Numerical Computation of Hydrodynamically and Thermally Developing Liquid Flow in Microchannels With Electrokinetics Effects

2004 ◽  
Vol 126 (1) ◽  
pp. 70-75 ◽  
Author(s):  
X. Y. Chen ◽  
K. C. Toh ◽  
C. Yang ◽  
J. C. Chai
Keyword(s):  
Liquid Flow ◽  
Electrical Potential ◽  
Planck Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Electrokinetic Effect ◽  
Proposed Model ◽  
Parallel Slit ◽  
Temperature Dependent Properties ◽  
Volume Method

Developing fluid flow and heat transfer with temperature dependent properties in microchannels with electrokinetic effects is investigated numerically. The electrokinetic effect on liquid flow in a parallel slit is modeled by the general Nernst-Planck equation describing anion and cation distributions, the Poisson equation determining the electrical potential profile, the continuity equation, and the modified Navier-Stokes equation governing the velocity field. A Finite-Volume Method is utilized to solve the proposed model.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

Analytical Solution of Hydrostatic Pocket Tilting

2016 ◽  
Vol 821 ◽  
pp. 113-119 ◽  
Author(s):  
Eduard Stach ◽  
Jiří Falta ◽  
Matěj Sulitka
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Detailed Model ◽  
Limit Values ◽  
Inertia Effects ◽  
Proposed Model ◽  
Machine Tool Structure

Tilting (parallelism error) of guiding surfaces may cause reduction of load capacity of hydrostatic (HS) guideways and bearings in machine tools (MT). Using coupled finite element (FE) computational models of MT structures, it is nowadays possible to determine the extent of guiding surfaces deformation caused by thermal effects, gravitational force, cutting forces and inertia effects. Assessment of maximum allowable tilt has so far been based merely on experience. The paper presents a detailed model developed for description of the effect of HS bearing tilt on the load capacity characteristics of HS guideways. The model allows an evaluation of the tilt influence on the change of the characteristics as well as determination of the limit values of allowable tilt in interaction with compliant machine tool structure. The proposed model is based on the model of flow over the land of the HS pocket under extended Navier-Stokes equation. The model is verified using an experimental test rig.

A Model for an Acoustically Driven Microbubble Inside a Rigid Tube

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Adnan Qamar ◽  
Ravi Samtaney
Keyword(s):  
Bubble Radius ◽  
Coupled Model ◽  
Tube Diameter ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Basic Model ◽  
Proposed Model ◽  
D 12 ◽  
Bubble Fragmentation

A theoretical framework to model the dynamics of acoustically driven microbubble inside a rigid tube is presented. The proposed model is not a variant of the conventional Rayleigh–Plesset category of models. It is derived from the reduced Navier–Stokes equation and is coupled with the evolving flow field solution inside the tube by a similarity transformation approach. The results are computed, and compared with experiments available in literature, for the initial bubble radius of Ro = 1.5 μm and 2 μm for the tube diameter of D = 12 μm and 200 μm with the acoustic parameters as utilized in the experiments. Results compare quite well with the existing experimental data. When compared to our earlier basic model, better agreement on a larger tube diameter is obtained with the proposed coupled model. The model also predicts, accurately, bubble fragmentation in terms of acoustic and geometric parameters.

Simulation on the Process of Cavity Wall Expansion of Cone at Constant Speed Water-Entry

2013 ◽  
Vol 419 ◽  
pp. 97-102
Author(s):  
Wei Cao ◽  
Chun Tao He ◽  
Cong Wang
Keyword(s):  
Computational Simulation ◽  
Water Entry ◽  
Constant Speed ◽  
Cavity Wall ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Half Angle ◽  
Expansion Dynamic ◽  
Different Depths ◽  
Volume Method

Computational simulation investigation which is based on the Navier-Stokes equation, finite-volume method, dynamic mesh method, and volume of fluid method, was carried out principally on the constant speed vertical water entry of the cone with 75 degree and a half angle. Based on this, the cavity generation and the process of cavity wall expansion of the cone with 75 degree and a half angle were analyzed. Through analyzing the expansion dynamic for the cavity wall in different depths, the velocity and acceleration with time in the process of cavity wall expansion were obtained, and the disturbances and splash feature laws of the free surface near the entrance of the cavity after cones water-entry were analyzed too.

