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在高转速、高温度、空间狭小、测量环境复杂的工作条件下。涡轮叶片传统的测量结果主要受到以下因素影响:1)不同温度下不同的表面发射率。表面形态和材料成分,发射率设定值与叶片表面发射率真实值之间的偏差影响温度测量结果。2)燃气的热辐射干扰。辐射高温计的光路中充满了高温和高压气体,气体不仅吸收叶片的部分辐射能,而且自身会辐射一定量的能量[11]。3)燃烧烟尘沉积物的污染。由于燃料的不完全燃烧,会产生残留的高温热颗粒,当这些热粒子进入辐射高温计的探测光路时,就像小而强的移动辐射源,部分辐射能量将被高温计接收并影响测量结果。4)高叶片速度。5)其他叶片和环境的反射辐射。背景辐射在目标表面的反射和目标自身的辐射相叠加,来自相邻热端部件的辐射所形成的反射量将直接影响测量结果[12]。
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辐射测温是非接触式测温方法中的一种,通过获取目标表面发出的热辐射能量进行温度测量。如图1所示。
由于燃油,燃煤和燃气的燃烧产物中有一定浓度的二氧化碳,水蒸气等具有相当大辐射能力的三原子,多原子气体,和氢气,氮气等无发射和吸收辐射能力的双原子气体,同时气体辐射对波长有选择性且气体辐射和吸收是在整个容积中进行的,所以通过传统测温方法测温常常会引入不可忽略的误差。采用红外辐射测温能进一步达到测量涡轮叶片工作温度的目的。红外辐射具有:1)响应时间短,反应迅速;2)不影响测量温度场;3)不破坏被测目标结构等诸多优势。随着科学技术的不断发展和交叉融合,红外辐射测温技术也正逐步应用于航空航天领域[13]。
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Stefan-Boltzmann定律阐述了黑体辐射力与热力学温度的关系[14]为:
$$ {{E}}_{{b}}{=\sigma }{{T}}^{{4}}={{C}}_{{0}}{\left(\frac{{T}}{{100}}\right)}^{{4}} $$ (1) 式中:$ {{C}}_{{0}} $为黑体辐射系数,值为${5.67 {\rm{W}}/}\left({{{\rm{m}}}}^{{2}}{ \cdot }{{{\rm{K}}}}^{{4}}\right)$;$ {\sigma } $称为黑体辐射常数,值为${5.67×}{{10}}^{{-8}}{{\rm{W}}/}\left({{{\rm{m}}}}^{{2}}{ \cdot }{{{\rm{K}}}}^{{4}}\right)$;该式表明随着温度的上升,辐射力急剧增加。
Max Planck定律解释了黑体辐射能按波长分布的规律:
$$ {{E}}_{{b \lambda }}=\frac{{{c}}_{{1}}{{ \lambda }}^{{-5}}}{{{e}}^{{{c}}_{{2}}/{ \lambda T}}{-1}} $$ (2) 式中:$ {{E}}_{{b \lambda }} $为黑体光谱辐射力$\left({{\rm{W}}}/{{{\rm{m}}}}^{{3}}\right)$;$ { \lambda } $为波长$\left({{\rm{m}}}\right)$;T为黑体热力学温度$\left({{\rm{K}}}\right)$;e为自然对数的底;$ {{c}}_{{1}} $为第一辐射常量,值为${3.741\;9}\times{{10}}^{{-16}}\;{{\rm{W}} \cdot }{{{\rm{m}}}}^{{2}}$;$ {{c}}_{{2}} $为第二辐射常量,值为${1.}{438 8}\times{{10}}^{{-2}}\;{{\rm{m}} \cdot {\rm{K}}}$;可知黑体光辐射力随着波长的增加,先增大后减小。
对应于最大光谱辐射力的波长$ {{ \lambda }}_{{m}} $与温度T一般由Wien位移定律解释:
$$ {{ \lambda }}_{{m}}{T}{=2.897\;6}\times{{10}}^{{-3}}{{\rm{m}} \cdot {\rm{K}}} $$ (3) 光谱辐射力曲线下的面积就是该温度下黑体的辐射力,得出了Stefan-Boltzmann定律与Max Planck定律的关系为:
$$ {{E}}_{{b}}=\underset{{0}}{\overset{{\infty}}{\int }}{{E}}_{{b \lambda }}{{\rm{d}} \lambda =}\underset{{0}}{\overset{{\infty}}{\int }}\frac{{{c}}_{{1}}{{ \lambda }}^{{-5}}}{{{{\rm{e}}}}^{{{c}}_{{2}}/{ \lambda T}}{-1}}{{\rm{d}} \lambda } $$ (4) -
准确求得叶片工作的真实温度关键在于准确描述反射量,在实际测量中,两个表面之间的辐射量传递与两个表面间的相对位置有关。两表面间的相对位置的变化,使得一个表面发出的辐射量到达另一个表面的比例随之变化,为此,必须引入角系数,采用离散化的方法对涡轮叶片网格单元进行角系数的计算,从而达到叶片温度更准确误差分析的目的[15]。
如图2所示,表面1发出的辐射能中落到表面2的百分数称为表面1对表面2的角系数,记为X1,2。同理定义角系数X2,1。
当一个微元表面dA1到另一个微元表面dA2,结合图2所示有:
