Teymour Javaherchi

Oskar Thulin

Alberto Aliseda

Array Optimization of Marine Hydrokinetic (MHK) Turbines

Using the Blade Element Momentum Theory

Goals

Develop a general numerical methodology for array optimization of horizontal axis MHK turbines.

Address and investigate the key variables in Marine Hydrokinetic (MHK) turbine array optimization (i.e. different operating conditions and spacing between devices)

Maximize energy extraction from a very concentrated resource in estuaries and rivers.

Numerical Methodology This model is an implementation of

Blade Element Momentum Theory (BEM) in ANSYS FLUENT.

Lift and Drag forces are calculated for each blade element based on their lift and drag coefficients as input for the model.

Calculated forces are averaged over a cycle of rotation.

Effect of rotating blades is simulated on the fluid through a body force.

Computational Domain for a Single Turbine

Vy = 2 [m/s] , Tip Speed Ratio (T.S.R) = 4.9

Constant

1 2 3 4 5 6 7 8 90

0.05

0.1

0.15

0.2

0.25

f(x) = 0.336190789602426 x -̂0.664820722159479R² = 0.985010098888595

Normalized Centerline Velocity Deficit in the Turbulent Wake

Y/R

Nor

mal

ized

Velo

city

Defic

it

1 2 3 4 5 6 7 8 90.000.010.020.030.040.050.060.070.080.090.10

f(x) = 0.0166157343759523 x^0.0706179072690834R² = 0.972352408211312

Normalized Momentum Deficit in the Turbulent Wake

Y/R

Nor

mal

ized

Mom

entu

m D

eficit

Thrust [kN] Torque [Nm] Max. AOA [°] Min. AOA [°] Calculated Power by VBM [kW]

Available Kinetic Energy Flux on

Turbine Plane [kW]Efficiency

[]

Turbine 1 75.739 54.042 10.246 6.561 96.207 327.848 0.294

Turbine 2 75.451 53.640 10.231 6.522 95.493 327.488 0.292

Turbine 7 67.443 43.297 8.150 5.838 77.080 226.572 0.340

Turbine 8 72.631 50.022 10.203 5.175 89.052 268.899 0.331

2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

0.3500

0.4000

0.4500

0.5000

Turbine Efficiency vs. Local Tip Speed RatioTurbine 1 SET1234Turbine 2 SET1234Turbine 3 SET1234Turbine 4 SET1234Turbine 5 SET1256Turbine 6 SET1256Turbine7 SET1278Turbine 8 SET1278Turbine 1 SET1256Turbine 2 SET1256Turbine 1 SET1278Turbine 2 SET1278Turbine 1 SET123456Turbine 2 SET123456Turbine 3 SET123456Turbine 4 SET123456Turbine 5 SET123456Turbine 6 SET123456

Local Tip Speed Ratio []

Effici

ency

[]

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.000.00

50.00

100.00

150.00

200.00

250.00

f(x) = 0.327945362397014 xR² = 0.999451852483521

Efficiency of Downstream Turbines at constant Tip Speed Ratio(T.S.R=4.9)

V_inf = 1 [m/s]

V_inf = 1.5 [m/s]

V_inf = 2 [m/s]

V_inf = 2.5 [m/s]

Available Kinetic Energy Flux at a Plane 2R Turbine Upstream [kW]

Calc

ulat

ed P

ower

by

VBM

[kW

]

Effect of Lateral Offset

9

-1 -0.5 0 0.5 1 1.5 2 2.5 340

60

80

100

Normalized power extracted by a 8R downstream turbine

1 radius

1,25 radius

1,5 radius

1,75 radius

Offset of the downstream turbine (R)

Nor

mal

ized

pow

er e

xtra

cted

(%)

Tip-TipDistance

+

+

-

8R

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 30

5

10

15

20

25

M_z axis vs. Offset Turbines 8R Downstream

1 radius

1.25 radius

1.5 radius

1.75 radius

Offset (R)

M_z

(kN

.m) Tip-Tip

Distance:

Conclusions A general numerical methodology was developed to study

the key parameters in array optimization of MHK turbine. Computed a constant efficiency for turbines operating in

arrays above a certain TSR (linear behavior), as well as the efficiency decay consistent with separated flow at low TSR (non-linear regime).

Tip-Tip distance has very small effect on efficiency of neighbor and downstream turbines.

Offset distance plays an important role in an array of turbine. A lateral offset of 1.75-2 radii provides optimum spacing and minimum loading stress on the device.

Acknowledgment

Research fellows from French Naval Academy:

Mario BeweretFlorian Riesemann