Can we Overcome the Betz Limit in Windpower Extraction?
October 23, 2009 by Windpower Engineering
Filed under Turbine Design, Wind Watch
Editor’s note:
Inventor Horia Nica has applied for a patent on a device that couples a vertical-axis wind turbine with a device that captures heat from passing wind, a capability conceived by early 20th century inventor Nicola Tesla. Furthermore, the captured thermal energy is transferred to the wind turbine as rotational kinetic energy, according to Nica. The Tesnic Inc website (tesnic.com) shows a few early concepts for such a device intended only for vertical-axis turbines. In a brief interview, Nica said he is now building a working model of the wind turbine and thermal-capture device that will allow extracting more energy from the wind than a turbine alone. The following white paper provides some mathematical validity for the idea.
–Paul Dvorak
On the possibility of overcoming Betz limit in wind-power extraction
Horia Nica,
Tesnic Inc.
Laval, Quebec, Canada
Tesnic.com
The energy in the wind has components of kinetic and heat energy. Existing wind technologies can extract only a fraction of the kinetic energy. The maximum theoretical value of kinetic energy extractable from the wind was demonstrated in 1919 by Albert Betz and it is known as Betz’s Law. According to it, the maximum coefficient of performance (Cp) in kinetic-energy extraction is 59.3%, which is also called the Betz Limit. Existing wind turbines actually have a lower Cp than the Betz Limit. What if the wind turbines could extract a portion of the heat energy from the wind in addition to its kinetic energy?
Assume an ideal wind turbine can extract the wind’s kinetic energy at the Betz Limit, 59.3% of the kinetic and that this ideal turbine has a frontal surface area of 100 m2 (10 m by 10 m). In a wind of 10 m/s and a temperature of 15 C, the energy extracted by such an ideal wind turbine is:
Ek= 0.5ρAV3Cp
Where Ek = kinetic energy in the wind, W; ρ = air density, kg/m3; A = area, m2; and V = wind speed, m/s. Then,
Ek = 0.5 * 1.225 * 100 * 1,000 * 0.593
Ek = 36,321 W , or
= 36.32 kW
After operating for one hour at these conditions, the turbine will produce:
Pk = 36.32 kWh
Now assume there exists a device that, if combined with the above ideal turbine, can extract a portion of the thermal energy in addition to the above calculated kinetic energy. Assume that with the device, a portion of the airflow exiting the turbine is slightly cooler than the input airflow. Assume 50% of the input airflow exits at 0.1° C lower.
In such case, the thermal power calculation is:
Pt = ρQair/hr ΔT Hair
Where Pt = thermal energy captured, kj; Qair/hr = volume of air flow per hour, m3/hr; ΔT = temperature difference, °C; and Hair = specific heat for air; kj/kg. Then
Pt =1.225 *( 100 m2 * 10 m/s * 3,600 s * 50%)* 0.1 * 1.005kj/kg
Pt = 221,602.5 kj
Knowing that 1 kilojoule (kj) = 0.0002777 kWh we obtain:
Pt = 61.55 kWh
The corresponding thermal energy is transferred to the wind turbine as rotational kinetic energy. Consequently the turbine in the above theoretical example, having a device that lowers the temperature of the exit airflow by only 0.1° C will be able to produce a total of:
Ptotal = Pk + Pt
= 97.87 kWh, which is 2.69 times more than the Betz Limit.
Therefore, in theory, wind power extraction can go beyond the Betz Limit and without contradicting Betz’s Law. The capability will result in future powerful wind turbines having smaller dimensions than current designs with the same capacity. Our recent patent application discloses a device able to capture the thermal energy as described above.
For more information, view Tesnic’s white paper here.
