Mass Flux Research Articles

Computational study of momentum interactions between fluid and a static particle under the impact of anisotropic Stefan flow

The microscale gas–particle interaction is the determining process for the macroscopic flow behaviors of gas–particle systems. Anisotropic Stefan flow is often manifested at the surface of the biomass particle when thermally decomposed. However, the influence of the anisotropic Stefan flow on the gas–particle interactions is not well understood. To this end, particle-resolved direct numerical simulations were carried out in this research to explore the momentum interactions between the gas flow and a static particle emitting mass flux at its surface. A signed distance function based immersed boundary method is first extended to account for the Stefan flow at the gas–particle interface and successfully validated by comparing with literature results in the case of no Stefan flow or uniform Stefan flow. It is found that the presence of the outward uniform Stefan flow leads to an expanded wake formation and the intensity of the vortex (Re ≥ 40) is enhanced as result of the Stefan flow. Subject to the impact of anisotropic Stefan flow parallel to the main flow, the low-speed region in the front and rear of the particle is reduced when the Stefan flow goes inwards, resulting in the increase in the drag coefficient. As the Stefan flow is outward, the low-speed region in the front of the particle is pushed forward by the emitting gas and the velocity magnitude in the wake region is increased, which behaves like an enlargement of the gas cushion and leads to a significant reduction of the drag coefficient comparing with a uniform Stefan flow. In contrast, the impact of anisotropic Stefan flow with the direction perpendicular to the main flow on the fluid–particle drag interaction is less significant due to the fact that the flow structure in the front and rear regions is not significantly disturbed.

Improving Aerosol Radiative Forcing and Climate in E3SM: Impacts of New Cloud Microphysics and Improved Wet Removal Treatments

AbstractNumerous Earth system models exhibit excessive aerosol effective forcing at the top of the atmosphere (TOA), including the Department of Energy's Energy Exascale Earth System Model (E3SM). Here, in the context of the E3SM version 3 effort, the predicted particle property (P3) stratiform cloud microphysics scheme and an enhanced deep convection parameterization suite (ZM_plus) are implemented into E3SM. The ZM_plus includes a convective cloud microphysics scheme, a multi‐scale coherent structure parameterization for mesoscale convective systems, and a revised cloud base mass flux formulation considering impacts of the large‐scale environment. The P3 scheme improved cloud and radiation particularly over the Northern Hemisphere and the frequency of heavy precipitation over the tropics, and the ZM_plus improved clouds in the tropics. P3 decreases aerosol effective forcing by 0.15 W m−2, while the ZM_plus increases it by 0.27 W m−2, resulting from excessive direct (0.31 W m−2) and indirect forcing (−1.79 W m−2). The excessive aerosol forcings are due to aerosol overestimation associated with insufficient aerosol wet removal. By improving the physical treatments in the aerosol wet removal, we effectively mitigate anthropogenic aerosol overestimation and thus attenuate direct (0.09 W m−2) and indirect aerosol forcing (−1.52 W m−2). Adjustment to primary organic matter hygroscopicity reduces direct and indirect forcing to more reasonable values: −0.13 W m−2 and −1.31 W m−2, respectively. On climatology, improved aerosol treatments mitigate overestimation of aerosol optical depth.

Heat transfer and visualization of flow boiling on nanowire surfaces in the microchannel

Enhancing heat transfer efficiency is crucial in heat exchange equipment. Although previous studies have focused on developing micro/nano-structured surfaces, further exploration into how surface structure can improve heat transfer efficiency (H) by altering bubble dynamics is still needed. This study aimed to innovatively analyze the impact of titanium carbide (TiC) nanowire heights—specifically 4 µm and 12 µm—on boiling heat transfer performance. Conducted under varying heat flux (Q) (50–200 W/m2) and mass flux (G) (200–300 kg/m2·s), our experiments assessed H, pressure drop (P), and local boiling curves. Using a high-speed camera, we observed complex periodic flow patterns on the 4 µm nanowire surface, including elongated bubble formation, expansion, local dryout, and subsequent fluid rewetting. Results showed that the 12 µm nanowire surface increased H by up to 19.84 % in single-phase conditions, while the 4 µm nanowire surface increased H by up to 27.9 % in two-phase conditions. These findings highlight the significant role of nanowire length and arrangement in optimizing boiling heat transfer performance. This work lays a foundation for further investigations into diverse nanowire materials and configurations.

