Force Balance Model Research Articles

Numerical simulation of subcooled boiling considering bubble sliding behavior in conventional channels

Subcooled boiling has a strong heat transfer capacity, and its heat transfer effect is closely related to the dynamic behavior of bubbles. Many researchers have discovered the bubble sliding behavior in subcooled boiling, which disrupts the thermal boundary layer and thus enhances the heat transfer capacity. This phenomenon occurs not only in narrow channels, but also in conventional channels. In this paper, the wall boiling model including the effect of the sliding bubbles and the nucleation sites density model with a wider application range. The bubble diameter is calculated from the force balance model and coupled into the wall boiling model. On the basis of verifying the accuracy of the model, the variation trend of bubble diameter, nucleation sites density and the relative contribution of each part of wall heat flux along the heating channel and the influence of different working conditions are analyzed. Under different working conditions, the calculated results are in good agreement with most of the experimental data, the error of 90% of the void fraction data is within 25%. In addition, the numerical results show that the relative contribution of bubble sliding quenching heat flux can up to 65%, so the effect of sliding bubbles on the relative contribution of each part of wall heat flux cannot be ignored. Different working conditions indirectly affect the heat flux of each part through the nucleation sites density and the diameter of the bubble.

Development of subcooled wall boiling model considering bubble sliding in narrow rectangular channel

Boiling two-phase flow simulation by two-fluid framework with interfacial interaction models has been successfully practiced in recent decades, and yet the model shows inability in simulating boiling two-phase flow in narrow rectangular channels, which are extensively existed in plate-type heat exchangers. This paper focused on the development of wall boiling model, which specifically considered the influence of bubble sliding in the description of wall boiling phenomena. The developed model describes the bubble behavior in nucleate boiling phase as the following sequences: nucleating, growing, detaching from nucleation site, sliding along the heated surface and then lifting off to the main flow. The sliding behavior was modeled according to the former experimental observation and measurement in the literatures. The departure and lift-off diameters were predicted by semi-mechanistic force-balance models. The developed model was implemented into CFD code and was applied to simulate several experimental subcooled boiling cases in a narrow rectangular channel. Results show that the developed model predicted wall temperature better against test data than the default RPI model, which proved the feasibility and suitability of present model in these cases. The evaporation heat flux calculated by developed model takes up less fraction, which accounts for the majority in RPI model.

Relationship of particle size, reaction and sticking behavior of iron ore fines toward efficient fluidized bed reduction

The relationship of particle size, reaction and sticking behavior of iron ore fines toward efficient fluidized bed hydrogen reduction were systematically investigated at 600–800 °C in a laboratory fluidized bed. First, the reduction kinetics were studied, and the results showed that hydrogen reduction of granulated iron ore was controlled by reduction reaction, and the activation energy was approximately 88.4 kJ/mol. The reduction rate of granulated iron ore with a diameter of 200 μm could be increased by 10 times as the reduction temperature rose from 600 to 800 °C. Then, a modified force balance model was established to distinguish the critical sticking point of granulated iron ore during high temperature fluidized bed hydrogen reduction, and it indicated that the defluidization temperature could be raised from 630 to 790 °C as the particle size was enlarged from 100 to 200 μm with a fluidization number of 10. Eventually, coupling the kinetic model and modified force balance model, the maximum gas utilization rate of fluidized bed hydrogen reduction was estimated, and it indicated that at reduction temperatures of 650–750 °C with particle sizes of 200–300 μm, the optimal gas utilization rate could be achieved, which was consistent with the experimental results. Contradictory to traditional understandings of chemical reaction engineering, due to the interaction of reduction performance and sticking behavior, too high of a reduction temperature or too small of a particle size might not be preferable for fluidized bed hydrogen reduction, and this study provided valuable references for industrial operation.

