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 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 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.

Divergent low-Froude-number series expansion of nonlinear free-surface flow problems

1978 ◽  
Vol 361 (1705) ◽  
pp. 207-224 ◽  
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Continuous Wave ◽  
Free Surface Flow ◽  
Formal Series ◽  
Surface Flow ◽  
Exponential Integral ◽  
Flow Problems ◽  
Low Froude Number ◽  
Nonlinear Free Surface

The low-Froude-number approximation in free-surface hydrodynamics is singular, and leads to formal series in powers of the Froude number with zero radius of convergence. The properties of these divergent series are discussed for several types of two-dimensional flows. It is shown that the divergence is of ‘n!' or exponential-integral character. A potential or actual lack of uniqueness is discovered and discussed. The series are summed by use of suitable nonlinear iterative transformations, giving good accuracy even for moderately large Froude number. Converged ' solutions ’ are obtained in this way, which possess jump discontinuities on the free surface. These jumps can be explained and, in principle, removed, by consideration of appropriate choices for the branch cut of the limiting exponential-integral solution. For example, we provide here a solution for a continuous wave-like flow, behind a semi-infinite moving body.

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.

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 A cusp-like free-surface flow due to a submerged source or sink

1984 ◽  
Vol 25 (4) ◽  
pp. 443-450 ◽  
Author(s):  
E. O. Tuck ◽  
J.-M. Vanden Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Line Source ◽  
Free Surface Flow ◽  
Surface Flow

AbstractA solution is found for a line source or sink beneath a free surface, at a unique squared Froude number of 12.622.

Model coupling techniques for free-surface flow problems: Part II

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1897-e1908 ◽  
Author(s):  
E. Miglio ◽  
S. Perotto ◽  
F. Saleri
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Model Coupling ◽  
Flow Problems ◽  
Coupling Techniques
Sign in / Sign up

Export Citation Format

Share Document