Viscous Two-phase Flow Research Articles

Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential

The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier–Stokes–Cahn–Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results.

A Compressible Formulation of the One-Fluid Model for Two-Phase Flows

In this paper, we introduce a compressible formulation for dealing with 2D/3D compressible interfacial flows. It integrates a monolithic solver to achieve robust velocity–pressure coupling, ensuring precision and stability across diverse fluid flow conditions, including incompressible and compressible single-phase and two-phase flows. Validation of the model is conducted through various test scenarios, including Sod’s shock tube problem, isothermal viscous two-phase flows without capillary effects, and the impact of drops on viscous liquid films. The results highlight the ability of the scheme to handle compressible flow situations with capillary effects, which are important in computational fluid dynamics (CFD).

A conservative sharp interface method for incompressible viscous two-phase flows with topology changes and large density ratio

Topology change of interfaces often leads to unresolved interface structures such as tiny droplets/bubbles, which requires the regularization of the order parameter and consequently causes artificial modification of volume fraction of the fluids. This could give rise to unphysical oscillation of pressure and cause the failure of computation, in particular for two-phase flows involving large density ratio. We develop a robust conservative sharp-interface method for incompressible viscous two-phase flows with topology changes and large density ratio. The method consists of a cut-cell meshing approach that dynamically generates unstructured meshes in the vicinity of the interface, a second-order finite volume scheme in the Arbitrary Lagrangian–Eulerian framework, and a projection method. The jump conditions at the interfaces are incorporated into the calculation of fluxes at the cell faces of the unstructured meshes that coincide with the reconstructed interfaces, to ensure that they are strictly satisfied at the interface. Unlike a pseudo-compressible formulation used in the previous study, the projection method prevents the oscillation of pressure in the presence of topology change. Special treatments are proposed to further improve the robustness of the method when dealing with unresolved interface structures, including removal of tiny droplets, adjustment of spatial discretization and restriction of the maximum curvature calculated. In such a way, two-phase flows involving topology change and large density ratio can be numerically resolved in a sharp-interface, efficient and robust manner. The performance of the proposed method is systematically examined by a series of numerical tests, including spurious currents, oscillation of a suspended droplet, droplet deformation in shear flows, breakup of a liquid thread, rising bubbles and partial coalescence of a droplet with a pool. The numerical results are compared against analytical solution, benchmark results or experimental data, and good agreement has been achieved.

A mass-preserving level set method for simulating 2D/3D fluid flows with deformed interface

This research paper focuses on the development of a novel interface-capturing solver for predicting two-phase flow in 2D/3D Cartesian meshes within the framework of Eulerian approaches. The primary objective is to ensure mass conservation and accurate capture of interface topology. To achieve this, a mass-preserving level set advection equation formulated as a scalar sign-distance function is proposed. The key innovation of the Eulerian solver lies in the incorporation of a scalar speed function for robust reconstruction of the classical level set equation. The effectiveness and reliability of the proposed flow solver in solving incompressible two-phase viscous flow equations are demonstrated through several benchmark problems.

Nonlinear stability of planar stationary solutions to the viscous two-phase flow model in [formula omitted

In this paper, we consider the outflow problem of the viscous two-phase flow model in R+3. We show the global existence of the strong solution to the outflow problem and its convergences to the corresponding the planar stationary solution as time grows up with respect to the supersonic, subsonic, or sonic state respectively at the far field.

Global classical solutions to the viscous two-phase flow model with slip boundary conditions in 3D exterior domains

We consider the two-phase flow model in 3D exterior domains with slip boundary conditions. We establish the global existence of classical solutions of this system, provided that the initial energy is suitably small. Furthermore, we prove that the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.

Методика проектирования и оптимизации лопастной системы радиально-осевой гидротурбины

A technique for designing the blade systems of Francis turbine is proposed. Starting with the determination the main parameters of the turbine components, where it is compatible with the operation of a hydraulic turbine at a given head. Also, the diameter of the impeller required to generate the nominal power. Then, using the realizing of the quasi-three-dimensional approach, the shape of the blade is obtained as a first approximation for a given blade, a series of calculations of three-dimensional single-phase and twophase viscous flow is performed to determine the efficiency of the turbine at different operating modes, the cavitation properties of the turbine, respectively. The critical cavitation coefficient is determined for three operating points of hydraulic turbines. Using Multi-objective Genetic Algorithm (MOGA), the optimization of energy and cavitation properties is carried out for three operations pointes. The mathematical model is based on the Latin hypercube method. As a result of the optimization, a significant improvement in the efficiency of the hydraulic turbine has been obtained, especially at partial loads.

