拓扑优化技术在抑制流体晃荡中的数值模拟研究

流体晃荡问题广泛存在于船舶与海洋工程领域,任何部分载液的储罐运载装备在运动过程中均存在晃荡问题.当外界激励频率接近液舱内流体自由液面的固有频率时,很容易产生剧烈的晃荡,产生极大的冲击力,进而引起结构损害.因此,研究有效的减晃方案,以抑制流体晃荡带来的冲击具有重要意义.该文研究了基于自主研制的数值程序模拟长方体液舱内的流...     

A circulating gravity wave in a cylindrical tank

A circular cylindrical vertical tank is partially filled with a liquid (Water) and a gas (air) above it. The top lid of the container rotates around the cylinder axis and induces a flow in the gas and the liquid. Above a critical rotational speed a large amplitude circulating gravity wave forms. The two phase flow problem will be reduced to a free surface single phase flow problem and the critical parameters, when the axis-symmetric flow becomes unstable with respect to the circulating gravity wave will be determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sequential Estimation of the Maximum in a Model for Corrosion Data

One method of monitoring corrosion in an underground storage tank involves placing a sensor in the tank and running it around the tank's interior. As it runs, the sensor records the local thickness of the tank. In this paper we consider the problem of estimating the maximum pit depth by providing a confidence interval that achieves both a specified confidence level and a specified degree of precision. A particular model, the three-parameter beta, is considered, and a stopping rule for determining the sample size is proposed. It is shown that the stopping rule achieves the desired confidence level and precision, asymptotically as the precision requirement becomes increasingly stringent. Moreover, the stopping rule is asymptotically efficient in terms of sample size. The limiting distribution of the stopping rule is derived, and simulation results are presented to supplement the asymptotics with finite sample size behavior.     

基于TNT当量法的储罐内爆压力简化计算与应力分析

以立式拱顶储罐为研究对象,综合考虑储罐内气体容积与几何结构的影响:依据TNT当量法推导了内爆载荷下储罐超压计算公式并计算得到了储罐内不同起爆点下的超压分布曲线.当起爆点在储罐中轴线时,罐顶或罐底压力约为相反侧的6倍;当起爆点在靠近罐壁一侧时,靠近爆炸点一侧的罐顶或罐底压力约为相反侧的30倍.最后,通过储罐内爆载荷下的动力学仿真计算,对储罐在不同起爆点和不同液位的破坏情况进行了评定.有限元计算结果表明:储罐在操作过程中应控制其液位在半罐以上,可保证在任意起爆点位置罐顶均先与罐底发生破坏.     

水塔水流量问题的广义线性回归解法

对估计水塔的水流量问题,给出一种直接对水位进行估计的广义线性回归解法,克服了由于加水过程带来的水位数据跳跃式变化的困难,同时又避免了由水位数据估计水流量产生的误差.     

Cylindrical Tank Filled With a Liquid in a Three-Dimensional Temperature Field

In the cylindrical coordinate system, we construct an exact solution of the threedimensional thermoelasticity problem for a tank filled with a liquid. After determining the temperature field from the heat conduction equation, we solve the equations of the asymmetrical problem of the theory of elasticity. In doing so, the system of resolving equations is reduced to four separate equations with respect to the displacements of the construction. Several exact solutions of boundary-value problems are found. The results are presented in the form of rather simple formulas.     

计及表面波的圆环形贮液容器的弯曲自由振动*

本文研究考虑表面波作用的圆环形贮液容器的弯曲自由振动问题,导出了贮液容器与液体耦联振动的振型函数和固有频率的精确计算公式,结果可借助于计算机求解.分析表明,水对容器的振动效应可等效于在内外环体上分别附着一不同的广义分布质量.     

Numerical modelling of the plane problem of the stress state of a tube immersed in a liquid

A numerical method for solving the plane problem of determining the stress state of a tube of arbitrary section immersed in a homogeneous incompressible liquid is proposed. The change from the boundary conditions for this problem to the boundary conditions for a biharmonic stress function is carried out, which enables the algorithm for solving boundary value problems in the case of a polyharmonic function developed earlier to be used to solve the problem under consideration. It is shown that the boundary conditions for doubly-connected domains contain three unknown constants. The conditions for finding these constants in a form that is convenient for the implementation of a numerical algorithm are obtained. Tubes with sections in the form of concentric, eccentric and elliptic rings are considered as examples.     

