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本文应用控制理论,采用提出的基于网格节点位置坐标直接变分法,研究建立了一般性优化问题的伴随系统,研究发展了基于控制理论的轴流式透平叶栅气动反设计优化方法与系统.该伴随系统的推导过程以尽可能的减少计算资源为宗旨,应用分部积分公式和连续伴随方法,最终得到的目标泛函变分的表达式中仅仅含有网格坐标变分的边界积分项,避免了梯度计算过程中网格内部节点的重复生成,相对于传统的伴随方法更进一步节省了计算资源.伴随系统的数值求解采用ROE格式近似黎曼通量和显式五步龙格-库塔时间推进法,并使用多重网格技术和当地时间步长加速收敛.为验证本文伴随系统的稳定性、通用性、收敛性和精确性,通过定义不同的目标函数进行了考核,研究结果表明,本文所研发的伴随系统和反设计优化系统具有优秀的鲁棒性和高效性,能够有效应用于轴流式透平叶栅气动反设计优化中.在此基础上,结合本文所研究的气动优化理论,建立了应用Euler方程和N-S方程的伴随方法叶栅气动反设计优化方法与系统,研发了轴流式叶栅的二维、三维无黏及黏性条件下的压力反设计、等熵马赫数反设计软件,成功进行了数值算例研究,验证了该优化系统的有效性和经济性.
In this paper, by using the control theory and the proposed direct variation method based on the location coordinates of grid nodes, the concomitant system of general optimization problems is established. The optimization method of aerodynamic reverse design of the axial turbine blade cascade based on the control theory and System.The derivation process of this concomitant system aims at reducing the computational resources as much as possible, applying the integral integral formula and the continuous adjoint method, the final target functional variational expression contains only the boundary integral of the grid coordinate variational Which avoids the repeated generation of nodes inside the grid during the gradient calculation process and further saves the computational resources compared with the traditional method of accompaniment.The numerical solution of the system with the ROE format approximates the Riemann flux and the explicit five-step Runge- Kuta time-propulsion method, and use the multi-grid technique and local time step to accelerate the convergence.In order to verify the stability, universality, convergence and accuracy of the system, we define the different objective function and evaluate the results. It shows that the concomitant system and reverse design optimization system developed in this paper have excellent robustness and high efficiency and can be effectively applied to the shaft On the basis of this, combined with the aerodynamic optimization theory studied in this paper, the concomitant method of Euler equations and NS equations was established to optimize the aerodynamic design of cascade airfoils, Flow Cascade two-dimensional, three-dimensional non-sticky and viscous pressure under the conditions of anti-design, isentropic Mach number of anti-design software, the successful numerical examples of research to verify the effectiveness and economy of the optimization system.