CFD investigation of counter rotating H-type Darrieus turbines in marine environment

POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell’Informazione

Corso di Laurea Magistrale in

Ingegneria Meccanica

Anno Accademico 2018/2019

Relatore:

Prof. Vincenzo Dossena

Corelatore: Prof. Giacomo Persico

Tesi di Laurea di:

Claudio PADRICELLI

Matricola: 858469

CFD INVESTIGATION OF COUNTER ROTATING H-TYPE

DARRIEUS TURBINES IN MARINE ENVIRONMENT

C

ONTENTS

2.1 OFFSHORE WIND ENERGY ... 5

2.2 HYDROKINETIC ENERGY ... 7

2.3 POTENTIAL ENERGY ... 11

2.4 WAVE ENERGY ... 13

2.5 OCEAN THERMAL ENERGY ... 15

2.6 SALINITY GRADIENT ... 15

2.7 MARINE BIOENERGY ... 15

3 VERTICAL AXIS TURBINE ...16

3.1 AERODYNAMIC MODEL AND PERFORMANCE PREDICTION ... 18

3.2 COUNTER ROTATING TURBINES ... 24

4 METHODOLOGY ... 31

4.1 CFD SIMULATION ... 31

4.2 OPENFOAM ... 41

5 CASE SETUP AND VALIDATION ... 44

5.1 SINGLE TURBINE ... 48

5.2 COUNTER ROTATING TURBINES ...61

6 RESULTS ... 70

6.1 VELOCITY FIELD ANALYSIS ... 70

6.2 GENERATED MECHANICAL POWER ... 74

6.3 POWER COEFFICIENT ... 75

6.4 POWER GENERATION DENSITY ... 76

6.5 CROSS STREAM EXTENSION OF THE WAKE ...77

7 CONCLUSIONS ... 80

APPENDIX A ... 82

DICTIONARIES FOR THE GENERATION OF THE MESH FOR THE SIMULATION OF THE SINGLE TURBINE ... 82

DICTIONARIES FOR THE GENERATION OF THE MESH FOR THE SIMULATION OF THE COUNTER ROTATING TURBINE ... 92

ACKNOWLEDGEMENTS ... 96

L

IST OF FIGURES

Figure 2.1 – Tides and lunar phases ... 3

Figure 2.2 – Global scale energy generation from renewable energy sources [43] ... 4

Figure 2.3 – Global installed capacity for wind energy conversion [44] ... 6

Figure 2.4 – Methods for tidal range exploitation [45] ... 12

Figure 2.5 – Wave energy conversion systems: a. oscillating water column [46], b. Wave Dragon [47], c. Manchester Bobber [48], d. Archimedes wave swing machines [49], e. Pelamis, f. PowerBuoy [50] ... 14

Figure 3.1 – Exempla of drag driven VATs ... 17

Figure 3.2 – Exempla of lift driven VATs ... 17

Figure 3.3 – Schematic of the Actuator Disc model ... 19

Figure 3.4 – Dependance of the velocity triangle of the blade from its azimuthal position ... 20

Figure 3.5 – System of fluid dynamic forces acting on the blade ... 21

Figure 3.6 – a. Schematic of the multiple stream-tube model, b. Schematic of the double stream-tube model, c. Schematic of the mutiple-double stream-tube model ... 23

Figure 3.7 – Turbine configurations investigated in [28]... 24

Figure 3.8 – Turbines array configurations investigated in [29] ... 25

Figure 3.9 – Comparison between vortices system in a school of fish and the configuation of the turbines array investigated in [30] ... 26

Figure 3.10 – Turbines configurations investigated in [27] ... 27

Figure 3.11 – Turbines configuration investigated in [31] ... 28

Figure 3.12 – left. Rendering of installed TWINFLOAT ®, right. Schematic of the configuration investigated in [33] ... 28

Figure 3.13 – left. Experimental setup built in [34], right. Turbines configurations investigated ... 29

Figure 3.14 – Turbines configurations investigated in [35] ... 29

Figure 3.15 – Velocity streamlines of the simulations computed in [36] ... 30

Figure 4.1 – Topology variation on structurated mesh due to the relative sliding of two regions of the grid ... 39

Figure 4.2 – case folder structure of a generic simulation performed with an OpenFOAM solver ... 41

Figure 4.3 – case folder of a CFD simulation performed with an OpenFOAM solver ... 43

Figure 5.1 – CAD representation of the configurations of the counter rotating

turbines investigated in the present thesis ... 45

Figure 5.2 – Schematic representation of the turbines configurations investigated in the present thesis ... 46

Figure 5.3 – Background mesh for the single turbine simulation ... 48

Figure 5.4 – (above) The utility snappyHexMex conforms the background mesh to the STL files of the blades. (below) Blade particular ... 49

Figure 5.5 – STL files modelling the blades of the turbine ... 49

Figure 5.6 – (above) Generating thin layers of cells around the blades and the AMI surfaces. (below) Blade particular ... 51

Figure 5.7 – Mesh sensitivity analysis on cross stream distance ... 53

Figure 5.8 – Mesh sensitivity analysis on stationary region grid refinement .... 54

Figure 5.9 – Mesh sensitivity analysis on upstream distance ... 55

Figure 5.10 – Mesh sensitivity analysis on downstream distance ... 55

Figure 5.11 – Cross stream dimension increase for correct development of velocity profile upstream the turbine ... 56

Figure 5.12 – Mesh sensitivity analysis on stationary region grid refinement ... 57

Figure 5.13 – Mesh sensitivity analysis on rotating region grid refinement ... 58

Figure 5.14 – Solution sensitivity analysis on flow model ... 60

Figure 5.15 – Comparison between the characteristic curve of a single turbine computed with CFD simulation and measured in [41] ... 60

Figure 5.16 – Background mesh for the counter rotating turbines simulation .. 62

Figure 5.17 – (left) “Castellated mesh” obtained with the utility snappyHexMesh. (right) Blade particular ... 63

Figure 5.18 – Blade particular of the mesh obtained with the utility extrudeMesh ... 63

Figure 5.19 – Blade particular of the “snapped” mesh ... 64

Figure 5.20 – (left) Generation of thin layers of cells around the blades. (right) Blade particular ... 65

Figure 5.21 – case folder structure for the simulation of the counter rotating turbines ... 65

Figure 5.22 – Explosion of the folder userBoundary ... 66

Figure 5.23 – Explosion of the folder counterBaseCase ... 67

Figure 5.24 – Explosion of the folder counterSTL ... 67

Figure 5.25 – Explosion of the folder counterMeshes ... 68

Figure 6.1 – Velocity field in the rotor disk for the isolated turbine ... 71 Figure 6.2 – Velocity field in the rotor field and in the near wake region for the counter rotating turbine in configuration A ... 72 Figure 6.3 – Velocity field in the rotor field and in the near wake region for the counter rotating turbine in configuration B ... 73 Figure 6.4 – Comparison between the unit mechanical power generated in the different configurations studied ...74 Figure 6.5 – Array configuration of turbines in configuration B...76 Figure 6.6 – Velocity field sampling sections layout ... 77 Figure 6.7 – Velocity profile in the near wake of the turbines for all the

configurations examined ... 78 Figure 6.8 – Wake evolution in the streamwise direction for all the

A

BSTRACT

In the present thesis, it has been investigated a new solution for exploiting hydrokinetic energy. This energy source can be forecast with higher accuracy, both in the short and in the long term, with respect to other renewable energy sources. The predictability is correlated to the dispatchability of the source, which is a key parameter in ensuring a higher penetration of renewable energy sources in the energetic industry.