$$ \begin{split} {{X}}_{{{\rm{d}}1,{\rm{d}}2}}=&\frac{{落到}{{\rm{d}}}{{A}}_{{2}}{上由}{{\rm{d}}}{{A}}_{{1}}{发出的辐射能}}{{{\rm{d}}}{{A}}_{{2}}{向外发出的总辐射能}} =\\ &\frac{{{I}}_{{b1}}{\cos}{{\theta}}_{{1}}{{\rm{d}}}{{A}}_{{1}}{{\rm{d}}}{{ {{\varOmega}} }}_{{1}}}{{{E}}_{{b1}}{{\rm{d}}}{{A}}_{{1}}}=\frac{{{\rm{d}}}{{A}}_{{2}}{\cos}{{\theta}}_{{1}}{\cos}{{\theta}}_{{2}}}{{{\text{π}}}{{r}}^{{2}}} \end{split} $$ (5) -
有n个等温漫灰体面组成的封闭系统下,见图3,已知各面温度,求各面有效辐射力,由辐射理论基础,每一个面都可列出三个方程为[16]:
k表面的外部热平衡式:
$$ {{Q}}_{{k}}={{q}}_{{k}}{{A}}_{{k}}=\left({{J}}_{{k}}-{{G}}_{{k}}\right){{A}}_{{k}} $$ (6) 式中:Q为表面的净热流量(W);q为辐射换热热流密度(W/m2);J为有效辐射力(W/m2);G为投射辐射力(W/m2)。
k表面的有效辐射表达式:
$$ {{J}}_{{k}}={{ \varepsilon }}_{{k}}{{E}}_{{bk}}+\left({1-}{{ \varepsilon }}_{{k}}\right){{G}}_{{k}}={{ \varepsilon }}_{{k}}{\sigma }{{T}}_{{k}}^{{4}}+\left({1-}{{ \varepsilon }}_{{k}}\right){{G}}_{{k}} $$ (7) k表面的投射辐射表达式:
$$ {{G}}_{{k}}{{A}}_{{k}}=\displaystyle\sum _{{i=1}}^{{n}}{{J}}_{{i}}{{A}}_{{i}}\varphi_{{i,k}} $$ (8) 联立公式(6)~(8),通过等式代换,若已知各表面面积,表面发射率ε及系统内所有的角系数$ \varphi $,各表面温度T,则可得到有效辐射力计算式为:
$$ {{J}}_{{k}}={{ \varepsilon }}_{{k}}{\sigma }{{T}}_{{k}}^{{4}}+\left({1-}{{ \varepsilon }}_{{k}}\right)\displaystyle\sum _{{i=1}}^{{n}}{{J}}_{{i}}\varphi_{{k,i}} $$ (9) 式中:$ {k=1,2,3,}\cdots $。由于有n个线性方程,所以使用线性代数的知识可得:
$$ {\sigma }{{T}}_{{k}}^{{4}}=\sum _{{i=1}}^{{n}}\frac{{\delta }_{{k,i}}-\left({1-}{{ \varepsilon }}_{{k}}\right){\varphi}_{{k,i}}}{{{ \varepsilon }}_{{k}}}{{J}}_{{i}}=\sum _{{k=1}}^{{n}}{{a}}_{{k,i}}{{J}}_{{i}} $$ (10) 其中,
$$ {{a}}_{{k,i}}=\frac{{\delta }_{{k,i}}-\left({1-}{{ \varepsilon }}_{{k}}\right){\varphi}_{{k,i}}}{{{ \varepsilon }}_{{k}}} $$ (11) $ {\delta }_{{k,i}} $为克罗内克算符,则:
$$ {\delta }_{{k,i}}=\left\{\begin{array}{*{20}{l}}{1}&{i}={k}\\ {0}&{i}{≠}{k}\end{array}\right. $$ (12) 则公式(10)可改写成如下形式:
$$ \left[{J}\right]=\frac{{\sigma }\left[{{T}}^{{4}}\right]}{\left[{A}\right]} $$ (13) 式中:[J]表示有效辐射列矩阵;[A]表示a的方矩阵;[T4]表示温度四次方的列矩阵,由上述理论公式反推导可知T-eff为:
$$ {T\text{-}eff=}\sqrt[{4}]{\frac{{J}}{{ \varepsilon \sigma }}} $$ (14) 式中:${T\text{-}eff}$表示该工况计算收敛时,有效辐射计算所得涡轮叶片上各网格单元温度。
则定义T-dif为:
$$ {T\text{-}dif=T\text{-}wall-T\text{-}eff} $$ (15) 式中:$ {T\text{-}dif} $表明叶片网格单元在测量和计算两种方法下的误差情况。$ {T\text{-}wall} $表示涡轮叶片在给定边界条件计算收敛时,此时叶片上各网格单元的温度。
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由于在实际有限面组成的辐射换热计算中,各表面有效辐射均匀的情况很少,当采用表面有效辐射均匀假设为基础的计算方法时,就会由计算原理的近似性引起误差,为研究数值计算结果的可靠性,使验证叶片计算的结果更具有说服力,采用大球内腔壁与腔内小球的辐射换热经典模型进行验证计算[12]。
两球均为等温灰体,设定内球面,外球面壁面温度,发射率等相关参数如图4所示[17]。文中通过fluent meshing采用非结构化网格对同心球模型进行网格划分,最小网格尺寸0.024 mm,最大网格尺寸0.63 mm,小球外壁面网格数量911个,大球内壁面网格数量5633个,模型满足计算要求。
