Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow through rockfill embankments: Reply

1996 ◽  
Vol 33 (1) ◽  
pp. 200-201
Author(s):  
David Hansen ◽  
Vinod K Garga ◽  
D Ronald Townsend
Keyword(s):  
Flow Equation ◽  
Darcy Flow ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Flow Through

Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow through rockfill embankments

1995 ◽  
Vol 32 (2) ◽  
pp. 223-232 ◽  
Author(s):  
David Hansen ◽  
Vinod K. Garga ◽  
D. Ronald Townsend
Keyword(s):  
Packed Column ◽  
Flow Equation ◽  
Hydraulic Gradient ◽  
Darcy Flow ◽  
Two Dimensional ◽  
Rating Curve ◽  
One Dimensional ◽  
Flow Equations ◽  
Flow Through ◽  
Hydraulics Laboratory

Porous embankments comprised of relatively homogeneous coarse rockfill can be used to reduce the amount of spillage at downstream hydro dams or to control the outflow from stormwater detention basins. The stage-discharge rating curve is important in the design of such applications. In general, the coarseness of the material causes the flow to be non-Darcy; that is, characterized by a nonlinear relationship between bulk velocity and hydraulic gradient. Six one-dimensional (1D) non-Darcy flow equations, appearing in the literature, are presented. A limited comparison between computed and experimental results is then made on the basis of 1D packed-column tests performed in the hydraulics laboratory of the University of Ottawa. The question as to how such 1D closed-conduit equations might be used to estimate the quantity of flow through a porous embankment is then addressed, considering that the latter has a free surface and is a two-dimensional (2D) flow. The problem is successfully dealt with using the concept of "effective hydraulic gradient," a concept reminiscent of the method of sections used to analyze confined 2D seepage problems. A general equation is presented in which the effective hydraulic gradient is shown to be a function of two factors: (1) the shape of the embankment and (2) the upstream depth, relative to the height of the dam. The development and verification of the equation for the effective hydraulic gradient is described, together with its use in obtaining a rating curve for a hypothetical flowthrough dam composed of rock material 0.25 m in diameter. Key words : non-Darcy flow, flowthrough rockfill, effective hydraulic gradient, stage-discharge rating curve.

Two-Dimensional Flow With Standing Vortexes in Ducts and Diffusers

1960 ◽  
Vol 82 (4) ◽  
pp. 921-927 ◽  
Author(s):  
Friedrich O. Ringleb
Keyword(s):  
Wind Tunnel ◽  
Potential Flow ◽  
Separation Control ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Princeton University ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
Trapping Devices

The conditions for the equilibrium of two vortexes in a two-dimensional flow through a duct or diffuser are derived. Potential-flow considerations and a few basic results from viscous-flow theory are used for the discussion of the role of cusps as separation control and trapping devices for standing vortexes. The investigations are applied to cusp diffusers especially with regard to the wind tunnel of the James Forrestal Research Center of Princeton University.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

Circulation Generation and Vortex Ring Formation by Conic Nozzles

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Moshe Rosenfeld ◽  
Kakani Katija ◽  
John O. Dabiri
Keyword(s):  
Vortex Ring ◽  
Vortex Generator ◽  
Ring Formation ◽  
Vortex Rings ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Vortex Ring Formation ◽  
Exit Nozzle ◽  
Two Dimensional Flow

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

scholarly journals AN ANALYSIS OF TWO-DIMENSIONAL FLOW THROUGH A WATER RESERVOIR USING MATHEMATICAL APPROACH

2019 ◽  
Vol 2 (1) ◽  
pp. 11-13
Author(s):  
Gohar Rehman ◽  
Qura Tul Ain ◽  
Muhammad Zaheer ◽  
Liulei Bao ◽  
Javed Iqbal
Keyword(s):  
Water Reservoir ◽  
Mathematical Approach ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Flow Through

Steady flow through non-uniform gauzes of arbitrary shape

1959 ◽  
Vol 5 (3) ◽  
pp. 355-368 ◽  
Author(s):  
J.W Elder
Keyword(s):  
Arbitrary Shape ◽  
Axisymmetric Flow ◽  
Circular Cone ◽  
The Other ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Uniform Shear ◽  
Two Dimensional Flow ◽  
Diverging Channel ◽  
Flow Through

The steady, two-dimensional flow through an arbitrarily-shaped gauze, of non-uniform properties, placed in a parallel channel is considered for the case in which viscosity can be ignored except in the immediate vicinity of the gauze. The equations are linearized by requiring departures from uniformity both in the flow and in the gauze parameters to be small. Knowledge of any three of the upstream profile, the downstream profile, the shape of the gauze and the gauze parameters, allows the other to be calculated from a linear relation between these four quantities. Particular solutions are given for the production of a uniform shear and the flow through linear and parabolic gauzes. The validity of the solution is verified by experiment. It is shown that the method can also be applied to two-dimensional flow in a diverging channel, axisymmetric flow in a circular pipe and in a circular cone and to flow through multiple gauzes.

scholarly journals Modeling of Transient Two Dimensional Flow in Saturated-Unsaturated Porous Media

2017 ◽  
Vol 13 (12) ◽  
pp. 195 ◽  
Author(s):  
Hassan Lemacha ◽  
Abdellatif Maslouhi ◽  
Moumtaz Razack
Keyword(s):  
Soil Surface ◽  
Flow Equation ◽  
Water Transfer ◽  
Richards Equation ◽  
Two Dimensional ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Finite Differences Method ◽  
Two Dimensional Flow ◽  
Unsaturated Zones

We study the transient two-dimensional flow problems related to the recharge of groundwater using an approach based on the physics of water transfer in the whole domain, including both the saturated and the unsaturated zones. Such a domain is limited by the soil surface and by the lower impervious boundary of the aquifer. The flow problem is solved using a numerical iterative procedure based on the alternate directions implicit finite differences method. To simulate the water transfer in an unsaturatedsaturated porous medium, we developed a mathematical model based on a single flow equation used for both zones. To this end, the unsaturated and saturated zones are regarded as only one continuum and the Richards equation is used for both zones. The simulated results were validated by the calculation of the mass balance, then on values obtained by an experimental model of 160 cm length and 50 cm in height. The numerical model reproduces in a satisfactory way the experimental results giving the spacetime evolution of the level of water table.

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