Consider the wind turbine of Example 1.3. To reduce the nacelle temperature to T_s = 30°C, the nacelle is vented and a fan is installed to force ambient air into and out of the nacelle enclosure. What is the minimum mass flow rate of air required if the air temperature increases to the nacelle surface temperature before exiting the nacelle? The specific heat of air is 1007 J/kg · K.

Example 1.3

The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has an efficiency of η_gb = 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of η_gen = 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D = 3 m. If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings temperatures are T_∞ = 25°C and T_sur = 20°C, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is ϵ = 0.83, and the convective heat transfer coefficient is h = 35 W/m² · K. The surface of the nacelle that is adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be neglected.

Transcribed Image Text:

Air Tsur T = 25°C = 20°C Hub h = 35 W/m2.K - L = 6 m ↑ D = 3 m T,,E = 0.83 Generator, = ngen = 0.95 = 0.93 Gearbox, 7gb Nacelle