Dispersed Flow Research Articles

Toward a Better Understanding of Reflood Thermal Hydraulics: A Summary of the OECD/NEA RBHT Project

Reflood thermal hydraulics remains a difficult and complex subject, and understanding the physical phenomena that occur during a reflood transient is important to nuclear safety. The Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) Rod Bundle Heat Transfer (RBHT) project was designed to provide unique experimental data for code assessment and model development. Participants, which came from 21 international organizations, used analysis codes including APROS, ATHLET, CATHARE, CTF, MARS, RELAP5, TRACE, and SPACE to simulate the tests performed in the RBHT facility. The experimental campaign carried out within the OECD/NEA RBHT project produced data for a total of 16 reflood tests conducted in two test series. An “open” test series consisted of 11 experiments, and a “blind” test series consisted of 5 experiments. In the blind tests, only the initial and boundary conditions were provided to participants prior to simulation of those experiments. Reflood rates ranged from 0.5 to 15 cm/s, thus producing data applicable to dispersed flow film boiling and inverted annular flow film boiling. Inlet subcooling ranged from 2.8 to 80 K. Tests with variable reflood rates and oscillatory reflood rates were included in the test matrix. This paper describes the project and presents a summary of major experimental and analytical findings.

Rotational Taylor dispersion in linear flows

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

Two-group interfacial area concentration model for dispersed gas-liquid flows in large-diameter pipes

Interfacial area concentration (IAC) plays a critical role in heat and mass transfers between gas and liquid phases through the interfaces. As interfacial area increases, mass and heat transfers between phases increase. Hence, a reliable IAC estimation is important for two-phase flow numerical simulations to conduct engineering designs and safety analyses. Gas bubbles show different behavior according to their shapes and sizes. Based on the size, gas bubbles can be classified into two groups that show different characteristics, such as IAC. Hence, two-group modeling helps to achieve a general approach for estimating the IAC in bubbly to beyond-bubbly flow regimes. Available models in the literature use empirical correlations to obtain group one and group two void fractions. These empirical approaches are not reliable for different flow conditions. In addition, these models are usually complex with several empirical constants. This study aims to develop a two-group area-averaged IAC model for upward vertical dispersed flows through large-diameter pipes. In addition, this study proposes using a general approach based on the two-group drift-flux model to calculate two-group void fractions rather than applying empirical correlations. The models are evaluated using 156 two-group measured data points in dispersed flow conditions through large-diameter pipes. The resulting prediction errors for group one and group two IAC models are 24.1 % and 34.2 %, and the errors for group one and group two void fraction predictions are 22.8 % and 25.6 %, respectively.

Unsteady solute dispersion in large arteries under periodic body acceleration

The present study investigates the effect of periodic body acceleration on solute dispersion in blood flow through large arteries. Transport coefficients (i.e., exchange, convection, and dispersion coefficients) and mean concentration of the solute are analyzed in the presence of wall absorption. The solute is quickly transported to the wall of arteries with a smaller radius, whereas the opposite is true for arteries with a larger radius. In the presence of body acceleration, the amplitude of fluctuations of the convection coefficient K1(t) increases significantly as the radius of the artery increases. In contrast, an opposite scenario exists for the dispersion coefficient K2(t). The solute dispersion process becomes more effective in arterial blood flow as the radius of the artery decreases. More interestingly, in large arteries with body acceleration, the solute is convected, dispersed, and distributed more toward the upstream direction owing to flow reversal during the diastolic phase of pressure pulsation. Note that this important feature of flow reversal is solely due to periodic body acceleration. For an artery with a small radius, under the influence of periodic body acceleration, the mean concentration of solute Cm is the minimum, and more axial spread is noticed in the axial direction. In contrast, an opposite scenario arises in the artery with a large radius. Additionally, the effect of body acceleration on the shear-induced diffusion of red blood cells is discussed in blood flow.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Investigation into shear-thinning behavior in wet spinning of carbon nanotube fibers modeled by power law viscosity model

The wet spinning of carbon nanotube (CNT) fibers, a representative solution processing of CNTs, has been advanced through the integration of well-established polymer sciences into their field. However, the flow behavior of CNT dispersions in the narrow spinning line, where its characteristics undergo changes due to the high-shear rate regime, has not been utilized to determine their spinnability, despite being a commonly employed method in the wet spinning of polymer fibers. Herein, we employed the power law viscosity model to investigate the correlation between flow behavior and the spinnability of CNT dispersion through the power law index which approaches to 0 as the shear-thinning behavior strengthens. We suggest that the spinnability of CNT dispersion is proportional to the degree of shear-thinning behavior of the dispersion. We ascribe this correlation to the integrity of CNT fibers which predominantly rely on the strong van der Waals forces between CNTs. These findings offer new insights into the role of fiber integrity in spinnability and provide a framework for optimizing the wet spinning process of CNT fibers through detailed analysis of dispersion flow behavior.

