scholarly journals Flow from a source above a sloping base

2020 ◽  
Vol 61 ◽  
pp. C75-C88
Author(s):  
Shaymaa Mukhlif Shraida ◽  
Graeme Hocking
Keyword(s):  
Free Surface ◽  
Flow Rate ◽  
Water Waves ◽  
Line Source ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Theoretical Research ◽  
Line Sink

We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3

scholarly journals Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink

1986 ◽  
Vol 28 (2) ◽  
pp. 260-270 ◽  
Author(s):  
I. L. Collings
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Ideal Fluid ◽  
Line Source ◽  
Steady Motion ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Flow Problems

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.

Unsteady free surface flow induced by a line sink in a fluid of finite depth

2008 ◽  
Vol 37 (3) ◽  
pp. 236-249 ◽  
Author(s):  
T.E. Stokes ◽  
G.C. Hocking ◽  
L.K. Forbes
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Line Sink

scholarly journals A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents

2016 ◽  
Vol 472 (2191) ◽  
pp. 20150833 ◽  
Author(s):  
Philippe H. Trinh
Keyword(s):  
Free Surface ◽  
Riemann Surface ◽  
Surface Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
The Body ◽  
Bluff Bodies ◽  
Free Surface Waves

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel.

Experimental Visualization of Lagrangian Coherent Structures in Aperiodic Free Surface Flow

2001 ◽  
Author(s):  
Antonis Chrisohoides ◽  
Fotis Sotiropoulos
Keyword(s):  
Free Surface ◽  
Coherent Structures ◽  
Finite Size ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Lagrangian Coherent Structures ◽  
Time Averaging ◽  
Complex Interactions ◽  
Passive Tracers

Abstract We propose a simple experimental technique for visualizing Lagrangian coherent structures (LCS) in turbulent free-surface flows. The technique employs digital photography to record the transport of passive tracers (small paper pieces) introduced manually at the free surface. Coherent eddies are detected by time-averaging the instantaneous light intensity fields on finite-size temporal windows. We demonstrate the potential of the method by applying it to visualize the flow in the vicinity of a surface-piercing rectangular block mounted at one corner of a rectangular open channel. We show that by appropriately selecting the time averaging window, the technique can reveal the presence of organized patterns in the chaotic instantaneous flow and elucidate their complex interactions.

scholarly journals The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

2017 ◽  
Vol 156 ◽  
pp. 526-533
Author(s):  
G.C. Hocking ◽  
H.H.N. Nguyen ◽  
T.E. Stokes ◽  
L.K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Effect Of Surface

scholarly journals A physically consistent particle method for high-viscous free-surface flow calculation

2021 ◽  
Author(s):  
Masahiro Kondo ◽  
Takahiro Fujiwara ◽  
Issei Masaie ◽  
Junichi Matsumoto
Keyword(s):  
Angular Momentum ◽  
Free Surface ◽  
Particle Method ◽  
Free Surface Flow ◽  
Momentum Conservation ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Particle Methods ◽  
Surface Flows ◽  
Angular Momentum Conservation

AbstractParticle methods for high-viscous free-surface flows are of great use to capture flow behaviors which are intermediate between solid and liquid. In general, it is important for numerical methods to satisfy the fundamental laws of physics such as the conservation laws of mass and momentum and the thermodynamic laws. Especially, the angular momentum conservation is necessary to calculate rotational motion of high-viscous objects. However, most of the particle methods do not satisfy the physical laws in their spatially discretized system. The angular momentum conservation law is broken mostly because of the viscosity models, which may result in physically strange behavior when high-viscous free-surface flow is calculated. In this study, a physically consistent particle method for high-viscous free-surface flows is developed. The present method was verified, and its performance was shown with calculating flow in a rotating circular pipe, high-viscous Taylor–Couette flow, and offset collision of a high-viscous object.

scholarly journals An open-channel flow meeting a barrier and forming one or two jets

2000 ◽  
Vol 41 (4) ◽  
pp. 458-472 ◽  
Author(s):  
L. H. Wiryanto ◽  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Vertical Wall ◽  
Open Channel Flow ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Surface Flow ◽  
Parameter Measuring ◽  
Two Jets

AbstractA steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.

Numerical Simulation of Free Surface Flows Using STACS-VOF Method

2007 ◽  
Author(s):  
Vedanth Srinivasan ◽  
De Ming Wang
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Current Method ◽  
Coupled System ◽  
Free Surface Flow ◽  
Surface Force ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Air Entrapment ◽  
Simple Strategy

This paper presents a numerical method that couples the incompressible Navier-Stokes equations with the Volume of Fluid method in a Cartesian co-ordinate system for tracking immiscible interfaces in multiple dimensions. The governing equations are discretized based on a finite volume method on a non-staggered fixed grid. The free surface flow problem is solved as a single phase flow system in which the free surface is captured using a Switching Technique for Advection and Capturing of Surfaces (STACS) scheme. The effects of surface tension at the interfaces are treated using a Continuum Surface Force (CSF) model. The pressure velocity coupling is achieved using a SIMPLE strategy. The coupled system, implemented in the commercial CFD software, AVL FIRE/SWIFT, is applied to a two dimensional dam breaking problem. The simulation results reveal a multitude of phenomena such as, free surface vortex generation, air entrapment and splashing of the liquid surge front. The computational results are in good agreement with experimental data, wherever available. The effects of time and grid resolution on the solution behavior are elaborated in detail. Different convection schemes are tested and the current method is compared to another existing interface capturing methodology.

Coupled Algebraic Multigrid for Free Surface Flow Simulations

2007 ◽  
Author(s):  
Philip J. Zwart ◽  
Alan D. Burns ◽  
Paul F. Galpin
Keyword(s):  
Free Surface ◽  
Volume Fraction ◽  
Mesh Size ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Solution Algorithm ◽  
Surface Flow ◽  
Algebraic Multigrid ◽  
Ansys Cfx ◽  
Velocity Pressure

An accurate, efficient algorithm for solving free surface flows with ANSYS CFX is described. Accuracy is achieved using a compressive advection discretization which maintains a sharp free surface interface representation without relying on a small timestep. Efficiency is obtained using a solution algorithm which implicitly couples velocity, pressure, and volume fractions in the same matrix, and solves these equations using algebraic multigrid. This coupled strategy overcomes difficulties encountered with segregated volume fraction algorithms, where heavy underrelaxation and long solution times are required. The resulting solution algorithm is scalable, leading to solution times which increase linearly with mesh size.

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