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At least 955 records · Page 53

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively--based on upscaled parameters such as surface area, solid volume, and effective reaction rate--and qualitatively--based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

58 GEOSCIENCES↗

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transport barriers to self-propelled particles in fluid flows

Here, we present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into xy space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Phase separation, edge currents, and Hall effect for active matter with Magnus dynamics

Here we examine run-and-tumble disks in two-dimensional systems where the particles also have a Magnus component to their dynamics. For increased activity, we find that the system forms a motility-induced phase-separated (MIPS) state with chiral edge flow around the clusters, where the direction of the current is correlated with the sign of the Magnus term. The stability of the MIPS state is non-monotonic as a function of increasing Magnus term amplitude, with the MIPS region first extending down to lower activities followed by a break up of MIPS at large Magnus amplitudes into a gel-like state. We examine the dynamics in the presence of quenched disorder and a uniform drive and find that the bulk flow exhibits a drive-dependent Hall angle. This is a result of the side jump effect produced by scattering from the pinning sites and is similar to the behavior found for skyrmions in chiral magnets with quenched disorder.

97 MATHEMATICS AND COMPUTING↗

Additional EIPC Study Analysis: Interim Report on High Priority Topics

Between 2010 and 2012 the Eastern Interconnection Planning Collaborative (EIPC) conducted a major long-term resource and transmission study of the Eastern Interconnection (EI). With guidance from a Stakeholder Steering Committee (SSC) that included representatives from the Eastern Interconnection States Planning Council (EISPC) among others, the project was conducted in two phases. Phase 1 involved a long-term capacity expansion analysis that involved creation of eight major futures plus 72 sensitivities. Three scenarios were selected for more extensive transmission- focused evaluation in Phase 2. Five power flow analyses, nine production cost model runs (including six sensitivities), and three capital cost estimations were developed during this second phase. The results from Phase 1 and 2 provided a wealth of data that could be examined further to address energy-related questions. A list of 13 topics was developed for further analysis; this paper discusses the first five.

Electricity Grid↗

Additional EIPC Study Analysis: Final Report

Between 2010 and 2012 the Eastern Interconnection Planning Collaborative (EIPC) conducted a major long-term resource and transmission study of the Eastern Interconnection (EI). With guidance from a Stakeholder Steering Committee (SSC) that included representatives from the Eastern Interconnection States Planning Council (EISPC) among others, the project was conducted in two phases. Phase 1 involved a long-term capacity expansion analysis that involved creation of eight major futures plus 72 sensitivities. Three scenarios were selected for more extensive transmission- focused evaluation in Phase 2. Five power flow analyses, nine production cost model runs (including six sensitivities), and three capital cost estimations were developed during this second phase. The results from Phase 1 and 2 provided a wealth of data that could be examined further to address energy-related questions. A list of 14 topics was developed for further analysis. This paper brings together the earlier interim reports of the first 13 topics plus one additional topic into a single final report.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Kinetic Model of the Long-Term Corrosion of Glass-Ceramic Materials

Multiphase waste forms show promise for increased waste loading and for the ability to dispose of contaminated solid and particulate waste through direct densification. However, achieving predictive capability for long-term durability of multiphase waste forms, and thus assessing their possible deployment, requires expanding the current, limited knowledge base. Here, we describe the development of a corrosion model of a two-phase waste form consisting of crystals of known volume fraction embedded in a glass matrix. This model accounts for the dissolution of both the crystalline and glass phases as well as the hydration of the glass phase through an ion exchange reaction. Because of the large difference in solubility between the two phases, the reactive surface of the crystalline phase is a function of the extent of dissolution of the glass phase in this model. Model parameterization was performed using corrosion data, such as from single-pass flow-through tests, for the individual phases. The parameterized corrosion model was evaluated against static dissolution test data for a glass-ceramic multiphase waste form. This evaluation demonstrated the model’s ability to reproduce the time-dependent release of key tracers of glass and crystalline phase dissolution. Hence, the development of a kinetic model provides a pathway for long-term durability predictions and thus the use of multiphase waste forms in nuclear cleanup missions.

