Rectangular Vessel Research Articles

Kinematics of the First Wave Faraday Mode on the Side Wall of a Rectangular Vessel

Kinematics of the First Wave Faraday Mode on the Side Wall of a Rectangular Vessel

Dynamic characteristics of a horizontal rectangular vessel partially or fully filled with a fluid

A theoretical framework is presented for free vibration of a flexible horizontal rectangular vessel, whether it is partially or fully filled with a fluid. The vibrational modal patterns of the vessel, whether dry or wet, are classified into symmetric and antisymmetric modes. The theoretical model conceptualizes the vessel as an unfolded plate with line supports simulating the vessel's corners. The motion of contained fluid is described using displacement potentials that adhere to the Laplace equation and fluid boundary conditions. Importantly, the proposed analytical approach accounts for the dynamic interaction between the vessel and the fluid, ensuring compatibility along their contacting surfaces. The Rayleigh-Ritz method is employed to formulate an eigenvalue problem, considering entire kinetic and strain energies of the fluid-filled vessel. The accuracy of the theoretical approach is checked by conducting finite element analyses. Remarkably, the natural frequencies obtained through commercial software align closely with the theoretical predictions for both dry and fluid-filled vessels. In instances of fully fluid-filled vessels, we can discern the presence of fluid contact at the vessel's upper plate by examining the natural frequencies and mode shapes. The proposed method offers applicability in dynamically analyzing water-filled spent fuel casks, enhancing safety during transportation.

Theoretical and experimental modeling of geodynamiс processes in uplift slopes

The flow structure created in a viscous medium at a constant inclination angle of the free surface of the uplift slope is analyzed. The velocity field in a high-viscosity uplift slope is determined under conditions of a horizontal pressure gradient. This pressure gradient occurs when the slope height decreases with distance from the main ridge. With a constant dynamic viscosity of the uplift slope, the flow velocity in it decreases with distance from the axis of the main ridge. In this case, the uplift slope is in conditions of compressive stresses, the consequence of which are thrusts and compression folds. Tensile stresses in the uplift slope exist with an increase in the flow velocity in the layer with distance from the main ridge axis. The flow velocity increases with decreasing viscosity of the layer with distance from the main ridge. The viscosity distribution on the base of the uplift slope at a distance from the axis of the main ridge is determined using the tension condition in the uplift slope. Expressions are presented for the forces causing the formation of a disruption between the blocks of the uplift slope. The magnitudes of these forces are estimated. A relation representing the condition for the formation of a disruption between the blocks is obtained. The formation of disruptions is governed by the change in viscosity along the uplift slope and the change in the flow velocity in it. When the disruption between the uplift slope is formed, free vertical boundaries of the blocks appear. The motion of a highly viscous liquid during the formation of a free vertical boundary of the block has been studied experimentally when the liquid flows out from a rectangular vessel. The experiments have revealed two outflow regimes: (i) the regime of constant thickness of the liquid layer; (ii) the regime of decreasing layer thickness. On the basis of experimental modeling the time of the first period after the formation of the slope rupture and the formation of the free volume between the blocks is estimated. During this period the height of the layer (slope) is practically constant and the layer length increases. The process of filling the free volume between the blocks with a high-viscosity slope material is considered. As the modeling shows, the filling rate of the free volume between the diverging blocks of the uplift slope is much higher than the formation rate of the free volume between these blocks. The parameters of the uplift slope blocks are determined. Among these parameters are block viscosity, slope height, flow velocity and forces acting on the blocks. The time-varying structure of the surface of the uplift slope is presented. There is a qualitative correspondence between the modeling results and the profile of the uplift slope for the north-western Caucasus.

