提高气冷涡轮气热耦合计算精度方法的研究
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摘要
航空发动机正朝着提高推重比与效率的方向发展,为了达到这个目的,涡轮入口温度不断提高,目前涡轮进口温度已经远远超过了叶片材料的屈服极限,这样就必须对叶片进行有效地冷却以维持叶片的正常工作。准确地预测涡轮叶片的温度场已经成为提高冷却效率、延长叶片工作寿命的关键问题。随着计算流体力学以及计算机技术的发展,气热耦合数值模拟已经成为预测涡轮叶片温度场的重要工具,本文的工作在于采用自编程序对气冷涡轮叶片进行气热耦合数值模拟,并对影响气热耦合计算精度的物理模型进行研究,以提高实际涡轮气热耦合数值仿真的准确性与可靠性,并初步建立与完善可用于实际涡轮仿真的气热耦合仿真平台。
冷气掺混是采用气膜冷却的涡轮主流道中很常见的物理现象,由于冷空气与燃气成分的差异,掺混必然会导致流道中工质组分的变化,进而使工质热物性变化,以某两级气冷涡轮为例,进行了考虑组分变化的气动计算,与仅采用单工质假设的结果对比发现,考虑组分变化后,不仅工质的热物性发生了变化,流场的结构以及流道中激波位置也有了较大的差异,这就表明为了提高气热耦合计算的精度,组分变化的影响是有必要考虑的。
然后研究了计算网格对气热耦合计算的影响,气热耦合涉及到流体和固体区域两个物理场的数据传递以及耦合求解,这是一个非线性的过程,而在流固交接面流体侧存在速度与温度附面层,在这两个附面层内,速度与温度等参数变化剧烈,气热耦合过程中的非线性更加剧烈,迭代过程受网格正交性的影响很大。以NASA-MARKⅡ叶片的5411试验工况为例,分别采用H型和H-O-H型网格对涡轮流道区域进行离散,进行气热耦合计算,结果表明在流固耦合交界面流体侧采用正交性差的H型网格很容易导致计算发散,而在该区域采用正交性较好的O型网格有利于迭代的进行。
对于采用弱耦合方式的气热耦合计算,需要采用耦合方法来实现流体与固体区域的数据传递。目前运用比较多的有两种耦合方法:间接耦合方法与直接耦合方法。采用上节中相同的算例与这两种耦合方法,分别进行了气热耦合计算。发现间接耦合方法会导致气热耦合计算的不稳定、收敛速度缓慢,而直接耦合方法则具有稳定性好,收敛速度较快的特点。
附面层转捩是涡轮叶片表面附面层流动过程中一个很重要的流动现象,以NASA-MARKⅡ叶片的多个试验工况为算例,采用不同湍流模型和转捩模型进行气热耦合计算,结果表明附面层的流态变化对涡轮叶片的传热影响很大,而且转捩不仅存在于叶片表面,在冷却空气流量较小时,冷却腔壁表面也存在较大范围的层流、转捩区域,研究还表明对附面层内的转捩预测是影响气热耦合计算精度的很重要的因素。全湍流模型不能够预测附面层转捩的起止位置以及转捩区长度,因此不能够准确地对涡轮叶片表面的传热过程进行预测,预测的叶片表面温度与试验测量值偏差很大;而建立在间歇因子基础上的转捩模型则可以预测出附面层的流态变化,预测的叶片表面温度与试验测量值吻合最好。此外,不同的转捩模型对转捩的预测能力也不尽相同,代数转捩模型只考虑到了间歇因子沿着流向的分布,而忽略了间歇因子沿着壁面法向的变化,这导致在叶片表面的一些区域预测的结果低于试验测量值,而间歇因子输运方程则可以模拟间歇因子的三维输运效应,尽管在原理上更符合实际情况,但是该模型对计算网格的要求很高,不仅增加了计算量,也影响了计算的收敛性。与CFX10,Gama-Theta模型的结果比较表明,本文开发的气热耦合求解器在激波诱发的转捩区域预测的结果不如CFX10的结果,但是在其它区域,本文预测的结果要更接近于实验测量值。
目前能量方程的封闭一般采用雷诺比拟方法,对湍流普朗特数取常数。但是与速度附面层类似,温度附面层也具有复合层性质,沿着壁面法线方向,湍流普朗特数是变化的。在气热耦合计算中,采用代数经验关联式对湍流普朗特数进行计算,结果表明,沿着壁面外法线方向,湍流普朗特数逐渐减小,但是在本文的计算中,考虑湍流普朗特数的变化预测的叶片表面温度与不考虑该参数变化的结果相差不大。
最后本文对一实际燃气轮机的低压涡轮导叶进行了气热耦合数值模拟。与绝热情况相比,采用单腔内冷方式的涡轮叶片表面温度都有所降低,温度最高区域位于叶片前缘与叶片尾缘;采用尾缘劈缝冷却后,涡轮叶片尾缘温度降低幅度最大,但是在其它区域的冷却效果要受到冷却腔内冷气的流动过程影响,这在冷却系统的设计中是需要认真考虑的。同时冷空气喷入主流会改变主流燃气的成分,影响工质的气体常数与定压比热等热物性质,其中气体常数降低,但是在整个流动区域内其值变化很小,而在冷气浓度比较大的区域,考虑组分扩散影响预测的定压比热比采用单工质假设的定压比热低,在仅采用了尾缘劈缝冷却而其他区域不采用气膜冷却的条件下,冷空气从劈缝喷出进入下游区域,尾缘上游区域冷气浓度特别小,此时考虑组分扩散与否,这两种情况下的叶片型面压力差异很小,而在叶片表面大部分区域型面温度差异也很小,但是在叶片压力面靠近劈缝区域,考虑组分扩散影响后,气体常数受组分以及温度的双重影响,其值与不考虑组分扩散的结果有较大差异。
The temperature at the turbine inlet is rising to improve the engine thrust and the cycle efficiency. Such temperature has exceeded the thermal yield limit of the blade material, thus an effective cooling system is needed to maintain the engine operation. Accurately predicting the blade thermal load becomes rather essential to improve the cooling efficency of cooling system and to extend the blade operating life. Nowadays coupled heat transfer (CHT) technique has been widely applied to predict the blade