Pair interactions between viscous drops in a viscoelastic matrix in free shear: Transition from passing to tumbling trajectories

Shear-induced pair interactions between viscous drops suspended in a viscoelastic matrix are numerically investigated examining the effects of elasticity and drop deformability on their post-collision trajectory. Two different trajectory types are identified depending on the Weissenberg number Wi and capillary number Ca. Drops suspended in a Newtonian matrix (Wi = 0.0) show a passing trajectory where drops slide past each other and separate in the stream-wise direction. However, when increasing the Weissenberg number above a critical value, a tumbling/doublet trajectory is observed where two drops rotate around the midpoint of the line joining their centers, as was also seen previously for rigid particles. The tumbling trajectory is explained by investigating the flow around a single drop in shear. Elasticity generates a larger region of spiraling streamlines around a drop, which, during a pair interaction, traps the second drop giving rise to the tumbling pair. Decreasing deformability (lower Ca) and increasing viscoelasticity (higher Wi) favor a tumbling trajectory. With simulations sweeping the parameter space, we obtain a phase plot of the two different trajectories as functions of Ca and Wi. Treating the tension along the curved streamlines due to the non-zero first normal stress difference in the viscoelastic medium as an enhancement to the interfacial tension, we have developed an approximate force balance model for the zone of spiraling streamlines. It qualitatively captures the observed scaling of the critical Ca and Wi values at the phase boundary. The effects of unequal size, initial configuration, and non-unity viscosity ratio are briefly investigated.

Determination of Skin Friction Factor in Gravel Bed Rivers: Considering the Effect of Large-Scale Topographic Forms in Non-Uniform Flows

Determination of skin friction factor has been a controversial topic, particularly in gravel-bed rivers where total flow resistance is influenced by the existence of small-scale skin roughness and large-scale topographic forms. The accuracy of existing models predicting skin friction factors in conditions where small-scale skin roughness and large-scale topographic forms exist is very low. The objective of this study is to develop a modified model that improves the accuracy of the determination of skin friction factors in gravel-bed rivers. To this end, 100 velocity profile data obtained from eight gravel-bed rivers were utilized to develop an analytical method that considers the momentum thickness of the boundary layer and its deviation in large-scale topographic bedforms in a 1D force-balance model. The results show that the accuracy of the skin friction factors is enhanced when (1) the model is in the form of an exponential function of energy slope, and (2) the deviation of momentum thickness is considered in the model. The proposed model results in high accuracy of the predicted skin friction factors for energy slopes between 0.001 and 0.1, which exist in most gravel-bed rivers with different morphologies. Additionally, this study model was used to modify the classic Einstein–Strickler equation. The modified equation resulted in improved accuracy of the predicted skin friction factors in non-uniform flow conditions even when velocity profiles and energy slope were not available.

Effects of non-wetting fraction and pitch distance in flow boiling heat transfer in a wettability-patterned microchannel

Flow boiling in microchannels offers a promising and attractive solution for thermal management of electronic devices and power systems. In this paper, microchannels composed of a hydrophilic surface with hydrophobic dots were studied to characterize the effects of non-wetting fraction and pitch distance of adjacent dots on flow boiling heat transfer and pressure drop. The pitch distances ranging from 122 µm to 172 µm were studied. Using deionized water as the working fluid, highly subcooled flow boiling experiments were conducted at different mass fluxes ranging from 41.1 to 246.6 kg/m2s over a heat flux up to 146.2 W/cm 2. Bubble dynamics and flow patterns were visualized using a high-speed camera. It was found that bubbles coalesced more easily, and flow patterns transited faster in the microchannel with smaller pitch distance. Heat transfer coefficient (HTC), critical heat flux (CHF) and pressure drop were found to significantly rely on the pitch distance of dots and the mass flux. Furthermore, based on a force-balance model, bubble detached diameters were predicted in hydrophilic, hydrophobic and wettability-patterned microchannels, respectively. This provides a useful insight to optimize the wettability pattern design and then improve flow boiling heat transfer in a microchannel.

A force-balance model for centrosome positioning and spindle elongation during interphase and anaphase B

A computational model in one dimension is proposed to position a single centrosome using astral microtubules (MTs) interacting with the cell cortex. The mechanism exploits mutually antagonistic pulling and pushing forces arising from the astral MTs’ binding to cortical dynein motors in the actin-rich cell cortex and their buckling while growing against the cell cortex, respectively. The underlying mechanism is extended to account for the elongation and positioning of the bipolar spindle during mitotic anaphase B. Besides astral MTs, the model for bipolar spindle involves interpolar microtubules (IPMTs). The composite model can predict spindle elongation and position under various circumstances. The outcome reveals that the bipolar spindle elongation, weakened by decreasing overlap between the antiparallel IPMTs in the spindle mid-zone, is recovered by the astral MTs. The one-dimensional models are extended in two dimensions to include the effect of cortical sliding of the astral MTs for studying the dynamics of the interphase centrosome and the anaphase B spindles in elongated cells. The results reveal that the dynamics in two dimensions stay qualitatively similar to the one dimension.

