Rigid Tank Research Articles

Simplified seismic analysis of rigid base liquid storage tanks under vertical excitation with soil-structure interaction : Haroun, M A; Abdel-Hafiz, E A Soil Dynam Earthq EngngV5, N4, Oct 1986, P217–P225

Simplified seismic analysis of rigid base liquid storage tanks under vertical excitation with soil-structure interaction : Haroun, M A; Abdel-Hafiz, E A Soil Dynam Earthq EngngV5, N4, Oct 1986, P217–P225

Hydrodynamic Pressures on Tanks by Momentum Balance

Abstract The application of the momentum balance method for the evaluation of the hydrodynamic pressures in a seismically excited rectangular tank is examined. The method was originally reported by Von Karman and has been recently rationalized by Housner. It uses two apparent masses derived according to the momentum balance in both the vertical and the horizontal directions. The application of the method in a seismic analysis of tanks has clarified a misinterpretation originally associated with the method. Both rigid and flexible tanks are treated, and the resulting hydrodynamic pressure distributions are compared with available solutions.

A simplified seismic analysis of rigid base liquid storage tanks under vertical exicitation with soil-structure interaction

A study is carried out to evaluate dynamic response of an elastic circular cylindrical tank having a rigid base under a vertical excitation taking into consideration the interaction with the foundation soil. At first, the soil is represented by frequency-independent parameters. Two coupled differential equations, governing the motion of the shell and the base, are solved using a step by step integration technique. The hydrodynamic pressures, acting on the shell and on the base, are derived from a velocity potential function which satisfies the Laplace equation and the appropriate boundary conditions. The response of the simplified model of a tank having a rigid base on a stiff foundation soil is compated to that obtained elsewhere to check the accuracy of the present model. Reasonable agreement is found between the maximum wall displacement and the associated stresses with those found by a more elaborate model. The interaction of the tank and the soil reduces the response than that calculated under the assumption of a rigid foundation soil. A parametric study to examine the effects of the height-to-radius ratio of the tank, and the effects of the shear wave velocity of the soil on the response is conducted. Varieties of foundation models are used to assess the sensitivity of the response to the variation in the soil parameters. Finally, a more representative solution for the problem in the frequency domain is obtained where the soil is appropriately modelled by frequency-dependent parameters. The transfer functions of the response of the tank wall and of the relative base motion are evaluated, and a comparison between the frequency-dependent and the frequency-independent solutions is made.

Equivalent circuit analysis of high-frequency ventilators including a new high-impedance flow-interrupting ventilator.

The small tidal volumes (VT) delivered to the lungs by highfrequency ventilators can be very sensitive to changes in the patient's respiratory mechanics. Analysis of a Thevenin equivalent circuit, consisting of a ventilator internal oscillatory pressure source in series with a ventilator internal impedance and a patient's respiratory impedance, reveals the need of a high-internal-impedance ventilator to minimize this VT sensitivity problem. We present a general methodology to estimate the internal impedance of any type of ventilator. The internal impedance, at a given frequency and flow setting, is calculated from the slope of the relationship between the generated peak-to-peak pressure and the VT delivered into a calibrated rigid tank through a varying constriction. We tested a typical high-frequency jet (HFJ) ventilator and a new high-impedance flow-interrupting (HIFI) ventilator consisting of a flow source, a rotary valve, a high-impedance expiratory tube, and a servocontrolled mean proximal airway pressure (MPAP) regulator. We found that the VT delivered by the HIFI ventilator was independent of MPAP and decreased by 12 percent after a fivefold increase in the constriction-tank system impedance. In contrast, the VT delivered by the HFJ ventilator decreased by 80 percent after a similar change in load. We therefore conclude that the VT delivered by the HIFI ventilator should be significantly less sensitive to changes in patient's respiratory impedance than the VT delivered by an HFJ ventilator.

