Mechanics of a Free-Surface Liquid Film Flow

1987 ◽  
Vol 54 (4) ◽  
pp. 951-954 ◽  
Author(s):  
Cyrus K. Aidun
Keyword(s):  
Differential Equation ◽  
Free Surface ◽  
Film Flow ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equation ◽  
Higher Order Terms ◽  
Liquid Film Flow ◽  
Surface Liquid ◽  
Similar Equation

The mechanics of a free surface viscous liquid curtain flowing steadily between two vertical guide wires under the influence of gravity is investigated. The Navier-Stokes equation is integrated over the film thickness and an integro-differential equation is derived for the average film velocity. An approximate nonlinear differential equation, attributed to G. I. Taylor, is obtained by neglecting the higher order terms. An analytical solution is obtained for a similar equation which neglects the surface tension effects and the results are compared with the experimental measurements of Brown (1961).

scholarly journals On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Asai Asaithambi
Keyword(s):  
Differential Equation ◽  
Computational Effort ◽  
Navier Stokes ◽  
Series Solutions ◽  
Third Order ◽  
Navier Stokes Equation ◽  
Order Problem ◽  
Algorithmic Differentiation ◽  
Blasius Problem ◽  
Recursive Evaluation

The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed.

Numerical Analysis of a Floating Body With Two-Dimensional Moonpool Including Piston Mode

2010 ◽  
Author(s):  
Jaekyung Heo ◽  
Jong-Chun Park ◽  
Moo-Hyun Kim ◽  
Weon-Cheol Koo
Keyword(s):  
Free Surface ◽  
Viscous Flow ◽  
Experimental Results ◽  
Floating Body ◽  
Navier Stokes ◽  
Linear Potential ◽  
Navier Stokes Equation ◽  
Nonlinear Potential ◽  
Heave Motion ◽  
Piston Mode

In this paper, the potential and viscous flows are simulated numerically around a 2-D floating body with a moonpool (or a small gap) with particular emphasis on the piston mode. The floating body with moonpool is forced to heave in time domain. Linear potential code is known to give overestimated free-surface heights inside the moonpool. Therefore, a free-surface lid in the gap or similar treatments are widely employed to suppress the exaggerated phenomenon by potential theory. On the other hand, Navier-Stokes equation solvers based on a FVM can be used to take account of viscosity. Wave height and phase shift inside and outside the moon-pool are computed and compared with experimental results by Faltinsen et al. (2007) over various heaving frequencies. Pressure and vorticity fields are investigated to better understand the mechanism of the sway force induced by the heave motion. Furthermore, a nonlinear potential code is utilized to compare with the viscous flow. The viscosity effects are investigated in more detail by solving Euler equations. It is found that the viscous flow simulations agree very well with the experimental results without any numerical treatment.

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.

Wave-in-Deck Load on a Jacket Platform, CFD Calculations Compared With Experiments

2014 ◽  
Author(s):  
Bogdan Iwanowski ◽  
Tone Vestbøstad ◽  
Marc Lefranc
Keyword(s):  
Free Surface ◽  
Industrial Application ◽  
Computational Models ◽  
Cfd Simulation ◽  
Navier Stokes ◽  
Extreme Wave ◽  
Navier Stokes Equation ◽  
Jacket Platform ◽  
Irregular Wave ◽  
Start Up

The paper presents an industrial application of CFD for calculation of Wave-In-Deck load due to an extreme wave. Particular attention is given to flow kinematics initialization that is necessary to start up a CFD simulation. The applied CFD code, ComFLOW, is a Navier-Stokes equation solver with an improved Volume of Fluid (iVOF) method employed to displace and re-construct fluids free surface. For incoming waves high enough for a negative air-gap and therefore with Wave-In-Deck loads, a jacket platform was tested in model basin, for both regular and irregular wave cases. One of goals of these model tests was verification of CFD codes. The experimental and computational models of the structure are exactly the same. In the paper, the measured Wave-In-Deck forces are compared with CFD results.

scholarly journals Simulation of free-surface flow in a tank using the Navier-Stokes model and unstructured finite volume method

2005 ◽  
Vol 219 (3) ◽  
pp. 251-266 ◽  
Author(s):  
X Zhang ◽  
N M Sudharsan ◽  
R Ajaykumar ◽  
K Kumar
Keyword(s):  
Free Surface ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Free Surface Flow ◽  
Offshore Structures ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Volume Method ◽  
Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

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