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基于分形方法的YSZ热障涂层有效热导率分析

  • 丁坤英

    机 构：

    中国民航大学 天津市民用航空器适航与维修重点实验室, 天津 300300

    ×
  • ， 李志远

    机 构：

    中国民航大学 天津市民用航空器适航与维修重点实验室, 天津 300300

    ×
  • ， 王者

    机 构：

    中国民航大学 天津市民用航空器适航与维修重点实验室, 天津 300300

    ×
  • ， 程涛涛

    机 构：

    中国民航大学 天津市民用航空器适航与维修重点实验室, 天津 300300

    ×

中国民航大学 天津市民用航空器适航与维修重点实验室, 天津 300300；

Analysis of YSZ Effective Thermal Conductivity Based on Fractal Theory

  • DING Kunying

    Affiliation：

    Tianjin Key Laboratory for Civil Aircraft Airworthiness and Maintenance, Civil Aviation University of China, Tianjin 300300 , China

    ×
  • ， LI Zhiyuan

    Affiliation：

    Tianjin Key Laboratory for Civil Aircraft Airworthiness and Maintenance, Civil Aviation University of China, Tianjin 300300 , China

    ×
  • ， WANG Zhe

    Affiliation：

    Tianjin Key Laboratory for Civil Aircraft Airworthiness and Maintenance, Civil Aviation University of China, Tianjin 300300 , China

    ×
  • ， CHENG Taotao

    Affiliation：

    Tianjin Key Laboratory for Civil Aircraft Airworthiness and Maintenance, Civil Aviation University of China, Tianjin 300300 , China

    ×

Tianjin Key Laboratory for Civil Aircraft Airworthiness and Maintenance, Civil Aviation University of China, Tianjin 300300 , China；

通讯作者:

丁坤英(1981—),男(汉),副教授,博士;研究方向:热喷涂;E-mail:dingkunying@126.com

中图分类号:TG174

文献标识码:A

文章编号:1007-9289(2020)03-0104-07

DOI:10.11933/j.issn.1007-9289.20190909001

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目录contents

    摘要

    陶瓷基热障涂层具有优异的阻热性能、耐热腐蚀性能以及热稳定性能,在航空发动机热端部件中广泛使用。 利用大气等离子喷涂方法制备 ZrO2 -8%Y2O3(YSZ)涂层,利用聚苯酯(PHB)调节涂层的孔隙形态和含量,利用扫描电镜(SEM)和图像软件分析涂层的截面形貌,计算了孔隙的分形维数,建立了基于分形维数的有效热导率计算方法,优化了热导率与涂层孔隙的定量关系。 同时利用导热仪测量面层的热导率,对有效热导率计算结果进行验证。 结果表明: YSZ 粉末中混合聚苯酯粉末可增加涂层中的孔隙含量;当 PHB 的质量含量达到 15%时,涂层孔隙率可增加至 30%左右。 较高的喷涂功率会形成扁平化的孔隙,孔隙分形维数的取值在 1~ 2,并且孔隙越扁平取值越大。 孔隙含量越大、形态越趋近于扁平化,涂层有效热导率越小。 把孔隙的分形维数引入到有效热导率的计算中,使得计算结果更加趋近于实测结果。

    Abstract

    Ceramic-based thermal barrier coatings are widely used in aeroengine hot-stage components since their excellent thermal resistance, hot corrosion resistance, and thermal stability. In the current paper, ZrO2 -8%Y2O3 (YSZ) as a kind of thermal barrier coating was deposited by atmospheric plasma spraying method. The morphology and porosity of the coating were adjusted by adding poly-hydroxybutyrate ( PHB). The coating cross-sections were observed by scanning electron microscopy ( SEM). A calculation formula of effective thermal conductivity based on the fractal dimensions of pores in the coating was established. Meanwhile, the calculation values were verified by a thermal conductivity meter. The results show that the porosity of the coating can be increased by mixing PHB powder and go up to about 30% as the mass fraction of PHB reaches 15%. The higher spraying power has a trend to generate the flat pores with larger fractal dimensions, resulting in the smaller effective thermal conductivity of the coating. The fractal dimension of pores is introduced into the calculation of effective thermal conductivity, which makes the calculated results more close to the measured ones.

