Two-phase Model Research Articles

Lubrication optimization of high-speed train drive gearbox

The gears in the high-speed heavy-duty gearbox of the high-speed train are typical high-speed heavy-duty gears. Combined with the transmission principle and structural characteristics of the high-speed train drive gearbox, to ensure adequate lubrication of meshing gears and bearings, an optimization of the lubricating oil flow inside the gearbox was conducted. The oil and gas two-phase flow model inside the gearbox adopts the VOF model, and the turbulence model adopts the standard κ-ε model. Fluent is used for simulation calculation. The results show that the exhaust port position of the gearbox has little effect on the flow of lubricating oil inside the gearbox; the overall pressure distribution inside the gearbox is relatively uniform, with higher pressure only at the meshing gears; the distribution of lubricating oil inside the gearbox is related to the rotation of the gears, and the flow velocity of lubricating oil is mainly affected by the rotation of the gears, with the maximum flow velocity appearing around the gears; the flow of lubricating oil inside the gearbox meets the lubrication requirements of the gearbox. These results provide support for the lubrication design, flow channel structure improvement, and effectiveness evaluation of high-speed train transmission gearboxes.

Modelling pressure dynamics of oil–gas two-phase flow in double-porosity media formation with permeability-stress sensitivity

Pressure dynamics can reflect the basic characteristics of fluid flow through underground porous formation. In this research, the oil–gas two-phase flow model for a double-porosity media formation with permeability-stress sensitivity was first established for three kinds of outer boundaries. The unified governing equation was deduced by utilizing the H function. The nonlinear mathematical model in consideration of permeability-stress sensitivity was linearized by implementing the canonical perturbation transformation and then solved by using the Laplace transformation. After that, a sequence of typical log–log curves of pressure dynamics influenced by various model parameters were plotted and analyzed. These curves reflect the typical characteristic of a V shape caused by the inter-porosity fluid flow from matrix toward natural fractures. Oil saturation and permeability-stress sensitivity coefficient have much influence on the pressure dynamics. Ultimately, the established model of oil–gas two-phase flow was validated through a well-test fitting interpretation for a real condensate gas well in a sandstone formation. This research can offer insights into the pressure dynamics dominated by the oil–gas two-phase flow in naturally fractured formations and the permeability-stress sensitivity effect.

Two-group drift-flux model in tight lattice subchannel

Tight lattice rod bundles can increase equipment compactness and improve heat exchange efficiency, and they are widely adopted in heat exchange engineering. Understanding the flow characteristics of gas-liquid two-phase flow in tight lattice subchannels is essential for developing heat exchangers and fuel assemblies with these tight bundles. The drift-flux model (DFM) is a crucial two-phase flow model extensively used in subchannel analysis codes. Investigating the DFM in tight lattice subchannels benefits the advancement of these codes. For two-phase flow interfacial structures, significant two-group characteristics exist, with bubbles divided into small (group-one) and large (group-two) bubbles. The substantial differences in flow characteristics between these two groups provide a solid foundation for developing a two-group DFM. This study examined the two-group characteristics of two-phase flow in a tight lattice interior subchannel and developed a corresponding two-group DFM. The two-group correlations for the distribution parameters and drift velocities at the tight lattice interior subchannel level were proposed and verified using experimental data. The accuracy of the developed two-group DFM in predicting group-wise void fraction and gas velocity was also verified. The standard relative deviation between the model predictions and experimental data was 8.11 % and 13.1 % for group-one and group-two void fractions and 8.33 % and 11.7 % for group-one and group-two gas velocities, respectively. This indicates satisfactory accuracy for the newly developed two-group DFM in a tight lattice interior subchannel.

