Liquid-gas Two-phase Flow Model Research Articles

Effect of Swirl Angle on Interaction between Swirl Oxygen Lance Jet and Melt Pool

In order to clarify the action law of the swirl oxygen lance jet on the melt pool of the converter and to determine the optimal swirl angle of the swirl oxygen lance for the 120t converter, this study establishes the gas-liquid two-phase flow model of the oxygen lance with different swirl angles based on the realizable k-ε model and the VOF multiphase flow model. The gas-liquid interface behavior during the interaction between the jet and the molten pool was analyzed, and the flow pattern of molten steel in the molten pool was mainly investigated. The results show that compared with traditional oxygen lance, the rotating oxygen lance jet enhances the stirring of the melt pool and intensifies the fluctuation of the melt pool liquid level. The depth of the impact cavity decreases with the increase of the swirl angle, but the diameter of the impact cavity increases with the increase of the swirl angle. When the jet with a swirl angle of 10 ° impacts the surface of the melt pool, the turbulence energy obtained by the molten steel is the highest, the average flow velocity inside the melt pool is the highest, and the molten steel is stirred more thoroughly, achieving better melting effects.

Research on simulation method of multiple time scales dissolution process in tube electrode pulse electrochemical machining

Tube electrode pulsed electrochemical machining (TE-PECM) has received widespread attention as an electrochemical perforation technique that is widely used for machining deep small holes/oblique small holes such as air film holes in blades. However, the TE-PECM process is characterized by complex multi-physics field coupling relationships and multiple time scales for multi-physics interactions, making the simulation of the pulsed electrolytic processing process computationally huge and difficult to perform. To accurately describe the multi-physical field coupling relationship for pulsed electrochemical processing. In this paper, a k-ε gas-liquid two-phase flow model has been introduced to model the interpolar gas-liquid two-phase flow field variation law, and on this basis, a coupled multi-physics field model for pulsed electrochemical machining processing is established to provide an accurate description of the interpolar multi-physics interaction mechanism. A quasi-steady-state iterative simplification algorithm based on heat source averaging is proposed to solve the problem that the time scale span of the dissolution process leads to a huge amount of simulation calculations. The simulation analyzes the dissolution characteristics at the micro time scale and macro time scale and compares them with the full precision method. The results show that the simulation accuracy of the two methods is the same, but the simulation calculation time of the simplified algorithm is reduced by two-thirds. The experimental platform was designed and built to carry out a series of experiments under different processing times, and the results effectively verified the correctness of the simulation method.

Lattice Boltzmann method for studying the dynamics of a single rising bubble in shear-thickening power-law fluids

Bubble motion in non-Newtonian fluids is widespread in various industrial processes such as crude oil extraction, enhancement of boiling heat transfer, CO<sub>2</sub> sequestration and wastewater treatments. Systems containing non-Newtonian liquids, as opposed to Newtonian liquids, have shear-dependent viscosity, which can alter the hydrodynamic characteristics of the bubbles, such as their size, deformation, instability, terminal velocity, shear rate, and ultimately affect the bubble rising behaviors. In this work, The dynamic behavior of bubble rising in a shear-thickened fluid was studied using an incompressible lattice Boltzmann non-Newtonian gas-liquid two-phase flow model. The effects of the rheological exponent <i>n</i>, the Eötvös number (<i>Eo</i>), and the Galilei number (<i>Ga</i>) on the bubble deformation, terminal velocity, and the shear rate were investigated. The numerical results show that the degree of bubble deformation increases as <i>Eo</i> grows, and the effect of <i>n</i> on bubble deformation degree is correlated with <i>Ga</i>. On the other hand, the terminal velocity of the bubbles increases monotonically and nonlinearly with <i>Ga</i> for a given <i>Eo</i> and <i>n</i>, and the effect of <i>n</i> on the terminal velocity of the bubbles gets stronger as <i>Ga</i> increases. When <i>Ga</i> is fixed and small, the terminal velocity of the bubble increases and then decreases with the increase of <i>n</i> at small <i>Eo</i>, and increases with the increase of <i>n</i> when <i>Eo</i> is large; but when <i>Ga</i> is fixed and large, the terminal velocity of the bubble increases with the increase of <i>n</i> in a more uniform manner. In addition, regions with high shear rates can be found near the left and right ends of the bubble. The size of these regions increases as both <i>Eo</i> and <i>Ga</i>, and it first increases and then decreases as <i>n</i> increases. Finally, the orthogonal experimental method was used to obtain the impact of the aforementioned three factors on the shear rate and terminal velocity. For the shear rate, the order of influence is <i>n</i>, <i>Ga</i> and <i>Eo</i> in descending order. For the terminal velocity, <i>Ga</i> has the greatest influence, followed by <i>n</i>, and <i>Eo</i> has the least influence.

