Two-phase Flow System Research Articles

Experimental investigation on temperature distribution characteristics inside the condensing tube of the R134a two-phase natural circulation loop

Temperature distribution of two-phase flow inside the condensing tube can effectively reflect the heat transfer characteristic of the fluid, playing a pivotal role in the study of heat transfer in two-phase flow systems. In this study, we use the stainless steel capillary sealed distributed fiber Bragg grating (S-DFBGs) to measure and characterize the temperature distribution of R134a fluid inside the condensing tube under steady-state (pump-driven two-phase circulation) and unsteady-state (type I and II density wave instabilities in two-phase natural circulation loop) conditions, and the frequency and time domain characteristics of the fluid temperature distribution inside the tube has been investigated in detail. Through frequency-domain analysis, the temperature spectrum inside the condensing tube can indentify two types of the instability together with flowrate and pressure. Through time-domain analysis, temperature distribution inside the condenser can dermine the phase transition point, hence the condensation length. Moreover, two types of the instability exhibit different temperature fluctuation characteristics, providing reliable and effective information for further research on two phase natural circulation instability mechanisms.

Numerical study of liquid sloshing in three-dimensional flexible cylindrical tank under multi-directional seismic excitation

The present study aims to evaluate the effect of the flexibility of three-dimensional (3D) cylindrical tank on liquid sloshing inside the tank as well as the influence of the hydrodynamic forces on the structure's deformation. A ground-supported cylindrical flexible tank filled with water and subjected to seismic excitation is investigated using a numerical coupling methodology to take into account the fluid–structure interactions. The Navier–Stokes equations in the fluid domain are solved using the finite volume method, while the finite element method is used to solve the linear-elastic equations of the structure. The arbitrary Lagrangian–Eulerian formulation is applied for the moving mesh in two-phase flow system. The simulations are conducted using free open-source software: OpenFOAM for fluid dynamics and FEniCS for solid mechanics, both utilize the preCICE library for data exchanging and fluid–structure coupling. The numerical methodology is validated by the experimental and numerical results given in literature. A multi-directional earthquake ground motion is then considered as external loading, and the elasticity of the tank wall is varied to investigate the effect on the fluid sloshing. It has been shown that the more flexible the tank walls are, the greater will be both the sloshing height and the structural deformations during an earthquake event. Several flow field information and structural responses have been provided, such as the sloshing height, hydrodynamic pressure, structure deformations, and structural stress distribution. The potential elephant's foot buckling phenomenon at the lower part of tank can also be predicted.

The Effect of Channel Surface Roughness on Two–Phase Flow Patterns: A Review

This review article highlights the critical impact of surface roughness in modifying the structure of two-phase flow within mini- and microchannels, particularly in processes such as boiling and condensation. Channel surface roughness enhances flow resistance, affects the distribution of vapor bubbles, and enhances heat transfer by providing additional nucleation sites. Several experiments have shown that while increased surface roughness enhances the efficiency of heat transfer, increased flow resistance may hurt system performance. This is so because too high a surface roughness negatively impacts flow resistance, a factor of importance in the optimization for a balance between heat transfer and flow resistance, especially in high-performance compact heat exchangers. Furthermore, the review identifies that higher-degree measurement and characterization techniques of the surface roughness are increasingly required, as traditional 2D parameters may not fully represent the actual physics of complex surface interactions in two-phase flow systems. Consequently, the article calls for further research that can examine the exact relationship between roughness, flow structure, and thermal performance with the aim of improving design strategies for future heat exchanger technologies.

Determination of grout compactness in rebar grouted splice sleeves using frequency domain characteristics of the excitation process

Grouted splice sleeves are widely used in assembly building connections. However, void defects within the sleeve directly affect the load-bearing capacity of the building structure. This paper presents a new method for detecting void defects inside a grouted splice sleeve based on the frequency domain characteristics of mechanical vibration waves. This method analyses the grouted spliced casing containing void defects as a gas-liquid two-phase flow system. To confirm the validity of the method, this paper builds a test setup for testing. The results showed that the test method can effectively detect the void defects and the volume of the defects inside the grouted splice sleeves when the grout is not solidified.

