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边界元法在气热耦合计算及冷却结构优化中的应用研究

Research on Conjugate Heat Transfer Simulation and Turbine Vane Cooling Structure Optimization with Bem

【作者】 王振峰

【导师】 韩万金; 黄洪雁;

【作者基本信息】 哈尔滨工业大学 , 动力机械及工程, 2010, 博士

【摘要】 航空发动机技术已成为衡量国家科技工业水平和综合国力的重要标志,为此各国竞相开展了航空发动机的高技术研究。随着航空工业的发展,对发动机提出了更高的要求,要求它有更高的推重比、更大的单位体积输出功率、更低的燃油消耗率及更好的可靠性能等。提高涡轮前燃气温度是提高发动机性能的有效途径,然而,涡轮进口温度的提高速度远远高于叶片材料耐温性能的发展速度,由此为保证涡轮叶片在高温环境下安全可靠地工作,必须采取有效的冷却技术和热防护措施。涡轮叶片温度场的准确预测可以有效地指导设计人员进行涡轮叶片冷却结构设计,以提高冷却效率、延长叶片工作寿命。本文的主要工作是在哈尔滨工业大学推进理论与技术研究所原有的流体计算程序基础上,搭建具有自主知识产权、适用于气冷涡轮叶栅气热耦合换热计算的数值仿真平台;并进一步深入分析湍流模型、冷却通道入口湍流特性条件以及换热系数实验准则式对气热耦合计算结果的影响。最后应用基于边界元方法(BEM)和有限差分方法(FDM)的气热耦合程序建立了气冷涡轮叶片冷却结构全耦合优化设计体系。本文首先对边界元法进行了深入的理论研究,详细推导了二维、三维边界元法求解势函数问题的控制方程,并建立边界元法计算固体区域热传导问题的数学模型,编写了二维、三维边界元程序。利用解析解和数值解对边界元程序进行准确性校验,计算结果表明,边界元法仅仅计算模型的表面网格单元,使得数值模拟的前处理和求解时间缩短。同时,由于其具备解析与离散相结合的特性,因此计算结果准确、计算精度较高。对三维边界元程序进行网格适应性研究,研究表明边界元方法对网格质量的依赖性很小。将边界元计算方法用于燃气涡轮叶栅气热耦合换热计算中,搭建起气热耦合数值仿真平台。并应用此气热耦合数值仿真平台数值模拟了NASA-MarkII涡轮叶栅具有典型流动特点的两个实验工况。分析数值模拟结果得出,三维气热耦合程序能够准确模拟不同流动特性的涡轮叶栅内部流动;叶栅内部温度场计算结果说明,在涡轮叶片表面的流体边界层内部温度梯度较大,传热过程剧烈,在流体边界层内部流体由顺压力梯度到逆压力梯度的过渡区域,由于叶栅内复杂的流动特点,采用B-L代数模型的三维气热耦合程序在预测边界层局部区域流体的传热特性时存在一定偏差。采用商业软件Fluent和CFX对相同的实验叶栅进行气热耦合计算,着重分析气热耦合计算的网格适应性、冷却通道入口不同湍流特性条件对耦合换热结果的影响以及不同湍流模型对具有流动分离特性的涡轮叶栅的流动、传热及热应力特性的预测能力。