Flat-bottom Tanks Research Articles

Evaluating the Seismic Resilience of Above-Ground Liquid Storage Tanks

Historical seismic events have repeatedly highlighted the susceptibility of above-ground liquid storage steel tanks, underscoring the critical need for their proper design to minimize potential damage due to seismic forces. A significant failure mechanism in these structures, which play essential roles in the extraction and distribution of various raw or refined materials—many of which are flammable or environmentally hazardous—is the dynamic buckling of the tank walls. This study introduces a numerical framework designed to assess the earthquake-induced hydrodynamic pressures exerted on the walls of cylindrical steel tanks. These pressures result from the inertial forces generated during seismic activity. The computational framework incorporates material and geometric nonlinearities and models the tanks using four-node shell elements with two-point integration, specifically Belytschko shell elements. The Arbitrary Lagrangian–Eulerian (ALE) method is employed to accommodate substantial structural and fluid deformations, enabling a full simulation of fluid–structure interaction through highly nonlinear algorithms. Experimental test data are utilized to validate the proposed modeling approach, particularly in replicating sloshing phenomena and identifying stress concentrations that may lead to wall buckling. The study further presents results from a parametric analysis that varies the height-to-radius and radius-to-thickness ratios of a typical anchored flat-bottomed tank, examining the seismic performance of this common storage system. These results provide insights into the relationship between tank properties and mechanical behavior under dynamic loading conditions.

Heat transfer coefficient evaluated for a designed jacketed vessel for parameter optimization in coal water slurry preparation using dual impellers

ABSTRACT This study examines the heat transfer coefficient during coal water slurry preparation in a jacketed vessel, focusing on key parameters influencing heat transfer. A dual impeller system is utilized to enhance mixing and heat transmission capacity. Using the Ant Colony Optimization (ACO) method, the equipment is designed, comprising a cylindrical flat-bottom tank with an impeller diameter of 0.079 m, a height of 0.3 m, and four uniformly positioned detachable flat baffles around the vessel’s perimeter. Experiments are conducted using the L27 orthogonal array at three different levels, varying impeller speed, clearance height to tank diameter ratio, slurry height to tank diameter ratio, and distance between the two impellers. Two categories of dual impeller experiments, propeller and Rushton, are examined. Statistical analysis indicates that impeller speed and Z/T ratio significantly influence heat transfer coefficient, while C/T ratio and distance between impellers have a lesser impact. In both propeller and Rushton experiments, impeller speed and Z/T ratio have the most substantial effect on heat transfer coefficient, contributing 62.907% and 59.47%, respectively, in propeller and Rushton experiments. These findings underscore the importance of impeller speed and Z/T ratio in enhancing heat transfer coefficient during coal water slurry preparation in a jacketed vessel.

Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation.

The dissolution testing method described in the United States Pharmacopeia (USP) Chapter ⟨711⟩ is widely used for assessing the release of active pharmaceutical ingredients from solid dosage forms. However, extensive use over the years has revealed certain issues, including high experimental intervariability observed in specific formulations and the settling of particles in the dead zone of the vessel. To address these concerns and gain a comprehensive understanding of the hydrodynamic conditions within the USP 2 apparatus, computational fluid dynamic simulations have been employed in this study. The base design employed in this study is the 900 mL USP 2 vessel along with a paddle stirrer at a 50 rpm rotational speed. Additionally, alternative stirrer designs, including the hydrofoil, pitched blade, and Rushton impeller, are investigated. A comparison is also made between a flat-bottom tank and the USP round-bottom vessel of the same volume and diameter. Furthermore, this work examines the impact of various parameters, such as clearance distance (distance between the bottom of the impeller and bottom of the vessel), number of impeller blades, impeller diameter, and impeller attachment angle. The volume-average shear rate (Stv), fluid velocity (Utv), and energy dissipation rates (ϵtv) represent the key properties evaluated in this study. Comparing the USP2 design and systems with the same stirrer but flat-bottom vessel reveals more homogeneous mixing compared to the USP2 design. Analyzing fluid flow streamlines in different designs demonstrates that hydrofoil stirrers generate more suspension or upward movement of fluid compared to paddle stirrers. Therefore, when impellers are of a similar size, hydrofoil designs generate higher fluid velocities in the coning area. Furthermore, the angle of blade attachment to the hub influences the fluid velocity in the coning area in a way that the 60° angle design generates more suspension than the 45° angle design. The findings indicate that the paddle stirrer design leads to a heterogeneous shear rate and velocity distributions within the vessel compared with the other designs, suggesting suboptimal performance. These insights provide valuable guidance for the development of improved in vitro dissolution testing devices, emphasizing the importance of optimized design considerations to minimize hydrodynamic variability, enhance dissolution characterization, and reduce variability in dissolution test results. Ultimately, such advancements hold potential for improving in vitro-in vivo correlations in drug development.

