A quasi-incompressible diffuse interface model with phase transition

2014 ◽  
Vol 24 (05) ◽  
pp. 827-861 ◽  
Author(s):  
Gonca L. Aki ◽  
Wolfgang Dreyer ◽  
Jan Giesselmann ◽  
Christiane Kraus
Keyword(s):  
Stokes Equations ◽  
Incompressible Fluids ◽  
The Other ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Navier Stokes Equations ◽  
Interfacial Conditions ◽  
Two Component

This work introduces a new thermodynamically consistent diffuse model for two-component flows of incompressible fluids. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. To this end, we consider two scaling regimes where in one case we recover the Euler equations and in the other case the Navier–Stokes equations in the bulk phases equipped with admissible interfacial conditions. For the Navier–Stokes regime, we further assume the densities of the fluids are close to each other in the sense of a small parameter which is related to the interfacial thickness of the diffuse model.

scholarly journals Stationary Cahn–Hilliard–Navier–Stokes equations for the diffuse interface model of compressible flows

2020 ◽  
Vol 30 (12) ◽  
pp. 2445-2486
Author(s):  
Zhilei Liang ◽  
Dehua Wang
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Approximate Solutions ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Approximation Procedure ◽  
Interface Model ◽  
Navier Stokes Equations ◽  
Concentration Difference ◽  
Wide Range

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations consist of the stationary Navier–Stokes equations for compressible fluids and a stationary Cahn–Hilliard type equation for the mass concentration difference. Approximate solutions are constructed through a two-level approximation procedure, and the limit of the sequence of approximate solutions is obtained by a weak convergence method. New ideas and estimates are developed to establish the existence of weak solutions with a wide range of adiabatic exponent.

scholarly journals Mixing of Particles in Micromixers under Different Angles and Velocities of the Incoming Water

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 577 ◽  
Author(s):  
Evangelos Karvelas ◽  
Christos Liosis ◽  
Theodoros Karakasidis ◽  
Ioannis Sarris
Keyword(s):  
Stokes Equations ◽  
Velocity Ratio ◽  
The Other ◽  
Navier Stokes ◽  
Contaminated Water ◽  
Solution Flow ◽  
Navier Stokes Equations ◽  
Inlet Velocity ◽  
Metal Capture ◽  
Discrete Motion

A possible solution for water purification from heavy metals is to capture them by using nanoparticles in microfluidic ducts. In this technique, heavy metal capture is achieved by effectively mixing two streams, a nanoparticle solution and the contaminated water. In the present work, particles and water mixing is numerically studied for various inlet velocity ratios and inflow angles of the two streams. The Navier-Stokes equations are solved for the water flow while the discrete motion of particles is evaluated by a Lagrangian method. Results showed that as the velocity ratio between the inlet streams increases, by increasing the particles solution flow, the mixing of particles with the contaminated water is increased. Thus, nanoparticles are more uniformly distributed in the duct. On the other hand, angle increase between the inflow streams ducts is found to be less significant.

scholarly journals Effects of Hydrostatic Pocket Shape on the Flow Pattern and Pressure Distribution

1995 ◽  
Vol 1 (3-4) ◽  
pp. 225-235 ◽  
Author(s):  
M. J. Braun ◽  
M. Dzodzo
Keyword(s):  
Numerical Simulation ◽  
Pressure Distribution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Collocated Grid ◽  
Dimensionless Formulation

The flow in a hydrostatic pocket is numerically simulated using a dimensionless formulation of the 2-D Navier-Stokes equations written in primitive variables, for a body fitted coordinates system, and applied through a collocated grid. In essence, we continue the work of Braun et al. 1993a, 1993b] and extend it to the study of the effects of the pocket geometric format on the flow pattern and pressure distribution. The model includes the coupling between the pocket flow and a finite length feedline flow, on one hand, and the pocket and its adjacent lands on the other hand. In this context we shall present, on a comparative basis, the flow and the pressure patterns at the runner surface for square, ramped-Rayleigh step, and arc of circle pockets. Geometrically all pockets have the same footprint, same lands length, and same capillary feedline. The numerical simulation uses the Reynolds number based on the lid(runner) velocity and the inlet jet strengthFas the dynamic similarity parameters. The study aims at establishing criteria for the optimization of the pocket geometry in the larger context of the performance of a hydrostatic bearing.

scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

scholarly journals Well-posedness of 2-D and 3-D swimming models in incompressible fluids governed by Navier–Stokes equations

2015 ◽  
Vol 429 (2) ◽  
pp. 1059-1085 ◽  
Author(s):  
Alexander Khapalov ◽  
Piermarco Cannarsa ◽  
Fabio S. Priuli ◽  
Giuseppe Floridia
Keyword(s):  
Stokes Equations ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations

scholarly journals A class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force

2018 ◽  
Vol 7 (3) ◽  
pp. 77
Author(s):  
Mushtaq Ahmed ◽  
Waseem Ahmed Khan ◽  
S M. Shad Ahsen
Keyword(s):  
Exact Solutions ◽  
Body Force ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Steady Motion ◽  
Incompressible Fluids ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case

This paper determines a class of exact solutions for plane steady motion of incompressible fluids of variable viscosity with body force term in the Navier-Stokes equations. The class consists of stream function  characterized by equation , in polar coordinates ,  where ,  and  are continuously differentiable functions, derivative of  is non-zero but double derivative of  is zero. We find exact solutions, for a suitable component of body force, considering two cases based on velocity profile. The first case fixes both the functions ,  and provides viscosity as function of temperature. Where as the second case fixes the function , leaves  arbitrary and provides viscosity and temperature for the arbitrary function . In both the cases, we can create infinite set of expressions for streamlines, viscosity function, generalized energy function and temperature distribution in the presence of body force.  

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