Multiphase Model Research Articles

Numerical Studies on Phase Change Material–Operated Condenser and Preheater for Energy‐Efficient Refrigeration Cycle

ABSTRACTThe study investigates using solid–liquid phase change materials (PCMs) as heat exchangers in energy‐efficient refrigeration systems. A modified refrigeration cycle flow model was proposed and progressively refined for better performance. Initial simulations used simplified U‐tube flow models to reduce complexity, analyzing PCM charging and discharging separately before integrating them into the modified refrigeration system. Various parameters were examined, including the mass flow rate of refrigerant R134a, inlet temperatures of hot and cold refrigerants, and the heat transfer area. The refrigerant, termed HotR, flows through the condenser, while the cooler refrigerant, ColdR, flows through the preheater. PCM acts as the condenser during charging and as the preheater during discharging. Simulation techniques such as the enthalpy‐porosity model for the PCM mushy region, the Lee model for evaporation–condensation, and the volume‐of‐fluid (VOF) multiphase model were utilized to model the PCM‐operated condenser accurately. The study offers valuable insights for optimizing PCM utilization in refrigeration cycles. It emphasizes the importance of refining charging and discharging processes to enhance system efficiency and condensation performance. Simulations showed the need for flow rate adjustments to achieve optimal condensation. Using HotR (343 K) and ColdR (263 K) inlet temperatures and a flow rate of 0.000824 kg/s, the system achieved up to 47% condensation and 25.08 K preheating with the integrated setup.

Numerical Study of Inclined Geometric Configurations of a Submerged Plate-Type Device as Breakwater and Wave Energy Converter in a Full-Scale Wave Channel

The climate crisis represents one of the greatest contemporary global challenges, requiring actions to mitigate its impacts and sustainable solutions to meet the growing demands for clean energy and coastal protection. Therefore, the study of devices such as the submerged plate (SP), which simultaneously acts as a breakwater (BW) and wave energy converter (WEC), is especially relevant. In this context, the present numerical study compares the efficiency of an SP device under regular waves across different geometric configurations considering inclination angles. To achieve this, a horizontal SP was adopted as a reference. Its thickness and total material volume were kept constant while ten alternative geometries, each with a different inclination for the SP, were proposed and investigated. The computational domain was modeled as a full-scale regular wave channel with each SP positioned below the free surface. The volume of fluid (VOF) multiphase model was employed to represent the interaction between water and air. The finite volume method (FVM) was applied to solve the transport equations for volume fraction, momentum, and mass. The SP’s efficiency as a BW was evaluated by assessing the free surface elevation upstream and downstream of the SP, while its efficiency as a WEC was measured by evaluating the axial velocity below the SP. Results indicated that the efficiency of the SP can vary significantly depending on its inclination, with the optimal case at θ = 15° showing improvements of 11.95% and 16.59%, respectively, as BW and WEC.

Oscillatory nature in melt-gas-powder interactions during laser powder bed fusion process revealed by CFD-DEM coupled modelling

ABSTRACT The laser powder bed fusion (LPBF) process encompasses interactions between different material states, including melt, gas, and powder. While observational techniques can capture specific states, they cannot be combined to produce a comprehensive monitoring how they are mutually interacted. Thus, an integrated modelling approach is a crucial solution for revealing their interactions. This study investigates melt-gas-powder dynamics under varying laser scan speeds through a coupled CFD-DEM multiphase model. Findings reveal that metal vapour consistently transitions from an initialisation phase to a processing phase, exhibiting consistent behaviour in the former but varied responses in the latter. A relationship is identified between scan speed and vapour flow angle (VFA), with higher speeds broadening the VFA. Significantly, three oscillatory behaviours are observed: first, the oscillation of locally intensified pressure (LIP) sites on keyhole walls, where vapour ejection modes shift and may become periodic at intermediate scan speeds; second, the oscillation of two induced argon vortex flows with opposite swirling directions; and third, a simultaneously induced varying drag force on powder spatter. These oscillations clarify various spatter mechanisms, offer insights for process optimisation, and suggest implications for process stability. The study also proposes future research directions to further elucidate these mechanisms.