thermal field. Otherwise there still are few investigations of numerical methods influencing on the CHT results. The purpose of this study is to improve the accuracy and reliability of CHT simulatioins, hence the effect of several numerical methods, including coolant diffusion, computational grids, coupling method, laminar-to-turbulent transition, closure of time-averaged energy equation and so on, on the blade thermal load prediction are investigated. And the server is HIT-3D.
Firstly the influences of coolant diffusion on the aerodynamic and thermal parameter distribution are investigated. Coolant mixing exists in the passages of film cooled turbines. Since the components of the cooling air and the gas are different, the coolant mixing would result in the variation of gas component in the passage, and then the thermal property of gas. A two-stage film cooled turbine is selected as the test case, and the aerodynamic simulations for gas with variation components and constant component are carried out. The comparision between the numerical results reveals that the simulation for the gas with variation components predicts different flow structure and shock wave postion compared with that for the constant component gas. Hence the component variation induced by coolant mixing should be taken account of in simulations of the film cooled turbines.
Secondly the influences of computational grids on the CHT simulation results are investigated. Physically the CHT simulation, relating to the data transimission between fluid and solid domains, is a non-linear process. Furthermore, such non-linarility is strengthened by the coupling of velocity and thermal boundary layers near the fluid/solid interface in the fluid domain. And the iteration could be affected by the orthogority of computational grids. The H-type and H-O-H-type grids are employed to discretize the turbine passage domain, and the No. 5411 case of NASA-MARKⅡvane is served as the test case. The CHT results show that the simulation with O-type grids near the fluid/solid interface in the fluid domain normally converges, while that with H-Type grids diverges.
Thirdly the influences of coupling methods on the stability and convergence of CHT simulations are studied. There are two kinds of the methods, the indirect coupling method and the direct coupling method. With the same test case as that mentioned above, CHT simulations with different coupling methods are carried out. And the numerical results show that the simulation by the indirect coupling method is with much instability, but that by the direct coupling mthod is rather stable and it converges quickly.
