Wave Energy Propulsion for Pure Car and Truck Carriers (Pctcs)
Total Page：16
File Type：pdf, Size：1020Kb
Wave Energy Propulsion for Pure Car and Truck Carriers (PCTCs) Master thesis by KTH Centre for Naval Architecture Ludvig af Klinteberg Supervisor: Mikael Huss, Wallenius Marine Examiner: Anders Ros´en,KTH Centre for Naval Architecture Stockholm, 2009 Abstract Wave Energy Propulsion for Pure Car and Truck Carriers (PCTC's) The development of ocean wave energy technology has in recent years seen a revival due to increased climate concerns and interest in sustainable en- ergy. This thesis investigates whether ocean wave energy could also be used for propulsion of commercial ships, with Pure Car and Truck Carriers (PCTC's) being the model ship type used. Based on current wave energy research four technologies are selected as candidates for wave energy propul- sion: bow overtopping, thrust generating foils, moving multi-point absorber and turbine-fitted anti-roll tanks. Analyses of the selected technologies indicate that the generated propulsive power does the overcome the added resistance from the system at the ship design speed and size used in the study. Conclusions are that further wave energy propulsion research should focus on systems for ships that are slower and smaller than current PCTC's. V˚agenergiframdrivningav biltransportfartyg (PCTC's) Utvecklingen av v˚agenergiteknikhar p˚asenare ˚arf˚attett uppsving i sam- band med ¨okande klimatoro och intresse f¨orf¨ornyelsebar energi. Detta exam- ensarbete utreder huruvida v˚agenergi¨aven skulle kunna anv¨andastill fram- drivning av kommersiella fartyg, och anv¨ander moderna biltransportfartyg (PCTC's - Pure Car and Truck Carriers) som fartygstyp f¨orutredningen. Med utg˚angspunkti aktuell v˚agenergiforskningtas fyra potentiella tekniker f¨orv˚agenergiframdrivning fram: "overtopping" i f¨oren,passiva fenor, "mov- ing multi-point absorber" samt antirullningstankar med turbiner. Analys av de valda teknikerna indikerar att den genererade framdrivande kraften blir mindre ¨ansystemets adderade framdrivningsmotst˚andvid den fartygshastighet och -l¨angdsom anv¨ands.Slutsatserna ¨aratt framtida forskn- ing om v˚agenergiframdrivningborde fokusera p˚afartyg som ¨armindre och l˚angsammare¨andagens PCTC-fartyg. Contents Contents ii 1 Introduction 1 2 Theory of ocean waves 2 2.1 Surface gravity waves . 2 2.1.1 Basic equations . 2 2.1.2 Deep water approximation . 5 2.1.3 Energy transport . 6 2.2 Ocean wave spectra . 7 3 Wave energy on worldwide route 9 4 Wave energy conversion 12 4.1 Overtopping devices . 12 4.1.1 Wave Dragon . 13 4.1.2 Sea Slot-cone Generator . 15 4.2 Oscillating water column . 16 4.3 Oscillating bodies . 17 4.4 Thrust generating foils . 20 5 Proposed technologies 21 5.1 Bow overtopping . 21 5.1.1 Ship motions . 22 5.1.2 Overtopping model . 23 5.1.3 Water acceleration effect . 27 5.1.4 Conclusions . 31 5.2 Thrust generating foils . 32 5.2.1 Modelling . 32 5.2.2 Studies . 33 ii CONTENTS iii 5.2.3 Numerical experiment . 33 5.2.4 Conclusions . 35 5.3 Moving Multi-Point Absorber . 36 5.3.1 Modelling . 37 5.3.2 Numerical solution . 38 5.3.3 Conclusions . 39 5.4 Turbine-fitted anti-roll tanks . 40 6 Conclusions 41 Bibliography 42 Nomenclature 45 Abbreviations 49 List of Figures 50 List of Tables 51 Chapter 1 Introduction This master thesis project has been carried out at Wallenius Marine in Stockholm, and the purpose of it has been to investigate the possibility of reducing the fuel consumption of Wallenius Lines' Pure Car and Truck Carriers (PCTC's) by extracting energy from sea waves. Wallenius works with a strong environmental vision, which in 2005 was expressed in the conceptual emission-free E/S Orcelle. The Orcelle would be driven by fuel cells together with a combination of solar, wind and wave energy systems. This project has started off from this vision, in order to investigate if wave energy propulsion really is a future possibility for the shipping industry. In the 1970's and early 1980's extensive research was made in wave energy conversion, including wave energy ship propulsion, motivated by high oil prices. Most projects however lost their funding when oil prices dropped again in the mid 1980's. In the last few years there has been a revival in wave energy technology and several wave energy conversion methods are now ready for large-scale implementation. This thesis summarises current wave energy research, with the purpose of identifying which techniques can be transferred onto a moving ship. Based on this summary a number of techniques have been chosen as possible candidates and investigated further, to evaluate if they could successfully be implemented on a PCTC. 1 Chapter 2 Theory of ocean waves 2.1 Surface gravity waves This chapter provides a brief introduction to the theory necessary for the analysis of ocean waves and the energy they transport. 