Technology and provenience of the oldest pottery in the northern Pannonian Basin indicates its affiliation to hunter-gatherers

Consensus holds that pottery technology came to Central Europe from the Northern Balkans with independent pottery traditions existing concurrently in Eastern Europe. An unusual grass-tempered pottery dating back to around 5800 cal BC found in lake sediments at Santovka, Slovakia, predated the earliest known Neolithic pottery in the region (~ 5500 cal BC), suggesting unexplored narratives of pottery introduction. Analyses of the pottery’s technology, origin, and grass temper shedding light on ceramic traditions' spread can unveil mobility patterns and community lifestyles. Our findings indicate a non-local provenance, low temperature firing, Festugc sp. grass temper and unique rectangular or cylindrical vessel shapes which align with Eastern European hunter-gatherer practices. Moreover, the pottery style and technology have no analogies in the contemporary Danubian pottery traditions and have more similarities to those of the Eastern traditions. The pottery's raw materials likely originated from distant areas, indicating extensive territorial access for its creators. Our findings imply late Mesolithic hunter-gatherers as the probable artisans and with implications for the site's significance in the late Mesolithic landscape.

Analysis of damage characteristics of the rectangular steel container under near-earth explosion loading

In this study, the dynamic response of a semi-buried steel vessel under a near-surface explosion shock load was investigated through full-scale model tests. A three-dimensional precise numerical simulation model of the semi-buried steel vessel structure was established, and the dynamic response and damage consequences under different load conditions were analyzed. The influence of the thickness of corrugated steel on the dynamic damage and antiknock properties of the structure was studied. The results show that the weak part of the rectangular steel vessel structure is mainly located at the connection between the blast-facing panel and the beam column under near-surface explosion conditions. The peak stress and displacement of the blasting surface decrease with the increase in the horizontal angle of the incident wave, whilst/while increase with the height of the explosion. Under the same explosive yield, the main failure mode of the structure is the tearing of the plate and beam under plastic deformation. Increasing the thickness of the corrugated steel can significantly restrain the plastic deformation and acceleration of the plate. When the thickness is increased from 2 mm to 6 mm, the antiknock performance is significantly improved. However, when the thickness is increased from 6 mm to 8 mm, the improvement in antiknock performance slows down. Increasing the height of the enclosing soil can also effectively improve the explosion-proof performance of the structure, with full burial providing the best effect. The research results provide a theoretical basis for the application of rectangular steel vessel structures in the field of protection engineering.

Numerical simulations of shallow-water sloshing coupled to horizontal vessel motion in the presence of a time-dependent porous baffle

Shallow-water fluid sloshing in the Lagrangian Particle Path formulation, with the addition of an energy-extracting porous baffle, is simulated numerically using a symplectic numerical scheme which captures, in an essential way, the energy exchange. The fluid motion in a rectangular vessel is dynamically coupled to a surface-piercing porous baffle. The fluid transmission through the baffle is characterized by a nonlinear Darcy–Forchheimer model equation. The numerical scheme is symplectic, based on the implicit-midpoint rule, and thus is strategically designed to maintain the energy partition between the fluid and vessel throughout numerous time steps. Our results demonstrate the non-conservative nature of the system, with the porous baffle effectively dissipating energy from the overall system. Furthermore, we present findings that demonstrate the role of time-periodic variations in baffle porosity on energy dissipation. By manipulating the frequency and magnitude of this time-dependent variability, it is established that a greater amount of energy can be extracted from the system compared with the optimal fixed porosity baffle. These results shed new light on potential strategies for enhancing energy dissipation in such configurations.

Multiple moonpools within a vessel free to heave and pitch: An experimental study