  • 0 引言

  • 由于优异的阻热性能、耐热腐蚀性能以及热稳定性能,陶瓷基热障涂层在航空发动机热端部件中大量采用。典型的热障涂层包含粘接层和陶瓷面层两部分,粘接层一般为抗氧化性能较好的NiCoCrAlY, 面层一般为阻热性能较好的ZrO2-8%Y2O3。热障涂层的制备方法常用的有两种:一种为电子束物理气相沉积(EB-PVD); 另一种为大气等离子喷涂(APS)。电子束物理气相沉积的涂层具有纵向结构,一般用来制备涡轮叶片上的热障涂层,这种热障涂层在热循环过程中具有良好的容应变能力,可以获得更好的热循环寿命;大气等离子喷涂方法制备的涂层具有层状结构,一般用来制备燃烧室部分的热障涂层,这种涂层具有更优异的隔热性能,减少燃烧室火焰筒薄壁受到的热冲击[1-3]。

  • 利用等离子喷涂方法制备的热障涂层内部存在着大量的孔隙,这种孔隙是涂层获得更优异阻热性能的关键。但是这类孔隙随着制备工艺和粉末原材料类型的变化而变化,从而使得等离子喷涂的热障涂层隔热性能存在着较大幅度的变化( APS热障涂层的导热率一般为0.8~1.2 W·m-1·K-1)。为了更准确地研究孔隙对热障涂层导热性能的影响,需要考虑孔隙的含量和分布[4-7]。

  • Masayuki Arai等[8] 研究表明,等离子喷涂的热障涂层的阻热性能并不完全与涂层的孔隙率成正比,较大等效直径的孔隙对于阻热的贡献更加显著。 Kulkarni等[9] 研究表明,孔隙的形状对涂层的阻热性能影响较大,扁平化的孔隙更有助于涂层阻热性能的提升。虽然已经有研究工作证明孔隙的分布和形态对导热性能有影响,但是由于热障涂层形貌的规律性较差,在孔隙分布和形态影响的定量化分析方面进展比较缓慢。

  • 在描绘复杂形貌方面,分形法是一种有效的手段,这种方法能够描绘复杂图像中颗粒的形状和分布。例如单鹂娜等[10]和刘洋等[11] 分别用分形维数和多重分形谱来表征球墨铸铁中石墨的形状和分布不均匀性。陈书赢和王海斗等[12] 将概率统计方法、分形方法与数字图像分析技术相结合,描述了孔隙数量、形态、尺寸及其分布等结构特征。

  • 文中利用大气等离子喷涂方法制备ZrO2-8%Y2O3(YSZ) 涂层,利用粉末中混合的聚苯酯调节涂层中孔隙的含量和分布,然后利用分形方法对涂层中的孔隙形态进行定量分析,优化目前热导率与涂层孔隙的定量关系式,进一步说明孔隙对于涂层阻热性能的影响。

  • 1 试验

  • 1.1 原材料和喷涂工艺

  • 采用美国Praxair公司生产的Co-110 型NiCoCrAlY粉末喷涂金属粘接层,粉末粒径为15~45 μm。采用自制的ZrO2-8%Y2O3(YSZ)团聚粉末喷涂陶瓷面层,其原材料是上海水田材料科技有限公司生产的粒径为1~3 μm的YSZ微粉,团聚后颗粒的粒径为38~75 μm(图1( a))。在YSZ粉末中混合自制的包覆型聚苯酯(PHB) 粉末,为了研究孔隙率和孔隙形态对导热性能的影响,聚苯酯粉末的粒径分别选取10~23 μm和25~45 μm两种,为了抑制它的烧损,利用溶胶凝胶法在其表面覆盖一层TiO2(图1(b))。采用美国Praxair公司生产的3710 型等离子喷涂设备在Ni718 合金表面制备热障涂层。通过改变面层粉末配比和调整喷涂功率来调节陶瓷面层中的孔隙含量和形态,具体参数见表1。

