Depth-averaged modeling of free surface flows in open channels with emerged and submerged vegetation

The resistance induced by vegetation on the flow in a watercourse should be considered in projects of watercourse management and river restoration. Depth-averaged numerical model is an efficient tool to study this problem. In this study, a depth-averaged model using the finite volume method on a staggered curvilinear grid and the SIMPLEC algorithm for numerical solution is developed for simulating the hydrodynamics of free surface flows in watercourses with vegetation. For the model formulation the vegetation resistance is treated as a momentum sink and represented by a Manning type equation, and turbulence is parameterized by the k–ε equations. An analytical equation is derived to represent the resistance induced by submerged vegetation by an equivalent Manning roughness coefficient. Numerical simulation is carried out for the flow in an open channel with a 180° bend, and the flow in a curved open channel partly covered by emerged vegetation, as well as the flow in a straight trapezoidal channel with submerged vegetation. The agreement between the computed results and the measured data is generally good, showing that the resistance due to emerged or submerged vegetation can be represented accurately by the Manning roughness equation. The computed results demonstrate that the depth-averaged modeling is a reasonable and efficient tool to study flows in watercourses with vegetations.     

A 3D non-linear k–ε turbulent model for prediction of flow and mass transport in channel with vegetation

The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.     

180°弯曲方管牛顿流体及一种非牛顿流体湍性流动的数值模拟

运用湍流k-ε模式及实测壁面函数分别模拟牛顿流体(清水)及一种非牛顿流体(聚合物稀薄减阻溶液)流经180°弯曲方管的湍性流动,取得与实测速度分布吻合较好的结果.对于湍流模式对存在大涡的复杂流动的适应性,根据计算和试验结果进行了分析和讨论.     

3D simulations and experiments of flow in a folded microchannel

We investigate the three–dimensional pressure–driven flow field in a folded microchannel. Experiments and numerical simulations are performed. A method termed “partial particle tracking”, resulting in partial velocity profiles, indicates that secondary flows exist. The comparison of numerical and experimental partial velocity fields shows good agreement. The existence of secondary flow results from centrifugal forces due to the curved channel geometry. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构（I）—试验模型、端壁与叶片表面拓扑结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量，应用拓扑学原理，分析了端壁与叶片表面拓扑结构，与直叶栅比较，叶片正弯消除了上通道涡分离线，并使二次涡由闭式分离转变为开式分离，而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构(Ⅰ)——试验模型、端壁与叶片表面拓扑结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量,应用拓扑学原理,分析了端壁与叶片表面拓扑结构。与直叶栅比较,叶片正弯消除了上通道涡分离线,并使二次涡由闭式分离转变为开式分离,而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构(Ⅱ)——横截面流场拓扑结构与叶栅旋涡结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量,应用拓扑学原理,分析了叶栅流道横截面内的拓扑结构。与直叶栅比较,叶片正弯消除了上通道涡分离线,并使二次涡由闭式分离转变为开式分离,而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

Numerical modelling of subcritical open channel flow using the K-ε turbulence model and the penalty function finite element technique

A numerical model has been developed that employs the penalty function finite element technique to solve the vertically averaged hydrodynamic and turbulence model equations for a water body using isoparametric elements. The full elliptic forms of the equations are solved, thereby allowing recirculating flows to be calculated. Alternative momentum dispersion and turbulence closure models are proposed and evaluated by comparing model predictions with experimental data for strongly curved subcritical open channel flow. The results of these simulations indicate that the depth-averaged two-equation k-ε turbulence model yields excellent agreement with experimental observations. In addition, it appears that neither the streamline curvature modification of the depth-averaged k-ε model, nor the momentum dispersion models based on the assumption of helicoidal flow in a curved channel, yield significant improvement in the present model predictions. Overall model predictions are found to be as good as those of a more complex and restricted three-dimensional model.     

Predicting the flow of two-phase food mixtures

The flows of single-phase liquids and two-phase food mixtureshave been predicted using a model that considers the mixtureas two interpenetrating phases—one liquid and the otherflowing solids. Mass and momentum balances for each phase aresolved using a finite-difference scheme. Predictions of the velocity profile of a single-phase non-Newtonianliquid down a pipe showed agreement with an analytical solutionto the problem. Predictions of the flow of the same liquid arounda 90° bend, with a dead leg, agreed with predictions froma commercial software package. The shear and normal stresses in a food mixture were measuredusing a large-scale annular shear cell. These data were incorporatedinto equations of the Herschel-Bulkley form of rheological modeland implemented in the finite-difference model. Predictionsindicated that mixtures consisting of liquid and solids of nearequal density will exhibit little difference in the velocitiesof the liquid and solids components when the mixture flows downa pipe. Flow profiles around the 90° bend and dead leg showedthe expected pattern of flow around the bend with very low liquidand solids velocities within the dead leg and no recirculationbehind the bend. Further work is needed to verify experimentallythese predictions and to apply the model to other process geometries.     

