Free-surface Hydrodynamics Research Articles

Numerical analysis of a Pelton bucket free surface sheet flow and dynamic performance affected by operating head

The present paper aims to find out the influence of operating head on the rotating bucket free surface sheet flow and hydrodynamics performance for a Pelton turbine. Three-dimensional unsteady air-water two-phase flow simulations in the rotating buckets were performed by adopting the shear stress transport curvature correction turbulence model and homogenous model. The sensitivities of the unsteady simulation results to moving mesh resolution and computational fluid dynamics solver time-step have been evaluated to discuss the effect of Courant–Friedrichs–Lewy conditions on the two-phase flow simulation. The accuracy of the numerical predicted flow pattern and the hydrodynamic performance results are reasonable when compared with the experimental data. The simulation results indicate that the remaining kinetic energy carried by the outflow under the nondesigned water head is the main reason for the efficiency loss in the Pelton turbine. Under low water head conditions, jet distortion caused by the Coanda effect and flow interference will lead to more severe efficiency deterioration.

A multi-region coupling scheme for compressible and incompressible flow solvers for two-phase flow in a numerical wave tank

We present a multi-region coupling procedure based on the finite-volume method and apply it to two-phase hydrodynamic free surface flow problems. The method combines the features of one incompressible and one compressible two-phase flow solvers to obtain a coupled system which is generally superior to either solver alone. The coupling strategy is based on a partitioned approach in which different solvers, pre-defined in different regions of the computational domain, exchange information through interfaces, i.e. areas separating these regions. The interfaces act as boundary conditions passing the information from one region to the other mimicking the finite-volume cell-to-face interpolation procedures. This results in high performance computing coupled simulations whose functionality can be further extended in order to build a generic numerical wave tank accounting for incompressible flow regions as well as compressibility and aeration effects. We select a series of preliminary benchmarks to verify this coupling procedure which includes the simulation of a hydrodynamic dam break, the propagation and reflection of regular waves, the convection of an inviscid vortex, pseudocavitation, a water column free drop in a closed tank and a plunging wave impact at a vertical wall. The obtained results agree well with exact solutions, laboratory experiments and other numerical data.

A conservative finite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids

In this article we propose a new conservative high resolution TVD (total variation diminishing) finite volume scheme with time-accurate local time stepping (LTS) on unstructured grids for the solution of scalar transport problems, which are typical in the context of water quality simulations. To keep the presentation of the new method as simple as possible, the algorithm is only derived in two space dimensions and for purely convective transport problems, hence neglecting diffusion and reaction terms. The new numerical method for the solution of the scalar transport is directly coupled to the hydrodynamic model of Casulli and Walters (2000) that provides the dynamics of the free surface and the velocity vector field based on a semi-implicit discretization of the shallow water equations. Wetting and drying is handled rigorously by the nonlinear algorithm proposed by Casulli (2009). The new time-accurate LTS algorithm allows a different time step size for each element of the unstructured grid, based on an element-local Courant-Friedrichs-Lewy (CFL) stability condition. The proposed method does not need any synchronization between different time steps of different elements and is by construction locally and globally conservative. The LTS scheme is based on a piecewise linear polynomial reconstruction in space–time using the MUSCL–Hancock method, to obtain second order of accuracy in both space and time.The new algorithm is first validated on some classical test cases for pure advection problems, for which exact solutions are known. In all cases we obtain a very good level of accuracy, showing also numerical convergence results; we furthermore confirm mass conservation up to machine precision and observe an improved computational efficiency compared to a standard second order TVD scheme for scalar transport with global time stepping (GTS). Then, the new LTS method is applied to some more complex problems, where the new scalar transport scheme has also been coupled to a semi-implicit model for the simulation of the free surface hydrodynamics, including nonlinear wetting and drying. The last application shown in this paper is carried out on a real geometry, for which we have taken available DTM data of the lake Guaiba in Brazil. Comparisons have been made in all cases with a second order TVD scheme based on GTS. For the new LTS algorithm we report a significant reduction in computational effort, with a savings of CPU time of the order of up to 95%.

