Experimental and numerical modeling of a sluice gate flow

Floodways, where a road embankment is permitted to be overtopped by flood water, are usually designed as broad-crested weirs. Determination of the water level above the floodway is crucial and related to road safety. Hydraulic performance of floodways can be assessed numerically using 1-D modelling or 3-D simulation using computational fluid dynamics (CFD) packages. Turbulence modelling is one of the key elements in CFD simulations. A wide variety of turbulence models are utilized in CFD packages; in order to identify the most relevant turbulence model for the case in question, 96 3-D CFD simulations were conducted using Flow-3D package, for 24 broad-crested weir configurations selected based on experimental data from a previous study. Four turbulence models (one-equation, k-ε, RNG k-ε, and k-ω) ere examined for each configuration. The volume of fluid (VOF) algorithm was adopted for free water surface determination. In addition, 24 1-D simulations using HEC-RAS-1-D were conducted for comparison with CFD results and experimental data. Validation of the simulated water free surface profiles versus the experimental measurements was carried out by the evaluation of the mean absolute error, the mean relative error percentage, and the root mean square error. It was concluded that the minimum error in simulating the full upstream to downstream free surface profile is achieved by using one-equation turbulence model with mixing length equal to 7% of the smallest domain dimension. Nevertheless, for the broad-crested weir upstream section, no significant difference in accuracy was found between all turbulence models and the one-dimensional analysis results, due to the low turbulence intensity at this part. For engineering design purposes, in which the water level is the main concern at the location of the flood way, the one-dimensional analysis has sufficient accuracy to determine the water level.

Laboratory experiments are conducted to measure the free-surface profile and the velocity field of an open channel flow over a semicylinder weir. The streamwise velocities of the flow are measured using a laser Doppler anemometer. The numerical simulation of the flow case having similar conditions with the experiment is performed. The basic equations of the problem are solved using the finite-volume method. A grid convergence analysis is applied to ensure the discretization error keeping within an acceptable limit for the predicted velocities. In the numerical modeling, the volume of fluid method is used to compute the free surface of the flow that interacts with the semicylindrical structure. In the numerical analysis, standard k-ε, renormalization group k-ε, realizable k-ε, modified k-ω, shear stress transport, and Reynolds stress turbulence closure models are employed. The computed results for the velocity field and free-surface profile of the flow are compared with the experimental data. The comparisons of the experimental and numerical results show that the numerical simulation using the Reynolds stress turbulence model provides better predictions for the horizontal velocities than the other turbulence models used herein.

In this study, the experimental data for two different flow rates collected earlier from a laboratory spillway model were used for the validation of the numerical results obtained for the same conditions. The governing equations of flow interacting with the spillway model were solved with finite volume method based on ANSYS-Fluent software package. In order to obtain grid independent numerical solutions, three different concentrations of grids (coarse, medium and fine) were designed and the suitability of the fine grid was tested with Grid Convergence Index (GCI) method. Six turbulence closure models namely; Standard k- (SKE), Renormalization-Group k- (RNG), Realizable k- (RKE), Modified k- (MKW), Shear Stress Transport (SST) and Reynolds Stress Model (RSM) were used for the numerical solution of the velocity field. For the calculation of water surface profile Volume of Fluid Method (VOF) was used. The free surface profiles and velocity field obtained from the numerical simulations were compared with measured values, and the success of the chosen turbulence closure models were discussed.

The characteristics of the trapezoidal weir flow are measured using a one-dimensional laser Doppler anemometer for two different flow conditions. The governing equations of the flow are solved using Standard k–e, Realizable k–e, Modified k–ω and Reynolds Stress Model based on the Reynolds-Averaged Navier–Stokes Equations and by Large Eddy and Detached Eddy Simulations. ANSYS-Fluent package program is used for the numerical analysis of flow with the same experimental conditions. The free surface of the trapezoidal weir flow is computed by the volume of fluid method. The effect of the selected grid structure on the numerical results is examined by Grid Convergence Index. Moreover, two-dimensional (2D) and three-dimensional (3D) analyses of the trapezoidal weir flow are included to estimate the effects of side walls. Experimental results of the velocity field and free surface profiles are compared to the numerical results of 2D and 3D simulations for the validation purposes. From the comparisons it is concluded that the Reynolds Stress Model estimates the flow field more accurately compared with those of the other models used in the present study. Furthermore, the flow characteristics such as turbulence kinetic energy, energy spectrum and pressure distributions for different flow rates are presented. Lastly, the discharge coefficients for different flow–weir configurations are compared experimentally and numerically.