A practical kinetic model for polyvinyl chloride polymerization in batch reactors

Vinyl chloride monomer plays a significant contribution to the chemical industry, serving as a fundamental component for the synthesis of polyvinyl chloride (PVC). This material is distinguished as one of the most extensively manufactured polymers worldwide, finding wide application due to its physical properties, providing good durability, affordable cost, and ease of handling. Although certain mathematical models can be found in literature, implementing the multiphase model with kinetic and diffusive effects demands a considerable set of adjustable parameters, making it challenging to reproduce in industrial sites. In contrast, this study describes the dynamic process of vinyl chloride (VC) polymerization by suspension in a batch reactor to produce PVC. The proposed approach considers a simplified yet robust model that requires fewer adjustable parameters, enabling easier implementation and corroborating with experimental data from the literature. By solving systems of algebraic and differential equations, the proposed model accurately reproduces experimental data for the conversion of VC to PVC, specifically for the initiators PW-40 and AIBN. Additionally, the model delivers superior results compared to those obtained using Aspen® Plus PVC module, a commercial platform widely employed in the industry for polymerization process modeling. These improvements are achieved without introducing excessive complexity, making the model a practical and efficient tool for industrial applications, such as the modeling and optimization of PVC reactors.

A Multi-Phase Analytical Model for Effective Electrical Conductivity of Polymer Matrix Composites Containing Micro-SiC Whiskers and Nano-Carbon Black Hybrids.

Multifunctional polymer composites containing micro/nano hybrid reinforcements have attracted intensive attention in the field of materials science and engineering. This paper develops a multi-phase analytical model for investigating the effective electrical conductivity of micro-silicon carbide (SiC) whisker/nano-carbon black (CB) polymer composites. First, CB nanoparticles are dispersed within the non-conducting epoxy to achieve a conductive CB-filled nanocomposite and its electrical conductivity is predicted. Some critical microstructures such as volume percentage and size of nanoparticles, and interphase characteristics surrounding the CB are micromechanically captured. Next, the electrical conductivity of randomly oriented SiC-containing composites in which the nanocomposite and whisker are considered as the matrix and reinforcement phases, respectively, is estimated. Influences of whisker aspect ratio and volume fraction on the effective electrical conductivity of the SiC/CB-containing polymer composites are explored. Some comparison studies are performed to validate the accuracy of the model. It is observed before the percolation threshold that the addition of nanoparticles with a uniform dispersion can improve the electrical conductivity of the polymer composites containing SiC/CB hybrids. Moreover, the results show that the electrical conductivity is more enhanced by the decrease in nanoparticle size. Interestingly, the composite percolation threshold is significantly reduced when SiC whiskers with a higher aspect ratio are added. This work will be favorable for the design of electro-conductive polymer composites with high performances.

Porothermoelasticity of thermally shocked asphalt material under a multi-phase lag model.

This investigation represents porothermoelastic asphalt material with thermal shock due to multi-phase lag model of thermoelasticity. By applying proper boundary conditions to the normal mode approach, we were able to achieve the precise solution. The graphs provide numerical results for the physical quantities supplied in physical domain. The temperature, displacement, and stress distribution numerical results are given and graphically displayed. To explain the impacts of voids, tine, and phase-lags on the field quantities, comparisons have been done. This research is interesting because it applies the multi-phase lag model and porothermoelasticity to asphalt materials, especially when considering thermal shock. The potential to enhance the longevity, performance, and sustainability of asphalt infrastructure-roadways, bridges, and runways-makes the significance wide. This research provides a more nuanced and realistic modeling method, which is crucial for developing more resilient and effective infrastructure, by taking into account delayed thermal and mechanical reactions as well as the interaction between heat, mechanical stress, and fluid flow.

