scholarly journals Direct numerical simulation of solidification with effects of density difference

2016 ◽  
Vol 38 (3) ◽  
pp. 193-204
Author(s):  
Vu Van Truong
Keyword(s):  
Stokes Equations ◽  
Solid Phase ◽  
Density Difference ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Liquid Phases ◽  
Solidification Processes ◽  
Solid Liquid Interface ◽  
Effects Of Density

In this paper, direct numerical simulations are presented for solidification with the effects of density difference between the solid and liquid phases. A front-tracking method is used. The solidification front, i.e. the solid-liquid interface separating solid and liquid, is represented by connected elements that move on a rectangular and stationary grid. The Navier-Stokes equations are solved by a projection method on the entire domain including the solid phase. An indicator function reconstructed from the front information is used to set the velocities in the solid phase to zero, and thus to enforce the no-slip condition at the interface. The method is validated through comparisons with exact solutions for one- and two-dimensional problems. The method is then used to simulate the solidification processes with the effects of volume change due to density difference

scholarly journals Effects of surfactant on propagation and rupture of a liquid plug in a tube

2019 ◽  
Vol 872 ◽  
pp. 407-437 ◽  
Author(s):  
M. Muradoglu ◽  
F. Romanò ◽  
H. Fujioka ◽  
J. B. Grotberg
Keyword(s):  
Shear Stress ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Thin Liquid Film ◽  
Front Tracking ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Liquid Plug ◽  
Front Tracking Method ◽  
Airway Walls

Surfactant-laden liquid plug propagation and rupture occurring in lower lung airways are studied computationally using a front-tracking method. The plug is driven by an applied constant pressure in a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier–Stokes equations are solved in the front-tracking framework. The numerical method is first validated for a surfactant-free case and the results are found to be in good agreement with the earlier simulations of Fujioka et al. (Phys. Fluids, vol. 20, 2008, 062104) and Hassan et al. (Intl J. Numer. Meth. Fluids, vol. 67, 2011, pp. 1373–1392). Then extensive simulations are performed to investigate the effects of surfactant on the mechanical stresses that could be injurious to epithelial cells, such as pressure and shear stress. It is found that the liquid plug ruptures violently to induce large pressure and shear stress on airway walls and even a tiny amount of surfactant significantly reduces the pressure and shear stress and thus improves cell survivability. However, addition of surfactant also delays the plug rupture and thus airway reopening.

Numerical Simulation of Crystallization of a Modified Metal Drop during Metal Spreading on a Substrate

2019 ◽  
pp. 18-39
Author(s):  
V.N. Popov ◽  
A.N. Cherepanov
Keyword(s):  
Numerical Simulation ◽  
Aluminum Alloy ◽  
Stokes Equations ◽  
Liquid Velocity ◽  
Solid Phase ◽  
Boussinesq Approximation ◽  
Solid Substrate ◽  
High Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations

The purpose of the research was to numerically simulate the processes when melting drops fall on a substrate. The paper deals with the solidification on the metal surface of a binary aluminum alloy modified by activated refractory nanosized particles, which are the centers of crystalline phase nucleation. We formulated a mathematical model which describes the thermo- and hydrodynamic phenomena in the drop upon interaction with a solid substrate, heterogeneous nucleation during melt cooling, and subsequent crystallization. The flow in a liquid is described by the Navier --- Stokes equations in the Boussinesq approximation. The position of the free boundary of the melt is fixed by marker particles moving with the local liquid velocity. On the melt --- substrate contact surface, thermal resistance is taken into account. The hydrodynamic problem is considered under conditions of crystallization of molten metal. The temperature conditions and the kinetics of the growth of the solid phase in the solidifying aluminum alloy are described for various sizes of formed splats. Satisfactory agreement was found between the shape of the splat obtained by the results of numerical simulation and the available experimental data. The adequacy of the crystallization model in the presence of ultradisperse refractory particles in a binary alloy is confirmed. It was determined that, regardless of the size of the drop, bulk crystallization of the metal takes place. It was found that at a high rate of collision of a drop with a substrate during the melt spreading, a small fraction of the solid phase can be formed.