The machines for the energy conversion process, on which this thesis have focused, are H-type Darrieus turbines. Recent studies have proven that, contrary to what happens for horizontal axis turbines, the performances of these machines are improved when placed at close distance. In particular, in the configurations tested in the present thesis, two identical turbines are aligned in the cross stream direction. The axes of rotation of the machines are at a distance of 1 rotor disk radius and the blades are angled so that the turbines rotate with opposite angular velocity. The results of the study have proven that the machines in such configuration reach a power coefficient double with respect to the isolated turbine. The investigation has been performed by means of 2 dimensional CFD simulations in a freestream environment. URANS numerical simulations have been carried out with solver in the software package OpenFOAM. The analysis of the results computed, performed by means of code written in Matlab software, has shown that the flow field generated by the interaction between the machine and the fluid is complex and dominated by the presence of vortical structures. The geometry of the machines modelled are taken from an experimental study in a table top water channel. Due to structural reasons, the characteristic Reynolds number of the flow is in the transition region. Hence the transitional flow model 𝑘 𝑘𝑙 𝜔 have been implemented in the simulations.

A thorough analysis of the parameters of the grid and of the flow model have been performed, in order ensure the independency of the solution from the mesh. The results have been validated with an experimental campaign carried out on the same turbine modelled in this thesis.

S

OMMARIO

Nel presente lavoro di tesi, è stata analizzata una soluzione innovativa per utilizzare l’energia idrocinetica. Le previsioni relative a questa tipologia di fonte energetica, sia nel breve che nel lungo termine, sono più accurate rispetto ad altre fonti di energia rinnovabili. La possibilità di prevedere la disponibilità della risorsa è correlata alla possibilità di generare energia quando viene richiesta dalla rete. Questo è un parametro cruciale per assicurare un maggiore utilizzo delle risorse rinnovabili nell’industria energetica.

Le macchine per la conversione di energia, sulle quali questa tesi si è focalizzata, sono le turbine Darrieus di tipo H. Recenti studi hanno dimostrato che, al contrario di quanto accade nelle turbine ad asse orizzontale, le performance di queste macchine migliorano se posizionate a breve distanza le une dalle altre. In particolare, nelle configurazioni, studiate in questa tesi, due turbine sono allineate perpendicolarmente alla direzione del fluido. Gli assi di rotazione delle macchine sono posti alla distanza di 1 raggio del disco del rotore e le pale sono angolate in modo che le turbine ruotino con velocità angolare opposta. I risultati dello studio dimostrano che le macchine in questa configurazione raggiungono un coefficiente di potenza doppio rispetto al caso di turbina isolata.

Lo studio è stato condotto con simulazioni CFD bidimensionali, che riproducevano un dominio aperto. Simulazioni numeriche URANS sono state eseguite con solver del pacchetto di software OpenFOAM. Le analisi sui risultati calcolati, condotte con un codice scritto in Matlab, hanno dimostrato che il campo di moto generato dall’interazione tra il fluido e la macchina è complesso e dominato da strutture vorticose. La geometria delle macchine è stata presa da uno studio sperimentale condotto in un canale ad acqua di piccole dimensioni. Per motivi strutturali il numero di Reynolds caratteristico del flusso è nella regione di transizione. Quindi è stato implementato nelle simulazioni il modello di flusso transazionale 𝑘 𝑘𝑙 𝜔.

È stata effettuata un’approfondita analisi sui parametri della griglia per assicurare l’indipendenza della soluzione dalla mesh. I risultati sono stati validati una campagna sperimentale condotta sulla stessa turbina studiata in questa tesi.

1 I

NTRODUCTION

The energy industry is driven by the same economic laws as all the other types of industries, hence the technologies installed in power plants are the ones that ensure the highest economic return on the investment. For this reason, most of the existing power plants exploit either fossil fuels or nuclear energy as source for the energy conversion. These energy sources generate pollutant gasses and toxic wastes that have caused many environmental issues. Renewable energy sources represent a more sustainable alternative as their pollutant byproducts, of the energy conversion process, are of order of magnitude smaller or in same case non existing at all. Using renewables energy is not yet economically competitive but government and researchers work, in different ways, to increase the profitability of these type of energy sources. The former with economic incentives for the investors the latter by finding new solutions and technologies.

In a power plant, the revenues depend on the unitary cost of the energy and on the quantity of energy sold to the grid. The unitary cost of the energy is a parameter which only the government and the energy market can variate; the quantity of energy sold depends on the flexibility of the power plant to follow the energy request of the grid, or, in other terms, on the possibility to provide to grid electrical energy at the exact moment as when it is required. This condition can not be always fulfilled by power plants that use renewable energy sources (from now on referred as renewable power plants) as they can generate electrical energy only when the resource is available (for example, solar fields do not produce energy at night). On the other hand, fossil fuels and nuclear based power plants (from now on referred as non-renewable power plants) do not have dispatchability issues, hence they represent a more reliable source of energy and income.

The costs can be grouped into two categories: capital expenditure (CAPEX) and operational expenditure (OPEX). The former comprises the costs related to the plant installation, while the latter comprises the running costs, i.e. salaries, costs of energy source, etc., and the costs of maintenance. The installation costs depend mainly on the nominal size of the power plant, the unitary cost of the machines and the costs related to the siting of the plant. The nominal size of the plant is design choice based on the break even point of the specific plant. The unitary cost of the machines depends on the economy of scale. The costs siting of the plant depends on the type of source used in the power plant and comprises also the cost of the infostructures required for the connection of the plant to the grid. For renewable power plants, the machines installed, generally, have to be customised for the specific power plant, moreover the siting depends on the location where the source is available, which is typically in remote areas, i.e. off shore wind farms or hydropower plants, that require high cost for the grid connection. Overall the CAPEX is typically much higher for renewable power plant. The siting of the plant affects also the maintenance costs, both in terms of accessibility to the failed component and life expectancy of the installed machine due to the mechanical stress that has to sustain. For some renewable power plants, the maintenance operation can be done only under certain weather conditions. Overall, even if the

source is available for free, also the OPEX is typically higher for renewable power plants.

Among the renewable energy sources, the exploitation of the kinetic energy of oceanic, marine or river currents, referred to as hydrokinetic energy, offers a big advantage in terms of predictability of the source. Many research facilities are testing turbines, for exploiting this energy sources, that are based on similar physical principles of the ones employed in wind farms, but with bigger the resistant sections due to the higher mechanical loading that have to bear. Hence, hydrokinetic power plants may be both economically and environmentally sustainable, thanks to a more predictable source and the employment of well studied technologies.

The aim of this thesis is to investigate by means of CFD simulations a new configuration for Darrieus turbines, which consist in installing fields of arrays of turbines at close distance. Recent studies have proven that, for this machine, the proximity with another Darrieus turbine has positive effects on its performances. This configuration has the potential of reducing the installation costs of the fields, by exploiting the economy of scale and of optimizing the usage of the area, as more power can be generated per unit surface. Moreover, the maintenance operations for Darrieus turbines are relatively easy to perform, with respect to other machines exploiting the same type of renewable energy source, due to the position of the electronic components.

In the second chapter, it is given a brief introduction of how liquid water masses can be exploited for generating energy.

In the first section of the third chapter, Darrieus turbines are briefly described and in the second section, the state of the art and relevant scientific articles are examined.