Regulating the Entire Journey of Pesticide Application on Surfaces of Hydrophobic Leaves Modified by Pathogens at Different Growth Stages.

Under the background of the strategy of reducing pesticide application and increasing efficiency, the mechanism and common technology of efficient and accurate target deposition of chemical pesticides are the key development direction. The interaction between pesticide droplets and a leaf surface affects the deposition behavior of pesticides. However, cucumber leaf surface modified by powdery mildew pathogens at different growth stages is more hydrophobic than a normal leaf surface, which hinders the accurate deposition of pesticides on cucumber powdery mildew leaves. Here, an effective strategy for controlling pesticide efficiency for the entire journey of pesticide application is proposed. Based on the impact dynamics of droplets, the dynamic direction of droplet bounce is determined, the trajectory of droplet rebound is preliminarily determined, and the pinning sites formed by droplets on the surface of cucumber leaves with powdery mildew are confirmed. By analyzing the dynamics in the retraction stage and the energy dissipation rate for droplets after impact, the basic parameters that can be used to simply characterize droplet rebound are screened out, and the effect of addition of an effective surfactant is determined by characterizing the basic parameters (energy dissipation rate, retraction rate, recovery coefficient). The molecular structure formed by the addition of nonionic surfactant in pesticide solution is more appropriate to the interaction between the powdery mildew layer and the pesticide solution, which ensured that the droplets are well wet and deposited on cucumber powdery mildew leaves. Meanwhile, a force balance model for the pesticide droplet wetting state is established to calculate the pinning force for the droplet and predict the transition direction for the droplet wetting state. Impact dynamics combined with force balance model analysis provides a constructive method to improve pesticide utilization during the entire journey for pesticide application on hydrophobic plant surfaces.

A novel analytical simulation method of utilization of surfactant-active nanoparticles for well injection enhancement in low-permeability reservoirs

In order to study the mechanism of surfactant-active nanoparticles in drag reduction and injection enhancement in low-permeability reservoirs and to simulate the rough condition of the pore surface of the reservoirs, we construct a microtube model with periodic rectangular groove structure and a force balance model of nanoparticles on rough surface to get the limit adhesion concentration fraction model of surfactant-active nanoparticles on pore surface. The method of characteristics (MOC) is used to analyze and simulate the seepage process of the suspension-adhesion-plugging coupling of surfactant-active nanoparticles in pores of low permeability reservoirs. By comprehensively considering reservoir damage caused by the mechanisms such as particle attachment and blockage and the slip effect established by nanoparticle attachment, a theoretical model for resistance reduction and injection enhancement of surfactant-active nanoparticles has been formed. The results show that comparing with the core without nanoparticles flooding, the pressure drop of the core decreases significantly after the injection of nanoparticles, and the pressure drop reaches 40%. At the same time, by comparing the water injection index before and after injection, the core injection capacity is significantly improved after the surfactant-active nanofluid injection. This model provides a certain theoretical basis for the technology of pressure reduction and injection enhancement of surfactant-active nanoparticles in low permeability reservoirs.

Mechanistic critical heat flux prediction for in-vessel retention conditions

In-vessel retention (IVR) is considered a feasible technique to keep reactor pressure vessel (RPV) integrity in a severe reactor accident. For light water reactor (LWR), the effectiveness of this strategy relies soundly on the critical heat flux (CHF) distribution over the external surface of the lower plenum of RPV, whose orientation varies gradually from downward-facing horizontal to vertical. The CHF prediction capability of the liquid sublayer dryout model is efficient for high mass flux in vertical flow boiling conditions. This paper focuses on how to adapt the model to the changed orientation of the heating surface. Bubble departure diameter (dB) and net vapor generation point (NVG), the starting point for the void fraction developing in a heating channel, is one of the important key points in the CHF prediction. Therefore, to assess the predictive potential of CHF under IVR, experimental research was performed to measure bubble departure diameter and NVG for a changing heating surface orientation from downward-facing horizontal to vertical with a mechanistic model basing on the force balance. A modified liquid sublayer dryout model was then proposed where the channel orientation effect is considered to measure the bubble departure diameter (vapor blanket diameter) using the improved force balance model. The NVG is modified according to the departure diameter. The predicted departure diameter and subcooling at NVG show good consistency with the experimental data, and the modified liquid sublayer dryout model can predict the CHF data with an average relative error of 18.36% in IVR.

