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