S. Lam, O. Lopez, B. Quintero and D. Meneses

Abstract This study presents two-dimensional and three-dimensional numerical simulations of a cross-flow vertical-axis marine current turbine (straight-bladed Darrieus type) with particular emphasis on rotor-performance prediction and hydrodynamic characteristics. Numerical investigations of a model turbine (torque coefficient, power coefficient, tangential force coefficient, normal force coefficient and flow behavior) were undertaken using developed computational models. Turbine design was studied using a time-accurate Reynolds-averaged Navier-Stokes (RANS) commercial solver (ANSYS-CFD). A physical transient rotor-stator model with a sliding mesh technique was used to capture change in flow field at a particular time step. A shear stress transport k-x turbulence model was used to model turbulent features of the flow. Two-dimensional simulations were employed to test the influence of the profile type and thickness not only in the output power coefficient of the turbine but also on the radial force over the turbine shaft, while three-dimensional simulations were used to compute the curve of power coefficient versus tip speed ratio. Moreover, several flow phenomena as the interference between blades and detached tip vortices and the development of von Karman vortices are identified in the simulations. These phenomena are the reason for the decrease of power coefficient in the three-dimensional case regarding the two-dimensional situation.

S. Lam (H) • B. Quintero

Energetics and Mechanics Department, Universidad Autonoma de Occidente, Cali, Colombia

e-mail: slain@uao. edu. co B. Quintero

e-mail: bquintero@uao. edu. co O. Lopez • D. Meneses

Mechanical Engineering Department, Universidad de los Andes, Bogota, Colombia e-mail: od. lopez20@uniandes. edu. co

D. Meneses

e-mail: dp. meneses@uniandes. edu. co

G. Ferreira (ed.), Alternative Energies, Advanced Structured Materials 34,

DOI: 10.1007/978-3-642-40680-5_6, © Springer-Verlag Berlin Heidelberg 2013

Exhaustion of fossil fuels resources combined with greenhouse gas negative impact has recently raised the interest for renewable energies. Among them, hydropower takes a particular place because of its huge potential. Numerous micro-hydro power plants, presently build on rivers and canals, contribute also to the global growth of the hydropower production. Beyond this classical exploitation, hydropower is heading toward huge ocean energy potential, especially kinetic energy of tidal currents. Tides are created by the gravitational attraction of the moon and the sun acting on the oceans of the rotating earth, the relative motions causing the surface of the oceans to be raised and lowered periodically. Tidal power can be extracted by impounding a tide with a barrage to recover potential energy, or alternatively by extracting kinetic energy directly from the tidal stream. Actually, harvesting the tidal current energy rather than the tidal head has lower environmental impact.

Water turbines shapes are inspired from wind turbine shapes. Most of them are driven by lift rather than by drag forces. They can be classified depending on the direction of the rotational axis relative to the water flow direction. Axial flow water turbines (AFWT) have their axis of rotation parallel to water stream direction. Other turbines, cross flow water turbines (CFWT) or Darrieus type water turbines, have rotational axis perpendicular to current direction. A vertical-axis turbine is able to extract power from any direction without adjustment.

Development and optimization of tidal turbines require accurate and time-efficient mathematical models. Based on the computational tools available, different models with different computational costs were developed and applied for optimization and analysis purposes. These models range from computationally inexpensive but low in accuracy momentum models, to three-dimensional computational fluid dynamics (CFD) models of turbine with all the physical details taken into account. It can be concluded from a comprehensive literature review that there are two main families of approaches to numerically model a tidal turbine: potential flow codes and CFD codes. With the use of powerful computers and parallel processing technology, CFD simulations are becoming more popular in industrial and academic sectors [1, 2]. Contrary to potential flow codes, CFD simulations do not need any external data (experimental lift and drag) and can include separation from foils and drag induced vortices from turbine’s shaft. Also, they are able to simulate dynamic stall phenomenon (although it is not perfect due to the limitations of turbulence models). CFD modelling is also a powerful tool for complex geometries. However, CFD simulations for tidal turbines still suffer from high computational cost and time. The main advantage of CFD is that it allows reproducing physical unsteady flow around turbine using the so-called sliding mesh methodology, wherein relative motion between steady domain and rotor (unsteady domain) is captured by coupling them through an interface, which is updated at each time step and allows conservative interchange of fluxes between both domains. Rotor grid turns at each time step an angle relative to steady domain. At each time step a new solution is calculated. Transient behavior is built by adding solutions at each time step. In this methodology, integral values (torque) must be averaged in a complete revolution. The main disadvantage of CFD regarding potential flow methods is its higher computational cost (CPU time and memory). This is the reason why there are not many publications applying this methodology to CFWT.