Étude locale du frottement pariétal dans un écoulement en conduite courbe

Résumé On étudie dans une conduite circulaire, coudée selon un demi-cercle, le frottement en paroi d'un écoulement en régime laminaire et turbulent. Les mesures sont effectuées selon la méthode électrochimique utilisant des sondes locales permettant de déterminer la répartition circonférentielle du frottement en plusieurs sections. On met en évidence la forte modification due au mouvement secondaire. Par intégration, on obtient la loi de perte de charge dans le coude. La mesure des taux de fluctuations en régime turbulent montre l'importante réduction du niveau de turbulence par rapport à celui relevé dans la conduite rectiligne amont.

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The study deals with wall friction measurements for a flow in a 180°-bend in laminar and turbulent regime. Local electrochemical probes give the circumferential evolution of the friction in several sections. As a consequence of the secondary motion, the important modification of the flow is pointed out. The pressure loss along the bend is obtained by integration. In turbulent flow, the fluctuation rate is lower in the bend compared with the inlet level corresponding to the flow in the upstream straight duct.

     

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces

A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. As computational tool, a flow solver based on the Boundary Element Method is used. The Euler-Lagrange formulation of multiphase flow is considered. In the case of a particle with a magnetic moment in a nonuniform external magnetic field, the Kelvin body force acts on a single particle. The derived Lagrangian particle tracking algorithm is used for simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic force. As a benchmark test case the magnetite particle motion in cellular flow field of water is computed with and without the action of the magnetic force. The effect of the Kelvin force on particle motion and separation from the main flow is studied for a predefined magnetic field and different values of magnetic flux density. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Iber: herramienta de simulación numérica del flujo en ríos

The recent requirements of Spanish regulations and directives, on their turn based on European directives, have led to the development of a new two dimensional open channel flow modelling tool. The tool, named Iber, combines a hydrodynamic module, a turbulence module and a sediment transport module, and is based in the finite volume method to solve the involved equations. The simulation code has been integrated in a pre-process and post-process interface based on GiD software, developed by CIMNE. The result is a flow and sediment modelling system for rivers and estuaries that uses advanced numerical schemes, robust and stable, which are especially suitable for discontinuous flows taking place in torrential and hydrologically irregular rivers.     

3‐D spatio–temporal structures of biofilms in a water channel

We develop a numerical predictive tool for multiphase fluid mixtures consisting of biofilms grown in a viscous fluid matrix by implementing a second‐order finite difference discretization of the multiphase biofilm model developed recently on a general purpose graphic processing unit. With this numerical tool, we study a 3‐D biomass–flow interaction resulting in biomass growth, structure formation, deformation, and detachment phenomena in biofilms grown in a water channel in quiescent state and subject to a shear flow condition, respectively. The numerical investigation is limited in the viscous regime of the biofilm–solvent mixture. In quiescent flows, the model predicts growth patterns consistent with experimental findings for single or multiple adjacent biofilm colonies, the so‐called mushroom shape growth pattern. The simulated biomass growth both in density and thickness matches very well with the experimentally grown biofilm in a water channel. When shear is imposed at a boundary, our numerical studies reproduce wavy patterns, pinching, and streaming phenomena observed in biofilms grown in a water channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Advected turbulent line thermal driven by concentration difference

The spatial evolution of an advected line thermal driven by concentration difference––a turbulent buoyant body of fluid, for which small density difference is caused by a proportional variation in scalar concentration, horizontally introduced at no excess momentum into a horizontal ambient current, is studied using the standard two-equation k– model with a buoyancy expansion. The numerical results show that the advected line thermal is characterized longitudinally by a flat trajectory with scalar dilution taking place essentially near the jet exit, and transversely by a vortex-pair flow and a kidney-shaped concentration structure with double peak maxima corresponding to stronger buoyancy effect; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless distance of around 10; the aspect ratio for the kidney-shaped sectional thermal is found to be around 1.2–1.4; the predicted flow feature and mixing rate are well supported by asymptotic dimensional analysis and related experimental data. The analogy between a steady advected line thermal and corresponding time-dependent line thermal is also found reasonable by a special exploration into the horizontal velocity distribution and the significance of horizontal diffusion effect of the advected line thermal. Only about half of the vertical momentum resulting from the buoyancy effect is found contained in the advected line thermal, corresponding to an added virtual mass coefficient of approximately 1 for the sectional thermal.     

