INFLUENCE OF FREE SURFACE ON LAMINAR FLOWS PAST A SURFACE-PIERCING CYLINDER NEAR A MOVING WALL

2021 ◽  
Vol 26 (2) ◽  
pp. 16-23
Author(s):  
Y.J. Kim ◽  
S.B. Lee
Keyword(s):  
Free Surface ◽  
Laminar Flows ◽  
Moving Wall

scholarly journals Coating Flow Near Channel Exit. A Theoretical Perspective

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 180
Author(s):  
Roger E. Khayat ◽  
Mohammad Tanvir Hossain
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Theoretical Perspective ◽  
Stress Singularity ◽  
Matched Asymptotic Expansion ◽  
Coating Film ◽  
Moving Wall ◽  
Slot Coating ◽  
Channel Exit

The planar flow of a steady moving-wall free-surface jet is examined theoretically for moderate inertia and surface tension. The method of matched asymptotic expansion and singular perturbation is used to explore the rich dynamics near the stress singularity. A thin-film approach is also proposed to capture the flow further downstream where the flow becomes of the boundary-layer type. We exploit the similarity character of the flow to circumvent the presence of the singularity. The study is of close relevance to slot and blade coating. The jet is found to always contract near the channel exit, but presents a mild expansion further downstream for a thick coating film. We predict that separation occurs upstream of the exit for slot coating, essentially for any coating thickness near the moving substrate, and for a thin film near the die. For capillary number of order one, the jet profile is not affected by surface tension but the normal stress along the free surface exhibits a maximum that strengthens with surface tension. In contrast to existing numerical findings, we predict the existence of upstream influence as indicated by the nonlinear pressure dependence on upstream distance and the pressure undershoot (overshoot) in blade (slot) coating at the exit.

scholarly journals Laminar Flow Structures Near a Circular Cylinder in between a Free-Surface and a Moving Wall

2012 ◽  
Vol 49 (3) ◽  
pp. 213-221 ◽  
Author(s):  
Jang-Hoon Seo ◽  
Jae-Hwan Jung ◽  
Hyun-Sik Yoon ◽  
Dong-Woo Park ◽  
Ho-Hwan Chun
Keyword(s):  
Free Surface ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Flow Structures ◽  
Moving Wall

scholarly journals Air Entrainment and Surface Fluctuations in a Turbulent Ship Hull Boundary Layer

2020 ◽  
Vol 64 (02) ◽  
pp. 185-201
Author(s):  
Naeem Masnadi ◽  
Martin A. Erinin ◽  
Nathan Washuta ◽  
Farshad Nasiri ◽  
Elias Balaras ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Outer Region ◽  
Surface Profile ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Quantitative Agreement ◽  
Surface Boundary ◽  
Moving Wall ◽  
Fluorescence Measurements

Air entrainment due to turbulence in a free-surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations (DNS). In the experiments, the moving wall is created by a laboratory-scale device composed of a surface-piercing stainless steel belt that travels in a loop around two vertical rollers; one length of the belt between the rollers simulates the moving wall. The belt accelerates suddenly from rest until reaching constant speed and creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer that would exist along a surface-piercing towed flat plate. We report cinematic laser-induced fluorescence measurements of water surface profile histories, cinematic observations and measurements of air entrainment events, and air bubble size distributions and motions. To complement the experiments, DNS of the temporally evolving turbulent boundary layer were conducted, considering both the air and water phases. Because of cost considerations, only a portion of the belt was simulated at a lower Reynolds number, keeping the Froude number, however, at the same levels as in the experiments. The results of the experiments and DNS are found to be in qualitative agreement and are used synergistically to explore the physics of the air entrainment process; quantitative agreement is not to be expected given the differences in setup and Reynolds numbers. In the experiments and DNS, the free-surface motion is found to consist of a region near the belt with fast-moving uncorrelated large-amplitude ripples and an outer region of small-amplitude propagating waves. Entrainment events similar to plunging breaking waves are found in the experiments, and these and other entrainment mechanisms are examined in detail in the DNS. The spatial distributions of bubble numbers and velocities are reported along with their diameter distributions.

The development of three-dimensional disturbances in an unstable film of liquid flowing down an inclined plane

1961 ◽  
Vol 10 (3) ◽  
pp. 401-419 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Harmonic Component ◽  
Fourier Integral ◽  
Initial Distribution ◽  
Laminar Flows ◽  
Complete Class ◽  
Amplification Rate ◽  
Bounded Disturbance ◽  
Small Disturbances

On the basis of results from a previous paper, expressions are found for the phase velocity and amplification rate of a wave travelling obliquely to the direction of flow. This wave comprises the general harmonic component of three-dimensional small disturbances, and accordingly a double Fourier integral is introduced to represent a bounded disturbance whose initial distribution over the free surface may be arbitrarily prescribed. Hence an asymptotic approximation is derived for a disturbance which is initially concentrated around a point on the free surface. Several distinctive properties of a localized unstable disturbance are noted: for instance, it lies mainly within an elliptical region whose area increases linearly with time as it moves downstream and which is modulated by long-crested waves. An experimental observation of a growing disturbance on an unstable film is recorded, and its main features are seen to be in agreement with the theory.In so far as linearized perturbation theory remains applicable, the effects investigated are common to a wide class of parallel and nearly parallel laminar flows. In the final part of the paper the method used to analyse the instability of a film is generalized in order to reveal the connexion between this and other problems; this aim is achieved by demonstrating collective properties of the complete class of flows in question, but particular reference is made to the example of laminary boundary layers and Poiseuille flow between parallel planes.

scholarly journals Stability of bedforms in laminar flows with free surface: from bars to ripples