由传热学[14]可知,其小球外壁面换热量为:
$$ Q=\frac{{{A}}_{{1}}\left({{E}}_{{b1}}-{{E}}_{{b2}}\right)}{{{1}}/{{{ \varepsilon }}_{{1}}}-\left({{1}}/{{{ \varepsilon }}_{{2}}}{-1}\right){{{A}}_{{1}}}/{{{A}}_{{2}}}} $$ (16) 由公式(6)知$ {q=}\dfrac{{Q}}{{{A}}_{{1}}} $,则:
$$ {J}={{E}}_{{b}}-\left(\frac{{1}}{{ \varepsilon }}{-1}\right){q} $$ (17) -
通过数值计算输出,并对角系数进行完整性验证[14]。输出小球外壁面的有效辐射J=3196.452W/m2,经公式(16)、(17)计算所得有效辐射J=3171.33W/m2。由于角系数为一个纯几何因子,取值仅与空间中两表面的形状大小和几何位置相关,与所研究表面的温度和发射率等特性无关。理论上,只要不断的增加网格量,就可以使角系数计算的结果更趋近真实值。则辐射热流量和辐射热流密度将更逼近真实值,该数值模拟计算结果与理论计算结果只相差25.122 W/m2。误差占计算结果7‰,满足验证假设,说明自定义编程计算具有一定的可靠性和可行性。
由于在实验环境条件下,不同温度下不同的表面发射率;燃气的热辐射干扰;燃烧烟尘沉积物的污染;叶片高速度;其他叶片和环境的反射辐射这五大影响因素不能完全规避,也无法就某一个影响因素进行实验验证分析。文中研究内容仅限于对含端壁涡轮导叶的反射辐射,有效辐射进行分析计算,是减少了其他干扰影响因素,特定环境下的数值模拟计算。
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文中选取涡轴发动机中具有复合冷却结构的一级导叶为研究对象,其结构如图5所示,叶片沿中截面切平面内部结构如图6所示。导叶全周期数目为20,计算域中只考虑单个叶片及由叶片所建立的流体域通道,叶片流体通道上下壁面设置为旋转周期边界。叶片叶根及叶顶处同端壁连接受到高温端壁导热作用影响,叶片固体外侧与高温燃气接触,与高温燃气接触的外表面设置为耦合换热边界。叶片中外部冷却主要为气膜冷却,内部冷却为套筒冲击冷却及内部流场对流换热冷却,并在尾缘劈缝前设置绕流柱,改变流动状态来强化对流换热冷却。
二次流从端壁单侧进入叶片内部流体域,端壁外侧与涡轮机匣内部二次流直接接触,从而进行对流—导热换热。计算域的上下壁面设置为旋转周期边界,从而对整个环形叶栅流体通道中叶片外表面的辐射换热进行分析研究。采用非结构化网格对叶片模型进行划分,叶片网格结构如图7所示。
模型采用流固耦合方式进行数值模拟计算,经过网格无关性验证后,模型网格划分数量确定为50万,对涡轮导叶外表面和内表面以及气膜孔区域附近的流体域设置8层边界层,同时设置第一层网格高度为0.05 mm,保证湍流模型及壁面函数所需求的y+值。绕流柱及尾缘劈缝等体积较小的结构进行局部加密,得到更加精细的网格分布。计算工况中辐射模型采用DO模型。离散方法采COUPLE算法,计算过程中的参数离散采用二阶迎风格式。在数值模拟过程中,固体域叶片和端壁材料统一设置为镍;流体域介质为混合气体介质和理想气体。其余边界条件设置如表1所示。
表 1 边界条件设定
Table 1. Boundary condition setting
Boundary condition Values Total gas inlet pressure/MPa 1.454 Total gas inlet
temperature/KNon-uniform total temperature Total pressure at
cold flow inlet/MPa1.5 Total temperature of
cold flow inlet/K750 Gas inlet turbulence 25% Cold flow inlet turbulence 5% 壁面有效辐射计算的矩阵维数数组定义15700×15700,叶片与端壁发射率为0.6,迭代精度为10 e-3,通过获取叶片与端壁的面网格数据,对整个计算域进行循环计算,进而方便地进行各网格单元的黑体辐射力、角系数、克罗内克算符的计算。采用高斯消去法的原理。对公式(13)进行有效辐射的计算,进而输出叶片的有效辐射,表面辐射分布情况,使用TECPLOT进行整合计算并输出误差分布情况。
有关数值模拟过程中辐射相关变量设置应注意以下几点:
1) 经调研叶片壁面辐射相关文献可知[18],燃烧室出口辐射强度约100000 W/m2,可以进而将其折算成温度为1 530 K的黑体辐射强度,参考该值给定导叶进口黑体辐射温度为1 400、1 600、1 800 K;
2)出口辐射温度主要是衡量导叶下游动叶壁面的辐射影响程度,其值基于当地燃气平均温度计算,当发动机处于OEI状态时,燃气温度提升,动叶表面温度提高,定义出口黑体辐射温度为1200、1400、1600 K,来计算出口辐射强度对导叶叶片外表面温度的影响;
3)将发射率的值定义为0.2、0.6、0.8[19]。H2O、CO2、N2和O2的组分占比为0.05、0.1、0.7、0.15。表2给出了计算工况中辐射相关变量的参数设置。
表 2 导叶辐射多参数敏感性分析算例编号设置
Table 2. Example number setting for multi parameter sensitivity analysis of guide vane radiation
