Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.

Analysis of turbulence on cylinder with additional fairing with free surface

In this study, two dimensional unsteady flow of cylinder and cylinder with additional fairing close to a free surface was numerically investigated. The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE). The Volume of Fluid(VOF) method applied to simulate a free surface. Non- uniform grid structures were used in the simulation with denser grids near the cylinder. Under the conditions of Reynolds number 150624, 210874, 210874 and 331373, the cylinders were simulated with different depths of invasion. It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers. When the cylinder close to the free surface, the drag coefficient, lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding. With additional fairing, can effectively reduce the influence of the free surface on the drag coefficient. Fairing will reduce lift coefficient at high Reynolds numbers, but increase lift coefficient when Reynolds numbers is small. Fairing can effectively reduce Strouhal numbers, thus can well suppress the vortex induced vibration.

Study on the Predictive Evaluation Method of Load Acting on the Roof and Internal Components of Cylindrical Tanks by Nonlinear Sloshing

When cylindrical tanks installed in the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage of the tank roof or outflow of internal liquid of the Tank. Therefore, it is important to predict the wave height of sloshing generated by earthquake motions. Sloshing is a type of vibration of free liquid surface, and if the sloshing wave height is small, it can be approximated with a linear vibration model. In this case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under earthquake motions. However, if the sloshing wave height increases, the sloshing becomes nonlinear, and necessary to evaluate the wave height using other methods such as numerical analysis. Design earthquake magnitude levels in Japan tend to increase in recent years, long-period components of earthquake wave which act on the sloshing wave height also increase instead of introducing seismic isolation mechanisms. To evaluate load acting on the internal components of cylindrical tanks by nonlinear sloshing, there are few applications which quantitatively evaluated the crest impact load of nonlinear sloshing. In order to evaluate the load acting on the internal components of cylindrical tanks, the range of applicability of the fluid flow analysis method which validated the analysis accuracy of impact load acting on the roof in a simple cylindrical tank in the past study (PVP2019-93442) is extended to cylindrical tanks with internal components.