Two-phase Flow Model Research Articles

Evolution of collisional condensation of biodiesel combustion particulate matter in engine exhaust pipe

To investigate the evolution of biodiesel combustion particulate matter (PM) within the engine exhaust system, PM samples were analyzed from diesel fuel, soybean oil methyl ester (SME), catering waste oil methyl ester (WME) and palm oil methyl ester (PME) at various locations along the engine exhaust pipe, and a gas-solid two-phase flow model of exhaust gas and PM was developed using the coupled computational fluid dynamics-discrete element method (CFD-DEM). The results indicate that the average primary particle diameter of biodiesel PM is smaller than that of diesel PM at the same position within the exhaust pipe, and it exhibits an increasing trend with respect to the iodine value of biodiesel. The adhesion forces of diesel, SME, WME, and PME PM at 0 m downstream from the exhaust pipe were measured as 9.83 nN, 16.74 nN, 26.54 nN, and 34.31 nN, respectively. The biodiesel PM with higher mass density readily formed structurally stable particulate agglomerates at the inlet of the exhaust pipe. With an increase in exhaust flow velocity, there was a corresponding rise in particle collision frequency. The initial agglomeration probability of particles exhibited an increase followed by a subsequent decrease. The normal overlap of particle collisions decreased with an increase in the Young's modulus of the particles, thereby reducing the likelihood of adsorption and adhesion during particle collision and hindering the formation of a greater number of particle aggregates.

Numerical Study on the Local Aggregation of Helium Bubbles in Liquid Lithium and Its Thermal Analysis

Abstract Liquid lithium is widely regarded as an optimal cooling medium for space nuclear reactors due to its exceptional heat transfer properties and low density. However, the helium bubbles generated by liquid lithium under space irradiation pose significant hazards to the safe and stable operation of nuclear reactions. This study employs the COMSOL finite element software to construct the level-set two-phase flow models and bubble stream model separately to investigate the local accumulation of helium bubbles and the overall flow of low-concentration gas–liquid mixtures. The main focus is on examining the different distributions of multiple helium bubbles randomly generated in local liquid lithium and the influence of boundary conditions on their accumulation morphology, as well as the impact of low-concentration bubble stream on their overall heat transfer performance. Agglomerated bubbles with radii between 5 μm and 150 μm are classified into three categories based on local concentrations: circular (≤20.37%), irregular elongated (up to 30.44%), and banded (up to 36.31%).The interconnected banded bubbles can be up to 8 times larger than irregularly elongated ones, and they have a positive effect on the distribution of physical quantities and wall temperature perturbations in the pipeline. The increase in inlet velocity triggers bubble impacts and fragmentation, further reducing thermal resistance and enhancing heat transfer performance. When the bubble diameter is less than 15 μm and the bubble concentration is within 1%, the influence of the mixed flow on overall heat transfer is not significant. This study provides insights for manipulating bubble structure and guiding localized and comprehensive thermal analyses.

A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor–Couette test case. To impose the boundary condition when the fluid–fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

Research on shutdown purge characteristics of proton exchange membrane fuel cells: Purge parameters conspicuity and residual water

This paper comprehensively investigates the purge mechanism of proton exchange membrane fuel cells during the shutdown process, which qualitatively examines the effect of purge parameters (including current density, stoichiometric ratio, and relative humidity) on water content variation, and further quantitatively investigates the remaining water content post-purge. In contrast to previous studies, this paper offers a novel perspective on analyzing the purge process and conducts a thorough examination of residual water content. This study presents a transient, isothermal, two-phase flow model for proton exchange membrane fuel cells, which is subsequently validated experimentally. Results indicate that the significance of purge parameters follows the descending order: stoichiometric ratio, relative humidity, and current density. During the purge, the stoichiometric ratio should be rapidly increased to above 9. Each incremental rise in the stoichiometric ratio from 6 to 14 leads to a respective reduction in residual membrane water content after purge of 2.19 %, 1.57 %, 1.18 %, 0.93 %, 0.76 %, 0.63 %, 0.53 %, and 0.46 %. Similarly, it is recommended to swiftly decrease relative humidity to below 40 %. Elevating the purge current density from 20 to 200 mA/cm2 decreases the time required to completely remove liquid water from 20.24 s to 6.59 s. Hence, employing a higher current density at the onset of the purge facilitates quicker removal of liquid water, albeit resulting in an increase in residual membrane water content post-purge, from 3.17 to 3.70. In summary, optimizing the purge strategy requires adjusting purge current densities according to the specific purge stage.