High resolution ship hydrodynamics simulations in open source environment

The numerical simulation of wake and free-surface flow around ships is a complex topic that involves multiple tasks: the generation of an optimal computational grid and the development of numerical algorithms capable to predict the flow field around a hull. In this paper, a numerical framework is developed aimed at high-resolution CFD simulations of turbulent, free-surface flows around ship hulls. The framework consists in the concatenation of “tools”, partly available in the open-source finite volume library OpenFOAM®. A novel, flexible mesh-generation algorithm is presented, capable of producing high-quality computational grids for free-surface ship hydrodynamics. The numerical frame work is used to solve some benchmark problems, providing results that are in excellent agreement with the experimental measures.

Free-surface hydrodynamics of a submerged prolate spheroid in finite water depth based on the method of multipole expansions

Free-surface hydrodynamics of a submerged elongated (prolate) spheroid in water of finite depth is considered by employing spheroidal harmonics and the method of multipole expansions. In particular, we present semi-analytic solutions for both the wave making resistance and wave diffraction fundamental problems. Although these two cases are generally treated separately, it is demonstrated here that by using the present general methodology, the analytic procedures of these two problems are quite similar and thus the corresponding solutions can be obtained by using almost a single effort. The motion of the prolate spheroid is rectilinear and steady in a direction parallel to the undisturbed free surface and rigid planar bottom. The ambient wave field is assumed to be monochromatic with an arbitrary inclination angle with respect to the body's major axis. The Green's function based solution, employs Havelock's formula for the ultimate image singularity system which avoids redundant surface integrations and solving integral equations. Numerical simulations of the linearized Kelvin-Neumann problem for the hydrodynamic forces and moments exerted on the moving spheroid for different depths of submergence and flow parameters are presented and compared against the existing data, given mainly for spherical shapes. The present method is claimed to be simpler to implement and more versatile, yet more accurate with respect to existing codes. Aside from free surface hydrodynamics, it can be also extended to other harmonic practical problems involving interacting ellipsoidal geometries in confined domain.

On the nonintegrability of the free surface hydrodynamics

The integrability of the compact 1D Zakharov equation has been analyzed. The numerical experiments show that the multiple collisions of breathers (which correspond to envelope solitons in the NLSE approximation) are not pure elastic. The amplitude of six-wave interactions for the compact 1D Zakharov equation has also been analyzed. It has been found that the six-wave amplitude is not canceled for this equation. Thus, the 1D Zakharov equation is not integrable.

A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint-Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.

Particle Manipulation Based on Optically Controlled Free Surface Hydrodynamics

Particle Manipulation Based on Optically Controlled Free Surface Hydrodynamics

Particle Manipulation Based on Optically Controlled Free Surface Hydrodynamics

Particle Manipulation Based on Optically Controlled Free Surface Hydrodynamics

Numerical verification of an Industrial code to simulate accurately large scale Hydrodynamics events

The use of finite-precision arithmetic generates round-off errors at each arithmetical expression so some mathematical properties are lost during the computing of a numerical code. Consequently, the same numerical code using the same input data could produce different results on different computers. The round-off error propagation is exacerbated in High Performance Computing since trillions of floating arithmetic operations can be performed each second. Moreover, due to the domain decomposition, the floating point arithmetic operations are not performed in the same order. There is therefore a need to detect the effect of round-off error propagation in order to make confidence about the results of the simulation. This paper deals with an overview of the numerical verification activities performed at EDF R&D on the parallel TELEMAC-2D code modelling the 2D free surface hydrodynamics. Firstly, a framework developed at EDF R&D to study the effect of the round-off error propagation on the quality of a simulation is exposed. Then, the xD+P approach which has been proposed to measure the numerical quality of the computed values is presented. Finally, a recent work dealing with the improvement of the floating point summation is discussed.

A coupled analysis of nonlinear sloshing and ship motion

Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure (Yan and Ma, 2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)’s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.