Fourthly the effects of laminar-to-turbulent transition on the thermal prediction of CHT simulations are investigated. Boundary layer transition is rather common in the boundary layer flows on the low-pressure turbine surface. With three different operating conditions of NASA-MARKⅡvane as test cases, CHT simulations by several full turbulence models and transition models are carried out. The numerical results are compared with the measured ones. It shows that the heat transfer is strongly affected by the laminar-to-turbulent transition in the boundary layer flow, and that the transition flow also exists on the cooling air channel walls when the cooling air mass flow is low. The transition predition is quite an essential factor that affects the accuracy of CHT simulations. The full turbulence models are not able to predict the transition onset and the length of transition zone, thus the simulations with such models over predict the vane thermal load. The transition models are able to predict the transition pocess, thus the simulations with such models predict thermal load much close to the measured ones. The algebraic transition model negelets the intermittency transportation along the normal direction to the wall, and it leads to lower temperature than the measured one at several nodes. The intermittency transportation equation, able to predict intermittency distribution in the complex and 3-D flow field, needs much finer grids than the algebraic one, and it costs more computational resourses. The comparision between the results by HIT-3D and those by CFX10 with Gama-Theta transition model proves the ability of HIT-3D in CHT simulations. The developed solver HIT-3D would predict results closer to the measured ones than CFX10 in the blade surface except the shock-induced transition zone.
Fifthly the effect of time-averaged energy equation closure on the CHT simulation is studied. The Reynolds analogy is a widely applied method for closing the time-averaged energy equation in simulations of inner flows. With such method, the constant turbulent Pradtl number is always employed. Otherwise the thermal boundary layer, similar to the velocity boundary layer, could be divided into several layers. Thus the turbulent Pradtl number is not constant. An algebraic correlation is utilized to coupute the turbulent Prandtl number in the thermal boundary layer. The CHT simulation with such algebraic correlation shows that the turbulent Prandle number vanishes along the outer normal direction to the wall. The predicted profile temperature is compared with that by the simulation with constant turbulent Pradtle number, but there is slignt difference between the predicted profile temperature distributions.
Finally the CHT simulatons of a low-pressure turbine in pratical operating conditions are carried out. And the effects of numerical methods on the thermal prediction of CHT simulations are discussed. Compared with the adiabatic results, the vane profile temperature with single cooling air channel is largely reduced, and the highest temperature in the vane surface exists at the leading and trailing edges. For the vane with two air cooling channels and a slot at the trailing edge, the traling edge is effectively cooled, but the cooling efficiency is affected by the flow in the cooling air channel. There is few even none cooling air at the upstream of vane trailing edge, and most of the cooling air flow towards the downstream of the vane. Taking account of the coolant diffusion effect, the gas constant changes slightly during the whole passage, but the constant-pressure specific heat is lower than that of consant component gas in the regions with more cooling air. The comparision between the predicted profile pressure of the CHT simulations for the gases with variable components and constant component is carried out, and little difference is found out. There is also comparision between the predicted profile temperature distributions, and the largest difference exists near the trailing edge in the pressure side.