In the first section of the fourth chapter, the concepts of CFD simulations and its main issues are outlined, and in the second section the software package OpenFOAM, employed for the simulations, is presented.

In the fifth chapter, the setup of the simulations and the analysis and validation process of the solution computed in the simulations, are described.

In the sixth chapter, the results obtained in the simulations are presented, comparing different configurations of Darrieus turbines.

2 B

LUE ENERGY

More than 70% of the Earth’s surface is covered by liquid water, which is constantly moving, due to the weather’s conditions, to the planet’s rotation, to the differences in the physical and chemical properties of the water or to the tides. The weather conditions, of most interest for the energy generation process, are the winds, in particular its speed and direction, and the rainfalls. Both are stochastic events thus they can not be precisely forecast. Rainfalls affect the flow of rivers and the level of the water in the basins. Winds generate the waves and affect the oceanic and marine currents.

The planet rotation causes the Coriolis effect, which in turn influences the oceanic currents for the water masses moving from the poles to the equator and vice versa. The temperature and salinity gradients within the water affect the local currents, where their driving force is sufficiently strong.

The tides are caused by Moon’s and Sun’s gravitational pull on liquid water. The influence of the gravitational field generated by the Moon is bigger than that of the Sun as it is closer and thus its variation between two antipodal points of the Earth is bigger. In fact, the gradient of the gravitational field decreases with the distance from body that generates the field. The intensity of the tides depends on the lunar phases: when the Sun, the Earth and the Moon are aligned the gravitational fields interfere constructively causing tides of biggest intensity (spring tides), while when the Moon is in quadrature the tides are of lowest intensity (neap tides). The effect of the relative positions of the bodies in the Sun – Earth – Moon system on the tides is shown in Figure 2.1.

In the regions near gulfs, the tides cause the increase (flood tide) and the decrease (ebb tide) of the level of the water, the difference between the maximum level of water and the minimum is called tidal range; due to Earth’s rotation, the effect alternates every 6 hours from flood tide to ebb tide and vice versa. In the regions near straits or a narrow channels, the tides produce currents that move masses of water toward the location where it is happening the flood tide, thus the direction of the currents changes every 6 hours. Both tidal range and tidal currents are exploited for electricity generation with different technologies as it will be described in the sections 2.2 and 2.3. The technologies exploiting the tidal range require the construction of dams or barrages, so their installation costs is higher than the technologies exploiting tidal currents, which, on the other hand, have higher grid connection costs as the machines are installed at a distance from the

shore and thus underwater cables are required. Altogether an optimal technology is still under research. The tides are very well predicted unlike other renewable energy sources such as solar or wind, however power plants exploiting this energy source do not have high equivalent hours due to the intrinsic variability of the demand and the variability of the resource with the lunar phases. In fact, as previously stated, the resource oscillates between its minimum value at neap tide and its maximum value at spring tide, hence the generators installed, which converts it into electrical energy, should be sized to its maximum value in order to completely exploit it, but this is not economically advantageous, hence smaller sized generator are typically installed, preventing to fully exploit all the available tidal energy.

Mankind has been using liquid water to produce useful work since the third century BC with the first watermills. Nowadays liquid water is exploited for electrical energy generation by many technologies, that can be subdivided into 7 categories, as described in [1], according to the physical principle used for energy conversion:

• Offshore wind energy • Hydrokinetic energy • Potential energy • Wave energy

• Ocean thermal energy • Salinity gradient • Marine bioenergy

The technologies that have already industrial applications are horizontal axis wind turbine for offshore wind energy and hydropower generation for potential energy; for all of the other categories, either there are research facilities in operation or they are still in the design and optimization phase. Figure 2.2 shows that hydropower and offshore wind energy represent more than the 60% of all the energy generated from renewable energy sources.

The technology studied in this thesis can be classified as hydrokinetic energy conversion system and it is not used in any industrial scale power plant, but it

Figure 2.2 – Global scale energy generation from renewable energy sources [43]

may improve the energy generation density of this category of plants, exploiting the positive interference of closely spaced Darrieus turbine. Thus, this solution could be the key for more compact power plants, with a smaller environmental footprint.

2.1 O

The technologies employed in this category are the same as the ones for onshore wind energy, i.e. horizontal and vertical axis turbines, between those two, only the former has industrial maturity.

The main advantages of offshore plants over onshore ones are: • Favourable velocity gradient of air in the vertical direction

• Less concerning issues in terms of visual and acoustic impact of the field; while the main disadvantages are that:

• The machines need floating platforms and mooring mechanisms

• The maintenance of the power field is more expensive and require certain weather conditions to be accomplished.

The disadvantages listed above are concerning issues also for the technologies exploiting wave energy and hydrokinetic energy, which are in a much early stage of development and so can benefit from the technological solutions developed for offshore wind energy.

According to reports of the International Energy Agency (IEA), as shown in Figure 2.3, the nominal installed power of offshore wind energy is raising with higher rate each year, while onshore nominal installed power has been increasing with a lower rate from the past 3 years. From 2017, new fields have been installed in China, Germany and the United Kingdom.

Figure 2.3 – Global installed capacity for wind energy conversion [44]

2.2 H

This category comprises different types of technologies which transform the kinetic energy of water into electrical energy. The machines that exploit wind energy, perform the same energy transformation but with a working fluid 800 times less dense. Hence, even if the physical principle is similar, the mechanical characteristics of the machines, performing the energy conversion, must be sized according to the density of the working fluid. The same machine could generate more power when a denser fluid is employed (provided that the velocity is kept constant), but also the mechanical stress would be higher due to the higher fluid dynamic loading.

The main advantages of hydrokinetic energy over wind energy are that: • The source is more predictable both in terms of direction and intensity • The free surface between water and air acts as a constrain, enhancing

blockage in the water

While the main disadvantages are that:

• The machines are more subjected to wear

• The influence of the velocity field in the working fluid can persist over a larger distance [1]

The technologies in this category can be employed for many applications [2]: • Tidal currents

• Ocean currents • River streams

• Man-made waterways • Industrial outflows

According to the application, different nomenclatures are adopted: “Water Current Turbine”, “Tidal Current Turbines”, “Tidal In-Stream Energy Converters”, “River Current Turbine”, “River Current Energy Conversion System”, “Water Turbine”. An official definition has been provided by the US Department of Energy in 2006, which defines those machines as “Low Power/Unconventional Systems” that use hydro resources with less than 8 feet head. This terminology is used for distinguishing the technologies exploiting hydroelectric energy from the conventional hydroelectric plants which use much higher head and/or capacity.

The machines can be classified into turbines systems and non-turbine systems. The former group can be further subclassified into [2]:

• Axial (Horizontal): Rotational axis of rotor is parallel to the incoming water stream

• Vertical axis: Rotational axis of the rotor is vertical to the water surface and also orthogonal to the incoming water stream

• Cross-flow: Rotational axis of rotor is parallel to the water surface but orthogonal to the incoming water stream

• Venturi: Accelerated water resulting from a choke system is used to run an in built or onshore turbine

• Gravitational vortex: Artificially induced vortex effects is used in driving a vertical turbine

And the latter group can be subclassified into:

• Flutter Vane: Systems that are based on the principle of power generation from hydroelastic resonance (flutter) in free-flowing water

• Piezoelectric: Piezo-property of polymers is utilized for electricity generation when a sheet of such material is placed in water stream

• Vortex induced vibrations: Employs vibrations resulting from vortices forming and shedding on downstream side of a bluff body in a current • Oscillating hydrofoil: Vertical oscillation of hydrofoils can be utilized in

generating pressurized fluids and subsequent turbine operation. A variant of this class includes biomimetic devices for energy harvesting

• Sails: Employs drag motion of linearly/circularly moving sheets of foils placed in water stream.