Moonpools in marine vessels and offshore platforms are vertical openings through the structure used to support underwater operations. Experimental investigations of multiple moonpool resonant responses coupled with vessel heave and pitch motions are presented in this study. For three moonpools at forward, central, and aft locations of a rectangular vessel, the simultaneous location-dependent free surface response amplitudes and oscillation phases are compared for a range of incident wave frequencies in the piston mode range. For the vessel free to heave and pitch, the central moonpool has the highest response amplitude; whereas, a previous study with fixed vessel (Garad et al. 2023) showed that the largest free surface responses are observed in the forward moonpool. Due to coupled hydrodynamic interactions between the moonpool oscillations and the vessel motions, the moonpool resonance frequency is linked with the vessel heave response. Multiple response amplitudes peaks are observed in the forward and aft moonpools due to body motions. The non-dimensional response amplitude increases nonlinearly with decreasing wave steepness close to the resonance frequency. The multiple moonpool oscillations show distinct phase differences from one another and with the outer wave, the individual values depending on the incident wave frequency. Considering the vessel motions, comparison with experiments without moonpools shows that the pitch response is increased due to multiple moonpool oscillations. The hydrodynamic interactions between multiple moonpools and a floating vessel have prospective applications in the case of marine platforms, where the resonant motions can be used for wave energy conversion through oscillating water column devices.

Dynamic sloshing in a rectangular vessel with porous baffles

The damping efficiency of vertical porous baffles is investigated for a dynamically coupled fluid-vessel system. The system comprises of a two-dimensional vessel, with a rectangular cross-section, partially filled with fluid, undergoing rectilinear motions with porous baffles obstructing the fluid motion. The baffles pierce the surface of the fluid, thus the problem can be considered as separate fluid filled regions of the vessel, connected by infinitely thin porous baffles, at which transmission conditions based on Darcy’s law are applied. The fluid is assumed to be inviscid, incompressible and irrotational such that the flow in each region is governed by a velocity potential. The application of Darcy’s law at the baffles is significant as it makes the system non-conservative, and thus the resulting characteristic equation for the normal modes leads to damped modes coupled to the moving vessel. Numerical evaluations of the characteristic equation show that the lowest frequency mode typically has the smallest decay rate, and hence will persist longest in an experimental setup. The maximum decay rate of the lowest frequency mode occurs when the baffles split the vessel into identically sized regions.

Frequencies and profiles of flexural-gravity waves

New results of experiments on the effect of a floating thin plate on the regularization of a standing Faraday gravity wave on the free surface of water in a rectangular vessel are presented. It is shown that an increase in the thickness of a floating plate significantly affects both the natural frequency of oscillations of the hydroelastic system and the shape of the profiles of the observed standing flexural-gravity waves. When the plate thickness is below the critical value, the waveform is described by the theory of non-linear gravity waves; at large thicknesses, the “dry beam” approximation should be used as approximating dependencies.

Numerical Investigations of Water Column Responses at Different Moonpool Locations Within a Fixed Vessel

Abstract The oscillating water column (OWC) responses within forward, central, and aft located moonpools for a fixed rectangular vessel are studied numerically under regular head wave conditions using Reynolds-averaged Navier–Stokes-based computational fluid dynamics calculations. The free surface elevation of the confined water inside the moonpool for the piston mode frequencies is studied independently for the forward, central, and aft moonpools, showing a strong dependence on location, draft, and incident wave frequency. The relative response is largely magnified for wave frequencies around the resonant range. It is observed that the free surface response amplitude is significantly higher in the forward moonpool location, and the results are in well comparison with experiments performed in the towing tank. The variation of dynamic pressure and its influence on the moonpool responses is investigated to understand the position-specific fluctuations, which showed the presence of harmonics. The phase difference between the water column oscillations within the moonpool and the propagating wave in the domain depends on its position. Finally, the effect of the moonpool in modifying the pressure field is studied by comparison with a vessel without moonpool for a common incident wave frequency.