Exploring submergence impact on flow-induced motion energy-harvesting with circular-triangular prisms

AbstractRecent advancements in energy-harvesting have utilized Flow-Induced Motion (FIM) as a renewable source, diverging from past efforts aimed at minimizing FIM's adverse effects. This study introduces kinetic energy converters using alternating lift technology (ALT), employing a prism with a Circular-Triangular (Cir-Tria) shape, coupled with a spring and damper, to generate energy. Utilizing computational fluid dynamics in OpenFOAM for Reynolds numbers between 2 × 103 and 13 × 103 and varying submergence depth ratio from 0.98 to 5.91, this research employs a moving computational grid, two-dimensional incompressible Navier–Stokes equations, the k-omega Shear Stress Transport (SST) turbulence model, the Volume of Fluid, VOF, two-phase model, and the cylinder mass–spring–damper equation. Findings show that approaching the flow surface negatively impacts the FIM response due to the interaction of vortices from the flow surface and the prism’s upper shear layer. This interaction weakens and neutralizes the upper vortices, altering the flow structure around the prism and the governing FIM phenomena. Proximity to the free surface significantly affects FIM responses, with a notable decrease in vibration amplitude and energy conversion as the submergence depth ratio increases from 0.98 to 5.91. Maximum system efficiency of 1.4% is observed in the VIV initial branch at infinite submergence (single-phase flow). Beyond a submergence depth ratio of 5.91, FIM amplitude and energy conversion flatten, indicating negligible free surface effects.

Analysis of heat generation and viscous dissipation with thermal radiation on unsteady hybrid nanofluid flow over a sphere with double-stratification: Case of modified Buongiorno's model

PurposeThis work uses entropy generation analysis to numerically analyze magnetohydrodynamics (MHD) unsteady flow, heat and mass transfer. The study considers changing viscosity, thermal radiation, viscous dissipation, mass suction, heat generation, and stratification processes in a hybrid nanofluid around a spinning sphere. A two-phase nanofluid flow model (Buongiorno model) is used to tackle the current challenge. Both the free stream velocity and the sphere's angular velocity changed over time. Design/methodology/approachThe case study's complicated partial differential equations are transformed into simpler ordinary differential equations utilizing similarity transformation. Implementing the fourth-order Runge-Kutta Fehlberg method with a shooting scheme in MATHEMATICA has allowed us to get numerical solutions for ordinary differential structures. FindingsThe many aspects of these regulated physical characteristics have been elucidated and thoroughly examined via the use of charts and tables. For increasing values of unsteadiness parameter, the velocity profiles in the x-direction grow while they decrease in the z-direction. On the other hand, the temperature profile exhibits a dual pattern, and the concentration profile decreases. As the chemical reaction parameter climbs from 0.25 to 1.0, the Sherwood number for the nanofluid rises by 6721.39% and for the hybrid nanofluid, 3818.9%. When Nr increases from 0.2 to 0.8, nanofluid Nusselt number climbs 22.5% and hybrid nanofluid's Nusselt number rises 21.9%. The Brinkmann number and nanoparticle volume percentage are strongly associated with entropy production. Entropy generation is dual for the temperature difference, magnetic, radiation, and changeable viscosity parameters. The findings are also compared to those from the existing literature and are in excellent agreement with them.

A Leakage Safety Discrimination Model and Method for Saline Aquifer CCS Based on Pressure Dynamics

The saline aquifer CCS is a crucial site for carbon storage. Safety monitoring is a key technology for saline aquifer CCS. Current CO2 leakage detection methods include microseismic, electromagnetic, and well-logging techniques. However, these methods face challenges, such as difficulties in determining CO2 migration fronts and predicting potential leakage events; as a result, the formulation of test timing and methods for these safety monitoring techniques are somewhat arbitrary. This study establishes a gas–water two-phase seepage model and solves it using a semi-analytical method to obtain the injection pressure and the derivative curve characteristics of the injection well. The pressure derivative curve can reflect the physical properties of the reservoir through which CO2 flows underground, and it can also be used to determine whether CO2 leakage has occurred, as well as the timing and amount of leakage, based on boundary responses. This study conducted sensitivity analyses on eight parameters to determine the impact of each parameter on the bottom-hole pressure and its derivatives, thereby obtaining the influence of its parameters on different flow stages. The research indicates that, when a steady-state flow characteristic appears at the outer boundary, CO2 leakage will occur. Additionally, the leakage location can be determined by calculating the distance from the injection well. This can guide the placement and measurement of safety monitoring methods for saline aquifer CCS. The method proposed in this paper can effectively monitor the timing, location, and amount of leakage, providing a technical safeguard for promoting CCS technology.

