基于流体子域法的带隔板矩形截面渡槽动力学特性研究

发布时间：2018-05-10 22:33

本文选题：流-固耦合 + 流体晃动　；参考：《南京工业大学》2015年硕士论文

【摘要】：渡槽是工程中常用的水工建筑物,主要用于输水、排水和通航,渡槽内流体的晃动对结构的安全性有重大的影响。实际工程中,在储液系统中安装防晃板是一种即经济又有效的方法,不仅可以抑制流体的晃动,还能增加结构的刚度,提高其抗震性能。因此,研究带隔板矩形截面渡槽内流体的动力学问题很有必要。本文基于势流理论,采用半解析法解决了单边带隔板和两边带隔板矩形截面渡槽内流体的动力学特性问题。本文首先介绍了带隔板的矩形截面渡槽内流体晃动特性的求解方法-流体子域法。通过引入人工边界,将复杂的流体子域沿隔板划分成若干具有简单边界条件的子域,再将子域的边界条件进行分解,使每组边界条件中只含有一个非齐次边界。利用分离变量法和叠加原理求解出每个子域含有待定系数的速度势函数的一般解。将速度势函数代入子域交界面上速度连续条件、压力连续条件和液体自由表面方程即可得到频率方程,利用Fourier级数将频率方程展开成齐次方程组,求解这个方程组即得到渡槽内流体的晃动特性。利用此方法分别求解了单边带隔板和两边带隔板矩形截面渡槽内液体的自由晃动特性,通过收敛性和比较研究证明本文方法的正确性,并且详细分析了隔板的参数对晃动特性的影响。在此基础上,本文解决了水平激励下单边带隔板的矩形截面渡槽内流体晃动响应问题。首先证明渡槽内流体自由晃动模态的正交性,再根据线性叠加原理,可将流体的速度势函数分解成两个部分:刚体速度势和摄动速度势。分别求解这两个速度势函数,通过子域的边界条件可以设出刚体速度势函数。利用模态叠加法,引入广义的时间坐标,设出以时间为变量的摄动速度势函数。将速度势函数代入子域交界面上速度连续条件、压力连续条件和自由液面方程即可得到动力响应方程。利用模态的正交性,将响应方程解耦成单自由度动力响应方程组,运用杜哈梅积分可以求解出晃动响应的解析解。建立二维ADINA有限元模型,将瞬态响应下的解析解与数值模拟结果进行对比,验证本文方法的正确性,并且详细分析了隔板参数对晃动响应的影响。本文的创新点在于采用流体子域法对复杂边界进行处理,得到带隔板矩形截面渡槽的动力学特性的高精度解。该方法程序编制简单,结果精度高,具有很强的实用性。通过算例分析,得到以下主要结论:(1)单边带隔板矩形渡槽的固有晃动频率随隔板长度的增加而减小,随隔板位置的升高而减小;隔板越接近液面,隔板长度对振型的影响越大;隔板越长,隔板上部液体的速度势越大;(2)两边带隔板矩形渡槽隔板对称布置与不对称布置相比,当隔板总长度相同时,隔板布置在同一个高度隔板,对称布置对频率影响更大,并且频率降低的更多;(3)简谐激励作用下,最大波高、基底剪力、倾覆弯矩幅值都随着隔板位置的增加单调减小,隔板越长,幅值越小;随着隔板长度的增加单调减小,且隔板越高,幅值越小;(4)对于某一个固定的地震激励,可以通过隔板位置和隔板长度的优化使得基底剪力和倾覆弯矩的幅值最小,这便为防晃板的优化设计提供了理论依据。
[Abstract]:Aqueduct is a commonly used hydraulic structure in engineering, which is mainly used for water transportation, drainage and navigation. The sloshing of fluid in the aqueduct has a great influence on the safety of the structure. In practical engineering, it is an economical and effective method to install anti sloshing plate in the liquid storage system. It can not only suppress the sloshing of the fluid, but also increase the stiffness of the structure and improve its structure. Therefore, it is necessary to study the dynamic problem of the fluid in a rectangular cross section aqueduct with a diaphragm. Based on the potential flow theory, a semi analytical method is used to solve the hydrodynamic characteristics of the internal fluid in a rectangular cross plate and rectangular cross plate aqueduct with two sides. First, the fluid sloshing in a rectangular cross section aqueduct with a baffle plate is introduced. By introducing artificial boundary, the complex fluid subdomains are divided into several subdomains with simple boundary conditions by introducing artificial boundaries, and then the boundary conditions of the subdomains are decomposed to make only one non homogeneous boundary in each boundary condition. Each subdomain is solved by the separation of variable method and the superposition principle. The general solution of the velocity potential function with the undetermined coefficient is replaced by the velocity potential function into the velocity continuum on the subdomain interface. The frequency equation can be obtained by the pressure continuity condition and the liquid free surface equation. The frequency equation is expanded into a homogeneous equation by Fourier series, and the sloshing characteristics of the fluid in the aqueduct are obtained by solving the equation. This method is used to solve the free sloshing characteristics of the liquid in the rectangular cross plate and the rectangular cross section aqueduct with both sides. Through the convergence and comparison, the correctness of the method is proved, and the influence of the parameters of the baffle on the sloshing characteristics is analyzed in detail. On this basis, this paper solves the single side baffle under the horizontal excitation. The problem of fluid sloshing in a rectangular cross section aqueduct is given. First, the orthogonality of the free sloshing mode of the fluid in the aqueduct is proved. Then, according to the linear superposition principle, the velocity potential function of the fluid can be decomposed into two parts: the velocity potential of the rigid body and the perturbed velocity potential. The two velocity potential functions are solved respectively, and the stiffness of the boundary conditions of the subdomain can be set out. The velocity potential function of the body velocity potential. By using the modal superposition method and introducing the generalized time coordinate, the perturbation velocity potential function with time variable is set up. The velocity potential function is replaced by the velocity continuous condition on the subdomain interface. The dynamic response equation can be obtained by the pressure continuity condition and the free liquid surface equation. The response equation is decoupled by the orthogonality of the modal. The dynamic response equations of single degree of freedom can be used to solve the analytical solution of the sloshing response by using the dukhami integral. A two-dimensional ADINA finite element model is established to compare the analytical solutions of the transient response with the numerical simulation results to verify the correctness of the method, and the influence of the septum parameters on the sloshing response is analyzed in detail. The innovation point of this paper is in this paper. The high precision solution of the dynamic characteristics of the rectangular cross section aqueduct with diaphragm is obtained by using the fluid subdomain method. The procedure is simple, the result is high, and it is practical. The following main conclusions are obtained by an example: (1) the natural sloshing frequency of the rectangular aqueduct with a single side baffle plate is long with the length of the baffle plate. It decreases with the increase of the degree of the partition, and decreases with the elevation of the partition position; the closer the partition board to the liquid surface, the greater the effect of the partition length on the vibration mode; the longer the partition board, the greater the velocity potential of the liquid in the upper baffle; (2) the partition plate is arranged at the same height, when the length of the partition is the same, when the length of the diaphragm is the same. The symmetrical arrangement has more influence on the frequency and more frequency. (3) under the effect of simple harmonic excitation, the maximum wave height, base shear, and the amplitude of the overturning moment decrease monotonically with the increase of the partition position, the longer the partition board, the smaller the amplitude; the higher the partition plate, the smaller the partition board, and (4) for a certain fixation. The earthquake excitation can minimize the amplitude of the base shear and the overturning moment through the optimization of the partition position and the length of the baffle plate, which provides a theoretical basis for the optimization of the anti sway plate.

【学位授予单位】：南京工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TV672.3;TV135.3

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