基于伴随方法的离心泵叶轮优化研究

发布时间：2018-11-11 21:31

【摘要】：随着现代流动测试技术及流动计算技术的发展,离心泵内流动结构及性能优化是目前水力研究的热点,也取得了众多研究成果。但是对离心泵的反问题及其优化研究进展缓慢,主要原因在于离心泵水力性能与内流道形状之间复杂的隐式关系。目前对于离心泵的水力优化方法主要包括基于演化算法的优化方法、基于梯度算法的优化方法、基于试验设计响应面优化方法等。基于演化算法及响应面方法的离心泵优化方法中,必须对每个样本进行目标函数的预估,设计变量维数较大时,要多次计算流场,计算量巨大。基于梯度优化方法的主要困难在于目标函数对设计变量的梯度矢量难以计算,计算量随设计变量的维数增大呈几何级数增大。随着流动理论的发展,伴随方法被广泛应用于流动的优化控制,A.Jameson提出采用伴随方法应用于航空翼型的优化,该方法能在求解具有流动约束问题的目标函数对控制变量的梯度时大大减小计算量。本研究提出采用伴随方法对离心泵进行反问题的优化研究。具体研究内容包括以下几个方面： 1.应用伴随方法进行了离心泵叶轮水力反设计研究。推导了伴随方程及边界条件的数学表达形式,推导了最终目标函数梯度矢量表达公式及数值求解方法,流场采用雷诺时均纳维-斯托克斯方程(Reynolds-averaged Navier-Stokes equations,RANS)求解,伴随变量场采用基于三维Euler方程的伴随方程求解。通过网格生成,流场计算,伴随方程的数值求解,最终目标函数的梯度矢量求解,叶片骨线更新程序及优化算法等的有效结合,成功地发展了离心泵三维叶轮的水力反设计。 2.详细推导了离心泵的反问题及其优化过程中所涉及变量的数学表达以及Comsol Multiphysics中系数型偏微分方程中各系数与伴随方程系数的一一对应关系,并建立了各自边界条件。 3.研究了基于伴随方法和三维Navier-Stokes方程的优化设计理论,在笛卡尔坐标下详细推导了该优化设计理论,得到了笛卡尔坐标系下伴随方程的数学描述形式,并结合给定的目标函数,推导了相应的伴随方程边界条件,以及关键的目标函数的最终梯度表达。 4.伴随方法求解的伴随变量场是基于离心泵模型CFD结果的耦合,本论文采用Comsol Multiphysics多物理场耦合软件进行了流场与伴随变量场的计算与结果的耦合,对以上两场结果应用MATLAB软件编制叶轮叶片骨线更新程序,程序稳定可行,并且经过适当修改还可用于其他的目标函数优化设计。 5.以设计工况点的流量Q、扬程H所对应的的效率作为优化目标,由于优化过程中扬程H的变化较小,将作用在叶轮上的扭矩作为优化目标函数,以给定的直叶片为初始叶型,应用伴随方法得到了目标函数变分对控制变量的梯度表达,沿着目标函数变分对控制变量的梯度矢量的负梯度方向更新叶片形状,逐步寻优,最终找到目标函数取最小值时的最优设计。此时,模型离心泵的扬程,效率和扭矩趋于稳定,表明该算法已经收敛。算例计算结果表明提出的伴随方法应用于低比转速离心泵的叶轮优化设计方案是可行的。
[Abstract]:With the development of modern flow test technology and mobile computing technology, the flow structure and performance optimization in centrifugal pump are the hot spots of hydraulic research. However, the research progress of the inverse problem and the optimization of the centrifugal pump is slow, mainly because of the complex implicit relationship between the hydraulic performance and the internal flow channel shape of the centrifugal pump. At present, the hydraulic optimization method for the centrifugal pump mainly includes the optimization method based on the evolutionary algorithm, the optimization method based on the gradient algorithm, the optimization method based on the test design response surface, and the like. In a centrifugal pump optimization method based on the evolutionary algorithm and the response surface method, it is necessary to estimate the objective function for each sample, and to calculate the flow field many times when the number of variable dimensions is large, and the calculation amount is huge. The main difficulty of the gradient optimization method is that the objective function is difficult to calculate the gradient vector of the design variable, and the calculated amount increases with the number of dimensions of the design variable as the geometric series. With the development of the flow theory, the accompanying method is widely used in the optimization control of the flow, A. Jameson proposes to apply the adjoint method to the optimization of the aerofoils, and the method can greatly reduce the calculation amount when solving the gradient of the control variable with the objective function with the flow constraint problem. In this study, an optimization study on the inverse problem of centrifugal pump is presented in this paper. The specific study includes the following aspects: 1. The hydraulic anti-design of the impeller of the centrifugal pump is carried out with the accompanying method. In this paper, the mathematical expression of the adjoint equation and the boundary condition is derived, and the expression formula and the numerical solution of the final objective function gradient vector are derived. The Reynolds-averaged Navier-Stokes equations (RANS) are used in the flow field. The adjoint equation based on the three-dimensional Euler equation is used for solving the adjoint variable field The solution of the three-dimensional impeller of the centrifugal pump has been successfully developed by the effective combination of the mesh generation, the flow field calculation, the numerical solution of the adjoint equation, the gradient vector solution of the final target function, the blade bone line updating program and the optimization algorithm. 2. The inverse problem of the centrifugal pump and the mathematical expression of the variables involved in the optimization of the centrifugal pump and the one-to-one correspondence between the coefficients of the coefficient type partial differential equation and the coefficient of the adjoint equation are derived in detail. The optimal design theory based on the adjoint method and the three-dimensional Navier-Stokes equations is derived from the boundary conditions. The optimal design theory is derived in detail under the Cartesian coordinates, and the mathematical description form of the adjoint equation under the Cartesian coordinate system is obtained. In combination with a given objective function, the corresponding boundary condition of the adjoint equation and the key objective function are derived. The final gradient expression of the number is 4. The adjoint variable field, which is solved with the method, is the coupling of the CFD result based on the centrifugal pump model. The coupling between the flow field and the adjoint variable field is carried out by using the Cosol Multiphysics multi-physical field coupling software, and the MATLAB software is applied to the above two results. The impeller blade bone line update procedure, which is stable and feasible, can also be used for proper modification The optimization design of the other objective functions. 5. The efficiency of the flow Q and the head H at the design condition point is used as the optimization target, and the torque acting on the impeller is used as the optimization objective function due to the small variation of the head H in the optimization process. The method obtains the gradient expression of the variable of the target function and the gradient vector of the control variable along the target function, The design of the pump when the objective function takes the minimum value. At this time, the head, efficiency and torque of the model centrifugal pump The results of the calculation show that the proposed method is applied to the low-specific speed centrifugation.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TH311

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