The mechanism by which thermal coupling leads to an asymptotic maldistribution stability boundary for flow boiling in parallel channels

Phase change heat transfer processes are attractive for the efficient thermal management of advanced semiconductor devices, with flow boiling in parallel microchannel heat sinks being one promising solution. However, there are several implementation challenges associated with two-phase flow in parallel microchannels, particularly flow maldistribution, which can adversely affect performance and reliability. Two-phase flow models can be useful in predicting and understanding the instability mechanisms that leads to maldistribution, such that parametric performance trends and safe regions of operation can be identified. Channel-to-channel thermal coupling has been shown to alleviate maldistribution, but it is not yet understood why this effect is limited to some critical lateral thermal conductance above which there is no further benefit. In the current work, a two-phase flow model with a lumped thermal capacitance representation of the heat sink wall is developed to identify the mechanism for this asymptotic maldistribution stability boundary for thermally coupled microchannels. The lumped model allows the nature of stability boundary to be explained via a scaling analysis of the eigenvalues. In such systems, it is identified that a single eigenvalue determines the occurrence of flow maldistribution. Scaling analysis shows that, for small values of thermal conductance, this eigenvalue becomes a quadratic function of thermal coupling, which enhances the stability of microchannels and moves the stability boundary. However, for large values of thermal conductance, the eigenvalue is dependent only on the fluid properties, leading to a limit at which thermal coupling can no further improve stability or affect the stability boundary. The lumped model developed in this work enables mechanistic understanding of the role of channel-to-channel thermal coupling on mitigating flow maldistribution and therefore may offer important guidance on the design of flow boiling systems and heat sinks.

Vertical displacement of a non-Newtonian Bingham plastic by a Newtonian phase in an axially composite reservoir

In general, oil reservoirs may consist of composite sedimentary structures composed of materials such as sand, clay, or limestone, which exhibit varying lithology due to sedimentary processes. A comprehensive knowledge of this lithology is essential for accurately assessing their hydrocarbon storage and production capacity. Additionally, this information is indispensable for the implementation of various recovery techniques such as waterflooding, gas injection, surfactant injection, polymer injection, alkaline water solution injection, and others. Highly viscous oil can exhibit non-Newtonian behavior during water injection in certain cases. The use of surfactants, alkaline, or polymer solutions in enhanced oil recovery also introduces non-Newtonian behavior. Recovery methods face challenges when non-Newtonian phases, gravity, and reservoir heterogeneity are combined. Against this backdrop, this work presents a mathematical model for immiscible two-phase flow in an axially composite reservoir with a periodic-layered structure. The model considers a non-Newtonian plastic Bingham-type phase extension of the Buckley-Leverett model. To address the porous medium’s heterogeneity with discontinuous flux functions, the numerical solutions were obtained using the Lax-Friedrichs and Lagrangian-Eulerian schemes. The numerical solutions were compared to analytical solutions obtained using an extended version of Oleinik’s geometric construction for discontinuous flux functions. The outcomes display shock and rarefaction waves, as well as a fixed shock due to the porous medium heterogeneity. The numerical results closely correspond with the analytical solutions, seen particularly in the greater accuracy of the Lagrangian-Eulerian method compared to the Lax-Friedrichs method.