计算结果表明,涡轮叶栅流动特性计算结果对边界层网格依赖性很小,对网格质量要求不高;而边界层不同的网格划分对叶栅内传热特性的预测略有差异,其主要影响因素为边界层网格厚度和流向网格加密程度。对于涡轮叶片冷却通道、冷却孔等内部流动,湍流强度完全依赖于上游流动的历史,冷却通道的入口湍流特性对通道内流动发展影响较大,从而冷却通道进口湍流特性条件能否正确给定对涡轮叶栅耦合换热计算结果的准确度具有较大影响。CFX提供的考虑转捩流动特性的k- -SST- -湍流模型能够准确分辨层流及转捩状态,对边界层内复杂流动和传热过程模拟较为准确,但其不足之处为,k- -SST- -湍流模型过高地估计了转捩区域的湍动能而造成转捩区的过大估计,从而使得对流换热系数计算值过大,温度偏高。而三维气热耦合程序采用的修正B-L代数模型能够更为准确模拟不存在分离或分离较小的涡轮叶栅热环境,计算结果显示,B-L代数模型除在叶片边界层转捩区域存在一定误差外,其余位置对涡轮叶栅传热特性的预测要强于CFX提供的k- -SST- -湍流模型计算结果。同时,从涡轮叶片热应力特性分析结果得出,在涡轮叶栅气热耦合计算中温度场预测结果的准确与否对涡轮叶片热应力结果预测、以至涡轮叶片寿命预估和冷却结构设计工作至关重要。将换热系数实验准则式引入气冷涡轮叶栅气热耦合计算中,在计算过程中考虑了基于气冷涡轮叶片冷却通道不同几何模型和实际工况的修正因子,详细对比分析涡轮叶片内冷通道的不同换热系数实验准则式对耦合计算结果的影响;分析气冷涡轮叶片内冷通道采用、不采用换热系数实验准则式对气热耦合计算结果的影响以及对不同湍流模型预测叶栅流动、传热过程准确程度的影响。计算结果表明,气冷涡轮叶栅气热耦合计算中,涡轮叶片冷却通道、冷却孔等位置采用修正的对流换热系数实验准则式可以得到准确的叶栅流场及叶片温度场分布。换热系数实验准则式的采用绕开了湍流模型对冷却通道流体区域的求解过程,使得湍流模型能够专一求解叶栅主流燃气区域流动和传热过程,从而能够更为准确分析不同湍流模型对叶栅主流区域流动、传热特性的计算能力。同时避免了湍流模型计算多区域流场时求解误差的叠加,并且节省计算时间。将三维气热耦合程序作为气冷涡轮叶栅数值模拟的主程序,建立了气冷涡轮叶片冷却结构全耦合优化设计体系。对NASA-MarkII涡轮叶栅10个径向冷却通道进行优化,在优化过程中将冷却通道孔径、冷却通道空间位置和流经冷却通道的冷气流量作为设计变量进行参数控制,并且对冷却通道孔径和位置进行必要的约束。优化目标函数包括涡轮叶片温度最大值、温度平均值以及冷却孔冷气流量。优化中通过加权求和的方法将多目标函数转化为单目标函数,寻求涡轮叶片冷却结构的最优解。得益于气热耦合程序中求解固体区域热传导问题的边界元程序模块,使得涡轮叶片冷却结构全耦合优化计算时间缩短,工作量减少。在优化过程中,边界元方法省去了固体区域网格重复生成、重复计算的过程,避免了固体区域网格与流体区域网格的插值误差,从而提高优化效率和问题求解的计算精度。优化结果表明,冷却通道位置以及冷却通道孔径的优化,使得叶片区域温度最大值降低;优化后冷气流量的减少,使得叶片区域平均温度略有提高,但提高幅度很小。另外,优化后冷却通道流体与涡轮叶片的换热受入口段的影响有所降低,从而使得涡轮叶片径向温度梯度减小。

