[TALK] Numerical Validation of the Two‐Scale Actuator Disc Theory for Marine Turbine Arrays

Numerical Validation of the Two‐Scale Actuator Disc Theory for Marine Turbine Arrays

Edgar Perez‐CamposTakafumi Nishino

Cranfield University

EWTEC 2015 9th September 2015

Two-Scale Actuator Disc Theory(a.k.a. Partial Tidal Array Theory)

Page 2Numerical Validation of the Two-Scale Actuator Disc TheoryE. Perez-Campos & T. Nishino

(a) Array-scaleflow expansionand mixing

(b) Device-scaleflow expansionand mixing

Scale Separation

Nishino & Willden (2012, JFM)

Two-Scale Actuator Disc Theory(a.k.a. Partial Tidal Array Theory)


(a) Array-scaleflow expansionand mixing

(b) Device-scaleflow expansionand mixing

Scale Separation

Nishino & Willden (2012, JFM)

Two-Scale Blockage Effect


Nishino & Willden(2012, JFM)

Betz limit: CP = 0.593(BG = BL = 0)

Garrett & Cummins (2007)for ‘single’ blockage (BG = BL)

Why is this important for tidal array design?

Page 5

Image: ScottishPower Renewables

Numerical Validation of the Two-Scale Actuator Disc TheoryE. Perez-Campos & T. Nishino

Tidal array design is a multi-scale problem:

• Blade (hydrofoil) scale: down to cm’s• Turbine (rotor) scale: 10~20m?• Array (farm) scale: up to a few km’s• Regional scale: up to hundreds of km’s

We cannot resolve all these scales at once.→ We need to understand the interaction between scales systematically.

Why is this important for tidal array design?

Page 6

Image: ScottishPower Renewables


Tidal array design is a multi-scale problem:

• Blade (hydrofoil) scale: down to cm’s• Turbine (rotor) scale: 10~20m?• Array (farm) scale: up to a few km’s• Regional scale: up to hundreds of km’s

We cannot resolve all these scales at once.→ We need to understand the interaction between scales systematically.

Blade Element Momentum Theory: can describe “blade” and “turbine” scales

Two-Scale Actuator Disc Theory: can describe “turbine” and “array” scales (?)

Two-Scale ADT: Corrections Required


We need several corrections to the original Two-Scale ADT (like we need, e.g. tip-loss and hub-loss corrections, to the original BEM theory):

• Short array end effect (Nishino & Willden 2013)

• Free surface effect (Vogel 2014)

• Seabed friction effect• Real device effect• Multi-row effect (Draper & Nishino 2014)

Two-Scale ADT: Corrections Required


We need several corrections to the original Two-Scale ADT (like we need, e.g. tip-loss and hub-loss corrections, to the original BEM theory):

• Short array end effect (Nishino & Willden 2013)

• Free surface effect (Vogel 2014)

• Seabed friction effect• Real device effect• Multi-row effect (Draper & Nishino 2014)

Multi-row effect is particularly important for tidal farm design, but difficult to model since it involves the effect of upstream turbine wakes on downstream turbines.

Flow expansion: (essentially) inviscid process → ADT can handle it

Wake mixing: viscous/turbulent flow process → ADT cannot handle it

X

Applications of Two-Scale ADT to Multiple Rows


There are two possible approaches:

Multiple fence approach(Draper & Nishino 2014)

Single fence approach(Nishino 2012; present study)

- Both models predict similar results (unless the total thrust is extremely large).- Both models assume complete device-wake mixing between each row.

What about the case with incomplete device-wake mixing between each row?

3D RANS Actuator Disc Simulations

Single row cases (8 discs x 1 row) Double row cases (8 discs x 2 rows)


3D RANS Actuator Disc Simulations

Page 11

- Lateral array of 8 or 16 porous disc models in a wide computational domain of 40d (width) x 2d (depth) x 200d (length), resulting in BG ≈ 0.08.

- Lateral gap between each turbine is varied between 0.25d and 4d.

- For double row cases, streamwise gap is fixed at 10d.

- Changing the disc resistance (for 8 or 16 discs all together) to find CPGmax.

- Laterally uniform but vertically sheared inflow.

- Please see the paper for further details.


Single Row Cases: Power Curves


CPG

aG

Lines: TheorySymbols: CFD

Blue: s/d = 0.25 ← optimalRed: s/d = 0.5Green: s/d = 1Black: s/d = 4

Double Row Cases: Streamwise Velocity


s/d = 0.25 s/d = 0.5

s/d = 1 s/d = 4

Double Row Cases: Power Curves


CPG

aG

Blue: s/d = 0.25 Red: s/d = 0.5Green: s/d = 1 ← optimal

Lines: TheorySymbols: CFD

Double Row Cases: CPGmax vs BL


CPGmax

BL

Curve: TheorySymbols: CFD

Staggered or Non-Staggered?


Non-staggered double row (s/d = 1)

Will the two-scale theory be no longer important for three or more rows?


Two-Scale ADT predicts that themaximum power is obtained at the smallest possible local blockage when we have three or more rows (unless the global blockage is high).

However…

There will still be an optimal local blockage if we aim to maximise the power density (i.e. power per unit farm-area), for example.

So, it will still be important.

1 row

2 rows

3 rows

BG

Nishino (2012)

Maximum power (per turbine) vs BL

Summary


- Tidal array design is a multi-scale problem.

- Two-scale ADT can describe the interactions of “device” and “array” scales.

- However, this theory needs several corrections (like the BEM theory needs tip-loss and hub-loss corrections, for example).

- Among others, how to model the multi-row effect is crucial.

- We currently have two theoretical approaches, but both approaches assume complete device-wake mixing between each row.

- Nevertheless, the theory still seems to agree qualitatively with CFD for double row cases with incomplete device-wake mixing.

- Two-scale ADT will be important even for 3 or more rows.

[TALK] Numerical Validation of the Two‐Scale Actuator Disc Theory for Marine Turbine Arrays

Documents