Using of multi-phase thermal model of the lattice Boltzmann method for simulation of two-phase Rayleigh–Bénard convective heat transfer

Using of multi-phase thermal model of the lattice Boltzmann method for simulation of two-phase Rayleigh–Bénard convective heat transfer

Oxidative Dissolution of Sulfide Minerals in Porous Media Under Evaporative Conditions: Multiphase Experiments and Process‐Based Modeling

AbstractThe dissolution of sulfide minerals in subsurface porous media has important environmental implications. We investigate the oxidative dissolution of pyrite under evaporative conditions and advance a mechanistic understanding of the interactions between multiple physical processes and mineral/surface reactions. We performed a set of experiments in which initially water saturated and anoxic soil columns, containing a top layer of pyrite, are exposed to the atmosphere under no evaporation (single‐phase) and natural evaporative (two‐phase) conditions. The oxidative dissolution of pyrite was monitored by non‐invasive high‐resolution measurements of oxygen and pH. Additionally, we developed and applied a multiphase and multicomponent reactive transport model to quantitatively describe the experimental outcomes and elucidate the interplay between the physico‐chemical mechanisms controlling the extent of pyrite dissolution. The results confirm that the extent of pyrite dissolution under single‐phase conditions was constrained by the slow diffusive transport of oxygen in the liquid phase. In contrast, during evaporation, the evolution of fluid phases and interphase mass transfer processes imposed distinct physical constraints on the dynamics of pyrite oxidation. Initially, the invasion of the gaseous phase led to a fast delivery of high oxygen concentrations in the reactive zone and thus markedly increased pyrite oxidation and acidity/sulfate production. However, such enhanced release of reaction products was progressively limited over time as drying conditions prevailed in the reactive zone and inhibited pyrite oxidation. The transient phase displacement was also found to control the distribution of aqueous species and formation of secondary minerals by creating spatio‐temporally variable redox conditions.

A multi-phase structured cascade model for mass training of community healthcare workers in performing clinical breast exams in remote regions.

Clinical breast exam (CBE) by outreach healthcare workers (HCW) may help downstage breast cancer in resource-limited areas where mammography may not be feasible. We evaluated the effectiveness of a pilot cascade-model training programme for HCWs in remote areas of Pakistan. The training programme comprised three phases. In phase one, fellowship-trained breast surgeons at a metropolitan academic centre trained six HCWs to perform CBEs. In phase two, these six HCWs (master trainers) trained 15 additional HCWs, implementing cascade training. In phase three, the consultant breast surgeon conducted a re-evaluation and refresher course for all 21 HCWs at least one year after the original training session. We assessed CBE ability and skills through pre- and post-changes through self-reported confidence and direct observation of procedural skills. Significant improvements in learners' self-reported confidence and CBE skills were observed in both phases one and two. The median scores in the learners' post-training self-reported confidence and CBE skills (inspection, palpation, and lymph node examination) improved by 20% and 46.2%, respectively, indicating excellent learning outcomes of the cascade training sessions. Phase three showed sustained high scores in self-reported confidence and CBE skills more than one year later. Mass training of outreach HCWs in remote regions in performing CBE may be possible with a structured multiphase cascade-training model and may be an important step in downstaging symptomatic breast cancer in low-resource settings.

Cooperative Low-Carbon Trajectory Planning of Multi-Arrival Aircraft for Continuous Descent Operation

To address the technical challenges of implementing Continuous Descent Operations (CDO) in high-traffic-density terminal control areas, we propose a cooperative low-carbon trajectory planning method for multiple arriving aircraft. Firstly, this study analyzes the CDO phases of aircraft in the terminal area, establishes a multi-phase optimal control model for the vertical profile, and introduces a novel vertical profile optimization method for CDO based on a genetic algorithm. Secondly, to tackle the challenges of CDO in busy terminal areas, a T-shaped arrival route structure is designed to provide alternative paths and to generate a set of four-dimensional (4D) alternative trajectories. A Mixed Integer Programming (MIP) model is constructed for the 4D trajectory planning of multiple aircraft, aiming to maximize the efficiency of arrival traffic flow while considering conflict constraints. The complex constrained MIP problem is transformed into an unconstrained problem using a penalty function method. Finally, experiments were conducted to evaluate the implementation of CDO in busy terminal areas. The results show that, compared to actual operations, the proposed optimization model significantly reduces the total aircraft operating time, fuel consumption, CO2 emissions, SO2 emissions, and NOx emissions. Specifically, with the optimization objective of minimizing total cost, the proposed method reduces the total operation time by 22.4%; fuel consumption, CO2 emissions, SO2 emissions by 22.9%, and NOx emissions by 23.7%. The method proposed in this paper not only produces efficient aircraft sequencing results, but also provides a feasible low-carbon trajectory for achieving optimal sequencing.