Migration of Leaked Oil Vapor in Underground Water-Sealed Oil Storage Cavern Considering the Influence of Fractures

During the operation of underground water-sealed oil storage caverns, a large amount of oil vapor is generated due to volatilization. Oil vapor can easily leak into the surrounding rock, and fractures in the surrounding rock are usually the dominant channels for oil vapor leakage. To study the influence of fractures on oil vapor leakage and migration in underground water-sealed oil storage caverns during the oil storage period, a gas–liquid two-phase flow model of the fracture–pore dual medium in fractured rock mass was established. The program was implemented on the COMSOL platform by using weak-form PDE (partial differential equation). Then, taking an underground water-sealed cavern of an oil reserve as an example, the influence of the characteristic parameters of a single fracture on the evolution process of oil vapor leakage and migration during the oil storage period of the underground water-sealed oil storage cavern was studied. The results were further applied to the Huangdao underground oil depot project. The results show that the spatial distribution of oil vapor leakage is mainly affected by fractures. Through parameter sensitivity analysis, it was found that the geometric characteristic parameters of fractures will have a certain impact on the migration field of oil vapor leakage in underground caverns. Specifically, fracture permeability (kf), fracture width (df), and fracture inclination (θ) are positively correlated with oil vapor leakage parameters (oil vapor leakage range and leakage volume), while the distance between the fracture and the middle cavern (s) is negatively correlated with oil vapor leakage parameters (oil vapor leakage range and leakage volume). The relative influence of fracture geometry parameters on the migration process of oil vapor leakage during the oil storage period of the underground water-sealed oil storage cavern is in the following order: kf> df> s > θ. Engineering application shows that the existence of fractures affects the spatial distribution of oil vapor leakage and migration, and the relationship between oil vapor leakage parameters and oil storage operation time is a positive power function. The gas–liquid two-phase flow model of the fracture–pore dual medium in fractured rock mass developed in this study could offer a numerical simulation tool to assess and mitigate the risk of oil vapor leakage. The research conclusions can provide some references for related problems encountered in similar projects.

Numerical analysis for jet flow field on cleaning the outer wall of the double-layer injection needle

To avoid cross-contamination between different samples, improve the cleaning effect of the outer wall of the inner needle of the digital PCR detector, and reduce the cost of cleaning solution, the cleaning jet was simulated by FLUENT software using VOF gas-liquid two-phase flow model and PISO algorithm. In a certain range, the inlet velocity, cleaning solution viscosity, interfacial tension, and contact angle are changed to simulate the theoretical cleaning of the outer wall of the injection probe and the selection of various parameters under the best cleaning conditions is determined. The results show that the increase of inlet velocity has no significant effect on the increase of wall static pressure and the decrease of velocity increases; the increase of viscosity will greatly reduce the flow rate; higher interfacial tension requires higher inlet velocity to form a continuous jet; increasing the contact angle will not significantly reduce the static pressure and flow rate, and the residual sample is easier to clean. When the inlet velocity of 200mm /s is selected, the fluorine oil with a viscosity of 0.00124Paꞏs and interfacial tension of 16.2dyn/cm is used and the wall is coated with Teflon, the cleaning effect, and economy are excellent.

