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The 22 nd Offshore Symposium Redefining Offshore Development: Technologies and Solutions Feb 2, 2017 | Houston, USA In this method, the propeller/turbine blade is solved in the lifting line model, and the duct is solved in the axisymmetric RANS solver. The blade is represented as an actuator disk with a pressure jump profile. : thrust on the propeller, : thrust on the duct. “RANS/Lifting Line Model Interaction Method for the Design of Ducted Propellers and Tidal Turbines” Weikang DU*, Spyros A. Kinnas * , Robin Martins Mendes ** , Thomas Le Quere ** *Ocean Engineering Group, The University of Texas at Austin **Ecole Navale, France Introduction Methodology Objectives Conclusions Results • Propeller and turbine design tools developed at UT’s OEG: • LLOPT: lifting line theory based optimization • LLOPT-BASE: circulation database searching method • CAVOPT-BASE: database-searching method for the design of propeller (coupled with VLM method) • CAVOPT-3D: nonlinear optimization method for propeller design (coupled with VLM method) • Wake alignment procedure: • Lerbs-Wrench formulas: assuming a constant pitch along the x-direction (LLOPT-LW) • Simplified Wake Alignment (LLOPT-SWA) • Full wake alignment (LLOPT-FWA) • However, the duct geometry is not taken into consideration in those methods In this paper, a RANS/lifting line model interaction method is proposed to consider the duct geometry in the design of propellers and tidal turbines. Blade (actuator disk) Lerbs-Wrench wake (helical wake) Real duct geometry RANS domain axis hub ∆ circulation pressure low pressure high actuator disk τ= + = = = = 1 2 2 2 = 1 2 2 2 = τ 2 2 = Q 1 2 2 3 η= Q = =U − ∗ Previous iteration τ= − • Viscous effect is included in two parts: • Non-slip boundary condition on duct • Drag-to-lift coefficient κ κ= =U + ∗ Propeller_case1 Without duct. LLOPT Duct is considered as image model (blade inside cylindrical tunnel). LLOPT LLOPT2NS flowchart Real duct geometry is considered. LLOPT2NS x r -0.4 -0.2 0 0.2 0.4 1 1.05 1.1 1.15 1.2 f 0 =-0.02, t 0 =0.15 x r -0.4 -0.2 0 0.2 0.4 1 1.05 1.1 1.15 1.2 f 0 =-0.04, t 0 =0.15 x r -0.4 -0.2 0 0.2 0.4 1 1.1 1.2 1.3 f 0 =-0.04, t 0 =0.30 x r -0.4 -0.2 0 0.2 0.4 1 1.1 1.2 1.3 f 0 =-0.02, t 0 =0.30 t 0 Efficiency 0.15 0.2 0.25 0.3 0.64 0.66 0.68 0.7 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 Propeller_case1 Propeller_case2 t 0 KT on the blade 0.15 0.2 0.25 0.3 0.08 0.085 0.09 0.095 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 Propeller_case1 Propeller_case2 t 0 KQ 0.15 0.2 0.25 0.3 0.112 0.114 0.116 0.118 0.12 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 Propeller_case1 Propeller_case2 Propeller case: J s =0.5, C Ts =1.0 t 0 U in 0.15 0.2 0.25 0.3 1.15 1.2 1.25 1.3 1.35 1.4 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 t 0 0.15 0.2 0.25 0.3 0.8 0.85 0.9 0.95 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 • With the increase of duct camber, the efficiency increases • With the increase of duct camber and thickness, both the inflow velocity and thrust on the duct increase Propeller case: J s =0.5 t 0 Efficiency 0.15 0.2 0.25 0.3 0.54 0.56 0.58 0.6 0.62 0.64 0.66 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 Propeller_case1 Propeller_case2 t 0 Efficiency 0.15 0.2 0.25 0.3 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 Propeller_case3 f 0 = -0.02 Propeller_case3 f 0 = -0.03 Propeller_case3 f 0 = -0.04 Propeller_case1 Propeller_case2 C Ts =2.0 C Ts =3.0 C Ts Efficiency 1 1.5 2 2.5 3 0.45 0.5 0.55 0.6 0.65 0.7 Propeller_case1 Propeller_case2 Propeller_case3 Propeller case, fixed duct geometry J s =0.5 J s Efficiency 0.5 0.6 0.7 0.8 0.9 1 0.6 0.65 0.7 0.75 Propeller_case1 Propeller_case2 Propeller_case3 C Ts =1.0 Turbine case, different duct angles • A RANS/lifting line model interaction method is proposed for the design of ducted propellers and tidal turbines. • The NACA a=0.8 camber and NACA 00 thickness are used. • For the propeller case, the influence of camber and thickness is studied; for the turbine case, the influence of duct angle is studied. • It is shown that the duct geometry has influence on the inflow velocity and KT on the blade for ducted propellers and turbines, which can not be taken into account in the image model. Proper designed duct can increase the efficiency significantly. • This method is proved to be reliable and efficient in designing ducted propellers and tidal turbines. • Turbine case: • Only U in is updated • The pressure jump is in the opposite direction, compared with the propeller case Propeller_case2 Propeller_case3 x r -0.2 -0.1 0 0.1 0.2 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Duct angle=11 degree Duct angle=13 degree Duct angle=15 degree X Y -1 -0.5 0 0.5 1 0 0.5 1 1.5 Pressure 300 240 180 120 60 0 -60 -120 -180 -240 -300 TSR Efficiency 7 7.5 8 8.5 9 9.5 10 0.42 0.44 0.46 0.48 0.5 0.52 Duct angle=11 degree Duct angle=13 degree Duct angle=15 degree Open turbine (without duct) (0,1) (0,0) c duct f 0 t 0 dx le axis x r -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 duct camber line blade (actuator disk) nose-tail line 11% to 22% efficiency increase
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