Capillary flow-MRI of micronized fat crystal dispersions: Effect of shear history on microstructure and flow

Micronized fat crystal (MFC) dispersions are a novel food ingredient enabling more efficient manufacturing of fat-based products as compared to established melt-cool processing. Yet, predicting rheological properties of MFC dispersions, remains a challenge. Here, we demonstrate how a capillary-flow Magnetic Resonance Imaging (MRI) platform provides quantitative measurements of local flow of MFC dispersions, inaccessible by global rheology. The measured 2D 1H MRI velocity maps unveiled a 5-fold velocity enhancement, and corresponding increase in wall slip, upon increasing the pre-shear time within 0–5 h, due to the 14 % increase in thickness of the crystalline nanoplatelets via recrystallization and aggregation of nanoplatelets. In the absence of pre-shearing, MFC dispersions exhibit an unsheared band at the walls of the capillary, likely arising from fouling and migration of thin nanoplatelets. In contrast to FCDs, flow cooperativity could not be observed for MFC dispersions due to the non-fractality of the fat crystal network. These results demonstrate that, by varying the pre-shear duration, the flow-microstructure properties of the MFC dispersions can be altered in a controlled manner. The approach presented here will allow for rapid assessment of shear-history dependence of flow properties of MFC dispersions under industrially relevant flow conditions.

Comparative experimental and numerical study of mixing efficiency in 3D-printed microfluidic droplet generators: T junction, cross junction, and asymmetric junctions with varying angles

In droplet-based microfluidics, rapid mixing during droplet formation enhances reaction uniformity, eliminating the need for micromixers. In this research, we conducted a comprehensive study by first employing a series of two-dimensional (2D) numerical simulations, followed by experimental investigations using 3D-printed microfluidic chips. We compared the mixing efficiency, droplet diameter, and droplet eccentricity of three different types of droplet generators: T junction, cross junction, and asymmetric droplet generators with various angles. Regarding mixing efficiency, we observed that the asymmetric droplet generators outperformed the cross junction by 30 % but fell slightly short of the mixing efficiency achieved by the T junction (1 %). Additionally, while the mixing index in the asymmetric generators closely matched that of the T junction, these asymmetric generators produced smaller droplets by 72 %. Increasing the angle in asymmetric droplet generators resulted in enhanced mixing efficiencies and an increase in droplet diameters. The asymmetric junction with a 30° angle could achieve a mixing efficiency of up to 80 %. Additionally, an analysis of the dispersed phase flow rate revealed that higher flow rates lead to larger droplet sizes and reduced mixing efficiencies. The asymmetric droplet generators improve mixing efficiency facilitating rapid reagent mixing, all while maintaining a small droplet diameter.

Structure of a Fourth-Order Dispersive Flow Equation Through the Generalized Hasimoto Transformation

Structure of a Fourth-Order Dispersive Flow Equation Through the Generalized Hasimoto Transformation

A deep learning-powered intelligent microdroplet analysis workflow for in-situ monitoring and evaluation of a dynamic emulsion

Accurately determining microdroplet size and uniformity in dispersed phase systems is key for assessing emulsion stability, and essential for quality monitoring and control of emulsion products. Microscopic imaging probes have provided intuitive and advanced insights for characterizing particle microscopic morphology and dispersion in multiphase flows. However, wide size distributions, edge-cutting, overlapping, and high-density target droplets can compromise the image processing accuracy, thereby affecting the precise assessment of emulsion status. In this study, we present a deep learning-based intelligent workflow for microdroplet characterization using an in-situ high-speed particle imaging probe combined with advanced image processing techniques. With the assistance of progressive automatic annotation, a droplet image database was constructed for training the Mask R-CNN model. By incorporating image patching and supervised data augmentation strategies, our well-trained model with accuracy of 95.5% can precisely detect, localize, and segment microscale droplets with various patterns. Additionally, the shape reconstruction module visualizes true shapes of overlapping and edge-cutting droplets, facilitating precise quantification of droplet size information. To validate the feasibility and generalizability of the proposed workflow, we obtained sufficient droplet images through offline sampling during emulsion processes while employing back and front illumination for in-situ monitoring. The automated method achieves precise droplet detection and size measurement, demonstrating its immense potential in online monitoring, evaluation, and control of emulsion quality.

