The fluid mechanics of slide coating

1989 ◽  
Vol 208 ◽  
pp. 321-354 ◽  
Author(s):  
K. N. Christodoulou ◽  
L. E. Scriven
Keyword(s):  
Liquid Films ◽  
Navier Stokes ◽  
Free Surfaces ◽  
Coating Flow ◽  
Slide Coating ◽  
Surface Profiles ◽  
Element Technique ◽  
Film Thinning ◽  
Inclined Surface ◽  
Dynamic Slip

Slide coating is a means of rapidly depositing multilayered liquid films of precise thickness and uniformity, as in manufacture of photographic products. Liquid is metered through one or more slots onto the inclined surface of the coating die, flows down that face and across a gap onto a fast-moving smooth surface. In this paper the steady, two-dimensional slide coating flow of a Newtonian liquid is analysed by solving the full Navier–Stokes system with the Galerkin/finite-element technique, spine parametrization of free surfaces and full Newton iteration. The lower meniscus in the gap is assumed to remain pinned at the die edge and the wetting-line singularity on the surface being coated is relieved by introducing dynamic-slip and contact-angle parameters. Results include the effects of several design and operating parameters on free-surface profiles and details of the flow field; these are presented by means of contours of kinematic and dynamic variables and local force balances over subdomains. The profiles show standing waves on the slide, rapid film thinning just before the gap, and exponential approach to the final film thickness on the web. As Reynolds number is raised and/or web speed is lowered several recirculation regions are predicted, deleterious features that have also been detected in experiments.

Two Dimensional Simulations of Enhanced Heat Transfer in an Intermittently Grooved Channel

2000 ◽  
Author(s):  
M. Greiner ◽  
P. F. Fischer ◽  
H. M. Tufo
Keyword(s):  
Heat Transfer ◽  
Local Heat Transfer ◽  
Spectral Element ◽  
Local Heat ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Number Range ◽  
Element Technique ◽  
Outflow Boundary

Abstract Two-dimensional Navier-Stokes simulations of heat and momentum transport in an intermittently grooved passage are performed using the spectral element technique for the Reynolds number range 600 ≤ Re ≤ 1800. The computational domain has seven contiguous transverse grooves cut symmetrically into opposite walls, followed by a flat section with the same length. Periodic inflow/outflow boundary conditions are employed. The development and decay of unsteady flow is observed in the grooved and flat sections, respectively. The axial variation of the unsteady component of velocity is compared to the local heat transfer, shear stress and pressure gradient. The results suggest that intermittently grooved passages may offer even higher heat transfer for a given pumping power than the levels observed in fully grooved passages.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

OPEN SOURCE COMPUTATIONS OF PLANING HULL RESISTANCE

2015 ◽  
Vol 157 (B2) ◽  
Author(s):  
M Ferrando ◽  
S Gaggero ◽  
D Villa
Keyword(s):  
Open Source ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equation ◽  
Free Surfaces ◽  
Hydrodynamic Parameters ◽  
Physical Problems ◽  
Engineering Problems ◽  
Simulation Strategy ◽  
Computational Fluid Dynamics Cfd

In recent years, the application of Computational Fluid Dynamics (CFD) methods experienced an exponential growth: the increase of the computational performances and the generalization of the Navier-Stokes equation to more complex physical problems made possible the solution of complex problems like free surfaces flows. The physical complexity of planing hulls flows poses some issues in the ability to numerically predict the global hydrodynamic parameters (hull resistance, dynamic attitude) of these configurations and on the expected confidence on the numerical results. In the last decade, commercial RANS software have been successfully applied for the prediction of the planing hull characteristics with reasonable correlation to the available experimental measurements. Recently, moreover, the interest in Open Source approaches, also for the solution of engineering problems, has rapidly grow. In this work, a set of calculations on a systematic series standard hull shape has been carried out, adopting from pre- to post- processing only Open Source tools. The comparison and the validation, through the available experimental measurements, of the computed results will define an optimal simulation strategy to include this kind of tools in the usual design loop.

Numerical Modeling of Si0.15Ge0.85 by the Traveling Solvent Method

2002 ◽  
Author(s):  
T. J. Makriyannis ◽  
M. Z. Saghir ◽  
D. Labrie
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Promising Technique ◽  
High Quality ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Buoyancy Convection ◽  
Strong Convection ◽  
Element Technique

The traveling solvent method (TSM) is a relatively new and promising technique for the production of high quality semiconductors. TSM has been tested on many alloys producing pure and homogeneous crystals. In the present study the effect of buoyancy convection on the growth of the Si0.15Ge0.85 crystal grown by the traveling solvent method is investigated under different heating conditions. The full Navier-Stokes equations together with the energy and solutal equations were solved numerically using the finite element technique. The model take into consideration the losses of heat by radiation and the use of the phase diagram to determine the silicon concentration at the growth interface. Results revealed a strong convection in the solvent, which in turn is detrimental to the growth uniformity in the crystal rod. Additional numerical results showed that the convective heat transfer significantly influences the solute distribution in the liquid zone and the growth rate increases substantially.

scholarly journals Numerical Modeling and Simulation of Wave Impact of a Circular Cylinder during the Submergence Process