Kerisit, Sebastien N.↗

Electric-field–induced assembly and propulsion of chiral colloidal clusters

Chiral molecules with opposite handedness exhibit distinct physical, chemical, or biological properties. They pose challenges as well as opportunities in understanding the phase behavior of soft matter, designing enantioselective catalysts, and manufacturing single-handed pharmaceuticals. Microscopic particles, arranged in a chiral configuration, could also exhibit unusual optical, electric, or magnetic responses. In this paper, we report a simple method to assemble achiral building blocks, i.e., the asymmetric colloidal dimers, into a family of chiral clusters. Under alternating current electric fields, two to four lying dimers associate closely with a central standing dimer and form both right- and left-handed clusters on a conducting substrate. The cluster configuration is primarily determined by the induced dipolar interactions between constituent dimers. Our theoretical model reveals that in-plane dipolar repulsion between petals in the cluster favors the achiral configuration, whereas out-of-plane attraction between the central dimer and surrounding petals favors a chiral arrangement. It is the competition between these two interactions that dictates the final configuration. The theoretical chirality phase diagram is found to be in excellent agreement with experimental observations. We further demonstrate that the broken symmetry in chiral clusters induces an unbalanced electrohydrodynamic flow surrounding them. As a result, they rotate in opposite directions according to their handedness. Both the assembly and propulsion mechanisms revealed here can be potentially applied to other types of asymmetric particles. Lastly, such kinds of chiral colloids will be useful for fabricating metamaterials, making model systems for both chiral molecules and active matter, or building propellers for microscale transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstration and Feasibility Analyses of using the Dual-Purpose Canister Drain Pipe to Support the Filling Process

This report documents experiments that are being used to determine the feasibility of filling dual-purpose canisters (DPCs) using the existing drain pipe. Mercury was identified as a surrogate filler for the initial experiments. Oak Ridge National Laboratory’s Target Test Facility (TTF), which is a full-scale Spallation Neutron Source (SNS) prototypical mercury loop, is being used for the planned pipe experiments using mercury. The pipe experiments were divided into two phases to provide a separate effects approach to the problem and to allow for development of system scalability. The first phase included taking strain measurements in a short length pipe, as well as measurements of flow-induced vibration. The second phase consists of the design and construction of a separated mercury flow loop capable of hosting exchangeable test sections and more localized instrumentation. Data acquisition of Phase I was performed during this reporting time period, and subsequent data reduction and data analysis will be performed in the future.

36 MATERIALS SCIENCE↗

A Study of Turbulence-Driven Inward Momentum Flux & Construction of a Difference Scheme for Fokker-Planck-Landau Operator

Momentum transport driven by microinstability is studied via analytic theories, gyrokinetic simulations, and experimental data analysis. A scenario for rotation profile evolution is constructed based on experimental observation that parallel flow initiates at edge region and penetrates into core region of tokamak [1]. In particular, turbulent diffusion and inward convective pinch are studied according to this scenario. For study of convective momentum pinch, toroidal ion temperature gradient mode near marginal stability is examined in kinetic limit. It is found from quasilinear estimation that the inward turbulent equipartition momentum pinch remains as the most robust part of pinch. In addition, it is found that ion temperature gradient driven momentum pinch is inward for typical parameters, while ion density gradient driven momentum pinch is outward. It is shown by theoretical formulas and experimental data analysis that momentum pinch velocity is sensitive to the electron to ion temperature ratio. For study of diffusive momentum transport, parallel shear flow instability is studied in fluid limit. Diffusion coefficient using mixing length estimate from nonlocal theory reveals that it has a strong dependence on the parallel flow shear and is mainly carried by fluctuations in short wavelength regime. Gyrokinetic simulation of collisionless parallel shear flow instability shows that the analytic prediction of diffusion coefficient is comparable to numerical values in the linear phase of the simulations. In the nonlinear phase, fluctuation energy gets transferred to the long wavelength regime. A two-dimensional, uniform velocity-grid based solver for the nonlinear Fokker-Planck-Landau (FPL) collision operator has been developed in the limit of strong magnetic field. The conservative and entropy increasing semidiscretized numerical scheme for the isotropic FPL equation by C. Buet et al. (2002) has been extended to 2D velocity space. A Picard fixed point method is used for semi-implicit time advance. One time evaluation of interpolation coefficients for probability distribution function is introduced so that numerical equilibrium is achieved with Maxwellian. However, positivity property is sacrificed at the saving of computational costs. In addition, a highly practical method is suggested to apply the velocity-grid based collision solver to particle-in-cell code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Demonstration and Feasibility Analyses of Using the Dual-Purpose Canister Drain Pipe to Support the Filling Process