Structural variety of developing and equilibrium horizontal convection confined in a rectangular vessel resulting from different heating plate arrangements

Structural variety of developing and equilibrium horizontal convection confined in a rectangular vessel resulting from different heating plate arrangements

Resonant Oscillations within Multiple Moonpools for a Fixed Rectangular Vessel

_ We present experimental results of resonant free surface oscillations within three circular moonpools arranged in tandem at forward, central, and aft positions of a fixed rectangular vessel in head waves. The piston mode resonance frequency is primarily captured, which decreases with the increase in the vessel draft. The aim is to study the effect of body diffraction on the free surface amplitude and phase of the oscillating water columns at the three locations. The results indicate that, in general, the forward moonpool has the highest response amplitude, whereas the relative amplitudes of the central and aft moonpools depend on the wave frequency. It is observed that the nondimensional response amplitude increases nonlinearly with decreasing wave steepness close to the resonance frequency, while the effect diminishes at lower wave frequencies. The oscillation phase differences between the moonpools show effects of wave-body interaction, a phenomenon dependent on the vessel draft and wave frequency. Finally, the study includes a comparison of the responses at the three moonpool locations between multiple and single configurations. Introduction A moonpool is a vertical opening through the ship deck and open to the sea at the bottom, which is installed in vessels specialized in certain offshore operations. Resonant water column oscillations are encountered in moonpools (Aalbers 1984) due to vessel operations in waves. On the other hand, oscillating water columns (OWCs) have been extensively researched, primarily due to their potential for ocean wave energy conversion (Evans 1978; Heath 2012; Falcão & Henriques 2016). Now, considering design perspectives, the focus of the studies on water column resonance in waves depends on the specific marine application. For example, wave energy converters would require maximized OWC responses for efficient energy capture (Evans & Porter 1995; Morris-Thomas et al. 2007), while large free surface oscillations within moonpools of drillships have adverse effects on the vessel dynamics (Fakuda 1977).

An Experimental Design on Coffee Extraction Factors Impacting the Measurable Percent of Total Dissolved Solids in Solution

There are numerous techniques and technologies used in the brewing of coffee today. This study is aimed to design an umbrella experiment to examine the impacting key factors consistent across all methods of extraction. These factors were identified as: grind size, roast type, steep time, grind to water as a mass-to-mass ratio and temperature. Samples were prepared by grinding the beans, weighing the beans and adding the appropriate amount to a rectangular glass vessel. Distilled water was used. French press was selected as the brewing technique. No agitation after the addition of grind was allowed. Water was heated to initial temperature and added to the vessel and a timer was started. Upon time completion aliquots were taken and analysed using a prism-based automatic temperature compensation (ATC) refractometer. Minitab 19.2020.1 (64-bit) was used for analysis of variance and optimisation. In the initial design of experiments, the five factors were considered at different levels. Three factors found significant in impacting %TDS (total dissolved solids) were: total steep time, grind-to-water ratio and roast type. To further refine the experiments, 23 full-factorial design was conducted for these three factors. Finally, optimisation was done to determine the factor levels to produce a cup of coffee for the target %TDS of 1.26. This research found that it is best to use medium roast coffee that is ground fine with a 0.08 grind-to-water ratio, with an initial temperature of 195 Fahrenheit in a French press, and the ideal steep time is 7 min. Previous studies have focused on the extraction methods. In this study, the method of extraction has been removed as a variable. Hence, the findings are very useful for food industry.

Laser welded lip seal for UHV class fusion vessels–A methodical study

Lip seals are considered, the most promising options for the vacuum boundary joints in large size vacuum vessels (like rectangular neutral beam vessel with an opening size of ∼30 m) of fusion machines. Lip seals are designed with the corner welding of 2 mm thickness sheets of SS304L with the welding penetration requirement of 3 mm. With the first phase of development, laser welding parameter optimization and the sensitivity analysis was carried out to understand the effect of manufacturing tolerances (like air gap between the plates, laser beam misalignment and plate misalignment) on the weld quality. To ascertain the defined tolerances, a specialized clamping tool was configured, designed, manufactured and tested by integrating that with the assembly of laser welding head and robotic arm. For the prototype welding demonstration, the Lip seal welding of a rectangular configuration and an elliptical configuration of size 3 m × 1.5 m (∼1/3rd size of Diagnostic Neutral Beam (DNB) vessel lip seal); and 1 m length with 1.2 m diameter (exact size of DNB high voltage bushing lip seal) are considered. Welding qualification was done with the Non-Destructive and Destructive examinations. Further, the camera based feedback system for the seam tracking was incorporated to the system, which enables the remote detection and correction of the weld path. This development also extended to enable the repair of welding operation.

