Slosh Wave Research Articles

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Sloshing effect analysis of liquid storage tank under seismic excitation

Sloshing wave height is a main parameter in the seismic design of liquid storage tanks, and severe sloshing may lead to the liquid leakage or buckling of the steel tank wall. To accurately evaluate the sloshing wave height of the tank under earthquake action, a total of three shaking table tests were conducted on the liquid storage tanks, and numerical simulation methods based on the direct coupling method as well as the bidirectional coupling method were implemented. The sloshing height results from tests and simulations were compared with the values obtained from the theoretical formula, and the applicability of various calculation methods was analyzed. Thereafter, the theoretical formula of the simplified mechanical model and the bidirectional coupling method were adopted to predict the sloshing wave height of tanks with various dimensions, and the theoretical formula was further modified. Simultaneously, the influence of pulse-like ground motion on sloshing effect and hydrodynamic pressure of large-scale liquefied natural gas (LNG) storage tanks was examined. Additionally, the GB 50341–2014, API 650–2013, and Eurocode 8–2006 were utilized to assess the sloshing wave height of large storage tanks subjected to seismic ground motion, and the applicability of the computed results has been further discussed. Based on the above research, practical design recommendations were proposed in this work, which can provide a guidance for the seismic design of storage tanks.

Nonlinear Multimodal Model for Tuned Sloshing Dampers With Nonflat Bottoms

Abstract A third-order nonlinear multimodal model is developed for tanks with nonflat bottoms. A six-node finite element model is used to determine the mode shapes of the velocity potential and the associated natural sloshing frequencies. Using this modal information, equations of motion are developed that accommodate the nonlinear coupling among the first three sloshing modes. Damping arising from screens is incorporated into the model using the principle of virtual work. The equations of motion are ordinary differential equations that are solved using the Runge–Kutta–Gill numerical time-stepping method. The model is evaluated with an existing third-order nonlinear multimodal model for a flat-bottom tank and is found to be in excellent agreement. Demonstrative simulations are conducted for tanks with sloped-, boxed-, and ramped-bottoms. The resulting sloshing forces and wave heights at the tank end wall are calculated and presented using time series plots and frequency response plots. The excitation of higher-order sloshing modes through modal coupling results in larger wave heights, and shallower wave troughs. The sloshing forces are less impacted by the responses of higher modes. Secondary resonances are clearly visible in several frequency response plots at frequencies that correspond to the natural sloshing frequency of a higher-order mode divided by an integer. The model is applicable to tanks that are of intermediate water depth with moderate excitation amplitudes, where the response of the second- and third-order sloshing modes are less than the fundamental mode.

Analytical Study of Elevated Service Reservoir with Water Baffles Under Seismic Loading

Around the world earthquakes occur often causing some serious damages to property and life. Earthquakes weaken the structure and cause it to fail suddenly. Elevated Water tanks are such structures which have heavier mass suspended at a height supported on slender staging. When earthquake is induced in the tanks, it generates wave sloshing, the motion of the water induced due to seismic excitation. This sloshing of the water inside the tank will move in relative direction the seismic excitation causing structural instability. The water inside the tank will also act as tuned liquid mass damper and absorbs most of the energy created during seismic excitation. In this paper we have analysed various arrangement of baffle walls inside the tank in order to determine the stresses and displacements induced by the sloshing motion of the water tank. The water inside the tank will also act as tuned liquid mass damper where it will reduce the energy generated due to seismic excitation. During sloshing motion, there is an increase in lateral pressure applied over the tank walls which has adverse effect on the displacement of the system. The displacement of the system increases due to sloshing activity. By providing baffle walls we can reduce this displacement induced due to sloshing and thereby reduce the stresses generated on the supporting structure. From this analytical work the latter said was very evident.