scholarly journals Dynamics of a contracting fluid compound filament with a variable density ratio

2021 ◽  
Vol 24 (2) ◽  
pp. first
Author(s):  
Truong V. Vu ◽  
Vinh T. Nguyen ◽  
Phan H. Nguyen ◽  
Nang X. Ho ◽  
Binh D. Pham ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Stokes Equations ◽  
Weighting Function ◽  
Density Ratio ◽  
Variable Density ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Fixed Grid ◽  
Eulerian Grid

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

Heat Transfer Mode and Effect of Fluid Flow on the Morphology of the Weld Pool

2021 ◽  
Vol 406 ◽  
pp. 66-77
Author(s):  
Abdel Halim Zitouni ◽  
Pierre Spiteri ◽  
Mouloud Aissani ◽  
Younes Benkheda
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Weld Pool ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transfer Mode ◽  
Thermal Fields ◽  
Welding Properties

In this work, the heat transfer by conduction and convection mode and effect of fluid flow on the morphology of the weld pool and the welding properties is investigated during Tungsten Inert Gas (TIG) process. In the first part, a computation code under Fortran was elaborated to solve the equations resulting from the finite difference discretization of the heat equation, taking into account the liquid-solid phase change with the associated boundary conditions. In order to calculate the velocity field during welding, the Navier-Stokes equations in the melt zone were simplified and solved considering their stream-vorticity formulation. A mathematical model was developed to study the effect of the melted liquid movement on the weld pool. The evolution of the fraction volume of the liquid and the thermal fields promoted the determination of the molten zone (MZ) and the Heat Affected Zone (HAT) dimensions, which seems to be in good agreement with literature.

Dynamics of homogeneous bubbly flows Part 1. Rise velocity and microstructure of the bubbles

2002 ◽  
Vol 466 ◽  
pp. 17-52 ◽  
Author(s):  
BERNARD BUNNER ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Void Fraction ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Rise Velocity ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Deformable Interface ◽  
The Individual ◽  
Average Rise

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The full Navier–Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 12–30, depending on the void fraction; deformations of the bubbles are small. Although the motion of the individual bubbles is unsteady, the simulations are carried out for a sufficient time that the average behaviour of the system is well defined. Simulations with different numbers of bubbles are used to explore the dependence of the statistical quantities on the size of the system. Examination of the microstructure of the bubbles reveals that the bubbles are dispersed approximately homogeneously through the flow field and that pairs of bubbles tend to align horizontally. The dependence of the statistical properties of the flow on the void fraction is analysed. The dispersion of the bubbles and the fluctuation characteristics, or ‘pseudo-turbulence’, of the liquid phase are examined in Part 2.

scholarly journals Numerical simulation of compressible cavitating two-phase flows with a pressure-based solver

2017 ◽  
Author(s):  
Marco Cristofaro ◽  
Wilfried Edelbauer ◽  
Manolis Gavaises ◽  
Phoevos Koukouvinis
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Test Case ◽  
Time Step ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Liquid Phases ◽  
Flow Features ◽  
Liquid Evaporation ◽  
Semi Empirical

This work intends to study the effect of compressibility on throttle flow simulations with a pressure–based solver.The simple micro throttle geometry allows easier access for obtaining experimental data compared to a real injector, but still maintaining the main flow features. For this reasons it represents a meaningful and well reported benchmark for validation of numerical methods developed for cavitating injector flows.An implicit pressure–based compressible solver is used on the filtered Navier–Stokes equations. Thus, no stability limitation is applied on the time step. A common pressure field is computed for all phases, but different velocity fields are solved for each phase, following the multi–fluid approach. The liquid evaporation rate is evaluated with a Rayleigh–Plesset equation based cavitation model and the Coherent Structure Model is adopted as closure for the sub–grid scales in the momentum equation.The aim of this study is to show the capabilities of the pressure–based solver to deal with both vapor and liquid phases considered compressible. A comparison between experimental results and compressible simulations is presented. Time–averaged vapor distribution and velocity profiles are reported and discussed.  The distribution of pressure maxima on the surface and the results from a semi–empirical erosion model are in good agreement with the erosion locations observed in the experiments. This test case aims to represent a benchmark for furtherapplication of the methodology to industrial relevant cases.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4629