Using the particle image velocimetry (PIV) technique, the laboratory experiments are conducted to measure the velocity fields of two-dimensional turbulent free surface flows upstream of rectangular and triangular broad-crested weirs. The experimental flow cases are analyzed theoretically by a computational fluid dynamics (CFD) modeling in which the finite element method is used to solve the governing equations. In the CFD simulation, the volume of fluid (VOF) method is used to compute the free surfaces of the flows. Using the standard k–ε and standard k–ω turbulence models, the numerical results for the velocity fields and flow profiles are compared with the experimental results for validation purposes. The computed results using k–ω turbulence model on compressed mesh systems are found in good agreement with measured data. The flow cases are also analyzed theoretically using the potential flow (PF) approach, and the numerical results for the velocity fields are compared with measurements.

Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

This paper presents simulated results of a computational study conducted to analyze the impulse waves generated by the subaerial landslide at Lituya Bay, Alaska. The volume of fluid method is used to track the free surface and shoreline movements. The renormalization group turbulence model and detached eddy simulation multiscale model were used to simulate turbulence dissipation. The subaerial landslide is simulated using a sliding mass. Results from the two-dimensional simulations are compared with the results from a scaled-down experiment. The experiment is carried out at a 1:675 scale. In the experimental setup, the subaerial rockslide impact into the Gilbert Inlet, wave generation, propagation, and runup on the headland slope is considered in a geometrically undistorted Froude similarity model. The rockslide is simulated by a granular material driven by a pneumatic acceleration mechanism so that the impact characteristics can be controlled. Simulations are performed for different values of the landslide density to estimate the influence of slide deformation on the generated tsunami characteristics. Simulated results show the complex flow patterns in terms of the velocity field, shoreline evolution, and free surface profiles. The predicted wave runup height is in close agreement with both the observed wave runup height and that obtained from the scaled-down experimental model.

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.

This paper aims to evaluate the effects of the opening width of a dam site on the evolution of partial dam-break waves over a fixed dry bed. The volume of fluid (VOF) method was used to scrutinize the propagation of the dam-break free surface. The model was validated using experimental data provided in the literature. At the same time, a sensitivity analysis was conducted on the size of the mesh cells and the turbulence model. However, the large eddy simulation (LES) method showed the highest accuracy among all the models. The results affirmed the crucial role of the opening width of the dam site in the flow characteristics. In this direction, diminishing the opening width results in a reduction of the wave-front travel distance, free surface gradient within the reservoir, outflow discharge values, damping the outflow hydrographs and decreasing the Froude number values at the dam site. Conversely, this leads to an increase in the air bubbles entrained within the wave and results in energy dissipation across the downstream channel.

Lateral intakes are used for water transmission and distribution on farms and irrigation networks. In present study, the flow field within a rectangular lateral intake in subcritical flow regime is numerically simulated in a three-dimensional. In this analysis of CFD, turbulence of flow field is simulated using standard $$k - \varepsilon$$ , and RNG $$k - \varepsilon$$ turbulence models, and changes of free surface is simulated by volume of fluid scheme. Comparison between CFD and experimental results showed that the numerical model simulated the free surface and velocity field with high accuracy. Root mean square error for longitudinal and transverse profiles of the flow free surface in the main channel is respectively calculated as 0.132% and 0.094%. Based on simulation results, with the flow progress towards the downstream diversion channel, the secondary circulation cell is developed. A relation is presented for calculating strength of the secondary flow with a nonlinear regression method and using Minitab software. Also, a relation is proposed for calculating the flow energy head within the downstream channel and lateral channel (E3, E2) compared to the flow energy head in the upstream intake (E1).

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.