Approximate analytical solution for supercritical flow in rectangular curved channels

In this study, we present an asymptotical mathematical model and an analytical solution for a supercritical flow in curved rectangular open channels. An original approach is proposed for solving the free-surface configuration and features of the flow in the presence of cross shock waves. The two-dimensional steady depth-averaged shallow water equations are transformed into an equivalent one-dimensional (1D) unsteady flow problem and a first order approximation is then obtained using small perturbation theory. Furthermore, the 1D asymptotic model is solved analytically by Laplace integral transformation and the two-dimensional flow field solution is reconstructed according to the translating planes. The free-surface profile along the outer chute wall and downstream channel was compared with the available experimental data, and the results indicated the satisfactory agreement of the maximum flow depth, peak positions, and wavelength. The proposed approach provides accurate predictions of the flow features and it facilitates the safe design of curved channel transitions.     

Assessment of an improved turbulence model in simulating the unsteady flows around a D-shaped cylinder and an open cavity

Most engineering flows are still predicted by the conventional Reynolds-averaged Navier-Stokes method because of the low requirements of the computational quantities. However, the resolution capability of Reynolds-averaged Navier-Stokes models is still open to deliberation, especially in the recirculation and wake regions, where the vortical flows dominate. In the present work, an improved turbulence model derived from the original shear stress transport k-ω model is proposed and its superiority is assessed by our modeling the unsteady flows around a D-shaped cylinder and an open cavity, corresponding to two different Reynolds numbers. The results are compared with results from experiments and other turbulence models in terms of the flow morphology and mean velocity profiles. This shows that the predictive accuracy of the modified turbulence model is increased significantly in the bluff body wake flows and in the shear layer and separation flows of the cavity. Some special vortex structures can be captured in the open cavity, in which the secondary vortex emerging from the shear layer and the separation vortex near the trailing edge can induce large flow instability, and this phenomenon should be eliminated in engineering applications. It is believed that this improved turbulence model can be used for the more complex turbomachinery flows with better prediction of the hydrodynamic/aerodynamic performance and the unsteady vortical flows, which can provide some guidelines to design or optimize rotating machines.     

Distribution of resistive body-force in curved free-surface flow

The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved-flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.     

Thermodynamics / turbulence analogy modelling dissipating molecular gas flows for high Knudsen numbers

Modelling micro channel flows momentum and heat diffusion / convection are recent parameters modelling the molecule velocity distribution. Macroscopic models describe velocity and energy / enthalpie with integrals of mass increments. Using microscopic models motion and forces of a molecular flow have to be computed by models of physical properties, whose are described by statistical power moments of the molecule velocity. Therefore dilute flows have to be investigated in small channels with a mean free path length of molecules higher than the channel width of the the micro channel itself (λ₀≥H₀). Modelling this process by a continuous flow the boundary conditions have to be modified (e.g. [6]). The present model uses the statistical approximation of the molecule velocity distribution to simulate the behaviour of this discrete flow with a weighted averaged molecule velocity ∼ξ_i, its standard deviation σ and the characterisic molecule collision rate z. The number density N per volume V near one position is used for the weighting factor averaging method describing the mean molecule velocity. The present model is validated computing Poiseuille and Couette flows with different Knudsen numbers. Showing the advantages of the present model the simulation results are compared with simulation results of the wall–distance depending diffusivity model of Lockerby and Reese [4] and BGK results of a Lattice–Boltzmann simulation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of the thermal behaviour of a shell-and-tube heat storage unit using phase change materials

This work presents a numerical study of a latent heat storage unit (LHSU) consisting of a shell-and-tube. The shell space is filled with two phase change materials (PCMs), P116 and n-octadecane, with different melting temperatures (50 °C and 27.7 °C, respectively). A heat transfer fluid (HTF: water) flows by forced convection through the inner tube, and transfers the heat to PCMs. In order to compare the thermal performances of the latent heat storage unit using two phase change materials (LHSU2) and a single PCM (LHSU1), a mathematical model based on the conservation energy equations was developed and validated with experimental data. Several numerical investigations were conducted in order to examine the impact of the key parameters: the HTF inlet temperature (ranges from 50 to 60 °C), the mass flow rate of the HTF and the proportion mass of PCMs, on the thermal performances of the latent heat storage units using two PCMs and a single PCM, during charging process (melting). This parametric study provides guidelines for system thermal performance and design optimization.     

Incompressible Navier-Stokes equation solvers based on lattice Boltzmann relaxation systems

In this talk some recent numerical results based on discrete-velocity relaxation systems will be presented. Discrete-velocity equations are derived from continuous Boltzmann-type equations with appropriate approximations suitable for incompressible flows. A relaxation system is derived by taking moments of the discrete-velocity equations. This approach is also extended to turbulence flows using Large-Eddy Simulation as well as thermal flows. The schemes are tested by solving a collection of examples. In particular the developed methods demonstrate potential as tools for Large-Eddy Simulation and flow with Radiative Heat transfer. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)