Design and optimization of a novel sinusoidal corrugated channel for microfluidic fuel cell with gas-liquid two-phase flow model

Membraneless microfluidic fuel cell (MMFC) has potential application prospects in micro-devices due to the characteristics of considerable output performance, superior cleanliness and easy miniaturization. Whereas, the performance of MMFC is restricted by the mass transfer of two-phase flow, which manifests as the inefficiency transportation in liquid phase and obstruction of gas phase. This paper proposes a novel sinusoidal corrugated channel (SCC) for MMFC though developing a three-dimensional two-phase model by coupling the multi-physics field to improve the cell performance in mass transfer, and further studies the two-phase flow characteristics of geometric parameters of SCC, including the amplitude A and angular frequency ω. Based on the optimal configuration in A of 0.5 mm and ω of 3 rad s−1, compared with the conventional straight channel, the increase ratios of maximum current density, power density, fuel utilization are 13.69%, 8.39% and 13.72%, respectively. Additionally, the gas volume fraction at the maximum power density decreases by 12.62%. This paper provides new insights and theoretical foundations for the study of MMFC flow field configurations, and furnishes references for the mass transfer intensification.

Numerical simulation and experimental study on an innovative vortex eliminator using a modified SST turbulence model for gas-liquid two-phase flow

Vortices in the turbine and pump threatens the safe operation of the unit. The purpose of this paper is to design an antivortex guide cone (AVGC) based on the dynamic characteristics of the vortices. A new approach with modified SAS-SST turbulence model was adopted to simulate the vortex, which is verified by model experiments. The velocity gradient is the key factor of vortex generation, so the antivortex device with vortex elimination blades adopt streamline structure to reduce the velocity gradient in vortex area. Three schemes with N0 (N0 is the number of vortex elimination blades) of 4, 6 and 8 are designed respectively. The study results indicate that the vortex elimination effect of AVGC varies greatly with different N0, resulting in great differences in the performance of the unit. Some local small-scale vortices still exist near AVGC in Scheme 1 (N0 = 4). In Scheme 2 (N0 = 6) is 6, vortices can be eliminated thoroughly with the least hydraulic loss and the unit efficiency improved by 1.8%. In Scheme 3 (N0 = 8), some new channel vortex will be generated in the blade channel, resulting in more hydraulic loss. Only the hydraulic loss produced by AVGC less than that produced by vortex that indicate the scheme is feasible. The research work can provide important academic value and engineering insights to eliminate vortex.

Simulations of Bubble Formation and Oscillation Behavior in Micro-Leakage Measurement System

In the process of measuring micro-leakage based on the bubble method, the physical parameters of the liquid phase have a great impact on the formation and movement of bubbles, thus affecting the measurement accuracy of the system. Therefore, it is of great significance to study the physical parameters of the liquid phase. At present, it is difficult to independently study the parameters of the liquid phase by experimental methods. In this paper, based on the Cahn-Hilliard phase field model, a gas-liquid two-phase flow model for the expression of leakage is established to independently study the influence of different physical parameters on the formation and movement of bubbles in the measuring system. Firstly, the effects of liquid medium density, dynamic viscosity coefficient and surface tension on the initial shape (aspect ratio), the generation period and the shape oscillation of bubbles after they leave the nozzle are analyzed. Then, an experimental platform for visualization of bubbles in two-phase flow based on machine vision is built, through which the morphological parameters of bubbles in the liquid phase can be obtained in real time. Finally, the results of visualization experiment and numerical simulation are compared. The results show that the initial aspect ratio error of bubbles obtained by visual experiment and numerical simulation is 1.8%, and the average oscillation period error is 12.3%. The results are basically consistent, which proves the rationality and correctness of the mathematical model established. It is found that the liquid with larger dynamic viscosity coefficient μ and density ρ and smaller surface tension σ can be selected as the liquid medium of the measurement system. It is more conducive to the accurate expression of micro-leakage in the measurement system, and the bubble shape can quickly reach a stable state. It provides theoretical support for improving the accuracy and stability of the micro-leakage measurement system.

Global strong solutions to the viscous liquid–gas two-phase flow model with slip boundary conditions in 3D exterior domains

This paper is concerned with the viscous liquid–gas two-phase flow model in a three-dimensional exterior domain with the slip boundary conditions. We are able to prove the existence of a global strong solution when the initial total energy is suitably small. The initial masses of liquid and gas are allowed to contain a vacuum, with no extra restriction between the initial masses of liquid and gas. It should be noted here that we consider the slip boundary condition in a three dimensional (3D) exterior domain which is in sharp contrast to result of Yu (2021) where they consider the Cauchy problem.