Contribution of hall and ion slip effects with generalized mass and heat fluxes with entropy analysis on three-dimensional Prandtl model

A major challenging proffered study rely on the inquisitive optimization of entropy together with thermal as well as mass transportation towards the chemically reactive 3-D Prandtl liquid under consideration of applied magnetic field, variable thermal conductivity and also diffusivity, hall current together with ion slip features, viscous dissipation and heat generation. Moreover, in present research study, model such as Cattaneo Christov heat flux was implemented in order to explore the thermal relaxation characteristics. By employing correspondence transformations, the system of modeled equations modified into non-linear ODEs system. The Optimal Homotopy Analysis methodology (OHAM) was adopted to solve the proffered problem. The influential arising constraints demeanor within both velocities (horizontal as well as vertical), temperature and concentration profiles were discussed and also shown graphically. Moreover, outcomes of diverse parameters were also examined and presented graphically within the entropy formation rate and also Bejan number. The effects of implanted factors across the drag force, the rate of thermal as well as mass transportation are accessible in current study via tables and validate the obtained results. Both velocity profiles (horizontal as well as vertical) decreased for increment in Hartman number whilst opposite demeanor seen for other considered constraints. Temperature profile drops for Prandtl number and elastic constraints whereas enhanced for other influential considered parameters whilst concentration profile augmented with Prandtl number. Present problem novelty relies on the modeling of comprehensive system of equations which modified into nonlinear ODEs. In order to obtain the solution numerically, technique such as Optimal Homotopy was opted.

Full-scale experimental and numerical study of smoke spread and temperature distribution in a room-corridor structure building

This paper aims to study the smoke spread and temperature distribution inside a full-scale room-corridor structure building. A series of experiments and simulations with different fuel properties and fuel configurations (crib and pool fires) were carried out. There was a barrier at the top of the left end of the corridor, and the end wall was on the right side. The fire source was located in the room. The evolution of the smoke spread process, pressure distribution, and temperature distribution in rooms and corridors were obtained and analyzed. The results indicate that the barrier and the end wall hinder the smoke spread and make it to accumulate below the corridor ceiling. This causes the smoke layer height of the corridor to be lower than the top of the door, which changes the pressure distribution inside and outside the room and also affects the temperature distribution. Based on the changes of pressure distribution, some correction formulas for the gas flow rate and mass flux at the opening are proposed. Under the effect of the barrier and the end wall, the smoke temperature in the room and the corridor increases. A smoke temperature decaying model along the corridor direction is proposed. Some methods are used and compared to calculate the smoke layer height based on the vertical temperature distribution. The smoke layer height determined by the buoyancy frequency method is most consistent with the experimental observation values.

Effect of bend orientation on the heat transfer performance of U-bend vapor generator in transcritical ORC

Adequate recognition of supercritical heat transfer characteristics in U-bends is important to guide the optimization of the design and practical application of heat exchanges containing U-bends. Past studies have focused on the heat transfer performance under different operating conditions and geometric parameters, however, the influence of bend orientation on the local heat transfer and overall performance of U-bends is still unclear and rarely reported. This work fills this gap with numerical simulation to quantitatively analyze and explain the heat transfer performance of U-bend vapor generators with three different bend orientations (horizontal, horizontally downward, and horizontally upward). The results show that as the ratio of heat flux to mass flux increases, bend orientation effects start to appear only when the buoyancy parameter Grq/Grth at the bend inlet is above 80 ∼ 95. In all three orientations, horizontally downward flow U-bend has the best average heat transfer performance within the bend, followed by horizontal and horizontal upwardly. However, there is no significant difference in the average performance of the three orientations over the entire bend-affecting region, with a maximum difference of only 5%. Therefore, when the downstream length is much greater than the bend, there is no need to consider the influence of flow orientation. Increasing the bend curvature considerably improves the heat transfer within the bend, and the downstream bend-affecting distance becomes larger as well. However, larger curvature also causes greater fluctuation in the heat transfer coefficient. Finally, heat transfer correlations were recommended and developed for all three orientations. Correlations predict over 93% of the entire dataset with a maximum error of 20%.