Preliminary results for a vortex induced, liquid handling and accountability procedure at zero gravity

Preliminary results are briefly summarized for a vortex induced, liquid handling and accountability process adapted to two phase fluids in zero gravity. The process, proposed by NASA Kennedy Space Center personnel and modelled at the National Bureau of Standards, for liquid transfer between two large rigid tanks in zero gravity, has been analysed for a selected range of fluid and flow parameters. This transfer process has been analysed in two stages. The initial ‘spin-up’ stage is modelled in the circular tank via tangential injection techniques. Vapour—liquid separation is predicted using an averaging process based on bubble and/or droplet drag characteristics, together with pertinent virtual mass considerations. The model produced permits the addition of other gas-liquid interactions. The subsequent liquid ‘pump-out’ stage is modelled using numerical computations of the conservative equations, applied to the annularized liquid layer that has been spun-up on the tank wall. Liquid pump-out is modelled for a range of parameters, such as Reynolds number and volume withdrawal rate. Examples are given to demonstrate both stages of the model. It is concluded that results are plausible and experimental vertification is now needed to validate the assumptions made, as well as the results predicted.

Damping in sloshing flow with ceiling effect

The sloshing flow, when the liquid free surface reaches in some instant during the oscillating period the ceiling of the tank, is analyzed. The damping factor is obtained by a simplified theory of small perturbation which evaluates the force at the ceiling on the assumption that the dominant motion of sloshing corresponds with that given by linear theory of a potential flow. The experimental investigation is carried out with a rigid tank partially filled by water, fixed to an oscillating table laterally excited by a sinusoidal force of given frequency and amplitude. The liquid velocity, near the free surface, is measured by a laser doppler velocimeter. The damping factor is obtained by the band width tecnique applied to the analysis of the velocity RMS versus the frequency of the acting force.

AN ANALYTICAL METHOD OF IMPULSIVE WATER PRESSURE ON THE WALL OF EGG-SHAPED SLUDGE DIGESTER TANK DURING EARTHQUAKES

Egg-shaped sludge digester tank model with the scale of 1/30 was made of acryloid plastic. Horizontal and rocking vibration tests of the tank model were carried out on the shaking table with rather high frequency (10-25Hz) and the impulsive water pressures on the tank wall in various water depth were measured. Theoretical solutions to analyze the impulsive water pressure in an axisymmetric rigid tank were deduced by using the transfer matrix method. It was proved that the theoretical values agreed well with the measured ones obtained from the model tests. The calculating diagrams were drawn to be able to obtain easily the equivalent mass of water in tank, its center of action and the equivalent moment of inertia of water.

Seismic design forces for cylindrical tanks on ground

A study is made on the hydrodynamic effect caused by seismic ground motions on the design of cylindrical on-ground liquid-storage tanks. The current techniques for determining the design base shear and overturning moment of the tank are reviewed, first treating the tank wall as rigid and then including the wall flexibility effect. By means of examples, these calculations are compared with those suggested by the National Building Code of Canada (NBCC). In addition, theoretically predicted values are compared with experimental data.It was found that in the case of tanks of high height to radius ratio and small wall thickness to radius ratio, the interaction of the fluid and wall flexibility can cause responses as high as two to three times those calculated based on rigid tank wall assumptions. The range of tank geometries under which the tank can be considered rigid is given. It is shown that the NBCC formula to establish seismic loads for tanks on ground is in general conservative, provided the acceleration ratio in the NBCC formulae takes on the value of maximum peak ground acceleration of the site. Key words: seismic, earthquake, hydrodynamic force, response, cylindrical tanks, design code.

On the architecture and function of cuttlefish bone

The internal shell of the cuttlefish, which acts as a rigid buoyancy tank, is structured to combine high compressive strength — since it must withstand the external hydrostatic pressure — with minimum weighT. The micro-architecture of cuttlebone has been examined by electron microscopy and the relevance of the structure to the mechanical duties required of the shellin vivo are briefly discussed. The inorganic calcareous structure is associated with an organic component which may act as a template for mineralization.