Asymmetric Sawtooth Microstructure-Induced Vapor Mobility for Suppressed Buoyancy Conditions: Terrestrial Experiment and Design for ISS Experiments

The lack of buoyancy forces in microgravity stagnates vapor bubbles on heated electronic surfaces, raising local surface temperatures above device operating limits. Though flow boiling can help dissipate higher heat fluxes, the addition of pumps and regulated flow loops increases design complexity for electronic systems. Passive directional motion of the fluid using an asymmetric sawtooth microstructure has demonstrated motion along the surface due to viscous forces. The current study explores the sawtooth microstructure in the nucleate boiling regime for a horizontal upward- and downward-facing orientation with varying sawtooth profiles (60°–30° and 75°–15°) in terrestrial gravity conditions as a precursor to the International Space Station (ISS) experiments. A laser powder bed fusion metal additive manufacturing technique was used to fabricate the test surfaces with 250- $\mu \text{m}$ nucleation sites located on the long slopes. For the test surface with cavities spaced 2-mm apart, the wall superheat was ~4 K lower compared to cavities spaced 1 mm apart in the upward-facing orientation. The downward-facing surface induced passive vapor mobility in the direction of the long slope, and a thin liquid film was observed between the vapor mass and microstructure. This liquid film thickness was predicted using a simplified force balance model modified from a prior parabolic flight experiment. The model predicted a uniform liquid film thickness of $49~\mu \text{m}$ for a vapor slug moving at 13.7 mm/s with the input heat flux at 1.25 W/cm2. These terrestrial tests in the adverse orientation suggest that the sawtooth microstructure will successfully induce vapor mobility in upcoming ISS microgravity experiments. Elements of the final flight ampoule, including the cooling zone, the two-stage pressure relief system, and the high-speed imagery setup, are discussed.

Critical layer thickness of wurtzite heterostructures with arbitrary pairs of growth planes and slip systems

We establish a calculation method to determine the critical layer thickness of the lattice relaxation in wurtzite heterostructures with arbitrary pairs of growth planes and slip systems. The calculation, which is based on the force balance model, takes the friction force and thermal assistance for the dislocation motion into account. Experimentally, Al x Ga1 − x N/AlN heterostructures are fabricated. The established method well reproduces the crystallographic orientations of experimentally observed dislocation lines.

Influence of Interfacial Force Models and Population Balance Models on the kLa Value in Stirred Bioreactors

Optimal oxygen supply is vitally important for the cultivation of aerobically growing cells, as it has a direct influence on cell growth and product formation. A process engineering parameter directly related to oxygen supply is the volumetric oxygen mass transfer coefficient kLa. It is the influences on kLa and computing time of different interfacial force and population balance models in stirred bioreactors that have been evaluated in this study. For this investigation, the OpenFOAM 7 open-source toolbox was utilized. Firstly, the Euler–Euler model with a constant bubble diameter was applied to a 2L scale bioreactor to statistically examine the influence of different interfacial models on the kLa value. It was shown that the kL model and the constant bubble diameter have the greatest influence on the calculated kLa value. To eliminate the problem of a constant bubble diameter and to take effects such as bubble breakup and coalescence into account, the Euler–Euler model was coupled with population balance models (PBM). For this purpose, four coalescence and five bubble breakup models were examined. Ultimately, it was established that, for all of the models tested, coupling computational fluid dynamics (CFD) with PBM resulted in better agreement with the experimental data than using the Euler–Euler model. However, it should be noted that the higher accuracy of the PBM coupled models requires twice the computation time.