Experimental and theoretical modeling of droplet break-up of W/O emulsion flow in ESPs

The behavior of water-in-oil emulsions flow within Electrical Submersible Pumps (ESPs) is of significant interest in the oil and gas industry due to its complex rheological characteristics, which are influenced by operational parameters and the chemical properties of both phases. Operational parameters such as dispersed phase fraction, temperature, flow rate, and pump design were investigated experimentally in this work. Improved semi-empirical models for mean and maximum droplet diameter estimation were also proposed. Through extensive experimentation and statistical analysis, this study reveals that smaller droplets form with increasing dispersed phase fraction and the flow geometry significantly affects droplet breakage intensity. The proposed models integrate the dispersed phase fraction, dimensionless flow rate, specific speed, and energy dissipation rate, exhibiting commendable alignment with experimental findings. This not only helps predict effective viscosity but offers valuable insights for further analyses, particularly regarding catastrophic phase inversion (CPI) prediction. These aspects have significant importance in the oil and gas industry and can enable the optimization of production systems and processing facilities.

Solute Dispersion in Casson Blood Flow through a Stenosed Artery with the Effect of Temperature and Electric Field

This study develops a mathematical model to address solute dispersion in arterial blood flow, particularly considering the effects of temperature and electric fields using the Casson fluid model. Given the physiological importance of drug delivery within the human vascular system, understanding these dynamics is crucial, especially in the presence of cardiovascular diseases (CVD). The Generalized Dispersion Model (GDM) is employed to simulate the dispersion function. Results demonstrate that elevated temperatures and electric fields enhance drug uptake and distribution by increasing blood flow. The model accurately predicts drug behavior in narrowed arteries, optimizing dosage regimens and improving therapeutic outcomes. Visual representations and detailed discussions of these findings are presented in the subsequent sections. The results are validated against a previous study that did not consider the effects of stenosis height, temperature and electric field. The findings suggest a strong agreement between the two studies. Additionally, an increase in mean absorption leads to an increase in velocity. When mean absorption increases, the functions of steady dispersion and overall dispersion decrease, while the function of unsteady dispersion increases. The reverse behavior is observed for the electric field. The study concludes that integrating temperature and electric field effects into drug delivery systems can significantly enhance treatment efficacy and reduce side effects, providing a valuable tool for advanced targeted therapies in CVD and cancer management.

Characterization of wind effect on environmental dispersion for a shallow wetland flow

The present work focuses on the dispersion of pollutants under the influence of wind and ecological degradation in a fully developed steady flow for a shallow wetland. The dispersion coefficient is determined by Aris’ method of moments and Meis’ multi-scale analysis. Based on the comparison study, the concentration profiles obtained using multi-scale analysis converge with Aris’ method of moments, indicating that both analytical approaches provide reliable and consistent descriptions of pollutant dispersion in the system. In first-order degradation reaction rates, high degradation rates lead to lower mean concentrations and potentially more pronounced concentration gradients, while low degradation rates result in higher mean concentrations. The critical length of the region influenced by the contaminated cloud is computed analytically. It shows that for the common contaminant constituent lead (Pb), initially, it increases gradually to reach the maximum; after that as time increases, it decreases to zero under wind conditions.

