Fuel Reserve Tanks Dynamic Analysis Due to Earthquake Loading

In this paper, the dynamic analysis of fuel storage tanks has been studied and some equations are presented for the created fluid waves due to storage tank motions. Also, the equations for finite elements of fluid and structure interactions, and boundary conditions dominant on structure and fluid, were researched. In this paper, a numerical simulation is performed for the dynamic analysis of a storage tank contained a fluid. This simulation has carried out by ANSYS software, using FSI solver (Fluid and Structure Interaction solver), and by considering the simulated fluid dynamic motions due to earthquake loading, based on velocities and movements of structure and fluid according to all boundary conditions dominant on structure and fluid. Keywords—fluid and structure interactions, finite element method, ANSYS – FSI I.INTRODUCTION YLINDRICAL layers with thin walls are widely being applied at different industries including storage tanks, silos, cooling towers, power plant reservoirs and so on. Thus, it is important to analyze such storage tanks from different views, and aspects. Among other subjects, storage tanks contained fluids as well as their interactions are of important issues in which researchers are interested. Given that the equations of fluid and structure interactions are nonlinear, analytical solutions aren’t often applied. Because by inserting inputs (entry data) in the equation to predict the interactions, the case becomes more complicated, therefore, numerical techniques are the only available procedures to achieve the accurate solutions. Based on studies by researchers, various solutions have been presented to conduct the dynamic analysis of fuel storage tanks. Among them, it can be mentioned the analysis of the finite elements of storage tank by Zinkovitch et. al [1]. Furthermore, this subject has many applications in industry, so a proper technique has been offered according to the current standard (such as API650) [2]. The design standard of API650 is based on displacing the fluid impacts on the storage tank walls with mass and spring, while this standard has a certain relationship between spring stiffness and the mass equivalent to height of fluid within the tank. This technique was suggested by Aaron and Hanzer for the first time [3]. 1 F.saadi. Author is with the Department of Mechanical ,Ahvaz Branch, Islamic Azad University, Ahvaz, IRAN (Phone:09161110171, EMail:[email protected]—[email protected]) 2 A.Aboudi Asl is with the National Iranian South Oil Company,Ahvaz, Iran (corresponding author to provide phone:0098-611-412-3937;fax:0098611-334-9405;E-Maile:[email protected]) This paper tried to investigate the required equations for evaluating fluid motions caused by tank pillar vibrations, then a numerical method has been presented to analyze the case by using ANSYS software, finally the obtained results have been compared with the results produced by the standard. II. THEORETICAL DISCUSSIONS By considering a cylindrical tank in fig. (1), and assuming that there is an ideal fluid within the storage tank, the boundaries of 1 and 2 are common to fluid and structure areas so the following expression is established: n f u n & = ∇ . φ (1) Where ф is velocity potential function, n is single vector perpendicular to on fluid area and û is wall velocity. If we want to show this expression based on acceleration and pressure, then we have; n u n P & & ρ − = ∂ ∂ (2) also, for area 3 as a fluid free surface, at first it is assumed P=0 for simplification. But this equation isn’t applied for every free surface gravity waves under different conditions, but considering the ratio of real level (height) of the fluid before earthquake to fluid level (height) after earthquake, “η” in figure (1), the pressure at that area will be P = ρ g η. As we know, equation of motion differential for a homogeneous substance with Cartesian coordinates, in the absence of any outside forces, is equal to: P t v ∇ = ∂ ∂ . ρ (3) Besides, if a wave height is defined “η”, the expression of t Vz ∂ ∂ = η is established, as well as by assuming that p value is constant, we will have: z P t ∂ ∂ − = ∂ ∂ 2 η ρ (4) F.Saadi,A.Aboudi Asl, Fuel Reserve Tanks Dynamic Analysis Due to Earthquake Loading C World Academy of Science, Engineering and Technology International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:5, No:6, 2011 1003 International Scholarly and Scientific Research & Innovation 5(6) 2011 scholar.waset.org/1999.8/954 In te rn at io na l S ci en ce I nd ex , M ec ha ni ca l a nd M ec ha tr on ic s E ng in ee ri ng V ol :5 , N o: 6, 2 01 1 w as et .o rg /P ub lic at io n/ 95 4 Now according to the above presentations, the following expression can be presented for fluid free surface: P g t P g z P & & 1 1 2 2 − = ∂ ∂ − = ∂ ∂ (5) A. Examining weakened version of fluid and structure interactions Now for all fluids, the weakened version of the fluid interactions can be stated as follow: ∫ Ω = ⎥⎦ ⎤ ⎢⎣ ⎡ ∇ + = f P P C P f 0 1 2 2 & & δ δπ (6) And if we want to indicate all areas (equations) defined in previous section (2-1) in weakened version, based on boundary conditions of the tanks, we will have: ∫ ∫ Ω Γ Γ + Ω ∂ ⎥⎦ ⎤ ⎢⎣ ⎡ ∇ ∇ + f d u Pn P P C P T T