Earthquake Response of Deformable Liquid Storage Tanks

A method for analyzing the earthquake response of deformable, cylindrical liquid storage tanks is presented. The method is based on superposition of the free lateral vibrational modes obtained by a finite-element approach and a boundary solution technique. The accuracy of such modes has been confirmed by vibration tests of full-scale tanks. Special attention is given to the cos θ-type modes for which there is a single cosine wave of deflection in the circumferential direction. The response of deformable tanks to known ground motions is then compared with that of similar rigid tanks to assess the influence of wall flexibility on their seismic behavior. In addition, detailed numerical examples are presented to illustrate the variation of the seismic response of two different classes of tanks, namely, “tall” and “broad” tanks. Finally, the significance of the cos nθ-type modes in the earthquake response analysis of irregular tanks is briefly discussed.

Three-Directional Fluid Pool Seismic Sloshing Analysis

Liquid sloshing in pool due to three-directional earthquake ground motion is analyzed. The liquid pool is represented by a rigid annular circular cylindrical tank. Analytical and numerical solutions are presented and their limitations are discussed. For a given seismic ground excitation time-history, the free surface and the pressure and velocity fields in the pool are calculated by superposition of modal responses. The results show that container vertical acceleration is of secondary importance in determining the free surface displacement, but has a major effect on the pressure load on the container boundary.

Hydroelastic vibrations in a rectangular container

The interaction of an elastic bottom with the liquid exhibiting a free liquid surface has been investigated for a rectangular container. For this reason the container bottom was considered either as a flexible membrane or as a thin elastic rectangular plate. Furthermore the hydroelastic problem of a liquid in a rigid rectangular tank in which the free liquid surface was covered by a flexible membrane or a thin elastic plate has also been treated. In both cases the coupled frequencies of the structure-liquid system has been obtained. It was found that even structural modes couple with odd liquid modes and vice versa and that the coupled frequencies exhibit decreased magnitude compared with the uncoupled structural frequencies and increased magnitude compared to the uncoupled liquid frequencies. They decrease with decreasing tension of the membrane or decreasing stiffness of the plate.

The computer code SEURBNUK-2 for fast reactor containment safety studies

The paper describes the theory and capabilities of the SEURBNUK-2 fluid flow code developed by JRC Ispra and AWRE Aldermaston for use in containment analysis for fast reactor safety studies. It is a 2D Eulerian code and is a major extension of the SURBOUM code developed earlier by Belgonucleaire and Aldermaston. SEURBNUK-2 has a full thin shell treatment for tanks of arbitrary shape and is able to include the effects of compressibility of the fluid. To check on the codes treatment of compressibility, results are presented for SEURBNUK calculations of an Ispra test shot 114 for the expansion of a Belgonucleaire charge in an overstrong water filled vessel. Comparisons are made both with experimental results and with calculations done on the 2D Lagrangian code REXCO-H and ASTARTE-2. A thin external deforming tank is chosen for the first test of the thin shell needed within the code though in this case the fluid was assumed incompressible. The problem has already been studied by REXCO and SURBOUM VD8 and the SEURBNUK results are compared with both experiment and these calculations. Comparisons have been made of the effect of using a full bending theory for the tank as opposed to a simple membrane treatment. It is shown that the inclusion of bending terms does not alter the ultimate strains significantly but does lead to much smoother results and values of the stress components in the wall. Results are presented for calculations on a U shaped tank containing fluid with cover gas simulating a bare primary tank. Three different calculations have been done involving rigid and flexible tanks and an incompressible and compressible treatment for the water. Comparisons are made between the three solutions both as regards final tank shape and energy distributions. The paper concludes with a calculation for a model reactor geometry which includes perforated diagrids dip plate and a deformable inner tank.