Characterizing Flow Dynamics in a Two-dimensional Flow Cell: Developing Methodologies for Enhanced Subsurface Contaminant Remediation Research

This study used a two-dimensional (2-D) flow cell apparatus (25 cm × 25 cm × 1 cm) to characterize water flow and contaminant transport in porous media. The primary objective was to enhance the understanding of flow dynamics and contaminant behavior in controlled 2-D environments, which is crucial for optimizing the application of remediation technologies to treat contaminants in saturated and unsaturated soil conditions. The 2-D cell was designed with transparent walls to simulate subsurface conditions using medium grained sand, allowing for precise control and observation of fluid movement under saturated and quasi-saturated (trapped air) conditions. Visualization techniques and flow measurement tools were employed to capture detailed data on flow patterns, velocities, and dispersion characteristics. Analysis of breakthrough curves for salt tracer tests using electrical conductivity measurements, alongside varying flow rates, flow fractions, and port configurations, provided significant insights into fluid behavior and contaminant transport. The study also explored the effects of varying salt concentrations (and solution densities) on flow dynamics, contributing to a better understanding of the role of contaminant concentration in contaminant plume development and remediation processes. Visual analysis using dyed contaminant complemented the quantitative data, offering real-time observations of flow patterns and contaminant distribution. A custom-built apparatus was used to control the hydraulic head of multiple outlet ports to sample water from different depths. The experiments demonstrated that gravity plays a crucial role in solute (salt) breakthrough, with lower ports showing earlier breakthrough. Flow fields formed vertically, from bottom-to-top, and horizontally, from inlet-to-outlet, with lower portions advancing sooner. However, multi-port configurations, especially involving five ports, disrupted the sequential breakthrough order, possibly due to convection in the clear well that formed the outlet boundary of the flow cell. These findings will support research students in conducting similar experiments with flow and transport that varies with depth, with future insights for professionals in developing and optimizing remediation strategies related to subsurface contaminant flow. Special thanks are extended to Liam Price, Julia-Barnes James, and Brooke Belfall who were helpful during the research and the experimentation process.

Solving crystallization/precipitation population balance models in CADET, Part II: Size-based Smoluchowski coagulation and fragmentation equations in batch and continuous modes

A particle size-based Smoluchowski coagulation and fragmentation equation was solved in the free and open source process modeling package CADET. The WFV and MCNP schemes were selected to discretize the internal particle size coordinate. Weights in these schemes were modified to preserve and conserve the zeroth and third moments for size-based equations. Modified propositions and proofs for the scheme are provided. Analytical Jacobians were derived and implemented to reduce the solver’s runtime. A two-dimensional Smoluchowski coagulation and fragmentation equation with axial position as external coordinate was formulated and discretized to support simulations of continuous particulate processes in dispersive plug flow reactors. Five 1D and four 2D test cases were used to validate the implementation and benchmark the solver’s performance. The runtime, L1 error norm, L1 error rate, particle size distribution moments up to sixth order and several scalar metrics were analyzed in detail.

Influence of entrainment on residual content of pollutants after absorber with sieve trays and wire demister

Entrainment is an important negative process that affects the efficiency of column units with a sieve trays. In sieve trays absorbers, entrainment leads to secondary contamination of the gas being purified by the reflux liquid. The sizes of entrainment droplets range widely from microns to millimeters and are the determining factor affecting the efficiency of demister. A review of studies on the flow rate and dispersion characteristics of entrainment removal from sieve trays is carried out, the research results are summarized in the form of a methodology for calculating the residual liquid content in gas after an absorber with a wire demister. In an absorber with cross-flow foam trays and a wire demister, there is an irreducible residual content of the reflux liquid, about several mg/m3, which practically does not change up to gas velocities of 1–1.5 m/s.

Direct numerical simulation of dispersion and mixing in gas–liquid Dean-Taylor flow with influence of a 90° bend

Gas-liquid capillary flow finds widespread applications in reaction engineering, owing to its ability to facilitate precise control and efficient mixing. Incorporating compact and regular design with Coiled Flow Inverter (CFI) enhances process efficiency due to improved mixing as well as heat and mass transfer leading to a narrow residence time distribution. The impact of Dean and Taylor flow phenomena on mixing and dispersion within these systems underscores their significance, but is still not yet fully understood. Direct numerical simulation based on finite element method enables full 3D resolution of the flow field and detailed examination of laminar flow profiles, providing valuable insights into flow dynamics. Notably, the deflection of flow velocity from the center axis contributes is followed by tracking of particle with defined starting positions, aiding in flow visualization and dispersion characterization. In this CFD study, the helical flow with the influence of the centrifugal force and pitch (Dean flow) as well as the capillary two-phase flow (Taylor bubble) is described and characterized by particle dispersion and related histograms. Future prospects in this field include advancements in imaging techniques to capture intricate flow patterns, as well as refined particle tracking methods to better understand complex flow behavior.

