Liquid-gas Two-phase Flow Model Research Articles

Numerical simulation of molecular conformation evolution during mold filling process in a complex cavity

In the mold filling process, polymer melt will suffer the shear stress and stretch, which has important influences on the mechanical properties and surface quality of the final plastic products. In this paper a gas-liquid two-phase flow model for a viscoelastic fluid is proposed and used to simulate the mold filling process, in which the finitely extensible nonlinear elastic dumbbell with Peterlin closure (FENE-P) model and cross-WLF viscosity model combined with Tait state equation are used to describe the constitutive relationship and viscosity change of the viscoelastic melt, respectively. Meanwhile, the improved coupled level-set and volume-of-fluid method is used to trace the melt front, and the finite volume method on non-staggered grid is used to solve the mass, momentum, and energy conservation equations. Firstly, the R-function, an excellent implicit modeling tool of constructive solid geometry, is employed to establish the shape level-set function to describe the complex mold cavities based on the signed distance functions that represent basic geometries. And the immersed boundary method is applied to dealing with the complex mold cavities by using the shape level-set function. The benchmark problem of the flow past a cylinder is simulated to verify the validity of the FENE-P model, where the orientational ellipses are used to describe the molecular orientation and deformation. Moreover, the visualization of polymer molecular deformation is achieved. Then, the non-isothermal filling process of the viscoelastic fluid is simulated in an annular mold cavity with two circular insets, and the behaviors of the molecular orientation, temperature and stress in the filling process are shown and analyzed in detail. Finally, the problems are also discussed that how the injection velocity, melt and mold temperatures influences on the molecular conformation and solidified layer thickness. Numerical results show that the computational framework proposed in this paper can be successfully used to simulate the non-isothermal mold filling process in the complex mold cavity. Increasing properly the injection velocity can reduce the heat loss and improve the strength of the weld line. The higher the melt or mold temperature, the thinner the solidified layer is. Thus, increasing the injection velocity, as well as raising the melt and the mold temperatures will improve or remove the weld line in melt filling process.

Numerical investigation of degas performance on impeller of medium-consistency pump

Medium-consistency technology is known as the process with high efficiency and low pollution. The gas distribution was simulated in the medium-consistency pump with different degas hole positions. Rheological behaviors of pulp suspension were obtained by experimental test. A modified Herschel–Bulkley model and the Eulerian gas–liquid two-phase flow model were utilized to approximately represent the behaviors of the medium-consistency pulp suspension. The results show that when the relative position is 0.53, the gas volume ratio is less than 0.1% at the pump outlet and 9.8% at the vacuum inlet, and the pump head is at the maximum. Because of the different numbers of the impeller blades and turbulence blades and the asymmetric volute structure, the gas is distributed unevenly in the impeller. In addition, the pump performance was tested in experiment and the results are used to validate computational fluid dynamics outcomes.

A horizontal stratified gas–liquid two-phase flow model for the two-fluid model in the WCOBRA/TRAC-TF2 PWR safety analysis code

For the two-phase flow in a horizontal pipe, individual phases may separate because of gravity. This horizontal stratification significantly impacts interfacial drag, interfacial heat transfer and wall drag of the two-phase flow. Due to the low interfacial drag and the low interfacial heat transfer, the horizontal stratification in reactor coolant systems is a highly important phenomenon during a postulated loss-of-coolant accident in PWR. The horizontal stratification also impacts other SBLOCA phenomena such as the offtake phenomenon and the cold leg direct contact condensation phenomenon.For the two-fluid model in the WCOBRA/TRAC-TF2 LOCA safety analysis computer code, a horizontal stratification criterion was developed following the inviscid Kelvin–Helmholtz neutral stability analysis. The horizontal stratification criterion combines the Taitel–Dukler model and the Wallis–Dobson model and captures the test data better. The stratification criterion was assessed against various experimental data with a wide range of pressures and pipe sizes. The stratification criterion also matches well with the transition boundaries predicted by the viscous Kelvin–Helmholtz model.The adequacy of the horizontal stratification model is confirmed by examining the predicted flow regime in a horizontal pipe with the measured data of the high pressure TPTF two-phase flow experiments. The void fractions for the horizontal flow are predicted with a good accuracy, which indicates that the interfacial drag and the wall drag in the two-fluid model are properly modeled and the two-fluid momentum equations with the hydraulic slope term reasonably capture the influence of inlet and outlet boundary conditions expected in the PWR LOCA simulation.

Blow up criterion of strong solution for 3D viscous liquid–gas two-phase flow model with vacuum

In this paper, we establish a blow-up criterion to the local strong solution to the three dimensional (3D) viscous liquid–gas two-phase flow model only in terms of the divergence of the velocity field. Moreover, the initial vacuum is allowed, and there is no extra restriction on viscous coefficients. Both the Cauchy problem and initial-boundary value problem are considered in this paper.