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

In this paper, a homogenized multiphase lattice Boltzmann (LB) model is established for parallelly simulating immiscible two-phase flow in both solid-free regions (pore scale) and porous areas (continuum scale). It combines the color-gradient multiphase model with the Darcy–Brinkman–Stokes method by adding a term that includes surface force and drag force of porous matrix to multiple-relaxation-time LB equation in moment space. Moreover, an improved algorithm is proposed to characterize and implement the apparent wettability in the locally homogenized porosity field. Validations and test cases are given to demonstrate the accuracy and robustness of this new model, as well as its applicability for trans-scale fluid simulation of transport and sorption behavior from porous (Darcy flow) area to free (Stokes flow) area. For practicality, the two-phase seepage flow in a composite rock structure with multiscale pores is simulated by this new model, and the effects of viscosity ratio and wettability on the displacement process are discussed.

Determining relative permeability and capillary pressure from mixed-wet core floods

The main goal of this paper is a laboratory method development for determining the capillary pressure and relative permeability from coreflooding test specifically for mixed-wet rocks. Previously, the steady-state transient test (SSTT) was designed to determine both relative permeability (Kr) and capillary pressure (Pc) from a single steady-state coreflood by using the transient data of routine steady-state tests. On the contrary to the previous works, where SSTT was developed for completely hydrophobic or hydrophilic outcrop cores, this paper determines Kr and Pc for mixed-wet cores. Depending on the capillary pressure equation applied, the mathematical model for two-phase flow in mixed-wet rocks contains one or two extra constants, so some extra measurements must be taken during SSTT, to determine Pc and Kr curves. We change the experimental protocol by establishing a uniform initial saturation Swi by evaporation method. We also include bump floods at two high rates for the alternative determination of saturation and relative permeability for residual oil. A new inverse solver determines the set of model constants that employs van Genuchten's Pc formula and a vaporization procedure for initial core saturation. The number of resulting model coefficients is equal to seven and matches the dimension of the measured data array for mixed-wet cores.The developed SSTT for mixed-wet rocks is applied and validated for both high-salinity (HS) and low-salinity (LS) waterfloods. Strong agreement between laboratory steady-state, transient, and bump-flood data and those obtained by mathematical modelling – R2 is above 0.99 for steady-state data and above 0.9 for transient data - validates the proposed SSTT procedure and inverse solver for mixed-wet cores and HS and LS waterfloods. Our findings indicate that low salinity has a greater effect in expanding the range of positive capillary pressure compared to high salinity. This suggests an increase in water-wettability as the salinity decreases.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 1 – Model formulation and numerical implementation

Two-phase flow boiling in heat sinks and cold plates is attractive for various thermal management applications due to high effective heat capacity rates and high heat transfer coefficients compared to single-phase operation. In addition, multi-physics topology optimization is sought for generation of high performance thermal management components. Yet, the design of heat sinks using topology optimization has been restricted to single-phase flow physics, due to incompatibility between available two-phase flow models and traditional single-phase topology optimization approaches. Interface-capturing two-phase flow models are too computationally expensive for optimization; mixture and two-fluid models that treat the liquid and vapor phases as an interpenetrating continuum with interfacial transport phenomena captured through empirical correlations are computationally tractable for heat-sink-scale optimization. However, the penalization approaches commonly used to define the structures formed during topology optimization results in arbitrary fin and channel geometries for which a universal two-phase flow correlation is not available. To enable coupling with two-phase mixture models, this work leverages a homogenization approach to topology optimization wherein heat sink designs are represented using spatially varying microstructures with optimized dimensions. A predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. This work is the first to develop a topology optimization algorithm using a mixture model for simulating two-phase flow boiling to design heat sinks and cold plates. Part 1 of this study develops and implements the algorithm to investigate topology optimized heat sinks at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared. There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. A companion paper (Part 2) focuses on manufacturing, model calibration, and experimental validation of the topology optimized heat sinks under two-phase flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