  • 图1 喷涂粉末的形貌

  • Fig.1 Morphologies of the powders for APS spraying

  • 表1 陶瓷面层的组成和形态特征

  • Table1 Fraction and morphology characters of the top coatings

  • 1.2 涂层截面形貌的观测和分析

  • 利用德国生产的LEO 1530VP型场发射扫描电子显微镜观察涂层的截面形貌,然后利用图像软件测量涂层中孔隙的面积占比 p,并测量单个孔隙面积 S 和周长 L。利用分形理论分析孔隙的截面形貌,孔隙的分形维数 D 与孔隙面积 S 和周长 L 的关系为[13-16] :

  • L=ASD2
    (1)
  • log⁡L=log⁡A+D2log⁡S
    (2)

  • 式中,孔隙周长 L 的单位为 μm,孔隙面积 S 的单位为 μm 2,A、D 无量纲。根据公式(1)和(2) 可以得到孔隙分形维数的分布,并利用最小二乘法确定 D 值,根据周长和面积的关系可知 D 值的范围为1~2 [12]。

  • 1.3 隔热性能测试

  • 将陶瓷面层从原有的试片上剥离并制成 Φ10×2 mm的待测试片。利用美国TA公司生产的DXF-900 型氙灯导热仪测量100~900℃条件下陶瓷面层的热导率,利用公式(3)计算涂层的热导率 κ(单位W·m-1·K-1)。

  • κ=ρ⋅Cp⋅α
    (3)

  • 式中,ρ 为利用阿基米德方法测得的涂层密度(单位kg·m-3),Cp 为涂层的等压比热容(单位J·kg-1·K-1),α 为导热仪测得的涂层热扩散系数(单位m 2·s-1)。

  • 2 结果与讨论

  • 等离子喷涂制备含有孔隙的YSZ陶瓷面层时,喷涂粒子被等离子弧加温和加速最后撞击到基体表面形成堆叠结构。喷涂粒子中的聚苯酯被留在层状结构中,通过后续的加温烧蚀后形成孔洞,其沉积过程示意图如图2 所示。利用扫描电镜观察陶瓷面层的截面形貌,并利用图像软件对其进行二值化分析,结果如图3 所示。当喷涂粉末中不含聚苯酯时,陶瓷层中孔隙的含量最低并且孔隙横截面积的平均等效直径最小,此时的孔隙是粉末在沉积堆叠过程中形成的固有孔隙(图3(a))。当喷涂粉末中混合聚苯酯后,涂层的孔隙率随着聚苯酯的含量增加而增加(图3(b)), 同时孔隙的平均等效直径也随着聚苯酯颗粒的增大而增大(图3(c))。面层3 和面层4 的喷涂粉末中混合的聚苯酯质量含量均为15%,聚苯酯的初始粒度均为25~45 μm,因此这两种陶瓷面层的孔隙率和孔隙的等效直径都比较接近(表1)。但是面层4 制备过程中采用了更高的喷涂功率(面层3 喷涂功率为32 kW,面层4 喷涂功率为36 kW),使得粉末颗粒沉积时温度和速度上升,更趋近于扁平化铺展,这使得面层4 的孔隙也呈扁平化形态(图3(d))。

