Stagnant Liquid Research Articles

Non-linear sloshing characteristics of liquid inside a chamfered bottom tank with submerged internal object under near-and far-fault earthquakes

Cylindrical and rectangular-shaped tanks have a concentration of stagnant impulsive liquid at the bottom corners that do not participate in sloshing. While used as tuned liquid dampers (TLDs), this non-participating fluid adds extra liquid mass to the tank but does not have any role in the vibration control aspect. In the present study, to decrease the stagnant impulsive liquid, a chamfered bottom-shaped tank with a submerged internal object is demonstrated. Due to the high-energy velocity pulse present in near-fault earthquakes, there is a possibility of violent liquid sloshing which may cause unwanted structural damage to the tank. Hence, the present study focuses on the influence of near- and far-fault earthquakes on the non-linear seismic behavior of the tank with submerged internal object. The non-linear sloshing is modeled using the finite element method based on a combined Eulerian-Lagrangian approach. The accuracy of the present non-linear numerical model is checked by verifying the results with the previously published results. In addition to the absolute response, the dynamic convective and impulsive response components are quantified. The proposed non-linear finite element scheme can be utilized in the context of structure-mounted chamfer bottom TLDs in the future.

Stagnant liquid layer as “Microreaction System” in submerged plasma Micro-Jet for formation of carbon quantum dots

This study aims to intensify reactivity via bespoke transient hydrodynamics in a plasma-activated three-phase catalyst system. Likewise, three-phase plasma systems in literature are not well designed, understood and commercially available. The synthesised N-doped carbon quantum dots, with application as fertilisers and wastewater treatment was evaluated as a model reaction. A plasma microjet was produced using a commercial plasma system, creating an almost flat, large interface covering a thin stagnant liquid layer with a catalyst bed underneath. In this hydrodynamic regime, plasma can penetrate the catalyst bed via the stagnant thin liquid film and polarise the plasma-liquid interface. The new process regime’s effectiveness is proven by the enhanced reaction rate achieved by raising liquid diffusivity toward the catalyst bed through solvent viscosity reduction. Results indicate that the reaction rate depends on the small surface area interacted with the plasma jet amid an excess of excited species, not the total gas–liquid interface area. The plasma process competes energetically with the best dielectric barrier discharge processes and uses less energy than microfluidic processing in chemical microreactors. High momentum transfer from the plasma jet to the liquid partly evaporates non-water additives, impacting process design and requiring reduction.

Development of a simplified one-dimensional CDA bubble model

Sodium-cooled fast reactors (SFRs) have high safety with an extremely low probability of a core disruptive accident (CDA). However, from a defense-in-depth perspective, the CDA sequence is still worth studying. Severe accidents in SFRs, such as unprotected loss of flow, might lead to a CDA during which fuel and some fission products could be instantly released from a large CDA bubble through potential leak paths in the top shield structure. Therefore, a reasonable prediction of dynamic behavior of a large-scale bubble within the sodium pool is vital for accurately evaluating the migration of source terms. In this study, we propose a simplified one-dimensional CDA bubble model that can handle heat and mass transfer in two-phase multicomponent materials in different computational domains during the rising of bubbles through the sodium pool toward the cover-gas region. In this model, an entrainment model based on the Rayleigh–Taylor instability and Kelvin–Helmholtz instability was used to explain the coolant entrainment through the gas/liquid boundary and jet fragmentation. The model also addresses the mitigation effect of non-condensable gases on the condensation of fuel, steel and sodium vapor at bubble interface. We evaluated the model using a past experiment on the expansion of a two-phase, large bubble with high pressure in a stagnant liquid pool conducted by Purdue University in the late 1970 s using a 1/7-scale model of Clinch River Breeder Reactor. Good agreement with the experimental data demonstrates that the developed model can reasonably represent the essential characteristics of dynamic behavior of a large, high-pressure bubble with heat and mass transfer in two-phase multicomponent materials. This is valuable for evaluating the migration of the source terms, which will be carried out in future studies.

