F uid pressures on unanchored rigid flat-bottom cylindrical tanks under action of uplifting acceleration
F uid pressures on unanchored rigid flat-bottom cylindrical tanks under action of uplifting acceleration
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上升加速度作用下无锚固刚性平底圆柱罐上的流体压力
DOI：
10.1115/1.4000374
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Y. Ando
中科院分区：
文献类型：
--
作者：
T. Taniguchi;Y. Ando
为了保护平底圆柱形储罐免受上提运动的严重破坏，必须准确评估伴随的流体压力。本文提出了一个数学解决方案，用于评估刚性平底圆柱形储罐上的流体压力，其方式与作者先前概述和讨论的程序相同（Taniguchi，T.，和Ando，Y.，2010年，“在抬升加速度作用下非锚固刚性矩形储罐上的流体压力”，ASME J.压力容器技术，132（1），第011801页）。在假设理想流体和速度势的情况下，柱坐标中的拉普拉斯方程给出了连续性方程，而由罐的壳体和底板的位移（及其时间导数）赋予的流体速度定义了边界条件。速度势用傅里叶-贝塞尔展开法求解，其对时间的导数给出罐内任意点的流体压力。实际上，设计者必须计算罐上的流体压力，罐的底板的周边在平面图中像新月一样离开地面。然而，不对称的边界条件所给予的流体速度所赋予的变形的新月形隆起区在底部不能适当地表示在圆柱坐标。本文探讨了切片模型的适用性，这是一个刚性的矩形罐的单位深度垂直切出一个刚性平底圆柱形罐与一定的偏差（平行）的中心线的罐。本文给出了一个求解刚性平底圆柱形贮箱上流体压力的数学解，该压力随贮箱转动底边上的角加速度变化，其形式为贮箱尺寸变量的显函数，但采用傅里叶级数。它很好地收敛于傅里叶级数的几个第一项，并准确地计算了储罐上的流体压力值。此外，对于偏离中心线的任意点，切片模型都能很好地逼近作用在刚性平底圆柱形贮箱壳体上的流体压力值。为了设计者的方便，还提供了描绘由最大切向加速度归一化的流体压力的图表，所述最大切向加速度由角加速度和罐的对角线的乘积给出。建议的数学和图形的方法是成本有效的，并在平底圆柱形罐，允许提升的底板的设计援助。
To protect flat-bottom cylindrical tanks against severe damage from uplift motion, accurate evaluation of accompanying fluid pressures is indispensable. This paper presents a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank in the same manner as the procedure outlined and discussed previously by the authors (Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801). With perfect fluid and velocity potential assumed, the Laplace equation in cylindrical coordinates gives a continuity equation, while fluid velocity imparted by the displacement (and its time derivatives) of the shell and bottom plate of the tank defines boundary conditions. The velocity potential is solved with the Fourier–Bessel expansion, and its derivative, with respect to time, gives the fluid pressure at an arbitrary point inside the tank. In practice, designers have to calculate the fluid pressure on the tank whose perimeter of the bottom plate lifts off the ground like a crescent in plan view. However, the asymmetric boundary condition given by the fluid velocity imparted by the deformation of the crescent-like uplift region at the bottom cannot be expressed properly in cylindrical coordinates. This paper examines applicability of a slice model, which is a rigid rectangular tank with a unit depth vertically sliced out of a rigid flat-bottom cylindrical tank with a certain deviation from (in parallel to) the center line of the tank. A mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with Fourier series. It well converges with a few first terms of the Fourier series and accurately calculates the values of the fluid pressure on the tank. In addition, the slice model approximates well the values of the fluid pressure on the shell of a rigid flat-bottom cylindrical tank for any points deviated from the center line. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. The proposed mathematical and graphical methods are cost effective and aid in the design of the flat-bottom cylindrical tanks that allow the uplifting of the bottom plate.