  • 图2 涂层的形成过程示意图

  • Fig.2 Schematic diagram of spraying

  • 图3 不同陶瓷涂层的横截面形貌

  • Fig.3 Cross-section morphologies of different top coatings

  • 涂层中孔隙的形态比较复杂,并且随着工艺的变化而变化,这些孔隙最终会影响涂层的隔热性能[17-20]。文中利用分形理论描述孔隙的形态, 利用公式(1) 和(2) 计算孔隙的分形维数,结果如图4 所示。根据公式(1) 和(2) 可知,分形维数 D 值与孔隙的周长和面积相关,而周长和面积的比值又是孔隙扁平化程度的体现,所以分形维数 D 的差异更多地体现的是孔隙扁平化程度的变化,D 值越大表明孔隙越呈现扁平化。面层4 中孔隙的分形维数(D=1.52)是4 种面层中最大的,表明此涂层中孔隙的形态更趋近于扁平化的形态。面层3(D=1.30)和面层2(D=1.24)的分形维数较为近似,反映了这两种涂层中孔隙的形态较为相似,且趋近于球形的形态。面层1 中孔隙的平均等效直径较小,分形维数(D=1.44)更多地体现了陶瓷涂层在沉积过程中形成的固有孔隙在轮廓形态上的不规则程度。

  • 为了分析孔隙对涂层热导率的影响,可以把孔隙等效成在涂层中随机分布的圆形孔洞,则含有孔隙涂层的有效热导率 κeff 为[21-23] :

  • κeff=κsνs+κgνg3κs2κs+κgνs+νg3κs2κs+κg
    (4)

  • 式中,κs 为无孔隙块体涂层材料的热导率, κg 为孔隙中空气的热导率,νs、νg 分别为涂层和孔隙的体积占比。当把空气的热导率( κg=0.026 W·m-1·K-1) κg 近似为0 时,有效热导率 κeff1 可近似为:

  • κeff1 ≈κs(1-p)
    (5)

  • 式中,p 为涂层的孔隙率。此种计算方法是将孔隙等效成圆形孔洞,未考虑孔隙形状的影响。为了考虑孔隙形态的影响,需要引入分形维数 D。分形维数是对孔隙形态的定量表征,随着孔隙变形程度的不同,分形维数的值在1~2 之间变动[24-27]。将表征孔隙形态的分形维数 D 引入到公式(5)中,形成改进后的有效热导率 κeff2 计算公式:

  • κeff2=κs1-DP
    (6)

  • 利用热导仪测量不同孔隙率涂层在100~900℃温度条件下的 κ′eff,其结果如图5 所示。

  • 从图5 中可以看出,在100~700℃ 的范围内,涂层的有效热导率随着温度的升高而降低;当温度高于700℃ 后有效热导率的下降趋势减少[28-29]。相同温度条件下,涂层的有效热导率受到孔隙的影响。随着孔隙率的上升陶瓷面层的有效热导率下降。当孔隙率相近时,扁平化程度高的孔隙(具有更大分形维数 D 值)可以使涂层获得更低的热导率。相同温度下,面层4 与面层3 相比下降15%左右。产生上述变化的原因是因为陶瓷面层的导热机制主要为声子的传导。温度升高会使点阵振动加剧,从而使得声子传导受到散射;与此同时涂层中的孔隙也会造成声子的散射,单位体积内垂直于热传导方向的孔隙边界面积越大,声子传导受到的影响越大。所以陶瓷面层的有效热导率同时受到温度和孔隙形态的影响。

  • 图4 周长面积幂率法计算分形维数 D

  • Fig.4 D calculated by power-low method

  • 图5 不同温度条件下的热导率

  • Fig.5 Thermal conductivities during different temperatures

  • 为了定量分析孔隙对涂层有效热导率的影响,利用相同的函数形式对有效热导率曲线进行拟合,结果如图5 中虚线所示。根据图5 的拟合结果可以推导实测涂层有效热导率 κ′eff 与无孔隙涂层热导率 κs 之间的关系式如下:

  • κeff '=κsD'
    (7)

  • 式中,D′为基于实际测量结果求出的热导率关系系数,该系数与温度无关。假设面层1 与无孔隙涂层的导热率相等,根据图5 的拟合结果可知,面层1、 2、 3、 4 的 D′ 值分别为0.99、 0.88、 0.66、0.56。根据公式(5)、(6)、(7)可以推导出有效热导率的相互比值 R 的关系为 κ′eff /κeff1/κeff2=D′/(1-p)/(1-Dp),相互比值 R 的结果如图6 所示。