Analysis of fluid storage tanks including foundation-superstructure interaction

An analytical formulation is developed to predict the flexural behavior of a cylindrical liquid storage tank resting on an isotropic elastic soil medium, which is modelled as a half space. The interface between the plate foundation and the soil medium is considered to be smooth and continuous. The plate deflection function is assumed in the form of a power series expansion in terms of the radial coordinate. The procedure accounts for the interactions between the tank wall and the plate foundation, and between the plate foundation and the soil medium. The principle of minimum potential energy is used to evaluate the unknown coefficients appearing in the assumed power series expansion and also the unknown interacting forces at the tank wall-plate foundation junction. Any number of terms can be considered in the assumed deflection function. Analytical expressions are obtained for the plate foundation deflections and radial moment, the contact stress distribution, the tank wall displacements, and the tank wall stress resultants. The results obtained compare well with the finite element analysis of a similar problem. Results of a parametric study are also presented to demonstrate the effect of the various geometric and material parameters on the flexural behavior of the system.     

近海圆柱形贮液罐的振动特性

本文主要研究近海圆柱形贮液罐振动特性,这是个典型液-壳相互作用体系的研究课题.文中提出的解析法,将液、壳轴向模态位移用同一完备正交级数表示,使液、壳振型解耦合.同时将液、壳振型函数分解为一个一致收敛级数和另一线性多项式,解决了振型级数的收敛性和可微性.这样就得到对应于不同液深、任意边界条件、受约束的近海贮液罐的耦合固有频率的精确值和相应振型分布.     

An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth

A general series-type theoretical formulation based on the linearized potential theory, the method of separation of variables, and the translational addition theorem for cylindrical Bessel functions is developed to study three-dimensional natural sloshing in a partially filled horizontally-mounted circular cylindrical tank of finite span. Assuming time-harmonic variations, the potential solutions associated with the Symmetric/Antisymmetric (S/A) modes of free liquid surface oscillations are first analytically expanded as series of bounded spatial functions with unknown modal coefficients. The impenetrability conditions of the rigid end-plates along with the free surface dynamic/kinematic boundary condition are then imposed. The zero-normal-velocity requirement of the lateral tank boundary is subsequently applied by innovative use of Graf's translational addition theorem for modified cylindrical Bessel functions. After truncation, four independent sets of homogeneous algebraic equations are obtained that are then numerically worked out for the natural sloshing eigen-frequencies and free surface oscillation mode shapes. Extensive numerical data include the first thirty six longitudinal/transverse Antisymmetric/Symmetric (AA, SA, AS, SS) dimensionless sloshing frequencies, for a wide range of liquid fill depths and container span to radius ratios. Also, the influence of fill depth on the free surface oscillation mode shapes is addressed through selected 2D images. Comprehensive numerical simulations illustrate the strong effects of container length and liquid fill depth on the calculated sloshing frequencies. It is revealed that the frequency branches with the same transverse mode number form a cluster that progressively merge together amid the tank fill-depth limits as the tank span ratio increases. On the other hand, when the tank length substantially decreases, the number of “frequency cross-overs” between various frequency clusters at certain liquid fill depths considerably increases. Moreover, primary advantages of proposed methodology in comparison to other approximate/numerical methods are explicitly pointed out, convergence of solution is tested, and accuracy/reliability of the results is demonstrated by comparisons with available data.     

Marine inventory routing: shipments planning

This paper addresses a shipments-planning problem faced by producers of large volume liquid bulk products. Producing origins with limited tank storage capacity supply multiple products by ships (or barges) to consuming destinations that also have limited storage capacity. Timing, origin, destination, and product quantities of shipments have to be determined in a manner that minimizes costs and does not violate storage capacity constraints at both ends (neither stopping production at the origins, nor running out of stock at the destinations). A mixed integer-programming model is used to derive cost effective solutions within a few minutes. A cost-based heuristic algorithm is used to assure that acceptable solutions are obtained quickly.     

贮液圆筒在水中的弯曲自由振动

本文研究了贮液圆筒在水中的弯曲自由振动问题,液体和水的深度均可任意,导出了水中贮液圆筒的振型函数及固有频率的精确计算公式,结果可由计算机解出.分析表明,液体和水对简体振动的影响各自等效一附着于筒体的广义分布质量.     

Nonlinear sloshing and passage through resonance in a shallow water tank

This paper is concerned with the effect of slowly changing the length of a tank on the nonlinear standing waves (free vibrations) and resonant forced oscillations of shallow water in the tank. The analysis begins with the Boussinesq equations. These are reduced to a nonlinear differential-difference equation for the slow variation of a Riemann invariant on one end. Then a multiple scale expansion yields a KdV equation with slowly changing coefficients for the standing wave problem, which is reduced to a KdV equation with a variable dispersion coefficient. The effect of changing the tank length on the number of solitons in the tank is investigated through numerical solutions of the variable coefficient KdV equation. A KdV equation which is “periodically” forced and slowly detuned results for the passage through resonance problem. Then the amplitude-frequency curves for the fundamental resonance and the first overtone are given numerically, as well as solutions corresponding to multiple equilibria. The evolution between multiple equilibria is also examined.Received: December 16, 2003     

