The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…
Experimental and Numerical Analysis of a Cross-Flow Turbine
An important component of the management cost of aqueducts is the energy costs. Part of these costs can be recovered by transforming some of the many existing energy dissipations into electric energy by means of economical turbines. This paper describes an experimental study that has been carried out in order to (1) test the performance of an economical cross-flow turbine that maintains high efficiency within a large range of water discharges, and (2) validate a new approximate formula relating main inlet velocity to inlet pressure. It is demonstrated that the proposed formula, on the basis of some simplifying assumptions, exactly links inlet velocity to inlet pressure with any possible geo…
Cross-Flow Turbine Design For Energy Production And Discharge Regulation
Cross-flow turbines are very efficient and cheap turbines that allow a very good cost/benefit ratio for energy production located at the end of conduits carrying water from a water source to a tank. In this paper a new design procedure for a cross-flow turbine working with a variable flow rate is proposed. The regulation of the head immediately upstream the turbine is faced by adopting a shaped semicircular segment moving around the impeller. The maximum efficiency of the turbine is attained by setting the velocity of the particles entering the impeller at about twice the velocity of the rotating system at the impeller inlet. If energy losses along the pipe are negligible, the semicircular …
MAST-RT0 SOLUTION OF 3D NAVIER STOKES EQUATIONS ON UNSTRUCTURED MESHS. PRELIMINARY RESULTS IN THE LAMINAR CASE
Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation
The shallow water equations are a mathematical tool widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. The interest of many researchers has been focused on the study of simplified forms of the original set of equations. One of the most commonly applied simplifications consists of neglecting the inertial terms. The effects of such a choice on the outputs of the simulations of flooding events are controversial and are an important topic of debate. In the present paper, two numerical models recently proposed for the solution of the complete and zero-inertia forms of the shallow water equations, are applied to several unsteady f…
A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography
Abstract We extend a recently proposed 2D depth-integrated Finite Volume solver for the nonlinear shallow water equations with non-hydrostatic pressure distribution. The proposed model is aimed at simulating both nonlinear and dispersive shallow water processes. We split the total pressure into its hydrostatic and dynamic components and solve a hydrostatic problem and a non-hydrostatic problem sequentially, in the framework of a fractional time step procedure. The dispersive properties are achieved by incorporating the non-hydrostatic pressure component in the governing equations. The governing equations are the depth-integrated continuity equation and the depth-integrated momentum equation…
MAST solution of advection problems in irrotational flow fields
Abstract A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the so…
Cross-flow Turbine Design for Variable Operating Conditions
Abstract The potential energy hidden in water resources is becoming more and more a significant economic value. The value of the hydroelectric energy is often magnified by the proximity of the turbine to pumps or other energy sinks owned by the same water manager. Cross-flow or Banki-Michel turbines are a very efficient and economic choice that allows a very good cost/benefit ratio for energy production located at the end of conduits carrying water from a water source to a tank. In the paper the optimum design of a cross-flow turbine is sought after, assuming a flow rate variable in time. Regulation of the discharge entering in the turbine is a key issue, which is faced adopting a shaped se…
Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes
Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The…
Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses
The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity regi…
Use of Heating Configuration to Control Marangoni Circulation during Droplet Evaporation
The present work presents a numerical study of the evaporation of a sessile liquid droplet deposited on a substrate and subjected to different heating configurations. The physical formulation accounts for evaporation, the Marangoni effect, conductive transfer in the support, radiative heating, and diffusion–convection in the droplet itself. The moving interface is solved using the Arbitrary Lagrangian–Eulerian (ALE) method. Simulations were performed using COMSOL Multiphysics. Different configurations were performed to investigate the effect of the heating conditions on the shape and intensity of the Marangoni circulations. A droplet can be heated by the substrate (different natures and thi…
Coupled Electric and Hydraulic Control of a PRS Turbine in a Real Transport Water Network
Although many devices have recently been proposed for pressure regulation and energy harvesting in water distribution and transport networks, very few applications are still documented in the scientific literature. A new in-line Banki turbine with positive outflow pressure and a mobile regulating flap, named Power Recovery System (PRS), was installed and tested in a real water transport network for the regulation of pressure and flow rate. The PRS turbine was directly connected to a 55 kW asynchronous generator with variable rotational velocity, and coupled to an inverter. The start-up tests showed how automatic adjustment of the flap position and the runner velocity variation are able to c…