Example
numberEntrance temperature/K Emissivity of wall Radiation
typeExport
temperature/K1 1400 0.6 Wall/Gas 1400 2 1600 0.6 Wall/Gas 1400 3 1800 0.6 Wall/Gas 1400 4 1600 0.6 Wall 1200 5 1600 0.6 Wall 1600 6 1600 0.8 Wall 1400 7 1600 0.2 Wall 1400 -
文中的收敛标准判断需满足以下三个要求:
1)各项残差稳定在10−3以下;
2)叶片表面温度不再随迭代步数变化;
3) UDS输出值趋于稳定。
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为研究不同进口辐射强度条件下,涡轮导叶在端壁反射辐射下的传热特性的影响,输出其有效辐射分布,改变进口辐射强度,在保证气体组分、叶片发射率、出口黑体辐射温度相同,不考虑燃气辐射影响的基础上选取算例1、2、3,通过计算其在端壁反射辐射情况下的有效辐射分布,以叶片壁面温度(T-wall)分布为基准进行对比研究。
从图8可知,在计算收敛后,其壁面温度分布如图8(b)、(e)、(h)所示,随着入口黑体辐射温度从1400 K提升至1800 K,叶片尾缘和叶片压力面的温度较高。再通过公式(14)反算出在该有效辐射下的温度分布(T-eff),如图8(a)、(d)、(g)所示,在改变进口黑体辐射的温度条件下,对叶片的壁面温度影响主要集中在叶片压力面区域,叶片压力面温度明显高于叶片吸力面区域,其次影响较大的区域主要为叶片前缘区域,这是由于进口黑体辐射温度投入辐射主要照射在叶片压力面及叶片压力面前缘附近,这部分区域接受到了较大的辐射能流。
图 8 不同进口辐射强度的叶片壁面温度及误差分布
Figure 8. Temperature and error distribution of blade wall with different inlet Radiant intensity
为进一步分析,将误差分布沿叶高方向输出,得到其误差分布如图9所示。笔者将沿不同叶高位置提取到的数据排列在−1~1之间,规定前缘中间位置为0处,则压力面中间位置在−0.5处,吸力面中间位置在0.5处。通过比较在不同进口辐射温度条件下的叶片误差分布,可以定性看出入口辐射温度的提高对于叶片前缘和压力面的温度变化影响最大,尾缘部分次之,且在有气膜孔的区域误差较为明显。由于入口直接受到燃烧室出口燃气辐射的作用,叶片前缘对于入口辐射温度的改变敏感,且尾缘部分冷却措施较少,受到端壁壁温温升的影响,使得此处辐射热流较大,带来较高的温度回升。由公式(15)得误差分布(T-dif)分析,如图8(c)、(f)、(i)所示,在叶片前缘区域计算误差最显著,高达到37.68 K。压力面在主流和二次流的综合作用下,反算出来的误差只在25 K左右。计算的有效辐射分布情况,进一步修正了叶片在不同进口辐射强度条件下的壁面误差分布情况。
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为研究出口辐射强度条件下对涡轮导叶在端壁反射辐射下壁面温度分布的影响,选取算例4、2、5,其出口黑体辐射温度分别为1200 、1400 、1600 K,通过计算其在端壁反射辐射情况下的有效辐射分布,以叶片壁面温度分布为基准进行对比研究。从图10可知,随着出口黑体辐射温度的升高,辐射热流量占比逐渐增大,吸力面靠近尾缘壁面处存在较为明显的温升。如图10(b)、(e)、(h)所示,叶片吸力面与尾缘受到出口黑体辐射温度的影响更高。出口黑体辐射温度为1600 K时,叶片吸力面及尾缘误差在10 K左右,主要影响区域在叶片吸力面区域,且温升都较小,未能对叶片外表面分布产生较大程度的影响。
图 10 不同出口辐射强度叶片壁面温度及误差分布
Figure 10. Distribution of blade wall temperature and error at different outlet radiant intensity
为进一步分析,将误差分布沿叶高方向输出,得到误差分布如图11所示。笔者将沿不同叶高位置提取到的数据排列在–1~1之间,规定前缘中间位置为0处,则压力面中间位置在–0.5处,吸力面中间位置在0.5处。在发动机实际工况下,下游动叶的等效黑体辐射温度远小于1600 K。对于文中计算工况而言,只在吸力面尾缘部分辐射能流较大,因此出口黑体辐射温度的变化对于涡轮导叶的影响较小。
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叶片表面发射率是研究金属吸收和发射辐射的重要参数之一。由于金属叶片表面发射率受温度影响较大,加入辐射会使叶片外表面温度产生较大变化,叶片热侧表面受到来自其他壁面辐射的来源主要由相邻导叶、动叶及相邻端壁组成。
文中叶片端壁未设置冷却措施,所以其温度高于相邻导叶外表面温度,辐射热流更大,由相邻端壁发射和反射的辐射热流会对叶片热侧接收热辐射产生一定程度上的影响。选取算例6、2、7,三个算例中叶片的表面发射率分别为0.8和0.6和0.2,通过计算其在端壁反射辐射情况下的有效辐射分布,以叶片壁面温度分布为基准进行对比研究。
当壁面发射率从0.8、0.6、0.2递减时,叶片压力面前缘区域的温度受发射率的影响较小,有效辐射反算的温度误差分布如图12所示。发射率越大,其在叶片压力面的腮区处的误差也越大。为进一步分析,将误差分布沿叶高方向输出,得到误差分布如图13所示在叶片前缘处的影响较叶片中部区域影响更大,叶片压力面区域较吸力面影响次之。笔者将沿不同叶高位置提取到的数据排列在–1~1之间,规定前缘中间位置为0处,则压力面中间位置在–0.5处,吸力面中间位置在0.5处。
