Axial Momentum Theory for Turbines with Co-axial Counter Rotating Rotors By Chawin Chantharasenawong Banterng Suwantragul Annop Ruangwiset Department of Mechanical Engineering, KMUTT Presented at the Commemorative International Conference on the Occasion of the 4 th Cycle Celebration of KMUTT Sustainable Development to Save the Earth: Technologies and Strategies Vision 2050 Millennium Hilton Hotel, Bangkok, Thailand 7-9 April 2009

Co-axial Twin Rotor HAWT Upstream rotor Downstream rotor Wind direction

Inspiration [5] Jung S N, No T S and Ryu K W (2004) Aerodynamic performance prediction of a 30kW counter-rotating wind turbine system, Renewable Energy, Vol. 30, pp

Existing Theory and Literature This image is taken from Actuator Disc Theory Mass conservation

The Betz Limit  Power coefficient The Betz limit states that for a single rotor wind turbine

Existing Theory and Literature [2] Newman B G (1983) Actuator-disc theory for vertical-axis wind turbine, Journal of Wind Engineering and Industrial Aerodynamics, Vol.15, pp

Existing Theory and Literature [3] Newman B G (1986) Multiple actuator-disc theory for wind turbine, Journal of Wind Engineering and Industrial Aerodynamics, Vol.24, pp

Methodology & Assumptions Rotor 1 Upstream Rotor 2 Downstream

Flow Velocities and Pressure Pressure profile in stream tube 1 Pressure profile in stream tube 2

 Axial loading on rotor  Bernoulli’s equation  Axial flow momentum equation Methodology

Inner Section of Upstream Rotor Pressure profile in stream tube 1  Axial loading on rotor  Bernoulli’s equation  Axial flow momentum equation

 Axial loading on rotor  Bernoulli’s equation  Axial flow momentum equation Inner Section of Upstream Rotor

Mechanical Power Inner section of upstream rotor Mechanical Power Rate of change of kinetic energy Outer section of upstream rotor Downstream rotor

Power Coefficient

Maximum Power Coefficient Determine maximum power coefficient 1.Mass conservation 2.Betz limit implies that Function of 5 variables Function of 2 variables

Optimisation Algorithm solution a c

Power coefficient of a turbine with two rotor discs a = 0 c = 0.418

Power coefficient of each rotor

Proposed design of a co-axial twin rotor counter rotating wind turbine a = 0 c = ‘bladeless’ area in upstream rotor (58% of rotor area) Wind speed at downstream rotor is 0.582V

Conclusions DesignC Pmax Single rotor disc0.593 Two rotor discs0.640 Infinite rotor discs0.667 Proposed design % ‘Bladeless’ area in upstream rotor 2. Wind speed at downstream rotor is 58.2% of free stream velocity 3. Wind speed at outer part of upstream rotor is 33.3% of free stream velocity (Betz limit condition) 4. Theoretical power coefficient increases to 0.814

Questions and Comments Thank you for your attention