Modeling of Oil–Water Two-Phase Flow in Horizontal Pipes Using CFD for the Prediction of Flow Patterns

A computational fluid dynamics study of the horizontal oil–water flow was performed using the Eulerian–Eulerian and mixture multiphase models in conjunction with the realizable k–ε turbulence model for the characterization of flow patterns. The experimental tests were carried out using water and mineral oil with a density of 880 kg/m3 and a viscosity of 180 cP, varying the superficial velocities of both fluids in ranges of 0.1–1.2 m/s and 0.1–0.5 m/s, respectively. The numerical model was defined under the same initial and boundary conditions as in the experiment. Moreover, the model is defined such that entering the fluids in a mixed state, the stratified pattern could form adequately with the two multiphase models. Although the Eulerian–Eulerian model, together with the geometric reconstruction scheme, allowed us to visualize the three-dimensional dispersed patterns in a very similar way to the experimental results, the mixture model did not exhibit such similarity, especially in the oil-in-water dispersions. Additionally, the Eulerian–Eulerian model was able to predict the experimental holdup values with an average error of 15.2%.

A Comparative Performance Evaluation of Mainstream Multiphase Models for Aerated Flow on Stepped Spillways

A systematic comparative evaluation of mainstream multiphase models for specific hydraulic structures is essential to investigate aerated flow characteristics and promote the models’ application. However, such evaluations remain scarce. In this paper, four multiphase models, namely the VOF, Mixture, and Eulerian models in Ansys Fluent and the aerated flow model in FLOW-3D (AFM-F3D), were comparatively introduced and tested for the aerated flow over stepped spillways. Simulation results, including water surface profiles, inception points of aeration, air concentrations, velocities, and turbulent kinetic energies from four models, are compared with each other and with available experimental data. It is discovered that both the VOF and Mixture models fail to reproduce the self-aeration and subsequent downward transport phenomenon. In contrast, AFM-F3D and the Eulerian models predict reliable aerated water surface profiles. AFM-F3D and the Eulerian model demonstrate superior performance in velocity and air concentration calculations, respectively. Based on overall performance, the Eulerian model is recommended for simulating aerated stepped spillway flows. These insights provide valuable guidance for selecting appropriate multiphase models based on specific engineering requirements.

Streamlining Linear Free Energy Relationships of Proteins through Dimensionality Analysis and Linear Modeling.

Linear free energy relationships (LFERs) are pivotal in predicting protein-water partition coefficients, with traditional one-parameter (1p-LFER) models often based on octanol. However, their limited scope has prompted a shift toward the more comprehensive but parameter-intensive Abraham solvation-based poly-parameter (pp-LFER) approach. This study introduces a two-parameter (2p-LFER) model, aiming to balance simplicity and predictive accuracy. We showed that the complex six-dimensional intermolecular interaction space, defined by the six Abraham solute descriptors, can be efficiently simplified into two key dimensions. These dimensions are effectively represented by the octanol-water (log Kow) and air-water (log Kaw) partition coefficients. Our 2p-LFER model, utilizing linear combinations of log Kow and log Kaw, showed promising results. It accurately predicted structural protein-water (log Kpw) and bovine serum albumin-water (log KBSA) partition coefficients, with R2 values of 0.878 and 0.760 and root mean squared errors (RMSEs) of 0.334 and 0.422, respectively. Additionally, the 2p-LFER model favorably compares with pp-LFER predictions for neutral per- and polyfluoroalkyl substances. In a multiphase partitioning model parametrized with 2p-LFER-derived coefficients, we observed close alignment with experimental in vivo and in vitro distribution data for diverse mammalian tissues/organs (n = 137, RMSE = 0.44 log unit) and milk-water partitioning data (n = 108, RMSE = 0.29 log units). The performance of the 2p-LFER is comparable to pp-LFER and significantly surpasses 1p-LFER. Our findings highlight the utility of the 2p-LFER model in estimating chemical partitioning to proteins based on hydrophobicity, volatility, and solubility, offering a viable alternative in scenarios where pp-LFER descriptors are unavailable.

Multimodal multiphasic preoperative image-based deep-learning predicts HCC outcomes after curative surgery.