Simulation of a two-phase loop thermosyphon using a new interface-resolved phase change model

The remarkable progress made in power electronics has been coupled with the miniaturization of systems, requiring high-performance cooling. A solution that has garnered significant interest involves the use of two-phase loops, in which heat transfer is associated with the phase change of the working-fluid. This paper aims at modeling two-phase flow with separated phases in a gravity-driven two-phase loop. The Volume-of-Fluid method is employed to capture the moving interface. Amid the variety of the phase change models available in the literature, we have chosen to employ a hybrid model: a subgrid-scale model to generate phase change at the wall in the absence of an interface, and a interface-resolved model for phase change at pre-existing liquid-vapor interfaces. These models have been implemented in the OpenFOAM computational code. The developed solver makes possible the simulation of compressible laminar two-phase flow with diabatic liquid-vapor phase change. Conjugate heat transfer between the wall and the fluid is also taken into account. Two-dimensional numerical simulations demonstrate that the developed solver is capable of reproducing flow regimes obtained from experiments, including the formation of Taylor bubbles and the propulsion of liquid from the evaporator to the condenser during geyser boiling. Furthermore, this study examines how the filling ratio affects flow regimes and performance.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 2 – Model calibration and experimental validation

Flow boiling offers increased heat transfer coefficients and effective heat capacity rates that can be leveraged by topology optimization (TO) to generate high-performance microchannel heat sinks. Topology optimization of heat sinks having two-phase flows can be accomplished using the homogenization approach wherein designs are represented as spatially varying distributions of microstructures, as demonstrated in Part 1 of this two-part study. Flow and heat transfer within the microstructures are captured using a two-phase mixture model featuring an effective porous medium formulation. However, closure of these governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. This Part 2 of our study successfully demonstrates a comprehensive end-to-end process for two-phase flow model calibration, topology optimized design generation, and experimental validation of optimized performance for flow boiling heat sinks. To this end, a TO algorithm with the homogenization approach and a two-phase mixture model is implemented using available flow boiling correlations for microchannels. A set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach.

Computational fluid dynamics simulations of single-bubble evolution under synergy of ultrasound and an electrostatic field

In the study reported here, a two-phase flow model was developed for the evolution of a single bubble under ultrasonic irradiation coupled with an electrostatic force. We started with the following assumptions: (I) the liquid is incompressible, (II) the effect of gravity is negligible in the liquid, (III) the bubble is insulating, and no free charges are distributed on the liquid–gas interface, and (IV) the liquid contains only one bubble. Using computational fluid dynamics, we analyzed how the bubble shape evolves under various conditions, and the main findings are as follows: (1) With increasing electric field strength, the bubble reaches a larger maximum area and a smaller minimum area. Furthermore, during the positive phase of ultrasound, a higher electric field strength leads to faster compression and a more slender bubble. (2) As the initial bubble radius is increased from 3 to 5 μm, the cavitation becomes significantly stronger, but when the initial bubble radius reaches 10 μm, the cavitation intensity decreases instead because of greater compression resistance caused by there being more gas in the bubble. (3) Cavitation cannot be triggered under an excessively low acoustic pressure amplitude, and an excessively high acoustic pressure amplitude results in weaker cavitation; the appropriate acoustic pressure amplitude is considered to be 1.35 atm.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil & gas industry, nuclear power plants, and CCUS. Reliable calculations of gas void fraction (or liquid holdup) play a central role in two-phase pipe flow models. In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions. Compared to existing methods and correlations, this new framework provides a simple, approximate, and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns. Notably, existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework. Different fractional flow models are applicable to different flow conditions, and they demonstrate good agreement against experimental data within 5% errors when compared with an experimental database comprising of 2754 data groups from 14 literature sources, covering various pipe geometries, flow patterns, fluid properties and flow inclinations. The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Quantitative characterization of imbibition in fractured porous media based on fractal theory