Some exempla of the machines designed for hydrokinetic energy conversion are listed in the Table 2.1.

Table 2.1

Device Classification Status Illustration

Oscillating Cascade

Power System [3] Flutter Vanes

Design and research phase

Solon Tidal Turbine

[4] Ducted horizontal axis turbine Successfully tested in 2008

bioSTREAM [5] Oscillating _{hydrofoil research phase} Design and

Tidal Fence Davis

Hydro Turbine [6] Ducted vertical axis turbine research phase Design and

Tidal Stream

Turbine [7] Horizontal axis turbine

Installed on the north coast of

Norway in September 2003

Rochester venturi [8] Venturi Installed demonstration site in the English Midlands in 2005

Lunar Energy Tidal Turbine [9] Ducted horizontal axis turbine Design and research phase

SeaGen [10] Horizontal axis _{twin turbine}

Installed in May 2008 in Northern

Ireland and grid connected

Deep Green [11] Sails

Tested in Northern Ireland and Wales, now it

is at the commercial phase

The energy

Harvesting Eel [12] Piezoelectric research phase Design and

Cormat [13] Contra rotating horizontal axis turbine

Ready for deployment

Neo-Aerodynamic

[14] Gravitational vortex Unknown

Evopod Tidal

Turbine [15] Horizontal axis turbine

Installed in Scotland, from

2014 to 2017

Gorlov Helical

Turbine [16] Cross-flow turbine

Tested in Massachusetts in

2004

Open Centre

Turbine [17] Horizontal axis turbine

Installed at the EMEC in Scotland.

Connected to UK national grid in

Kobold [18] Vertical axis _turbine

A pre-commercial model has been tested in Messina

Strait, Italy in spring 2001

SR250 [19] Horizontal axis _turbine

Field tests have been carried out in

the EMEC in the Orkney, the technology is at commercial phase TidEl Stream

Generator [20] Horizontal axis twin turbine

A 1/10th scale model has been tested. The device

is still under development

Atlantisstrom [21] Cross-flow _turbine

A grid connected commercial model

has been tested in Vestmanna Sund

in 2014

DeltaStream

Turbine [22] Horizontal axis turbine

Full production was planned for summer 2009

Free Flow Turbines

[23] Horizontal axis turbine

Grid connected demonstration has

been installed in East river, New York from 2006 to

2009 Vortex Induced

vibration for aquatic clean energy (VIVACE) [24] Vortex Induced Vibration Multiple pre-commercial models have been

deployed in St. Clair River in Michigan, USA

2.3 P

The technologies in this category transform the potential energy of masses of liquid water into electrical energy. They can be employed in mainly 2 applications:

• Hydropower • Tidal range

Hydropower plants are the technology with the higher cumulative nominal installed power among all the technologies which exploit renewable energy sources, according to IEA. They employ dams for creating artificial basins for water storage at a certain altitude, the basins can be fed by rivers, by pumps or by rainfalls. For the energy conversion process, the water flows from the basin to a plant, which is located at a lower altitude. The potential energy of the mass of water is transformed into kinetic energy of the flow, a turbine transforms it into mechanical energy of a rotating shaft, which, in turn, drives a generator that transforms it into electrical energy. The type of turbine employed, depends on the geodetic jump and the volumetric flow of water:

• Pelton turbines are used for high geodetic jumps and low volumetric flow rates,

• Francis turbines are used for medium geodetic jumps and medium volumetric flow rates

• Kaplan turbines are used for low geodetic jumps and high volumetric flow rates.

The biggest hydropower plant is installed in China over river Yangtze and it has a nominal power of 22 GW, while the biggest installed in Italy is in Entracque and it has a nominal power of 1,1 GW.

The exploitation of tidal range for generating electrical power, can be carried out with 3 methods:

• Ebb generation • Flood generation • Two-way generation

In the first two methods only 2 tides generate electricity per day. In the first case, the tide fills a basin during the flood tide, once filled the level of the water is kept constant with the use of slice gates. When the ebb tide has lowered the sea level, the water stored in the basin flows through a turbine and the energy conversion process is similar to the one described for the hydropower plants. For the flood generation method, the energy conversion happens during the flood tide. In fact, in this case, the slice gates are kept closed at the beginning of the flood tide and the basin enclosed is kept as dry as possible. When the flood tide increases the water level up to a given threshold, the water fills the dry basin, flowing to a turbine. This method can have some impact on the other activities for which the basin can be employed; hence a minimum level of water must be kept for ensuring navigation, but decreasing the maximum head exploitable. For two-way generation method, both the flood tide and the ebb tide are employed for the

electrical energy generation. Thus, the water head exploited in those plants is lower than the maximum available, but the energy conversion is performed 4 times per day. The turbines, employed in the two-way generation method, are required to be able to work in both flow directions. Moreover, pumping is sometimes used as it can increase the water level in the basin and, although this process requires energy, it is gained back as the electrical energy generation is proportional to the square of the difference between the water levels at the two ends of the turbine [25]. Those 3 methods are schematized in Figure 2.4

Tidal range power generation can have some environmental issues as it can change the tidal motions in a given location, raising problems in terms on stagnation, loss of water quality, changes to sediment transport, salinity and biodiversity [1]

The machine used for tidal range power generation are Kaplan turbines or bulb turbine which modify the Kaplan project from a vertical axis device to a horizontal axis one, in order to allow the water to flow in both directions. Only in Annapolis, Canada straflo turbines are employed.

The first operating plant using tidal range is la Rance in France with an installed power of 240 MW. It uses a hydrostatic head of 5 m and operates in two-way generation [26]. The plant with the biggest installed power is on lake Sihwa in South Korea with an installed power of 254 MW but is only uses flood generation.

2.4 W

Waves are caused by the winds blowing on the surface of water, the height of the wave can be influenced also by the conformation of the seabed. In general, the frequency and the height of the wave are very difficult to forecast precisely on the long term. Forecasting agencies use statistical techniques and physical-based models, with the help of neural networks, regression-based techniques and genetic programming. The National Oceanic and Atmospheric Administration and the National Weather Service can produce forecasts of up to 180 h using WAVEWATCH-III [27].

The technologies in this category are at research state with few testing machines in operation. The machines can be categorized according to the energy conversion method in:

• Oscillating water columns • Overtopping devices • Wave activated bodies

In the first category, the machines have a partially submerged structure, in which the water level changes due to the incoming waves. The air present above the water surface and enclosed in the structure is pressured and depressured as a consequence of the variation of the water level. The air, in turn, drives a turbine mounted on top of the structure as shown in Figure 2.5.a. In the second category, the machines have a floating structure, held in position by a mooring system which traps water that overtops due to the waves. The overtopping water is collected and gravity forces is through a low-head turbine, that is exploited for the electrical energy generation. An example is the Wave Dragon whose prototype has been tested in Nissum Bredning, Denmark, Figure 2.5.b. In the last category, there are many different machines, some projects in design phase are:

• The Manchester Bobber (Figure 2.5.c) has all the moving parts and the electrical components above sea level, which intrinsically increases robustness and reliability. Its frame is secured to the seabed, while some floats slides in a linear motion caused by the waves in vertical rails in the frame. The alternating motion is exploited for the electrical energy generation.