An analytical approach to explain complex flow in spiral concentrator and development of flow equations

A spiral concentrator is a density separation equipment used to beneficiate coal and various minerals such as iron ore, chromite ore, gold, beach sand minerals, etc. The flow pattern developed in the equipment is complex and unique, yet the operation is straightforward with low capital and operating expenditure. Spirals are applied for beneficiation of material in a size range that is finer than 2 mm and can recover heavy minerals as fine as 0.01 mm. The understanding of the unique flow pattern has kept researchers engaged over the last few decades.With a clear understanding, it could be controlled and modified to improve the operating efficiency, Ep (Ecart Probable Error also known as a probable error in separation) and acceptability of spiral concentrators for processing of fines and slimes, currently being discarded and dumped in the tailing ponds.An attempt has been made in the present paper to explain the generation of complex flow patterns using classical solid mechanics in the fluid and slurry system. The findings could describe the selective separation of particles in different zones in a cross-section considered on the spiral trough. The paper also discusses the application of the force balance model to explain the generation of secondary circulation.Due to laminar and turbulent flow regimes in the spiral concentrator, various equations have been proposed in the literature, consisting of different equations for different zones. An attempt has been made to present a unified flow equation to calculate flow velocity to varying positions on the spiral trough.

Application of the Force Balance Model and Fractal Scaling Analysis for Size Estimation of the Complex-Agglomerates in a Conical Fluidized Bed

The size estimating of fluidized Titania agglomerates in a conical fluidized bed was studied by force balance model and fractal scaling analysis. The primary size of Titania Nano Particles (NPs) was 21 nm, while for complex agglomerates was in the size range of several hundred micrometers. The formation mechanism of simple-agglomerate and complex-agglomerate structures was studied experimentally. The size distribution and morphology of agglomerates were determined by advanced laser dynamic imaging and scanning electron microscopy. The AFM-nanoindentation test was used to determine the elastic modulus of agglomerates with porous structures. The size distribution of Titania NP agglomerates was estimated by the fractal analysis through the relationship between the number of particles and gyration diameter. The fractal exponent obtained from the power-law scaling of agglomerates and the complex agglomerate sizes were determined experimentally and theoretically. A simple theoretical model was applied to estimate the complex agglomerates' size based on the equilibrium of the separation and cohesion forces. The proposed model showed satisfactory results compared with the experimental data. The results of the present study can help to determine the critical gas velocity in achieving the desired agglomerate size of Titania NPs.

Experimental investigations and development of mathematical model to estimate drop diameter and jet length

The key process used in nuclear industries for the management of radiotoxicity associated with spent fuel in a closed fuel cycle is solvent extraction. An understanding of hydrodynamics and mass transfer is of primary importance for the design of mass transfer equipment used in solvent extraction processes. Understanding the interfacial phenomenon and the associated hydrodynamics of the liquid drops is essential for model-based design of mass transfer devices. In this work, the phenomenon of drop formation at the tip of a nozzle submerged in quiescent immiscible liquid phase is revisited. Previously reported force balance based models and empirical correlations are analyzed. Experiments are carried out to capture the process of drop formation using high-speed imaging technique. The images are digitally processed to measure the average drop diameter. A correlation based on the force balance model is proposed to estimate drop diameter and jet length. The average drop diameter obtained from the proposed model is in good agreement with experimental data with an average error of 6.3%. The developed model is applicable in both the necking as well as jetting regime and is validated for liquid-liquid systems having low, moderate and high interfacial tension.

Force balance model predictions of sliding bubbles velocity in vertical subcooled boiling flow

In flow boiling systems, bubbles tend to slide along the wall as they depart from nucleation sites where they originate. This behavior has a profound impact on the wall heat transfer as evidenced in previous experiments. As a result, the heat transfer modeling associated with sliding bubbles has gained great attention within the CFD boiling heat transfer community. The modeling efforts are primarily aimed at improving the Heat Flux Partitioning (HFP) model by accounting for the heat transfer mechanisms introduced by sliding bubbles. The performance of the HFP model depends inherently on the accuracy of sub-models to predict the fundamental bubble parameters, such as bubble departure and lift-off diameters. Similarly, the accurate prediction of sliding bubble parameters, such as sliding bubble growth and sliding bubble velocity, is critical to improving the HFP model when taking into account the effect of sliding bubbles. Of the many sliding bubble parameters, this paper deals with the sliding bubble velocity. Specifically, a force balance model is presented and assessed in view of the sliding bubble velocity prediction. The experimental results from Maity (2000)[1] and Yoo et al. (2016)[2] are used to demonstrate the force balance model accuracy under various subcooled boiling conditions of both, water and refrigerant (NOVEC-7000) flowing upward in vertical channels. We performed a parametric study of the key sub-models (e.g., drag force, bubble growth) used in the force balance equation, together with a direct comparison with proposed models from other researchers. Then, a new force balance model is proposed which outperforms previous models and consistently well-predicts both sliding bubble velocity and growth.