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

The impact of slide deformation and geometry on surface waves generated by submarine landslides is studied using a computational model based on Navier-Stokes equations. The volume of fluid (VOF) method is used to track the free surface and shoreline movements. The Renormalization Group (RNG) turbulence model and the Detached Eddy Simulation (DES) multiscale model are used to simulate turbulence dissipation. Three-dimensional simulations are first compared with available experimental data involving the generation of waves by a rigid block sliding down an inclined plane. The role of slide deformation on the characteristics of the generated waves is evaluated. The results from the simulations are compared with the experimental data for the rigid slide. Simulated results highlight the importance and complexity of slide deformation on the generated wave characteristics and runup/rundown at various locations. Computed results also show the complex three-dimensional flow patterns in terms of the velocity field, shoreline evolution, and free-surface profiles. Predicted numerical results for time histories of free-surface fluctuations and the runup/rundown at various locations are found to be in good agreement with the available experimental data for the rigid slide. The location of the slide (whether it is fully submerged or aerial) also seems to influence the runup and wave height. Introduction Tsunamis are surface waves caused by the impulsive perturbation of the sea. Apart from co-seismic sea bottom displacement due to earthquakes, subaerial and submarine landslides can also produce localized tsunamis with large and complex wave runup. The wave characteristics and hazards related to tsunamis generated by submarine landslides have been an area of active research (Masson et al. 2006, Fine et al. 2005, Longva et al. 2003). Submarine landslides, which often accompany large earthquakes, can disturb the overlying water column as sediment and rock slump down slope. Any type of geophysical mass flow including debris flows, debris avalanches, landslides, and rockfalls can create submarine landslide-generated tsunamis. Earthquakes can also play an indirect role as the landslide-triggering mechanism. In addition to bringing devastating consequences and destruction to human lives, landslide-generated tsunamis constitute a threat in terms of direct wave impact or currents to offshore installations including oil platforms, risers, pipelines, and ships and to coastal installations. Coastal or shallow water structures are more prone to destruction due to higher wave current velocities in these places. Although the generation and propagation of earthquake-generated tsunamis have been studied for several decades and are now relatively well understood, such is not the case for landslide-generated tsunamis. While the mechanisms that generate these types of tsunami flows are generally understood, the ability to predict the flows they produce at coastlines still represents a formidable challenge due to the complexities of coastline formations and the presence of numerous coastal structures that interact and alter the flow. The generation and effects of landslide-generated tsunamis are complex and variable.

Surface waves generated by submarine landslides are studied using a computational model based on Navier-Stokes equations. The volume of fluid (VOF) method is used to track the free surface and shoreline movements. A Renormalization Group (RNG) turbulence model and Detached Eddy Simulation (DES) multiscale model are used to simulate turbulence dissipation. The submarine landslide is simulated using a sliding mass. The three-dimensional numerical simulations are carried out for a freely falling wedge representing the landslide and subsequent wave generations. Simulation results are compared with the experimental data. Modeled illustrate the effect of slide geometry, computational grid, turbulence model parameters, and slide material density on the predicted wave characteristics and runup/rundown at various locations. Computed results also show the complex three-dimensional flow patterns in terms of the velocity field, shoreline evolution, and free-surface profiles. Predicted numerical results for time histories of free-surface fluctuations and the runup/rundown at various locations are in good agreement with the available experimental data.

The numerical modeling of two-dimensional turbulent flow around a horizontal wall-mounted circular cylinder at Reynolds numbers in the range of 1000≤ReD≤7000 is investigated. Ansys® 10.0-FLOTRAN program package is used to solve the governing equations by finite element method, and the performance of the standard k-ε, standard k-ω and SST turbulence models are examined. A sensitivity study for the three turbulence models is carried out on eight computational meshes with different densities and structures. The computational velocity fields from the present simulations are compared with the experimental results obtained from particle image velocimetry (PIV) measurements for validation purposes. The point of the boundary layer detachment from the cylinder surface and the lengths of primary and secondary separation regions occurring around the cylinder are determined numerically and compared with those obtained experimentally. From these comparisons it is found that the numerical modeling using either of k-ω and SST turbulence models is reasonably successful. Using the results of numerical solutions, the drag and lift coefficients, Cd and Cl, are also calculated and compared with the measured values.