摘要
航空工业的发展趋势要求发动机具备更高的涡轮入口温度，提高涡轮入口温度对叶片的热防护提出了更高的要求，因此需要设计复杂的冷却结构来降低叶片的温度，而冷却结构的改型设计需要准确地预测叶片的温度，同时叶片的强度校核也需要计算高温及冷却不均形成的热应力，单纯的气动计算已经无法满足高性能设计的要求，因此全三维的气热弹多场耦合计算方法成为现代高性能发动机设计的必备工具。本文的工作主要是开发了全三维的基于非结构化网格的气热弹耦合计算程序，对其进行了实验、解析解验证，并将其应用在气冷涡轮的传热和强度分析中，并且对高精度的离散方法及多场耦合方法进行了研究。
首先推导了三维N-S方程的有限体积离散格式，介绍了MUSUL方法，及其线性重构求解梯度所采用的最小二乘法，为了保持稳定性采用了Venkatakrishnan限制器。给出了预处理方法的具体过程，及求解对流项的预处理AUSM+格式，详细推导了基于预处理方法的LU-SGS隐式时间推进方法。通过方腔流、无粘Bump流动及平板流动验证了三维程序计算的准确性及预处理方法的有效性，采用T3A、T3A-和S&K三个算例对转捩模型进行了验证。针对二维非结构化网格上高精度WENO格式线性权的负值问题，提出了一种求最优线性权的方法，建立了求解的具体数学模型，通过前台阶绕流和双马赫反射问题验证了程序在处理间断问题时的敏感性和稳定性。
然后研究了固体场的求解方法，采用有限体积法求解了导热方程，采用全隐式的求解方法，具有较高的计算效率。采用加权最小二乘法构造了高精度的梯度计算方法，通过与解析解的对比验证了该方法有效地提高了导热计算的精度。采用高精度的有限元方法求解了热弹耦合问题，介绍了有限元离散方程建立的具体过程及求解方法。通过有限长圆筒的解析解对程序的精度进行了验证，结果表明，本文的有限元程序整体精度很高，在给定精确温度解的条件下，计算的位移和解析解吻合很好，误差在1%的范围。计算的轴向、周向和径向应力与解析解基本吻合。并以某燃气轮机涡轮叶片为例，将程序计算的温度、热变形和热应力与商业软件ACE的计算结果进行对比，验证了程序的精度及对复杂模型的适用性。
最后将多物理场的求解方法按照不同的耦合方式耦合开发了气热弹耦合计算程序，气热部分采用双向耦合，热弹采用单向耦合。将面积加权类的插值方法应用在交界面的数据传递上，通过与精确解的对比验证了插值程序的精度。对C3X的4521工况进行了气热耦合计算，并与其传热实验进行对比，验证了气热耦合计算的精度，计算得温度和换热系数与实验值吻合较好。通过MARKIⅡ的4311和5411号实验工况，研究了转捩对传热计算的影响，可以看出，采用转捩模型后能够提高层流区和转捩区传热计算的精度。转捩模型对压力的影响很小，对于存在激波和边界层干扰的区域，传热计算仍存在较大误差。在已有程序HIT-3D的基础上验证了气热耦合及湍流模型对温度计算的影响，结果表明，耦合壁面的温度要比绝热壁面的温度低大约30%，BL模型计算的转捩区温度与实验值相差10%，q-ω模型、BL加AGS转捩模型、SST-Gama模型计算的温度与实验结果的差值在5%以内，计算的精度相对较高。应用热弹计算程序对MARKⅡ叶片和某低压涡轮导叶传热分析的结果进行了热弹分析，证明了采用转捩模型有助于更加准确地验证涡轮叶片的安全可靠性。最后应用气热弹耦合平台对某低压涡轮导叶进行了气热弹多场耦合计算，研究了其转捩流动特性以及传热特性，分析了局部高温区的分部及最大应力集中位置，为冷却结构的改型提供了依据，同商业软件对比验证了程序计算的准确性，虽然存在由过约束导致的应力超常现象，但是可以利用应力的分布趋势来辅助进行叶片的改型和优化。
The development of aviation industry requires better performance of turbine engines, mainly including two important parameters: efficiency and thrust-weight ratio. Since the inlet temperature plays a critical role in turbine efficiency, the temperature needs to be increased in order to elevate turbine efficiency. However, the increase of inlet temperature requires effective thermal protection method. Also, the accurate prediction of temperature of air-cooled turbine blade becomes more important to the optimization of cooling structure and prediction of safety and stability of blade. Along with the progress of computer science, the conjugate heat transfer simulation (CHT) has become an important tool to predict blade temperature. Due to the contact between high temperature gas and coolant, great temperature gradient would exist in blade. The uneven temperature distribution and thermal expansion under constraint will produce large thermal stress and deformation, which will lower the life span of blade, even damage blade. Thus, to ensure safety and stability of blade, it is necessary to take into account of thermal-elastic coupling simulation. The main task of this paper includes the development of a full three-dimension (3D) thermal-flow-elastic coupling self-programming code based on unstructured mesh, the application of this code in heat transfer and strength analysis in air-cooled turbine, and the investigation on high order accuracy discrete method and multiphysical fields coupling method.