An Exactly Curl-Free Staggered Semi-Implicit Finite Volume Scheme for a First Order Hyperbolic Model of Viscous Two-Phase Flows with Surface Tension

An Exactly Curl-Free Staggered Semi-Implicit Finite Volume Scheme for a First Order Hyperbolic Model of Viscous Two-Phase Flows with Surface Tension

Boundary vorticity dynamics of two-phase viscous flow

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.

A Navier–Stokes numerical wave tank with a pressure-based relaxation zone method

In the relaxation zone method for numerical wave tank modelling, the numerical fields are usually relaxed in the generation zone to the solution given by the potential theory. In the adopted procedure, the two-phase viscous flow is blended with the potential solution and this underlying inconsistency in the generation region can lead to instability in the flow. In this work, we present a new method for the wave generation in the context of the relaxation zone method which overcome the issue on the velocity forcing by introducing a body force equal to the potential pressure gradient. Results show that the method gives accurate results when compared with classical test case for wave propagation.

Global Classical Solutions to the Viscous Two-Phase Flow Model with Navier-type Slip Boundary Condition in 2D Bounded Domains

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small. Moreover, the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.

Development of numerical methods to simulate the melting of a thermal protection system

In this paper, numerical methods are developed and detailed in order to be able to compute the ablation of metallic thermal protection system. In this complex multi-physics problem, the thermal state inside a solid domain and a two-phase viscous flow have to be computed. Since the two fluid phases are non-miscible, an extension of the five-equation model to dissipative effects is considered. An operator splitting strategy is used to separate the different phenomena according to their own propagation speed. An implicit time integration is performed for the acoustic+dissipative step while the transport step is computed with an explicit scheme. The hyperbolic part of the acoustic+dissipative step is solved in a non-conservative form using a Godunov-type scheme based on a simple Riemann solver. A classical discretization is used for the dissipative terms, and also for the heat equation inside the solid domain. Several approaches are detailed in order to prevent the numerical diffusion of the material interface in the transport step. Finally, since moving grids are used to capture accurately the melting front, an ALE formulation of the numerical schemes for both fluid and solid domains is given in a multidimensional framework. A fluid-solid coupling algorithm is then proposed to compute such a complex multi-physics problem.Numerical simulations show the validity and the robustness of the implicit-explicit scheme used for the discretization of the five-equation system. The last test case, namely the melting of an aluminium solid block by a lid-driven cavity filled with air, shows that the numerical tools developed here are robust enough to compute complex configurations involving a two-phase flow with high density ratios and a solid part.

Distributed Optimal Control of the 2D Cahn–Hilliard–Oberbeck–Boussinesq System for Nonisothermal Viscous Two-Phase Flows

We analyze a distributed optimal control problem where the state equation is governed by the coupling of the two-dimensional Cahn–Hilliard and Oberbeck–Boussinesq systems modelling incompressible viscous two-phase flows with convective heat transfer. Pointwise constraints are imposed on the controls that act as external sources in the fluid and convection–diffusion equations. The objective functional is of tracking-type that consists of a weighted energy of the difference between the state and a desired target. We establish the existence of optimal controls, the differentiability of the control-to-state operator, and the necessary and sufficient optimality conditions. For initial and target data with finite energy norms, limited space–time regularity of the adjoint states arises due to convection and surface tension.

Frictional Pressure Drop and Liquid Holdup of Churn Flow in Vertical Pipes with Different Viscosities

Churn flow commonly exists in the pipe of heavy oil, and the characteristics of churn flow should be widely understood. In this paper, we carried out air and viscous oil two-phase flow experiments, and the diameter of the test section is 60 mm. The viscosity range of the oil was 100~480 mPa·s. Based on the measured liquid holdup and pressure drop data of churn flow, it can be concluded that, due to the existence of liquid film backflow, positive and negative frictional pressure drop can be found and the change of frictional pressure drop with the superficial gas velocity is related to superficial liquid velocity. With the increase of viscosity, the change rate of frictional pressure drop increases with the increase of the superficial gas velocity. Combining our previous work and the Taitel model, we proposed a new pressure drop model for viscous oil-air two-phase churn flow in vertical pipes. By comparing the predicted values of existing models with the measured pressure drop data, the proposed model has better performance in predicting the pressure drop.