This work documents experiments that are being used to determine the feasibility of filling dual-purpose canisters (DPCs) using the existing drain pipe. Mercury was identified as a surrogate filler for the initial experiments. Oak Ridge National Laboratory’s Target Test Facility (TTF), which is a full-scale Spallation Neutron Source (SNS) prototypical mercury loop, is being used for the planned pipe experiments using mercury. The pipe experiments were divided into two phases to provide a separate effects approach to the problem and to allow for development of system scalability. The first phase included taking strain measurements in a short length pipe, as well as measurements of flow-induced vibration. The second phase consists of the design and construction of a separated mercury flow loop capable of hosting exchangeable test sections and more localized instrumentation. Data acquisition of Phase I was performed during this work and is presented in the form of strain measurements and vibration frequency.

Dominguez-Ontiveros, Elvis↗

Internal Nozzle Flow Simulations of Gasoline-Like Fuels under Diesel Operating Conditions

Spray formation in internal combustion engines with direct injection is strictly correlated with internal nozzle flow characteristics, which are in turn influenced by fuel physical properties and injector needle motion. This paper pre-sents a series of 3D simulations that model the in-nozzle flow in a 5-hole mini-sac diesel injector. Two gasoline-like naphtha fuels, namely full-range and light naphtha, were tested under operating conditions typical of diesel applica-tions and were compared with n-dodecane, selected from a palette used as diesel surrogates. Validated methodolo-gies from our previous work were employed to account for realistic needle motion. The multi-phase nature of the problem was described by the mixture model assumption with the Volume of Fluid method. Cavitation effects were included by means of the Homogeneous Relaxation Model and turbulence closure was achieved with the Standard k-ε model in an Unsteady Reynolds-Averaged Navier-Stokes formulation. The results revealed that injector perfor-mance and propensity to cavitation are influenced by the fuel properties. Analyses of several physical quantities were carried out to highlight the fuel-to-fuel differences in terms of mass flow rate, discharge coefficients, and fuel vapor volume fraction inside the orifices. A series of parametric investigations was also performed to assess the fuel response to varied fuel injection temperature, injection pressure, and cross-sectional orifice area. For all cases, the strict correlation between cavitation magnitude and saturation pressure was confirmed. Owing to their higher volatil-ity, the two gasoline-like fuels were characterized by higher cavitation across all the simulated conditions. Occur-rence of cavitation was mostly found at the needle seat and at the orifice inlets during the injection event’s transient, when very small gaps exist between the needle and its seat. This behavior tended to disappear at maximum needle lift, where cavitation was absent for all fuels. Differences in mass flow rate between the naphtha fuels and n-dodecane were measured and ascribed to the different densities of the three fuels. Nevertheless, they were found to be smaller than expected, owing to the lower viscosity of the gasoline-like fuels. This beneficial influence of the lower viscosity was shown to be less effective at higher temperature, where the relative viscosity differences de-creased.

Torelli, R.↗

Device Scale Modeling of Solvent Absorption using MFIX-TFM

Recent climate change is largely attributed to greenhouse gases (e.g., carbon dioxide, methane) and fossil fuels account for a large majority of global CO 2 emissions. That said, fossil fuels will continue to play a significant role in the generation of power for the foreseeable future. The extent to which CO 2 is emitted needs to be reduced, however, carbon capture and sequestration are also necessary actions to tackle climate change. Different approaches exist for CO 2 capture including both post-combustion and pre-combustion technologies, oxy-fuel combustion and/or chemical looping combustion. The focus of this effort is on post-combustion solvent-absorption technology. To apply CO 2 technologies at commercial scale, the availability and maturity and the potential for scalability of that technology need to be considered. Solvent absorption is a proven technology but not at the scale needed by typical power plant. The scale up and down and design of laboratory and commercial packed bed reactors depends heavily on the specific knowledge of two-phase pressure drop, liquid holdup, the wetting efficiency and mass transfer efficiency as a function of operating conditions. Simple scaling rules often fail to provide proper design. Conventional reactor design modeling approaches will generally characterize complex non-ideal flow and mixing patterns using simplified and/or mechanistic flow assumptions. While there are varying levels of complexity used within these approaches, none of these models resolve the local velocity fields. Consequently, they are unable to account for important design factors such as flow maldistribution and channeling from a fundamental perspective. Ideally design would be aided by development of predictive models based on truer representation of the physical and chemical processes that occur at different scales. Computational fluid dynamic (CFD) models are based on multidimensional flow equations with first principle foundations. CFD models can include a more accurate physical description of flow processes and be modified to include more complex behavior. Wetting performance and spatial liquid distribution inside the absorber are recognized as weak areas of knowledge requiring further investigation. CFD tools offer a possible method to investigating such topics and gaining a better understanding of their influence on reactor performance. This report focuses first on describing a hydrodynamic model for countercurrent gas-liquid flow through a packed column and then on the chemistry, heat and mass transfer specific to CO 2 absorption using monoethanolamine (MEA). The indicated model is implemented in MFIX, a CFD open source software package. The user defined functions needed to build this model are described in detail along with the keywords for the corresponding input file. A test case is outlined along with a few results. The example serves to briefly illustrate the developed CFD tool and its potential capability to investigate solvent absorption.