Probabilistic evaluation of earthquake-induced sloshing wave height in above-ground liquid storage tanks

Past earthquakes have repeatedly demonstrated the need to properly design above-ground liquid storage tanks to mitigate their potential for damage due to seismic actions. One important damage mechanism in these plant items is the height of the sloshing wave exceeding the freeboard height provided to the tank. This paper proposes and presents a probabilistic framework to evaluate risk-oriented safety factors that can aid in the design of the freeboard height. The procedure is based on a series of dynamic analyses performed over a tank portfolio. The process accounts for record-to-record variability by using a set of 50 historical ground motion records, while it accounts for the variability in the geometric properties of tank prototypes by generating a random population of 100 cylindrical tanks through Monte Carlo simulation. The randomly generated tank properties are used to develop a simple mechanics-based model for each simulated tank, which is then subjected to the 50 ground motion records scaled to three seismic intensities by using two record scaling strategies. The trends in the resulting sloshing wave height values in relation to the randomly generated tank geometric properties are thoroughly analyzed and discussed, indicating that large and squat tank archetypes are particularly sensitive to sloshing. Finally, two sets of risk-oriented safety factors are developed by comparing the results of the set of dynamic simulations with those computed by using the prescriptions given by American standards.

Suppression of Sloshing Wave Height by Installation of Perforated Plate in Real Water Tank

Suppression of Sloshing Wave Height by Installation of Perforated Plate in Real Water Tank

Numerical and Experimental Evaluation of Sloshing Wave Force Caused by Dynamic Loads in Liquid Tanks

Proper evaluation of forces exerted on a solid boundary by liquid sloshing is difficult. If the free board in a liquid storage tank is insufficient, the sloshing waves caused by seismic excitation will collide with the tank roof and may cause major damage. The current study investigated the sloshing wave impact force (SWIF) in full-scale liquid storage tanks using numerical simulation based on the lattice Boltzmann method (LBM). Several shaking table tests have been conducted on a small-scale rectangular tank to validate the numerical model. The results of a standard dam break test have been used to express the validity of the proposed numerical model. This comparison confirms the validity of the numerical strategy for simulating the effect of sloshing. After validating the numerical model, it has been applied to a practical parametric study of SWIF in full-scale liquid tanks. The results of numerical simulation indicate that the simplified method recommended by related codes and standards for calculating SWIF in liquid tanks significantly underestimates the sloshing force. This confirms that the dynamic nature of sloshing should be considered in the design process of liquid storage tanks.

Effect of Installation of a Perforated Plate on Suppression of Sloshing Wave Height in a Rectangular Water Tank at Long-Period Earthquake

本研究では，地震時における矩形水槽内のスロッシング波高の抑制対策として多孔板の設置を提案し，水槽内でのスロッシング挙動について実験的に検討した．開孔率および孔径を組み合わせた多孔板を水槽の中間位置に設置し，振動数をある間隔で変えて水槽内の波高を測定した．また，多孔板を中間位置に設置できない場合を想定して，多孔板の設置位置を変えた実験も行った．

Numerical simulation of partially filled liquid containers with special type bottom geometry under earthquake excitation

Numerical simulation of liquid in partially filled tank of flat bottom and bottom box shape is investigated in the present paper. Previously, dynamic response of flat bottom tank has been carried out numerously, but the dynamic response of bottom box tank remains unclear. Therefor a parametric study on bottom box shape tank is carried out to understand the dynamic response of contained liquid under both harmonic excitation and real earthquake excitation. The efficacy of the present numerical model is verified by comparing the results with the published results. Galerkin’s finite element method is used to derive the modal equations of motion for sloshing. The slosh wave displacement, hydrodynamic pressure distribution and the base shear, are quantified for the bottom box shape tank. According to the dynamic analysis results larger size of bottom box significantly reduces the effective mass of liquid which keeps the container on safer side than the flat bottom container.

Evaluation of dynamic characteristics of liquid sloshing in sloped bottom tanks

Sloshing characteristics in partially filled slo-ped bottom container is investigated numerically. Galer-kin finite element method is used to derive the modal equation of motion for sloshing in 2D tank. The dynamic charcateristics of liquid sloshing in V-shaped bottom and the trapezoid tank are the critical investigations in the present work under the action of periodic ground motion. The liquid domain in V-shaped bottom and the trapezoid tank is discretized with a combination of three node triangular and four-node quadrilateral elements for this analysis. The reliability of the present numerical method is verified by comparing the results with the available analytical and experimental results for $$30^\circ $$ trapezoid tank and $$20^\circ $$ V-shaped bottom tank. Further, a parametric study on the V-shaped bottom and trapezoid tank is carried out to determine it’s dynamic behavior. The dynamic response of trapezoid tank under horizontal harmonic motion is manifested in terms of slosh wave displacement, base shear force at tank bottom and overturning base moment which remained limited for sloped bottom container.