HCCrecurrence frequently occurs after curative surgery. Histologicalmicrovascular invasion (MVI) predicts recurrence but cannot provide preoperative prognostication, whereas clinical prediction scores have variable performances. Recurr-NET, a multimodal multiphasic residual-network random survival forest deep-learning model incorporating preoperative CT and clinical parameters, was developed to predict HCC recurrence. Preoperative triphasic CT scans were retrieved from patients with resected histology-confirmed HCC from 4 centers in Hong Kong (internal cohort). The internal cohort was randomly divided in an 8:2 ratio into training and internal validation. External testing was performed in an independent cohort from Taiwan.Among 1231 patients (age 62.4y, 83.1% male, 86.8% viral hepatitis, and median follow-up 65.1mo), cumulative HCC recurrence rates at years 2 and 5 were 41.8% and 56.4%, respectively. Recurr-NET achieved excellent accuracy in predicting recurrence from years 1 to 5 (internal cohort AUROC 0.770-0.857; external AUROC 0.758-0.798), significantly outperforming MVI (internal AUROC 0.518-0.590; external AUROC 0.557-0.615) and multiple clinical risk scores (ERASL-PRE, ERASL-POST, DFT, and Shim scores) (internal AUROC 0.523-0.587, external AUROC: 0.524-0.620), respectively (all p < 0.001). Recurr-NET was superior to MVI in stratifying recurrence risks at year 2 (internal: 72.5% vs. 50.0% in MVI; external: 65.3% vs. 46.6% in MVI) and year 5 (internal: 86.4% vs. 62.5% in MVI; external: 81.4% vs. 63.8% in MVI) (all p < 0.001). Recurr-NET was also superior to MVI in stratifying liver-related and all-cause mortality (all p < 0.001). The performance of Recurr-NET remained robust in subgroup analyses. Recurr-NET accurately predicted HCC recurrence, outperforming MVI and clinical prediction scores, highlighting its potential in preoperative prognostication.

A multiphase model for fluid–particle flows with added mass and phase change

In our prior work, a kinetic-based model for fluid–particle flows with added mass was derived (Fox et al., 2020) and successfully validated for non-reacting cases without mass transfer (Boniou and Fox, 2023). In this work, the multiphase model is extended to allow for the added-mass phase to have a different temperature and density than the particle and bulk-fluid phases, and to account for mass transfer from the particle phase to the added-mass phase. For this purpose, mass and energy transfer between particles and their added mass, and the added-mass and bulk-fluid phases are included. As before, the particle-phase density ρp is assumed constant, but now the added-mass density ρa is allowed to differ from the bulk-fluid density ρf. These densities are coupled through the assumption that their pressures are equal, i.e., pa=pf, and determined by a fluid-phase equation of state. Since mass transfer will change the particle volume, an additional balance equation for the particle number density Nd is required to complete the multiphase model. The computational algorithm for the extended model is tested using sublimation and condensation of carbon-dioxide particles interacting with a strong shock wave.

Large Contributions of Gas‐Particle Partitioning and Heterogenous Processes to Particulate Nitroaromatic Compounds at a Mountain Site Revealed by Observation‐Based and Multiphase Modeling

AbstractParticulate nitroaromatic compounds (NACs), among the major atmospheric components of light‐absorbing brown carbon, have garnered increasing attentions due to their impacts on atmospheric environment and ecological health. However, there is a scarcity of comprehensive understanding on their origins and formation pathways. In this study, 14 particulate NACs were measured at high time resolution at the summit of Mount Tai over North China Plain in winter with an average concentration of 30.5 ng m−3. The relatively higher concentrations and distinct diurnal profiles of NACs suggest the occurrence of strong secondary formation driven from polluted urban plumes transported by mountain‐valley breezes, elevated NOx and precursor levels, and strong oxidation capacity. An observationally constrained multiphase chemical box model was developed and employed to elucidate the origins and formation pathways of NACs. They mainly came from the air mass transport from the polluted urban regions to the mountaintop during the day, while the nocturnal NACs formation is dominated by the partitioning of gaseous NACs to the particle phase and heterogenous processes on aerosols. This work provides observational evidence of elevated NACs levels at high mountain site as well as modeling reference for multiphase processes of particulate NACs and the contributions from different formation pathways to a large degree addressing the problem of underestimation in traditional models.

