Models of In-stream Tidal Powerin the Minas Passage

Richard Karstenwith lots of help from

Justine McMillan, Megan Lickley, Mike Deveau, Ron HaynesDepartment of Mathematics & Statistics, Acadia University

Dave Greenberg and others at B.I.O.Chris Garrett, Patrick Cummins, Brian Arbic

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Outline

1 Numerical Model

2 Power Estimates

3 Impact on the tides

4 Conclusions

5 Continuing work

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Numerical Model

Numerical Model

Finite-Volume Coastal Ocean Model (FVCOM 2.5)(Changsheng Chen, Robert Beardsley, Geoffrey Cowles)(http://fvcom.smast.umassd.edu/index.html)

A 3-D unstructured-grid, free-surface, primitive equation,finite-volume coastal ocean circulation model.Include:

wetting/drying onopen boundary forced by M2sponge layer at boundaryconstant density2D or 3D (usually 11 parabolic layers)Highest resolution in the Minas Passage

Run on ACMMaC and ACE-net computer clusters (4 to 64processors per job)

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Numerical Model

Original Grids from David Greenberg

Scotia-Fundy-Maine Grid

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Numerical Model

Original Grids from David Greenberg

Upper Bay of Fundy

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Numerical Model

Adjustments to FVCOM

Model "turbines"

increased bottomfriction (2D)momentum drag (3D)quadratic drag

Turbine Wake: Horizontal

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Numerical Model

Adjustments to FVCOM

Model "turbines"

increased bottomfriction (2D)momentum drag (3D)quadratic drag

Turbine Wake: Vertical

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Numerical Model

Adjustments to FVCOM

Vary frequency of M2 forcing

Determination ofresonance frequencyDetermine howturbines affect this

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Numerical Model

Matlab code

Run simulationsAnalyze Tides (amps, phaseetc)Power/energy balancesComparisons to theoryOptimization

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Numerical Model

Matlab code

Code to quickly double resolution:(Linear interpolation of bathymetry and forcing.)

Original Upper Grid:Turbine area 335m x 335 m

Double resolution:Turbine area 170m X 170m

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Power Estimates

Energy and PowerPotential Kinetic Estimated

Area Energy Energy PowerMinas Passage and Basin 8.2× 1013J 1.6× 1013J 8.7 GW

Bay of Fundy 4.38× 1014J 2.31× 1014J 60 GW

Power = 2× (mean total energy)/(π/ω)

Velocity at flood tide Time-averaged speed

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Power Estimates

Power Density

PA

=12ρ|u|3 kW/m2

Bay of Fundy Minas Passage

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Power Estimates

Power Estimate: standard

Total Power Based on Kinetic Energy Flux:

PKE =12ρAcu3

Maximum Average Power Estimate for the Minas Passage(Triton(2006)):

Pmax = 1.9 GW

NS DoE electrical power generation estimate:

%15Pmax = 0.3 GW

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Power Estimates

Power Estimate: New

Power estimate should reflect tidal forcing:(Chris Garrett and Patrick Cummins):

Pmax = Acu × Force = flux× tidal head =14ρgaQ

a = 4.7m, Q = 7.5× 105m3/s

Power Estimates for Minas Passage:

Pmax = 8.5GW

NS DoE electrical power generation estimate:

%15Pmax = 1.2 GW

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Power Estimates

Modelling the Minas Passage

Bay of Fundy Minas Passage Minas Basin

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Power Estimates

Turbines affect the tides

Bay of Fundy Minas Passage Minas Basin

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Power Estimates

Model: Chris Garrett and Patrick Cummins

Bay of Fundy

Forcing tidesηo = a cos(ωt)

Minas Passage

Volume Flux: Qc = Length

Cross−sectionalArea

λ = nonlinear drag

Minas Basin

Surface Area: Abηb = Ra cos(ωt − φ)

Momentum equation:

cdQdt

+ λ|Q|Q = g (ηo − ηb)

Continuity:

Q = Abdηb

dt

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Power Estimates

Turbine Power

Pmax = λT |Q|Q2 =23/2 δT Pref

R0

[(1− ε)2 +

√(1− ε)4 + 4(δT + δ0)2

]3/2 .

