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In this study, the finite-element method is used to investigate the seismic behavior of rectangular liquid tanks in two-dimensional space. This method is capable of considering both impulsive and convective responses of liquid-tank system. Two different finite-element models corresponding with shallow and tall tank configurations are studied under the effects of both horizontal and vertical ground motions using the scaled earthquake components of the 1940 El-Centro earthquake record. The containers are assumed fixed to the rigid ground. Fluid-structure interaction effects on the dynamic response of fluid containers are taken into account incorporating wall flexibility. The results show that the wall flexibility and fluid damping properties have a major effect on seismic behavior of liquid tanks and should be considered in design criteria of tanks. The effect of vertical acceleration on the dynamic response of the liquid tanks is found to be less significant when horizontal and vertical ground motions are considered together. The results in this study are verified and compared with those obtained by numerical methods and other available methods in the literature. DOI: 10.1061/(ASCE)ST.1943-541X.0000123 CE Database subject headings: Dynamic response; Finite element method; Storage tanks; Ground motion; Liquids. Author keywords: Sloshing; Rectangular tank; Dynamic analysis; Tank flexibility; Finite element; Liquid containing.

Storage tanks are commonly installed in a combined sewer system to control the discharge of combined sewer overflows that have been identified as a leading source for receiving water pollution. The traditional approach to determine the distribution of storage tank volume in the sewer system is confined to the use of objectives within the system itself due to the limits of separate modeling of urban wastewater systems, consisting of the sewer system, wastewater-treatment plant, and receiving water. The aim of this study is to investigate the optimal distribution and control of storage tanks with an objective to mitigate the impact of new residential development on receiving water quality from an integrated modeling perspective. An integrated urban wastewater model has been used to test three optimization scenarios: optimal flow rate control, storage distribution, and a combination of these two. In addition to the cost of storage tank construction, two receiving water quality indicators, dissolved oxygen and ammonium concentration, are used as optimization objectives. Results show the benefits of direct evaluation of receiving water quality impact in the context of storage distribution optimization. Results indicate that storage allocation should be considered in conjunction with optimal flow rate control to achieve the maximum effectiveness in water pollution mitigation. DOI: 10.1061/(ASCE)EE.1943-7870.0000161 CE Database subject headings: Storage tanks; Urban areas; Wastewater management; Water quality; Combined sewers; Overflow; Optimization. Author keywords: New development; Storage tank; Urban wastewater system; Water quality; Combined sewer overflow; Multiobjective optimization; Integrated modeling.

Thermal mixing and stratification are explored experimentally in a horizontal cylindrical tank, which simulates a storage of water heated by a solar collector. The tank is 70 cm long and 24 cm in diameter. The study is conducted in a transient mode, namely, the tank is filled with hot water, which in the course of operation is replaced by the tap water in a stratified way or by mixing. The flow rates of 2 l/min, 3 l/min, 5 l/min, and 7 l/min are explored. Temperature of hot water is usually about 55[degrees]C, while the tap water is about 20[degrees]C. In the experiments, both flow visualization and temperature measurements are used. The effects of port location and deflector installation are examined. The experimental results are presented in a dimensionless form, as the normalized outlet temperature versus dimensionless time. Three-dimensional transient numerical simulations, done using the FLUENT 6 software, provide an additional insight in the process of mixing inside the tank. [DOI: 10.1115/1.3142801]

An explicit analytical solution is derived for sloshing in a cylindrical liquid storage tank with a single-deck type floating roof under seismic excitation. The floating roof is composed of an inner deck, which may be idealized as an isotropic elastic plate with uniform thickness and mass, and connected to an outer pontoon, which can be modeled as an elastic curved beam. The contained liquid is assumed to be inviscid, incompressible, and irrotational. By expanding the response of the floating roof into free-vibration modes in air and applying the Fourier-Bessel expansion technique in cylindrical coordinates, the solution is obtained in an explicit form, which is exact within the framework of linear potential theory. Numerical results are presented to investigate the effect of the type (single-deck or double-deck) and stiffness of the floating roof on the sloshing response. [DOI: 10.1115/1.3062939] Keywords: liquid storage tank, floating roof, single-deck, sloshing, fluid-structure interaction, potential theory, long-period ground motion

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored. CE Database subject headings: Foundation design; Earthquakes; Soil-structure interaction; Damping; Storage tanks; Soil structures; Seismic effects.