Using the total chemical potential to generalize the capillary pressure concept and therefrom derive a governing equation for two-phase flow in porous media

This work presents a governing equation (GE) for two-phase flow in porous media connecting capillary pressure to frictional pressure loss and external chemical potential supplied to a system in either stationary or diffusive equilibrium. It is based on the difference between non-wetting and wetting phase chemical potential (physically, pressure or energy density), which leads to a generalization of the capillary pressure concept. The difference in phase internal chemical potentials is characterized by changes in both interfacial areas and entropy densities due to variation in fluid saturations and is balanced by the system external chemical potential supplied. A definition of the capillary pressure concept is formulated based on the diffusive equilibrium criterion. The GE can explain the origin of the dynamic capillary pressure term, hysteresis, and connect the shift in the capillary pressure curve upon injecting water phases with varying salinities to all the other chemical potentials acting. It can connect, constrain, and potentially quantify all effects which can be formulated in terms of chemical potentials since it is based on a balance equation all two-phase flow systems must obey when either in stationary or diffusive equilibrium.

Scale reduction Transformer-based soft measurement of oil–water two-phase flow

In addressing the challenge of parameter measurement in high-water-content oil–water two-phase flow, we independently develop a dual-helix microwave sensor measurement system. Using this system, we conduct vertically upward experiments on oil–water two-phase flow and collect time-series signals characterizing microwave attenuation. Based on signal characteristics, we design a scale reduction Transformer soft measurement model (SRSM-Transformer). The time filter module effectively facilitates the aggregation and embedding of channel features with diverse physical significance. Additionally, the scale reduction temporal module models global information from a multi-resolution perspective, enabling the model to flexibly extract multi-scale feature information from fluid signals. Demonstrating pronounced superiority over existing models, our proposed model achieves recognition accuracies of 93.63% for total flow rate and 95.73% for water content. This research provides a new direction for modeling complex industrial oil–water two-phase flow systems and measuring multi-coupled key parameters.

A numerical investigation to assess changes to displacement front and by-passed zones employing kinetic interface-sensitive tracer

An important aspect in groundwater remediation is to understand changes of multiphase fluid front morphology and stagnant regions on macro scale. However, the prediction of those changes during two-phase flow remains a challenging task due to the interplay of various physical factors. Recent laboratory experiments have demonstrated tracers' ability to predict deformation in the front of a two-phase flow system by utilizing a new reactive tracer known as, the kinetic interface sensitive tracer (KIS). This research employs a reactive transport model coupled with a macro-scale two-phase flow model to numerically analyse how viscosity ratio, capillary number, and heterogeneities on the tracer's signal and its impact the frontal deformation. One homogeneous and two heterogeneous types of porous media are considered. The background porous medium is a fine-grained, low-permeability medium, with a coarser, high-permeability lenses, generating heterogeneous material properties. The high-permeability lenses account for 25 % of the total model area and are arranged in either periodic or random patterns. The findings are evaluated using four parameters (effective front length, swept area, front roughness, and transition zone length). The flow patterns dominating the shape of the front are characterized by the viscous and capillary forces i.e. capillary number and the viscosity ratio between the two fluids. The results show that changes in flow regimes can be quantified using effective front length, thus employing the effective front length the viscous fingering regions can be quantified. Furthermore, front roughness and transition zone length are extracted and their relevance to the by-passed zones is presented. The slope of the reactive KIS tracer breakthrough curve, plotted on a phase diagram, can also be used to predict the existence of the by-passed zones for a low viscosity ratio. Finally, changes in front roughness and transition zone length induced by the inclusions are correlated to the slope of the KIS tracer BTC. The findings of this study can contribute to a better understanding of the impact of different flow regimes on the KIS tracer breakthrough signals and the linkages between the tracer signals and the front sizes.

On the analysis of static thermal instabilities occurring in two-phase flow systems

In this study, we investigate a novel type of static thermal instability that occurs in two-phase flow systems. The instability is theoretically and experimentally confirmed to occur for flow boiling micro-channel scenarios and flow condensing scenarios. The theory presented is independent of the evaporator geometry as well as flow boiling/condensing situations. A stability criteria is derived using a Reynolds Transport approach applied to the evaporator of a two-phase pumped loop (TPPL) system. The theory is then validated experimentally using a TPPL containing a parallel micro-channel evaporator. The instability is confirmed with pressure, temperature, and void fraction measurements acquired at the exit of the evaporator. The findings reveal that static thermal instabilities can arise when simultaneous heat addition and reduction in system saturation temperature occurs (or vice versa). The implications of the thermal instability result in dramatic changes in evaporator heat flux, as well as a flow transition from stratified laminar flow to vigorous turbulent flow with high void fractions. By identifying the additional instability mechanisms, this work contributes to enhancing system reliability and predictability of TPPL systems.