Analytical models for critical heights of vortexing in flat and spherical bottom tanks with siphon and bottom drains

Critical height or critical submergence is liquid level at which air-core vortex extends from the free surface into drain hole when a liquid is drained from a container/tank. Extensive analytical and experimental studies have been reported on critical height of bath tub vortex, for liquid draining downward from flat bottom propellant tanks. Rockets making use of liquid propellants mostly employ spherical bottom propellant tanks as well as siphon or upward drain flow. Keeping in view of such practical applications, analytical models are developed for critical height, considering the effects of siphon drain and the shape of tank bottom. Additional design parameters influencing the behavior for each case are identified. Appropriate governing equations and a solution methodology are developed pertinent to the system considered, to predict the critical height for siphon drain and spherical bottom tank independently as well as for both combined. The results indicate that the critical height for spherical bottom tank is higher than for flat bottom tank, due to higher local flow velocity. Siphon geometry can be designed for critical height much less than normal drain from flat bottom tank. These observations are in accordance with the results published in the literature. This paper reports the analytical models and solution methodology to predict the critical height for vortexing for normal draining from spherical tank bottom, siphon draining from both flat and spherical bottom tanks.

Design of RCC Structure Instead of Brick Structure in Water Retaining and Sedimentation & Storage

The design of reinforced concrete (RCC) structures for water retaining applications has become a popular alternative to traditional brick structures. RCC structures offer advantages such as durability, strength, and resistance to weathering and water. This paper explores the design considerations and challenges associated with the use of RCC structures for water retaining applications. It discusses the design codes and criteria, including load calculations, concrete strength, and reinforcement detailing. Additionally, the paper highlights the different types of RCC structures used for water retaining applications, such as flat-bottomed tanks, elevated tanks, and circular tanks. It also examines the advantages and disadvantages of each structure type, as well as the design considerations and challenges specific to each. Finally, the paper provides insight into the construction process of RCC structures, including site preparation, formwork, reinforcement, and concrete pouring.

Influence of Impeller and Mixing Tank Shapes on the Solid–Liquid Mixing Characteristics of Vanadium-Bearing Shale Based on the DEM-VOF Method

The mixing tank is important equipment for industrial applications in the wet vanadium extraction process, but in practice, there are problems, such as uneven mixing of minerals. In this study, the effect of different types of impellers and different mixing tank structures on the suspended mass of particles was simulated using the discrete element method and volume of fluid method (DEM-VOF). The simulation results show that the round-bottomed tank performed mixing better than the flat-bottomed tank at different particle densities, and the flat-bottomed tank was prone to particle stratification and other phenomena. The round-bottomed mixing tank could better improve the solid–liquid suspension effect. In this study, the coefficient of variation σ was introduced to characterize the suspended mass of particles. By monitoring the σ value, it was found that the blade pitch angle 45 (BPA45) had the best mixing uniformity in the inclined pitched blade turbine (PBT). As the PBT impeller pitch angle increased, the particle suspension increased. When comparing different types of impellers, the Rushton exhibited a 45% improvement in mixing uniformity relative to the BPA45. Second, the width and height of the trough bottom projection were optimized and their σ values were calculated separately for different parameter conditions. The width of 0.05 m and height T/4 (T being the diameter of the tank) were finally determined to be the optimum parameters for the optimal design of the vanadium shale leaching mixing trough.

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.

Numerical Modeling of the Wave-Plate-Current Interaction by the Boundary Element Method

The aim of this work is to propose a numerical study of the interaction of a wave-horizontal plate fixed and completely immersed in a flat-bottomed tank with a uniform current flowing in the same direction as the incident wave. We investigate in particular the effect of the plate at minimizing the impact of the wave on the coast of beaches by studying the free surface elevation and the reflection coefficient, as well as the influence of the various geometrical parameters on the latter, taking into account the presence of the current. The numerical method used in this study is the boundary element method (BEM), and the results obtained will be confronted with experimental and analytical data existing in the literature.