  • 由图6 可知,采用式(5)计算面层的有效热导率,当孔隙率低于10%时计算值与实测值的结果偏差(Δ1=[(1-p)-D′]/D′)在3%以内;但是当孔隙含量上升至30%左右时,式(5)的计算值与实测值之间相差约10%,若面层中孔隙呈扁平状分布时,这种偏差还将进一步增加到30%左右。采用式(6)优化有效热导率计算结果,可以使得计算结果与实测结果的偏差(Δ2=[(1-Dp)-D′]/D′)控制在5%以内,具体参见表2。

  • 图6 涂层热导率对比分析(D′实际有效热导率关系系数,1-p 优化前有效热导率关系系数,1-Dp 优化后有效热导率关系系数)

  • Fig.6 Thermal conductivities comparative analysis( D′-Coefficient of actual effective thermal conductivity, 1-p-nonoptimized coefficient of effective thermal conductivity, 1-Dp-optimized coefficient of effective thermal conductivity)

  • 综合上述结果可知,陶瓷面层的导热机制主要为声子传导,涂层中的孔隙将对声子的传导造成散射,垂直于传热方向的孔隙边界尺寸影响声子的散射程度。将孔隙的分形维数引入到热导率的计算过程中,可以充分考虑孔隙的形态对热导率的影响,提高计算结果的精度。

  • 表2 有效热导率分析结果

  • Table2 Analysis results of effective thermal conductivities

  • 3 结论

  • (1) 利用YSZ粉末中混合PHB粉末的方法可以增加等离子喷涂涂层中的孔隙含量。当混合的PHB的质量含量达到15%时,涂层的孔隙率可以增加到30%左右。这种孔隙的形态与喷涂工艺有关,当采用较大功率喷涂时可以形成扁平化的孔隙。

  • (2) 采用分形理论对孔隙的形态进行定量的表征。分形维数的取值范围在1~2 之间,并且与孔隙的形态有关。孔隙的形态越扁平,分形维数的取值越大。

  • (3) 孔隙的含量与形态影响着涂层的有效热导率。孔隙含量越大、形态越趋近于扁平化, 涂层有效热导率越小。把分形维数引入到有效热导率的计算中,可以将计算结果与实测结果之间的偏差减少到5%以内。

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  • 基本信息

    中图分类号: TG174
    文献标识码: A
    DOI: 10.11933/j.issn.1007-9289.20190909001
    文章编号: 1007-9289(2020)03-0104-07

    基金信息

    国家自然科学基金(51501222)；
    民航局科技项目(MHRD20160106)；
    Supported by National Natural Science Foundation of China (51501222) ；
    Science and Technology Program of Civil Aviation of China (MHRD20160106)；

    引用信息

    丁坤英, 李志远, 王者, 等. 基于分形方法的 YSZ 热障涂层有效热导率分析[J]. 中国表面工程, 2020, 33(3): 104-110.

    DING K Y, LI Z Y, WANG Z, et al. Analysis of YSZ effective thermal conductivity based on fractal theory[J]. China Surface Engineering, 2020, 33(3): 104-110.

    稿件历史

    收稿日期: 2019-09-09

  • 参考文献

    • [1] ZHANG W W,LI G R,ZHANG Q,et al.Bimodal TBCs with low thermal conductivity deposited by a powder-suspen-sion co-spray process [J].Journal of Materials Science & Technology,2018,34(8):1293-1304.

    • [2] WANG Y Z,LI J L,LIU H Z,et al.Study on thermal resist-ance performance of 8YSZ thermal barrier coatings[J].Inter-national Journal of Thermal Sciences,2017,122:12-25.

    • [3] ADAMCZYK W P,KRUCZEK T,MOSKAL G,et al.Non-destructive technique of measuring heat conductivity of ther-mal barrier coatings [J].International Journal of Heat and Mass Transfer,2017,111:442-450.