Mesoscale Modeling of Microcapsule-Based Self-Healing Cementitious Composites under Dynamic Splitting Tension

Microcapsule-based self-healing cementitious composite (MSCC) offers autonomous damage repair, extending the service life of structures. However, most of the existing studies focus on static behavior and healing effectiveness but rarely explore dynamic responses. This study developed the mesoscale modeling approach to investigate MSCC behavior under dynamic split tensile loading. At the mesoscale, MSCC can be treated as a four-phase composite consisting of coarse aggregates, interfacial transition zones, cement mortar, and microcapsules. Alternatively, it can be simplified as a two-phase composite comprising a homogeneous mortar matrix and microcapsules. Four-phase and two-phase mesoscale MSCC models were developed for 2D simulations, while a two-phase 3D model was also developed for comparison. Mesoscale numerical simulations were conducted based on Split-Hopkinson Pressure Bar Brazilian disk-splitting tests, considering various strain rates. Simulation results of different mesoscale models were compared with experimental results. All of the models accurately predicted the tensile strength of MSCC, with the 2D four-phase model providing the best representation of failure modes and crack propagation. Both experimental and numerical data exhibited obvious strain rate effects, indicating that MSCC’s mechanical properties were sensitive to the loading rate. Dynamic increase factors were obtained, quantifying rate sensitivity. The obtained dynamic mechanical properties of MSCC provide insights for designing MSCC components and structures that can better withstand collisions or explosions.

Sewer transport conditions and their role in the decay of endogenous SARS-CoV-2 and pepper mild mottle virus from source to collection

This study presents a comprehensive analysis of the decay patterns of endogenous SARS-CoV-2 and Pepper mild mottle virus (PMMoV) within wastewaters spiked with stool from infected patients expressing COVID-19 symptoms, and hence explores the decay of endogenous SARS-CoV-2 and PMMoV targets in wastewaters from source to collection of the sample. Stool samples from infected patients were used as endogenous viral material to more accurately mirror real-world decay processes compared to more traditionally used lab-propagated spike-ins. As such, this study includes data on early decay stages of endogenous viral targets in wastewaters that are typically overlooked when performing decay studies on wastewaters harvested from wastewater treatment plants that contain already-degraded endogenous material. The two distinct sewer transport conditions of dynamic suspended sewer transport and bed and near-bed sewer transport were simulated in this study at temperatures of 4 °C, 12 °C and 20 °C to elucidate decay under these two dominant transport conditions within wastewater infrastructure. The dynamic suspended sewer transport was simulated over 35 h, representing typical flow conditions, whereas bed and near-bed transport extended to 60 days to reflect the prolonged settling of solids in sewer systems during reduced flow periods. In dynamic suspended sewer transport, no decay was observed for SARS-CoV-2, PMMoV, or total RNA over the 35-h period, and temperature ranging from 4 °C to 20 °C had no noticeable effect. Conversely, experiments simulating bed and near-bed transport conditions revealed significant decreases in SARS-CoV-2 and total RNA concentrations by day 2, and PMMoV concentrations by day 3. Only PMMoV exhibited a clear trend of increasing decay constant with higher temperatures, suggesting that while temperature influences decay dynamics, its impact may be less significant than previously assumed, particularly for endogenous RNA that is bound to dissolved organic matter in wastewater. First order decay models were inadequate for accurately fitting decay curves of SARS-CoV-2, PMMoV, and total RNA in bed and near-bed transport conditions. F-tests confirmed the superior fit of the two-phase decay model compared to first order decay models across temperatures of 4 °C–20 °C. Finally, and most importantly, total RNA normalization emerged as an appropriate approach for correcting the time decay of SARS-CoV-2 exposed to bed and near-bed transport conditions. These findings highlight the importance of considering decay from the point of entry in the sewers, sewer transport conditions, and normalization strategies when assessing and modelling the impact of viral decay rates in wastewater systems. This study also emphasizes the need for ongoing research into the diverse and multifaceted factors that influence these decay rates, which is crucial for accurate public health monitoring and response strategies.