A finite element method (FEM)-based formulation is developed for an effective computation of the eigenmode frequencies, the decomposition of total liquid mass into impulsive and convective parts, and the distribution of wall pressures due to sloshing in liquid storage tanks of arbitrary shape and fill height. The fluid motion is considered to be inviscid (slip wall condition) and linear (small free-surface steepness). The natural modal frequencies and shapes of the sloshing modes are computed, as a function of the tank fill height, on the basis of a conventional FEM modeling. These results form the basis for a convective-impulsive decomposition of the total liquid mass, at any fill height, for the first few (two or three at most) sloshing modes, which are by far the most important ones in comparison to all other higher modes. This results into a simple yet accurate and robust model of discrete masses and springs for the sloshing behavior. The methodology is validated through comparison studies involving vertical cylindrical tanks. Additionally, the application of the proposed methodology to conical tanks and to the seismic analysis of spherical tanks on a rigid or flexible supporting system is demonstrated and the results are compared to those obtained by rigorous FEM analyses. [DOI: 10.1115/1.2967834]

The connection of a local support to an elevated cylindrical metal silo shell is a long-standing difficult problem in shell analysis, and most designs are based on simple ideas using past experiences of successes and failures. Smaller silo structures are often supported on local brackets attached to the side of the shell, but very few investigations of the behavior or strength of such an arrangement have ever been made. This paper presents an outline description of the behavior of a cylindrical steel shell that is discretely supported on several brackets, each rigidly connected to a stiff column or floor. The linear, materially nonlinear, geometrically nonlinear, and bifurcation behaviors of the shell under these conditions are outlined. In this problem the prebuckling deformations, bifurcation mode, and plastic collapse mode are each local. This configuration presents some interesting questions concerning the relative importance of geometric nonlinearity and geometric imperfections. The problem is recommended to advanced shell analysts as a benchmark test of their analysis and interpretation techniques. DOI: 10.1061/(ASCE)0733-9445(2008)134:8(1269) CE Database subject headings: Shell structures; Supports; Silos; Tanks; Cylinders; Elastoplasticity; Collapse.

Surge protection devices, such as surge tanks and air chambers, have been modeled with the impulse response method for transient analysis of water distribution systems. The lumped inertia model and continuity equation are used to represent nonpipe hydraulic elements. Results of pressure or discharge variations obtained by using the impulse response method and the method of characteristics are in good agreement. The impulse response method provides total pressure and discharge along any pipeline segment by direct integration of the ratio of complex head or complex discharge to a complex downstream discharge, respectively. A modification is proposed so that transition between turbulent and laminar flows can be considered. The representation of hydraulic devices has been incorporated into the impedance matrix method, which was developed for heterogeneous and multilooped pipe network systems. The potential advantages of the proposed method over other conventional approaches were investigated by applying the proposed method to hypothetical pipe network systems. CE Database subject headings: Pipe networks; Water tank; Water supply; Water hammers; Water pipelines.

Ambient flow field and circulation patterns induced by circular bubble plumes and water jets in tanks of different sizes were studied in rectangular and square water tanks. A nonstationary nature of the flow was observed in all experiments and its dominant oscillation frequency was found to directly relate to the tank size. The flow circulation patterns were similar for bubble plumes and water jets, but changed significantly with tank size and geometry. Strong three-dimensional effects were observed in a rectangular tank, resulting in flow entraining in the longer plane and flow detraining in the shorter plane, especially for the bubble plume tests. A relationship was developed to relate the tank size to the patterns of circulation cells. Nearly isotropic turbulent flow conditions were obtained in all experiments, but the effect of tank size and geometry on the magnitude of the turbulent stresses was more pronounced in the bubble plume tests. DOI: 10.1061/(ASCE)0733-9429(2008)134:6(833) CE Database subject headings: Bubbles; Water circulation; Water tanks; Water jets; Mixing; Plumes; Geometry; Turbulent flow.