Simulation of Dendritic Growth Using a VOF Method

2009 ◽  
Author(s):  
Joaqui´n Lo´pez ◽  
Julio Herna´ndez ◽  
Claudio Zanzi ◽  
Fe´lix Faura ◽  
Pablo Go´mez
Keyword(s):  
Dendritic Growth ◽  
Piecewise Linear ◽  
Height Function ◽  
Vof Method ◽  
Three Dimensions ◽  
Advection Equation ◽  
Thermal Gradients ◽  
Interfacial Flows ◽  
Thermal Boundary Conditions ◽  
Interface Curvature

The volume of fluid (VOF) method is one of the most widely used methods to simulate interfacial flows using fixed grids. However, its application to phase change processes in solidification problems is relatively infrequent. In this work, preliminary results of the application of a new methodology to the simulation of dendritic growth of pure metals is presented. The proposed approach is based on a recent VOF method with PLIC (piecewise linear interface calculation) reconstruction of the interface. A diffused-interface method is used to solve the energy equation, which avoids the need of applying the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to accurately obtain the front velocity, are calculated with the aid of a distance function. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lo´pez et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Herna´ndez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]). The interface curvature is computed using an improved height function (HF) technique, which provides second-order accuracy. The assessment of the proposed methodology is carried out by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.

An Improved Anti-Diffusive VOF Method to Predict Two-Fluid Free Surface Flows

2011 ◽  
Author(s):  
Y. G. Chen ◽  
W. G. Price ◽  
P. Temarel
Keyword(s):  
Free Surface ◽  
Diffusion Processes ◽  
Volume Fraction ◽  
Volume Of Fluid ◽  
Free Surface Flows ◽  
Vof Method ◽  
Advection Equation ◽  
Diffusion Term ◽  
Surface Flows ◽  
Two Fluid

This investigation continues the development of an anti-diffusive volume of fluid method [1] by improving accuracy through the addition of an artificial diffusion term, with a negative diffusion coefficient, to the original advection equation describing the evolution of the fluid volume fraction. The advection and diffusion processes are split into a set of two partial differential equations (PDEs). The improved anti-diffusive Volume of Fluid (VOF) method is coupled with a two-fluid flow solver to predict free surface flows and illustrated by examples given in two-dimensional flows. The first numerical example is a solitary wave travelling in a tank. The second example is a plunging wave generated by flow over a submerged obstacle of prescribed shape on a horizontal floor. The computational results are validated against available experimental data.

Dendritic Growth in Terrestrial and Microgravity Conditions

1994 ◽  
Vol 367 ◽  
Author(s):  
M.E. Glicksman ◽  
M.B. Koss ◽  
L.T. Bushnell ◽  
J.C. Lacombe ◽  
E.A. Winsa
Keyword(s):  
Dendritic Growth ◽  
Space Shuttle ◽  
Microgravity Environment ◽  
Radius Of Curvature ◽  
Thermal Gradients ◽  
Growth Data ◽  
Diffusion Solution ◽  
Microgravity Conditions ◽  
Space Shuttle Columbia ◽  
Tip Velocity

AbstractDendritic growth is the most ubiquitous form of crystal growth encountered when metals and alloys solidify under low thermal gradients. The growth of thermal dendrites in pure melts is generally acknowledged to be controlled by the diffusive transport of latent heat from the moving crystal-melt interface into its supercooled melt. However, this formulation is incomplete, and the physics of an additional selection rule, coupled to the transport solution, is necessary to predict uniquely the dendrite tip velocity and radius of curvature as a function of the supercooling. Unfortunately, experimental confirmation or evidence is ambiguous, because dendritic growth can be severely complicated by buoyancy induced convection. Recent experiments performed in the microgravity environment of the space shuttle Columbia (STS-62) quantitatively show that convection alters tip velocities and radii of curvature of succinonitrile (SCN) dendrites. In addition, these data can be used to evaluate how well the Ivantsov diffusion solution, coupled to a scaling constant, matches the dendritic growth data under microgravity conditions.

scholarly journals A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Liqun Wang ◽  
Songming Hou ◽  
Liwei Shi
Keyword(s):  
Finite Element ◽  
Piecewise Linear ◽  
Main Idea ◽  
Three Dimensions ◽  
Test Function ◽  
Linear System Of Equations ◽  
Elasticity Equations ◽  
Matrix Coefficients ◽  
The Matrix ◽  
3D Elasticity

Interface problems occur frequently when two or more materials meet. Solving elasticity equations with sharp-edged interfaces in three dimensions is a very complicated and challenging problem for most existing methods. There are several difficulties: the coupled elliptic system, the matrix coefficients, the sharp-edged interface, and three dimensions. An accurate and efficient method is desired. In this paper, an efficient nontraditional finite element method with nonbody-fitting grids is proposed to solve elasticity equations with sharp-edged interfaces in three dimensions. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up).