On the resistance of arbitrarily ring‐stiffened welded bins subject to axial compression

AbstractRing‐stiffened flat bottom tanks are widely used in many industries for the storage of liquids, such as oil, fertilizers, water, sewage and sludge. Material efficiency is achieved by combining thin plates with ring‐stiffeners. When the bin is covered by a dome or cone roof, high meridional forces due to live or snow loads may trigger axial buckling of the shell. Ring stiffeners are beneficial, not just against buckling due to wind, but to reduce the risk of stability failure of tanks and silos caused by meridional compression as well.This paper presents the outcome of a parametrical study concerned with axial buckling and the most effective placement of the stiffening rings depending on the stiffener distance, cross‐sectional area and slenderness of the cylinder. Buckling curve parameters are deduced using the modified capacity curve. These allow the direct application of the analysis results in a hand calculation procedure that enables practitioners to take into account the benefits, which come with ring stiffeners against buckling due to axial compression.

Computational Liquid Dynamic Simulation Mixing Time from Side Inlet Mixer Tank

This study aims to investigate the mixing time of the side-entry mixer tank and the influence of the propeller's rotational speed on mixing time by the Computational Fluid Dynamic (CFD) method. The tank's model is a flat-bottom cylinder tank whose diameter is 40 cm with a 6 cm propeller contains three blades. The tracer, HCL 37%, was injected on the water's surface while the propeller's rotation speed is varied 100 rpm, 200 rpm, 300 rpm, and 400 rpm. The simulation process is examined using CFD FLUENT 17.1, with a turbulence model is k-ɛ RNG. Its conditions are single-phase then proceeded using species transport. Furthermore, the monitoring point's simulation is identical to the experimental data monitoring probe, which is used to inspect the mass fraction at each point. After all, this simulation contains three processes: pre-processing, solving, and post-processing. as a result, the propeller's higher rotational speed makes the mixing time shorter in the CFD method, which has a good agreement with the experimental method. Moreover, this study also examines the impact of the grid's type and the geometric size for the mixing process in the side-entry mixer tank.

Development and application of 3D-PTV measurements to lab-scale stirred vessel flows

In this work, guidelines for reliable 3D-PTV measurements of fluid flows in stirred vessels at the lab-scale have been developed. The flow of water at Re=12,000 in a flat bottom cylindrical tank (T=180 mm) stirred with a 6 blades Rushton turbine (c=D=T/3) has been measured at different camera frame rates (125 – 3600 fps) and tracer concentrations (0.001 – 0.010 px−2). The best compromise between the number of measured data, tracking efficiency and CPU time (206 frame-1, 39% efficiency, 0.026 min frame-1) has been obtained at 125 fps and 0.002 px−2. These results can be expressed in terms of the normalized parameters φ∼0.5 and p∼2 and scaled to different experimental conditions. The Savitzky–Golay filter, used to enhance the measurements signal-to-noise ratio, has been optimized by testing different values of the polynomial order (0–3) and filter width (321 data points). A 2nd order, 11-points filter gave the best results, based on considerations regarding the reduced Chi-squared and velocity distributions. With the best conditions and filter, the uncertainty in the measured tracer positions was in the order of 255 μm. Finally, un unbiased distribution of the flow decorrelation time has been determined from the velocity autocorrelation functions along the trajectories longer than 6 impeller revolutions. This method could be used to compare the macro-mixing performance in different flow systems.

Modeling and design of a tuned liquid damper using triangular-bottom tank by a concentrated mass model

Rectangular flat-bottom liquid tanks known as tuned liquid dampers (TLDs) are often used as passive mechanical dampers. Sloped- and triangular-bottom TLDs have been reported to be more effective than flat-bottom TLDs, but optimum tuning and damping of sloped- and triangular-bottom TLDs have not yet been proposed, and nonlinear analysis of such TLDs has not been performed. This study aims to establish a practical analytical model for nonlinear sloshing in a triangular-bottom TLD and a method for designing a TLD using a triangular-bottom tank. We modify the concentrated mass model proposed in our previous paper to simulate nonlinear shallow water wave phenomena in a triangular-bottom tank. To confirm the validity of the modified model, its results are compared with the natural frequencies in a triangular-bottom tank obtained from FEM and experimental results for a triangular-bottom tank. All the model results agree well with the FEM and experimental results. Furthermore, optimum tuning and damping based on the concentrated mass model are derived in the case of a triangular-bottom TLD, and the physical reason why a triangular-bottom TLD is more effective than a flat-bottom TLD is investigated.

