Multiphase Flow Model Research Articles

Investigation of thermodynamic process in a humidifier of humidification–dehumidification system based on a computational fluid dynamics model

Humidification–dehumidification is well-suited for solar-powered operation. Packed bed humidifier is an essential system component for water evaporation. Computational fluid dynamics (CFD) simulation of the packed bed humidifier is a challenging multiscale task. The simultaneous capture of micro flow properties and macro transfer performance by existing CFD models is inadequate. This paper presents a novel CFD model for a structured packed bed humidifier. The Eulerian method is applied to the multiphase flow and several simplified models are proposed to evaluate the influence of the microstructure on the transfer properties. The model can predict the overall transfer performance and partially reflect the micro flow characteristics. It is found that the air temperature increases rapidly when the packing height is < 0.3 m, while the liquid temperature decreases rapidly when the height is > 1.65 m or <0.45 m. Under different conditions, the outlet relative humidity of the air is all between 95 % and 99 %. The maximum evaluation error of gained output ratio of the humidification–dehumidification system can reach 10 % under the saturated air assumption. With a maximum of 10.85 % and a minimum of 3.46 %, the proportion of sensible heat transfer in the total energy transfer decreases with the packing height.

Investigation on particle slug flow using large eddy simulation combined a particle kinetic energy model

In this study, an investigation on particle hydrodynamic behaviors of gas-particle slug flow is modeled and numerically simulated. A novelty particle kinetic energy model at subgrid-scale level is developed to consider the effect of gas turbulence on particle movement and a four-way coupling approach is combined. Anisotropic particle dispersions and the multiphase interactions is revealed by using a second-order moment turbulence model and large eddy simulation is performed to solve the Euler-Euler two-fluid transport equations, Predictions are well agreed with the experimental data and reported results by discrete particle model built-in the multiphase flow model with interphase exchanges code. Bubble motions have great effects on the particle dynamics due to bubble entrainment. Flow patterns of particle circulation are generated between higher and lower concentrations. The largest frequency of power spectrum density at center of top surface is approximately 4.5 times larger than that of wall region. Bubblelike granular temperatures are much larger than smaller-scale particle granular temperature. At the top surface, maximum value of vertical bubblelike Reynolds stress is found at x/W = 0.28, it is 4.0 times larger than that of the lateral x-direction. In addition, the mean values, and the standard deviation of SGS particle kinetic energy at center are both approximately 3.5 times larger than those of z = 10.0 cm. For particle shear stress at middle section, maximum ratios of mean value and standard deviation at central regions to those of walls reach up to 8.0 and 11.0.

Understanding cavitation bubble collapse and rebound near a solid wall

The collapse of cavitation bubbles is known for its intense and aggressive behavior, producing concentrated bursts of energy that can cause erosion, noise, and damage to metallic surfaces and mechanical equipment. However, this concentrated energy also offers significant potential for various applications in biomedical science, industrial engineering, and related technologies. This study presents a comprehensive numerical investigation of the collapse and rebound of cavitation bubbles near a wall using a conservative, compressible multiphase flow model. Laser-generated cavitation bubbles growing, collapsing, and rebounding in distilled water near a wall at three standoff distances were experimentally studied to validate the numerical method. The results show good agreement between the bubble shapes and radii from the numerical simulations and experiments. Additionally, velocity of microjets and thermodynamics of the bubble collapse were validated against the reference data in the literature. Subsequently, the pressure and temperature distributions and jet shapes were examined in detail, exploring the impact of standoff distances ranging from 0.2 to 1.8. A quantitative analysis of the pressure and temperature produced on the wall, as well as the jet velocity and bubble movement during the collapse, was systematically conducted. Jet velocities observed ranged from 30 m/s to 130 m/s, and numerical simulations were compared with experimental data from the literature, showing good agreement. Maximum temperature and pressure induced at the wall center can reach up to 616.2 K and 139.5 MPa, respectively. The detailed analyses in this study provide significant insights into the behavior of cavitation bubbles and the effect of standoff distance on their collapse and rebound near a wall.

