2009 OCEN300 MINI-TERM PROJECT

Research on Ocean Hydro-kinetic Power

Team selects a research topic related to ocean wave energy and tidal/current energy conversion.

Select a particular concept and describe how it works.

Discuss pros and cons compared with other existing concepts.

Discuss its feasibility in USA,where? Discuss the estimated cost when

realized as a proto-type system. Discuss the ideas how the existing

technology and cost-effectiveness can be improved.

Prepare a 4-page report summarizing the study. (Report due on 5/3)

Prepare a team presentation. (Schedule: 4/26 A-D; 4/28 E-H)

A:Blockhus Gavin, Boenisch Michael, Church Timothy, Collins Benjamin

B: Collins Patrick, Crowder Nick, Davenport Eliot, Del Molino Angel

C: Deschamps Doug, Erwin Richard, Fuhr Curtis, Gaenzle Greg

D: Gaitan Colton, Holcomb Ryan, Kinard Matt, Kopper Lauren

E: Krohn Nathan, Liles Gary, Lawal Tes, Miller Blaze

F: Munoz Ian, Nowak Jonathan, Oberg James, Oriaku Joel

G:Sanchez Eduardo, Scheidler Adam, Sebesta James, Valle Arnold

H: Wissing John, Won Young, Zambrano Hector

Blockhus Gavin

Boenisch Michael

Church Timothy

Collins Benjamin

Collins Patrick

Crowder Nick

Davenport Eliot

Del Molino Angel

Deschamps Doug

Erwin Richard

Fuhr Curtis

Gaenzle Greg

Gaitan Colton

Holcomb Ryan

Kinard Matt

Kopper Lauren

Krohn Nathan

Liles Gary

Lawal Tes

Miller Blaze

Munoz Ian

Nowak Jonathan

Oberg James

Oriaku Joel

Sanchez Eduardo

Scheidler Adam

Sebesta James

Valle Arnold

Wissing John

Won Young

Zambrano Hector

Deterministic vs. Stochastic Process

Deterministic: if a future event can be predicted

Stochastic: if a future event can only be predicted statistically

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

T

Time t

Regular and Irregular Waves

Ocean waves are almost always irregular and often multi-directional (short-crested).

Irregular waves can be viewed as the superposition of a number of regular waves.

Regular waves have a single frequency, wavelength and amplitude (height).

Wave Pattern Combining Four Regular Waves

FFT & IFFT – (Inverse) Fast Fourier Transform.

Actual (multi-directional) vs. Design (uni-directional) Seas

Continuous Random VariablesExample: Record of ocean surface

0 2000 4000 6000 8000-5

-4

-3

-2

-1

0

1

2

3

4

5

Time (sec)

Wave ele

vatio

n (m

) Wave elevation time history

0 0.5 1 1.5 20

1

2

3

4

5

6

(rad/sec)

Wave ele

vatio

n (m

2 sec)

Response spectrum

Generated wave spectrum

Theoretical wave spectrum

0 2000 4000 6000 80008

10

12

14

16

18

20

Time (sec)

Wind S

peed (m

/s)

Wind speed time history

0 0.5 1 1.5 20

5

10

15

20

25

30

35

40

(rad/sec)

Wave elevation (m

2 sec)

Response spectrum

Generated wind spectrum

Theoretical windspectrum

Discrete Random Variables

Examples

Coin Flip: # of head in N coin flips

Dice: sum of the #s in N throws of dice

Wave height distribution in a 20-minute ocean-surface record

Discrete Random Variable

Three successive coin flips Random variable s= #of heads

Find the mean value & s.d.

If the # of trials is large, the random variable (# of heads) follows Gaussian distribution!!

Go Lady Aggies! Championship!

2nd EXAM: 4/14 (Thur.)

Open everything!

Covers everything up to 4/12!More weight for the content after Ex.I

Discrete Multi-random-variable Ex

Wave height & wave period joint distribution

Continuous Random Variable

PDF f(x)=-x + k (0<x<1)

(1) Find k(2) Find the mean value of x(3) Find probability (0<x<1/2)

Gambling with Your Friend: lucrative or ridiculous offer? How much risk?

Game: 100 coin flipsIf # of heads > 60 : receive $1000,Otherwise : give $100

Decision Making should be based on “expected value”=

probability x assigned value

Central Limit Theorem

If r is a sum of N independent random variables, and it is not always true that a particular few dominate the sum, the CDF of r approaches the Gaussian CDF as

N becomes large

Ocean Surface: Zero-mean Gaussian Process

Find Prob[η>3m]

When standard deviation=2m

Find Prob[2m< η<4m]

Schedule

4/8: no class (make up on 4/29) 4/10: Dr. Ryu from SOFEC will give a

lecture on WOW and application of wave theory

4/15: Video showing 4/17: Ex II 4/22: Field trip to OTRC 4/24,29: TP Presentation

http://www.vestas.com/en/wind-power-solutions/offshore/offshore-wind-turbines.aspx

http://www.youtube.com/watch?v=fTY4oI2egWI

Grading Policy

HW: 20% (5 sets) Mini-Project: 10% EX 1: 20% EX 2: 20% -> 35% FINAL: 30% -> 35%

TP Presentation: peer-reviewed

M.H. Kim 60% Peer-Evaluation 40% (self, highest,

lowest not included)

Gambling with Your Friend: lucrative or ridiculous offer? How much risk?

