1 Counter Rotating Propeller Design using Blade Element Momentum Theory Kiran Siddappaji Mark G. Turner University of Cincinnati I. I NTRODUCTION Counter-rotating propeller (CRProp) has many advantages over single propeller systems. Rotational energy lost in the slipstream is recovered by the aft rotor, smaller diameter and lower loading per blade and total torque is balanced due to the opposite rotation of the rotors [1]. A design method is presented using Blade Element Momentum Theory (BEMT) combining Blade Momentum (BMT) and Blade Element (BET) theories. The tip loss effect (Prandtl’s) and the wake rotation due to the front rotor is also accounted. The individual axial and angular induction factors and due to the interaction between the rotors are calculated iteratively. A good initial geometry obtained by this process is parametrically modified using an in-house 3D geometry generator (3DBGB)[2]. A 3D CFD analysis is performed and a structural analysis to avoid structural failure and hence an optimum CRProp is designed. II. APPLICATION An unducted CRProp is designed for an Octocopter with 150 pounds (667.24 N) of thrust per pod, suitable for rescue and relief operations in natural disaster areas. The design details are in Table I. Rotor Properties Units FRONT AFT Hub Dia. cm 10.00 10.00 Tip Dia. cm 130.00 130.00 Vz m/s 15.0 19.0 - 27.7 Blade number - 3 3 TSR (λ) - 9.181 -5.008 RPM - 2023 -1920 chord m specified[3] specified[3] Thrust N 333.62 335.80 Torque Nm 44.08 -26.42 Power kW 12.11 6.98 Table I DESIGN PROPERTIES OF THE CRPROP. III. METHODOLOGY The CRProp configuration and the streamtube is shown in Figure 1. The streamtube contraction is exactly opposite to the streamtube expansion in a wind turbine case [4]. The velocity triangles are shown in Figure 2. Axial and angular momentum conservation across the rotating disks give the incremental thrust and torque for the front (dT 1 , dQ 1 ) and aft rotor (dT 2 , dQ 2 ) as below, where F total is the total loss factor. dT 1 = 4F total a 1 (1 + a 1 )ρV 2 z πrdr (1) dQ 1 = 4F total a ′ 1 (1 + a 1 )ρV z Ω 1 πr 3 dr (2) dT 2 = 4F total a 2 (1 + a 2 )(1 + 2a 1 ) 2 ρV 2 z πrdr (3) dQ 2 = 4F total (a ′ 2 - a ′ 12 )(1 + a 2 )(1 + 2a 1 )ρV z πr 3 dr (4) In equation 4, a ′ 12 is the angular induction factor due to the wake rotation at the inlet of the aft rotor defined below, ω 12 is the wake rotation speed and Ω 2 is the aft rotor rotation speed. a ′ 12 = -ω 12 2Ω 2 (5) Figure 1. CRProp configuration and axial velocities at different stations.[4]