Corrosion behavior of magnetron sputtering Fe31Cr20Al17Ti16Nb16 high entropy coating in liquid lead-bismuth eutectic with different oxygen concentration at 500 °C

The major concern of the structure integrity of lead cooled reactor is the corrosion behavior of fuel cladding and other core internal materials. Magnetron sputtering technology is adopted as an surface coating method to improve the corrosion resistance of nuclear fuel cladding exposed to liquid lead-bismuth eutectic (LBE). Fe31Cr20Al17Ti16Nb16 high entropy alloy (HEA) coatings were prepared on tubular ferritic/martensitic (F/M) steel which is the candidate fuel cladding material, and the corrosion behaviors of Fe31Cr20Al17Ti16Nb16 coatings in LBE are investigated in this work. F/M steel specimens with Fe31Cr20Al17Ti16Nb16 coatings were exposed to 500 °C stagnant liquid LBE with oxygen concentration of Co ≈ 1 × 10−4 wt% and Co ≈ 1 × 10−7 wt% for 1000 h respectively. The primary findings suggest that the oxygen content of LBE mainly affects the morphology of duplex oxide layers generated during corrosion process, which resulting from the different inward diffusion flux of oxygen. In oxygen-saturated (Co ≈ 1 × 10−4 wt%) LBE, the overall oxide layer exhibits bulging and incompact morphology and infiltration of Pb is probed at inner Cr2O3 oxide layer, larger-sized cavities (the observed maximum dimension reaches 233.5 nm) distribute close to the outer Fe3O4/FeCr2O4 layer; In oxygen-depleted (Co ≈ 1 × 10−7 wt%) LBE, duplex oxide layer presents relatively dense and uniform state, tiny cavities (observed maximum dimension is 38.3 nm) dispersing at the internal of oxide areas. Corrosion rates of the Fe31Cr20Al17Ti16Nb16 coatings under two oxygen situations are 2 orders of magnitude lower than uncoated F/M steel under same exposure condition, the oxide layers with better uniformity and density produced in Co ≈ 1 × 10−7 wt% LBE indicating the better application advantage of Fe31Cr20Al17Ti16Nb16 coatings in oxygen-depleted LBE.

Thermocapillary central lamella recess during droplet impacts onto a heated wall

We experimentally observe a new phenomenon, the formation of a toroidal region of lower film thickness in the center of the lamella formed during high Weber number water droplet impacts onto smooth heated walls. This region forms around the air bubble, which is entrapped during the initial impact phase at the impact center. Our study encompasses a variation of the droplet size, impact velocity, surface wettability and temperature. We show how this phenomenon can be explained considering a two-step process involving thermocapillary convection in two separate regions: The temperature gradient along the surface of the entrapped air bubble caused by heat conduction induces flow that pumps warmer liquid to the lamella-ambient interface due to the Marangoni effect. The non-uniform temperature distribution along it then causes fluid acceleration in the radial direction, depleting the fluid volume around the bubble in a self-amplifying manner. We use direct numerical simulations of a stagnant liquid film with an enclosed bubble at the wall to confirm this theory.

