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Direct numerical simulations are performed to investigate the characteristics of a turbulent core–annular flow with water-lubricated high viscosity oil in a horizontal pipe. Six different superficial velocity ratios ($\\,j_w/j_o = 0.057\\unicode{x2013}0.41$) are examined by changing the water superficial velocity $j_w$ for a fixed oil superficial velocity $j_o$. The pressure drops in the pipe and the shapes of the phase interface agree well with those from previous experiments. The oil core flow is almost a plug flow, and the gaps between the phase interface and pipe wall are narrow and wide near the upper and lower surfaces of the pipe, respectively, due to the buoyancy. Within a narrow gap, water is confined mostly in a valley region of the wavy phase interface and hardly goes through its crest. On the other hand, water near the phase interface at a wide gap convects downstream almost at the core speed and the flow near the wall is similar to that of single-phase wall-bounded turbulent flow. The annular flow is characterized by three different regimes depending on the clearance Reynolds number ($Re_c$) based on the core velocity and local gap size: laminar Couette flow driven by the core for $Re_c \\le 600$, transitional flow for $600 < Re_c < 2500$ and turbulent flow for $Re_c \\ge 2500$. The minimum pressure drop occurs at $j_w/j_o = 0.11$ in the early transition regime. For all $j_w/j_o$ considered, the negative lift force acting on the core comes from the pressure force which balances the buoyancy.

Predicting the temperature distribution in laminar two-phase flows is essential in a wide range of engineering applications, like heat dissipation of electronic equipment and thermal design of biological reactors. Motivated by this, we extend the classical Graetz problem, studying the heat transfer between two flowing phases in a core-annular flow configuration. Using a rigorous two-scale asymptotic analysis, we derived two coupled one-dimensional advection–diffusion heat-transfer equations (one for each phase) embedding the effects of advection, diffusion (both axial and transverse) and viscous dissipation. Specifically, the heat-transfer mechanisms are described through effective velocity and effective diffusion coefficients, while the interaction between the phases is accounted for via ad hoc coupling and source terms, respectively. The dynamics of the problem is controlled by seven dimensionless groups: the Péclet and Brinkman numbers, the heat flux, the viscosity, thermal diffusivity and thermal conductivity ratios, and the volume fraction. Our analysis reveals the existence of two main regimes, depending on the disparity in thermal conductivity between the phases. When the conductivity ratio is of order one, the problem is strongly coupled; otherwise, the phases are thermally decoupled. Interestingly, we investigate the evolution of the heat-transfer coefficient in the thin-film limit, shedding light on the most common assumptions underlying extensively used models in the context of film flows. Finally, we derived closed-form scaling laws for the Nusselt number clarifying the impact of the phases topology on heat-transfer dynamics. Since our model has been derived by first principles, we hope that it will improve the understanding of two-phase forced convection.

The linear stability characteristics of pressure-driven core-annular pipe flow of two immiscible fluids are considered to investigate the effects of the density and viscosity ratios, the Reynolds number, the interface location and the interfacial tension. Both liquid–liquid and gas–liquid systems are examined. A new type of interfacial mode associated with the axisymmetric and corkscrew perturbations is discovered for certain ranges of the viscosity and density ratios in the immiscible liquid–liquid system. Two distinct unstable regions at long and short wavelengths are observed. The long-wavelength unstable region forms a close loop, indicating that it is not a Tollmien–Schlichting mode. The new interfacial mode observed in the present study is similar to that discovered by Mohammadi & Smits (J. Fluid Mech., vol. 826, 2017, pp. 128–157) in two-layer Couette flow for low viscosity ratios. In contrast to the two distinct unstable regions found in the immiscible configuration, the corresponding miscible system contains only one unstable mode. It is found that, in the liquid–liquid systems, the corkscrew (axisymmetric) perturbation is dominant when the annular fluid is less (more) viscous than the core fluid. On the other hand, the axisymmetric perturbation is always the dominant one in the gas–liquid system. In gas–liquid systems, the interfacial tension stabilises the short-wave and destabilises the long-wave perturbations, while increasing the interface radius stabilises the flow due to the presence of a plug region in the pipe.

Understanding droplet sizes is crucial for modeling gas–liquid annular flow and has many applications across various industries. This paper presents a comprehensive review and analysis of experimental data on droplet-size characteristics in gas–liquid annular flow from the open-source literature. The existing models for droplet-size predictions are evaluated against experimental data. Based on the data analysis, we propose two new correlations to predict the maximum droplet diameter and Sauter mean droplet diameter. Model evaluation and parametric study show that the new correlations capture the effects of fluid properties and flowing conditions on the droplet diameters well, outperforming other existing models. The average absolute relative errors are reduced to 14.8% and 29% for the maximum droplet diameter and the Sauter mean droplet diameter, respectively.

Buoyancy-driven exchange flows are common to a variety of natural and engineering systems, ranging from persistently active volcanoes to counterflows in oceanic straits. Laboratory experiments of exchange flows have been used as surrogates to elucidate the basic features of such flows. The resulting data have been analysed and interpreted mostly through core–annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we demonstrate that some of the variability observed in laboratory experiments and natural systems is a consequence of the inherent bistability of core–annular flow. Using a core–annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes, we identify two mathematically valid solutions at steady state: a solution with fast flow in a thin core and a solution with relatively slow flow in a thick core. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Through direct numerical simulations, we confirm the hypothesis that core–annular flow in vertical tubes is inherently bistable. Our simulations suggest that the bistability of core–annular flow is linked to the boundary conditions of the domain, which implies that is not possible to predict the realized flow field from the material parameters of the fluids and the tube geometry alone. Our finding that buoyancy-driven exchange flows are inherently bistable systems is consistent with previous experimental data, but is in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. Our results have important implications for data interpretation by analytical models and may also have interesting ramifications for understanding volcanic degassing.

Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

We experimentally study the transition from droplet to wave regimes in microfluidic liquid–liquid multiphase flows having large differences in viscosity. A unified approach based on periodic pattern analysis is employed to study relationships between dispersed and separated flow regimes, including dripping, jetting, capillary waves, inertial waves and core–annular flows over a wide range of flow rates and viscosity contrasts. We examine the morphology and dynamics of each flow regime based on wavelength, frequency and velocity of repeating unit cells to elucidate their connections and to develop predictive capabilities based on dimensionless control parameters. We demonstrate in particular that pattern selection is contingent upon the propagation velocity of droplets and waves at the transition. We also investigate microfluidic wave breaking phenomena with the formation of ligaments and droplets from wave crests in both capillary and inertial wave regimes. This work expands conventional multiphase flow regimes observed in microchannels and shows new routes to disperse highly viscous materials using interfacial waves dynamics in confined microsystems.

The coated particle ICD water control technology has been widely used in horizontal well completion in offshore oil fields in recent years, but there is a lack of research on the simulation and prediction methods for liquid production profiles. By analyzing the dynamic inflow process of fluid, starting from the laws of momentum conservation and mass conservation, a coupled mathematical model of horizontal well reservoir wellbore pressure drop considering the mechanism of annular flow resistance was established, and solved through programming. Based on the actual well data of a certain block in an offshore oilfield, a horizontal well reservoir production model was established. The calculation results of the example show that the annular flow resistance and water control technology can effectively control the balanced liquid production of horizontal wells, thereby increasing the anhydrous oil recovery period and improving the oil recovery rate of the oilfield; The coupling model simulation and prediction method can fully reflect the mutual influence between the oil reservoir, wellbore annulus, ICD, and horizontal wellbore; The effective diameter of the ICD valve affects the changes in oil production and water content. The placement of the ICD well section has a significant effect on water control, and the compactness of the filled particles has a certain impact on pressure and water content changes.

The characteristics of a turbulent core-annular flow with water-lubricated high viscosity oil in a vertical pipe are investigated using direct numerical simulation, in conjunction with a level-set method to track the phase interface between oil and water. At a given mean wall friction ( $Re_{\\unicode[STIX]{x1D70F}}=u_{\\unicode[STIX]{x1D70F}}R/\\unicode[STIX]{x1D708}_{w}=720$ , where $u_{\\unicode[STIX]{x1D70F}}$ is the friction velocity, $R$ is the pipe radius and $\\unicode[STIX]{x1D708}_{w}$ is the kinematic viscosity of water), the total volume flow rate of a core-annular flow is similar to that of a turbulent single-phase pipe flow of water, indicating that water lubrication is an effective tool to transport high viscosity oil in a pipe. The high viscosity oil flow in the core region is almost a plug flow due to its high viscosity, and the water flow in the annular region is turbulent except for the case of large oil volume fraction (e.g. 0.91 in the present study). With decreasing oil volume fraction, the mean velocity profile in the annulus becomes more like that of turbulent pipe flow, but the streamwise evolution of vortical structures is obstructed by the phase interface wave. In a reference frame moving with the core velocity, water is observed to be trapped inside the wave valley in the annulus, and only a small amount of water runs through the wave crest. The phase interface of the core-annular flow consists of different streamwise and azimuthal wavenumber components for different oil holdups. The azimuthal wavenumber spectra of the phase interface amplitude have largest power at the smallest wavenumber whose corresponding wavelength is the pipe circumference, while the streamwise wavenumber having the largest power decreases with decreasing oil volume fraction. The overall convection velocity of the phase interface is slightly lower than the core velocity. Finally, we suggest a predictive oil holdup model by defining the displacement thickness in the annulus and considering the boundary layer characteristics of water flow. This model predicts the variation of the oil holdup with the superficial velocity ratio very well.

Recent advancements in drilling technology have driven substantial progress in cuttings removal tool development, particularly for addressing borehole cleaning challenges in highly deviated directional critical factors in operational safety and efficiency improvement. Despite these innovations, two fundamental challenges persist: an incomplete understanding of mechanistic cuttings removal processes and an insufficient methodological framework for optimal tool installation. Studying the installation positions and assessing the effects of two cuttings removal are essential steps to advance the application of such tools. This investigation was initiated with a comprehensive analysis of particle settling dynamics and migration behaviors in annular wellbore spaces. Building upon Moore's terminal settling velocity equation, a modified model was developed to characterize the transport patterns of cuttings. Through model integration, the precise positioning of the efficient Vortex Cuttings Removal Tool (VCRT) was determined at 188 m from the bit. Subsequently, Computational Fluid Dynamics (CFD) numerical simulation was employed to reveal distinct annular flow field characteristics between VCRT and conventional drilling tools. Field validation in Well Z401X demonstrated a strong correlation between empirical measurements and simulated predictions, with pressure drop deviations of 6.25% and rotational speed variances limited to 7.50%. Analytical results confirmed VCRT's superior performance, exhibited 36.43% reductions in cuttings accumulation at the wellbore's lower quadrant compared to conventional drilling tools. The application of VCRT accelerated cuttings migration velocity in the annular space, significantly increasing the volume of returned onsite cuttings. Friction resistance decreased by approximately 35.90%, indicating higher cuttings removal efficiency than conventional drilling tools.