Simultaneous measurement of solid concentration and solid moisture in gas–solid two-phase flow using a dual-modality electrical sensor

Abstract In a gas–solid two-phase flow system, simultaneous measurement of solid concentration and solid moisture is essential for some applications. However, during the measurement process, solid concentration and solid moisture are coupled in the measurement signals when the measurement signal is sensitive to both solid concentration and moisture. This makes it challenging to measure them simultaneously in the same measurement field. To solve this issue, a novel measurement method is proposed in this study, which uses a dual-modality electrical sensor to achieve simultaneous measurement of solid concentration and solid moisture in gas–solid two-phase flow. The dual-modality electrical sensor features a simple structure and captures measurement signals of capacitance and angle of dielectric loss within the same measurement section. With the above signals which are both sensitive to solid concentration and moisture, an iterative correction calculation method is adopted to achieve the simultaneous measurement of solid concentration and solid moisture. During the calculation process, the measured parameters are decoupled and continuously corrected until the related error values meet the threshold requirement. Numerical simulation experiments under three typical distributions and physical experiments under roping flow are carried out to verify the proposed measurement method. The results prove the effectiveness of the proposed measurement method in the simultaneous measurement of solid concentration and solid moisture for gas–solid two-phase flow.

Determination of optimal air supply form on sludge convective drying process: A CFD-DEM study

Convective thermal drying is usually used in sludge dryers, and the air supply forms significantly affect the sludge drying efficiency. In this work, the drying process of multi-layered sludge is numerically simulated using a coupled computational fluid dynamics-discrete element method (CFD-DEM) approach. Better than our previous work, the current CFD-DEM model further considers the dynamic process of humidity within the flow field. Firstly, the CFD-DEM model is validated based on the mechanistic experimental data. Then, extensive numerical simulations are carried out to investigate the two-layered sludge drying process in the dryer, and the effects of two conventional air supply forms (Top-to-Bottom and Bottom-to-Top) as well as a novel air supply form (Side-assist) on the two-phase flow system are discussed. The simulation results provide in detail the dynamic processes of momentum, heat and mass (moisture) in the convective drying system under different working conditions. Following recommendations are presented to facilitate the operation of the dryer: Bottom-to-Top is better for sludge drying and tends to utilize less heat from the heat source compared to the Top-to-Bottom. The drying efficiency can be further improved by supplying the Side-assist with an optimal flow ratio of side-wind to bottom-wind. Numerical results show that the optimal flow ratio is related to the total air volume, the deflection angle and the side-wind temperature. The present study reveals in depth the impact mechanism of the air supply form on the convective thermal drying process of sludge, which contributes to the design and optimization of high-efficiency dryers.

Modeling and simulation of air-water upward annular flow characteristics in a vertical tube using CFD

Annular flow refers to a special type of two-phase flow pattern in which liquid flows as a thin film at the periphery of a pipe, tube, or conduit, and gas with relatively high velocity flows at the center of the flow section. This gas also includes dispersed liquid droplets. The liquid film flow rate continuously changes inside the tube due to two processes-entrainment and deposition. To determine the liquid holdup, pressure drop, the onset of dryout, and heat transfer characteristics in annular flow, it is important to have proper knowledge of flow characteristics. Especially a better understanding of entrainment fraction is important for the heat transfer and safe operation of two-phase flow systems operating in an annular two-phase flow regime. Therefore, the objective of this work is to develop a computational model for the simulation of the annular two-phase flow regime and assess the various existing models for the entrainment rate. In this work, Computational Fluid Dynamics (CFD) in ANSYS FLUENT has been applied to determine annular flow characteristics such as liquid film thickness, film velocity, entrainment rate, deposition rate, and entrainment fraction for various gas-liquid flow conditions in a vertical upward tube. The gas core with droplets was simulated using the Discrete Phase Model (DPM) which is based on the Eulerian-Lagrangian approach. The Eulerian Wall Film (EWF) model was utilized to simulate liquid film on the tube wall. Three different models of Entrainment rate were implemented and assessed through user-defined functions (UDF) in ANSYS. Finally, entrainment for fully developed flow was determined and compared with the experimental data available in the literature. From the simulations, it was obtained that the Bertodano correlation performed best in predicting entrainment fraction and the results were within the ±30 % limit when compared to experimental data.