09 BIOMASS FUELS↗

The roles of the binodal curve and the spinodal curve in expansions from the supercritical state with flashing

Data extracted from time-of-flight (TOF) measurements made on steady-state He free jets at Göttingen already in 1986 and for pulsed Ne free jets investigated recently at Tel Aviv have been added to an earlier plot of terminal condensed-phase mass fraction x{sub 2∞} as a function of the dimensionless scaling parameter Γ. Γ characterizes the source (fluid species, temperature, pressure and throat diameter); values of x{sub 2∞} are extracted from TOF measurements using conservation of energy in the free-jet expansion. For nozzles consisting of an orifice in a thin plate; the extracted data yield 22 data points which are correlated satisfactorily by a single curve. The Ne free jets were expanded from a conical nozzle with a 20° half angle; the three extracted data points stand together but apart from the aforementioned curve, indicating that the presence of the conical wall influences significantly the expansion and hence the condensation. The 22 data points for the expansions via an orifice consist of 15 measurements with expansions from the gas-phase side of the binodal curve which crossed the binodal curve downstream from the sonic point and 7 measurements with expansions of the gas-phase product of the flashing which occurred after an expansion from the liquid-phase side of the binodal curve crossed the binodal curve upstream from the sonic point. The association of these 22 points with a single curve supports the alternating-phase model for flows with flashing upstream from the sonic point proposed earlier. In order to assess the role of the spinodal curve in such expansions, the spinodal curves for He and Ne were computed using general multi-parameter Helmholtz-free-energy equation-of-state formulations. Then, for the several sets of source-chamber conditions used in the free-jet measurements, thermodynamic states at key locations in the free-jet expansions (binodal curve, sonic point and spinodal curve) were evaluated, with the expansion presumed to be metastable from the binodal curve to the spinodal curve. TOF distributions with more than two peaks (interpreted earlier as superimposed alternating-state TOF distributions) indicated flashing of the metastable flow downstream from the binodal curve but upstream from the sonic point. This relatively early flashing is due apparently to destabilizing interactions with the walls of the source. If the expansion crosses the binodal curve downstream from the nozzle, the metastable fluid does not interact with surfaces and flashing might be delayed until the expansion reaches the spinodal curve. It is concluded that, if the expansion crosses the binodal curve before reaching the sonic point, the resulting metastable fluid downstream from the binodal curve interacts with the adjacent surfaces and flashes into liquid and vapor phases which expand alternately through the nozzle; the two associated alternating TOF distributions are superposed by the chopping process so that the result has the appearance of a single distribution with three peaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TEMPORAL VARIABILITY FROM THE TWO-COMPONENT ADVECTIVE FLOW SOLUTION AND ITS OBSERVATIONAL EVIDENCE

In the propagating oscillatory shock model, the oscillation of the post-shock region, i.e., the Compton cloud, causes the observed low-frequency quasi-periodic oscillations (QPOs). The evolution of QPO frequency is explained by the systematic variation of the Compton cloud size, i.e., the steady radial movement of the shock front, which is triggered by the cooling of the post-shock region. Thus, analysis of the energy-dependent temporal properties in different variability timescales can diagnose the dynamics and geometry of accretion flows around black holes. We study these properties for the high-inclination black hole source XTE J1550-564 during its 1998 outburst and the low-inclination black hole source GX 339-4 during its 2006–07 outburst using RXTE /PCA data, and we find that they can satisfactorily explain the time lags associated with the QPOs from these systems. We find a smooth decrease of the time lag as a function of time in the rising phase of both sources. In the declining phase, the time lag increases with time. We find a systematic evolution of QPO frequency and hard lags in these outbursts. In XTE J1550-564, the lag changes from hard to soft (i.e., from a positive to a negative value) at a crossing frequency (ν {sub c}) of ∼3.4 Hz. We present possible mechanisms to explain the lag behavior of high and low-inclination sources within the framework of a single two-component advective flow model.