Surrogate-based structural optimization design of large-scale rectangular pressure vessel using radial point interpolation method

Large-scale rectangular pressure vessel possesses wide application due to volume efficiency and the convenience of transporting and installing. Despite there being increasing emphasis on weight reduction, the optimization design method for large-scale rectangular pressure vessel is still under development due to complicated geometry and engineering constraints that make conventional optimization approaches incapable. Therefore, a surrogate-based optimization design method is proposed in this work to resolve the aforementioned difficulties. The proposed technique adopts radial point interpolation method to construct surrogate model, which is validated with classical numerical examples and a rectangular pressure vessel, i.e., the test section of a large-scale water tunnel. Fair convergence and precision have been revealed. Then, the surrogate-based optimization framework is established on the basis of the surrogate model, involving optimization scheme, sampling range and constraints, sampling method, standard optimization model and method. Subsequently, the investigated rectangular pressure vessel is optimized using the developed method. The optimized structure maintains good machinability and reduces weight by 10.06% in comparison to the results of preliminary routine structural design, proving that the developed technique possesses good capacity for the optimization design of large-scale rectangular pressure vessels.

ГЕОДИНАМИЧЕСКИЕ ПРОЦЕССЫ В СКЛОНЕ ПОДНЯТИЯ

The flow for the uplift slope is considered in the viscous liquid model. The relevance of the study is justified by the need for experimental and theoretical analysis of the geodynamic processes occurring in the slopes of rises. The object of the study is the slopes of rises, formed by mantle thermochemical plumes which have not come to the surface. The objectives of the study are to present the velocity profile of the viscous flow of the uplift slope and to determine the friction coefficient for it; to find out the effect of the dynamic viscosity coefficient of the slope on the appearance of compressive and tensile stresses; on the basis of laboratory and theoretical simulations to find out the hydrodynamics of the flow when the liquid flows from a rectangular vessel and using the results of geodynamic simulations to determine the flow parameters in the area of the uplift slope fault formation. The flow occurring in a viscous liquid at a constant inclination angle of the free surface of the elevation slope is considered. In a highly viscous liquid at low flow velocities, the inertial terms in the equation of motion can be neglected. For this case, the solution of the equation of motion in a layer with an inclined free surface at a constant horizontal pressure gradient is obtained. The flow velocity profile in such a layer and the relation for the maximum flow velocity are obtained. The tangential stress on the sole of the layer is determined. The tangential stress does not depend on the viscosity, but depends on the layer thickness. With a constant viscosity of the layer, the elevation slope is under conditions of compressive stresses. Strain conditions for the uplift slope are possible when the viscosity of the layer decreases with distance from the main ridge. Discontinuities occur on the elevation slopes due to changes in viscosity along the slope and changes in the velocity. Under the influence of gravitational forces caused by the density difference at the rupture boundary, flow occurs and the resulting free volume is filled. The motion in a highly viscous liquid during the formation of a free vertical surface has been studied experimentally when liquid flows out of a transparent rectangular vessel. Photographs of the free surface were obtained. A linear dependence of the relative height of the free surface location on the relative horizontal coordinate is observed. Expressions are obtained for the average velocity and expiration time of a viscous liquid from a rectangular vessel. Estimates of the average velocity and outflow time for the specified slope parameters are presented

Experimental validation of liquid metal MHD numerical models

This study is aimed at experimental validation of a numerical model of fully coupled electromagnetic and fluid dynamics processes. The experiment is a laboratory-scale system, where a rotating permanent magnet induces an intense flow and free surface deformation of liquid Galinstan in a rectangular vessel. The numerical model is two-phase, 3D, transient, turbulent, and is constructed using ElmerFEM, OpenFOAM and EOF-Library codes. Validation is based on optical imaging of free surface projections. Statistical data, such as the time-average and standard deviation of the free surface profile, are compared with experiments and simulations. Results show that a Large Eddy Simulation turbulence model gives a good agreement with experiments, whereas a Reynolds-Averaged Navier-Stokes k-ω SST model causes artificial damping of free surface deformation. Figs 8, Refs 9.