Iterative solutions of mildly nonlinear systems

The correct numerical modelling of free-surface hydrodynamics often requires the solution of diagonally nonlinear systems. In doing this, one may substantially enhance the model accuracy while fulfilling relevant physical constraints. This is the case when a suitable semi-implicit discretization is used, e.g., to solve the one-dimensional or the multi-dimensional shallow water equations; to model axially symmetric flows in compliant arterial systems; to solve the Boussinesq equation in confined–unconfined aquifers; or to solve the mixed form of the Richards equation. In this paper two nested iterative methods for solving a mildly nonlinear system of the form V(η)+Tη=b are proposed and analysed. It is shown that the inner and the outer iterates are monotone, and converge to the exact solution for a wide class of mildly nonlinear systems of applied interest. A simple, and yet non-trivial test problem derived from the mathematical modelling of flows in porous media is formulated and solved with the proposed methods.

Characteristic time scales for predicting the scalar flux at a free surface in turbulent open-channel flows

The purpose of this study is to predict the turbulent scalar flux at a free surface subject to a fully developed turbulent flow based on a hydrodynamic analysis of turbulence in the region close to the free surface. The effect of the Reynolds number on turbulent scalar transfer mechanisms is extensively examined. A direct numerical simulation technique is applied to achieve the purpose. The surface-renewal approximation is used to correlate the free-surface hydrodynamics and scalar transport at the free surface. Two types of characteristic time scales have been examined for predicting turbulent scalar flux. One is the time scale derived from the characteristic length and velocity scale at the free surface. The other is the reciprocal of the root-mean-square surface divergence. The results of this study show that scalar transport at the free surface can be predicted successfully using these time scales based on the concept of the surface-renewal approximation. V C 2012 American

Compact equation for gravity waves on deep water

Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.

"Scale oriented" embedded modeling of the North-Western Mediterranean in the frame of MFSTEP

Abstract. An embedded forecasting system was developed for the North-Western Mediterranean at 3-km resolution. The system is based on the Symphonie hydrodynamic free surface model and on the variational initialization and forcing platform VIFOP. The regional model is initialized and forced at its open lateral boundaries by the MFS GCM and forced at the surface by the ALADIN numerical weather prediction model. Once a week, a five-day forecast is produced after a hindcast of seven days. This pre-modeling period of 7 days before beginning the forecast allows the development of the small scale features associated to the high resolution. The relevance of the 5-day forecast strategy has been examined by comparing the forecasted fields to hindcast fields (forced by meteorological and oceanic analyses) considered as a reference. Mismatches remain at a very low level indicating a good quality of the forecasted forcing fields and also possibly to the strong wind conditions which prevailed during the period. The embedded forecasts have been compared to the MFS observing system (SST and MedArgo) during 6 forecast cycles between September 2004 and February 2005. It was basically found that in the North-Western Mediterranean, the MFS basin-scale model and thus the regional model forecasts are characterized by large negative biases of salinity in the first 100 m under the surface leading thus to too light subsurface waters. The underestimation of temperature by the regional model just below the surface and its overestimation at 30m deep can be attributed to an overestimation of the turbulent mixing. The regional model allows to represent a number of processes especially those induced by the wind as coastal upwelling under stratified conditions, dense water formation over the Gulf of Lion shelf, deep mixing in the convection zone or influence on the Northern Current penetration in the Gulf of Lion.

Numerical Investigation of Bubble‐induced Marangoni Convection

The liquid motion induced by surface tension variation, termed the thermocapillary or Marangoni effect, and its contribution to boiling heat transfer has long been a very controversial issue. In the past this convection was not the subject of much attention because, under terrestrial conditions, it is superimposed by the strong buoyancy convection, which makes it difficult to obtain quantitative experimental results. The scenario under consideration in this paper may be applicable to the analysis of boiling heat transfer, specifically the bubble waiting period and, possibly, the bubble growth period. To elucidate the influence of Marangoni convection on local heat transfer, this work numerically investigates the presence of a hemispherical bubble of constant radius, R(b)= 1.0 mm, situated on a heated wall immersed in a liquid silicone oil (Pr= 82.5) layer of constant depth H= 5.0 mm. A comprehensive description of the flow driven by surface tension gradients along the liquid-vapor interface required the solution of the nonlinear equations of free-surface hydrodynamics. For this problem, the procedure involved solution of the coupled equations of fluid mechanics and heat transfer using the finite-difference numerical technique. Simulations were carried out under zero-gravity conditions for temperatures of 50, 40, 30, 20, 10, and 1 K, corresponding to Marangoni numbers of 915, 732, 550, 366, 183, and 18.3, respectively. The predicted thermal and flow fields have been used to describe the enhancement of the heat transfer as a result of thermocapillary convection around a stationary bubble maintained on a heated surface. It was found that the heat transfer enhancement, as quantified by both the radius of enhancement and the ratio of Marangoni heat transfer to that of pure molecular diffusion, increases asymptotically with increasing Marangoni number. For the range of Marangoni numbers tested, a 1.18-fold improvement in the heat transfer was predicted within the region of R(b)< or = r< or = 7R(b).