Data-Driven Shelf Stocking: Robustness and Vertical-Location Effect

In this article, we study a shelf-stock allocation problem in a data-driven setting where the demand distribution is unknown. The retailer needs to decide which commodities to place on each level of the shelf (location decision), and determine the stock level for each selected commodity at the shelf (stock decision) that can be adjusted based on updated demand prediction, under constraints on allocation and capacity, so as to maximize total expected profit. Key issues of the problem include demand endogeneity on vertical-location effect and the demand ambiguity that may arise from the ever shorter life cycles of commodities and other complicated determinants. We address the problem in a rolling-horizon fashion and develop a two-phase data-driven robust optimization model leveraging a decision-dependent Wasserstein metric that incorporates time-series demand forecasts and captures vertical-location effect under demand ambiguity. We derive tractable solution schemes for the model, in which the phase-I model determines the optimal location decision by solving one instance of mixed-integer linear program, while the phase-II model admits an analytical solution for updating the optimal stock. Furthermore, we discuss the sensitivity implications on how the ambiguity aversion impacts the optimal stock, and prove the consistency of the model solution under regularity condition on the underlying demand process that well justifies the asymptotic performance of the proposed data-driven approach. Finally, we extend our model to incorporate substitution effect, and conduct sufficient numerical experiments with real-life data that demonstrate the performance of our model.

Exploring the properties of the obscured hyperluminous quasar COS-87259 at z = 6.853

ABSTRACT In this paper we explore the properties of the $z=6.853$ obscured hyperluminous quasar COS-87259, discovered in the Cosmological Evolution Survey (COSMOS) field, with our recently developed Bayesian spectral energy distribution (SED) fitting code SMART (Spectral energy distributions Markov chain Analysis with Radiative Transfer models). SMART fits SEDs exclusively with multicomponent radiative transfer models that constitute four different types of pre-computed libraries for the active galactic nucleus (AGN) torus, the starburst, and the spheroidal or disc host. We explore two smooth radiative transfer models for the AGN torus and two two-phase models, in order to put constraints on the AGN fraction of the galaxy, the black hole mass, and its star formation rate (SFR). We find that either of the smooth tapered disc or the two-phase flared disc models provide a good fit to the SED of COS-87259. The best-fitting models predict an AGN fraction in the range $86-92$ per cent, a bolometric AGN luminosity of $5.8-10.3 \times 10^{13} L_\odot$, a black hole mass of $1.8-3.2 \times 10^{9} M_\odot$ (assuming the quasar is accreting at the Eddington limit), and an SFR in the range $1985-2001~M_\odot \rm yr^{-1}$. The predicted space density of such objects in the redshift range $4-7$ is $\sim 20$ times more than that of co-eval unobscured quasars.