There are not many previous studies approaching the simulation of vertical axis machines, considering air or water as fluid, from the same perspective as suggested here. Ferreira [3], employing air as fluid, presented a detailed state of art of different strategies for predicting aerodynamic characteristics of a VAWT. This author performs an exhaustive study about the ability of different turbulence models (Spalart-Allmaras, k-s, Detached Eddy Simulation, DES, and Large Eddy Simulation, LES) to reproduce the dynamics of the detached vortices from a single airfoil in two dimensions during its trajectory in the half cycle upstream of a VAWT. The best comparisons with experiments are obtained for LES, but the computational cost is prohibitive to think about useful design and evaluations from a practical point of view. This fact is common when LES is applied to industrial relevant flows.

Also using air as fluid, Maitre et al. [4] applied the sliding mesh strategy to a two bladed VAWT using Fluent v. 6.0 software combined with the one equation turbulence model Spalart-Allmaras. These authors defined two zones, an outer fixed zone and another inner rotating zone containing the blades. The results were compared with fairly old experimental data [5], obtaining an overprediction for the measured aerodynamic forces on the airfoils. However, in this paper no geometric details of the considered turbine were given.

Using water as fluid, Nabavi [6] performed a two-dimensional very detailed numerical study about hydrodynamic performance of a three-bladed CFWT introduced in a duct, to accelerate flow upstream the turbine. The author compared the two dimensional computational results obtained with Fluent in free flow conditions with own experimental measurements, resulting in an overprediction of the power coefficient. This result is in line with that obtained by Maitre et al. [4] because both used Spalart-Allmaras turbulence model. Additionally, Nabavi [6] tried other RANS models (k-s, k-ю and Reynolds Stress model) obtaining similar qualitative results. However, the authors believe that the use of the Spalart – Allmaras turbulence model in these specific simulations cannot be recommended in general because of the high adverse pressure gradients appearing in vertical CFWT and the lack of streamlines curvature correction of the model.

Dai and Lam [7] also performed a two-dimensional numerical study of three – bladed CFWT using the software ANSYS CFX v. 11, which is extensively employed for numerical simulation of hydraulic turbo machines. In this case, the turbulence model chosen was the two equation model SST (Shear Stress Transport). As in [6], they validate their numerical results versus own experimental measurements. The quantitative results of the validation are, however, only provided in a point, comparing them with the experiments and also with the results obtained by the double multiple stream tube model. As in the former studies, the averaged values of the torque provided by CFD are above the experimental values. In this study, enough information was provided about geometric parameters of turbine, so this configuration has been chosen in present work.

Howell et al. [8] developed a combined experimental and computational study of the aerodynamics and performance of a small (aspect ratio of 4) vertical axis wind turbine straight-bladed Darrieus type with three blades. Two – as well as three-dimensional numerical simulations were performed using the commercial code Fluent in connection with the k-s RNG turbulence model. Authors found that the power coefficient of the two-dimensional computations was significantly higher than that of the three-dimensional calculations and the experimental measurements, which was attributed to the presence of the over tip vortices in the three-dimensional situation.

This study performs full transient simulations of flow around a CFWT using CFD tools, including underlying turbulence of fluid flow and also viscous effects, without employing tabulated lift and drag data. This reason has motivated the choice of the sliding mesh method, which is the only one that allows describing the real unsteady behaviour of the CFWT blades in the fluid domain. Two dimensional simulations are used to study the influence of selected geometrical parameters of the airfoil on the performance (torque, tangential force and normal force coefficients) of the turbine. The airfoil thickness and symmetry were the selected factors for the present parametric study. Three-dimensional simulations allow identifying several flow phenomena, as detachment of blade tip vortices and vortex pairing shedding, relevant in the fluid dynamics of cross flow water turbines.