scholarly journals Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions

1993 ◽  
Vol 34 (3) ◽  
pp. 368-376 ◽  
Author(s):  
Hocine Mekias ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Surface Profile ◽  
Free Surface Flow ◽  
Shear Layers ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Infinite Depth ◽  
Free Surface Profile ◽  
Series Truncation Method

AbstractTwo-dimensional free-surface flows produced by a submerged source in a fluid of infinite depth are considered. It is assumed that the point on the free surface just above the source is a stagnation point and that the fluid outside two shear layers is at rest. The free-surface profile and the shape of the shear layers are determined numerically by using a series-truncation method. It is shown that there is a solution for each value of the Froude number F > 0. When F tends to infinity, the flow also describes a thin jet impinging in a fluid at rest.

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.

scholarly journals A model for the free-surface flow due to a submerged source in water of infinite depth

1998 ◽  
Vol 39 (4) ◽  
pp. 528-538 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Nonuniform Distribution ◽  
Infinite Depth ◽  
Collocation Points ◽  
Series Truncation Method

AbstractWe consider a free-surface flow due to a source submerged in a fluid of infinite depth. It is assumed that there is a stagnation point on the free surface just above the source. The free-surface condition is linearized around the rigid-lid solution, and the resulting equations are solved numerically by a series truncation method with a nonuniform distribution of collocation points. Solutions are presented for various values of the Froude number. It is shown that for sufficiently large values of the Froude number, there is a train of waves on the free surface. The wavelength of these waves decreases as the distance from the source increases.

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 Meshless particle modelling of free surface flow over spillways

2015 ◽  
Vol 18 (2) ◽  
pp. 354-370 ◽  
Author(s):  
Ehsan Jafari-Nodoushan ◽  
Khosrow Hosseini ◽  
Ahmad Shakibaeinia ◽  
Seyed-Farhad Mousavi
Keyword(s):  
Free Surface ◽  
Surface Profile ◽  
Particle Method ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Weakly Compressible ◽  
Wall Boundary Conditions ◽  
Free Surface Profile ◽  
Moving Particle ◽  
Lagrangian Particle Method

A meshless Lagrangian (particle) method based on the weakly compressible moving particle semi-implicit formulation (WC-MPS) is developed and analysed for simulation of flow over spillways. To improve the accuracy of the model for pressure and velocity calculation, some modifications are proposed and evaluated for the inflow and wall boundary conditions implementation methods. The final model is applied for simulation of flow over the 45° and 60° ogee spillways (with different inflow rates) and also shallow flow over a spillway-like curved bed channel. To evaluate the model, the numerical results of free surface profile and velocity and pressure field are compared with the available experimental measurements. Comparisons show the results’ accuracy of the developed model and proposed improvements. The results of this study will not only provide a reliable numerical tool for modelling of flow over spillways, but also provide an insight for better understating flow pattern over these hydraulic structures.

Free Surface Flow Profile and Fluctuations of a Circular Hydraulic Jump Formed by an Impinging Jet

1995 ◽  
Vol 117 (4) ◽  
pp. 677-682 ◽  
Author(s):  
J. W. Stevens
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Surface Profile ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Profile ◽  
Flow Depth ◽  
Supercritical Flow ◽  
Jump Size ◽  
Free Surface Profile

A fine wire probe was used to make quantitative measurements of the free surface profile and surface fluctuations around the hydraulic jump formed by a normally impinging free liquid jet. Representative magnitudes of both radial and axial fluctuations were presented for two nozzle sizes and several jet Reynolds numbers and subcritical flow depths. The results were compared to previous measurements of the supercritical flow depth and to theoretical predictions of the circular hydraulic jump size. The agreement appeared reasonable for the supercritical flow depth while the analytical expressions predicted a shorter hydraulic jump than that found by the measurements for the same supercritical flow conditions.

Two-dimensional natural element analysis of double-free surface flow under a radial gate

2012 ◽  
Vol 39 (6) ◽  
pp. 643-653 ◽  
Author(s):  
Farhang Daneshmand ◽  
S.A. Samad Javanmard ◽  
Jan F. Adamowski ◽  
Tahereh Liaghat ◽  
Mohammad Mohsen Moshksar
Keyword(s):  
Free Surface ◽  
Surface Profile ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Free Surface Profile ◽  
Natural Element ◽  
Gravity Driven ◽  
Radial Gate

The gravity-driven free surface flow problems for which both the solid and free surface boundaries are highly curved are very difficult to solve. A computational scheme using a variable domain and a fixed domain natural element method (NEM) is developed in the present study for the computation of the free surface profile, velocity and pressure distributions, and the flow rate of a 2D gravity fluid flow through a conduit and under a radial gate. The problem involves two highly curved unknown free surfaces and arbitrary curved-shaped boundaries. These features make the problem more complicated than flow under a sluice gate or over a weir. The fluid is assumed to be inviscid and incompressible and the results obtained are confirmed by conducting a hydraulic model test. The results are in agreement with other flow solutions for free surface profiles and pressure distributions.