Natural Frequency Measurements of the Fluid-Elastic-Coupled Shell Plate Vibration in a Large-Sized Cylindrical Steel Tank by Microtremor Observations

AbstractNaturally occurring microtremor observations measured the natural frequencies of the fluid-elastic-coupled shell plate vibration (bulging) in a large flat-bottomed cylindrical steel tank with a capacity of 125,000-m3. Five peaks appear in the observed microtremor spectral ratios of the top or midheight of the shell plate to the bottom on the tank foundation. Comparing the spectral ratios to the solutions obtained by FEM eigenvalue analysis assuming a fixed base suggests that the five peaks are the bulging modes of (m, n)=(1, 1–5), where m and n denote the vertical order and the circumferential wavenumber, respectively. The measured non-soil-coupled natural frequencies from the spectral ratio agree fairly well with those obtained from FEM analysis. The measured natural frequencies of the fundamental mode (m = n = 1) also agree well with those projected by a simplified equation developed under the assumption of a fixed base, which is adopted in the seismic codes of the Japanese Fire Service Act. This equation should provide a reliable soil-coupled natural frequency of the fundamental mode for a tank situated on firm ground in which the storage-soil-coupled effects are presumed weak. Additionally, a simple method is presented to determine the non-soil-coupled natural frequency of the fundamental mode from the observed microtremor spectral ratios without referencing the FEM eigenvalue solutions. This simple method works very well for the tank examined.

Numerical investigation of flow behavior in double-rushton turbine stirred tank bioreactor

The current research focuses on the numerical simulation to scrutinize the divergent flow characteristics in a stirred tank bioreactor. The reactor is composed of a cylindrical flat-bottom tank equipped with two Rushton six-blade impellers and four baffles on the wall of the tank. The turbulent flow within the reactor is modeled with the Large Eddy Simulation model. The traditional subgrid model of Smagorinsky was used to solve turbulent small-scale structures with Smagorinsky constant C s = 0.1 The influence of the reactor components (i.e., cylindrical wall, baffles, shaft, and Rushton turbines) on the liquid-flow field has been obtained using the immersed boundary method. A highly parallelized computer code is developed to perform the simulation on a multi-core Graphics Processing Unit platform. The results are demonstrated in phase average flow velocities and turbulent statistics, with validation from the available experimental data reported in the literature.

Static and dynamic behavior of cellular glass products used for the bottom insulation of flat bottom tanks

AbstractThis paper gives a general introduction to the design of load bearing insulation systems made from cellular glass for flat bottom tanks used to store cryogenic liquids. The mechanical properties of cellular glass are summarized and the current situation of the set of rules and regulations regarding design and construction of bottom insulation systems is presented. The intention of this paper is to bring attention to the dynamic behavior of cellular glass bottom insulation systems under horizontal earthquake acceleration. Within this paper, the basic results of cyclic shear force tests performed on cellular glass blocks are presented. The intention of these tests was to determine the dynamic behavior of a bottom insulation system exposed to shear inducing seismic actions. A procedure for implementing the dynamic properties of cellular glass into a multi modal dynamic model is presented and verified by a dynamic calculation.

Reducing of weight variation in soaking step of shrimp processing: effects of iced storage time and soaking equipment

The aim of shrimp soaking is to improve functional properties and yield of a shrimp product. The weight variation in the soaking step in actual production is larger than that in the laboratory due to many uncontrollable factors that have not been identified. The objective of this work, therefore, was to investigate the causes that provoke the difference in yield calculation between the laboratory and the real production conditions to improve the soaking process of shrimp within the regulated time. First, the effect of storage time in ice (0 and 24 h) on soaking yield variation was studied. Then, the effect of soaking equipment, i.e. flat bottom tank with rod impeller and cone bottom tank with paddle blade impeller, on weight variation was determined. The result revealed that the iced storage time and the design of soaking equipment had no significant effect on the variations of yield and weight (p ≥ 0.05). Nevertheless, water holding capacities after soaking and cooking were significantly influenced by the iced storage period (p < 0.05). The result revealed that the 24-h iced storage significantly reduced the yields of soaking, cooking, and freezing.