Comprehensive analysis and identification of energy performance and unsteady two-phase flow patterns based on experiments and comparison between two distinct multiphase flow models

ABSTRACT In the petroleum sector, electrical submersible pumps (ESP) face numerous challenges when handling multiphase flow of gas and liquid. The primary challenge is from the build-up of the gas-bubbles within the impellers of ESPs, leading from moderate to severe deterioration in pump efficiency. Consequently, a comprehensive investigation is conducted, involving a combination of experimental and numerical analyses, to thoroughly explore the effects of gas entrainment on the performance and intricate internal flow mechanisms of a five-stage mixed-flow ESP. All these analysis was carried out under both design (Qd ) and off-design conditions (0.8Qd , and 1.2Qd ). For unsteady numerical calculations, two widely used multiphase-models: The volume of fluid (VOF) and The Euler-Euler model are employed and compared to investigate the versatility/validity of these models in predicting multiphase performance of ESP. The comparison between tests, Eulerian, and VOF models demonstrated that the Eulerian model aligns well with the experimental results. and shows higher-adaptability pattern with the test results. This reveals its best capability/versatility in predicting two-phase performance and internal-flow results for ESP. Moreover, it can more accurately capture the phase slippage inside ESP under two-phase flow. Additionally, this work provides a vision to the broad-applicability of Eulerian-model for complicated machinery such as ESP.

A single mesh approximation for modeling multiphase flow in heterogeneous porous media

The control volume finite element (CVFE) approach is based on the discretization of primary flow and transport unknowns on two different meshes. The element mesh, used to represent the physical properties of the medium, differs from the control volume mesh necessary to ensure a mass conservative solution. The inherent two mesh feature of the CVFE approximation introduces inconsistency in the transport solution due to the averaging of physical and computed quantities between neighboring elements in the mesh. In this work, we present a consistent approach for modeling multiphase flow and transport in heterogeneous porous media. The approach is applied in the CVFE framework by enabling the discretization of primary unknowns on a single mesh. We combine the discretization of an element-wise, discontinuous pressure approximation with a first-order, discontinuous velocity approximation to resolve the elliptic or parabolic flow problem. The effectiveness of the formulation is achieved by exploiting the same finite element mesh as the flow problem, when updating the saturation solution. This direct mapping between the flow and transport mesh is simple yet effective for establishing a consistent solution in addition to circumventing the non-physical mass leakage exhibited in the classical CVFE method. We describe the interface approximations and the discontinuous terms needed for consistent solutions. The method is well suited to model flow in complex geometrical subsurface domains and is shown to be numerically stable while providing locally and globally mass conservative solutions. We apply the approach to several domains with complex geometrical features to emphasize the superiority of the approximation over conventional methods. The analysis shows over two orders of magnitude reduction in solution error compared to the classical CVFE. The new formulation effectively captures accurate transport solutions, even in the presence of varying material properties, without the need for mesh refinement.

Rainfall-Triggered Landslides and Numerical Modeling of Subsequent Debris Flows at Kalli Village of Suntar Formation in the Lesser Himalayas in Nepal

Hazardous debris flows are common in the tectonically active young Himalayas. The present study is focused on the recurrent, almost seasonal, landslides and debris flows initiated from Kalli village in Achham District of Nepal, located in the Lesser Himalayas. Such geological hazards pose a significant threat to the neighboring communities. The field survey reveals vulnerable engineering geological conditions and adverse environmental factors in the study area. It is found that a typical complete debris transport process may consist of two stages depending on the rainfall intensity. In the first stage, debris flows mobilized from a landslide have low mobility and their runout distance is quite modest; in the second stage, with an increase in water content they are able to travel a longer distance. Numerical simulations based on a multi-phase flow model are conducted to analyze the characteristics of the debris flows in motion, including the debris deposition profiles and runout distances in both stages. Overall, the numerical results are reasonably consistent with relevant field observations. Future debris flows may likely occur again in this area due to the presence of large soil blocks separated by tension cracks, rampant in the field; numerical simulations predict that these potential debris flows may exhibit similar characteristics to past events.