A Study of Multi-Step Overfall Flows by Computational Fluid Dynamics

2013 ◽  
Vol 405-408 ◽  
pp. 3208-3212
Author(s):  
Jyh Haw Tang ◽  
Ming Kuan Sun ◽  
Ying Chen
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Surface Profile ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows ◽  
Engineering Designs ◽  
Free Surface Profile ◽  
Free Overfall

This paper proposes the least-squares finite element method (LSFEM) for simulating the free surface flows in multi-step free overfalls. Motion of the free surface flows is represented with two-phased surface profiles by solving the Navier-Stokes equations. The fluid is considered to be incompressible and the dynamic and kinematic boundary conditions of free surface are described in an Eulerian coordinate system. In this simulation, the volume of fluid (VOF) method and continuous stress force (CSF) models in association of color function are incorporated for the determination of the interface between water and air. The simulation results from the LSFEM model are carefully verified for the unit-step free overfall case. The quantitative comparisons in terms of the parameters such as different inflow rates, reattached length, water height after the fall and critical depth with previous numerical results or experimental measurements are shown to be in good agreement. In order to understand more about the complicate free surface profile of a dual-step free overfall, the LSFEM model is simulated for different inflow rates. In comparison with the available experimental data, it is shown that the LSFEM can effectively simulate the multi-step free overfall flow phenomena. Our study presents some regression formula for the dual-step free overfall, it is hoped that these formula will be helpful for the engineering designs and applications.

Improvement of Pressure Calculations in the Moving Particle Semi-Implicit Method for Free-Surface Flows

2019 ◽  
Vol 17 (09) ◽  
pp. 1950062 ◽  
Author(s):  
Wenjin Gou ◽  
Shuai Zhang ◽  
Yao Zheng
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Boundary ◽  
Navier Stokes Equation ◽  
Surface Flows ◽  
Mps Method ◽  
Flow Simulations ◽  
Moving Particle

In this paper, numerical improvements are implemented for solving for the pressure in the moving particle semi-implicit (MPS) method for free-surface flow simulations. The tensile instability problem is solved using a dynamic stabilization (DS) algorithm. The low numerical diffusion of this algorithm is shown through numerical tests. A free-surface treatment that includes an accurate free-surface particle detection algorithm and the implicit application of a free-surface boundary condition is used. The solution of the Navier–Stokes equation is improved using a particle shifting (PS) algorithm. The proposed MPS method for free-surface flow simulations is successfully applied in several benchmark tests and two- and three-dimensional dam break problems. The numerical simulation results agree well with the analytical and empirical ones. It is shown that the proposed MPS method effectively improves the stability and accuracy of simulations of free-surface flows.

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 SPH Open Boundary Simulation of Free-Surface Flow Over Ogee-crested Spillway

2021 ◽  
Vol 28 (2) ◽  
pp. 137-151
Author(s):  
Rizgar Karim ◽  
Jowhar Mohammad
Keyword(s):  
Free Surface ◽  
Open Source ◽  
Water Surface ◽  
Surface Profile ◽  
Free Surface Flow ◽  
The United States ◽  
Surface Flow ◽  
Absolute Difference ◽  
Open Boundary ◽  
Water Surface Profile

This study was conducted to compare water surface profiles with standard ogeecrested spillways. Different methods were used, such as (experimental models, numerical models, and design nomographs for the United States Army Corps of Engineers, USACE). In accordance with the USACE specifications, three different models were constructed from rigid foam and then installed in a testing flume. The water surface profile has been recorded for these models with different design heads. For modeling the experimental model configurations, a numerical model based on the smoothed particle hydrodynamics (SPH) technique was used and is developed to simulate the water surface profile of the flow over the ogee-crested spillway. A 2D SPHysics open-source software has been used in this study, using the SPH formulation to model fluid flow, developing the SPH boundary procedure to handle open-boundary simulations, and modifying the open-source SPHysics code for this purpose. The maximum absolute difference between the measured and computed results of the water surface profile for all head ratios of (H/Hd), does not exceed 4.63% at the crest region, the numerical results for the water surface profile showed good agreement with the physical model results. The results obtained experimentally and numerically by SPH are compared with the CFD results in order to be more reassuring from the results. Additional comparisons were made using interpolated data from USACE, Waterways Experiment Station (WES), and design nomographs. The SPH technique is considered very promising and effective for free surface flow applications.

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