Numerical analysis of a new cross-flow type hydraulic turbine for high head and low flow rate
Cross-flow turbines have recently been proposed for energy recovery in aqueducts when the outlet pressure is greater than zero, owing to their constructive simplicity and good efficiency within a large range of flow rates and head drops. In the case of high head drop (higher than 150 m) and relatively small discharge (lower than 0.2 m3/s), the traditional design of these turbines leads to very small widths of the nozzle and the runner; as a consequence, friction losses grow dramatically and efficiency drops down to very low values. Standard Pelton turbines require zero outlet pressure and cannot be used as alternatives. A new counter-pressure hydraulic turbine for high head and low flow rat…
A new solver for incompressible non-isothermal flows in natural and mixed convection over unstructured grids
Abstract In the present paper we propose a new numerical methodology for the solution of 2D non-isothermal incompressible flows for natural and mixed convection in irregular geometries. The governing equations are the Incompressible Navier-Stokes Equations and the Energy Conservation Equation. Fluid velocity and temperature are coupled in the buoyancy term of the momentum equations according to the Oberbeck–Boussinesq approximation. The governing equations are discretized over unstructured triangular meshes satisfying the Delaunay property. Thanks to the Oberbeck–Boussinesq hypothesis, the flow and energy problems are solved in an uncoupled way, and two fractional time step procedures are s…
Banki-Michell Optimal Design by Computational Fluid Dynamics Testing and Hydrodynamic Analysis
In hydropower, the exploitation of small power sources requires the use of small turbines that combine efficiency and economy. Banki-Michell turbines represent a possible choice for their simplicity and for their good efficiency under variable load conditions. Several experimental and numerical tests have already been designed for examining the best geometry and optimal design of cross-flow type machines, but a theoretical framework for a sequential design of the turbine parameters, taking full advantage of recently expanded computational capabilities, is still missing. To this aim, after a review of the available criteria for Banki-Michell parameter design, a novel two-step procedure is de…
MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains
A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedr…
Impeller optimization in crossflow hydraulic turbines
Crossflow turbines represent a valuable choice for energy recovery in aqueducts, due to their constructive simplicity and good efficiency under variable head jump conditions. Several experimental and numerical studies concerning the optimal design of crossflow hydraulic turbines have already been proposed, but all of them assume that structural safety is fully compatible with the sought after geometry. We show first, with reference to a specific study case, that the geometry of the most efficient impeller would lead shortly, using blades with a traditional circular profile made with standard material, to their mechanical failure. A methodology for fully coupled fluid dynamic and mechanical …
Performance Improvement of a Drag Hydrokinetic Turbine
Hydropower is at present in many locations, among all the other possible renewable energy sources, the best one for net cost per unit power. In contrast to traditional installation, based on water storage in artificial basins, free flow river turbines also provide a very low environmental impact due to their negligible effect on solid transport. Among them, kinetic turbines with vertical axis are very inexpensive and have almost zero impact on fish and local fauna. In application to tidal waves and sea waves, where vertically averaged velocities have alternate direction, a Savonius rotor also has the advantage of being productive during the whole time cycle. In this work, the effect of an u…
Experimental and numerical analysis of a backpressure Banki inline turbine for pressure regulation and energy production
Abstract Water distribution networks have become, in recent years, a major opportunity for the harvesting of renewable energy, which is otherwise dissipated though hydrovalves installed for discharge and pressure regulation. Mini and micro hydroturbines have the capability of providing the same functionality of hydrovalves, producing at the same time a relevant amount of electric power. In this paper a 10 kW prototype of a new compact in-line turbine, named Power Recovery System (PRS), has been designed, constructed and tested in the hydraulic laboratory of the University of Palermo. The proposed device is a Banki-type micro-turbine, with positive outflow pressure and a mobile regulating fl…
Performance improvement of a Savonius water rotor with novel blade shapes
Abstract Savonius water rotor is a prominent drag based turbine able to extract energy available in flowing water with low velocity like river streams, tidal currents or other man made water canals. However, in view of its low performance, an enhanced design of the rotor blades is necessary to better its efficiency. Therefore, the present study aims to improve the efficiency of Savonius rotor by changing the blade design. Different blade shapes were investigated numerically using computational fluid dynamics (CFD). Using conventional design, the peak power coefficient was found to be 0.166 at tip-speed ratio of 0.78. However, the peak power coefficient reaches 0.184 using the optimal blade …