79 ASTRONOMY AND ASTROPHYSICS↗

Shock tube experiments on the three-layer Richtmyer–Meshkov instability

Here, a vertical shock tube is used for experiments on the three-layer Richtmyer–Meshkov instability. Two closely spaced membrane-less interfaces are formed by the flow of two different sects of three gases: one with air above CO 2 above SF 6 and the other with helium above air above SF 6 . The lightest of the three gases enters the shock tube at the top of the driven section and flows downward. Conversely, the heaviest gas enters at the bottom of the shock tube and flows upward while the intermediate density gas enters at the middle through porous plates. All three gases are allowed to escape through holes at the layer location, leaving an approximately 30-mm layer of intermediate-density gas suspended between the lightest gas from above and the heaviest gas from below. A single-mode, two-dimensional initial perturbation is then imposed on the lower interface by oscillating the shock tube in the horizontal direction. The flow is visualized by seeding the intermediate gas with particles and illuminating it with a pulsed laser. Image sequences are then captured using high-speed video cameras. Perturbation amplitude measurements are made from the three-layer system and compared with measurements from 2, two-layer systems. It is observed that the presence of the upper, initially flat interface produces a decrease in growth of instability amplitude in the nonlinear phase over an equivalent single-interface configuration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Saturation of fishbone instability through zonal flows driven by energetic particle transport in tokamak plasmas

Gyrokinetic and kinetic-MHD simulations are performed for the fishbone instability in the DIII-D discharge #178631, chosen for validation of first-principles simulations to predict the energetic particle (EP) transport in an ITER prefusion baseline scenario. Fishbone modes are found to generate zonal flows, which dominate the fishbone saturation. The underlying mechanisms of the two-way fishbone-zonal flows nonlinear interplay are discussed in details. Numerical and analytical analyses identify the fishbone-induced EP redistribution as the dominant generation mechanism for zonal flows. The zonal flows modify the nonlinear dynamics of phase space zonal structures, which reduces the amount of EPs able to resonate with the mode, leading to an early fishbone saturation. Simulation results including zonal flows agree quantitatively with DIII-D experimental measurements of the fishbone saturation amplitude and EP transport, supporting this novel saturation mechanism by self- generated zonal flows. Moreover, the wave-particle mode-locking mechanism is shown to determine quantitatively the fishbone frequency down-chirping, as evident in GTC simulation results in agreement with predictions from analytical theory. Finally, the
fishbone-induced zonal flows are possibly responsible for the formation of an ion-ITB in the DIII-D discharge. Based on the low EP transport and the large zonal flow shearing rates associated with the fishbone instability in gyrokinetic simulations of the ITER scenario, it is conjectured that high performance scenarios could be designed in ITER burning plasmas through fishbone-induced ITBs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Wettability Effects on Falling Film Flow and Heat Transfer Over Horizontal Tubes in Jet Flow Mode

The performance of a falling-film heat exchanger is strongly linked to the surface characteristics and the heat transfer processes that take place over the tubes. The primary aim of this numerical study is to characterize the influence of surface wettability on the film flow behavior and its associated surface heat transfer in the jet-flow mode. Volume of fluid (VOF) based simulations are carried out for horizontal tubes with different surface wettabilities. The wettability of the tube surfaces is represented using the Kistler's dynamic contact angle model. Surface wettability effects ranging from superhydrophilic to superhydrophobic are studied by varying the equilibrium contact angle from 2 deg to 175 deg. Two different liquid mass flow rates of 0.06 and 0.18 kg/m-s corresponding to the inline and staggered jet flow modes are studied. Results are presented in terms of the liquid film thickness, the contact areas between the different phases (solid–liquid and liquid–air), and the heat transfer coefficient or Nusselt number. The resistance imposed by the increasing contact angles inhibits the extent of the liquid spreading over the tube surface, and this, in turn, influences the liquid film thickness, and the wetted area of the tube surface. A significant decrement in the heat transfer rate from the tube surfaces was observed as the equilibrium contact angle increased from 2 deg to 175 deg. The local distributions of the Nusselt number over the tube surface are strongly influenced by the flow recirculation in the liquid bulk.

Engineering↗