NUMERICAL MODELING OF BUBBLE DYNAMICS USING INTERFACE CAPTURING METHOD

In the present numerical study, a dynamics of single gas bubble (circular in 2D and spherical in 3D) rising in a stagnant viscous liquid due to the buoyancy is presented using various volume of fluid (VOF) based computational fluid dynamics (CFD) solvers such as commercial Converge and Star CCM+, and open source OpenFOAM<sup>®</sup> platform. To capture the interface dynamics, either an interpolated curved interface based on the high-resolution interface framework or a mass conservative VOF approach with a planar sharp interface based geometric reconstruction of the piecewise-linear interface calculation (PLIC) scheme was used. Both qualitative and quantitative analysis of air bubble rising upward inside the quiescent water column at ratios of low density, ρ<sub>r</sub> = 10 and high density, ρ<sub>r</sub> = 1000 are simulated and evaluated similar to report by Hysing et al. The proposed numerical models can simulate a wide range of density and viscosity ratios. In this study, a robustness and accuracy of the solvers are evaluated and comparative study between open source OpenFOAM<sup>®</sup> solver with commercial solvers such as Converge and Star CCM+. Based on the present numerical results, the gas bubble base undergoes severe deformations for the high density ratio, ρ<sub>r</sub> = 1000 and high viscosity ratio, μ<sub>r</sub> = 100 compared to low density ratio, ρ<sub>r</sub> = 10 and low viscosity ratio, μ<sub>r</sub> = 10. Any of the solvers can be used to simulate complex multiphase flow situations encountered in many industrial applications.

Dynamics of single bubble ascension in stagnant liquid: An investigation into multiphase flow effects on hydrodynamic characteristics using computational simulation

Industrial operations often involve multiphase flows, where the motion of bubbles plays a crucial role in determining hydrodynamic properties. In the context of modern practices, advanced computational solvers are increasingly employed to simulate the interactions and trajectories of bubbles within complex flows. This study stands out in its unique examination of the computational software COMSOL's capability to accurately simulate the upward motion of a single bubble within quiescent water, akin to a liquid-like environment. The novelty lies in the comprehensive coverage of various container diameters (ranging from 10 to 80 mm) and heights (from 25 to 300 mm) relative to the air bubble diameter (ranging from 0.5 to 8 mm). Through meticulous comparisons between nine empirical formulas and numerically projected bubble ascent through a water column, a remarkable level of agreement emerges, underscoring the precision and consistency of the simulations. These simulations unveil intriguing findings, shedding light on the intricate interplay of forces governing bubble behavior. Notably, variations in drag forces induce changes in bubble shapes as a function of diameter, while the ascent of bubbles is accompanied by distinctive vortices, resulting in fascinating asymmetry. Furthermore, vorticity concentrates within the bubble, particularly in lighter fluid regions characterized by reduced pressure. The study also unveils how larger aspect ratios minimize flow drag, consequently boosting ascent velocities, and demonstrates the influence of container diameter on the rising velocity. Gravitational forces are found to reduce ascent velocities at greater column heights, while the rate of air bubble rise escalates with its size. This meticulous exploration of bubble dynamics in multiphase flows yields invaluable insights for diverse industrial applications, ultimately enhancing our understanding of this complex phenomenon. The strong alignment observed between empirical formulations and numerical simulations within the COMSOL framework underscores the utility of such computational tools for the study and design of multiphase flows' intricate dynamics.

Investigation of key parameters for the operation of a sodium heat pipe with visualization using X-ray radiography

Alkali metal heat pipes are considered as a promising primary cooling system of special-purpose nuclear reactors. For the deployment, it is important to understand the heat pipe’s behaviors under different operation conditions. In this paper, the startup characteristics and operation performance of three sodium heat pipes with 67%, 102% and 172% sodium filling ratios, respectively, were investigated, and the two-phase sodium flow was visualized using high-speed, high-resolution x-ray radiography. The boiling flow regimes in the evaporator region were categorized into stagnant sodium liquid pool, geyser boiling and developed boiling. The effect of key parameters, such as the boundary conditions of the evaporator and condenser, the sodium filling ratio, and the inclination angle were investigated. It was found that the heater power and condenser cooling conditions have a great influence on the operation temperature within the achievable range of heat transfer rate. The filling ratio and inclination angle affect the boiling phenomena and the heat pipe operational range. The experiments can provide valuable data for heat pipe model validation as well as the design of the special-purpose nuclear reactor and other high-temperature heat pipe systems.