In low-permeability reservoirs, such as shale and tight sandstone, imbibition is an important mechanism for enhancing oil recovery. After hydraulic fracturing treatment, these reservoirs create a network of fracture pathways for fluid flow. Therefore, understanding the imbibition mechanisms in fractured porous media and quantitatively characterizing oil–water distribution are crucial for the development of low-permeability reservoirs. In this study, a mathematical model of two-phase flow in porous media with branching fractures was established. The phase-field method was employed to track the oil–water interface, and quantitative characterization of imbibition was conducted based on fractal theory, and the effects of wetting phase injection rate, the number of disconnected fractures, fracture spacing, and fracture morphology on imbibition in branched fracture porous media were discussed. The research findings indicate that in branched fracture porous media, both co-current and countercurrent imbibition processes occur simultaneously, and there exists a diffusion interface layer with a certain thickness at the oil–water interface. The hydraulic pressure generated by the wetting phase injection rate provides the driving force for imbibition oil recovery, but it also affects the contact time between the wetting and non-wetting phases. The presence of disconnected fractures hinders the propagation of hydraulic pressure, reducing the effectiveness of imbibition. The imbibition displacement zone is limited and occurs only within a certain range near the fractures. As the number of branching fractures increases, the channels for the wetting phase to enter matrix pores are enhanced, resulting in higher efficiency of imbibition displacement of the oil phase. The results of this research can provide guidance for the design of fracturing programs and recovery prediction in low-permeability reservoirs.

Numerical Simulation of Tailings Mortar Flowing from Dam Break by Variable Concentration Two-phase Flow Algorithm

A dam break accident of tailings pond may result in serious loss of the residents' lives and property, and usually leads to surrounding environmental disaster. Accurately calculating the flowing distance and inundation range of discharged tailings is important but remains to be solved. The main feature of tailings mortar movement is that solid particles continue to sink and accumulate during the flow process, which makes the solid concentration in the mortar constantly change, thus altering the rheological properties of the mortar. Therefore, the advancement of tailings mortar is a kind of two-phase unsteady flow with variable solid-phase concentration. In conventional numerical calculations of tailings flow, the rheological parameters of the Bingham model used are given fixed values with no consideration of concentration change, resulting in inaccurate calculation results and difficulty reflecting the phenomenon of tailings sands accumulation along the way. In this paper, a variable concentration two-phase flow model is proposed and then applied to a typical tailings dam failure case. The flow features and inundation range of the tailings mortar are analyzed and are found to be basically consistent with the field investigation, which means the proposed two-phase flow algorithm is reasonable and reliable.

A local scour model for single pile on silty seabed considering soil cohesion (SedCohFOAM): Model and validation

In this study, the sediment transport two-phase flow model named SedFOAM is expanded to include soil cohesion, creating a new model named SedCohFOAM within OpenFOAM. The local scouring flume experiment involving a pile on silty seabed and sandy seabed is conducted in a curved flume. Due to the influence of cohesion, the scouring depth at different locations on sandy seabed is 15%–18% greater than that on silty seabed. Observations from this experiment informed the analysis of force balance, wherein the agglomerated silt particles are modeled as large singular entities and the cohesive force is treated as a downward influence that keeps the aggregated particles stationary. Meanwhile, the experimental outcomes are utilized to validate the accuracy of the SedCohFOAM model. The numerical findings demonstrated that SedCohFOAM can simulate the flow field distribution around the pile, variations in seabed shear stress, and alterations in seabed surface morphology. Compared with the SedFOAM model, the SedCohFOAM model has a significantly reduced simulation error in simulating scour on silty seabed. When comparing the cross-sectional profiles of the scour holes derived from the flume experiments with those simulated by SedCohFOAM, it was observed that the ultimate-equilibrium scour depth predicted by the model is consistently lower, but the scour radius in the numerical simulations is larger. The deviation from the experimental results is nearly within 8%, while when the flow velocity is high, the simulation error of the simulated scouring depth behind the pile and the scouring radius in front of pile is amplified.