Scale effects on rotating detonation rocket engine operation

Rotating detonation rocket engines are propulsive devices employing detonation waves moving circumferentially around an annular channel that consume axially fed propellants. Theoretically, this provides benefits with respect to combustion pressure gain and thermodynamic efficiency when compared to deflagration-based combustors. To facilitate size scaling of these devices, the relationships between geometric parameters, performance, and wave dynamics have been investigated with gaseous methane-oxygen propellant. Empirical relations were derived between combustor geometry, fueling conditions, and engine operation, as well as correlation to thermodynamic parameters calculated with chemical kinetics codes. The radius of curvature effects were explored in annular combustors having outer diameters of 25 mm, 51 mm, and 76 mm with a fixed gap width of 5 mm. The injectors were scaled to have same oxidizer-to-fuel injector port area ratio, impingement distance, and injector-to-gap area ratio. Larger combustors had higher wave counts during operation at a given mass flux and equivalence ratio. Combustor axial pressures were found to be more dependent on propellant mass flux and equivalence ratio than geometry. Mass flux and the inner-to-outer radius ratio, the latter of which was related to other geometric ratios, dictated the operating mode transition thresholds and the number of resulting waves, respectively.

Machine-learning-based modeling of saturated flow boiling in pin-fin micro heat sinks with expanding flow passages

For high potential flow-boiling-based thermal management systems, to better understand the underlying flow physics and to present an effective predictive approach have critical importance. Different from the existing literature, this study, for the first time, takes the machine learning (ML) algorithms into consideration for flow boiling in expanding type micro-pin-fin heat sinks (ETMPFHS). A new database including saturated flow boiling data in ETMPFHS is obtained for various operational conditions. Mass flux (G = 150, 210, 270 and 330 kg m−2 s−1), inlet temperature (Ti = 40, 49, 58, 67 and 76 °C) and effective heat flux (approximately, qeff″= 241 to 460 kW m−2) are the variable parameters. In this study, advanced ML algorithms including Support Vector Machine (SVM), Artificial Neural Network (ANN), Regression Trees (RT) and Linear Regression (LR) are used. It is concluded that, for flow boiling in ETMPFHS, the ANN emerges as the most effective model for prediction of htp, ΔT, and ΔP, followed by SVM, while RT and LR present poorer results in terms of predictive accuracy and reliability. Trends of predictions of both the ANN and SVM nearly overlap the experimental data; while both the RT and LR show different trends against the experimental results.

Theoretical analysis to optimize heat extraction from a solar pond integrated with a carbon dioxide heat pump

Heat pumps integrated with renewable energy sources represent an efficient approach to residential heating and cooling, with minimal environmental impact and reduced carbon emissions. While these systems have been extensively researched, there is a necessity to broaden their scope by investigating novel approaches to energy capture and storage that are adopted to the specific characteristics of the region. This study analyzes the effects of different operating parameters on heat extraction from a solar pond integrated with a heat pump using carbon dioxide under transcritical conditions. Subsequently, an optimization examination is conducted to assess and determine the conditions required to achieve the maximum heat extraction rate and the minimum pumping power. The outcomes of this investigation demonstrate that the carbon dioxide mass flux and operating pressure exert a greater influence on the responses compared to the inlet temperature of carbon dioxide and the lower convective zone temperature of the solar pond. Additionally, within the investigated range of mass flux, the highest level of heat extraction occurs at operating pressures near the critical point of carbon dioxide, approximately 7.5 MPa. To meet the demand for maximum heat extraction from the solar pond, the optimal conditions result in an overall performance improvement of 2.61 times compared to the reference state. Furthermore, optimizing the system to maximize heat extraction from the solar pond while using the minimum pumping power results in a total performance enhancement of 4.13 times.

Experimental study on thermal-hydraulic performance of helically coiled tubes steam generator of lead-bismuth reactor

The advantages of the helically coiled tube steam generator lie not only in its high heat transfer efficiency but also in its compact structure, which is initially used in Pb–Bi–SCO2 reactors, and its main function is to transfer the heat from the lead-bismuth side to the SCO2 side. In this experiment, two sets of helical heat exchanger tubes are selected as the objects of investigation. Experiments are conducted on the heat transfer performance of a helical tube to study the influence of structural parameters, mass flux, pressure, and heat flux on the heat transfer characteristics during subcooled boiling and post-dryout. Considering the results of the study, new heat transfer characteristic correlations are derived for the subcooled boiling and post-dryout heat transfer regions, which provide data and theoretical support for the engineering application and thermal hydraulic analysis of steam generators.