Investigation on interphase mass transfer coefficient of a deformable bubble with density contrast using phase-field lattice Boltzmann method

The gas–liquid mass transfer process with density contrast is modeled in this paper using a phase-field Lattice Boltzmann (LB) method. In this method, the phase-field model used to calculate the flow field and the continuous species transfer model used to calculate the concentration distribution are coupled by introducing the divergence condition of the velocity in the presence of mass transfer into the Allen-Cahn equation. For a deformable bubble rising in stagnant liquid, a two-dimensional parameter dependence study is conducted and the results indicate that an increase in initial diameter, as well as a decrease in liquid diffusion coefficient or liquid viscosity, can improve the steady-state value for the Sherwood number, whereas the distribution coefficient has a little impact on this steady-state value. Furthermore, a correlation originally proposed by Takemura and Yabe (1998) modified with a shape factor can be used to predict the steady-state Sherwood number in the numerical results.

Bubble Formation and Motion in Liquids—A Review

In flotation, a bubble acts as a carrier for attached particles. The properties of the gas–liquid interface of the bubble are one of the main factors determining the bubble motion and flotation efficiency. Monitoring of the bubble motion may deliver interesting information about the state of the gas–liquid interface. In the case of pure liquids, a bubble surface is fully mobile, while the presence of surface-active substances (e.g., surfactants) causes diminishing bubble velocity due to the retardation of the interface fluidity. The theoretical prediction of the terminal velocity value for the bubble has been investigated for over a century, delivering a number of various models describing bubble motion in a liquid. This narrative review is devoted to the motion of the bubble in stagnant liquids and is divided into three main sections describing: (i) experimental techniques for tracking bubble motion, (ii) bubble motion and shape deformation in clean water, and (iii) bubble motion in solutions of surface-active substances.

Dynamics of a Rising Taylor Drop in a Stagnant Shear-Thinning Liquid

Dynamics of a Rising Taylor Drop in a Stagnant Shear-Thinning Liquid

Numerical study of flashing pipe flow using a TFM-PBM coupled method: Effect of interfacial heat transfer and bubble coalescence and breakup

In the present work, the two-fluid model (TFM) is coupled with the population balance model (PBM) to trace the spatial and temporal change of bubble size and interfacial area concentration (IAC) in flashing flows. The model is first validated for bubble growing in stagnant superheated liquid, and satisfactory predictions of the bubble size under low and moderate superheat are obtained. It is then applied to flashing pipe flows, which are characterized by low superheat and high turbulence intensities. The results show that in these cases, coalescence and breakup are important phenomena changing the bubble size distribution in addition to growth. The neglect of their contribution leads to a significant under-prediction of the bubble size and consequently over-prediction of IAC. In addition, choosing an appropriate closure for interfacial heat transfer coefficient (HTC) is another key point in flashing simulation. In high-Reynolds cases (e.g. Re > 106), the enhancement due to turbulence is non-negligible.

Momentum exchange modeling for coarsely resolved interfaces in a multifield two‐fluid model

AbstractMorphology‐adaptive multiphase models are becoming more established for the numerical description of complex gas‐liquid flows adapting dynamically to the local flow morphology. In the present study, two different numerical methods originally designed for distinct flow morphologies are combined, namely the volume‐of‐fluid and the Euler–Euler method. Both edge cases have been proven to be capable of delivering reliable predictions in the respective use cases. The long‐term goal is to improve the prediction of gas‐liquid flows, regardless of the flow regime in a specific application. To capture the system dynamics with a given grid resolution, the flow fields need to be predicted as precise as possible, while the shape of structures such as gas bubbles need to be recovered adequately in topology and shape. The goal is to obtain reliable predictions on intermediate mesh resolutions rather than relying on fine meshes requiring more computational resources. Therefore, a procedure is proposed to locally measure the degree of resolution. With this information, the hydrodynamics in the interface region can be controlled by means of a dedicated interfacial drag formulation in order to improve simulation results across several levels of spatial resolution. A modified formulation of buoyancy is proposed to prevent unphysical oscillations of vertical velocity near a horizontal interface. The functionality is demonstrated in a three‐dimensional case of a gas bubble rising in stagnant liquid and in a co‐current stratified air‐water channel flow in two‐dimensional space. The choice of these different applications demonstrates the general applicability of the proposed model framework.

