An Adaptive-Grid Projection Method for High Density Ratio Interfacial Flows

2013 ◽  
Author(s):  
Pablo Gómez ◽  
Claudio Zanzi ◽  
Julián Palacios ◽  
Julio Hernández ◽  
Joaquín López
Keyword(s):  
Numerical Model ◽  
Level Set ◽  
Projection Method ◽  
Stokes Equations ◽  
Density Ratio ◽  
Adaptive Grid ◽  
Advection Equation ◽  
Interfacial Flows ◽  
Level Set Function ◽  
The Impact

A graded-adaptive grid projection method to solve the Navier-Stokes equations for incompressible interfacial flows characterized by large density ratios is presented. The numerical model is similar to the one we proposed in [7] and extended to 3D problems in [8]. The free surface is described using a level set method. A Godunov-type method and a Crank-Nicholson temporal discretization scheme are used to solve the advection equation of the level set function and to update of the momentum equation. The reinitialization procedure of the distance function is based on solving a hyperbolic equation to steady state using third-order Runge-Kutta and fifth-order WENO schemes. The conservation equations are discretized on a rectangular adaptive grid with an octree data structure and the pressure stored at the grid cell vertices. In order to avoid spurious pressure oscillations, the velocity components are stored at the cell edges. This new storage scheme combines the advantages of vertex-based schemes, in which the nodes where the pressure is stored are aligned, and cell center-based schemes, which avoid pressure-velocity coupling problems. The numerical model incorporates a continuous surface tension model based on the balanced-force algorithm proposed in [6]. A special treatment of T-nodes (nodes located at vertices, edges or faces of cells belonging to two different refinement levels) is proposed that considerably improves the efficiency of the method. Several tests in two and three dimensions have been carried out to assess the accuracy and efficiency of the proposed method. In this work we present some numerical results for a 3D kinematic test, which are compared with those obtained by other authors. We also present results for the impact of a drop of water onto a liquid surface, which are compared with experimental visualization results.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows (Keynote)

2003 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

Insights Into Sloshing Impact Pressures Through Level Set Modeling of Liquid Droplet Impacting a Wall

2015 ◽  
Author(s):  
Nitin Repalle ◽  
Krish P. Thiagarajan ◽  
Murali Kantharaj
Keyword(s):  
Level Set ◽  
Power Law ◽  
Stokes Equations ◽  
Solid Wall ◽  
Liquid Droplet ◽  
Density Ratio ◽  
Impact Pressure ◽  
Normal Velocity ◽  
Fluid Medium ◽  
Level Set Function

This research arose from the need to understand the behavior of impact pressure caused by droplets formed during liquid sloshing in a tank. The two phase problem of a cylindrical liquid droplet of diameter D surrounded by a lighter fluid medium, impacting at some angle on a solid wall is studied. The incompressible two-dimensional continuity and Navier Stokes equations are solved by a two-step projection predictor-corrector algorithm, with a third-order Total Variation Diminishing (TVD) Runge-Kutta method for time stepping. The interface of the droplet is tracked by the zero contour of a level set function, which is allowed to evolve over time. Numerical simulation of impact pressure was found to agree well with the measured pressures, in particular at lower droplet velocities where compressibility effects can be ignored. A parametric study was conducted with a droplet of diameter 0.01 m traveling at four different impact angles between 45–90°. Velocities from 3.0–6.0 m/s, corresponding to Reynolds numbers from 2.9E05–4.8E05, and Weber numbers 1.25E04–5.0E05 were considered. The simulated impact pressure maximum plotted against the normal velocity of incidence shows a power law type behavior that is quite insensitive to the density ratio of the two fluids. The relationship between the velocity of the sloshing wave front and resultant pressure obtained from an experiment was found to be well predicted by the power law relationship for the liquid droplet impact.

Parallelized numerical modeling of the interaction of a solid object with immiscible incompressible two-phase fluid flow

2017 ◽  
Vol 34 (3) ◽  
pp. 709-724 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
R. Nikbakhti ◽  
Amirreza Ghasemi ◽  
Faraz Hedayati ◽  
Amir Malvandi
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
High Density ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
Solid Object ◽  
Computational Tool ◽  
Two Phase ◽  
Content Type

Purpose A numerical method is developed to capture the interaction of solid object with two-phase flow with high density ratios. The current computational tool would be the first step of accurate modeling of wave energy converters in which the immense energy of the ocean can be extracted at low cost. Design/methodology/approach The full two-dimensional Navier–Stokes equations are discretized on a regular structured grid, and the two-step projection method along with multi-processing (OpenMP) is used to efficiently solve the flow equations. The level set and the immersed boundary methods are used to capture the free surface of a fluid and a solid object, respectively. The full two-dimensional Navier–Stokes equations are solved on a regular structured grid to resolve the flow field. Level set and immersed boundary methods are used to capture the free surface of liquid and solid object, respectively. A proper contact angle between the solid object and the fluid is used to enhance the accuracy of the advection of the mass and momentum of the fluids in three-phase cells. Findings The computational tool is verified based on numerical and experimental data with two scenarios: a cylinder falling into a rectangular domain due to gravity and a dam breaking in the presence of a fixed obstacle. In the former validation simulation, the accuracy of the immersed boundary method is verified. However, the accuracy of the level set method while the computational tool can model the high-density ratio is confirmed in the dam-breaking simulation. The results obtained from the current method are in good agreement with experimental data and other numerical studies. Practical/implications The computational tool is capable of being parallelized to reduce the computational cost; therefore, an OpenMP is used to solve the flow equations. Its application is seen in the following: wind energy conversion, interaction of solid object such as wind turbine with water waves, etc. Originality/value A high efficient CFD approach method is introduced to capture the interaction of solid object with a two-phase flow where they have high-density ratio. The current method has the ability to efficiently be parallelized.