Transport scaling in porous media convection

We present a theory to describe the Nusselt number, $\operatorname {\mathit {Nu}}$ , corresponding to the heat or mass flux, as a function of the Rayleigh–Darcy number, $\operatorname {\mathit {Ra}}$ , the ratio of buoyant driving force over diffusive dissipation, in convective porous media flows. First, we derive exact relationships within the system for the kinetic energy and the thermal dissipation rate. Second, by segregating the thermal dissipation rate into contributions from the boundary layer and the bulk, which is inspired by the ideas of the Grossmann and Lohse theory (J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we derive the scaling relation for $\operatorname {\mathit {Nu}}$ as a function of $\operatorname {\mathit {Ra}}$ and provide a robust theoretical explanation for the empirical relations proposed in previous studies. Specifically, by incorporating the length scale of the flow structure into the theory, we demonstrate why heat or mass transport differs between two-dimensional and three-dimensional porous media convection. Our model is in excellent agreement with the data obtained from numerical simulations, affirming its validity and predictive capabilities.

Influence of Operation Parameters on Thermohydraulic Performance of Supercritical CO2 in a Printed Circuit Heat Exchanger

The performance of recuperative printed circuit heat exchangers is critical in supercritical CO2 (sCO2) power generation applications. This article presents a three-dimensional numerical model of sCO2 flowing in a printed circuit heat exchanger and investigates its thermohydraulic performance under different operation conditions. The simulations employ the standard k-ε turbulent model, and consider entrance effects, conjugate heat transfer, real gas thermophysical properties and buoyancy effects. The heat exchanger operation parameters cover mass flux from 254.6 to 1273.2 kg/m2s, inlet temperature 50–150 °C and outlet pressure 100–250 bar on the cold side, and 300–500 °C and 75–150 bar on the hot side. Results show that increasing CO2 mass flux leads to a significantly increased heat transfer coefficient, a slight increase in temperature difference between the hot and cold CO2, as well as larger pressure drop and lower friction factor on both sides. Increasing the cold CO2 pressure, decreasing the cold CO2 temperature, and increasing the hot CO2 temperature result in a higher heat transfer rate of the heat exchanger. Increasing the CO2 temperature on each side causes increased pressure drops on both sides. Increasing the CO2 pressure on each side reduces the pressure drop on each side.

Numerical study on regenerative cooling technology with endothermic hydrocarbon fuel: A comprehensive review

This paper summarizes the phenomena and challenges in regenerative cooling, including transcritical thermophysical properties, fuel pyrolysis, and surface coking. The corresponding numerical methods are classified according to their characteristics, including the fuel surrogate, pyrolysis, surface coking, and turbulence models. The scope of application and the advantages and disadvantages of the models are discussed. Currently, only the differential global reaction method achieves model generality over a wide range of continuous pressures (3–7 MPa) and conversion rates (up to 75%), and it is recommended to adopt non-invasive methods and direct cooling unit to improve the accuracy of pyrolysis models. Future surface coking studies should focus on two-way coupling and consider coking and species concentration interaction. The actual coking distribution and porous effects need to be investigated simultaneously, and more kinetic models are urgently required to meet a wide range of pressures. Besides, an overview of parameterized studies in recent years is presented, including operating pressure, heat flux, mass flux, flow direction, flight acceleration and channel configuration. The weaknesses of existing parametrical studies are analyzed from a practical point of view. Heat transfer correlations of endothermic hydrocarbon fuels are also summarized and classified. Establishing heat transfer correlations for the hot spot of the heated side is essential for designing the regenerative cooling system, and the surface coking effect should be introduced.

Research on the Performance and Computational Fluid Dynamics Numerical Simulation of Plate Air Gap Membrane Distillation Module.

Membrane distillation (MD) is widely used in the field of seawater desalination. Among its various sub-categories, air gap membrane distillation (AGMD) stands out due to its high thermal efficiency and compatibility with low-grade heat sources. This study delves into the impact of varying operating conditions on AGMD performance, employing numerical simulations which are grounded in experimental validation. The objective was to enhance the performance of AGMD, mitigate polarization phenomena, and provide a reference for optimizing membrane component design. The results show that the agreements between the simulated and the experimental values were high. When increasing the feed temperature and decreasing the coolant temperature, the impact of polarization phenomena on the performance of AGMD was reduced. The mass flux, Total Permeate Concentration (TPC), and heat flux increased by 81.69%, 36.89%, and 118.01%, respectively, when the feed temperature was increased from 50 °C to 75 °C. When the coolant temperature decreased from 22 °C to 7 °C, the mass flux increased by 37.06%. The response surface analysis revealed that the feed temperature has significant influence on AGMD performance, and there is a noticeable interaction between the feed temperature and coolant temperature. These findings will play key roles in practical applications.

