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

Water impact phenomenon in the case of a circular cylinder is an important issue in offshore industry where cross members may be in the splash zone of the incident wave. An analytical method as well as a numerical solution are employed to study the water entry problem of a circular section. The procedure for derivation of the analytical formulas is demonstrated step by step. The volume of fluid (VOF) simulation of the water entry problem is also performed to offer comparison of the results of the linearized analytical solution with a fully nonlinear and viscous fluid flow solution. To achieve this, the FLOW-3D code is utilized. Some consideration has also been given to the points of intersection of the free surface and the body, where the singularities exist in the free surface deformation and velocities, as predicted by the linear theory. These singularities appear to be avoided in the real fluid by the formation of jets which quickly break up into sprays under the action of surface tension. Slamming force, free surface profile, impact force, pressure distribution and evolution of intersection points are also presented and comparisons of the obtained results against the results of previous studies illustrate favorable agreements.

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are ob- tained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bub- ble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under dif- ferent parameters can be observed in our model, as demon- strated in our calculation results.

Water entry is a fluid–structure interaction process closely related to the ocean environment. Repeated water entries take place when ships are sailing in an ocean environment, e.g., ocean currents, which greatly affect the ship's safety and stability in navigation. In this paper, we adopt a smoothed particle hydrodynamics method to numerically study the water entry of a bow-flare ship body section under ocean currents. We simulate the process of water entry under different current velocities and analyze in detail the fluid field regarding the free surface evolution, the velocity and pressure distributions, and the body's forces and motions. It is revealed that the ocean current can induce multidirectional fluid impacts, and a stagnation point with zero velocity occurs at the upstream side. Asymmetric fluid fields including the evolution of the free surface and the velocity and pressure distributions around the body can also be found. In addition, discrepancies are caused in the formation time and the range of the high-pressure region. These fluid field changes greatly affect the ship body's dynamic responses. However, the effects of the ocean current are mainly reflected in the direction of the current flow and are relatively small in the direction perpendicular to the flow.

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress.Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves.In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.

A comparison study of water impact and water exit models

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of $\Z^d$. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of $\Z^3$ belongs to the interval $[0.78595,0.78599]$, improving best previously known estimate of (approximately) $[0.7850,0.7862]$ obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}. Moreover, we show that given a target additive error $\epsilon>0$, the computational effort of our method for these two models is $(1/\epsilon)^{O(1)}$ \emph{both} for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require $\exp\big((1/\epsilon)^{O(1)}\big)$ computation effort.