Quantitative derivation of a two-phase porous media system from the one-velocity Baer–Nunziato and Kapila systems

We derive a novel two-phase flow system in porous media as a relaxation limit of compressible multi-fluid systems. Considering a one-velocity Baer–Nunziato system with friction forces, we first justify its pressure-relaxation limit toward a Kapila model in a uniform manner with respect to the time-relaxation parameter associated with the friction forces. Then, we show that the diffusely rescaled solutions of the damped Kapila system converge to the solutions of the new two-phase porous media system as the time-relaxation parameter tends to zero. In addition, we also prove the convergence of the Baer–Nunziato system to the same two-phase porous media system as both relaxation parameters tend to zero. For each relaxation limit, we exhibit sharp rates of convergence in a critical regularity setting. Our proof is based on an elaborate low-frequency and high-frequency analysis via the Littlewood–Paley decomposition and includes three main ingredients: a refined spectral analysis of the linearized problem to determine the frequency threshold explicitly in terms of the time-relaxation parameter, the introduction of an effective flux in the low-frequency region to overcome the loss of parameters due to the overdamping phenomenon, and renormalized energy estimates in the high-frequency region to cancel higher-order nonlinear terms. To justify the convergence rates, we discover several auxiliary unknowns allowing us to recover crucial O(ε) bounds.

Influences of directional aperture heterogeneity on the performances of two-phase enhanced geothermal system considering the CO2 buoyant force

The technology of Enhanced Geothermal System (EGS) using CO2 as working fluid is believed to be a promising method for harnessing geothermal energy, contributing to the reduction of atmospheric greenhouse gas emissions and decreasing the dependency on traditional fossil fuels. Due to the buoyant force of CO2 in water-saturated EGS, the effects of aperture heterogeneity on fluid flow and heat transfer may be directional and differ in the two-phase flow system from the traditional single-phase EGS. In this case, we employed a thermal-hydraulic coupled model, considering a structured fracture geometry to comprehensively investigate the effect of directional distributed aperture combined with buoyant force on the EGS energy performances. The Monte Carlo method is applied to ensure that the simulation results reach statistical equilibrium. Results show that the vertical aperture heterogeneity leads to poorer energy output and carbon sequestration in a two-phase EGS, compared to the horizontal aperture heterogeneity. On the other hand, the negative effects of directional aperture heterogeneity on the total EGS energy output become more significant with the decreasing fracture density. Finally, compared to the EGS using water as the working fluid, those employing CO2 exhibits greater sensitivity to directional aperture heterogeneity for both high and low fracture-density networks due to the buoyant force of CO2.

Deep learning-assisted dual-modal tomography for phase flow rate estimation in two-phase oil-water flow systems

Accurately estimating phase flow rates in multiphase systems is crucial for many industries, where precise measurements are essential for operational efficiency and safety. Addressing this issue, this paper introduces an approach that employs deep learning-assisted dual-modal electromagnetic flow tomography (EMFT) and electrical tomography (ET) to predict both oil and water flow rates in two-phase oil-water flows. To facilitate the generation of the data, we first simulate diverse flow conditions using COMSOL Multiphysics software and the convection–diffusion equation, aiming to create a realistic representation of two-phase oil-water flows. The dual-modal system measurement data, generated from these simulations and simulated by using a dense finite element mesh, provide reliable inputs for the deep learning model. Moreover, this study also integrates experimental data into both the training and testing phases, improving the ability of the proposed approach to estimate flow rates accurately in practical investigations. The results from laboratory experiments demonstrate the potential of the deep learning-assisted dual-modal ET and EMFT approach in effectively resolving the challenges of estimating flow rates in two-phase oil-water flow systems. By combining the deep learning capabilities with dual-modal tomography, this study offers valuable insights for future applications and represents a significant step forward in the field of multiphase flow rate estimation.

Numerical simulation of non-spherical microparticles' deposition on single fiber

As a classical gas-solid two-phase flow system, the processes of fiber filtering microparticles are prevalent in nature and engineering. However, the impact of microparticle shape on fiber filtration processes is still largely unexplored. Herein, using the self-developed spheropolyhedral-based discrete element lattice Boltzmann method, the filtration process of non-spherical microparticles through a single fiber is investigated. Results show that the single fiber efficiency (SFE) for non-spherical particles exhibits a trend of initially increasing and subsequently decreasing trend with the increase in Stokes number (St), which is similar to the case of spherical particles. However, it is interesting to note that the peak values of SFE increase significantly with decreasing particle sphericity (ψ) and the corresponding St values become larger. As ψ decreases from 1.0 (sphere) to 0.671 (tetrahedron), the SFE increase from 0.205 to 0.49 and the corresponding St rises from 1.0 to 1.75. The enhanced SFE can be explained by elevated collision probability and adhesion probability, based on detailed particle kinematics and dynamics behavior analysis as well as microscopic depositional structure evaluation. The depositional structures of the non-spherical particles have larger capture areas, leading to higher initial collision probabilities. Meanwhile, the anisotropic collisions between non-spherical particles and fibers greatly contribute to higher secondary collision probabilities. In addition, compared to spherical particles of the same volume, the non-spherical particles experience greater fluid resistance, resulting in lower initial collision velocities and larger initial adhesion probabilities. The face-to-face contacts between non-spherical particles also lead to stronger interparticle adhesion and enhanced adhesion probabilities.