Natural convection characteristics of phase-change material emulsions in a rectangular vessel with vertical heating/cooling walls

Emulsions in which phase-change-material (PCM) particles are dispersed are termed PCM emulsions (PCMEs). PCMEs have a high fluidity and a high thermal energy storage density because of the latent heat of the PCM particles, and thus they have attracted attention for potential use as an efficient thermal energy storage and transport media. In thermal energy storage inside a heat storage tank, the heat is stored in PCMEs by natural convection heat transfer. Therefore, it is important in the practical use of PCMEs to understand the natural convection characteristics of PCMEs. In this study, the natural convection characteristics of PCMEs inside a rectangular vessel were investigated experimentally. The state of convection formed in PCMEs by natural convection and the heat-transfer characteristics were investigated. The aspect ratio of the rectangular vessel was changed to 2, 3 and 4, and the effect of the aspect ratio on the state of convection and the heat-transfer characteristics was investigated. The state of convection that formed inside PCME without a phase change of PCM particles was the same as that of a single-phase fluid, such as water. The formation of multiple convection layers was confirmed in PCME because of the phase change of PCM particles. The experimental results showed that the formation of the multiple convection layers was attributed to the density distribution of the PCMEs, which depends on the PCME temperature and the PCM particle state. The aspect ratio of the rectangular vessel did not affect the formation of multiple convection layers, and formation was confirmed in all 2, 3 and 4 aspect ratios. An examination of the heat-transfer characteristics of the PCME showed that the heat transfer was promoted when accompanied by a PCM particle phase change. The amount of PCM particles that melted and solidified in the rectangular vessel affected the heat-transfer promoting effect. This tendency was the same for all aspect ratio, but the heat-transfer promoting effect was most remarkable when the aspect ratio was 3.

Surface gravity waves in a wedge-shaped vessel

The results of experiments on the excitation of standing surface gravity waves in a cylindrical vessel with a wedge-shaped base are presented. The fundamental difference from the liquid wave motions in a rectangular vessel is the absence of spatial symmetry for the profile of maximum development and an increase in the wave amplitude towards the wedge tip. To describe waves in a wedge-shaped vessel, a numerical-analytical model of long waves in a vessel of variable width and a linear model of standing waves in a vessel with a base in the form of a circular sector with a small central angle are used.

Effect of vent area on the vented methane-air deflagrations in a 1 m3 rectangular vessel with and without obstacles

The effects of vent area on pressure and flame evolution in a 1 m3 vessel with and without obstacles were investigated. Five pressure peaks of Popen, Pout, Pext, Phel, and Pvib, which correspond to vent activation, flame venting, external explosion, Helmholtz oscillation, and the coupling of acoustic waves and flames, respectively, were observed without obstacles when the vent coefficient Kv ≤ 6.25. However, the pressure peaks of Pext and Pout from the external explosion and flame venting disappeared when Kv > 6.25. Moreover, the pressure peaks of Popen and Pvib produced by vent activation and acoustically enhanced combustion become dominant when Kv ≥ 12.5. With the installation of obstacles, the pressure peak Pvib induced by acoustically enhanced combustion disappeared. The other four pressure peaks were observed when Kv < 6.25. The pressure peaks induced by the external explosion and the Helmholtz oscillation disappeared when Kv ≥ 12.5. Nevertheless, the pressure peak resulting from the obstacles was observed and became dominant at Kv ≥ 12.5. It takes less time for the external flame to propagate to the maximum displacement in the tests with obstacles than that without obstacles, and the maximum flame length for the former is smaller than the latter.