【摘要】：隨著現(xiàn)代流動(dòng)測(cè)試技術(shù)及流動(dòng)計(jì)算技術(shù)的發(fā)展,離心泵內(nèi)流動(dòng)結(jié)構(gòu)及性能優(yōu)化是目前水力研究的熱點(diǎn),也取得了眾多研究成果。但是對(duì)離心泵的反問題及其優(yōu)化研究進(jìn)展緩慢,主要原因在于離心泵水力性能與內(nèi)流道形狀之間復(fù)雜的隱式關(guān)系。目前對(duì)于離心泵的水力優(yōu)化方法主要包括基于演化算法的優(yōu)化方法、基于梯度算法的優(yōu)化方法、基于試驗(yàn)設(shè)計(jì)響應(yīng)面優(yōu)化方法等。基于演化算法及響應(yīng)面方法的離心泵優(yōu)化方法中,必須對(duì)每個(gè)樣本進(jìn)行目標(biāo)函數(shù)的預(yù)估,設(shè)計(jì)變量維數(shù)較大時(shí),要多次計(jì)算流場(chǎng),計(jì)算量巨大�；谔荻葍�(yōu)化方法的主要困難在于目標(biāo)函數(shù)對(duì)設(shè)計(jì)變量的梯度矢量難以計(jì)算,計(jì)算量隨設(shè)計(jì)變量的維數(shù)增大呈幾何級(jí)數(shù)增大。隨著流動(dòng)理論的發(fā)展,伴隨方法被廣泛應(yīng)用于流動(dòng)的優(yōu)化控制,A.Jameson提出采用伴隨方法應(yīng)用于航空翼型的優(yōu)化,該方法能在求解具有流動(dòng)約束問題的目標(biāo)函數(shù)對(duì)控制變量的梯度時(shí)大大減小計(jì)算量。本研究提出采用伴隨方法對(duì)離心泵進(jìn)行反問題的優(yōu)化研究。具體研究?jī)?nèi)容包括以下幾個(gè)方面： 1.應(yīng)用伴隨方法進(jìn)行了離心泵葉輪水力反設(shè)計(jì)研究。推導(dǎo)了伴隨方程及邊界條件的數(shù)學(xué)表達(dá)形式,推導(dǎo)了最終目標(biāo)函數(shù)梯度矢量表達(dá)公式及數(shù)值求解方法,流場(chǎng)采用雷諾時(shí)均納維-斯托克斯方程(Reynolds-averaged Navier-Stokes equations,RANS)求解,伴隨變量場(chǎng)采用基于三維Euler方程的伴隨方程求解。通過網(wǎng)格生成,流場(chǎng)計(jì)算,伴隨方程的數(shù)值求解,最終目標(biāo)函數(shù)的梯度矢量求解,葉片骨線更新程序及優(yōu)化算法等的有效結(jié)合,成功地發(fā)展了離心泵三維葉輪的水力反設(shè)計(jì)。 2.詳細(xì)推導(dǎo)了離心泵的反問題及其優(yōu)化過程中所涉及變量的數(shù)學(xué)表達(dá)以及Comsol Multiphysics中系數(shù)型偏微分方程中各系數(shù)與伴隨方程系數(shù)的一一對(duì)應(yīng)關(guān)系,并建立了各自邊界條件。 3.研究了基于伴隨方法和三維Navier-Stokes方程的優(yōu)化設(shè)計(jì)理論,在笛卡爾坐標(biāo)下詳細(xì)推導(dǎo)了該優(yōu)化設(shè)計(jì)理論,得到了笛卡爾坐標(biāo)系下伴隨方程的數(shù)學(xué)描述形式,并結(jié)合給定的目標(biāo)函數(shù),推導(dǎo)了相應(yīng)的伴隨方程邊界條件,以及關(guān)鍵的目標(biāo)函數(shù)的最終梯度表達(dá)。 4.伴隨方法求解的伴隨變量場(chǎng)是基于離心泵模型CFD結(jié)果的耦合,本論文采用Comsol Multiphysics多物理場(chǎng)耦合軟件進(jìn)行了流場(chǎng)與伴隨變量場(chǎng)的計(jì)算與結(jié)果的耦合,對(duì)以上兩場(chǎng)結(jié)果應(yīng)用MATLAB軟件編制葉輪葉片骨線更新程序,程序穩(wěn)定可行,并且經(jīng)過適當(dāng)修改還可用于其他的目標(biāo)函數(shù)優(yōu)化設(shè)計(jì)。 5.以設(shè)計(jì)工況點(diǎn)的流量Q、揚(yáng)程H所對(duì)應(yīng)的的效率作為優(yōu)化目標(biāo),由于優(yōu)化過程中揚(yáng)程H的變化較小,將作用在葉輪上的扭矩作為優(yōu)化目標(biāo)函數(shù),以給定的直葉片為初始葉型,應(yīng)用伴隨方法得到了目標(biāo)函數(shù)變分對(duì)控制變量的梯度表達(dá),沿著目標(biāo)函數(shù)變分對(duì)控制變量的梯度矢量的負(fù)梯度方向更新葉片形狀,逐步尋優(yōu),最終找到目標(biāo)函數(shù)取最小值時(shí)的最優(yōu)設(shè)計(jì)。此時(shí),模型離心泵的揚(yáng)程,效率和扭矩趨于穩(wěn)定,表明該算法已經(jīng)收斂。算例計(jì)算結(jié)果表明提出的伴隨方法應(yīng)用于低比轉(zhuǎn)速離心泵的葉輪優(yōu)化設(shè)計(jì)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.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TH311

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