Three-dimensional lattice Boltzmann model with self-tuning equationof state for multiphase flows.

In this work, the recent lattice Boltzmann (LB) model with self-tuning equationof state (EOS) [Huang et al., Phys. Rev. E 99, 023303 (2019)2470-004510.1103/PhysRevE.99.023303] is extended to three dimensions for the simulation of multiphase flows, which is based on the standard three-dimensional 27-velocity lattice and multiple-relaxation-time collision operator. To achieve the self-tuning EOS, the equilibrium moment is devised by introducing a built-in variable, and the collision matrix is improved by introducing some velocity-dependent nondiagonal elements. Meanwhile, the additional cubic terms of velocity in recovering the Newtonian viscous stress are eliminated to enhance the numerical accuracy. For modeling multiphase flows, an attractive pairwise interaction force is introduced to mimic the long-range molecular interaction, and a consistent scheme is proposed to compensate for the ɛ^{3}-order discrete lattice effect. Thermodynamic consistency in a strict sense is established for the multiphase LB model with self-tuning EOS, and the wetting condition is also treated in a thermodynamically consistent manner. As a result, the contact angle, surface tension, and interface thickness can be independently adjusted in the present theoretical framework. Numerical tests are first performed to validate the multiphase LB model with self-tuning EOS and the theoretical analyses of bulk and surface thermodynamics. The collision of equal-sized droplets is then simulated to demonstrate the applicability and effectiveness of the present LB model for multiphase flows.

Computing Relative Permeability and Capillary Pressure of Heterogeneous Rocks Using Realistic Boundary Conditions

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.

A one-domain pore-resolved approach for multiphase flows in porous media

Modeling multiphase flow in porous structures remains a challenge due to the complexity of handling multiple interfaces. This paper presents a one-domain pore-resolved simulation approach for immiscible two-phase flows in porous media, using a monolithic fluid–solid coupling framework to implicitly consider the existence of solid objects, with the fluid–fluid interfaces captured through solving an algebraic volume of fluid equation. Fluid interfacial tension is considered by integrating a continuum surface force, and the wall wettability condition is imposed by modifying the contact angle of the fluid interface at the embedded solid surface. The resulting equations are simple and stable, as there are no empirical models or parameters involved for the interface representation. This approach has been validated through performing a series of test-case simulations, including capillary-dominated flow, capillary rise with gravity, Taylor film formation, and finally two-phase flow in a heterogeneous porous structure. The numerical approach is demonstrated to be well suited for investigating pore-scale two-phase flows in realistic porous media.

Investigation on flow structure and pressure fluctuation of gas-liquid two-phase flow in a mixed flow pump

Abstract Mixed flow pump is characterized by high-efficiency operation and wide range of flow rate conditions, while research on transporting gas-liquid two-phase flow is quite limited. The present work investigates the energy performance, two-phase flow pattern and pressure fluctuations of a mixed flow pump, on basis of the numerical method of inhomogeneous Eulerian-Eulerian multiphase flow model. Results show that the pump head and efficiency decline with the increase of gas volume fraction. In impeller, gas phase is mainly distributed at the tip clearance, the blade pressure side and suction side, and the hub outlet. The low pressure of tip leakage vortex core leads to the gas phase concentration and the formation of gas strip. Moreover, X-shaped gas strip appears at high gas volume fraction (GVF). In guide vane, gas phase is mainly distributed at the leading edge of blade pressure side, the blade suction side, and the middle of passage. As the inlet GVF increases, the spatial-temporal evolution of the gas phase shows obvious differences. The strong gas-liquid interaction causes broad low-frequency fluctuations, and the rotor-stator interference causes significant blade passing frequencies in the mixed flow pump.