Game: 100 coin flipsIf # of heads > 60 : receive $1000,Otherwise : give $100

Decision Making should be based on “expected value”=

probability x assigned value

4/21 (Thursday) Field Trip

11:10OTRC

11:40Haynes Lab

Random Waves

Frequency domain: Spectrum

Time domain: Time series

FFT (Fast Fourier Transform)

Time domain.Random elevation

Wave spectrum

Time and frequency domain of waves

How do we generalize to short-crested sea?

Regularwave components.Random phases.

Random wave simulation

η(t)=ΣAj cos(ωjt+ej)

Where

Aj=

ej= random phase uniformly distributed bet. 0 & 2π

2 ( )jS

2s m s

15.0

7.5

0.75 1.5min

max

1rad s

H1/3=8m,T2=10s

Number of wave components N

max min / N

Wave amplitude of wavecomponent j:

2j jA s

How energy in a wave spectrum can be distributed to individual regular wave components: η(t)=ΣAj cos(ωjt+ej)

Nyquist Criterion: η(t)=ΣAj cos(ωjt+ej)

Tmax=2π /Δ ω : repeated after this! Solution: use irregular Δ ω or perturb central

component frequency ωj

Δt < π / ωmax

Discrete spectrum to Continuous spectrum:By using FFT, we get Aj. Then, S(ω) = Aj²/2Δω

P-M (Pierson-Moskowitz) spectrumFully-developed sea:1-parameter: Vw

2-parameter: Hs & Tp

JONSWAP (Joint North-Sea Wave Project) spectrum: storm sea

3-parameter: Hs & Tp & γ(overshoot parameter; 2-3)

k-th moment of wave spectrum

Mean period T1=2π mo/m1

Mean period T2=2π √mo/m2

( )kkm S d

( )kkm S d

GaussianInput

LinearSystem

GaussianOutput

GaussianInput

NonlinearSystem

Non GaussianOutput

Short-term statistics

Given significant wave height and mean/peak wave period

Assume long-crested sea A linear system allows us to add the

response in each regular wave component

22

0

( )( )s H d

Square of RAO (ratio between response and incident wave amplitude

Wave spectrum

Variance of the response

Ocean Wave Statistics

Stationary Process: statistical properties are independent of time.

Homogeneous Process: statistical properties are independent of space.

Ergodic Process: ensemble(sample) mean=time mean

Random Waves

Frequency domain: Spectrum

Time domain: Time series

FFT (Fast Fourier Transform)

Ocean Wave Statistics: zero-mean Gaussian Process

Find Prob[η>3m] when s.d.=2m

Find Prob[2m<η<4m]

Surface & Wave-height Distribution

Ocean Surface: zero-mean Gaussian (Central limit theorem)

Distribution (symmetric)

Wave Height: Rayleigh Distribution (H>0, non-symmetric)

Assume: Gaussian + narrow banded

Wave-height statistics from time series

If zero-mean process

Standard deviation=rms

Example

When measured 5 wave heights are 3.0, 3.5, 4.0, 4.2, 5.0(m), respectively

Find mean wave height

Find the rms wave height.

Find Prob[H>4.1m]

Example

When the area of the given wave amplitude spectrum is 18-m²

Find Prob[2m<η<4m] What is the significant wave height Hs? What is the probability [H<12m]

If 600 waves are measured, how many waves are expected to exceed H=1.2Hs?

What is the expected maximum wave height?

Extreme values in a sea state

Most probable largest value in a storm of duration t:

Rayleigh distribution

max 2log /x nx t T

1. 2.max 4 3order order

x xx

The Børresen formula

Long-term wave statistics: scatter diagram

Ex. Use of wave scatter diagram

Prob [3m<Hs<4m and 9s<Tp<10s] =?

Prob [Hs>2m]=?

Sea State for Hs=2.2m and Tp=7.9s?

Total force = Inertia force + drag force

Inertia coefficient Drag coefficient CD

V=displaced volume S=Projected (frontal) area

vvSCdt

vdCF DI

2

1

C CI M 1

Seasonal Loop Current in GOM

Morison Eq with Steady Current U

UvUvSCdt

vdCF DI

)(2

1

Stochastic Approach

For design, typically assume collinear (100-yr:production, 10-yr: drilling)

Irregular wave(JONSWAP)+wind(API) and steady current for 3 hours

100-yr storm revised after RITA1000-yr check is recommended

Time series or Spectral analysis

Revised GOM Design Condition

Wind(m/s) Hs (m) Current m/s

West-100 39.9 13.1 2

West-1000 49.9 16.4 2.5

WesC100 38.1 12.3 1.9

WesC1000 47.6 15.4 2.4

Cent-100 48 15.8 2.4

Cent-1000 60 19.8 3

East-100 38.4 12.2 1.9

East-1000 48 15.3 2.4

WAVE FORECASTING

Wind Stress Factor (Adjusted wind velocity)

UA = 0.71 U (U in m/s) 0.59 (U in mph)

1.23

Use forecast diagram

Given= fetch, duration, and UA

Example 1: fetch=30km, duration=5 hrs, and UA =20m/s

U-D Combo: Hs=2.5mU-F Combo: Hs=1.75m

Choose the smaller! Fetch-limited!

Use forecast diagram

Given= fetch, duration, and UA

Example 1: fetch=30km, duration=3 hrs, and UA =20m/s

U-D Combo: Hs=1.7mU-F Combo: Hs=1.75m

Choose the smaller! Duration-limited!