On the well-posedness for a multi-dimensional compressible viscous liquid–gas two-phase flow model in critical spaces

This paper is dedicated to study of the Cauchy problem for a multi-dimensional (\({N \geq 2}\)) compressible viscous liquid–gas two-phase flow model. We prove the local well-posedness of the system for large data in critical Besov spaces based on the L p framework under the sole assumption that the initial liquid mass is bounded away from zero.

Global existence and optimal convergence rates for the strong solutions in [formula omitted] to the 3D viscous liquid–gas two-phase flow model

This paper is concerned with the Cauchy problem of the three-dimensional viscous liquid–gas two-phase flow model. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small and its L1-norm is bounded. Moreover, the optimal convergence rates are also obtained for such a solution.

Pressure Wave Propagation with Bubble Breakup Phenomena in a Venturi Tube

A micro-bubble generator with a venturi tube generates many micro-bubbles and pressure waves with bubble breakup phenomena. However, physical characteristics of the pressure wave in the venturi tube are not clarified. In the present study, a propagation speed and a pressure value of the pressure wave in the venturi tube were measured by an observation with a high speed video camera and a pressure transducer. In addition, an effect of void fraction on the pressure wave was investigated with the observation, the pressure measurement and a void fraction measurement with a constant electric current method. From these measurements, it was confirmed that the propagation speed decreased with an increase of the void fraction. Besides, the speed followed a sonic speed of a homogeneous model for gas-liquid two-phase flow. Therefore the pressure wave propagation was affected by the gas volume of bubbly flow.

Numerical Simulation of Filling Process in Large Steel-Ingot

A three dimensional incompressible gas-liquid two-phase flow model is proposed to accurately simulate the fluid flow of casting's mould filling process. The gas entrapment during mould filling is studied under different initial velocity and pressure conditions. The simulation results show that the velocity of change has a larger effect on gas entrapment, Initial velocity affects the distribution of temperature field,meanwhile gas entrapment parts specialized sampling is proceeded for qualitative detection at the scene. The simulated result is consistent with the experimental result, which can be reference for the process parameters selection and mold design of filling process in large steel-ingot. Keywords: gas entrapment, the filling process , the numerical simulation

Simulation of Microbubbles Drag Reduction on Nonsmooth Surface with Hydrophobic Property

The friction resistance accounts for a large proportion of the total resistance, during the navigation of ships and underwater vehicles. Drag reduction techniques can significantly reduce the friction resistance of the wall and improve the speed of navigation. This paper combine microbubbles drag reduction technology and nonsmooth and hydrophobic surface technology. Building different analysis models, considering the dimples size of nonsmooth surface , the contact angle of surface and wall roughness, study the law between drag reduction and parameters of the wall by gas-liquid two-phase flow model. Under the same conditions, analysis results show that the performance of drag reduction is mainly determined by the dimple size of nonsmooth surface. The lager dimples cause stronger turbulence and loss more energy. The drag reduction effect is declined. There is a linear relationship between the drag reduction and the contact angle of hydrophobic surface. The drag reduction is enhanced by increasing the contact angle. But the principle is complicated between drag reduction and the roughness of the wall. There are different roughness to achieve the best effect under different flow velocities.

1618 Phase-field気液二相流モデルによる壁面上液滴落下シミュレーション

1618 Phase-field気液二相流モデルによる壁面上液滴落下シミュレーション

A blow-up criterion of strong solutions to a viscous liquid–gas two-phase flow model with vacuum in 3D

In this paper, we get a blow-up criterion for the strong solutions to the 3D viscous liquid–gas two-phase flow model with vacuum. More precisely, we prove that the bound of Lt1Lx∞ norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions.

Blow-up criterion for 3D viscous liquid–gas two-phase flow model

This work deals with the blow-up criterion for the strong solution to the three-dimensional viscous liquid–gas two-phase flow model in terms of the L1(0,T;L∞)-norm of the gradient of the velocity with two types of boundary conditions: the Dirichlet boundary condition and the Navier-slip boundary condition. There is no extra restriction on viscosity coefficients. The result also applies to the whole space case.

A note on viscous liquid–gas two-phase flow model with mass-dependent viscosity and vacuum

In this paper, we consider a free boundary value problem for two-phase liquid–gas model with mass-dependent viscosity coefficient; the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid, and the fluid velocities are unequal, i.e., ug≠ul. The local existence of a weak solution is established when the initial gas mass connects to vacuum continuously.

A blow-up criterion of strong solution to a 3D viscous liquid–gas two-phase flow model with vacuum

In this paper, we get a unique local strong solution to a 3D viscous liquid–gas two-phase flow model in a smooth bounded domain. Besides, a blow-up criterion of the strong solution for 253μ>λ is obtained. The method can be applied to study a blow-up criterion of the strong solution to Navier–Stokes equations for 253μ>λ, which improves the corresponding result about Navier–Stokes equations in Sun et al. (2011) [15] where 7μ>λ. Moreover, all the results permit the appearance of vacuum.