Boiling critical characteristics in narrow rectangular channel under local heat flux concentration conditions

For the establishment of predicting method of local concentrated critical heat flux (CHF) in narrow rectangular channels, and also technical support for the preparation of long-life and high-performance dispersive plate fuel, this work simulates Dry-out type CHF under local concentration of heat flux condition by using Eulerian multiphase model and Enhanced near-wall treatment. The distribution of near-wall temperature and void fraction under different heat flux was calculated by Computational Fluid Dynamics (CFD) method. Dry-out CHF was predicted based on highly and quickly wall temperature rise. The influence of system pressure, mass flow rate and inlet subcooling degree were discussed on Dry-out CHF. Compared with uniform heating, the predicted average heat flux on CHF is lower under local heat flux concentration, and location of CHF is related to the position of heat flux concentration area. This work’s research method in Ansys Fluent could be applied to forecast Dry-out CHF in narrow rectangular channel under local concentration of heat flux condition.

Level-Set Method Based Predictive Modeling to Track the Evolution of Surface During Pulsed Laser Surface Melting

Abstract The objective of this study is to investigate the evolution of surface geometry during pulsed laser surface melting (pLSM) via level-set method-based interface tracking numerical framework. Existing models to track surface geometry are inaccurate and computationally expensive. Therefore, they have limited use in gaining understanding of the surface evolution during pLSM. A numerical model, integrating the level-set approach, fluid flow, and heat transfer dynamics, is detailed in this paper. The multi-phase numerical model achieves accurate tracking of interface for a single pulse by implementing the volumetric laser heat source on the moving interface by modifying Beer–Lambert's law. The accuracy of the single pulse model is confirmed by comparing its peak-to-valley height (PVH) to the experimental data. The deviation in PVH is limited to about 15%, with a maximum root mean square error of ∼0.24 µm, highlighting the model's reliability. Additionally, the evolved surface of a single pulse from the model is replicated over an area with dedicated overlaps to generate the predicted textured surface with reasonable accuracy. Some inaccuracies in the predicted surface roughness values were observed because the textures were generated based on a single pulse geometry computed on an initially flat surface. Nonetheless, the results highlight a significant development in numerical frameworks for pLSM and can be used as a tool to gain deeper insights into the process and for process optimization.

Application of neural networks for determining the parameters of PVT-models used in solving hydrodynamic modeling problems

The article presents an overview of the application of machine learning models for problems of modeling the phase state of hydrocarbon systems. Determination of the state of a hydrocarbon system is possible in the presence of nonhydrocarbon components when performing hydrodynamic calculations on multiphase models. Such calculations are in demand when solving problems of both forecasting and adapting models to actual development data. It is shown that when adjusting models to actual data, the accuracy of reproducing laboratory experiments is in some cases higher than when using equations of state. But in some cases, the use of neural networks turns out to be useless. For relatively “simple” fluid systems, an increase in the complexity of the tool used does not provide an increase in accuracy compared to simple regression models. Another problem is the lack of a working tool that would completely replace the use of equations of state to assess the state of a fluid model when performing hydrodynamic calculations.

An Analysis of Dynamic Recrystallization During the Reduction Pretreatment Process Using a Multiscale Model

In this study, a multiscale model is developed through secondary development (UMAT and UEXTERNALDB) in Abaqus with the objective of simulating the thermal deformation process with dynamic recrystallization behavior. The model couples the finite element method (FEM) with the multiphase field model (MPFM), thereby establishing bidirectional coupling between macroscopic mechanical behavior and microstructural evolution. A comparison between the single-element hot compression simulation and experimental results demonstrates that the model accurately simulates both the macroscopic mechanical behavior and microstructural evolution during the thermal deformation process, thereby exhibiting high precision. Simulations of the reduction pretreatment (RP) process under different reduction amounts and billet surface temperatures demonstrate that increasing the reduction amount and billet surface temperature significantly enhances both plastic deformation and the volume fraction of dynamic recrystallization in the billet core. This results in the closure of core voids and the refinement of the core microstructure, thereby providing valuable guidance for the development of optimal reduction pretreatment (RP) processes.