【Abstract】 Aircraft engine technology has become an important indicator for measuringthe science and technology level and comprehensive national strength. So manystates begin to carry out the aircraft engine’s high-tech research. With thedevelopment of aviation industry, the engine is made a higher demand. It needs tohave a higher thrust-weight ratio, a greater output power per unit volume, a lowerfuel consumption and a better reliability. Increasing turbine inlet gas temperature isan effective way to improve engine performance. However, turbine inlettemperature increased much faster than the blade material heat resistance rate ofdevelopment. So the efficient cooling technology and thermal protection measuresmust be adopted for ensuring turbine safety and reliability work. The accurateprediction of the turbines thermal environment can effectively guide the researcherto design turbine blade cooling structure, to improve cooling efficiency and extendthe working life of turbine. The purpose this study is to set up a numericalsimulation platform of air-cooled turbine conjugate heat transfer calculation withindependent intellectual property rights. The numerical simulation platform is basedon the fluid solver of Propulsion Theory and Technology Institute of HarbinInstitute of Technology. In addition, this paper researches detailedly the effect ofturbulence models, turbulence characteristics conditions of cooling channelentrance and heat transfer coefficient experimental criteria on the conjugate heattransfer results. Using the Boundary Element Method (BEM)/Finite DifferenceMethod (FDM) conjugate heat transfer solver, this paper sets up the full conjugateoptimization design system for air-cooled turbine vane cooling structure.Firstly, the BEM theory was study deep and then the controlling equations of2D and 3D BEM solving the potential function were deduced detailedly. The paperset up the BEM mathematical model for the solution of the solid regional heatconduction problem and compiled the 2D and 3D boundary element programs. Theprogram verification work was finished with the analytical and numerical solutions.The results showed that the BEM is that no volumetric grid is required inside thesolid, so it saves the numerical simulation pre-processing time and computation time. At the same time, the analytical and discrete combination characteristics makethe BEM get the accurate results and higher accuracy. The research results of BEMadaptation of the grid showed that the BEM has little dependence on the gridquality.The BEM was applied to the conjugate heat transfer analysis of gas turbinevane and a numerical simulation platform of air-cooled turbine conjugate heattransfer calculation was set up. The conjugate heat transfer numerical simulationplatform was employed to simulate the two different typical flow characteristicsexperimental conditions of NASA-MarkII turbine guide vane. The calculationresults showed that three-dimensional conjugate heat transfer solver can simulateaccurately different flow characteristics of turbine vane. The temperaturedistribution results showed that within flow boundary layer of turbine blade surfacethe temperature gradient is great and heat transfer course is severe. The complicatedflow characteristics make the 3D conjugate heat transfer solver which adopted theB-L algebraic model has a little error for the calculation of turbine vane heattransfer characteristics.Secondly, computational fluid dynamics software Fluent and CFX wereemployed to simulate the same experimental turbine vane with the conjugate heattransfer method. The paper finished the grid adaptation research of conjugate heattransfer calculation and cooling channel inlet turbulence characteristics conditionsresearch. In addition, the paper researched the effect of turbulence models on theflow, heat transfer and thermal stress characteristics for the turbine vane with theflow separation characteristics. The results showed that the flow characteristicsresult has little dependence on the flow boundary layer grid and has lower demandfor the grid quality. However, the grid quality has some effect on heat transfercharacteristics results. The main factors are the flow boundary layer thickness andthe grid refinement along flow direction. For internal flow of turbine blade coolingchannels or cooling holes, the turbulence intensity at the inlets is totally dependenton the upstream history of the flow. So the inlet turbulence characteristics have agreat effect on the flow development and conjugate heat transfer results of air-cooled turbine vane. CFX provides the K- -SST- - turbulence model whichconsiders the transition flow characteristics. The results showed that K- -SST- - turbulence models can exactly simulate the laminar flow and transition flow status and can predict accurately flow and heat transfer characteristics of turbinevane. But k- -SST- - turbulence model overestimates the turbulence kineticenergy of blade local region and makes the heat transfer coefficient higher. It causesthat local region temperature is higher. The 3D conjugate heat transfer solveradopted the B-L algebraic model. The calculation results of B-L algebra turbulencemodel showed that B-L model can simulate accurately turbine vane thermalenvironment without flow separation or with small flow separation. The results ofB-L model are more accurate than K- -SST- - turbulence model besides it hasa little temperature error in the suction side transition region. Simultaneously,turbine blade thermal stress results showed that the temperature distribution resulthas a great effect on the prediction of turbine blade thermal stress and life cycle,which can guide effectively the researcher to design the cooling structure of turbineblade.In addition, heat transfer coefficient experimental criteria were applied to theconjugate heat transfer calculation of air-cooled turbine vane. Heat transfercoefficient experimental criteria consider the correction coefficient which based onthe different geometry and work conditions of air-cooled turbine vane inner-coolingchannels. The paper analyzed the effect of different heat transfer coefficientexperimental criteria on conjugate heat transfer calculation results. At the same time,the paper also analyzed the prediction ability of the different turbulence models forturbine flow and heat transfer course when the air-cooled turbine vane inner-cooling channels adopted and not adopted the heat transfer coefficient experimentalcriteria. The results showed that the conjugate heat transfer calculation of turbineblade cooling channels or cooling holes which adopted the heat transfer coefficientexperimental criteria can get the accurate turbine flow field and temperature fielddistribution. This method avoids the solution process of turbine vane coolingchannels and makes the different turbulence models simulate single the turbinecascade main flow region. Thus this method avoids the accumulative error of multi-zone flow field calculation and saves the calculation time.Finally, using conjugate heat transfer solver, this paper set up the fullconjugate optimization design system for air-cooled turbine vane cooling structure.The analysis involved the optimization of location, size and coolant mass flow often internal cooling passages of NASA-MarkII air-cooled turbine vane. The optimization objectives included the maximum temperature, the averagetemperature and coolant mass flow. In order to meet the optimal solution, multi-objective function was transformed into a single objective function through a formof weighted sum of particular criteria. Owe to the BEM which was employed tosolve the solid region heat transfer problem, the full conjugate optimizationcalculation time was saved. In the optimization process the BEM avoided therepeated generation and calculation work of solid region grid. At the same time, itavoided the Interpolation error between solid region grid and fluid region grid andimproved the optimize efficiency and solution accuracy. The optimization resultsshowed that the full conjugate optimization calculation decreased the maximumtemperature and saved the coolant mass flow. The average temperature increased,but the amplitude was very small. In addition, optimization calculation decreasedthe effect of entrance on cooling channels heat transfer and reduced radialtemperature gradient of turbine blade.

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