    • [4] LIU J H,LIU Y B,HE X,et al.Study on TBCs insulation characteristics of a turbine blade under serving conditions[J].Case Studies in Thermal Engineering,2016,8:250-259.

    • [5] GAO L H,GUO H B,WEI L L,et al.Microstructure,ther-mal conductivity and thermal cycling behavior of thermal barri-er coatings prepared by plasma spray physical vapor deposition [J].Surface & Coatings Technology,2015,276:424-430.

    • [6] WANG Y Z,LIU H Z,LING X X,et al.Effects of pore mi-crostructure on the effective thermal conductivity of thermal barrier coatings [J].Applied Thermal Engineering,2016,102:234-242.

    • [7] 李建超,何箐,吕玉芬,等.热障涂层无损检测技术研究进展[J].中国表面工程,2019,32(2):16-26.LI J C,HE J,LV Y F,et al.Research progress on non-de-structive testing method of thermal barrier coatings[J].China Surface Engineering,2019,32(2):16-26(in Chinese).

    • [8] ARAI M,OCHIAI H,SUIDZU T.A novel low-thermal-con-ductivity plasma-sprayed thermal barrier coating controlled by large pores[J].Surface & Coatings Technology,2016,285:120-127.

    • [9] KULKARNI A,WANG Z,NAKAMURA T,et al.Compre-hensive microstructural characterization and predictive prop-erty modeling of plasma-sprayed zirconia coatings[J].Acta Materialia,2003,51(9):2457-2475.

    • [10] 单鹂娜,李大勇.分形学在球墨铸铁石墨形态模糊评价系统中的应用[J].中国铸造装备与技术,2005,2:14-16.SHAN L N,LI D Y.Application of fractal in fuzzy evaluation system of graphite shape in nodular cast iro [J].China Foundry Machinery & Technology,2005,2:14-16(in Chi-nese).

    • [11] 刘洋,杨弋涛,姜磊,等.基于多重分形理论的球铁石墨颗粒分散均匀性的分析[J].铸造,2007,2:167-169.LIU Y,YANG Y T,JIANG L,et al.Analysis of the graphiteparticles distribution in spheroidal graphite cast iron based onmulti-fractal theory[J].Foundry,2007,2:167-169(in Chinese).

    • [12] 陈书赢,王海斗,马国政,等.等离子喷涂层原生性孔隙几何结构的分形及统计特性[J].物理学报,2015,64(24):101-108.CHEN S Y,WANG H D,MA G Z,et al.Fractal and statis-tical properties of the geometrical structure of natural pores within plasma sprayed coatings [J].Journal of Physics,2015,64(24):101-108(in Chinese).

    • [13] 李建明,林汉同,朱光喜,等.基于分形的铸铁石墨颗粒形态的评定方法[J].铸造,1997,6:18-20.LI J M,LIN H T,ZHU G X,et al.Method for evaluating the graphite form in cast iron based on fractal[J].Foundry,1997,6:18-20(in Chinese).

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    • [16] WANG Y Y,MA C,LIU Y F,et al.A model for the effec-tive thermal conductivity of moist porous building materials based on fractal theory[J].International Journal of Heat and Mass Transfer,2018,125:387-399.

    • [17] PIA G,CASNEDI L.Heat transfer in high porous alumina:Experimental data interpretation by different modeling ap-proaches [J].Ceramics International,2017,43(12):9184-9190.

    • [18] GU S,LU T J,HASS D D,et al.Thermal conductivity of zirconia coatings with zig-zag pore microstructures[J].Acta Materialia,2001,49(13):2539-2547.

    • [19] 阚安康,康利云,曹丹,等.基于 Lattice-Boltzmann 方法的纳米颗粒多孔介质导热特性[J].化工学报,2015,66(11):4412-4417.KAN A K,KANG L Y,CAO D,et al.Thermal conduction characteristic of nano-granule porous material using lattice-Boltzmann method [J].CIESC Journal,2015,66(11):4412-4417(in Chinese).

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