Pre- Trip Parking Choice and Parking Guidance System for City of New Delhi: A Comprehensive Two-Phase Model

Pre- Trip Parking Choice and Parking Guidance System for City of New Delhi: A Comprehensive Two-Phase Model

Heat transfer and entropy generation characteristics of nanofluid flow over bluff bodies under steady and unsteady flow: A two-phase approach

Owing to higher thermal conductivity, nanofluids have the potential to be the coolant for various applications ranging from internal to external flows. A two-phase model is implemented to model the interaction between nanoparticles and base fluid to obtain accurate results. Heat transfer and entropy generation characteristics of nanofluid (Al2O3 and water) flow over bluff bodies such as circular and square cylinders for steady (20 < Re < 100) and unsteady (Re = 150 and 300) flow conditions have been carried out for various volume fractions (0.5–2 %). The same has been expressed in quantitative and qualitative aspects with parameters such as mean Nusselt number, surface Nusselt number, heat transfer enhancement ratio, and entropy generation. Heat transfer rate increases with an increase in flow rate and volume fraction for both steady and unsteady flow. Heat transfer enhancement in steady flow ranges from 1.10 to 1.35. For unsteady flow (Re = 150 & Re = 300), nanofluid's heat transfer enhancement ratio is higher than water in the range of 1.10–1.8. This is attributed to the early separation of flow and the presence of large recirculatory regions. With the increase in Re, the entropy generation decreases for circular and square cylinders. Compared to nanofluid, the entropy generation is higher for water.

Heat transfer performance and startup characteristics of separated gravity heat pipe

Separated gravity heat pipes, with distinct arrangements of evaporating and condensing sections, offer low thermal resistance, high heat transfer efficiency, and a simple structure, making them suitable for passive cooling of spent fuel pools through gravity-driven processes. In this study, a steady-state, one-dimensional, two-phase flow model is developed to analyze phase change heat transfer in a separated gravity heat pipe. The research investigates the impact of liquid filling rate and vacuum level on heat pipe operation. The findings reveal a notable increase in pressure drop inside the tube with higher liquid filling rates, which diminishes the adaptability of the heat pipe as pressure rises, resulting in a narrower range of effective liquid filling rates. Specifically, the liquid filling rate of the heat pipe ranges from 38 % to 72 % at P = 13.75 kPa and from 44 % to 68 % at P = 15.75 kPa. Additionally, a startup prediction model is formulated based on a thermal resistance network model using the ideal gas assumption. Two startup states—namely, the initial startup state and the subsequent startup state—are proposed for large-scale separated gravity heat pipe arrays. The heat pipe achieves the large-temperature-difference initial startup state at a 50 % liquid filling rate within 7 min before transitioning to the subsequent startup state. The vapor mass, heat transfer coefficient, and working fluid temperature initially increase and then decrease over time, with varying peak times. As the liquid filling rate increases, the maximum vapor mass also increases. The heat transfer coefficient peaks at a 60 % liquid filling rate before subsequently declining. The optimal liquid filling rate of 60 % is identified based on startup time, heat transfer coefficient, and overall heat transfer efficiency.

Numerical simulation of a hybrid energy system proposed for low carbon data center

Low-carbon energy application for both large grid and distributed energy consumers is an urgent problem to be solved. Data centers (DC) are the typical distributed large-size energy consumers, and the application of renewable energy and energy storage is a promising solution for data center decarbonization. This paper developed a complete hybrid energy system (HES) simulation process for data center applications. The photovoltaic (PV) cell, hydrogen electrolysis, hydrogen storage, proton exchange membrane fuel cell (PEMFC), lithium battery (BAT), grid, and data center load are considered in the HES. A one-dimensional two-phase flow PEMFC model is developed. The detailed mass transfer process inside the PEMFC cell is modeled. The PEMFC model-solving algorithm is developed and integrated into the HES simulation program. The energy management system (EMS) based on a logical flow chart energy management strategy is integrated by editable subfunction. The HES simulation program is coded and implemented based on the MATLAB-SIMULINK environment. The yearly HES performance simulations are conducted and analyzed for a 200 kW data center in Xi’an with different HES parameters and an appropriate HES parameter arrangement is provided. The main contribution of this work is the development of an editable HES simulation program that is extensible for data center applications.