A three-dimensional ISPH-FVM coupling method for simulation of bubble rising in viscous stagnant liquid

The bubble rising problem has always been one of the research hotpots in the field of multiphase flow simulation due to the complex topological evolution of the phase interface. In this paper, an approach of coupling incompressible smoothed particle hydrodynamic (ISPH) and finite volume method (FVM) in three-dimensional space (abbreviated as 3D ISPH-FVM coupling method) is developed to simulate the bubble rising in viscous stagnant liquid. In the 3D ISPH-FVM coupling method, the coupling framework between the two numerical schemes is established through the information exchange at the overlapping regions. The effect of surface tension is evaluated by implementing the 3D continuum surface force model (CSF). To verify the interface capture accuracy of the 3D ISPH-FVM coupling method, several benchmark cases are tested. Then, the single bubble rising in viscous fluid is simulated by 3D ISPH-FVM coupling method, in which the results are compared with the experimental data and other numerical results in the literatures. To further explore the ability of 3D ISPH-FVM coupling method in bubble rising simulation, the effect of some parameters (including numerical and physical parameters) on single bubble rising is investigated. Afterwards, the dynamics phenomena of two bubbles coalescence are also studied. Numerical results validate the robustness and stability of the present coupling model in simulating the bubble rising.

CFD simulation of a small bubble motion in 3D flow domain: effect of liquid density, viscosity and surface tension

The motion of spherical and slightly deformed bubbles rising rectilinearly in a stagnant liquid was numerically simulated in a fully three-dimensional domain using the CFD solver COMSOL Multiphysics. The interface was tracked by the built-in conservative Level set method on a fixed numerical grid. The purpose of this work was to study the single bubble motion in three industrially used liquids that differ significantly in surface tension, density, and viscosity. The motion of bubbles with diameters up to 1.6 mm was also studied experimentally using a high-speed camera. The data obtained together with the results of theoretical models for bubble motion were used for the validation of the simulation data. Using a 3D domain, very good agreement was obtained in both bubble shape deformations and bubble terminal velocity. The best results were achieved for propanol with low surface tension and low viscosity. In the case of high surface tension and low viscosity liquid (water), both the bubble deformation and the bubble velocity were slightly underestimated. In the case of glycerol (high surface tension and viscosity), the negligible bubble deformation is correctly calculated, but the velocity is again slightly underestimated.Graphical abstract

Performance of Sc-Y-ODS variant of Eurofer steel in stagnant PbLi at 600°C

This paper represents a part of the research of structural materials for fusion systems. The performance of a conventionally formed Eurofer-97 steel and its Sc-Y-ODS variant developed by our group was assessed in a stagnant liquid PbLi environment. The experiments were performed at 600°C for 500 and 1000 hours, and the subsequent microscopical investigation identified a solution-based attack as the dominant corrosion damage of both materials. The metal loss of the conventional Eurofer-97 steel was 66.2 µm after 1000 h exposure, corresponding to a rate of 580 µm/year. In contrast, the ODS Eurofer variant strengthened with various fine Sc-Y complex oxides showed a 70% lower corrosion damage, mainly owing to formation of a Sc-Y-rich Pb surface layer. To understand the degradation process in more detail, both materials were characterized before and after the PbLi exposure in terms of their microstructures and mechanical behavior including hardness, tensile, impact and static fracture toughness tests.