Turbine drag

Pmax = 6.9 GW

%15Pmax = 1 GW

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Power Estimates

Making the tides do the work

Work done by tides = natural dissipation + turbine power

Turbine drag

Max Power = 1/2 Max Work = 1/2 (1/2 ρgaQ)

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Impact on the tides

Impact on the Minas Basin tides

Amplitude

Turbine drag

Phase lag, φ

Turbine drag

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Impact on the tides

Change in Tides

Relative percent change in the Minas Basin tides: ∆η

For small P :

P ≈ (0.77GW)∆η

∆η ≈ 1.3P %

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Impact on the tides

Far Field Effects

Change in tidal amplitude (cm) at maximum power:

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Impact on the tides

Far-Field Effects

Relative change in tidal amplitude (%) at maximum power:

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Impact on the tides

Far-Field Effects

Relative change in tidal amplitude (%) at P = 2.56 GW:

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Impact on the tides

Resonance

Total Energy vs. period of forcing tide

Case PeriodUndisturbed 12.85P= 2.6 GW 12.80P= 6.9 GW 12.59Barrier 12.50

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Conclusions

Conclusions

Simple nonlinear drag theory agrees with numerical simulationsPmax = 6.9 GW (more than three times previous estimate)At maximum power a 40% reduction in tidesAt low power about 0.7 GW for each percent change in tidesExtracting power from the Minas Passage pushes system closerto resonancePapers:

J. M. McMillan and M. J. Lickley, 2008: “The Potential of Tidal Power from the Bay of Fundy.” SIAMUndergraduate Research Online, 1, Issue 1, http://www.siam.org/students/siuro/published.php

R. H. Karsten, J. M. McMillan, M. J. Lickley, and R. D. Haynes, 2008: “Assessment of Tidal Current Energy in the

Minas Passage, Bay of Fundy.” Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power

and Energy, 222, 493–507.

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Continuing work

Continuing work

Realistic turbinesPartial turbine fencesOptimum turbineplacementEnvironmental impactsOther sites: UngavaBay/Hudson Strait

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Continuing work

Realistic Isolated Turbine

Turbine Wake: Horizontal Turbine Wake: Vertical

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Continuing work

Isolated Turbines

Isolated turbine:Lanchester-Betz limit

P = 0.59(

12

Au3)

"Single" 214 MW turbineP = 0.8

(12Au3)

Change in speed

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Continuing work

Partial fences

Partial fences in channel:Garrett and Cummins (JFM2007)

Pmax

Pref=

2

3(

1 + AAc

)

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Continuing work

Optimizing Turbine Location

Power = 5.4 GW Power = 4.4 GW

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Continuing work

Particle Tracing

Pollution distribution Migration patterns

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Continuing work

Future Work: Bay of Fundy

Work with Brian Sanderson:

Power Relative Change for 7GW

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Continuing work

Future Work: 3D runs

Following Sucsy, Pearce, Panchang (JPO 1992)

Speed vs. depth and time Two Layers: Power

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Continuing work

Upper Grid

Work done by tides = natural dissipation + turbine power

Turbine drag

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Continuing work

Upper Grid

Work done by tides = natural dissipation + turbine power

Turbine drag

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Continuing work

Tidal Head

ηo − ηb = a√

1− 2R cosφ+ R2 cos(ωt − Φ)

Turbine dragRichard Karsten (Acadia University) Tidal Power Models April 15, 2009 36 / 39

Continuing work

Far-Field Effects

Extracting any powerhas system wideeffectsLocal change is largest

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Continuing work

Continuing work:3D model

Simulation

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Continuing work

Turbine Fence Width

Turbines Power

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