图 12 不同表面发射率叶片壁面温度及误差分布
Figure 12. Wall temperature and error distribution of blades with different surface Emissivity
图 13 不同表面发射率叶片误差沿叶高分布
Figure 13. Error distribution of blades with different surface Emissivity along blade height
由于气膜孔在前缘位置排布,相较叶片本身角系数较大,在压力面及吸力面气膜孔附近温度变化更为剧烈,叶片表面发射率的改变使叶片可以接收更大的辐射热流,在发动机实际工况下,叶片通道内环境温度较高,由于金属材料的发射率对温度敏感,且随温度的升高而增大,发射率的变化会对于叶片表面温度分布产生较为明显的影响,在高温时,热辐射对于叶片外表面温度变化的影响更大。
Research on the error influence mechanism of infrared temperature measurement of turbine guide vanes with end walls
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摘要: 由于涡轮叶片所处的工作环境复杂,受到壁面及燃气辐射干扰,导致测温十分困难。为进一步分析涡轮叶片表面在端壁影响下的温度分布情况,采用数值模拟结合自定义编程的方式进行了含端壁涡轮导叶的温度误差验证计算。利用自定义编程对经典同心球模型进行了角系数,有效辐射等可靠性验证计算,验证方法可靠。基于该方法进行了端壁与涡轮导叶各网格单元的角系数,叶片表面间的辐射换热计算,输出涡轮导叶的表面辐射特性分布,运用玻尔兹曼定律反推导出该工况涡轮导叶所受到的辐射能流分布情况;计算分析了不同误差影响机理下,含端壁的涡轮导叶温度误差分布情况,探明了热辐射环境下对叶片表面辐射特性的影响。结果表明:当进口黑体辐射温度在1400~1800 K之间,进口辐射强度是对叶片换热影响最大的因素;利用有效辐射和所计算的误差分布可知,进口辐射温度影响区域主要是叶片前缘区域,最大计算误差不超过2.82%;通过有效辐射及误差分布可见,出口黑体辐射温度的变化对于涡轮导叶的影响较小,受温度影响区域也主要为叶片前缘区域,最大计算误差不超过2.35%;叶片表面发射率与温度成正相关,当叶片表面发射率增大时,叶片表面温度随之均匀升高,在真实工况下,叶片材料物性的改变较小,在发动机设计中可以近似忽略由于叶片温度变化导致物性参数改变带来的影响。Abstract:
Objective With the rapid development of national defense industry and science and technology, more in-depth application and research of gas turbine engines in aviation, power generation, chemical industry, ship and power engineering are also conducted. Due to the complex working environment of turbine blades, the particularity of temperature measurement, and the interference of wall and gas radiation, the traditional temperature measurement technology has been unable to meet its needs. In order to accurately measure the working temperature of turbine blades in complex high-temperature environments, ensure that the highest temperature and temperature gradient on the blade surface are suitable for the blade design life, and improve the safety and efficiency of gas turbine operation, infrared temperature measurement technology was used to correct the temperature of the blades under high operating conditions. Methods With a discretized pure three-dimensional model and a radiation correction method based on infrared temperature measurement of turbine blades, the temperature error verification calculation of turbine guide vanes with end walls was carried out using numerical simulation combined with User Defined Function (UDF) custom