Monotonic solution of heterogeneous anisotropic diffusion problems
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…
Anisotropic potential of velocity fields in real fluids: Application to the MAST solution of shallow water equations
In the present paper it is first shown that, due to their structure, the general governing equations of uncompressible real fluids can be regarded as an "anisotropic" potential flow problem and closed streamlines cannot occur at any time. For a discretized velocity field, a fast iterative procedure is proposed to order the computational elements at the beginning of each time level, allowing a sequential solution element by element of the advection problem. Some closed circuits could appear due to the discretization error and the elements involved in these circuits could not be ordered. We prove in the paper that the total flux of these not ordered elements goes to zero by refining the compu…
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…
Hydropower Potential in Water Distribution Networks: Pressure Control by PATs
Pressure control is one of the main techniques to control leakages in Water Distribution Networks (WDNs) and to prevent pipe damage, improving the delivery standards of a water supply systems. Pressure reducing stations (PRSs) equipped by either pressure reducing valves or motor driven regulating valves are commonly used to dissipate excess hydraulic head in WDNs. An integrated new technical solution with economic and system flexibility benefits is presented which replaces PRSs with pumps used as turbines (PATs). Optimal PAT performance is obtained by a Variable Operating Strategy (VOS), recently developed for the design of small hydropower plants on the basis of valve time operation, and n…
A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model
Abstract A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are…
Using unsteady-state water level data to estimate channel roughness and discharge hydrograph
A novel methodology for simultaneous discharge and channel roughness estimation is developed and applied to data sets available at three experimental sites. The methodology is based on the synchronous measurement of water level data in two river sections far some kilometers from each other, as well as on the use of a diffusive flow routing solver and does not require any direct velocity measurement. The methodology is first analyzed for the simplest case of a channel with a large slope, where the kinematic assumption holds. A sensitivity and a model error analysis are carried out in this hypothesis in order to show the stability of the results with respect to the error in the input paramete…
Investigation of the hemodynamic flow conditions and blood-induced stresses inside an abdominal aortic aneurysm by means of a SPH numerical model.
The estimation of blood flow-induced loads occurring on the artery wall is affected by uncertainties hidden in the complex interaction of the pulsatile flow, the mechanical parameters of the artery, and the external support conditions. To circumvent these difficulties, a specific tool is developed by combining the aorta displacements measured by an electrocardiogram-gated-computed tomography angiography, with the blood velocity field computed by a smoothed particle hydrodynamics (SPH) numerical model. In the present work, the SPH model has been specifically adapted to the solution of the 3D Navier-Stokes equations inside a domain with boundaries of prescribed motion. Images of the abdominal…
Performance Study of Twisted Darrieus Hydrokinetic Turbine With Novel Blade Design
Abstract Twisted Darrieus water turbine is receiving growing attention for small-scale hydropower generation. Accordingly, the need for raised water energy conversion incentivizes researchers to focus on the blade shape optimization of twisted Darrieus turbine. In view of this, experimental analysis has been performed to appraise the efficiency of a spiral Darrieus water rotor in the present work. To better the performance parameters of the studied water rotor with twisted blades, three novel blade shapes, namely U-shaped blade, V-shaped blade, and W-shaped blade, have been numerically tested using a computational fluid dynamics three-dimensional numerical model. The maximum power coefficie…
Discharge estimation in open channels by means of water level hydrograph analysis
A new methodology, based on the synchronous measurement of stage hydrographs in two river sections located some kilometers from each other, was developed to estimate the discharge hydrograph in the upstream section. The methodology is based on the one-parameter calibration of a numerical flow routing algorithm, solving the Saint-Venant equations in diffusive or complete form. The methodology was validated using results of laboratory experiments carried out at the Polytechnic of Bari University. A known discharge hydrograph was generated in the upstream tank of a rectangular flume, where two water level sensors were located. Two different bed materials have been used, to account for differen…
Hydraulic Dynamic Calculation and Simulation
Hydraulic dynamics is emerging as a basic concept with applications and important implications for many industrial, civil, and environmental engineering problems [...]