Multiscale simulation of spray and mixture formation for a coaxial atomizer

Coaxial atomization is an established atomization strategy for many stationary combustion systems. While modeling spray formation in coaxial atomization is challenging due to the existence of a wide range of length and time scales, typical models introduce a substantial uncertainty for Euler–Lagrange simulations of the actual application, e.g., a spray flame. To reduce uncertainties, a recently proposed multiscale approach is adopted for simulations of realistic applications in this work. The multiscale approach uses three one-way coupled simulation domainss that cover the internal nozzle flow, the interfacial flow of the near-field, and the dispersed flow of the far-field. The capabilities of the approach are explored by applying it to a standardized non-reacting experiment from the flame spray pyrolysis research community. In order to assess the relevance for application simulations, results are discussed in the context of mixture formation. The results are compared against shadowgraphy images of the near-field and measured droplet statistics in the far-field. It is found that the multiscale approach is capable of providing similarly accurate droplet statistics as experiments or models derived from them. In addition, it is found that the breakup dynamics in the near-field introduce substantial mixture fraction fluctuations. These fluctuations are only included because of the deterministic coupling of the multiscale approach and are typically neglected in conventional approaches.

Effects of temperature-dependent viscosity on thermal drawdown-induced fracture flow channeling in enhanced geothermal systems

Harnessing geothermal energy from an enhanced geothermal system (EGS) highly depends on fracture flow and heat transport processes. Thermal drawdown-induced thermal stress has been characterized as a major reason for severe fracture flow channeling (short-circuiting), which further leads to premature thermal breakthrough and impairs long-term thermal performance. In the present study, we quantitatively analyzed a potential flow channeling mitigation mechanism, i.e., the increase of water viscosity with temperature reduction. Through a field-scale single-fracture EGS model that incorporates thermal-hydro-mechanical coupled processes and temperature-dependent water viscosity, we demonstrate that the increase of water viscosity during heat extraction promotes a dispersed fracture flow pattern, which can effectively mitigate thermal drawdown-induced flow channeling and improve long-term thermal performance. The mitigation effect is more noticeable for homogeneous aperture scenarios than for heterogeneous aperture scenarios, especially in the early period of heat production. With a higher in-situ stress and smaller rock Young's modulus, the flow channeling effect of thermal stress becomes weak, and therefore the temperature-dependent viscosity exhibits a more significant flow channeling mitigation effect. The results from the current study provide valuable insights into the optimization of fracture flow and heat transport to achieve more efficient and sustainable energy production from EGSs.

Enhanced Marangoni flow to fabricate uniform and porous SiO2 films: Toward superior high transparency, antifogging, and self- cleaning properties

Fogging on transparent substrate greatly impacts transmittance, causing inconvenience and potential hazards. Increasing surface roughness to enhance hydrophilicity often reduces transmittance. Here, by enhancing the Marangoni flow to inhibit the coffee-ring effect during SiO2 droplet drying, we propose for the first time to manufacture superhydrophilic and high-transmittance coatings with porous structures on various substrates, including glass and resin. This approach relies on a simple, potentially large-scale ultrasonic spray method to enhance the Marangoni flow of SiO2 dispersion with different particle sizes by adding multiple surfactants to reduce the surface tension of the dispersion. The water contact angle of the SiO2 film decreases to below 5° within 0.5 s, imparting anti-fogging properties to the substrate. The film exhibits a transmittance of 93.1 % at 580 nm, surpassing the inherent 90.8 % transmittance of the bare glass. Notably, the film shows remarkable self-cleaning properties due to potent hydration from eco-friendly SiO2 nanoparticles and the porous structure. Owing to the hydrogen bonding between tightly packed small-sized SiO2 particles as well as between the particles and substrate, the surface morphology of the film on glass remains intact even after washing, and soaking. The porous SiO2 film, with a contact angle dropping to below 5° within 0.5 s, maintains its superhydrophilicity even after being exposed to high temperatures, UV irradiation, and humidity conditions. The simple production process of the porous SiO2 films offers a promising method for preparing high-transmittance anti-fogging films with significant industrial potential.