Flux enhancement and cake formation in air-sparged cross-flow microfiltration

Abstract The flux enhancement in cross-flow microfiltration of submicron particles by sparged air-bubble is studied. The effects of operating conditions, such as air-bubble velocity, suspension velocity and filtration pressure, on the cake properties and filtration flux are discussed thoroughly. The results show that the pseudo-steady filtration flux increases as the air-bubble velocity and filtration pressure increase. The sparged air-bubble can significantly improve filtration flux, but the flux enhancement is more remarkable in the lower air-bubble velocity region. A gas–liquid two-phase flow model is adopted for estimating the shear stress acting on the membrane surface under various operating conditions. The cake mass can be significantly reduced by increasing the shear stress acting on the membrane surface. However, the SEM analysis illustrates that the particle packing structure becomes more compact as the air-bubble velocity increases. This results in a slightly higher average specific cake filtration resistance under higher air-bubble velocity. Consequently, a minimum flux occurs at the critical shear stress, e.g., τ w = 1.1 N/m 2 in this study, when these effects are both taken into consideration. As the shear stress increases by increasing the suspension or gas-bubble velocity, the filtration flux decreases in the low shear stress region but, on the contrary, quickly increases in the high shear stress region. Furthermore, a force balance model is derived for understanding the particle deposition on the membrane surface. The relationship among filtration flux, shear stress and overall filtration resistance is obtained and verified by experimental data.

A Mechanistic Model for Gas-liquid Two-phase Flow in Slightly Inclined Pipes: To Improve Predictions of Flow Patterns and Pressure Drops.

This paper describes experimental and modeling studies to investigate the behavior of gas-liquid two-phase flow in horizontal and slightly inclined pipelines. The studies were performed with experimental data newly obtained at over 1000 flow conditions that were designed to cover all the flow patterns. The experiments were conducted at a test loop of a 54.9 mm diameter, 105.0 m long pipeline, with 0, 5, and 10 degree inclination of the test section. A new mechanistic model for horizontal and slightly inclined flow was developed implementing transition criteria between the flow patterns, correlation for liquid holdup, and flow models for pressure drop computation. The criteria for the transition boundaries between flow regions were determined for eight flow patterns matching the predicted flow patterns with the experimental observations. For stable dispersed bubble flow, constraints on the bubble size were additionally applied. At the transition between stratified and non-stratified flow, we added such a criterion that slug flow can remain stable at much lower flow rates of liquid. The froth flow region was newly modeled to reproduce the experimental observations between annular and slug flow. The pressure drops were computed for individual conditions of the experimental measurements. Excellent performance of the model was demonstrated by good agreements between the computed results and the experimental data. Correct identification of the flow pattern is crucial for accurate estimation of pressure drops, particularly for those near the transition boundaries. Use of appropriate friction factors is of primary importance for pressure drop calculations in any of the flow patterns.

ALE Finite Element Method Based on an Incompressible Two-Fluid Model for Gas-Liquid Two-Phase Flow Including Moving Boundary.

ALE Finite Element Method Based on an Incompressible Two-Fluid Model for Gas-Liquid Two-Phase Flow Including Moving Boundary.

Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model

In this paper a detailed hydrodynamic model for gas-liquid two-phase flow will be presented. The model is based on a mixed Eulerian-Lagrangian approach and describes the time-dependent two-dimensional motion of small, spherical gas bubbles in a bubble column operating in the homogeneous regime. The motion of these bubbles is calculated from a force balance for each individual bubble, accounting for all relevant forces acting on them. Contributions from liquid-phase pressure gradient, drag, virtual mass, liquid-phase vorticity and gravity are considered, whereas direct bubble-bubble interactions are accounted for via an interaction model resembling the collision model developed by Hoomans et al. (1996) to model gas-fluidized beds. The liquid-phase hydrodynamics are described using the volume-averaged, unsteady, Navier-Stokes equations. A preliminary model validation has been performed by comparing the computational results with experimental observations published previously in literature by various authors. The model is shown to predict correctly the motion of a bubble plume in a pseudo-two-dimensional bubble column operated at different superficial gas velocities, provided that a detailed description of the bubble dynamics is incorporated in the model. The effect of bubble column aspect ratio on the hydrodynamic behaviour of the column has also been investigated. Our model predicts the effect of aspect ratio on the flow structure in the bubble column. The importance of the various forces acting on the bubbles will also be discussed and it will be shown that the added mass force and the lift force cannot be neglected in bubble column simulation. Finally, the model has been used to study the start-up behaviour of a two-dimensional bubble column. It will be shown that the history of the gas-liquid two-phase flow significantly affects the flow structure ultimately obtained in a bubble column. This finding has, to our knowledge, not been reported before in literature.