冷气掺混是采用气膜冷却的涡轮主流道中很常见的物理现象,由于冷空气与燃气成分的差异,掺混必然会导致流道中工质组分的变化,进而使工质热物性变化,以某两级气冷涡轮为例,进行了考虑组分变化的气动计算,与仅采用单工质假设的结果对比发现,考虑组分变化后,不仅工质的热物性发生了变化,流场的结构以及流道中激波位置也有了较大的差异,这就表明为了提高气热耦合计算的精度,组分变化的影响是有必要考虑的。
然后研究了计算网格对气热耦合计算的影响,气热耦合涉及到流体和固体区域两个物理场的数据传递以及耦合求解,这是一个非线性的过程,而在流固交接面流体侧存在速度与温度附面层,在这两个附面层内,速度与温度等参数变化剧烈,气热耦合过程中的非线性更加剧烈,迭代过程受网格正交性的影响很大。以NASA-MARKⅡ叶片的5411试验工况为例,分别采用H型和H-O-H型网格对涡轮流道区域进行离散,进行气热耦合计算,结果表明在流固耦合交界面流体侧采用正交性差的H型网格很容易导致计算发散,而在该区域采用正交性较好的O型网格有利于迭代的进行。
对于采用弱耦合方式的气热耦合计算,需要采用耦合方法来实现流体与固体区域的数据传递。目前运用比较多的有两种耦合方法:间接耦合方法与直接耦合方法。采用上节中相同的算例与这两种耦合方法,分别进行了气热耦合计算。发现间接耦合方法会导致气热耦合计算的不稳定、收敛速度缓慢,而直接耦合方法则具有稳定性好,收敛速度较快的特点。
附面层转捩是涡轮叶片表面附面层流动过程中一个很重要的流动现象,以NASA-MARKⅡ叶片的多个试验工况为算例,采用不同湍流模型和转捩模型进行气热耦合计算,结果表明附面层的流态变化对涡轮叶片的传热影响很大,而且转捩不仅存在于叶片表面,在冷却空气流量较小时,冷却腔壁表面也存在较大范围的层流、转捩区域,研究还表明对附面层内的转捩预测是影响气热耦合计算精度的很重要的因素。全湍流模型不能够预测附面层转捩的起止位置以及转捩区长度,因此不能够准确地对涡轮叶片表面的传热过程进行预测,预测的叶片表面温度与试验测量值偏差很大;而建立在间歇因子基础上的转捩模型则可以预测出附面层的流态变化,预测的叶片表面温度与试验测量值吻合最好。此外,不同的转捩模型对转捩的预测能力也不尽相同,代数转捩模型只考虑到了间歇因子沿着流向的分布,而忽略了间歇因子沿着壁面法向的变化,这导致在叶片表面的一些区域预测的结果低于试验测量值,而间歇因子输运方程则可以模拟间歇因子的三维输运效应,尽管在原理上更符合实际情况,但是该模型对计算网格的要求很高,不仅增加了计算量,也影响了计算的收敛性。与CFX10,Gama-Theta模型的结果比较表明,本文开发的气热耦合求解器在激波诱发的转捩区域预测的结果不如CFX10的结果,但是在其它区域,本文预测的结果要更接近于实验测量值。
目前能量方程的封闭一般采用雷诺比拟方法,对湍流普朗特数取常数。但是与速度附面层类似,温度附面层也具有复合层性质,沿着壁面法线方向,湍流普朗特数是变化的。在气热耦合计算中,采用代数经验关联式对湍流普朗特数进行计算,结果表明,沿着壁面外法线方向,湍流普朗特数逐渐减小,但是在本文的计算中,考虑湍流普朗特数的变化预测的叶片表面温度与不考虑该参数变化的结果相差不大。
最后本文对一实际燃气轮机的低压涡轮导叶进行了气热耦合数值模拟。与绝热情况相比,采用单腔内冷方式的涡轮叶片表面温度都有所降低,温度最高区域位于叶片前缘与叶片尾缘;采用尾缘劈缝冷却后,涡轮叶片尾缘温度降低幅度最大,但是在其它区域的冷却效果要受到冷却腔内冷气的流动过程影响,这在冷却系统的设计中是需要认真考虑的。同时冷空气喷入主流会改变主流燃气的成分,影响工质的气体常数与定压比热等热物性质,其中气体常数降低,但是在整个流动区域内其值变化很小,而在冷气浓度比较大的区域,考虑组分扩散影响预测的定压比热比采用单工质假设的定压比热低,在仅采用了尾缘劈缝冷却而其他区域不采用气膜冷却的条件下,冷空气从劈缝喷出进入下游区域,尾缘上游区域冷气浓度特别小,此时考虑组分扩散与否,这两种情况下的叶片型面压力差异很小,而在叶片表面大部分区域型面温度差异也很小,但是在叶片压力面靠近劈缝区域,考虑组分扩散影响后,气体常数受组分以及温度的双重影响,其值与不考虑组分扩散的结果有较大差异。
The temperature at the turbine inlet is rising to improve the engine thrust and the cycle efficiency. Such temperature has exceeded the thermal yield limit of the blade material, thus an effective cooling system is needed to maintain the engine operation. Accurately predicting the blade thermal load becomes rather essential to improve the cooling efficency of cooling system and to extend the blade operating life. Nowadays coupled heat transfer (CHT) technique has been widely applied to predict the blade thermal field. Otherwise there still are few investigations of numerical methods influencing on the CHT results. The purpose of this study is to improve the accuracy and reliability of CHT simulatioins, hence the effect of several numerical methods, including coolant diffusion, computational grids, coupling method, laminar-to-turbulent transition, closure of time-averaged energy equation and so on, on the blade thermal load prediction are investigated. And the server is HIT-3D.
Firstly the influences of coolant diffusion on the aerodynamic and thermal parameter distribution are investigated. Coolant mixing exists in the passages of film cooled turbines. Since the components of the cooling air and the gas are different, the coolant mixing would result in the variation of gas component in the passage, and then the thermal property of gas. A two-stage film cooled turbine is selected as the test case, and the aerodynamic simulations for gas with variation components and constant component are carried out. The comparision between the numerical results reveals that the simulation for the gas with variation components predicts different flow structure and shock wave postion compared with that for the constant component gas. Hence the component variation induced by coolant mixing should be taken account of in simulations of the film cooled turbines.