Nonlinear solutions of free surface flow under a sluice gate are studied. Upstream, the fluid is assumed to be infinitely deep, and the gate is at an angle to the horizontal axis. The flow emerges from the gate and produces a uniform flow far downstream. The problem is solved numerically by a boundary element method derived from an integral equation along the free surface. An analytical function is constructed, related to the upstream flow, so that the integral equation is solvable. As a result, a free surface flow with smooth detachment from the edge of the gate is obtained for relatively large upstream Froude numbers. As the Froude number decreases, a free surface with back flow near the edge of the gate occurs, until at a certain Froude number a stagnation point occurs. References D. D. Frangmeier, T. S. Strelkoff, Solution for gravity flow under a sluice gate, ASCE J. Engng. Mech. Div. , 94 , 1968, 153--176. B. E. Lorock, Gravity-affected flow from planer sluice gate, ASCE J. Engng. Mech. Div. , 96 , 1969, 1211--1226. Y. K. Chung, Solution of flow under sluice gates, ASCE J. Engng. Mech. Div. , 98 , 1972, 121--140. J. Asavanant, J.-M. Vanden-Broeck, Nonlinear free surface flows emerging from vessels and flows under a sluice gate, J. Austral. Math. Soc. , 38 , 1996, 63--86. doi:10.1017/S0334270000000473 J.-M. Vanden-Broeck, Numerical calculations of the free-surface flow under a sluice gate, J. Fluid Mech. , 330 , 1996, 339--347. http://journals.cambridge.org/abstract_S0022112096003849 B. J. Binder, J.-M. Vanden-Broeck, Free surface flows past surfboards and sluice gates, Eur. J. Appl. Maths. , 16 , 2005, 601--619 doi:10.1017/S0956792505006443 B. J. Binder, J.-M. Vanden-Broeck, The effect of disturbances on the flows under a sluice gate and past an inclined plate, J. Fluid Mech. , 576 , 2007, 475--490 doi:10.1017/S0022112007004806 J.-M. Vanden-Broeck, E. O. Tuck, Flow near the interaction of a free surface with a vertical wall, SIAM J. Appl. Math. , 54 , 1994, 1--33. doi:10.1137/S0036139992240838 L. H. Wiryanto, J. Widjaja, B. Supriyanto, Free-surface flow under a sluice gate from deep water, Bul. Malay. Math. Soc. , 34 , 2011, 601--609. http://www.emis.de/journals/BMMSS/vol34_3_17.html L. H. Wiryanto, E. O. Tuck, A back-turning jet formed by a uniform shallow stream hitting a vertical wall, Proc. Int. Conf. on Dif. Eqs. , Kluwer Academic Press, 1997. L. H. Wiryanto, E. O. Tuck, An open-channel flow meeting a barrier and forming one or two jets, J. Austral. Math. Soc. , 41 , 2000, 458--472. doi:10.1017/S0334270000011760 L. H. Wiryanto, Small Froude number solutions of flow caused by a line source, J. Indones. Math. Soc. , 6 , 2000, 1--6. G. C. Hocking, L. K. Forbes, A note on the flow induced by a line sink beneath a free surface, J. Austral. Math. Soc. B , 32 , 1991, 251--260. doi:10.1017/S0956792507006924 G. C. Hocking, L. K. Forbes, Subcritical free-surface flow caused by a line source in a fluid of finite depth, J. Eng. Math. , 26 , 1992, 455--466. doi:10.1007/BF00042763 L. H. Wiryanto, Zero gravity of a jet emerging from a slit, J. Indones. Math. Soc. , 12 , 2006, 89--98. L. M. Milne-Thomson, Theoretical hydrodynamics . Dover Publications, Inc., 1968, 274--281.

A recently developed and validated open-source nonequilibrium Navier–Stokes solver, hyperReactingFoam is used for analyses of Mach 7 flows of air with 8.0 megajoules per kilogram (MJ/kg) stagnation enthalpy over double wedges with four distinct aft angles of 45°, 50°, 55°, and 60°. The validation studies contain both qualitative and quantitative comparisons of the obtained results with experimental and two numerical results available in the literature for the 30°–55° double wedge model. Physics and characteristics of the flows are revealed by comparing the shock structures, chemical compositions, surface pressure, and wall heat flux distributions of each aft angle. It is seen that increased aft angle significantly enhances the magnitudes of wall heat flux and surface pressure. Fluctuations of wall heat flux and surface pressure distributions in time significantly increase along the second wedge surface in the case of higher aft angles. Faster chemical reaction rates take place also for larger aft angles, regardless of the assumption of the flow to be in thermal equilibrium or nonequilibrium. The flow is observed to be chemically frozen downstream of the expansion corner. Time-averaged wall heat flux magnitudes of the flow for the aft angle values of 55° and 60° are found to be three times larger than of the flow with 2.1 MJ/kg stagnation enthalpy.

Laboratory experiments are conducted to measure the velocities of 2D turbulent open channel flow upstream of a vertical sluice gate. The flow case having the same conditions with the experiment is analyzed by computational fluid dynamics simulation. The finite element method is used to solve the governing equations by employing the standard k –ε and standard k–ω turbulence closure models. The volume of fluid method is used to determine the free surface of the flow. The numerical results for the velocity field and the free surface profile from eight different computational meshes are compared with the experimental data, and based on the comparisons; the most suitable mesh system among the eight is selected. The comparisons of the numerical and experimental results show that the numerical simulation using the k–ε turbulence closure model predicts the velocity field and free surface profile more accurately compared to that of the k–ω turbulence model.