A Phase-Field Model for Wet Snow Metamorphism.

The microstructure of snow determines its fundamental properties such as mechanical strength, reflectivity, or thermo-hydraulic properties. Snow undergoes continuous microstructural changes due to local gradients in temperature, humidity, or curvature, in a process known as snow metamorphism. In this work, we focus on wet snow metamorphism, which occurs when the temperature is close to the melting point and involves phase transitions among liquid water, water vapor, and solid ice. We propose a pore-scale phase-field model that simultaneously captures the three relevant phase change phenomena: sublimation (deposition), evaporation (condensation), and melting (solidification). The phase-field formulation allows one to track the temperature evolution among the three phases and the water vapor concentration in the air. Our three-phase model recovers the corresponding two-phase transition model when one phase is not present in the system. 2D simulations of the model unveil the impact of humidity and temperature on the dynamics of wet snow metamorphism at the pore scale. We also explore the role of liquid melt content in controlling the dynamics of snow metamorphism in contrast to the dry regime before percolation onsets. The model can be readily extended to incorporate two-phase flow and may be the basis for investigating other problems involving water phase transitions in a vapor-solid-liquid system, such as airplane icing or thermal spray coating.

Numerical study of proton exchange membrane water electrolyzer performance based on catalyst layer agglomerate model

In this work, a two-dimensional two-phase model of proton exchange membrane water electrolyzer (PEMWE) is developed, in which the catalyst layer (CL) is represented using agglomerate model. The effects of CL composition, porous transport layer (PTL) material properties and operating conditions on PEMWE performance are investigated. The results indicate that small size of catalyst agglomerate around 0.25 μm would benefit PEMWE performance. Appropriate increase of catalyst loading, porosity and ionomer volume fraction in the CL improves PEMWE performance, but their further increment leads to high mass transfer resistance, limiting the improvement of electrolyzer performance. The porosity and ionomer volume fraction of the catalyst layer are suggested to be lower than 0.5 and 0.6, respectively. The catalyst loading should be lower than 1.5 mg cm−2 when the CL porosity is higher than 0.3. The PTLs with high permeability, porosity and low contact angle is beneficial for the gas–liquid two-phase flow and avoiding the overheat and water shortage in the electrolyzer. Increasing the inlet velocity accelerates the bubble removal process, but might results in significant temperature drop, degrading the PEMWE performance. The most suitable temperature of inlet liquid is around 353.15 K. The results provide important guidance for the optimization design of high-performance PEMWE.

Comparison of rotor hovering aerodynamic performance in free-surface and ground effects using numerical methods

The aerodynamic performance of the rotor hovering on the air–water free-surface, which is significant for cross-medium unmanned aerial vehicles, is merely studied. In this study, a compressible two-phase flow model is used to compare the aerodynamic performance in the free-surface effect (FSE) and the ground effect (GE) with various dimensionless distances, γ, between the rotor and the ground (or free-surface). According to the results, the vortex core in FSE moves further in both vertical and radial directions than in GE for the early stages. Additionally, the blade surface is separated into three parts. In zone I, the aerodynamic performance is mostly determined by proximity effects. For both FSE and GE, the downward induced velocity at the rotor disk rises with increasing γ, leading to a decrease in the sectional thrust coefficient CT,S. By the way, CT,S is larger in FSE. In zone III, the aerodynamic performance is mostly governed by the blade tip vortex. The trend of aerodynamic performance with γ is reversed compared with zone I. The above-mentioned two opposing tendencies result in a smaller rotor thrust in FSE than in GE within the range of 0.60≤γ≤3.00, but a higher rotor thrust in FSE within the range of γ≤0.60.