Numerical investigation on dynamic flow characteristics of methane condensation in microchannels

Microchannel condensers play an essential role in cryogenic two-phase heat management systems due to their efficient heat transfer characteristics. Thus, it is worth conducting an in-depth study on microscale condensation characteristics of cryogenic fluids. This paper delves into the flow condensation process of methane in microchannels. A two-dimensional transient model with high accuracy for cryogenic fluids has been developed by combining a self-defined program for the source term of the phase transition model. The model fully considers the boundary layer thickness and accurately explores the mesh accuracy. The complete condensation flow patterns are captured for various vapor quality, mass flux, and wall subcooling degrees. The injection flow is a unique flow regime for condensation in microchannels. The decrease in wall subcooling degree and increase in mass flux leads to the separation point at the neck of the injected flow moving towards the exit, while the annular flow region is expanding and the flow pattern transition is lagging. The mass flux improves the heat transfer coefficient more significantly at high vapor quality. During injection and bubble flow, the wall shear stress and local heat transfer coefficient are subject to bouncing and oscillations, which may induce fluctuations in the upstream annular flow. The prediction performance of six classical heat transfer correlations is evaluated. The results indicate that the Nie et al. correlation has the highest comprehensive prediction accuracy with MRD and MARD of -5.00 % and 15.83 %, respectively.

Implementing the predictor-corrector approach to examine the thermo-solutal convection for buongiorno eyring-powell nanofluid model with squeezed microcantilivier surface

The Buongiorno nanofluid model serves as a foundational model for theoretical and experimental research in the field of nanofluids, and this model can be applied to various engineering problems, including heat exchangers, biomedical applications, solar collectors, nuclear reactors, and different cooling systems in the automotive and electronics industries. The use of nanofluids in the Eyring-Powell fluid over a squeezed sensing surfaces is a vital area of research for the design and improvement of microfluidic devices and sensors, which find widespread usage in industrial and medical applications. The main purpose of this work is to note the augmentation in thermal conductivity by using the Buongiorno nanofluid model along with the natural convective flow of non-Newtonian Eyring-Powell fluid that is moving on the squeezed sensory surface along with slip velocity. The viscosity of a fluid is assumed to be dependent on temperature. The Cattaneo-Christov heat and mass flux and chemical reaction are assumed to determine the combined effect of heat and mass transport. The governing model of equations is in the form of dimensional partial differential equations, and we have to convert these equations into ordinary differential equations; therefore, a set of similarity transformations is adopted for making the equations into dimensionless form. The numerical results were obtained by adopting the predictor and corrector multistep method, namely the ‘Adams-Bashforth’ technique, in Matlab software. The use of natural convective flow enhances the velocity region. The velocity slip parameter increases the velocity of the fluid, whereas the viscosity parameter drops the velocity profile. The thermophoresis and Brownian motion parameters are the sources of the increment in the temperature region. The thermal relaxation and solutal relaxation parameters are the sources of decline in the temperature region. The squeezing parameter is the source of reduction in the skin friction, whereas the result indicates that the fluid parameter, Grashof number, and viscosity coefficients increase the skin friction.

Implicit finite difference simulations for unsteady oscillating flow of Walters-B nanofluid with microbes using the Cattaneo–Christov model

The thermal importance of nanoparticles in different fields of engineering is still a developing issue that necessitates additional focused consideration. The suspension of non-Newtonian fluids with nonmaterials has various applications in areas such as enhanced thermal systems, energy processes, aerospace engineering, and chemical industries. Following such motivations, this work aims to analyze the heat and mass transfer flow of Walters-B nanofluid in the presence of microorganisms. The fluid motion is presumed to be nonsteady over a surface that undergoes periodic acceleration. The motivations for studying nanofluid’s oscillating flow are its use in effective mixing processes, combustion stability, and process efficiency. The text provides a detailed explanation of the saturation of porous media. A modified theory for heat and mass fluxes, known as the Cattaneo–Christov approach, suggests an extension in heat equations. Moreover, it supports the interaction of radiation phenomena for enhancing heat transfer. It is noteworthy that the entire problem is represented using extremely nonlinear partial differential equations (PDEs). The CFD study utilizing the renowned implicit finite difference method (FDM) has been effectively employed to propose a numerical solution for the problem. The numerical results are deemed valid and confirmed within certain limiting cases, based on the available data. The evaluation of velocity, skin friction coefficient, Nusselt number, and Sherwood number as a function of time has been demonstrated for various parameters. It is asserted that the wall shear force exhibited an oscillating pattern with a greater magnitude as a result of the viscoelastic parameter. The Nusselt number and Sherwood number exhibit slight acceleration as a result of changes in the Prandtl number and Schmidt number, respectively. The proposed model is specifically designed for use in heat exchangers, vibrational systems, compact designs, and vibration control.

