WAVE ENERGY UTILIZATION Antnio F. O. Falco Instituto Superior - PowerPoint PPT Presentation

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Università degli Studi di Firenze, 18-19 April 2012 WAVE ENERGY UTILIZATION António F. O. Falcão Instituto Superior Técnico, Universidade Técnica de Lisboa

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Part 1 Wave Energy Resource

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 WAVE ENERGY Typical values of wave energy flux SOLAR (annual average): ENERGY Deep water : 6-70 kW/m Near shore : lower values, Depending on: WIND • bottom slope ENERGY • local depth (wave breaking) • bottom roughness (friction) • bottom configuration (diffraction, refraction) WAVE Close to the surface (h<20m): ENERGY density flux of energy (kW/m 2 ) much higher than wind energy

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 World distribution of wave energy level Annual-averaged values in kW/m (deep water, open sea)

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 THE WAVES AS ENERGY RESOURCE The waves are generated by the wind . In deep water ( > 100 - 200m ) they travel large distances (thousands of km) practically without dissipation. The characteristics of the waves (height, period, etc.) depend on:  Sea surface area acted upon by the wind: “fetch”  Duration of wind action “Swell”: wave generated at a long distance (mid ocean). “ Wind sea ”: waves generated locally. In general, swell is more energetic than wind sea.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 FLUID MOTION IN WAVES • Perfect fluid (no viscosity)  Incompressible flow    V 0  Irrotational flow       V 0 or V 2 Laplace equation    0 Boundary conditions • At the free-surface: p  p at  At the bottom:  n  V 0  The free-surface is unknown, which makes the problem non-linear. In general the boundary condition is applied at the undisturbed free-surface (flat surface): LINEAR THEORY.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 The simplest solution: the sinusoidal regular wave z crest 0 x trough    z h        2 2 2          const cosh ( z h ) sin t x   0       T        2 2 2             const exp z sin t x If h 0       T T = period (s), f = 1/ T = frequency (Hz or c/s),      = radian frequency (rad/s), 2 f 2 T λ = wavelength (m), = wave number (m -1 )   /  k 2

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012     2 2           Free-surface elevation   ( x , t ) A sin t x A sin( t kx ) 0 0    T A = wave amplitude H = 2 A = wave height (from trough to crest)        2 2 2           const exp z sin t x 0       T The disturbance decreases with the distance to the surface. In deep water, the decrease is exponential: the disturbance practically vanishes at a depth of about 1/2 wavelength.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 In deep water , the water particles have circular orbits . The orbit radius decreases exponentially with the distance to the surface.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 In water of finite depth , the orbits are ellipses . The ellipses become flat near the bottom.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Propagation velocity (phase velocity)     c T k From the boundary condition at the sea surface:   h  c tanh g c The velocity of propagation c depends on the wave period T (or frequency ω or f ) and also on the water depth h. The sea is a dispersive medium for surface waves. The speed of sound in air is independent of frequency.

INTERNATIONAL PHD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012  c   c   h  2  h g h  

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012   h Limiting situations  c tanh g c  h In deep water (in practice if h > λ /2) :   tanh tanh( kh ) 1 c g g gT    c   k 2 In shallow water (in practice if h << λ )  tanh( kh ) kh c  gh c does not depend on T

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Example 2   T 8 s g 9 , 8 m/s  gT 9 , 8 8      cT    Deep water 12 , 5 m/s c 12 , 5 8 100 m   2 2 Shallow water h = 1 m       cT    c gh 9 , 8 1 3 , 1 m/s 3 , 1 8 25 , 0 m/s   2 2 Intermediate water depth h = 15 m     0 , 785 rad/s T 8    h 0 , 785 0 , 785 15     c 10 , 2 m/s c tanh c tanh g c 9 , 8 c   cT    10 , 2 8 81 , 8 m

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012  T 8 s  h (m) c (m/s) (m) 1 3,10 24,8 3 5,25 42,0 5 6,63 53,0 10 8,86 70,9 15 10,22 81,8 20 11,09 88,7 25 11,65 93,2 30 12,00 96,0 40 12,33 98,6 50 12,44 99,5 12,48 99,8 

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Refraction effects due to bottom bathymetry The propagation velocity c decreases with decreasing depth h. As the waves propagate in decreasing depth, their crests tend to become parallel to the shoreline wave crests shoreline

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 crests rays shoreline Dispersion of energy at a bay. shoreline Concentration of energy at a headland.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 Group velocity or velocity of propagation of energy The velocity of propagation of wave energy , , is different from (smaller than) c g the phase velocity or velocity of propagagtion of the crests c . 1 In deep water, it is  c g c 2 In sound waves, there is no difference between the two velocities.

INTERNATIONAL PhD COURSE XXVII ° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012 ENERGY OF THE WAVES  Kinetic energy (circular or elliptic orbits) v  Potential energy (sea surface is not plane) In deep water, energy per unit horizontal area , time-averaged: 1 1 2 2      H  W W gA gH ( 2 A ) kin pot 4 16 1 1 2 2 2       W W W gA gH ( J m ) kin pot 2 8