Array Optimization of Marine Hydrokinetic MHK Turbines Using

Array Optimization of Marine Hydrokinetic (MHK) Turbines Using the Blade Element Momentum Theory Teymour Javaherchi Oskar Thulin Alberto Aliseda

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

Normalized Centerline Velocity Deficit in the Turbulent Wake R 2 = 0. 985 0. 2 0. 15 0. 1 0. 05 0 0 1 2 3 4 Y/R 5 6 7 8 Normalized Momentum Deficit Normalized Velocity Deficit 0. 25 Constant 9 Normalized Momentum Deficit in the Turbulent Wake 0. 10 0. 09 0. 08 0. 07 0. 06 0. 05 0. 04 0. 03 0. 02 0. 01 0. 00 R 2 = 0. 97 0 1 2 3 4 Y/R 5 6 7 8 9

Max. AOA [°] Min. AOA [°] Calculated Power by VBM [k. W] Available Kinetic Efficiency Energy Flux on [] Turbine Plane [k. W] Thrust [k. N] Torque [Nm] 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

Turbine Efficiency vs. Local Tip Speed Ratio 0. 5000 0. 4500 0. 4000 Efficiency [] 0. 3500 0. 3000 0. 2500 0. 2000 0. 1500 0. 1000 0. 0500 0. 000 1. 000 2. 000 3. 000 4. 000 5. 000 6. 000 Local Tip Speed Ratio [] 7. 000 8. 000 9. 000 10. 000 Turbine 1 SET 1234 Turbine 2 SET 1234 Turbine 3 SET 1234 Turbine 4 SET 1234 Turbine 5 SET 1256 Turbine 6 SET 1256 Turbine 7 SET 1278 Turbine 8 SET 1278 Turbine 1 SET 1256 Turbine 2 SET 1256 Turbine 1 SET 1278 Turbine 2 SET 1278 Turbine 1 SET 123456 Turbine 2 SET 123456 Turbine 3 SET 123456 Turbine 4 SET 123456 Turbine 5 SET 123456 Turbine 6 SET 123456

Efficiency of Downstream Turbines at constant Tip Speed Ratio (T. S. R=4. 9) Calculated Power by VBM [k. W] 250. 00 R 2 = 0. 999 200. 00 V_inf = 1 [m/s] 150. 00 V_inf = 1. 5 [m/s] V_inf = 2 [m/s] 100. 00 V_inf = 2. 5 [m/s] 50. 00 100. 00 200. 00 300. 00 400. 00 500. 00 600. 00 700. 00 Available Kinetic Energy Flux at a Plane 2 R Turbine Upstream [k. W]

Effect of Lateral Offset Normalized power extracted (%) Normalized power extracted by a 8 R downstream turbine 100 Tip-Tip Distance 80 1 radius 1, 25 radius 60 1, 5 radius - + 8 R 1, 75 radius + 40 -1 -0. 5 0 0. 5 1 1. 5 2 2. 5 3 Offset of the downstream turbine (R) 9

M_z axis vs. Offset Turbines 8 R Downstream 25 M_z (k. N. m) 20 Tip-Tip Distance: 15 1 radius 1. 25 radius 10 1. 5 radius 1. 75 radius 5 0 -1 -0. 75 -0. 25 0. 75 1 1. 25 Offset (R) 1. 5 1. 75 2 2. 25 2. 75 3

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 Beweret Florian Riesemann