Experimental Study on the Mass Flow Rate Characteristics of a Fluidized Bed Powder Fuel Feeding System

In this study, a fluidized bed powder fuel feeding system that controls flow using the principle of two-phase gas-solid choking is proposed. Experiments based on real-time weighing methods were conducted to explore the flow rate characteristics under various total pressure and throttle-orifice area conditions. The experimental results showed that as the total pressure increased, the powder flow rate first decreased and then increased. To achieve the same increase in powder mass flow rate by altering the pressure, fine powder requires a greater pressure increment than coarse powder. A choked flow formula based on the gas-solid two-phase nonequilibrium model was derived, for investigating the influence of these two factors on the powder flow rate. Compared with the experimental results, this formula predicts the powder flow rates within a 20 % error margin. This model provides more precise guidance for engineering designs. The studied powder fuel-feeding system was connected to a powder engine, and hot-fire tests were conducted. The results showed that the pressure fluctuation in the powder engine combustion chamber did not exceed 2.5 %, confirming the feasibility and stability of the powder supply in the fluidized bed powder fuel feeding system.

Numerical study on cavitation generation induced by the high-speed jet impact on the water surface

The complex interaction between shock waves and two-phase interfaces can generate cavitation. In this study, the cavitation induced by the high-speed jet impact on the water surface was investigated. The mixture fluid is modeled using the barotropic equation of state under the framework of the two-phase flow model, which can describe the mixture of air, water, and vapor with any proportion. Through constructing a 1D Riemann problem for the impact-induced cavitation phase transition, it indicates that the coupling effect of multiple rarefaction waves emitted from the two-phase interface is responsible for the cavitation phase transition inside the liquid. Then, a 3D (three-dimensional) simulation regarding the impact of a high-speed jet on the water surface was conducted and validated against previous experiments that captured the cavitation phase transition phenomenon in the central region after the jet impact. The 3D simulation results revealed the spatial structure and development process of shock waves in detail. The coupling effects of shock waves and two-phase interfaces generate a ring-shaped rarefaction wave, which develops radially inward and superimposes, resulting in the formation of acorn-shaped cavitation bubble nuclei inside the water. The 3D simulation can provide spatial shock/rarefaction wave structures and internal flow details that have never been obtained in experiments, such as shock generation and propagation, rarefaction wave generation and center convergence, and the internal structure of acorn-shaped cavitation nucleation. Furthermore, the influence of the jet velocity on the cavitation intensity was analyzed, and a quantitative relationship was provided.

A New model of gas-water two-phase seepage based on Newton's law of motion

The pore throat size, structure distribution, and lithology of porous media in gas reservoirs are varied, and the gas-water two-phase seepage law is complex, making it difficult to describe the seepage model. Newton's law of motion is a basic law of motion in classical mechanics, and its application in gas-water two-phase seepage modeling is an innovative practice of classical mechanics in seepage mechanics systems. Based on Newton's three laws of motion, a gas-water two-phase seepage model was established from the force analysis of fluid, and the relationship between velocity and pressure difference, pipe radius, water film thickness, viscosity, etc. was derived under the condition that the model reached a stable state, i.e., force balance. The relationship is referred to as the steady-state model. Subsequently. the equivalent permeability representation model was derived based on the steady-state model to calculate the permeability of rock samples with different channel distribution characteristics. The results were consistent with the measured values, and there is a good correspondence between channel distribution characteristics and permeability. The relative permeability calculation method was established based on the steady-state model and capillary pressure curve. The obtained relative permeability curve aligned with the two-phase seepage law and coincides with the relative permeability curve obtained by Poiseuille's law. Finally, a new productivity equation was derived based on the steady-state model, and the Inflow Performance Relationship (IPR) curve calculated by the gas well example was consistent with the traditional equation. The research results were based on the force analysis of fluid in porous media and fundamentally explored the law of fluid flow. The derived seepage model can be used to calculate reservoir permeability, the gas-water relative permeability curve, and gas well productivity analysis and to effectively guide gas reservoir development. The study was a successful application of the basic theory of mechanics in gas-water two-phase seepage in gas reservoirs.