programming. Custom programming was used to perform reliability verification calculations on the classic concentric sphere model, such as angle coefficients and effective radiation. Based on this method, the angle coefficients of each grid element between the end wall and turbine guide vanes were calculated, and the radiation heat transfer between the blade surfaces was calculated. The surface radiation characteristics distribution of the turbine guide vanes was output, and the radiation energy flow distribution of the turbine guide vanes under this operating condition was derived using Boltzmann's law. We calculated and analyzed the temperature error distribution of turbine guide vanes with end walls under different error influence mechanisms, explored the influence of thermal radiation environment on blade surface radiation characteristics, and discussed the effect of effective radiation on turbine blade temperature measurement. Results and Discussions From Figure 8, it can be seen that after convergence, as the inlet blackbody radiation temperature increases from 1400 K to 1800 K, the temperature at the trailing edge and pressure surface of the blade is higher. Under changing the temperature conditions of imported blackbody radiation, the impact on the wall temperature of the blade is mainly concentrated in the pressure surface area of the blade. The pressure surface temperature of the blade is significantly higher than that of the suction surface area, and the second most influential area is mainly the leading edge area of the blade; From Figure 10, it can be seen that as the outlet blackbody radiation temperature increases, the proportion of radiation heat flow rate gradually increases, and there is a significant temperature rise near the trailing edge wall of the suction surface. As shown in Figure 10 (b), (e), (h), the suction surface and trailing edge of the blade are more affected by the outlet blackbody radiation temperature. When the export blackbody radiation temperature is 1600 K, the calculated error of the blade suction surface and trailing edge is about 10 K. The impact area of the export blackbody radiation is mainly in the blade suction surface area, and the temperature rise is relatively small, which has not had a significant impact on the distribution of the outer surface of the blade; When the wall emissivity decreases from 0.8, 0.6, and 0.2, the temperature in the leading edge area