3D numerical study of a single Taylor bubble rising along an inclined tube through Newtonian and non-Newtonian liquids

Slug flow is an important gas-liquid flow pattern characterized by large bullet-shaped bubbles (Taylor bubbles) and is widely found in industrial and natural applications. The hydrodynamics are complex and depend on tube dimensions and orientation, operating conditions, and physical properties. Therefore, detailed knowledge of slug flow hydrodynamics can provide insight into a robust and safe intensification of industrial processes in several fields.This work fills a gap in knowledge by producing new information about slug flow in inclined tubes. For the first time with complete conservative equations, CFD tools are applied to simulate 3D systems composed of isolated Taylor bubbles rising through stagnant liquids in tubes with different inclinations. This study addresses Newtonian liquids with different viscosities and non-Newtonian liquids with shear-thickening behavior.The effects of geometric and physical properties are assessed, and descriptions of bubble shape and velocity, liquid film thickness, velocity profiles around the bubble, and liquid wake characteristics are presented and discussed.The results allow to conclude that the tube inclination deeply impacts the flow by changing the bubble position, velocity, shape, and the way the liquid flows around it. The inclination effect coupled with different liquid rheology introduced even more complexity to the hydrodynamic features.

Numerical study of rising Taylor bubbles driven by buoyancy and additional pressure

The Taylor bubble driven by buoyancy and additional pressure is in a non-equilibrium state, which bubble and liquid flow have an accelerated tendency of rising, and the bubble behavior is significantly different with the Taylor bubble in stagnant liquid. In order to understand the dynamic properties of such bubbles, a numerical study was conducted using the coupled level-set and volume-of-fluid (CLSVOF) method combined with the stress-blended eddy simulation (SBES) model. The research results indicated that, due to the additional pressure, the difference between the bubble pressure head and the liquid column height is larger than zero, the pressure gradient force acting on the liquid column is greater than the force of gravity, this makes the bubble have an accelerating upward trend. The bubble shape and liquid film thickness are closely related to the relative bubble velocity, the correlation between dimensionless liquid film thickness and Reynolds number of relative bubble velocity was proposed. In addition, the article analyzed the influence mechanism of bubble shape, which is determined by the stress state of the fluid surrounding the bubble. Under the additional pressure, the axial stress on the bubble top increases significantly, while the radial stress remains almost invariable, which makes the bubble shape gradually become thinner.

In Situ TEM Observation of Stagnant Liquid Layer Activation in Nanochannel.

The kinetics of mass transfer in a stagnant fluid layer next to an interface govern numerous dynamic reactions in diffusional micro/nanopores, such as catalysis, fuel cells, and chemical separation. However, the effect of the interplay between stagnant liquid and flowing fluid on the micro/nanoscopic mass transfer dynamics remains poorly understood. Here, by using liquid cell transmission electron microscopy (TEM), we directly tracked microfluid unit migration at the nanoscale. By tracking the trajectories, an unexpected mass transfer phenomenon in which fluid units in the stagnant liquid layer migrated two orders faster during gas-liquid interface updating was identified. Molecular dynamics (MD) simulations indicated that the chemical potential difference between nanoscale liquid layers led to convective flow, which greatly enhanced mass transfer on the surface. Our study opens up a pathway toward research on mass transfer in the surface liquid layers at high spatial and temporal resolutions.

Effect of engraved concentric circles on pool boiling of water

Abstract Pool boiling takes place when a stagnant liquid is placed on a surface above the saturation temperature of the liquid. Thermal studies have attracted a large number of researchers working in different segments of the industry to meet the heating and cooling demands of each individual. The pool boiling is a highly effective technique of convective heat transfer to maintain the system operation under safe temperature and safe temperature limits for better performance and longevity. This study investigates the effect of engraved concentric circles on aluminium disc in de-ionized water. The experiments are conducted by varying pitch ratio (P) and indentation ratio (I) of engraved concentric circles in the range of 0.0125–0.05, and 0.002–0.008, respectively. The maximum enhancement in the boiling heat transfer coefficient is found to be 21.11% more than that of a plain surface corresponding to the pitch ratio of 0.0125 and indentation ratio of 0.008.