A numerical oil spill model based on a hybrid method

The purpose of this paper is the development of a hybrid particle tracking/Eulerian–Lagrangian approach for the simulation of spilled oil in coastal areas. Oil discharge from the source is modeled by the release of particles. When the oil slick thickness or the oil concentration reaches a critical value, particles are mapped on slick thickness or node concentrations, and the calculations proceed in the Eulerian–Lagrangian mode. To acquire accurate environment information, the model is coupled with the 3-D free-surface hydrodynamics model (POM) and the third-generation wave model (SWAN). By simulating the oil processes of spreading, advection, turbulent diffusion, evaporation, emulsification, dissolution and shoreline deposition, it has the ability to predict the horizontal movement of surface oil slick, the vertical distribution of oil particles, the concentration in the water column and the mass balance of spilled oil. An accidental oil release near Dalian coastal waters is simulated to validate the developed model. Compared with the satellite images of oil slicks on the surface, the numerical results indicate that the model has a reasonable accuracy.

Iterative Solution of Piecewise Linear Systems

The correct formulation of numerical models for free-surface hydrodynamics often requires the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In so doing one may prevent the development of unrealistic negative water depths. The resulting piecewise linear systems are equivalent to particular linear complementarity problems whose solutions could be obtained by using, for example, interior point methods. These methods may have a favorable convergence property, but they are purely iterative and convergence to the exact solution is proven only in the limit of an infinite number of iterations. In the present paper a simple Newton-type procedure for certain piecewise linear systems is derived and discussed. This procedure is shown to have a finite termination property, i.e., it converges to the exact solution in a finite number of steps, and, actually, it converges very quickly, as confirmed by a few numerical tests.

On the regularity of the Neumann problem for free surfaces with surface tension

In 1952 H. Lewy established that a hydrodynamic free surface which is at least C 1 in a neighborhood of a point q situated on the free surface is automatically C, possibly in a smaller neighborhood of q. This local result is an example which preceeds the theory developed by D. Kinderlehrer, L. Nirenberg and J. Spruck (1977-79), proving that in many cases free surfaces cannot have an arbitrary regularity; in particular, there exist k, μ such that if the surface in question is C k,μ , then automatically is C ω . In this paper we extend their methods to Neumann type problems for free surfaces with surface tension.

A Three‐Dimensional Computational Fluid Dynamics (CFD) Model Analysis of Free Surface Hydrodynamics and Fish Passage Energetics in a Vertical‐Slot Fishway

AbstractA three‐dimensional (3‐D), computational fluid dynamics model of a vertical‐slot fishway was used to characterize fishway hydrodynamics. The computational grid of a seven‐pool fishway, consisting of about half a million hexahedral and prism cells, simulates the spatial variations of water surface and velocity in the model domain. Model results indicate a strong 3‐D velocity field in the fishway, with eddies, flow separations, vortices, upwellings, and downwellings. Velocities and drag forces encountered by upstream migrating fish and energy expenditures in ascending the fishway are determined from the fishway hydrodynamics. The computed results are consistent with published information. Based on burst swimming speeds, the species of salmon Oncorhynchus spp. capable of migrating through the fishway were identified. Because the upriver spawning migration of adult salmon is energetically expensive, a quantification of energy expenditure in the fishways could be utilized for optimizing the design, operation, and management of fishways. Though this paper presents a model of a vertical‐slot fishway, the modeling approach is applicable to other types of fishways.