 王宝 2014 航空材料学报 34 83Google Scholar

    Mi G B, Cao C X, Huang X, Cao J X, Wang B 2014 J. Aeron. Mater. 34 83Google 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 2284Google Scholar

    [27]

    Chen K M, Zhang Q Y, Li X X, Wang L, Cui X H, Wang S Q 2014 Tribo. Trans. 57 838Google 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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出版历程
  • 收稿日期:  2020-02-27
  • 修回日期:  2020-07-16
  • 上网日期:  2020-10-21
  • 刊出日期:  2020-11-05

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