Numerical Solution of Two-Fluid Electroosmotic Flow

2005 ◽  
Author(s):  
Yandong Gao ◽  
Y. F. Yap ◽  
T. N. Wong ◽  
J. C. Chai ◽  
C. Yang ◽  
...  
Keyword(s):  
Level Set ◽  
Numerical Scheme ◽  
Flow Direction ◽  
Electrical Potential ◽  
Mass Conservation ◽  
Viscous Force ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Two Fluids ◽  
Two Fluid

Two-fluid flows in microchannel are often found in biological analysis, such as during ion exchange or solvent extraction from one phase to another. In this article, a numerical scheme is presented to describe a two-fluid flow in microchannel with electroosmotic (EO) effects. In this two-fluid system, the interfacial viscous force of a high EO mobility fluid drags a low EO mobility fluid; the high EO mobility fluid is driven by electroosmosis. We particularly analyze the electric double layer (EDL) regions close to the wall and the interface in the high EO mobility fluid. As the governing equation of the electrical potential is singularly perturbed, finer meshes are adopted to capture these EDL regions. In simulation, the interface between the two fluids evolves along the flow direction as the flow develops. Level set method is used to capture the interface implicitly. A localized mass preservation scheme is used to ensure mass conservation. A finite-volume method is used to solve the coupled electric potential equation, level set equations and Navier-Stokes equation. The validity of the numerical scheme is evaluated by comparing its predictions with the results of the analytical solutions in the fully developed regions. The interface positions; pressure gradients; mass flow rates and velocity profiles of the two fluids along the channels are obtained numerically.

Melting of Powder Particles in a Low Pressure Plasma Jet

1983 ◽  
Vol 30 ◽  
Author(s):  
D. Wei ◽  
D. Apelian ◽  
S. M. Correa ◽  
M. Paliwal
Keyword(s):  
Plasma Jet ◽  
Low Pressure ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Navier Stokes Equation ◽  
Free Jet ◽  
Binary Model ◽  
Proposed Model ◽  
Powder Particles ◽  
Heat And Momentum Transfer

ABSTRACTA numerical model has been developed to predict the temperature profile of particles injected in a D.C. plasma jet. The equations governing particle melting were applied to spherical powders of binary model alloys. Thermophysical properties of the gas and the powder material have been taken to be temperature dependent. In the proposed model, the latent heat of melting was taken into account by introducing apparent enthalpy as a function of the fraction of liquid formed which can be derived from equations describing non-equilibrium melting. The temperature and velocity profiles of the plasma jet used in this analysis are for a free jet (without target interference) and were calculated using the parabolic Navier-Stokes equation with a K-E turbulence model. Correction factors have been introduced to take into account non-continuum effects encountered in the low pressure environment and the results show that both heat and momentum transfer between the plasma gas and the injected particles are reduced.

scholarly journals Simulation of free-surface flow in a tank using the Navier-Stokes model and unstructured finite volume method

2005 ◽  
Vol 219 (3) ◽  
pp. 251-266 ◽  
Author(s):  
X Zhang ◽  
N M Sudharsan ◽  
R Ajaykumar ◽  
K Kumar
Keyword(s):  
Free Surface ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Free Surface Flow ◽  
Offshore Structures ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Volume Method ◽  
Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS

2007 ◽  
Vol 17 (07) ◽  
pp. 1039-1063 ◽  
Author(s):  
A. MELLET ◽  
A. VASSEUR
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Fluid Velocity ◽  
Planck Equation ◽  
Coupled System ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equation ◽  
Reflection Boundary ◽  
Fokker Planck

We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

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