A 2DH hybrid Boussinesq-NSWE solver for near-shore hydrodynamics

This paper presents a numerical model that simulates the nearshore circulation and the propagation of waves in two horizontal dimensions (2DH) across the coastal zone, from intermediate depth to zero depth. Pre-breaking, wave propagation is calculated using a Boussinesq equation set with enhanced dispersion characteristics, discretised using second-order central differences and solved using the conjugate gradient method with fourth order Runge-Kutta time integration. In the breaker zone, the Boussinesq dispersive terms are gradually switched off, and the resulting non-linear shallow water equations solved using a finite volume MUSCL-Hancock scheme with an HLLC approximate Riemann solver. Broken waves are treated as hydraulic bores. A wetting and drying algorithm models the moving wet/dry front at the shore. Waves are generated by a line of independently moving piston paddles which are represented through a linear mapping, stretching and compressing the grid in the region of the paddles. Model verification tests include wave sloshing in a frictionless basin, seiching in a parabolic basin with bed friction, solitary wave propagation over a horizontal bed, and the interaction of a solitary wave with a conical island. After calibration, the model simulates the generation of wave-induced currents by regular waves as they interact with sinusoidal and tricuspate beaches, and the propagation of a uni-directional focused wave group over a plane beach. Results are compared against previously published laboratory data. The validation tests confirm that the 2DH model reproduces several important coastal hydrodynamic phenomena including wave-induced currents and multi-component wave packets. The model can thus be used to replicate wave basin experiments, and could be extended to multi-directional waves, leading to a better understanding of hydrodynamic processes in shallow coastal waters.

Global force and moment in rectangular tanks through a modal method for wave sloshing

Basing on a modal description of the sloshing phenomenon, formulas for the global force and moment acting on two-dimensional rectangular tanks are proposed. These are extensively validated through comparison with experimental data for roll motions at different angles of excitement. Moreover, to extend the applicability of the modal method to the most violent breaking cases, a diffusive variant of the scheme is proposed. This relies on the use of a proper diffusive term in the continuity equation and allows for the overcoming of some numerical issues related to the sloshing dynamics in very shallow waters. Finally, a qualitative description of the interaction between diffusion, dispersion and nonlinearities has been proposed for the present modal scheme, along with a physical interpretation of the diffusive term.

Angle Compensation and Asymmetry Effect of Light Diffracted by Millimeter Liquid Surface Slosh Wave**Supported by the Open Research Fund of State Key Laboratory of Transient Optics and Photonics of Chinese Academy of Sciences under Grant No SKLST201508, the China Postdoctoral Science Foundation Funded Project under Grant No 2015M580945, and the Government of Chaoyang District Postdoctoral Research Foundation.

The angle compensation method is adopted to detect sloshing waves by laser diffraction, in the case that the wavelength of the sloshing waves is much greater than that of the incident light. The clear diffraction pattern is observed to be of asymmetry, involving orders, position and interval of the diffraction spots that are discovered during the light grazing incidence. It is found that the larger the angle of incidence is, the more obvious the asymmetry is. The higher the negative diffraction orders are, the smaller the intervals between spots are. On the contrary, in the positive region, the higher the diffraction orders are, the larger the spot intervals are. The positive interval is larger than that of the same negative diffraction order. If the incident angle reaches 1.558 rad in the experiment, all positive diffraction orders completely vanish. Based on the mechanism of phase modulation and with the Fourier transform method, the relations between the incident angle and position, interval spaces, and orders of diffraction spots are derived theoretically. The theoretical calculations are compared with the experimental data, and the comparison shows that the theoretical calculations are in good agreement with the experimental measurement.

Variational finite element methods for waves in a Hele-Shaw tank

The damped motion of driven water waves in a Hele-Shaw tank is investigated variationally and numerically. The equations governing the hydrodynamics of the problem are derived from a variational principle for shallow water. The variational principle includes the effects of surface tension, linear momentum damping due to the proximity of the tank walls and incoming volume flux through one of the boundaries representing the generation of waves by a wave pump. The model equations are solved numerically using (dis)continuous Galerkin finite element methods and are compared to exact linear wave sloshing and driven wave sloshing results. Numerical solutions of the nonlinear shallow water-wave equations are also validated against laboratory experiments of artificially driven waves in the Hele-Shaw tank.

