2009 OCEN300 MINI-TERM PROJECT Research on Ocean Hydro- kinetic Power Team selects a research...
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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
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).
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.
2nd EXAM: 4/14 (Thur.)
Open everything!
Covers everything up to 4/12!More weight for the content after Ex.I
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
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
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)
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
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
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
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
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!