Numerical studies of two-phase water hammer flows using Godunov methods

In this paper, an explicit finite volume Godunov-type scheme is applied for a two-phase homogeneous water hammer flow model. The developed finite volume method is based on an exact Riemann solver for a gas–liquid two-phase flow model. This paper investigates the case of a water hammer problem caused by a rapid closing valve located in upstream of the pipeline. The performance of the proposed numerical method is validated against experimental data from literature. The good agreement found between the numerical and experimental results confirms the accuracy and the robustness of both the numerical methods and the proposed exact Riemann solver.

Modelling of paddy soil using the CFD-DEM coupling method

Soil dynamics has been the core of studying the mechanism of soil-tool interaction. However, it is very challenging to study the dynamics of paddy soil that contains a significant amount of water. In this study, a paddy soil model, namely coupling model was developed using the CFD-DEM coupling method. In the coupling model, spherical particles with Johnson-Kendall-Roberts (JKR) surface energy were used to represent paddy soil. The Volume of Fluid (VOF) gas-liquid two-phase flow model was used to represent the characteristics of the water in paddy field. A test and a simulation of soil rotation were performed to calibrate the critical model parameter of soil particle, JKR surface energy. The calibrated value was 2.5 J·m−2, and the relative average error between the simulation and the test was 1.27 %. To verify the accuracy of the coupling model, an experiment of a fertilizer banding opener was conducted in a paddy soil in laboratory conditions. Also, the interaction of the opener with paddy soil was simulated using the coupling model. Then, soil disturbance characteristics and the soil resistance force of the opener were compared between the experiment and model prediction. When using the coupling model to predict, the relative errors were less than 10 % for soil disturbance characteristics and less than 15 % for soil resistance force. This suggests that the model developed using the CFD-DEM coupling method is able to predict the dynamics of soil-tool interaction in paddy fields with reasonably good accuracies.

Investigation on the two-phase flow and heat transfer behaviors in a new central uniform dispersion-type heat exchanger

In order to improve the temperature uniformity of multiple chips, a new central uniform distributed heat exchanger (CUD) is designed. Firstly, adopting ethanol solution as coolant, the cooling ability of the heat exchanger is numerically investigated by using VOF gas-liquid two-phase flow model, and the two-phase flow experimental system is established to verify the correctness of the numerical results. The results show that the Tavg (average temperature of heat sources) error range between the experimental and numerical values is 1 K ~ 3 K, and the relative error of SDT (standard deviation of temperature) is 6% ~ 10%. This verifies the accuracy of the numerical simulation method. Secondly, the two-phase flow boiling heat transfer behavior are compared with that of single-phase flow with water as coolant. The results show that with the increase of inlet flow, the thermal resistance and average temperature of two-phase flow change are less than that of single-phase flow. This indicating that two-phase flow has better advantages in improving the temperature uniformity of multiple heat sources. Thirdly, the heat transfer characteristics of radiators with different Wi are studied. Compared with Case1, the boiling heat transfer coefficient of Case3 and Case4 can be increased by 12.3% and 18.3%, respectively. However, Case3 is a better choice by weighing the pressure drop. Finally, the prediction functions of the boiling heat transfer coefficient and pressure drop is established, and the multi-objective genetic algorithm is used to obtain the best parameters of this heat exchanger. The average heat transfer coefficient of the optimized heat exchanger can be increased by 7.56%, and the pressure drop can be reduced by 3.54% compared to the exchanger before optimization. Furthermore, the heat dissipation ability of the optimized heat exchanger design is studied numerically. The simulated results are in good agreement with the optimization results.

Modeling and Numerical Simulation of the Inlet Velocity on Oil–Water Two-Phase Vapor Separation Efficiency by the Hydrocyclone