A Developed Numerical Method for Turbulent Unsteady Fluid Flow in Two-Phase Systems with Moving Interface

2017 ◽  
Vol 14 (06) ◽  
pp. 1750063 ◽  
Author(s):  
A. M. Hegab ◽  
S. A. Gutub ◽  
A. Balabel
Keyword(s):  
Numerical Model ◽  
Gas Phase ◽  
Level Set ◽  
The Body ◽  
Phase System ◽  
Computational Domain ◽  
Two Phase ◽  
Moving Interface ◽  
Level Set Function ◽  
Gas System

This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents the surface and the body forces as boundary value conditions on the interface. The adapted approaches enable accurate modeling of fluid flows driven by either body or surface forces. The moving interface is tracked and captured using the level set function that initially defined for both fluids in the computational domain. To asses the developed numerical model and its versatility, a selection of different unsteady test cases including oscillation of a capillary wave, sloshing in a rectangular tank, the broken-dam problem involving different density fluids, simulation of air/water flow, and finally the moving interface between the solid and gas phases of solid rocket propellant combustion were examined. The latter case model allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady nonuniform regression of either liquid or the propellant solid surfaces. The propagation of the unsteady nonplanar regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The computational results demonstrate a remarkable capability of the developed numerical model to predict the dynamical characteristics of the liquid–gas and solid–gas flows, which is of great importance in many civilian and military industrial and engineering applications.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

NUMERICAL SIMULATION OF RAYLEIGH–TAYLOR INSTABILITY BASED ON AN IMPROVED PARTICLE LEVEL SET METHOD

2014 ◽  
Vol 11 (04) ◽  
pp. 1350094 ◽  
Author(s):  
HUI TIAN ◽  
GUOJUN LI ◽  
XIONGWEN ZHANG
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Wide Range ◽  
Particle Level ◽  
Rayleigh Taylor Instability ◽  
Particle Level Set Method

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

Fluid-Structure Simulations for a 2D Fire Applications

2005 ◽  
Author(s):  
Wei Xie ◽  
Changsong Luo ◽  
Paul E. DesJardin
Keyword(s):  
Mass Transfer ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Algorithms ◽  
Thermal Response ◽  
Navier Stokes ◽  
Fire Plume ◽  
Fluid Structure ◽  
Local Boundary ◽  
Level Set Function

This study is on the development of numerical algorithms and models for simulation of a structure response in a fire. The flow field from the fire plume is modeled using the 2D Navier-Stokes equations supplemented with a transport equation for thermal energy and solved using a vorticity-streamfunction approach. Coupling of the fluid to the FEM based structure model is based on the use of a level set method describing the structure geometry in the fluid domain. The level set function allows for computation of normal gradients at the fluid-solid interface to enforce local boundary conditions of heat and mass transfer at prescribed fluid-structure coupling time increments. Numerical simulations of a two-dimensional composite cantilever beam subject to convection heat loading from a fire plume are presented requiring coupling of both the thermal and mass transfer processes at the fluid-structure interface. Results are presented showing the thermal response of a composite beam to a fire plume and the sensitivity of the heating to fire location.

On the Boundary Condition for the Level Set Function in the Numerical Simulation of Moving Contact Lines

2020 ◽  
Author(s):  
Pablo Gómez ◽  
Adolfo Esteban ◽  
Claudio Zanzi ◽  
Joaquín López ◽  
Julio Hernández
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Solid Wall ◽  
Interfacial Flows ◽  
Moving Contact ◽  
Level Set Function ◽  
Static Contact ◽  
Set Function

Abstract We present a method based on a level set formulation to reproduce the behavior of the contact line on solid walls in the simulation of 3D unsteady interfacial flows characterized by large density ratios. The level set method poses a particular difficulty, related to the reinitialization procedure, when used in the simulation of interfacial flows in which the interface intersects a solid wall, due to the appearance of a blind zone where standard reinitialization procedures produce inconsistent results. The proposed method overcomes this difficulty by introducing a boundary condition for the level set function on the solid surface based on the normal extension of the contact angle from the interface along the solid wall. In order to reproduce the dynamics of the contact line we use a simplified model that imposes a boundary condition on the interface curvature based on the static contact angle, and define a thin slip zone at the solid wall around the contact line. To assess the accuracy and robustness of the proposed method, we conducted several preliminary numerical tests in three dimensions, whose results are compared with analytical solutions and other results available in the literature.

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