2009 ◽  
Vol 642 ◽  
pp. 329-348 ◽  
Author(s):  
O. DEVAUCHELLE ◽  
L. MALVERTI ◽  
É. LAJEUNESSE ◽  
P.-Y. LAGRÉE ◽  
C. JOSSERAND ◽  
...  
Keyword(s):  
Free Surface ◽  
Stability Analysis ◽  
Stokes Equations ◽  
Transport Model ◽  
Bedload Transport ◽  
Laminar Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability

The present paper is devoted to the formation of sand patterns by laminar flows. It focuses on the rhomboid beach pattern, formed during the backswash. A recent bedload transport model, based on a moving-grains balance, is generalized in three dimensions for viscous flows. The water flow is modelled by the full incompressible Navier–Stokes equations with a free surface. A linear stability analysis then shows the simultaneous existence of two distinct instabilities, namely ripples and bars. The comparison of the bar instability characteristics with laboratory rhomboid patterns indicates that the latter could result from the nonlinear evolution of unstable bars. This result, together with the sensibility of the stability analysis with respect to the parameters of the transport law, suggests that the rhomboid pattern could help improving sediment transport models, so critical to geomorphologists.

scholarly journals On periodic geophysical water flows with discontinuous vorticity in the equatorial f -plane approximation

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170096 ◽  
Author(s):  
Calin Iulian Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Small Amplitude ◽  
Wave Speed ◽  
Laminar Flows ◽  
Local Bifurcation ◽  
Two Dimensional ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Water Flows

We are concerned here with geophysical water waves arising as the free surface of water flows governed by the f -plane approximation. Allowing for an arbitrary bounded discontinuous vorticity, we prove the existence of steady periodic two-dimensional waves of small amplitude. We illustrate the local bifurcation result by means of an analysis of the dispersion relation for a two-layered fluid consisting of a layer of constant non-zero vorticity γ 1 adjacent to the surface situated above another layer of constant non-zero vorticity γ 2 ≠ γ 1 adjacent to the bed. For certain vorticities γ 1 , γ 2 , we also provide estimates for the wave speed c in terms of the speed at the surface of the bifurcation inducing laminar flows. This article is part of the theme issue ‘Nonlinear water waves’.

Flow of Moving Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Rizwana Amin ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Equations Of Motion ◽  
Outer Region ◽  
Moving Wall ◽  
Moderate Reynolds Number ◽  
Boundary Layer Region ◽  
Asymptotic Development ◽  
Layer Region

The two-dimensional jet flow of a Newtonian fluid at moderate Reynolds Number emerging from a channel where the upper plate is moving is examined theoretically in this study. In this case, the equations of motion are reduced by expanding the flow field about the basic Couette flow. Inertia is assumed to be large enough, allowing asymptotic development in terms of the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow in the free surface and the moving wall. The influence of this boundary layer is investigated with the aid of the method of matched asymptotic expansions. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface and the flow both in the inner (boundary-layer) region and in the outer region of the core. The influence of wall velocity on the shape of the free surface, the velocity and stress is emphasized. The formulation allows for the determination of the steady state flow and free surface profiles analytically. The present work provides the conditions near exit, with the help of Higher-order boundary-layer effects (i.e. the cubic term of the inverse Reynolds number), to determine the jet structure further downstream.

Effect of Wall Movement on a Jet Depositing on a Moving Wall at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Yahia Hussain ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Core Region ◽  
Relaxation Length ◽  
Moving Wall ◽  
The Core ◽  
Wall Movement ◽  
Moderate Reynolds Number ◽  
Surface Jet

The steady flow of a moderately inertial jet depositing on a moving wall, is examined theoretically near channel exit. The free surface jet emerges from a channel and adheres to a wall, which may move in the same or opposite direction to the acting channel pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow field is obtained as a composite expansion by matching the flow in the boundary layer regions near the free surface, with the flow in the core region. The influence of inertia and wall velocity on the shape of the free surface, the velocity and stress is emphasized. It is found that the viscous relaxation length is essentially uninfluenced by the velocity of a forward moving wall. In contrast, it diminishes rapidly with the velocity of a backward moving wall.

Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Stefano Lovato ◽  
Serge L. Toxopeus ◽  
Just W. Settels ◽  
Geert H. Keetels ◽  
Guilherme Vaz
Keyword(s):  
Free Surface ◽  
Newtonian Fluid ◽  
Analytical Solutions ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Laminar Flows ◽  
Phase Flow ◽  
Code Verification ◽  
Two Phase ◽  
Flow Solver

Abstract The presence of complex fluids in nature and industrial applications combined with the rapid growth of computer power over the past decades has led to an increasing number of numerical studies of non-Newtonian flows. In most cases, non-Newtonian models can be implemented in existing Newtonian solvers by relatively simple modifications of the viscosity. However, due to the scarcity of analytical solutions for non-Newtonian fluid flows and the widespread use of regularization methods, performing rigorous code verification is a challenging task. The method of manufactured solutions (MMS) is a powerful tool to generate analytical solutions for code verification. In this article, we present and discuss the results of three verification exercises based on MMS: (i) steady single-phase flow; (ii) unsteady two-phase flow with a smooth interface; (iii) unsteady two-phase flow with a free surface. The first and second exercises showed that rigorous verification of non-Newtonian fluid solvers is possible both on single- and two-phase flows. The third exercise revealed that “spurious velocities” typical of free-surface calculations with the Volume-of-Fluid model lead to “spurious viscosities” in the non-Newtonian fluid. The procedure is illustrated herein on a second-order finite volume flow solver, using the regularized Herschel-Bulkley fluid model as an example. The same methodology is however applicable to any flow solver and to all the rheological models falling under the class of generalized Newtonian fluid models.

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