Application of NEM in seepage analysis with a free surface

In this work a novel meshless technique for mold filling simulation is presented. The governing equation for this kind of problem is named Hele-Shaw and it is derivated applying some simplifications on the 3D conservation equations. This approach is also commonly called 21/2D, referring to limitations of the mold geometry to narrow and weakly curved channels. Since products manufactured by injection molding in real life, as for example buckets, automobiles bumpers and cell phone casings, are not expected to be planar, in this work the mold cavity is modeled by point set surfaces. Thus, no computational effort referring to either mesh generation or mesh maintenance is required for the numerical solution of the governing equations. The developed technique for simulating the free surface position, velocity and pressure distribution in the injection molding process using this 21/2D approach is presented and discussed. The details of our framework, which is based on Smoothed Particle Hydrodynamics Method and a Meshless Volume of Fluid Method is also presented.

ABSTRACTIn this paper, a domain-topology-based, two-phase, incompressible flow model is proposed to simulate transient flow variations associated with the gate opening motions of water conservancy projects, such as hydropower stations with plain and radial gates. The research source code is written in the OpenFOAM platform and incorporates the interDyMFoam solver. Two benchmark experiments were performed in the laboratory to validate the numerical results. The water level, pressure, flow pattern and development of vortices were recorded for comparison with numerical solutions. The results show that the relative error associated with the weir flow time was less than 5.00%. Moreover, good agreement was obtained between the time history curves of the free surface elevation and pressure based on numerical and experiment results. The detailed flow pattern reflects the simulation capability of the model, which can be used to numerically investigate the generation mechanisms of vertical vortices around gate grooves. The proposed model can be applied to further investigate flow variations in real hydraulic engineering applications.

In the present paper the author treats the potential flows of the sink and source lying on the straight boundaries of the field in a half strip form. Seven flow mode in three cases of the distribution of the sink and source are discussed. As an extension of one of the flow modes a vortex is superposed on a source situated at a point in the limited field. Thus, the author studies, as an example of the above flow, the manner of motion of water with a whirling in the draft tube pit of a water trubine. The distributions of velocity and pressure, the profiles of free surfaces and the position of stagnation are determined. The results of calculations agree well with those of gentle flow in the experiments with a model pit and draft tube carried out by the author in the Hydraulic laboratory of Waseda University and the experiments show that the characteristics yet remain even in the agitational flow. The stagnation point correspond to the position at which the free surface takes maximum height, and its position on the boundary suggests the strength of a whirling effort. At a point of draft tube outlet the free surface attains a considerably low level which may be accounted for one of the causes of the vibration of a draft tube.

Simulating the flow among solid particles by many pipe flows which are generated by random numbers, the piezometric head (the pressure head and the potential head) is computed along each pipe. Taking the average of the piezometric heads of many pipe flows gives the free surface profile in the porous media. The free surface profile in the rectangular and the trapezoidal shapes is computed. This method is applicable to the case of arbitrary boundaries and turbulent flow. Introduction One of the most important problems in ground water flow is the determination of the free surface location. Generally, the location of the free surface is obtained by solving Laplace equation numerically and applying the kinematic and the dynamic boundary conditions on the free surface. In this study, the flow among solid particles is approximated by the combination of many pipe flows. The dimension and the direction of each pipe are simulated by generating many random numbers, so called Monte Carlo simulation. The locations of the free surface are determined by taking the average of piezometric heads in all pipe flows at the same position. Since the flow resistance of pipe flow is applicable to turbulent and laminar flows, this method is employed to the both flow regimes. Method of Approach To obtain the location of the water surface, let us consider a simple case of the rectangular porous media as shown in Fig.l. The pipe line simulated Transactions on Modelling and Simulation vol 6, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X