Erosion Wear Analysis on Valve Cage of Cage-Typed Sleeve Control Valve for Coal Liquefaction

Abstract Cage-typed sleeve control valve (CSCV) is the key basic equipment in direct coal liquefaction projects. The working condition of CSCV has the characteristics of high-pressure difference, high velocity, and high solid content. There is a general issue of liquid–solid two-phase erosion wear in CSCV, which can easily lead to the failure of the internal structure in the valve cage. Therefore, it is necessary to study erosion wear characteristics of internal structures in the valve cage. Considering the real conditions of erosion wear in the valve cage, a simplified T-shaped flow path is designed, and the precision of both the liquid–solid two-phase flow model and the erosion prediction model is validated. The flow characteristics and erosion wear characteristics in the T-shaped flow path under different working conditions are studied. Based on the simulation results of different structural parameters and boundary conditions, the erosion wear of the T-shaped flow path is predicted and calculated by the response surface method. Subsequently, the prediction formula for the maximum erosion rate is derived. The formula enables the swift determination of optimal structural parameters for the flow path, aiming to mitigate damage to the valve caused by erosion wear. This work can quickly predict the erosion wear rate of the key areas in the valve cage, which can provide a certain reference value for the life prediction and structural optimization of CSCV, and it can also benefit the safety and maintenance of the coal liquefaction system.

Numerical study of structural optimization for improving gas-liquid flow and microalgae carbon fixation rate in air-lift photobioreactors

In this paper, the gas-liquid flow pattern and CO2 dissolution transport process of microalgae solution in an air-lift photobioreactor (PBR) are investigated by numerical simulations. In order to promote the gas-liquid mass transfer efficiency to enhance the carbon fixation, we propose different optimization schemes for the structure. Firstly, a two-phase flow model and a mass transfer model are employed to investigate the fluid flow characteristics. The flow state is evaluated by velocity in light direction, turbulent kinetic energy (TKE), gas hold-up and CO2 mass transfer coefficient. The results show that the gas flow rate of 0.2 V/V/min is the optimum value for the inlet. Secondly, CO2 mass transfer and carbon fixation rates are analyzed for different inlet CO2 volume fractions. With the increase of CO2 volume fraction, the carbon fixation rate first increases and then decreases, the highest fixation rate reaching 2.21 × 10−4 mol m−3 s−1 at 6 %. Finally, based on numerical simulations, three optimized structures with different spacing of baffles are proposed and evaluated the performance in comparison with the original. The results show that the gas distribution and CO2 mass transfer are significantly improved, with the one-sided baffle structure is the best. In summary, this study provides a new and useful reference to evaluate the gas-liquid mixing and improve the microalgae carbon fixation rate.

A two-phase flow model for sedimentation and consolidation

Sedimentation and consolidation, a multi-physical phenomenon of great significance in aquatic environments, usually involves dynamic pore pressure, inertial effects, fluid-particle interphase interaction and solid stress. However, simplified models for sedimentation and consolidation typically assume hydrostatic mixture pressure and neglect inertial effects without proper justifications. Here, a one-dimensional three-equation two-phase flow model (TTP) is proposed for sedimentation and consolidation, which directly resolves dynamic fluid pressure and inertial terms. The present TTP model is benchmarked against a series of experimental cases and two existing four-equation two-phase flow (FTP) models. It features encouraging performance as compared to measured data and computed results of the existing FTP model. Furthermore, the present TTP model shows superior computing efficiency over the FTP models. To investigate the influences of inertial effects and non-hydrostatic mixture pressure, two simplified versions of the TTP model are constructed and compared with the TTP model. It is shown that incorporating inertial effects and non-hydrostatic fluid pressure are important for accurately predicting the sedimentation-consolidation process. The present study facilitates a promising framework for modelling sedimentation and consolidation, thereby supporting effective sediment management.

Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary

Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary