Study On The Dynamic Characteristic Of The Liquid-filled Rectangular Aqueduct Equipped With Annular Baffles Using The Fluid Sub-domain Method

The aqueduct which is widely used for water conveyance and navigation, is common equipment in hydraulic structures. The liquid sloshing has a great impact on the structure safety. The use of internal baffles is considered to be a common technique to reduce the liquid sloshing. Therefore, it is necessary to study on the dynamic problems of stratified fluid in the rectangular aqueduct. Based on the potential flow theory, the paper solved these problems by a semi-analytical method.Firstly, the method of solving sloshing characteristics problems of rectangular aqueduct equipped with rigid baffles was introduced. The complicated liquid domain is divided into several simple sub-domains. The velocity potential function with unknown coefficients was gained by method of separation of variables and superposition principle. Taking the velocity potential function into the free surface condition and the artificial interface conditions, the eigen-frequency equation was established by the Fourier series expansions. Solve the equation to get the liquid sloshing characteristics in the rectangular aqueduct. Stable and fast numerical computations are observed by the convergence study. The influences of the parameters of baffles are expounded in detail.Secondly, the semi-analytical solution for sloshing responses of stratified liquid in rectangular aqueduct with rigid baffles was provided. The orthogonality among the modes of liquid velocity potential is demonstrated. Separate the fluid domain into several sub-domains along the location of the baffles. Based on the superposition principle, the total velocity potential function of forced vibration was considered to be the sum of the rigid part and the liquid perturbed part. The rigid potential was obtained by non-homogeneous boundary condition. And the liquid perturbed potential of every sub-domain was expressed at the generalized coordinates with unknown coefficients about time variables. According to continuity conditions of velocity and pressure of liquid at interfaces as well as the free surface wave condition, the dynamic response equation group was established by the orthogonality of generalized coordinates to the sloshing responses of stratified liquid. Establishing two-dimensional finite element model of ADINA and comparing the analytical solution to numerical simulate solution that proves the method of this paper is accurate. Finally, the surface wave height, hydrodynamic pressure distribution, resultant hydrodynamic force and moment subjected to harmonic and seismic lateral excitations are discussed in detail.The innovation point of this paper lies in using the fluid sub-domain method to deal with complicated boundary conditions to obtain the high precision solution about dynamic problems of stratified fluid in rectangular aqueduct with rigid baffles. The present method is general and simple in programming. The results have a high precision. According to the example analyses, the following main conclusions were illustrated:(1) The sloshing frequencies of the rectangular aqueduct with baffles reduce with the height of the baffles increasing. And the sloshing frequencies of the rectangular aqueduct with baffles reduce with the height of the baffles increasing. The closer the baffle approaches the liquid surface, the greater influence the length of the baffle has on the vibration modes. The longer the baffle is, the larger the velocity potential function of the liquid which is in the upper part of the baffle is.(2) Compared the symmetric arrangement with the asymmetric arrangement of the partition on both sides of the aqueduct, when the total length of baffle are the same and the partition arranged at the same height, the symmetric arrangement have more influence on the frequency and the reduction of frequency is more.(3) The maximum values of the surface wave height, base shear force and overturning moment for the rectangular aqueduct subjected to lateral harmonic excitation reduce with the baffle’s height increasing. While The maximum values of the surface wave height, base shear force and overturning moment subjected reduce with the length of the baffle increasing.(4) For one certain fixed seismic excitation, the optimization of the baffle’s location and the baffle’s length can make the amplitude of base shear force and overturning moment minimum, this provides theory basis for the optimization design of baffles.