Second-order cnoidal waves at the free surface and interface of a two-fluid system

1987 ◽  
Vol 8 (6) ◽  
pp. 497-502 ◽  
Author(s):  
Liu Yu-lu ◽  
Dai Shi-qiang
Keyword(s):  
Free Surface ◽  
Second Order ◽  
Fluid System ◽  
Cnoidal Waves ◽  
Surface And Interface ◽  
Two Fluid

scholarly journals On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Chi-Min Liu ◽  
Hwung-Hweng Hwung ◽  
Ray-Yeng Yang
Keyword(s):  
Transfer Functions ◽  
Perturbation Technique ◽  
Wave Theory ◽  
Order Theory ◽  
Second Order ◽  
Stokes Wave ◽  
Order Effects ◽  
Fluid System ◽  
Two Fluids ◽  
Two Fluid

Second-order solutions of internal and surface waves in a two-fluid system are theoretically analyzed in this study. Using the perturbation technique, the derivation of second-order solutions for internal waves is revisited, and the results are expressed in one-by-one forms instead of a matrix form. Second-order solutions arising from the interactions of two arbitrary linear waves of different frequencies contain the sum-frequency (superharmonic) and the difference-frequency (subharmonic) components, which are separately examined. Internal Stokes wave being a special case of present solutions is firstly investigated. Next, the convergence of second-order theory and the second-order effects on wave profiles are analyzed. For general cases, the effects of the thickness ratio of two fluids and the ratio of wavenumbers of two first-order waves on second-order wave characteristics, which include transfer functions and particle velocities, are also examined. Moreover, most existing theories for the one-fluid and two-fluid systems can be deduced from present solutions.

Numerical Simulation of Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics

2010 ◽  
Author(s):  
Samir Hassan Sadek ◽  
Mehmet Yildiz
Keyword(s):  
Free Surface ◽  
Smoothed Particle Hydrodynamics ◽  
Second Order ◽  
Rheological Parameters ◽  
Die Swell ◽  
Two Dimensional ◽  
Polymeric Fluid ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Second Order Fluids

This work presents the development of both weakly compressible and incompressible Smoothed Particle Hydrodynamics (SPH) models for simulating two-dimensional transient viscoelastic free surface flow which has extensive applications in polymer processing industries. As an illustration with industrial significance, we have chosen to model the extrudate swell of a second-order polymeric fluid. The extrudate or die swell is a phenomenon that takes place during the extrusion of polymeric fluids. When a polymeric fluid is forced through a die to give a polymer its desired shape, due to its viscoelastic non-Newtonian nature, it shows a tendency to swell or contract at the die exit depending on its rheological parameters. The die swell phenomenon is a typical example of a free surface problem where the free surface is formed at the die exit after the polymeric fluid has been extruded. The swelling process leads to an undesired increase in the dimensions of the extrudate. To be able to obtain a near-net shape product, the flow in the extrusion process should be well-understood to shed some light on the important process parameters behind the swelling phenomenon. To this end, a systematic study has been carried out to compare constitutive models proposed in literature for second-order fluids in terms of their ability to capture the physics behind the swelling phenomenon. The effect of various process and rheological parameters on the die swell such as the extrusion velocity, normal stress coefficients, and Reynolds and Deborah numbers have also been investigated. The models developed here can predict both swelling and contraction of the extrudate successfully. The die swell problem was solved for a wide range of Deborah numbers and for two different Re numbers. The numerical model was validated through the solution of fully developed Newtonian and Non-Newtonian viscoelastic flows in a two-dimensional channel, and the results of these two benchmark problems were compared with analytic solutions, and good agreements were obtained.

scholarly journals Asymptotic behaviour of dam break flow for small times

2019 ◽  
pp. 7-27
Author(s):  
Дамла Исидичи Демирель ◽  
Алессандро Яфрати ◽  
Александр Коробкин ◽  
Огуз Йилмаз
Keyword(s):  
Free Surface ◽  
Corner Point ◽  
Domain Decomposition Method ◽  
Second Order ◽  
Lagrangian Description ◽  
Bottom Part ◽  
Free Surfaces ◽  
Lagrangian Variables ◽  
Gravity Driven Flow ◽  
Horizontal Portion

Двумерное импульсное течение жидкости изучается в рамках теории потенциального потока. Первоначально жидкость находится в состоянии покоя и удерживается на одной стороне вертикальной пластины. Она внезапно убирается и поток жидкости начинает течь под действием силы тяжести. Внимание уделяется особому поведению поля скоростей в нижней точке, где вертикальная свободная поверхность встречается с жестким дном. Линейная задача решается методом рядов Фурье. Решение внутренней области находится с помощью преобразования Меллина в нижней точке. Формирование струи наблюдается в нижней точке. Разрыв в верхней угловой точке исследуется с помощью Лагранжевых переменных. Для внешней задачи второго порядка используется метод декомпозиции области. Сравнение форм свободных поверхностей вблизи верхней угловой точки с решениями переднего и второго порядка показывает, что внешнее решение второго порядка имеет большее различие в вертикальной свободной поверхности, чем в горизонтальной части, по сравнению с решением ведущего порядка. Получена картина форм свободных поверхностей с использованием Лагранжевого описания для верхней части и Эйлерого описания для нижней части во втором порядке. Two dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

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