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaozhou Hu ◽  
Yiyao Jiang ◽  
Daojun Cai
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Wave Load ◽  
Wave Impact ◽  
Rans Equations ◽  
Wave Slamming ◽  
Surface Profiles ◽  
Numerical Wave

Wave slamming loads on a circular cylinder during water entry and the subsequence submergence process are predicted based on a numerical wave load model. The wave impact problems are analyzed by solving Reynolds-Averaged Navier-Stokes (RANS) equations and VOF equations. A finite volume approach (FV) is employed to implement the discretization of the RANS equations. A two-dimensional numerical wave tank is established to simulate regular ocean waves. The wave slamming problems are investigated by deploying a circular cylinder into waves with a constant vertical velocity. The present numerical method is validated using other numerical or theoretical results in accordance with varying free surface profiles when a circular cylinder sinks in calm water. A numerical example is given to show the submergence process of the circular cylinder in waves, and both free surface profiles and the pressure distributions on the cylinder of different time instants are obtained. Time histories of hydrodynamic load on the cylinder during the submergence process for different wave impact angles, wave heights, and wave periods are obtained, and results are analyzed in detail.

Simulations of Three-Dimensional Flow and Augmented Heat Transfer in a Symmetrically Grooved Channel

2000 ◽  
Vol 122 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M. Greiner ◽  
R. J. Faulkner ◽  
V. T. Van ◽  
H. M. Tufo ◽  
P. F. Fischer
Keyword(s):  
Three Dimensional ◽  
Spectral Element ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Transverse Grooves ◽  
Flow Transitions ◽  
Element Technique ◽  
Good Agreement

Navier-Stokes simulations of three-dimensional flow and augmented convection in a channel with symmetric, transverse grooves on two opposite walls were performed for 180⩽Re⩽1600 using the spectral element technique. A series of flow transitions was observed as the Reynolds number was increased, from steady two-dimensional flow, to traveling two and three-dimensional wave structures, and finally to three-dimensional mixing. Three-dimensional simulations exhibited good agreement with local and spatially averaged Nusselt number and friction factor measurements over the range 800⩽Re⩽1600. [S0022-1481(00)00904-X]

scholarly journals The primary instability of falling films in the presence of soluble surfactants

2013 ◽  
Vol 729 ◽  
pp. 123-150 ◽  
Author(s):  
George Karapetsas ◽  
Vasilis Bontozoglou
Keyword(s):  
Stokes Equations ◽  
Liquid Films ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Desorption Kinetics ◽  
Order Of Magnitude ◽  
Soluble Surfactants ◽  
Experimental Findings ◽  
Adsorption Desorption ◽  
Primary Instability

AbstractWe investigate the linear stability of a film flowing down a solid substrate in the presence of soluble surfactants. The Navier–Stokes equations for the liquid motion are considered, together with advection–diffusion equations for the concentrations of the species involved, which include monomers dissolved in the bulk and adsorbed at the liquid–air and at the liquid–substrate interfaces. The adsorption–desorption kinetics of the surfactant at both interfaces is explicitly accounted for. An Orr–Sommerfeld eigenvalue problem is formulated, and solved analytically in the limit of long-wave disturbances and numerically for arbitrary wavelength using a finite element method. An extensive parametric study is performed to reveal the role of surfactant solubility and adsorption–desorption kinetics. The results quantify the stabilizing effect of soluble surfactants due to the presence of Marangoni stresses, and indicate that moderately soluble surfactants may be more effective than insoluble ones. Disturbances of finite wavelength are stabilized by more than an order of magnitude, and their detailed behaviour depends in a non-monotonic way on the amount of surfactant and on its solubility and kinetics. The above predictions provide insights for the interpretation of recent experimental findings on the primary instability and on the ensuing unstable dynamics of liquid films doped with soluble surfactants.

Interface Stabilized Nanoscale Quasi-Liquid Films

2009 ◽  
Vol 17 (4) ◽  
pp. 22-27 ◽  
Author(s):  
Jian Luo ◽  
Shen J. Dillon ◽  
Martin P. Harmer
Keyword(s):  
High Temperature ◽  
Binary Systems ◽  
Liquid Films ◽  
Interfacial Phenomena ◽  
Metallic Materials ◽  
Average Composition ◽  
Free Surfaces ◽  
Mechanical And Physical Properties ◽  
Interfacial Films ◽  
Equilibrium Thickness

A unique class of impurity-based quasi-liquid films has been widely observed at free surfaces, grain boundaries (GBs), and hetero-phase interfaces in ceramic and metallic materials (Figure 1). These nanometer-thick interfacial films can be alternatively understood to be: (a) quasi-liquid layers that adopt an “equilibrium” thickness in response to a balance of attractive and repulsive interfacial forces (in a high-temperature colloidal theory) or (b) multilayer adsorbates with thickness and average composition set by bulk dopant activities [1–2]. In several model binary systems, such quasi-liquid, interfacial films are found to be thermodynamically stable well below the bulk solidus lines, provoking analogies to the simpler interfacial phenomena of premelting in unary systems [3] and prewetting in binary de-mixed liquids [4]. These interfacial films exhibit structures and compositions that are neither observed nor stable as bulk phases, as well as transport, mechanical, and physical properties that are markedly different from bulk phases.

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