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.

Culture of the seaweed Ulva ohnoi integrated in a Solea senegalensis recirculating system: influence of light and biomass stocking density on macroalgae productivity

A growth model was developed to optimize the management of multi-trophic aquaculture systems by analyzing the influence of light and biomass stocking density (SD) in the productivity of Ulva ohnoi fed with the effluents from Solea senegalensis culture tanks. Growth rates and productivity were determined in three flat bottom algae tanks with different incident photon irradiances (E0) (163, 280, and 886 μmol photons m−2 s−1), photoperiod 12:12 h, and with stocking densities ranging from 82 to 340 gdw m−2. The distribution of photon irradiance in the algae tanks was estimated as a function of the E0 and SD. The results obtained showed that the algae exposed to the highest E0 (886 μmol photons m−2 s−1) and SD below 170 gdw m−2 showed a strong decrease in their growth rate, together with morphological changes. The model proposed to estimate the specific growth rate (μNET), on the basis of E0 and SD, assumed that photosynthetic activity is dependent on the local photon flux density and, therefore, spatially distributed in the tank. Non-linear regression used to estimate the growth kinetic parameters showed a standard deviation of the distance between measured and fitted μNET data values equal to 0.011 day−1. In terms of biomass productivity per unit area (BPA), the model shows, for each E0 level, a trend to increase with SD, achieving a maximum BPA, where SD can be considered optimal, and decreasing for higher SD values. The optimal SD and the maximum BPA achievable can be also determined as a function of E0.

Validation of the nonhydrostatic General Curvilinear Coastal Ocean Model (GCCOM) for stratified flows

While global- and basin-scale processes can be captured quite well with computationally-inexpensive hydrostatic models, smaller-scale features such as shoaling nonlinear internal waves and bores, coastal fronts, and other convective processes require the use of a nonhydrostatic model to accurately capture dynamics. Here the nonhydrostatic capabilities of the General Curvilinear Coastal Ocean Model (GCCOM) in a stratified environment are introduced. GCCOM is a three-dimensional, nonhydrostatic Large Eddy Simulation (LES), rigid lid model that has the ability to run in a fully three-dimensional general curvilinear coordinate system. This model was previously validated for unstratified flows with curvilinear coordinates. Here, recent advances of the model to simulate stratified flows are presented, focusing on sigma coordinate grids with both flat bottom geometry and a local gently sloping seamount. In particular, a suite of test cases widely used as benchmarks for assessing the nonhydrostatic capabilities for gravity-driven flows and internal waves is presented: an internal seiche in a flat bottom tank, the classic lock release and gravity current experiment, and a field-scale internal wave beam experiment consisting of an oscillating tidal flow over a topographic ridge. GCCOM shows excellent agreement with the benchmark test cases and is able to accurately resolve complex nonhydrostatic phenomena in stratified flows. Future studies will utilize the model capabilities for realistic field-scale internal wave simulations.

Demonstration of an Overground Hot Water Store in Segmental Construction for District Heating Systems

Thermal energy stores can significantly improve the efficiency and environment-friendliness of the heat supply by storing heat surpluses and supply heat to the consumer if necessary. Therefore, a high demand for cost-effective storage technologies with low energy losses exists. For hot water storage tanks using the displacement principle significant optimization potentials exist regarding currently at the market available storage technologies, in particular pressure vessels and flat-bottom tanks. A new tank design eliminates disadvantages and offers numerous benefits. A demonstrator with a new design was already built in cooperation with scientific and industrial partners as part of the OBSERW project in Nortorf (Germany). The demonstrator is a small-scale hot water storage tank with a volume of approx. 100 m³. It allows numerous tests with low energy and time effort. The main novelty of the construction is an indoor floating ceiling, with the loading device (e. g. a radial diffuser) attached directly to it. A flexible connection allows the free movement of the floating ceiling between a top and bottom dead centre. This work describes the function of the storage tank and presents first operation experiences.