The density of tar vapor and water vapor produced by coal pyrolysis is different. Different centrifugal forces will be generated when they flow through the hydrocyclone. The water vapor and tar vapor are divided into inner and outer layers. According to this phenomenon, the moisture in the tar can be removed. In this paper, a Eulerian gas–liquid two-phase flow model is established by numerical simulation to study the effect of inlet velocity on the separation effect of a designed hydrocyclone (split ratio 0.2). The results show that the inlet velocity and moisture content have an influence on the volume distribution characteristics, tangential velocity, axial velocity, pressure drop distribution, and separation efficiency of tar vapor and water vapor in the hydrocyclone. When the inlet velocity increases from 2.0 to 12.0 m/s, the central swirl intensity increases, and the negative pressure sweep range at the overflow outlet increases. The axial velocity increased from 2.8 to 14.9 m/s, tar vapor content at the overflow outlet decreased from 74% to 37%, and at the underflow outlet increased from 89% to 92%. When the moisture content is lower than 10%, the hydrocyclone with the split ratio of 0.20 is no longer suitable for the separation of oil–water two-phase vapor. However, when the water content is higher than 20%, the purity of tar vapor at the underflow outlet can reach 92%, and the overflow outlet needs multistage separation to realize tar purification.

Evolution of gas kick and overflow in wellbore and formation pressure inversion method under the condition of failure in well shut-in during a blowout

With ongoing development of oil exploration and techniques, there is a significant need for improved well control strategies and formation pressure prediction methods. In this paper, a gas-liquid transient drift flow model was established according to the gas-liquid two-phase flow characteristics during the gas kick. A Roe scheme was used for numerical calculation based on the finite volume method. The changes of bottom-hole pressure, casing pressure, the development law of cross-sectional gas holdup, and gas velocity, along with the vertical well depth, were analyzed through simulation examples. The time-series characteristics of mud pit gain were obtained by adjusting the formation parameter. The complex nonlinear mapping relationship between the formation parameters and the mud pit gain was established. The long short-term memory network (LSTM) of deep learning was used to obtain a formation pressure inversion when the blowout is out of control and the well cannot be shut-in. Experimental data from a well were used to verify the gas-liquid two-phase transient drift flow model based on the finite volume method, demonstrating that this method is reliable, with greatly improved prediction accuracy. This approach provides theoretical support for the early monitoring of gas kick during drilling, and for well-killing design and construction after uncontrolled blowout.

Investigation of two-phase jet flow from a degassing pipe used for a lake with potential gas-driven eruption

Gas-driven limnic eruption can happen in a lake with an aqueous gas solution that becomes supersaturated due to some reason. In this case, the exsolution of massive gases dissolved in the water could occur in a very short time, resulting in a disaster as happened in the Lake Nyos (Cameroon, Africa) in 1986. Using degassing pipe to artificially release the dissolved gases is a good way to minimize the risk of an eruption. In this study, a transient multi-component gas-liquid two-phase flow model of the degassing pipe used in Lake Nyos has been established and verified with the observed eruption data. The drift flux model has been used for modelling of a transient multi-component gas-liquid flow formed due to the spontaneous exsolution of gases dissolved in the water inside the degassing pipe. The governing equations for the mechanistic drift model include continuity equation for each phase, a single momentum equation for a homogeneous mixture of the fluid, constitutive equations for mass transfer rates between the phases, and the drift velocity formulas. The model considered not only CO2 but also CH4 as dissolved gases. The “chain reaction” conjecture predicted to have the degassing-point migrating downward with time during the transient degassing process is verified by using this model. The relationship between the eruption height and the CO2 concentration at the bottom of the degassing pipe has been simulated in detail. This relationship supplies people with a quick and convenient way to estimate the CO2 concentration in the lake, based on which one can evaluate the risk of lake eruption and hence to formulate or adjust the degassing plan. In addition, the effects of diameter and equivalent roughness of the degassing pipe on the eruption height has been investigated. Meanwhile, the eruption height upper-limit in different lake-depth scenarios has also been determined. Finally, the role of CH4 component in the degassing process has been analyzed. Although the influence of CH4 on eruption height can be neglected in Lake Nyos' case, CH4 as a dissolved gas plays an important role at Lake Kivu. The multi-component gas-liquid flow model developed in this study is useful to study the role of CH4 in the degassing process.