• The Archimedes wave swing machine (Figure 2.5.d) is a cylindrical shaped buoy, submerged underwater and tethered to the seabed. The machine has a floating part which can move in a linear motion with respect to a base

which is kept in position by chains, the linear motion is caused by the incoming waves and it is exploited to generate electrical energy.

There are also projects ready for commercialization:

• The Pelamis (Figure 2.5.e) is made up of cylindrical inter-connected floating sections which move relatively to each other due to wave. The relative motion is exploited for generating electrical energy. It was connected to the grid in 2004 but the firm producing it has gone into administration thus the machine is no more in operation.

• The PowerBuoy, produced by the Ocean Power Technology (Figure 2.5.f), it is made up of a central cylinder moored to the seabed and a free-floating structure. The free-floating structure operates as a point absorber, which oscillates up and down in the waves. The mechanical motion being converted into electricity.

Figure 2.5 – Wave energy conversion systems: a. oscillating water column [46], b. Wave Dragon [47], c. Manchester Bobber [48], d. Archimedes wave

2.5 O

The technologies in this category exploit the thermal capacity of water. A thermo-dynamic cycle is performed between the temperature levels of water at the surface and at a certain depth in either closed-cycles or open-cycles or hybrid cycles. It has been proven to be too costly for field test, although some small-scale testing facilities are present in USA, Nauru, India and Japan.

2.6 S

Salinity gradient in sea or ocean water can be exploited by different technologies, two of them are already used in pilot plants:

• Pressure-retarded osmosis (PRO) • Reversed electro-dialysis (RED)

The former has been used in Tofte, in Norway, but the plant ceased operation soon because of fouling issues on the membrane. The latter has been used in Afsluitdijk, in the Netherlands. Many technical problems have been reported using RED, which prevent this technology to be fully implemented, such as: damage to membranes by natural impurities in water, filtration of particles, biofouling, the effect of multivalent ions on system performance, the impact on marine species of substantial pumping process and the necessity to minimize internal resistance.

2.7 M

Marine algae can be fermented to produce biomethane and/or biohydrogen, those, in turn, can have many applications, such us:

• Powering aquaculture systems offshore

• Using hydrogen generated from renewable energy sources for upgrading the carbon dioxide produced by the algae to biomethane exploited in the existing plants that use biogas

The exploitation of algae for biogas production can have a positive impact on the environment in:

• Reducing eutrophication in fish farms by growing seaweed adjacent to them;

• Acting as energy reservoirs and sequester of carbon from the atmosphere thanks to their fast growth rate.

Moreover, it offers a resolution to the controversy surrounding the sustainability of the production of biogases from biomass produced on land, where there is competition between food and fuel. The exploitation of algae to produce biogases is still in research phase.

3 V

ERTICAL AXIS TURBINE

The vertical axis turbines (VATs) are devices that transform the kinetic energy of a fluid into mechanical energy of a rotating shaft. This energy conversion depends on the interaction between the fluids that flows across the machine, which is typically referred to as working fluid, and the moving parts of the machine. VATs can be classified according to mainly two parameters:

• The working fluid

• The type of fluid dynamic force that is prevalent in the energy conversion process

The working fluids that are typically employed are air, exploited by vertical axis wind turbines (VAWTs) or water, exploited by vertical axis hydrokinetic turbines (VAHTs). The same equations can describe both the VAWTs and the VAHTs, as both working fluids are assumed to be incompressible. This assumption can be valid also for air since the Mach number that characterise the flow is typically much lower than 0.3. The first analytical models for the VATs were developed for wind applications.

For what concerns the classification according to the fluid dynamic forces prevalent in the energy conversion process, the VATs can be split into drag driven turbines and lift driven turbines. The drag driven turbines exploit a non symmetrical geometries (with respect to the flow direction) of their moving parts in order to have a non uniform drag coefficient distribution over the whole machine. The resultant drag force is not applied on the axis of rotation thus a net torque is generated. Some exempla of drag driven machines are shown in Figure 3.1

• The Savonius turbine (Figure 3.1.a and Figure 3.1.b) is the most common drag driven VAT and it is employed for some small scale application. Its S-shaped rotor is designed so that the drag force is stronger on the blade that faces the wind with its concave side. Different designs are possible, by varying the relative position of the blades or the number of blades.

• The cup anemometer (Figure 3.1.c) is typically employed during the wind campaigns for measuring the velocity distribution of the resource. Typically it has 3 hemispherical blades and exploits a similar principle as the Savonius turbine

• The half-shield wind turbine (Figure 3.1.d) does not have many applications. It has straight blades and a shielding panel that mechanically blocks the flow of the fluid. The panel need to be correctly positioned with respect to the wind direction in order to shield only half of the blades, so that fluid dynamic drag forces are applied on the other half of the blades, generating a net torque on the machine.

• The Panemone wind generator (Figure 3.1.e) does not have many applications. Each of its blade can to pivot around an axis framed on the rotor at a distance from the axis of rotation of the machine. While the rotor spins, each blade will tend to rotate around its pivoting axis aligning in the wind direction, in order to minimize the its resistive surface. A mechanical

stop on the rotor prevents the blade to pivot freely during the complete rotation of the machine. The stop is designed so that the pivoting motion of each blade is hindered during half of the complete rotation of the machine. So that the resistive surface of each blade will increase from its minimum value generating a net torque on the rotation axis of the machine.

The system of forces of the lift driven turbines, is much complex and it will be examined in the section 3.1. Those machines have been studied thoughtfully by the aeronautical engineer Gorges Jean Marie Darrieus, who in 1926 patented his turbines with a number of different configurations: H Darrieus (Figure 3.2.a), Delta Darrieus (Figure 3.2.b) and Troposkien (Figure 3.2.c); others turbines have been designed starting from these turbines: twisted blade Gorlov turbine (Figure 3.2.d) or the Cycloturbine (Figure 3.2.e), both driven on H Darrieus turbines, the former has helical blades and the latter has straight blades with variable stagger angle.

In general, lift driven turbines have higher performance coefficient than drag driven turbines, but they have a lower starting torque thus they require external devices for being set in motion. The tangential velocity of the drag driven turbines is limited by the velocity of the fluid because the aerodynamic force depends on

Figure 3.1 – Exempla of drag driven VATs

difference between the two velocities. Hence the angular velocity of drag driven turbines is typically lower than that of lift driven turbines for which this limitation does not apply; thus drag driven turbines have lower noise levels and vibrations issues.

As stated in the section 2.1, VATs do not have many commercial applications, but horizontal axis turbines (HATs) are preferred instead. HATs have higher performance coefficients, thus the electrical energy generated is higher per single machine for a given resource. VATs offer however some advantages over HATs such as:

• Do not require yaw mechanisms

• Have easier design, lower manufacturing and maintenance costs due to the position of the generator, which is at ground level and typically directly connected to the rotating axis of the turbine, moreover the blade geometry is easier as it has no swirl or tapering

• Can be installed with a lower spacing among them, thus more electrical energy can be generated per unit area [28]

3.1 A

The fluid dynamics of VATs is complex, different models can be employed for describing the flow field of the working fluid and predict performances of the machines with increasing level of precision. A simplified analysis, typically used for HATs, can be done considering a 1 dimensional case, under the following assumptions (actuator disk model):

• Incompressible fluid • Steady state flow • Inviscid flow

• No swirl in the wake of the turbine

• The turbine is modelled as an actuator section where the energy is transferred from the flow to the machine causing a discontinuity in the pressure field (Figure 3.3)

• At a sufficient distance from the turbine, in both the upstream and the downstream direction, the fluid is at ambient pressure

The presence of the turbine causes a continuous reduction of the velocity of the fluid from the free stream value (𝑉0) (Figure 3.3), thus the stream tube containing

the flow particles that cross the actuator disk diverge as modelled with the mass balance equation.