Enhanced Photocatalytic Water Decontamination by Micro-Nano Bubbles: Measurements and Mechanisms.

Despite recent advancements in photocatalysis enabled by materials science innovations, the application of photocatalysts in water treatment is still hampered due to low overall efficiency. Herein, we present a TiO2 photocatalytic process with significantly enhanced efficiency by the introduction of micro-nano bubbles (MNBs). Notably, the removal rate of a model organic contaminant (methylene blue, MB) in an air MNB-assisted photocatalytic degradation (PCD) process was 41-141% higher than that obtained in conventional macrobubble (MaB)-assisted PCD under identical conditions. Experimental observations and supporting mechanistic modeling suggest that the enhanced photocatalytic degradation is attributed to the combined effects of increased dissolution of oxygen, improved colloidal stability and dispersion of the TiO2 nanocatalysts, and interfacial photoelectric effects of TiO2/MNB suspensions. The maximum dissolved oxygen (DO) concentration of the MNB suspension (i.e., 11.7 mg/L) was 32% higher than that of an MaB-aerated aqueous solution (i.e., 8.8 mg/L), thus accelerating the hole oxidation of H2O on TiO2. We further confirmed that the MNBs induced unique light-scattering effects, consequently increasing the optical path length in the TiO2/MNB suspension by 7.6%. A force balance model confirmed that a three-phase contact was formed on the surface of the bubble-TiO2 complex, which promoted high complex stability and PCD performance. Overall, this study demonstrates the enhanced photocatalytic water decontamination by MNBs and provides the underlying mechanisms for the process.

Advanced boiling heat transfer model for a horizontal tube with numerical analysis of bubble behaviours

The boiling heat transfer model for a horizontal tube is developed herein, with numerical investigations to realistically simulate bubble nucleation site distributions and bubble behaviours. Accordingly, a new heat partitioning model was proposed to reflect the bubble sliding phenomena more realistically than the extant heat partitioning models for horizontal tubes. The bubble trajectories, merging, lift-off, and distribution of nucleation sites were numerically analysed based on the force balance model, bubble tracking method, and Latin-hypercube sampling. The proposed approach can overcome the limitations of the arithmetic heat partitioning model, which does not reflect bubble mergers and the random nature of the nucleation site distribution. Distinctive bubble behaviours on a horizontal tube can be reproduced by the present model, including bubble sliding, departure, lift-off, and merger. The numerical model presented here considers bubble sliding based on a mechanistic force balance model and bubble merger based on the bubble tracking method. The Monte Carlo method was applied to determine the spatial distribution of the nucleation sites, and statistical information on the wall heat transfer and contribution of each heat transfer mechanism were obtained via extensive calculations. The method developed herein was applied to evaluate the wall heat transfer in horizontal heaters. Further, the proposed numerical boiling heat transfer model was validated against an extant experimental database of horizontal heat exchanger tubes, and the model was observed to predict the wall heat flux with satisfactory accuracy.

Asymmetric Bubble Formation at Rectangular Orifices.

Bubble formation in liquids is frequently observed in nature and applied in various industrial processes. These include pool and flow boiling for thermal management systems, where bubbles may form asymmetrically at narrow slits and in convective flows. While previous studies have focused on symmetric bubble formation at circular orifices, the dynamics of asymmetric bubble formation remains poorly understood. Here, we experimentally investigate bubble formation at rectangular orifices and examine the effects of the orifice size and aspect ratio and the gas flow rate on the bubble size. The asymmetric bubble shape evolution at the rectangular orifice is analyzed, and we find that the size of the bubble neck is controlled either by the orifice size or by the capillary length. Based on these findings, we develop a static force balance model to predict the bubble size in the quasi-static regime, where the roles of Bond number and aspect ratio are identified. The bubble size evolution in the dynamic regime is further understood by introducing a Weber number that evaluates the effect of the virtual mass force induced by gas flow. Our study provides physical understanding of the dynamics of asymmetric bubble formation and guidance to predict the bubble size at asymmetric orifices.