Low-Head Hydropower for Energy Recovery in Wastewater Systems
Hydraulic turbines for energy recovery in wastewater treatment plants, with relatively large discharges values and small head jumps, are usually screw Archimedes or Kaplan types. In the specific case of a small head jump (about 3 m) underlying a rectangular weir in the major Palermo (Italy) water treatment plant, a traditional Kaplan solution is compared with two other new proposals: a Hydrostatic Pressure Machine (HPM) located at the upstream channel and a cross-flow turbine (CFT) located in a specific underground room downstream of the same channel. The fluid mechanical formulations of the flow through these turbines are analyzed and the characteristic parameters are stated. Numerical ana…
A Marching in Space and Time (MAST) solver of the shallow water equations. Part I: The 1D model
A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of Partial Differential Equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to …
Numerical Simulations of the Hydrodynamics of the Abdominal Aorta Aneurysm (AAA) Using a Smoothed Particle Hydrodynamics Code with Deformable Wall Preliminary Results
We present some preliminary results of the numerical simulations of the hydrodynamic characteristics of an abdominal aorta aneurysm (AAA) patient specific test case. Images of the AAA lumen have been acquired in 10 discrete time-steps through a stabilized cardiac cycle by electrocardiogram-gated computer tomography angiography, and are used to approximate the in vivo, time dependent kinematic fields of the (internal) arterial wall. The flow field is simulated by a Smoothed Particle SPH numerical model, where the kinematics of the boundary of the computational domain (the internal aortic vessel) is the one computed by the above procedure. The outputs of the SPH model, i.e., pressure and flow…
Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver
Due to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, non- hydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractional- time-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydro…
A novel pressure regulation system based on Banki hydro turbine for energy recovery under in-range and out-range discharge conditions
Abstract Efficiency improvement of water distribution networks needs to be in place to guarantee a long life period under suitable operating conditions. Excessive pressure is among the well-known issues encountered in water distribution networks which can cause strength damages to the piping system. In order to overcome this drawback and to reach a suitable water pressure delivery, the present work suggests a novel pressure regulation system. This regulation system is consisting of a Banki turbine equipped with a mobile flap as a control device. The suggested pressure regulation system was experimentally and numerically investigated under in-range i.e. like actual water distribution network…
Diffusive Modeling of Aggradation and Degradation in Artificial Channels
The unsteady flow and solid transport simulation problem in artificial channels is solved using a three-equation model, coupled with a local erosion law. The three equations are the water mass and momentum balance equations, as well as the total solid load balance equation. It is shown that even during severe hydrological events inertial terms can be neglected in the momentum equation without any substantial change in the solution sought. Empirical equilibrium formulas were used to estimate the solid load as a function of the flow variables. Local erosion, due to the scour generated at the jump between two channels connected at different bottom elevations, was estimated adapting a literatur…
OTTIMIZZAZIONE FLUIDO-MECCANICA DI TURBINE IDRAULICHE CROSSFLOW
MAST-RT0 solution of 3D Navier Stokes equations in very irregular domains. Preliminary results in the laminar case
A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedr…
The FLO Diffusive 1D-2D Model for Simulation of River Flooding
An integrated 1D-2D model for the solution of the diffusive approximation of the shallow water equations, named FLO, is proposed in the present paper. Governing equations are solved using the MArching in Space and Time (MAST) approach. The 2D floodplain domain is discretized using a triangular mesh, and standard river sections are used for modeling 1D flow inside the section width occurring with low or standard discharges. 1D elements, inside the 1D domain, are quadrilaterals bounded by the trace of two consecutive sections and by the sides connecting their extreme points. The water level is assumed to vary linearly inside each quadrilateral along the flow direction, but to remain constant …
Design of Reliable and Efficient Banki-Type Turbines
A new shape for the external surface of the Crossflow turbine blades is proposed, which allows for the preservation of hydraulic efficiency in spite of a significant maximum blade thickness providing mechanic robustness and reliability. The final shape of the blades is assessed using an iterative solution for two uncoupled models: a 2D computational fluid dynamic (CFD) and a structural 3D finite element method (FEM) analysis of a single blade. Application of the proposed methodology to the design of a power recovery system (PRS) turbine, a new backpressure Crossflow-type inline turbine for pressure regulation, and energy production in a real Sicilian site follows.
The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media
A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection-diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations sy…