Nonlinear sloshing and passage through resonance in a shallow water tank

This paper is concerned with the effect of slowly changing the length of a tank on the nonlinear standing waves (free vibrations) and resonant forced oscillations of shallow water in the tank. The analysis begins with the Boussinesq equations. These are reduced to a nonlinear differential-difference equation for the slow variation of a Riemann invariant on one end. Then a multiple scale expansion yields a KdV equation with slowly changing coefficients for the standing wave problem, which is reduced to a KdV equation with a variable dispersion coefficient. The effect of changing the tank length on the number of solitons in the tank is investigated through numerical solutions of the variable coefficient KdV equation. A KdV equation which is “periodically” forced and slowly detuned results for the passage through resonance problem. Then the amplitude-frequency curves for the fundamental resonance and the first overtone are given numerically, as well as solutions corresponding to multiple equilibria. The evolution between multiple equilibria is also examined.     

Stressed state of a circular hollow porous liquid-saturated cylinder rotating around its axis with constant angular velocity

We have obtained an exact solution of the plane problem for a porous tube rotating around its fixed axis of symmetry. The material of the tube is saturated with an ideal compressible liquid. Within the framework of the Bowen theory, for constructing the initial relations, we take into account the interconnections between stress tensors, strain tensors, relative density of the liquid filler, and varying porosity of the material. We present relations for the radial displacements, components of the stress tensor and densities in the skeleton and liquid filler, and also the porosity and mass concentration of the mixture. We have carried out a numerical analysis of the radial distributions of these characteristics for solid and hollow cylinders made of sandstone and saturated with kerosene. The critical numbers of revolution for tubes of saturated and dry materials have been found.     

CFD modeling of hydrodynamic characteristics of a gas–liquid two-phase stirred tank

A three-dimensional CFD model was developed in this work to simulate hydrodynamic characteristics of a gas–liquid two-phase stirred tank with two six-bladed turbines and four baffles, coupling of the Multiple Size Group model to determine bubble size distribution. Important hydrodynamic parameters of the multi-phase system such as volume-averaged overall and time-averaged local gas holdups and axial liquid velocities along time and transversal courses were simulated and analyzed in detail, under varied operating conditions (inlet air flow rate and impeller rotation speed). Model predictions of local transient gas holdup and liquid velocity distributions on vertical and horizontal sections of the tank were also carried out. The overall flow patterns were discussed in detail to assess the mixing. Bubble size distributions were further predicted to reveal the unique properties of gas phase. Experimental measurements of overall gas holdups and local axial liquid velocities were used to validate the developed model.     

Axially symmetric wave motion of a viscous liquid in a linearly viscoelastic tube

The problem of the propagation of progressive waves in a tube made of a linearly viscoelastic material which encloses a viscous Newtonian liquid is examined. For numerical calculations, it is proposed that the behavior of the tube wall material be described by the Voigt model. Dispersion curves are constructed for this case.S. M. Kirov Azerbaidzhan State University, Baku. Translated from Mekhanika Polimerov, No. 2, pp. 317–321, March–April, 1976.     

圆柱贮箱液体非线性晃动的多维模态分析方法

将Faltinsen等提出的多维模态理论应用到求解圆柱贮箱液体非线性晃动问题中．根据Narimanov-Moiseiev的三阶渐近假设关系,通过选取主导模态以及确定它们的阶次关系,将一般形式的无穷维模态系统降为五维渐近模态系统,即描述自由液面波高的广义坐标之间相互耦合的二阶非线性常微分方程组．通过对这个模态系统的数值积分,得到了与以前的理论分析和实验结果相吻合的非线性现象．研究结果表明,多维模态方法是用来求解液体非线性晃动动力学的一个很好的工具．在我们的下一步工作中,将继续发展这种方法,用来研究更为复杂的晃动问题．     

Specific features of application of perturbation techniques in problems of nonlinear oscillations of a liquid with free surface in cavities of noncylindrical shape

We consider the problem of nonlinear oscillations of an ideal incompressible liquid in a tank of a body-of-revolution shape. It is shown that the ordinary way of application of perturbation techniques results in the violation of solvability conditions of the problem. To avoid this contradiction we introduce some additional conditions and revise previously used approaches. We construct a discrete nonlinear model of the investigated problem on the basis of the Hamilton-Ostrogradskii variational formulation of the mechanical problem, preliminarily satisfying the kinematic boundary conditions and solvability conditions of the problem. Numerical examples testify to the efficiency of the constructed model. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 44–70, January, 2007.