2.1.1 Basic equations The equations governing ocean waves can be derived from the basic principles of fluid dynamics, the Navier-Stokes equations1. For a Newtonian fluid the equations for conservation of mass and momentum can be written on Cartesian tensor form (using the Einstein summation convention) as @ρ @ + (ρuj) = 0 (2.1) @t @xj @ui @ui 1 @p 1 @τij + uj = − + + fi (2.2) @t @xj ρ @xi ρ @xj where ui is the velocity vector, ρ is the density of the fluid, p is the total pressure, fi is the external force and τij is the viscous stress tensor 1For a complete treatment of Navier-Stokes equations and surface gravity waves, see [14]. 2 CHAPTER 2. THEORY OF OCEAN WAVES 3 @ui @uj 2 @ur τij = µw + − δij (2.3) @xj @xi 3 @xr where µw is the dynamic viscosity of sea water. For an incompressible fluid, which for our purposes is a valid approximation of sea water, the density ρ is constant, reducing the conservation of mass to @u i = 0 (2.4) @xj Using this, equations (2.1) and (2.2) reduce to the incompressible Navier-Stokes equations: r · u = 0 (2.5) @u 1 + (u · r) u = − rp + µ r2u + f (2.6) @t ρ w To further simplify the equations the following assumptions are made for ocean waves: 1. µw = 0, viscosity is neglected. 2. r × u = 0, the flow is irrotational. 3. f = −∇(gz), the only external force is gravity. 4. Small amplitude waves, allowing the problem to be linearised by neglecting velocities of second order and higher. 5. Surface tension effects can be neglected. Assuming that the flow is irrotational, there exists a scalar velocity potential u = rφ (2.7) which reduces the conservation of mass (2.5) to the Laplace equation r2φ = 0 (2.8) CHAPTER 2. THEORY OF OCEAN WAVES 4 Applying the above assumptions the momentum equation (2.6) is reduced to the linearised Bernoulli equation @φ p + + gz = 0 (2.9) @t ρ To solve this equation a case is considered where the waves propagate in the x direction and the motion is restricted to the xz plane. The surface displacement ζ(x; t) of the wave is measured from the undisturbed free surface at z = 0. Two boundary conditions are specified at the free surface and one at the bottom, where z = −h0. The boundary condition at the bottom is @φ u = = 0 at z = −h (2.10) z @z 0 The first boundary condition at the free surface is the kinematic boundary condition, which implies that a fluid particle at the surface never leaves the surface. @ζ @ζ @φ + u = u = at z = ζ (2.11) @t x @x z @z This is linearised and approximated to a first order of accuracy @ζ @φ = at z = 0 (2.12) @t @z The second surface boundary condition is the dynamic condition, that the pressure just below the free surface is equal to the ambient pressure (neglecting surface ten- sion). Taking the ambient pressure to be zero, this is written p = 0 at z = ζ (2.13) which upon insertion into (2.9) and evaluation at z = 0 rather than z = ζ (small amplitude waves) gives @φ = −gζ at z = 0 (2.14) @t CHAPTER 2. THEORY OF OCEAN WAVES 5 An ansatz for ζ(x; t) is required in order to solve Eq. (2.8) using conditions (2.10), (2.12) and (2.14). Assuming a sinusoidal waveform with amplitude H=2, angular frequency ! and wavenumber k H ζ(x; t) = cos(kx − !t) (2.15) 2 results in the solution H! cosh k(z + h ) φ = 0 sin(kx − !t) (2.16) 2k sinh kh0 H ζ = cos(kx − !t) (2.17) 2 2 ! = gk tanh(kh0) (2.18) which means that the free surface displacement is sinusoidal with a wave height H between crest and trough. Eq. (2.18) is the dispersion relation, λ = 2π=k is the wavelength and T = 2π=! is the wave period. 2.1.2 Deep water approximation On deep water where h0 is large the dispersion relation (2.18) can be reduced to !2 = gk (2.19) since tanh(x) ! 1 as x ! 1. In reality this approximation is valid when h0 > λ/3. The phase speed c ≡ !=k of the wave can then be written r gλ rg c = = (2.20) 2π k Since the propagation speed of a wave depends on its wavenumber, waves of different lengths will propagate at different speeds and disperse. Because of this a system such as this, where c depends on k, is called dispersive. In a dispersive system the energy of the waves does not propagate with the phase speed. Instead it propagates with the group speed cg ≡ d!=dk, which for deep water becomes 1rg gT c = = (2.21) g 2 k 4π CHAPTER 2.