Numerical study of gas–liquid two-phase flow and noise characteristics for a water injection launching concentric canister launcher

Abstract In view of the poor thermodynamic environment problem of the self-powered launch of land-based concentric canister launcher (CCL), the launching scheme of injecting water at the bottom of launching tube is adopted to improve the thermodynamic environment of the launching system fundamentally. The solution program for liquid water vaporization is compiled and embedded into the homogeneous gas–liquid two-phase flow model, the source phase corrections of the momentum equation and the energy equation are also performed, and then the three-dimensional gas–liquid two-phase fluid dynamics model is established for the land-based CCL; analysis shows that the improvement of the thermal environment of the 35° and 45° water injection schemes is more better among these schemes. So coupling the mixture model, vaporization program and FW–H (Ffowcs Williams Hawkings) noise model, the noise distribution law in the bottom of the launcher cube for 35 and 45 water injection angles is discussed; in the intermediate frequency range, the −45° water injection scheme is about 2–10 dB higher than the noise signal of the −30° water injection scheme. Finally, it is recommended to optimize the overall thermal environment of the CCL by using the −30° preferred water injection scheme with both cooling effect and noise control.

Study on Flow Characteristics of Working Medium in Microchannel Simulated by Porous Media Model

As a phase change evaporator, a microchannel array heat exchanger is of great significance in the field of microscale heat dissipation. The performance of which strongly depends on the flow resistance, capillary force, and other factors. In order to improve the heat dissipation efficiency, it is necessary to perform an in-depth study of the characteristics of microchannel flow using numerical simulation. However, the current simulation model requires high computational cost and long simulation time. To solve this problem, this paper simplifies the numerical simulation of the rectangular parallel array microchannels by building the basic flow model based on the concept of porous media. In addition, we explore the effect of aspect-ratio (AR), hydraulic diameter, inlet velocity, and other parameters of fluid flow behavior inside the microchannels. Meanwhile, a user-defined function (UDF) is formulated to add the capillary force into the model to introduce capillary force into the porous media model. Through the above research, the paper establishes the porous media model for single-phase and gas-liquid two-phase flow, which acts as a simplification of microchannel array simulation without grossly affecting the results obtained. In addition, we designed and manufactured experiments using silicon-based microchannel heat exchangers with different-ratios, and combined with the visualization method to measure the performance of the device and compared them with simulation results. The theoretical model is verified through the suction experiment of array microchannel evaporator capillary core. The simplified model of microchannel array significantly saves the computational cost and time, and provides guidance for the related experimental researches.

Modeling of multiphase flow in marine gas hydrate production system and its application to control the production pressure difference

The accuracy control of the production pressure difference is of great importance to the efficient development of marine gas hydrates through depressurization. But from the field trial production, the existing control method of bottom hole pressure is difficult to achieve the expected depressurization target. To this end, a transient gas-liquid two-phase flow model in marine gas hydrate production system was established, which considers the coupling interactions of the wellbore, the formation and the downhole electric submersible pump (ESP). Besides, an automatic control method of production pressure differential was proposed through real-time optimization of the pump displacement. Using the model, a series of numerical simulations were performed to study the multiphase flow rules in the production well. The results indicated the depressurization process could be divided into four stages based on the characteristics of gas-liquid flow in different pipelines. During the depressurization, the liquid level in the well exhibited a trend of first falling and then rising, and may eventually reach the wellhead for continuous drainage. In addition, sensitivity analysis showed that the smaller the pipe diameter, the higher the gas-liquid separation efficiency, and the greater the possibility of continuous drainage from the gas production pipeline. As the result, it was verified that the proposed model and method can achieve the expected depressurization well, which will provide useful references for the production design during the development of marine natural gas hydrate resources.

Study on Flow Interference of Multi-group Parallel Jets between Heat Transfer Tubes

In order to find an approach to optimize the hydraulic cleaning equipment of steam generator secondary side of CPR1000 reactor, the Computational Fluid Dynamics (CFD) method was used to simulate the flow of multiple groups of parallel jets. In this simulation, the RNG k-ε turbulence model and the gas-liquid two-phase flow model is employed to distribute the jet flow between heat transfer tubes. The results show that with the increase of the jet angle, the pressure aggregation on the tube sheet decreases obviously, which is caused by the deflection force due to the pressure difference between the two sides of the jet. With the jets distance increasing, the interaction between jets decreases obviously. When the distance is up to more than nine times of tube spacing, the force that causes deflection of the jet will almost disappear. With this distance, the jets can maintain a good linearity and obtain a satisfied cleaning effect on the heat transfer tubes.

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

ABSTRACT Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow. However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semi-empirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.