Significance of variable thermal conductivity and suction/injection in unsteady MHD mixed convection flow of Casson Williamson nanofluid through heat and mass transport with gyrotactic microorganisms

AbstractThe present paper explores a two‐dimensional mixed bio‐convective unsteady viscous hydro‐magnetic Casson Williamson nanofluid flow model with heat and mass transport incorporating motile microorganisms towards a stretchy spinning disc. The flow concept is accomplished by rotating a stretched disc with a time‐varying angular velocity. By applying a magnetic field normal to the axial direction, a magnetic interaction is taken into consideration. The Casson Williamson nanofluid contains nanosized particles suspended with swimming motile microorganisms and the rotation of the disc is exhibited by buoyancy forces, thermophoresis, suction/injection, zero mass flux conditions, variable thermal conductivity, Joule heating and so forth. The obtained flow narrating differential equations of the model are transformed into ordinary differential system. This is accomplished by simulating boundary value problems using the shooting technique using the ‘ND‐Solve’ approach included in the Mathematica software (Mathematica 12). The implications of the engaged parameters such as Williamson fluid parameter, Casson fluid (CF) parameter, thermophoresis parameter, Brownian motion parameter and so forth, on both axial and radial velocities, temperature, concentration of nanoparticles and microorganisms are explained by means of graphical and tabular constructions. This paper's validity has been confirmed and its findings align with those of other previously published papers. Furthermore, it is found that both the axial and radial velocity profiles are seen to be diminishing functions of the CF parameter. The identified observation may have theoretical implications for a number of engineering procedures, solar energy systems, biofuel cells and extrusion system improvement. Moreover, this work finds application in micro‐fabrication techniques and the chemical industry.

Glyphosate contamination in European rivers not from herbicide application?

The most widely used herbicide glyphosate contaminates surface waters around the globe. Both agriculture and urban applications are discussed as sources for glyphosate. To better delineate these sources, we investigated long-term time series of concentrations of glyphosate and its main transformation product aminomethylphosphonic acid (AMPA) in a large meta-analysis of about 100 sites in the USA and Europe. The U.S. data reveal pulses of glyphosate and AMPA when the discharge of the river is high, likely indicating mobilization by rain after herbicide application. In contrast, European concentration patterns of glyphosate and AMPA show a typical cyclic-seasonal component in their concentration patterns, correlating with patterns of wastewater markers such as pharmaceuticals, which is consistent with the frequent detection of these compounds in wastewater treatment plants. Our large meta-analysis clearly shows that for more than a decade, municipal wastewater was a very important source of glyphosate. In addition, European river water data show rather high and constant base mass fluxes of glyphosate all over the year, not expected from herbicide application. From our meta-analysis, we define criteria for a source of glyphosate, which was hidden so far. AMPA is known to be a transformation product not only of glyphosate but also of aminopolyphosphonates used as antiscalants in many applications. As they are used in laundry detergents in Europe but not in the USA, we hypothesize that glyphosate may also be a transformation product of aminopolyphosphonates.

Inconsistencies in unstructured geometric volume-of-fluid methods for two-phase flows with high density ratios

Geometric flux-based Volume-of-Fluid (VOF) methods (Marić et al., 2020) are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier–Stokes equations without phase-change (Liu et al., 2023), discretization may easily introduce inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the ρLENT unstructured Level Set/Front Tracking method (Liu et al., 2023) to flux-based geometric VOF methods (Marić et al., 2020), and implement our discretization into the plicRDF-isoAdvector geometrical VOF method (Roenby et al., 2016). We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume can ensure equivalence between the mass conservation equation and the phase indicator (volume conservation) if consistent discretization schemes are chosen for the temporal and convective term. Based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. We confirm the consistency by solving an auxiliary mass conservation equation with a geometrical calculation of the face-centered density (Liu et al., 2023). We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios within [1, 106] and viscosity ratios within [102, 105].