The Bernoulli principle, the mass and momentum balances can be applied for characterizing the machine, the pressure field and velocity field according to this model. Applying the mass balance on the control volume (CV) 1, 2 and 3, shown in Figure 3.3:

𝑚̇ = 𝜌𝐴0 𝑉0 = 𝜌𝐴1𝑉1 = 𝜌𝐴2𝑉2 = 𝜌𝐴3𝑉3

Given 𝐴1 = 𝐴2 = 𝐴𝐷, it follows that

𝑉₁ = 𝑉₂ = 𝑉_𝐷 3. 1

Where it can be demonstrated that:

𝑉_𝐷 = 𝑉0+ 𝑉3

2 3. 2

The Bernoulli principle on control volumes 1 and 3, shown in Figure 3.3, can be written: 𝑝0 + 1 2𝜌 𝑉₀2 2 = 𝑝1+ 1 2𝜌 𝑉₁2 2 𝑝2+ 1 2𝜌 𝑉₂2 2 = 𝑝3+ 1 2𝜌 𝑉₃2 2 3. 3

By substituting the 3.1 and the 3.2 in the 3.3, with the assumption that 𝑝0 = 𝑝3, it is obtained: 𝑝₁− 𝑝₂ = 1 2𝜌(𝑉∞ 2_{− 𝑉} 32) 3. 4

Applying the momentum balance on the control volume 2, shown in Figure 3.3, it is possible to compute the aerodynamic force on the actuator disc:

𝐹𝐷 = 𝐴𝐷(𝑝1− 𝑝2) 3. 5

The mechanical power transferred to the machine can be computed:

𝑃 = 𝐹_𝐷𝑉_𝐷 3. 6

It can be defined the induction factor (𝑎), that takes into account the reduction in velocity due to the disturbance in the velocity field caused by the turbine as:

𝑎 =𝑉0− 𝑉𝐷

𝑉₀ 3. 7

The 3.6 can be rewritten taking into account the 3.4, the 3.5 and the 3.7: 𝑃 =1

2𝜌𝐴𝐷𝑉0

3_{(4𝑎(1 − 𝑎)}2_{) 3. 8}

Thus, the power coefficient is defined as, taking into account the 3.8: 𝑐_𝑃 = 𝑃

1

2 𝜌𝐴𝐷𝑉02

= 4𝑎(1 − 𝑎)2

The optimal value of power coefficient is obtained for 𝑎 = 1/3 and is defined as Betz limits 𝑐𝑃𝐵𝑒𝑡𝑧= 16/27 ≈ 0.59.

A more refined analysis can be performed considering a 2 dimensional model, that takes into account the fluid dynamic forces and the energy transfer for a single rotating blade; the performance of the turbine is obtained computing the

Figure 3.4 – Dependance of the velocity triangle of the blade from its azimuthal position

superposition of the effects of 𝑁 blades of the machine, each considered as isolated. The fluid dynamic forces depend on the relative velocity between the fluid and the blade, the velocity triangle for a single blade is shown in Figure 3.4: The blade has an anticlockwise rotation around its axis and the position of the blade along its trajectory is defined by the azimuthal angle (𝜃) whose origin is shown in Figure 3.4. The path of the blade can be divided in windward path, from 𝜃 = 0 to 𝜃 = 𝜋, and leeward path from 𝜃 = 𝜋 to 𝜃 = 2𝜋. The angle of attack of the blade (𝛼) depends on the azimuthal angle and on the blade speed ratio (𝜆), which is defined as:

𝜆 =𝜔𝑅

𝑉₀ 3. 9

The angle of attach is described by the equation: 𝛼 = 𝑎𝑡𝑎𝑛 ( (1 − 𝑎) 𝑠𝑖𝑛 𝜃

(1 − 𝑎) 𝑐𝑜𝑠 𝜃 + 𝜆) − 𝛾 3. 10

Where the first term is the angle formed by the relative velocity and the tangent to the blade’s path at the azimuthal position of the blade, defined as 𝛼𝑓, and 𝛾 is

the stagger angle. For 𝜆 smaller than or equal to 1 the angle of attack goes from −𝜋 to 𝜋 a complete rotation of the blade, thus at a certain azimuthal angle it will stall; if 𝜆 is sufficiently high than it is possible that the blade will not stall during the whole rotation. The effect of the blade speed ratio on the power coefficient will be discussed later in this paragraph.

The system of forces acting on the single blade is shown in Figure 3.5 and can be analysed according to the Blade Element Theory (BET). The analysis is performed for a blade that has an infinitesimal extension (𝑑𝑧) in the direction parallel to the axis of rotation, the overall force can be computed integrating along the span of the blade.

The infinitesimal aerodynamic forces acting on the blade are:

𝑑𝐿 =1 2𝜌𝑐𝐿𝑊𝐷 2_{𝑐 𝑑𝑧 3. 11} 𝑑𝐷 =1 2𝜌𝑐𝐷𝑊𝐷 2_{𝑐 𝑑𝑧 3. 12}

Where 𝑐𝐿 and 𝑐𝐷 are respectively the lift and drag coefficients, which depend on

the angle of attack and the Reynolds number of the flow, 𝑊𝐷 is the relative

velocity of the fluid, 𝑐 is the chord length. The overall force is applied in a point defined centre of pressure of the blade, which is locate at a distance of one quarter of the chord length, from the leading edge. In this point the mechanical connection between the blade and the strut of the turbine should be done for structural reasons. The overall infinitesimal force, obtained by summing the infinitesimal lift force and drag force, can be broken down into a radial component and a tangential component, as shown inFigure 3.5. The two components, taking into account 3.11 and 3.12, can be written as:

𝑑𝐹𝑇 = 1 2𝜌(𝑐𝐿𝑠𝑖𝑛 𝛼𝑓− 𝑐𝐷𝑐𝑜𝑠 𝛼𝑓)𝑊𝐷 2_{𝑐 𝑑𝑧 3. 13} 𝑑𝐹_𝑁 =1 2𝜌(𝑐𝐿cos 𝛼𝑓+ 𝑐𝐷sin 𝛼𝑓)𝑊𝐷 2_{𝑐 𝑑𝑧}

The overall torque around the axis of rotation considering the 𝑁 blades of the turbine, can be obtained from 3.13:

𝑑𝑇 =1

2𝜌𝑁𝑅(𝑐𝐿𝑠𝑖𝑛 𝛼𝑓− 𝑐𝐷𝑐𝑜𝑠 𝛼𝑓)𝑐𝑊𝐷

2 _{𝑑𝑧 3. 14}

Thus, the mechanical power can be obtained from 3.14: 𝑑𝑃 = 𝜔𝑑𝑇 =1

2𝜌𝑁𝑅𝜔(𝑐𝐿𝑠𝑖𝑛 𝛼𝑓− 𝑐𝐷𝑐𝑜𝑠 𝛼𝑓)𝑐𝑊𝐷

2 _{𝑑𝑧 3. 15}

And the power coefficient can be defined: 𝑐𝑃 =

𝑑𝑃 1

2 𝜌𝑉03𝐷 𝑑𝑧

3. 16

By substituting the 3.15 in the 3.16: 𝑐𝑝 = 𝜔𝑅 𝑉0 𝑁𝑐 𝐷 𝑊2 𝑉₀2 (𝑐𝐿𝑠𝑖𝑛 𝛼𝑓− 𝑐𝐷𝑐𝑜𝑠 𝛼𝑓) 3. 17