Secondly the influences of computational grids on the CHT simulation results are investigated. Physically the CHT simulation, relating to the data transimission between fluid and solid domains, is a non-linear process. Furthermore, such non-linarility is strengthened by the coupling of velocity and thermal boundary layers near the fluid/solid interface in the fluid domain. And the iteration could be affected by the orthogority of computational grids. The H-type and H-O-H-type grids are employed to discretize the turbine passage domain, and the No. 5411 case of NASA-MARKⅡvane is served as the test case. The CHT results show that the simulation with O-type grids near the fluid/solid interface in the fluid domain normally converges, while that with H-Type grids diverges.
Thirdly the influences of coupling methods on the stability and convergence of CHT simulations are studied. There are two kinds of the methods, the indirect coupling method and the direct coupling method. With the same test case as that mentioned above, CHT simulations with different coupling methods are carried out. And the numerical results show that the simulation by the indirect coupling method is with much instability, but that by the direct coupling mthod is rather stable and it converges quickly.
Fourthly the effects of laminar-to-turbulent transition on the thermal prediction of CHT simulations are investigated. Boundary layer transition is rather common in the boundary layer flows on the low-pressure turbine surface. With three different operating conditions of NASA-MARKⅡvane as test cases, CHT simulations by several full turbulence models and transition models are carried out. The numerical results are compared with the measured ones. It shows that the heat transfer is strongly affected by the laminar-to-turbulent transition in the boundary layer flow, and that the transition flow also exists on the cooling air channel walls when the cooling air mass flow is low. The transition predition is quite an essential factor that affects the accuracy of CHT simulations. The full turbulence models are not able to predict the transition onset and the length of transition zone, thus the simulations with such models over predict the vane thermal load. The transition models are able to predict the transition pocess, thus the simulations with such models predict thermal load much close to the measured ones. The algebraic transition model negelets the intermittency transportation along the normal direction to the wall, and it leads to lower temperature than the measured one at several nodes. The intermittency transportation equation, able to predict intermittency distribution in the complex and 3-D flow field, needs much finer grids than the algebraic one, and it costs more computational resourses. The comparision between the results by HIT-3D and those by CFX10 with Gama-Theta transition model proves the ability of HIT-3D in CHT simulations. The developed solver HIT-3D would predict results closer to the measured ones than CFX10 in the blade surface except the shock-induced transition zone.
Fifthly the effect of time-averaged energy equation closure on the CHT simulation is studied. The Reynolds analogy is a widely applied method for closing the time-averaged energy equation in simulations of inner flows. With such method, the constant turbulent Pradtl number is always employed. Otherwise the thermal boundary layer, similar to the velocity boundary layer, could be divided into several layers. Thus the turbulent Pradtl number is not constant. An algebraic correlation is utilized to coupute the turbulent Prandtl number in the thermal boundary layer. The CHT simulation with such algebraic correlation shows that the turbulent Prandle number vanishes along the outer normal direction to the wall. The predicted profile temperature is compared with that by the simulation with constant turbulent Pradtle number, but there is slignt difference between the predicted profile temperature distributions.
Finally the CHT simulatons of a low-pressure turbine in pratical operating conditions are carried out. And the effects of numerical methods on the thermal prediction of CHT simulations are discussed. Compared with the adiabatic results, the vane profile temperature with single cooling air channel is largely reduced, and the highest temperature in the vane surface exists at the leading and trailing edges. For the vane with two air cooling channels and a slot at the trailing edge, the traling edge is effectively cooled, but the cooling efficiency is affected by the flow in the cooling air channel. There is few even none cooling air at the upstream of vane trailing edge, and most of the cooling air flow towards the downstream of the vane. Taking account of the coolant diffusion effect, the gas constant changes slightly during the whole passage, but the constant-pressure specific heat is lower than that of consant component gas in the regions with more cooling air. The comparision between the predicted profile pressure of the CHT simulations for the gases with variable components and constant component is carried out, and little difference is found out. There is also comparision between the predicted profile temperature distributions, and the largest difference exists near the trailing edge in the pressure side.
引文
1张彦仲. 21世纪航空科学技术发展展望. International Aviation. 2001, 2:12~15
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