of the blade pressure surface is less affected by the emissivity. The temperature error distribution of the effective radiation inverse calculation is shown in Figure 12. The larger the emissivity, the greater the error at the gill area of the blade pressure surface. From the error distribution Figure 13, it can be seen that the influence at the leading edge of the blade is greater than that in the middle area of the blade, and the influence in the pressure surface area of the blade is secondary to that of the suction surface. Conclusions When the temperature of imported blackbody radiation is between 1 400 K and 1 800 K, the intensity of imported radiation has the greatest impact on blade heat transfer; Based on the effective radiation and the calculated error distribution, it can be concluded that the main area affected by the inlet radiation temperature is the leading edge area of the blade, with a maximum calculation error not exceeding 2.82%; Through effective radiation and error distribution, it can be seen that the change in outlet blackbody radiation temperature has a relatively small impact on the turbine guide vanes, and the temperature affected area is mainly the leading edge area of the blade. The maximum calculation error shall not exceed 2.35%; The emissivity of the blade surface is positively correlated with temperature. As the emissivity of the blade surface increases, the surface temperature of the blade uniformly rises accordingly. Under real operating conditions, the changes in the physical properties of blade materials are relatively small, and the impact of changes in physical parameters caused by blade temperature changes can be approximately ignored in engine design. -
表 1 边界条件设定
Table 1. Boundary condition setting
Boundary condition Values Total gas inlet pressure/MPa 1.454 Total gas inlet
temperature/KNon-uniform total temperature Total pressure at
cold flow inlet/MPa1.5 Total temperature of
cold flow inlet/K750 Gas inlet turbulence 25% Cold flow inlet turbulence 5% 表 2 导叶辐射多参数敏感性分析算例编号设置
Table 2. Example number setting for multi parameter sensitivity analysis of guide vane radiation
Example
numberEntrance temperature/K Emissivity of wall Radiation
typeExport
temperature/K1 1400 0.6 Wall/Gas 1400 2 1600 0.6 Wall/Gas 1400 3 1800 0.6 Wall/Gas 1400 4 1600 0.6 Wall 1200 5 1600 0.6 Wall 1600 6 1600 0.8 Wall 1400 7 1600 0.2 Wall 1400 -
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