Autoparametric resonance in a structure containing a liquid, Part I: Two mode interaction

An elastic structure carrying a rigid circular cylindrical tank containing a liquid with a free surface is considered. Autoparametric coupling between a single structural freedom and the first antisymmetric sloshing mode is investigated theoretically and experimentally. Under the condition of principal internal resonance (i.e., when the structure natural frequency equals twice the liquid sloshing frequency) the response of the system is obtained by an asymptotic approximation taken to the second order. Both theoretical and experimental results show that the coupling between liquid sloshing and vertical structure vibration is rather weak.

Wide-Range Calibration System for Pressure-Gradient Hydrophones

A gradient hydrophone calibrator consists of a precisely made water-filled tank, with ports to receive the hydrophones to be calibrated and the reference pressure hydrophones, which is set into axial oscillation with suitable drivers to develop a standing wave of sound in the water. An improved calibrator is described, which, by using a very rigid tank, covers a range of 3–2500 Hz. Measurements are simplified through use of electrical feedback, which maintains a constant pressure-gradient versus frequency function. The applications and limitations of this system to the measurement of sensitivity, frequency response, and phase response of pressure-gradient and pressure hydrophones, and for obtaining the polar patterns of gradient hydrophones, are described.

Natural frequencies of viscous liquids in rectangular tanks

A procedure for calculating natural oscillating frequencies of viscous liquids in rigid rectangular tanks is suggested together with diagrams for obtaining the values by means of dimensionless coefficients. Experimental results are compared with the theoretical ones and are found to be in good agreement.

Dynamic behavior of liquids in elastic tanks

The finite element procedure is used in conjunction with a simple source distribution on all surfaces of a liquid, which is contained in a tank of virtually arbitrary geometry, to obtain expressions for the mass and stiffness (because of the gravity) matrices of the liquid. The accuracy of the formulation is evaluated by the numerical solution of eigenvalue problems appropriate to simple rigid tanks for which exact analytical solutions are available. Good agreement is obtained. Once the mass and stiffness matrices of the liquid are obtained, they can be combined with those of an elastic tank in order to study the dynamic behavior of liquids in elastic tanks. The matrices for the elastic tank can be generated by any of a variety of currently available finite element or finite difference programs. The dynamic behavior of a liquid in an elastic circular cylindrical tank is treated by making use of a standard finite element program. Very good agreement with the known exact analytical results is obtained. In addition, a tank geometry which cannot be readily analyzed by any of the previously available methods is considered.

On the change of natural frequencies of a sloshing liquid by movable devices

The present paper investigates the effectiveness of a movable device (mat), which is either immersed in an ideal fluid or covers the liquid free surface, to change the natural frequencies of a sloshing liquid in a circular cylindrical rigid tank. It is demonstrated that such a device reduces the frequencies of the free oscillations of the liquid substantially.

Low-Gravity Fuel Sloshing in an Arbitrary Axisymmetric Rigid Tank

Solutions to free and forced oscillations have been found in terms of an auxiliary set of eigenfunctions through the use of a modified Galerkin procedure. The slosh force and moment for an arbitrary axisymmetric rigid tank at arbitrary Bond number have been derived for both pitching and translation, and expressed in terms of characteristics of an equivalent spring-mass system. Numerical examples have been constructed which which compare favorably with available theories and experiments.

Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravity

Analyses and experimental comparisons are given for liquid sloshing in a rigid cylindrical tank under conditions of moderately small axial accelerations; in particular, the theory is valid for Bond numbers larger than 10. The analytical results are put in the form of an equivalent mechanical model, and it is shown that the sloshing mass and the natural frequency of the first mode, for a liquid having a 0 deg contact angle at the tank walls, are smaller than for high-g conditions. The experimental data, obtained by using several small-diameter tanks and three different liquids, are compared to the predictions of the mechanical model; good correlation is found in most cases for the sloshing forces and natural frequency as a function of Bond number.