scholarly journals An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

1998 ◽  
Vol 09 (08) ◽  
pp. 1393-1404 ◽  
Author(s):  
D. J. Holdych ◽  
D. Rovas ◽  
J. G. Georgiadis ◽  
R. O. Buckius
Keyword(s):  
Multiphase Flow ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Effective Field ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Physical Parameters ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Definition Of

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

Lattice-Boltzmann Simulation of Two-Phase Fluid Flows

1998 ◽  
Vol 09 (08) ◽  
pp. 1383-1391 ◽  
Author(s):  
Yu Chen ◽  
Shulong Teng ◽  
Takauki Shukuwa ◽  
Hirotada Ohashi
Keyword(s):  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Interface Model ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Lattice Boltzmann Simulation ◽  
Dam Breaking ◽  
Volumetric Stress ◽  
Phase Fluid

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.

Numerical Simulation of High Reynolds Number Flow Structure in a Lid-Driven Cavity Using MRT-LES

2014 ◽  
Vol 554 ◽  
pp. 665-669
Author(s):  
Leila Jahanshaloo ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Technique ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Reynolds Number Flow ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical and fluid mechanics problems. In this paper multi-relaxation lattice Boltzmann model (MRT) coupled with a Large Eddy Simulation (LES) and the equation are applied for driven cavity flow at different Reynolds number (1000-10000) and the results are compared with the previous published papers which solve the Navier stokes equation directly. The comparisons between the simulated results show that the lattice Boltzmann method has the capacity to solve the complex flows with reasonable accuracy and reliability. Keywords: Two-dimensional flows, Lattice Boltzmann method, Turbulent flow, MRT, LES.

Filter-Based Unsteady RANS Computations for Single-Phase and Cavitating Flows

Volume 3 ◽  
2004 ◽  
Author(s):  
Jiongyang Wu ◽  
Wei Shyy ◽  
Stein T. Johansen
Keyword(s):  
Eddy Viscosity ◽  
Single Phase ◽  
Experimental Information ◽  
Time Dependent ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Filter Size ◽  
The Impact

The widely used Reynolds-Averaged Navier-Stokes (RANS) approach, such as the k-ε two-equation model, has been found to over-predict the eddy viscosity and can dampen out the time dependent fluid dynamics in both single- and two-phase flows. To improve the predictive capability of this type of engineering turbulence closures, a consistent method is offered to bridge the gap between DNS, LES and RANS models. Based on the filter size, conditional averaging is adopted for the Navier-Stokes equation to introduce one more parameter into the definition of the eddy viscosity. Both time-dependent single-phase and cavitating flows are simulated by a pressure-based method and finite volume approach in the framework of the Favre-averaged equations coupled with the new turbulence model. The impact of the filter-based concept, including the filter size and grid dependencies, is investigated using the standard k-ε model and with the available experimental information.

Mathematical Simulation of Different Argon Blowing Style in Ladle Furnace

2005 ◽  
Vol 475-479 ◽  
pp. 3211-3214
Author(s):  
San Bing Ren ◽  
Jun Fei Fan ◽  
Zong Ze Huang ◽  
Yi Sheng Chen ◽  
You Duo He
Keyword(s):  
Mathematical Simulation ◽  
Stokes Equation ◽  
Molten Steel ◽  
Navier Stokes ◽  
Ladle Furnace ◽  
Phase Zone ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Flow Variables ◽  
Turbulence Parameters

In the present paper, applied the experiential correlation, the gas holdup and distribution of two phase zone which formed by argon blown were determined. The flow variables of molten steel and turbulence parameters in the Ladle Furnace were estimated utilizing the results of frontal calculation and through numerically solution momentum Navier-Stokes equation in conjunction with k-εturbulence model. Several different spray styles including blowing through single hole, double holes, top lance were simulated and compared in this project.

A Sharp Surface Tension Modeling Method for Capillarity-Dominant Two-Phase Incompressible Flows

2007 ◽  
Author(s):  
Zhaoyuan Wang ◽  
Albert Y. Tong
Keyword(s):  
Surface Tension ◽  
Incompressible Flows ◽  
Jump Condition ◽  
Navier Stokes ◽  
Pressure Jump ◽  
Interfacial Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Numerical Instabilities ◽  
Spurious Currents

A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.

scholarly journals Influence of the Moment in Mathematical Models for Open Systems

2021 ◽  
Vol 16 ◽  
pp. 250-260
Author(s):  
Evelina Prozorova
Keyword(s):  
Mathematical Models ◽  
Stress Tensor ◽  
Open Systems ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Collective Effects ◽  
Physical Parameters ◽  
Potential Flows ◽  
The Moment ◽  
Definition Of

Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.