Considering the 3.9, the 3.7 and defining the solidity of the machine: 𝜎 = 𝑁𝑐

𝐷 The equation 3.17, can be rewritten:

𝑐_𝑝= 𝜆𝜎(1 − 𝑎)2_{(𝑠𝑖𝑛}2_𝛼 𝑓+ ( 𝜆 1 − 𝑎+ 𝑐𝑜𝑠 𝛼𝑓) 2 ) (𝑐_𝐿𝑠𝑖𝑛 𝛼_𝑓− 𝑐_𝐷𝑐𝑜𝑠 𝛼_𝑓) 3. 18

The equation 3.18 shows the main parameters to take into account when designing a vertical axis turbine. Although not formally expressed, each parameter depends on some of the others:

• The blade speed ratio affects the angle of attack and thus the lift and drag coefficients, so that for low values of 𝜆 the lift coefficient is high and the drag coefficient is low but the power coefficient is directly proportional to 𝜆, vice versa for high values of the blade speed ratio the angle of attack is small and the lift coefficient has small values and the induction coefficient increases.

• The solidity affects the induction coefficient, for high values of solidity the induction coefficient increases.

In equation 3.18, the power coefficient depends on the azimuthal angle of the blades, the phase averaged value of the power coefficient is defined as the integral mean value on a complete rotation.

This model assumes that the fluid velocity is constant with the azimuthal angle of the blade. More refined models consider the dependence of the induction factor with the azimuthal angle (multiple stream-tube model) and the effect of the different blade-fluid interaction in the windward and in the leeward path (double stream-tube model). According to the multiple stream-tube model, schematized in Figure 3.6.a, the rotor disk in split into stream-tubes of constant azimuthal

Figure 3.6 – a. Schematic of the multiple stream-tube model, b. Schematic of the double stream-tube model, c. Schematic of the mutiple-double stream-tube

angle increase and for each tube, it is computed the value of the induction factor. The double stream-tube model can be described as a tandem application of the actuator disk model, it is schematized in Figure 3.6.b. This model better approximates the fluid-blade energy exchange and the power coefficient computed accordingly is higher than the Betz limit. Those two models are combined in the so called double multiple stream model, whose schematic is shown in Figure 3.6.c

The type of machine studied in this thesis requires a level of precision which is beyond the one reached by the models cited in this paragraph. The positive interference of counter rotating vertical axis turbine depends on the interaction between the complex vorticial structures that are generated on the wake of the turbines. For this reason, it has been chosen to analyse the performance of the counter rotating turbines with CFD numerical simulation using OpenFOAM transient solver.

3.2 C

In recent years, VATs are regaining researchers interest due to new studies concerning array configuration for closely spaced machines in power fields. Single isolated HATs have higher power coefficient with respect to single isolated VATs, however they need to be placed at 3 to 5 diameters distance in crossflow direction and at 8 to 10 diameters distance in downflow direction. The typical generated power per unit surface for a HATs field is 3Wm^-2, while VATs field could be capable of reaching values of power generation density one order of magnitude higher [28], which will make VATs a better choice with respect to HATs for big power field applications.

SANDIA National Laboratories have studied thoughtfully VATs in different configurations: isolated and array configuration of closely spaced machines. In [29], Sharzle et al. investigated a system of two identical Darrieus turbines having the same sense of rotation (corotating) and whose axes of rotation are placed at a distance of 3 radii. The authors implemented a numerical code based on vortex/lifting-line model without the effects of freestream turbulence and tested the performances of the two turbines in different relative position with respect to the flow direction (Figure 3.7).

The results show that the proximity of the turbines does not affect the performances of corotating turbines unless one is directly downstream of the other (configuration A and E). The power coefficient evaluated in the different configuration are summarised in Table 3.1.

Successive research [30] by Rajagopalan et al. investigates the performance of arrays of VATs in different configurations. A finite difference model was

Table 3.1 – Results obtained in [28]

implemented that modelled the turbines as momentum sources (thus avoiding the computation of blade flow) in a laminar flow. The machines modelled produce symmetrical wake which the authors justified by comparing their results with phase average values of the real flow field. The configurations studied are shown in Figure 3.8

The power coefficients of the single turbine in the array configuration are displayed in the figures together with the average power coefficient of all the turbines (CPAV) and the power coefficient of an isolated turbine (CPSA). The average power coefficient of the turbines in the array strongly depend on the configuration: for the one shown in Figure 3.8.b, Figure 3.8.c, Figure 3.8.d and Figure 3.8.e it is higher than the isolated turbine, while for the one in Figure 3.8.a, Figure 3.8.f and Figure 3.8.e it is lower. Akin to what proven in [29] when the two turbines are aligned to the flow direction the power coefficient of the turbine directly in the wake of other is significantly decreased as shown in Table 3.1. In Figure 3.8.f and Figure 3.8.g, it is possible to find turbines aligned to the flow direction (i.e. turbines 11 and 31, 12 and 32, 13 and 33, 71 and 51, 72 and 52, 73 and 53 for Figure 3.8.f and turbines 11 and 37, 12 and 36, 21 and 44, 22 and 45, 31 and 51, 32 and 52 for Figure 3.8.f), whose power coefficient is not decreased as much as for respective turbines the configuration in Figure 3.8.a.

Other research groups in California Institute of Technology investigated closely spaced turbines having opposite sense of rotation (counter rotating) via theoretical models and experimental studies. The first theoretical model, proposed by Whittlesey at al. in [31], is based on 2 dimensional potential flow equations. The model is used for testing the performances of an array of turbines placed according to the arrangement of the shed vortices in the wake of schooling fish as shown in Figure 3.9

A Savonius turbines has been used for validating the model, but the authors extend the validity of the results for both drag based and lift based turbines. The results do show a decrease in the average power coefficient of the turbines in the configuration studied with respect to the isolated turbine. Nevertheless, the power density generation of a wind farm of VATs forecasted according to the author’s model and configuration is much greater than the one for HOWT farms, suggesting an optimised usage of land surface is possible with VATs farms.

Figure 3.9 – Comparison between vortices system in a school of fish and the configuation of the turbines array investigated in [30]

Dabiri presents an experimental study on counter rotating VATs in [28]. The author investigates the performances of two counter rotating turbines in various relative position with respect to the flow direction and of multiple counter rotating turbines in different configuration (Figure 3.10) in order to predict the performance of an array of counter rotating machines.

For the two counter rotating turbines, the author measured an increase of the power coefficient of the coupled machines with respect to the isolated machine over a wide range of incoming flow directions.

According to the author, the energy generation process for VATs farms depends on two kinetic energy fluxes:

• The horizontal kinetic energy flux is the kinetic energy of the fluid upwind the farm, which is collected by the first rows of turbines

• The planform kinetic energy flux is the kinetic energy provided to the fluid by the turbulence from the undisturbed flow above the farm and it is responsible of reenergising the fluid after it has already crossed different rows of turbines.