Characteristic of Free-rolling Motion of Twodimensional Rectangular Body in the Regular Wave

his study investigated the characteristics of rolling motion of rectangular body for regular waves with a range of wave periods that are equal to and longer than its natural roll period. Using the volume of fluid (VOF) method based on the finite volume method with standard k-ε turbulence model, twodimensional (2D) incompressible viscous two-phase flow is simulated in a wave tank with the rectangular body. The present study introduces a wave period ratio (Tr=TW/TN) of an incident wave period (TW) to the roll natural period (TN) of body. The wide range of 1≤ Tr ≤2.5 is considered in this study. In the wave periods considered in this study, the roll motion shows two distinct patterns. One is the single oscillatory motion which appears in the period ratio of 1≤ Tr ≤1.7. The other is the double oscillatory motion in 1.8≤ Tr ≤2.5. In these two regimes, flow and the roll motion of the rectangular body, which are induced by the fluid flow-structure interaction for various wave periods, are carefully investigated to reveal the mechanism of two roll modes.

Coupling analysis for sway motion box with internal liquid sloshing under wave actions

This work investigates the coupling effects of internal sloshing flow on the sway motion response of rectangular box sections. The impulse-response-function method is employed for external wave action, while the viscous two-phase flow model with the volume of fluid interface capturing technique based on the OpenFOAM® package is adopted for the internal sloshing flow. A new lower critical frequency is defined to understand the coupling effects of the internal sloshing flow, which is the corresponding frequency of the minimal sway motion amplitude. The external wave and internal sloshing forces are out-of-phase at the lower critical frequency. The numerical simulations show that the lower critical frequency is equivalent to the sloshing natural frequency when the internal sloshing flow is in the non-breaking pattern. The non-breaking sloshing-induced force approaches the same magnitude as the external wave force, which leads to a zero-amplitude sway motion. When the internal sloshing exhibits the breaking phenomenon, a phase transition of the internal sloshing force can occur, which causes the lower critical frequency to be smaller than the sloshing natural frequency. The increased incident wave amplitude or decreased tank breadth can strengthen the nonlinear behavior of the sloshing coupling action. That is, the sway motion response deviates more from the linear sloshing flow results, including the smaller lower critical frequency and the larger minimal sway motion amplitude. However, with the increased breaking-sloshing-induced nonlinearity, the difference in the sway motion response between the coupling and uncoupling results reduces, which implies a lower coupling effect.

Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line

Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line

A New Model for Predicting Slug Flow Liquid Holdup in Vertical Pipes with Different Viscosities

The development of heavy oil has attracted attention in recent times. With increasing fluid viscosity, slug flow has become the most common flow pattern in oil and gas pipeline flow. The accurate prediction of slug flow parameters is an urgent problem to be solved in heavy oil development. In this paper, gas–liquid two-phase flow experiments with different viscosities were carried out in a 60-mm vertical pipe. The superficial velocity ranges of gas and liquid were 0.51–7.42 m/s and 0.08–0.21 m/s, respectively. Based on the measured data, the investigation revealed that liquid holdup increases with an increase in viscosity and superficial liquid velocity. This study presents a new liquid holdup model of slug flow for viscous two-phase flow in vertical pipes. Based on the statistical analysis, the proposed correlation accurately predicts the liquid holdup of slug flow in a vertical pipe for the present measured data and performs best in comparison with existing correlations.

Linear and Nonlinear Stability Analysis in Microfluidic Systems

In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologi... | Find, read and cite all the research you need on Tech Science Press

The suitability of the dimensionless terms used in correlating slug liquid holdup with flow parameters in viscous two-phase flows

Empirical correlations have been proposed for estimating slug liquid holdup, HLS, using Froude number, NFr, viscosity number, Nμ, and inverse viscosity number, Nf. Some of these correlations show physically inconsistent behavior when tested against each flow parameter due to relying on regression analysis without considering the effect of each flow parameter included in these numbers.This work analyzes the performance of these numbers and provides guidelines for the selection of the correct combination of non-dimensional numbers. Our analyses indicate that the Nμ is not suitable for revealing the effect of liquid viscosity on HLS; instead it reveals the effect of mixture velocity due to its dominant effect. Also, the product of the NFr and Nμ, both with positive exponents, is unsuitable for correlating HLS with liquid viscosity. This combination results in a decrease in HLS with increasing liquid viscosity, contradicting the experimental observations. Furthermore, the product of the NFr and Nf, both with positive exponents, results in a decrease in HLS with increasing pipe diameter, opposing experimental findings reported in the literature. Finally it is concluded that the most suitable combination for correlating HLS is the product of the NFr with a positive exponent, and the Nμ with a negative exponent.