PERFORMANCE OF AN RCC FRAME BUILDING SUBJECTED TO HYDRODYNAMIC FORCE AT EACH FLOOR LEVEL - A CASE STUDY

Buildings are essential in all populated cities. To increase value in certain buildings there are associated risks that we take like providing swimming pool at each floor level. Water carrying structures are more important that must remain functional following disasters such as earthquake. Most of the failures of structures after earthquakes are suspected to have resulted from the dynamic buckling caused by overturning moments of seismically induced liquid inertia and surface slosh waves. This paper investigates the hydrostatic and the hydrodynamic behavior of water in the swimming pool when subjected to earthquake forces. The main object of this paper is 1). To compare the static and dynamic analysis of the building. 2) The study of hydrodynamic effects.

Voluntary work and the relationship with unemployment, health, and well-being: a two-year follow-up study contrasting a materialistic and psychosocial pathway perspective.

In the present study we contrast materialistic (i.e., income and economic inequality) and psychosocial (i.e., social circumstances) pathway perspectives on whether volunteering while being unemployed mitigates the well-documented negative effects of unemployment on health, health behaviors, and well-being. We test our hypotheses using data from the 2010 and 2012 waves of the Swedish Longitudinal Occupational Study of Health (SLOSH; n = 717). This is a nationally representative, longitudinal, cohort survey. We compared groups of individuals who were (a) unemployed and volunteering during both SLOSH waves (n = 58), (b) unemployed and not volunteering during both SLOSH waves (n = 194), (c) employed and volunteering during both SLOSH waves (n = 139), and (d) employed and not volunteering during both SLOSH waves (n = 326). Conducting a path analysis in Mplus, we examined the interaction effects between labor market status (i.e., employed or unemployed) and voluntary work (i.e., volunteering or not) when predicting changes in health, health behaviors, and psychological well-being. Our results indicate that volunteering during unemployment significantly decreased the likelihood to smoke, the amount of cigarettes smoked, the likelihood of consuming alcohol, and the likelihood of being diagnosed with hypertension. These results support a psychosocial pathway perspective. For all other indicators no such buffering interaction effect was obtained, thereby supporting a materialistic pathway perspective. Nevertheless, for some indicators, volunteering was found to be beneficial for both the unemployed and employed. Consequently, integrating both perspectives might offer a better explanation for the onset of ill-health and ill-being.

Modeling of Ullage Collapse Within Rocket Propellant Tanks at Reduced Gravity

Orbital maneuvers of upper-stage rockets may generate propellant slosh waves and propellant breakup into droplets within the oxidizer and fuel tanks. When many droplets are created, increased propellant evaporation may occur and lead to a significant reduction in ullage gas temperature and pressure, known as ullage collapse. This work presents a new method that uses a numerical tool to predict the droplet distribution created during a maneuver, and subsequently uses an analytical model to calculate the droplet evaporation and consequent change in tank temperature and pressure. This new hybrid method uses less computational time than a detailed computational fluid dynamics model and is capable of providing mission planners with an improved tool to assess the impact of propellant evaporation on the requirements of additional helium mass for tank repressurization. The new method is applied to predict evaporation and the consequent ullage collapse in an upper-stage propellant tank undergoing simulated orbital maneuvers at microgravity levels.

A CIP-based numerical simulation of free surface flow related to freak waves

An enhanced numerical model for simulating two-dimensional incompressible viscous flow with distorted free surface is reported. The numerical simulation is carried out through the CIP (Constrained Interpolation Profile)-based method, which is described in the paper. A more accurate interface capturing scheme, the VOF/WLIC scheme (VOF: Volume-of-Fluid; WLIC: weighed line interface calculation), is adopted as the interface capturing method. To assess the developed algorithm and its versatility, a selection of test problems are examined, i.e. the square wave propagation, the Zalesak’s rigid body rotation, dam breaking problem with and without obstacles, wave sloshing in an excited wave tank and interaction between extreme waves and a floating body. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results. These examples demonstrate that the use of the VOF/WLIC scheme in the free surface capturing makes better results and also the proposed CIP-based model is capable of predicting the freak wave-related phenomena.