Research on the cooling mechanism of low-temperature liquid jet mixing in high-temperature and high-speed airflow

The multi-stage water spray cooling system of the space launch site involves a complex gas–liquid two-phase mixed cooling problem in the process of spraying water onto the rocket engine gas jet. To investigate the complex multiphase flow field of the interaction between the airflow and liquid water jet, the Mixture multiphase flow model is adopted, which is coupled with the vaporization equation and component transport model of liquid water. The computational fluid dynamics method is used to numerically analyze the mixing and cooling mechanism of low-temperature liquid jet in high-temperature and high-speed gas flow. The results show that mixing low-temperature liquid jets in high-temperature and high-speed airflow can cause the exchange of momentum and energy, resulting in pressure loss and temperature reduction in the gas phase flow field. Due to the acceleration of transverse airflow, the diffusion flow range of the jet is significantly increased, and violent vaporization occurs, which further consume a large amount of airflow energy. The mixing cooling effect of transverse airflow and liquid water jet is directly related to the mass flow rate ratio of the jet to airflow. In addition, directly designing liquid water jet orifices on the solid wall of the guiding device can achieve the effect of improving the gas flow field environment. This conclusion can provide theoretical reference for the thermal protection design of ground launch devices in space launch site.

An enhanced compressible two-phase flow model with detailed chemistry under the adaptive mesh refinement frame

In the present study, an enhanced compressible two-phase flow model is advanced, considering the effect of chemical reactions within a detailed mechanism. In this model, two immiscible fluids (liquid and gaseous mixture) are accurately separated with the resolved interface. Unlike the classical five-equation two-phase flow model, the thermal properties of gases are no longer assumed to be constant but rather vary as functions of temperature. A modified mechanical relaxation procedure is proposed and employed at the gas-liquid interface to prevent the occurrence of nonphysical pressure oscillation. In the gaseous mixture, numerous gas components are included and resolved by their mass fraction among the gaseous mixture. In this model, the heat release effect is simulated by a detailed chemistry. Furthermore, the numerical results of several benchmark problems in one dimension and two dimensions demonstrate the efficacy of the proposed compressible multiphase flow model, such as the air shock tube, the gaseous detonation tube, the shock-droplet interaction, and especially the detonation-droplet interaction that has received little focused interest and investigations. Moreover, a self-developed adaptive mesh refinement strategy is performed for a high efficiency of numerical solving.

Numerical investigation of sequential water entry for two projectiles at varied entry angles

In this paper, the effect of the water entry angle on the sequential water entry process of two projectiles was investigated numerically. A numerical method is established based on the STAR-CCM+ fluid simulation software, which employs the finite volume method, the volume of fluid multiphase flow model, and overlapping grid technology. The validity of the numerical method was confirmed by comparing the simulation results with experimental data. The sequential water entry processes are simulated at angles of 90°, 75°, 60°, 45°, and 30°, respectively. The flow field characteristics, motion stability, and drag reduction of both projectiles are analyzed. The results show that projectile 1 generates a series of air bubbles shedding from its cavity's tail, which distorts projectile 2's cavity. This air bubble reduces the wet area at projectile 2's head, enhancing its drag reduction capability. Projectile 1's motion remains unaffected by projectile 2 under varying water entry angles, while distinct motion characteristics are observed in projectile 2 due to significant interference from projectile 1. These results provide valuable theoretical insights for further research on sequentially launched trans-media weapons.

A three-dimensional pseudo-potential multiphase model with super-large density ratio and adjustable surface tension

In this paper, an improved three-dimensional pseudo-potential multiphase flow model is proposed. A high-precision difference scheme is employed to improve the computational accuracy of the interaction forces to achieve super-large density ratio. The present model is verified to obtain two-phase density ratio up to hundreds of thousands for all selected equations of state, and the spurious currents can be suppressed to a relatively low level. A modification pressure tensor is introduced to implement a wide range of surface tension adjustments independently of the density ratio. The model is applied to simulate droplet impacts on a liquid film as well as droplet impacts on a dry surface. Numerical results show that the model still has good numerical stability in simulating complex fluid problems with very large density ratio, adjustable surface tension, high Reynolds number, or containing the wettable surface. In addition, to improve the computational efficiency, an efficient parallel algorithm based on graphics processing unit (GPU) is designed for the present model. A maximum speedup ratio of 687 times is obtained compared to the corresponding CPU-based serial algorithm, which can significantly accelerate the numerical simulation study.