On the development of LS-assisted VOF method for incompressible interfacial flows

2020 ◽  
Vol 406 ◽  
pp. 109188
Author(s):  
H.L. Wen ◽  
C.H. Yu ◽  
Tony W.H. Sheu
Keyword(s):  
Vof Method ◽  
Interfacial Flows

Linearized oscillations of a vortex column: the singular eigenfunctions

2014 ◽  
Vol 741 ◽  
pp. 404-460 ◽  
Author(s):  
Anubhab Roy ◽  
Ganesh Subramanian
Keyword(s):  
Critical Radius ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Initial Distribution ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Rankine Vortex ◽  
Parallel Flows ◽  
Lord Kelvin

AbstractIn 1880 Lord Kelvin analysed the linearized inviscid oscillations of a Rankine vortex as part of a theory of vortex atoms. These eponymously named neutrally stable modes are, however, exceptional regular oscillations that make up the discrete spectrum of the Rankine vortex. In this paper, we examine the singular oscillations that make up the continuous spectrum (CS) and span the entire base state range of frequencies. In two dimensions, the CS eigenfunctions have a twin-vortex-sheet structure similar to that known from earlier investigations of parallel flows with piecewise linear velocity profiles. The vortex sheets are cylindrical, being threaded by axial lines, with one sheet at the edge of the core and the other at the critical radius in the irrotational exterior; the latter refers to the radial location at which the fluid co-rotates with the eigenmode. In three dimensions, the CS eigenfunctions have core vorticity and may be classified into two families based on the singularity at the critical radius. For the first family, the singularity is a cylindrical vortex sheet threaded by helical vortex lines, while for the second family it has a localized dipole structure with radial vorticity. The presence of perturbation vorticity in the otherwise irrotational exterior implies that the CS modes, unlike the Kelvin modes, offer a modal interpretation for the (linearized) interaction of the Rankine vortex with an external vortical disturbance. It is shown that an arbitrary initial distribution of perturbation vorticity, both in two and three dimensions, may be evolved as a superposition over the discrete and CS modes; this modal representation being equivalent to a solution of the corresponding initial value problem. For the restricted case of an initial axial vorticity distribution in two dimensions, the modal representation may be generalized to a smooth vortex. Finally, for the three-dimensional case, the analogy between rotational flows and stratified shear flows, and the known analytical solution for stratified Couette flow, are used to clarify the singular manner in which the modal superposition for a smooth vortex approaches the Rankine limit.

scholarly journals Convection Effects in Three-Dimensional Dendritic Growth

2001 ◽  
Vol 701 ◽  
Author(s):  
Yili Lu ◽  
C. Beckermann ◽  
A. Karma
Keyword(s):  
Dendritic Growth ◽  
Strong Influence ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Temperature Fields ◽  
Growth Morphology ◽  
Pure Material ◽  
Detailed Understanding

ABSTRACTA phase-field model is developed to simulate free dendritic growth coupled with fluid flow for a pure material in three dimensions. The preliminary results presented here illustrate the strong influence of convection on the three-dimensional (3D) dendrite growth morphology. The knowledge of the flow and temperature fields in the melt from the simulations allows for a detailed understanding of the convection effects on dendritic growth.

scholarly journals Convection Effects in Three-Dimensional Dendritic Growth

2002 ◽  
Author(s):  
Yili Lu ◽  
C. Beckermann ◽  
A. Karma
Keyword(s):  
Dendritic Growth ◽  
Strong Influence ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Temperature Fields ◽  
Detailed Knowledge ◽  
Growth Morphology ◽  
Pure Material

A phase-field model is developed to simulate free dendritic growth coupled with fluid flow for a pure material in three dimensions. The preliminary results presented here illustrate the strong influence of convection on the three-dimensional (3D) dendrite growth morphology. The detailed knowledge of the flow and temperature fields in the melt around the dendrite from the simulations allows for a detailed understanding of the convection effects on dendritic growth.

Sign in / Sign up

Export Citation Format

Share Document