scholarly journals Sustained gravity currents in a channel

2016 ◽  
Vol 798 ◽  
pp. 853-888 ◽  
Author(s):  
Andrew J. Hogg ◽  
Mohamad M. Nasr-Azadani ◽  
Marius Ungarish ◽  
Eckart Meiburg
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Analytical Techniques ◽  
Direct Numerical Simulations ◽  
Density Difference ◽  
Water Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Layer ◽  
Dense Fluid

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.

scholarly journals Deposition of Colloidal Particles during the Evaporation of Sessile Drops: Dilute Colloidal Dispersions

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Pei-Fang Sung ◽  
Lihui Wang ◽  
Michael T. Harris
Keyword(s):  
Particle Deposition ◽  
Colloidal Particles ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Deposition Patterns ◽  
High Particle Concentration ◽  
High Particle ◽  
Sessile Drops

The deposition of colloidal silica particles during the evaporation of sessile drops on a smooth substrate has been modeled by the simultaneous solution of the Navier–Stokes equations, the convective-diffusive equation for particles, and the diffusion equation for evaporated vapor in the gas phase. Isothermal conditions were assumed. A mapping was created to show the conditions for various deposition patterns for very dilute suspensions. Based on values of the Peclet (Pe) number and Damkholer numbers (Da and Da−1), the effects of adsorption and desorption were discussed according to the map. Simulations were also done for suspensions with a high particle concentration to form a solid phase during the evaporation by using a packing criterion. The simulations predicted the height and width of the ring deposit near the contact line, and the results compared favorably to experimental particle deposition patterns.

Numerical Simulation of Drop Formation From a Nozzle in Liquid-Liquid Systems

2003 ◽  
Author(s):  
Shunji Homma ◽  
Haruhisa Honda ◽  
Jiro Koga ◽  
Shiro Matsumoto ◽  
Museok Song ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Simulation Code ◽  
Navier Stokes Equations ◽  
Liquid Drops ◽  
Front Tracking Method ◽  
Satellite Drops ◽  
Liquid Systems

Numerical simulation code is developed to study the formation of liquid drops from a nozzle into another quiescent liquid. The Navier-Stokes equations for two immiscible, incompressible, Newtonian fluids are solved on a fixed, staggered grid of cylindrical axisymmetric coordinates. Interfacial motion is captured using a Front-Tracking Method. The time variation of interfacial shape simulated by the code is in excellent agreement with experiments. Simulation results show that the viscosity ratio affects the size of the satellite drops.

MATHEMATICAL MODELING OF A TURBULENT FLOW IN A CENTRIFUGAL SEPARATOR

2021 ◽  
pp. 121-138
Author(s):  
Z.M. Malikov ◽  
◽  
M.E. Madaliev ◽  
Keyword(s):  
Mathematical Modeling ◽  
Turbulent Flow ◽  
Gas Flow ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Centrifugal Separator ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Carrier Gas Flow

The numerical results of mathematical modeling of a two-phase axisymmetric swirling turbulent flow in a separation zone of a centrifugal separator are presented. The motion of the carrier gas flow is described by the Reynolds-averaged Navier-Stokes equations. A system of equations is enclosed by the Spalart-Allmaras turbulence model. The study is based on the obtained fields of averaged velocities of the carrier medium, with account for turbulent diffusion. Numerical solution to the problem is implemented using the semi-implicit method for pressure linked equations (SIMPLE). The results obtained when the solid phase effect on the air flow dynamics is taken into account are compared with those obtained when the effect is left out of account. The numerical calculations are validated using the experimental data.

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