Effects of CO2 Geosequestration on Opalinus Clay

CO2 geosequestration is an important contributor to United Nations Sustainable Development Goal 13, i.e., Climate Action, which states a global Net-Zero CO2 emissions by 2050. A potential impact of CO2 geosequestration in depleted oil and gas reservoirs is the variations in induced pressure across the caprocks, which can lead to significant local variations in CO2 saturation. A detailed understanding of the relationship between the pressure gradient across the caprock and local CO2 concentration is of utmost importance for assessing the potential of CO2 geosequestration. Achieving this through experimental techniques is extremely difficult, and thus, we employ a coupled Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) based solver to mimic sub-critical CO2 injection in Opalinus Clay under various pressure gradients across the sample. The geomechanical and multiphase flow modelling utilising Darcy Law helps evaluate local variations in CO2 concentration in Opalinus Clay. Well-validated numerical results indicate favourable sub-critical CO2 geosequestration under a positive pressure gradient across Opalinus Clay. In the absence of a positive pressure gradient, a peak CO2 concentration of 5% has been recorded, which increases substantially (above 90%) as the pressure gradient across the sample increases.

Effects of scaling criteria on modelling of multi-phase flow in the packed bed using coarse grain CFD-DEM

The numerical modelling with computational fluid dynamics coupled with discrete element method (CFD-DEM) could be of high fidelity but rather time consuming, which leads to the development of coarse grain DEM (CFD-CGDEM). This paper describes the effects of scaling criteria for CFD-CGDEM on the modelling of multi-phase flow in packed bed. Four representative scaling criteria for particles contact interaction are discussed to analyze the packing structure and pressure drop and compare the relative deviation between CFD-CGDEM and CFD-DEM. It is found that when the spring constant in CFD-CGDEM is enlarged by α3 or α2 times or remains the same as that in original CFD-DEM, as α is defined as coarsen degree which is referred as the ratio between parcel size and particle size, a relatively large spring constant should be chosen to maintain the similar porosity and pressure drop. However, when the spring constant in CFD-CGDEM was scaled moderately by α times, the modelling results of CFD-CGDEM are comparable to data from CFD-DEM regardless of the value of spring constant. Furthermore, a quantitative analysis shows that the relative deviation in porosity and pressure drop between CFD-DEM and CFD-CGDEM will be enhanced as coarsen degree increases but the variation is insignificant with domain size for periodic boundary. The increase of parcel size could affect the simulation of porosity in packed bed and deviate the predicted hydrodynamics away from the CFD-DEM. In addition, the comparison of computational efficiency illustrates the speed up of CFD-CGDEM increases with the coarsen degree while the relative deviation also increases. This study provides instructive guidance for the application of CFD-CGDEM to model the multiphase flow in packed beds.

Directional saturation of a strongly bimodal pore size distribution carbon interlock fabric: Measurement and multiphase flow modeling

This study focuses on the analysis of the directionality of saturation of materials with bimodal pore size distributions. The material studied is an anisotropic carbon interlock with highly contrasted dual-scale porosity, with heavy warp and light weft tows. Experimentally, 6 configurations are tested using injection combined with dielectric sensors to measure saturation times and unsaturated lengths. The experimental results show that this material has a high contrast in dual-scale porosity and the unsaturation is anisotropic. In parallel, a two-phase flow in porous media continuum model is developed within the OpenFOAM® toolbox of libraries to simulate the transient impregnation. The need to use a tensorial relative permeability and its alignment with the saturated permeability is analyzed by a numerical multiphase mesoscale flow model. The combined experimental and numerical analysis paves the way for a methodology to analyze the saturation of various bimodal pore size distribution materials.