An explicit approximation of the central angle for the curved interface in double-circle model for horizontal two-phase stratified flow

Stratified flow in horizontal tubes is frequently observed in gas-liquid two-phase flow system. In the two-fluid modeling, it is important to define the interface shape in solving the balance equations to determine the key parameters such as the interfacial transfer terms, void fraction, and pressure drop. A double-circle model is usually introduced to depict the concave-down interface in a horizontal circular tube under the stratified-wavy flow condition. However, calculation of the central angle in the double-circle model, which represents the interfacial curvature, requires an appropriate iterative numerical root-finding scheme to solve the implicit transcendental equation. In this study, an explicit approximate equation has been proposed without requirement of the iterative scheme and numerical instability, which is expected to improve the coding process and computation efficiency in the analysis code with the two-fluid model.

The subdivision-based IGA-EIEQ numerical scheme for the Navier–Stokes equations coupled with Cahn–Hilliard phase-field model of two-phase incompressible flow on complex curved surfaces

We develop an accurate and robust numerical scheme for solving the incompressible hydrodynamically coupled Cahn–Hilliard system of the two-phase fluid flow system on complex surfaces. Our algorithm leverages a number of efficient techniques, including the subdivision-based isogeometric analysis (IGA) method for spatial discretization, the explicit Invariant Energy Quadratization (EIEQ) method for linearizing nonlinear potentials, the Zero-Energy-Contribution (ZEC) method for decoupling, and the projection method for the Navier–Stokes equation to facilitate fully decoupled type implementations. The integration of these methodologies results in a fully discrete scheme with desired properties such as linearity, second-order temporal accuracy, full decoupling, and unconditional energy stability. The implementation of the scheme is straightforward, requiring the solution of a few elliptic equations with constant coefficients at each time step. The rigorous stability proof of unconditional energy stability and the implementation procedure are given in detail. Numerous numerical simulations on complex curved surfaces are carried out to verify the effectiveness of the proposed numerical scheme.

Oscillatory flow driven microdroplet breakup dynamics and microparticle formation in LMPA-water two phase flow system

This study presents a mathematical modeling and numerical investigation of oscillatory flow induced microdroplet breakup in low melting point alloy (LMPA)-in-water two-phase flow system in a microchannel. The effects of perturbation flow Weber number, and oscillating frequencies on the droplet breakup dynamics have been elucidated. Lowering the wall temperature will accelerate the solidification process of LMPA droplets, giving rise to the rapid formation of ultra-small particles with size down to 1 micron in less than 3 ms. The versatile approach combines oscillatory flow dominated droplet breakup process and phase change process, leading to the formation of LMPA microparticles with monodispersed size distribution and well-tailored properties by using a straight microchannel, which obviates the need for sophisticated design and complex fabrication process of microdevices. This work will provide a strategy to manipulating LMPA droplet size and structure for the massive production of ultra-small LMPA microparticles via a facile control over the flow conditions in the two-phase flow in a microfluidic system. It will open up for a diversity of applications of LMPA microparticles in various fields such as energy storage and thermal management.

CFD verification of total pressure loss coefficient for gas-liquid two-phase flow

Traditionally, we design gas-liquid two-phase flow systems with pressure loss that is assumed by homogeneous flow. However, in real phenomena, the flow rate of water or air through a system cannot be correctly predicted unless we evaluate by the total pressure loss. there are currently few methods for measuring total pressure loss, and the value of total pressure loss is not yet clearly. Therefore, we devised a method to measure total pressure loss by pump Q-H characteristic and succeeded in measuring total pressure loss indirectly. We compared the test results with the analysis to clarify the prediction accuracy of the analysis using commercial codes. We apply three two-phase flow models for the simulation: a VOF model, a homogeneous flow model, and a two-fluid model. The simulation results of comparison between each fluid model indicated that the VOF model predicted with the best accuracy, with the error of 46% compared to the test results. This study provides a benchmark for the current commercial code, and the prediction accuracy of the different models provides a direction for future improvements in the analysis.

Singularity for the Drift-Flux System of Two-Phase Flow with the Generalized Chaplygin Gas

Singularity for the Drift-Flux System of Two-Phase Flow with the Generalized Chaplygin Gas