Lattice Boltzmann Simulation of Surface Tension Dominated Vortices Behaviour in Two-Phase Mixing Layer

2006 ◽  
Author(s):  
Y. Y. Yan ◽  
Y. Q. Zu
Keyword(s):  
Surface Tension ◽  
Multiphase Flow ◽  
Lattice Boltzmann ◽  
Mixing Layer ◽  
Vertical Direction ◽  
Immiscible Fluids ◽  
Interfacial Interactions ◽  
Two Phase ◽  
Phase Mixing ◽  
Two Fluids

Surface tension dominating mixings and interfacial interactions are major phenomena of multiphase flow in microchannels and a variety of micro mixers. Such phenomena are concerned with interfacial interactions not only at fluid-solid interface but also at different fluids/phases interfaces. In this paper, vortices behaviours in a mixing layer of two immiscible fluids are studied numerically. The lattice Boltzmann method (LBM) is employed to simulat surface tension dominated mixing process. As a mesoscopic numerical method, the LBM has many advantages, which include the ability of incorporating microscopic interactions, the simplicity of programming and the nature of parallel algorithm and is therefore ideal for simulating multiphase flow. In this article, the index function methodology of the LBM is employed to simulate surface tension dominated vertices behaviour in a two-dimensional immiscible two-phase mixing layer. The initial interface between two-fluids is evenly distributed around the midpoint in vertical direction. Different velocity perturbations which consist of a basic wave and a series of sub-harmonic waves are forced at the entrance of a rectangular mixing layer of the flow field. By changing the strength of surface tension and the combinations of perturbation waves, the effects of the surface tension and the velocity perturbation on vortices merging are investigated. The vortices contours and frequency spectrums are used to analyse the mechanism of vortices merging. Some interesting phenomena, which do not take place in a single-phase mixing layer, are observed and the corresponding mechanism is discussed in details.

Two-Phase Fluid Modeling of Magnetic Drug Targeting in a Permeable Microvessel Implanted With a Toroidal Permanent Magnetic Stent

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Chibin Zhang ◽  
Kangli Xia ◽  
Keya Xu ◽  
Xiaohui Lin ◽  
Shuyun Jiang ◽  
...  
Keyword(s):  
Stokes Equation ◽  
Drug Targeting ◽  
Drug Carrier ◽  
Navier Stokes ◽  
Magnetic Drug Targeting ◽  
Tissue Fluid ◽  
Momentum Exchange ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Phase Fluid

The key to effective magnetic drug targeting (MDT) is to improve the aggregation of magnetic drug carrier particles (MDCPs) at the target site. Compared to related theoretical models, the novelty of this investigation is mainly reflected in that the microvascular blood is considered as a two-phase fluid composed of a continuous phase (plasma) and a discrete phase (red blood cells (RBCs)). And plasma flow state is quantitatively described based on the Navier–Stokes equation of two-phase flow theory, the effect of momentum exchange between the two-phase interface is considered in the Navier–Stokes equation. Besides, the coupling effect between plasma pressure and tissue fluid pressure is considered. The random motion effects and the collision effects of MDCPs transported in the blood are quantitatively described using the Boltzmann equation. The results show that the capture efficiency (CE) presents a nonlinear increase with the increase of magnetic induction intensity and a nonlinear decrease with the increase of plasma velocity, but an approximately linear increase with the increase of the particle radius. Furthermore, greater permeability of the microvessel wall promotes the aggregation of MDCPs. The CE predicted by the model agrees well with the experimental results.

A Note on Mixture Density Using the Shannak Definition

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Multiphase Flow ◽  
Pressure Gradient ◽  
Froude Number ◽  
Liquid Density ◽  
Dimensionless Numbers ◽  
Two Phase ◽  
Phase Density ◽  
Mixture Density ◽  
Circular Pipes ◽  
Definition Of

In this study, a note on mixture density using the Shannak definition of the Froude number is presented (Shannak, B., 2009, “Dimensionless Numbers for Two-Phase and Multiphase Flow,” Proceedings of the International Conference on Applications and Design in Mechanical Engineering (ICADME), Penang, Malaysia, Oct. 11–13, 2009). From the definition of the two-phase Froude number, an expression of the two-phase density is obtained. The definition of the two-phase density can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels, and microchannels. We cannot have gas density≤two-phase density≤liquid density for 0≤mass quality≤1. Therefore, attention must be paid when using the obtained expression of the two-phase density in this note at any x value.

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