A reduction-consistent phase field model for non-isothermal multiphase flows of N immiscible incompressible fluids

In this study, we developed a reduction-consistent phase field model for non-isothermal incompressible N-phase flows. The model is based on the high-order spectral element method. To account for thermocapillary effects, we reformulated the continuum surface force model specifically for N-phase flows. In order to enhance computational efficiency, time-independent coefficient matrices for all variables involved were reconstructed, and an unsymmetrized multifrontal LU factorization was employed to solve the linear algebraic equations, which is derived by discretization. To verify the model effectiveness in calculating surface tension and describing three-phase interfacial dynamics, we conducted several experiments, including the stationary two-droplet example, the three-phase droplet spreading, and the equilibrium morphology of double emulsion droplet. Through these experiments, both the reduction-consistency and robustness of our model were demonstrated. Moreover, we validated the proposed model's applicability to non-isothermal three-phase flows by investigating the thermocapillary migration of single droplet and two droplets of different phases. Notably, we explored the thermocapillary migration of three-phase double droplets, focusing particularly on how the encapsulation process affects overall thermocapillary motion. Our findings indicate that the interaction between the two vortices near the interfaces of the two droplets strongly influences their migration behavior.

Study of intermittent jets and free-surface-pressurized flow in large hydropower tailrace tunnel

The tailrace tunnel system, as a core component of hydroelectric power stations, directly influences the stability and efficiency of the power generation process. Transient conditions often lead to the occurrence of complex unsteady flow phenomena in the tailrace tunnel. In this study, numerical methods integrating open channel flow, multiphase flow, and compressible models were combined to conduct hydraulic analysis of the tailrace system in large hydroelectric power stations. Under specific conditions, periodic jet phenomena were observed, corroborating field observations. The research revealed that the proximity of downstream water levels to the crest level of the tailrace outlet is a prerequisite for the periodic jetting phenomenon, with a sudden rise in water level serving as a triggering condition. Although the surge shaft effectively mitigates wave action, it fails to entirely eliminate the influence of pressure pulsations, resulting in a 23.2% increase in pressure pulsation amplitude in the turbine area. However, the efficiency of the turbine unit is hardly affected; only a slight loss of energy occurs due to the increase in local turbulent entropy production, deemed inconsequential for the overall system. This study aims to investigate the complex response of tailrace tunnel systems in hydroelectric power generation amidst abrupt changes in downstream river, providing crucial insights for the engineering design and operation of large-scale power stations.

Numerical study on the effect of smoke emitted from the vents on the roof of a diesel train on the intake of downstream air-conditioning units

Constrained by economic development and geographical features, numerous railway lines remain unelectrified, underscoring the expansive potential of diesel trains. Diesel engine emissions discharged from the roof of trains pose a challenge as some of the smoke infiltrates the cabin through the intake of roof-mounted air-conditioning units (ACUs). This intrusion diminishes the indoor air quality, posing health risks to passengers and potentially jeopardizing their safety. This study employs the shear stress transport k-omega turbulence model to formulate a multiphase flow model for simulating smoke diffusion in diesel trains. Additionally, we conducted an optimization design to minimize smoke entry into the ACUs. This study defined six cases based on variations in the shape and height of the cover and the spacing of the smoke vents. The results show that the effect of the diffusion characteristics decreased with the cover height. With the progression of airflow diffusion, the effect of the smoke vent structure on the concentration diminished farther from the vents. The minimum smoke mass flow rate into the intake occurred with the vent spacing of 2.14 m and without a cover, resulting in a 57.0% decrease compared with the maximum. Thus, a smoke vent spacing of 2.14 m without a cover was deemed to be the optimal configuration. The research results provide certain engineering guidance significance for the design and operation of train-smoke vent structures.