First, the finite volume method (FVM) discrete format of3D Navier-Stokes (NS) equations is derived. The MUSUL method is introduced. The least-squares method is used to compute gradients. Venkatakrishnan limiter is used to guarantee stability. For the negative value of linear weight of high order WENO on unstructured meshes, a technique of solving optimal linear weight is presented; and detailed mathematical model is established. Through front step flow and double Mach reflection cases, the code’s stability and sensibility of processing discontinuities was verified. The detailed progress of preconditioning and AUSM+format for solving convective terms were presented. The detailed implicit LU-SGS method based on preconditioning was derived. Through cavity flow, inviscid bump flow and plate flow, the code’s accuracy of calculating convective flux and viscid flux was verified. T3A、T3A-and S&K cases were used to verify transition model. For negative value of high-order WENO linear weight on two-dimension (2D) unstructured mesh, a solving method of optimal linear weight was proposed; and detailed solving mathematical model was established. Through front-ward step flow and double Mach reflection cases, the sensitiveness and stability of the code to solve discontinuity problem were verified.
Second, solving method of solid field was investigated; and FVM was used to solve heat conduction equation. The full implicit solving method was used, which has relatively high calculation efficiency. The weighted least-squares method was used to construct a high order accuracy solving method of gradient. Analytic solutions were used to verify that the effective improvement of the heat transfer calculation. High order accuracy FEM was used to solve thermal-elastic problems. The detailed process and solving method of establishing FEM discrete equation were introduced. The code was verified by analytic solutions of thermal stress produced by thermal expansion of a finite length cylinder. The result shows that the general accuracy of the FEM code is very high. Under given accurate temperature solution, the calculated displacement agrees well with the analytic solution; and the error is around1%. The calculated axial, circumferential, and radial stress are in good agreement with analytic solutions. And a low-pressure turbine guide vane was used as a case to compare the calculated temperature, thermal deformation and thermal stress with the result of a commercial program ACE. The accuracy and adaptation of complex model of this code was verified.
Finally, a thermal-flow-elastic coupling simulation code, which is used to solve multiphysical fields, was developed by different coupling methods. The CHT part is bidirectional coupling. The thermal-elastic part is undirectional coupling. The area-weighted interpolation method was used on the data transfer at interface. Through comparison with given accurate solutions, the accuracy of the interpolation code was verified. CHT simulation was conducted on C3X4521case; and the result was compared with heat transfer experimental data. The CHT simulation accuracy was verified; and the calculated heat transfer coefficient agrees well with experimental data. From MARKⅡ4311and5411operating cases, the effect of transition on heat transfer was investigated. From the comparison, it can be noted that the transition model can improve the heat transfer simulation accuracy in laminar region and transition region. The effect of transition on pressure is slight. For the region where shock interacts with boundary layer, the heat transfer simulation is still not accurate. Under the basis of an existing code HIT-3D, the effect of CHT and transition model on temperature calculation was verified. The result shows the wall temperature of CHT is30%lower than that of adiabatic wall. The error of temperature in transition region between BL and experimental data is10%. The error between calculated temperature of q-ω model、BL+AGS transition model and SST-Gama model and experimental data is5%. The calculation accuracy is relatively high. The thermal-elastic analysis of heat transfer results of MARKⅡ vane and a low-pressure turbine vane was conducted. It proves that transition model can help verify the safety and stability of turbine blade more accurately. Last, thermal-flow-elastic multiphysical coupling simulation of a low-pressure turbine vane was conducted by using the thermal-flow-elastic coupling platform. The transition flow and heat transfer characteristics were studied; and the high temperature partial zone and largest stress concentration position were analyzed. These give help of remodeling cooling structure. The accuracy of the result of the code was verified by comparing with commercial code. Although the supernormal stress phenomenon induced by over constraints exists, the stress distribution trend can still be used to help remodel and optimize blade profile.
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