The power density generation of an array of counterrotating vertical axis turbines is correlated to the planform kinetic energy flux. The planform kinetic energy flux depends on the velocity of the fluid directly above the wind farm, which depends, in turn, on the specific weather of the site, on the spatial density of the farm and other parameters not investigates by the study. For a decrease of less than the 66% with respect to the undisturbed velocity upstream of the field, the planform kinetic energy flux has the same magnitude of the power generation density of HATs farms, while for a decrease of less than 25%, the planform kinetic energy flux is one order of magnitude higher than the power generation density of HATs farms. Hence according to the author, VATs farms have the potential of reaching values of power generation density significantly higher than the ones of HATs farms.

Kinzel et al. present a follow up experimental study in [32]. The authors tested the configuration in Figure 3.11 and performed several measurements in order to reconstruct the flow field at the centreline between the counter rotating turbines The measured velocity field shows that the fluid recovers to 95% of the upstream velocity after approximately 6 diameters, which is a significant improvement over the 14 diameters needed for horizontal axis wind turbines. Moreover, according to the authors, the measurements confirm the hypothesis that the planform kinetic energy flux can be the primary power source for the downstream rows of turbines in the VATs fields.

Araya et al. propose a low order model for VATs farms based on leaky Renkine bodies in [33]. It is a two dimensional model, whose aim is to give a first assessment of a VATs farm configuration, the authors support that it is a conservative model thus the losses are overestimated. The main mechanism responsible for the enhancement of performances of closely spaced VATs found by the authors is the turbine blockage, which locally accelerates the flow adjacent to a turbines and thus increase the performance of the neighbouring turbines. The French firm Nenuphar has been investigating counter rotating VATs for offshore wind applications. Their concept, the TWINFLOAT ® (Figure 3.12 (left)), consists of two H Darrieus turbines, each machine has 2 blades and it has a rated power of 2.5 MW. In [34], it is presented a 2 dimensional CFD simulation of the flow at a horizontal mid-plane of the TWINFLOAT ®, above the central and radial struts, Figure 3.12 (right).

The simulation has been carried out with the commercial Ansys-Fluent V15, with an inviscid ARDEMA solver developed by ADWEN OFFSHORE and NENUPHAR. Various configurations have been tested for different relative distances of the axis of rotations and blade speed ratios. The study showed an increase in the normalized tangential force on both the windward and leeward path, an increase in the power coefficient at all the relative distances tested and an increase of the optimal blade speed ratio for the counter rotating turbines with respect to the isolated machine. The analysis of the flow field shows a forced flow region in between the two turbines and an increase of angle of attach in the windward path.

Figure 3.12 – left. Rendering of installed TWINFLOAT ®, right. Schematic of the configuration investigated in [33]

A follow up experimental study [35], by Vergaerde at al., examines the performances of a couple of two-bladed counter rotating turbines in the Politecnico di Milano GVPM wind tunnel. The experimental setup and the configurations tested are shown in Figure 3.13. The experiments show an increase in power coefficient for both the configurations tested. It is of notice that the counter rotating turbines are not mechanically linked via gearing systems or timing belt, nevertheless the authors reported that the rotors tend to synchronise spontaneously and that the synchronous rotation is a stable condition for the system which may last seemingly forever [35], even when one is brought out of synchronisation.

A research group in University of Pisa carried out several CFD simulation on counter rotating turbines. In [36], Zanforlin and Nishino analyse two counter rotating vertical axis wind turbines, but as pointed out by the authors the results can be applied also for tidal and marine turbines. Different configurations, incoming flow directions and blade speed ratio have been tested and compared to the case of an isolated turbines. The optimal condition according to the authors is the configuration A inFigure 3.14, but the superiority of one configuration […]

may depend on the turbine solidity and the fluid properties [36].

The authors highlight 2 characteristics of the flow field which, according to the authors, are linked to the increase in power coefficient:

• The reduction of the cross stream component of the velocity of the fluid on the windward path that makes the direction of the flow approaching the blade more favourable to generate lift and torque

• Wake contraction in the leeward path

In [37], Zanforlin et al. analyse the performances of an array of 3 tidal turbines compared to an isolated one, through CFD simulations. Two configurations have

Figure 3.14 – Turbines configurations investigated in [35] Figure 3.13 – left. Experimental setup built in [34], right. Turbines

been investigated in particular: 3 counter rotating turbines positioned along a straight line or 3 co rotating turbines positioned as the vertices of an equilateral triangle layout as shown in Figure 3.15. The increase in overall performances of turbines in former configurations is greater than the one for the latter.

The authors highlight 3 phenomena:

• The turbines blockage entails flow acceleration outside of the turbine(s) and inside the aisles between the turbines

• The streamlines approaching the turbines at the inner sides of the arrangement are constrained parallel to the streamwise direction, whereas for an isolated turbine the flow diverges at the sides

• A wake contraction is seen at the inner sides of the arrangement

4 M

ETHODOLOGY

In the first section of this chapter, the basic principles of Computational Fluid Dynamics (CFD) will be presented and in the second section, the software used for the simulations will be briefly described.

4.1 CFD

The fluid dynamic analysis of a system is performed with a set of partial differential equations (PDE), known as the Navier-Stokes (NS) equations, which are derived from the conservation equations of certain flow properties on a given control volume. From a mathematical point of view, the NS equations without any simplifying assumption, does not have an analytical solution yet. The CFD simulation of a system is performed with an algebraic approximation of the NS equations, which can be easily solved with the aid of a calculator.

The conservation equation for a scalar flow property 𝜙 on a control volume can be written as:

𝜕

𝜕𝑡∫ 𝜙 𝑑𝛺_𝛺 + ∫𝜙𝑈_𝑆 ⃗⃗ 𝑑𝑆 = ∫𝑘𝜌𝛻⃗ 𝜙 𝑑𝑆 _𝑆 + ∫ 𝑄_𝛺 𝑣 𝑑𝛺+ ∫𝑄_𝑆⃗ 𝑆 𝑑𝑆 4. 1 Where the first volume integral at left hand side (l.h.s.) of the equation is the variation in time of 𝜙 over the volume (Ω); the second surface integral on l.h.s. is the convective flux of 𝜙 across the boundary of the volume (𝑆); the first surface integral on the right hand side (r.h.s.) is the diffusive flux of 𝜙 across 𝑆; the second is the volumetric source term and the third is the surface source term. If the conserved property is a vector, the equation has the same structure, but the proper notation must be used for the flow property, employing 𝜙⃗ instead of 𝜙. The PDE can be obtained from 4.1 applying the Gauss’ divergence theorem:

𝜕(𝜙)

𝜕𝑡 + ∇⃗⃗ ⋅ (𝜙𝑈⃗⃗ ) = ∇⃗⃗ ⋅ (𝑘𝜌∇⃗⃗ 𝜙) + 𝑄𝑣+ ∇⃗⃗ ⋅ (𝑄⃗ 𝑆) The conserved flow properties in the fluid dynamic analysis are:

• Mass

• Momentum • Energy

The equation for the conservation of mass is formulated for a control volume approach. It can be written as:

𝜕(𝜌)

𝜕𝑡 + 𝛻⃗ ⋅ (𝜌𝑈⃗⃗ ) = 0 4. 2

According to equation 4.2, the mass does not diffuse and neither it is generated or destroyed. If the fluid is a mixture of different chemical species, it can be written a mass balance equation for each one. The generation of new species or the variation of the concentrations of the existing ones due to chemical reaction in the flow, are taken into account modifying equation 4.2 accordingly.