Power Plant Engineering

116 POWER PLANT ENGINEERING

Example 11. A horizontal shaft, propeller type wind-turbine is located in area having following
wind characteristics :

Speed of wind 10 m/s at 1 atm and 15°C. Calculate the following:

1. Air density ρ
   2. Total power density in wind stream, W/m^2
   3. Maximum possible obtainable power density, W/m^2
   4. Actual obtainable power density, W/m^2
   5. Total power from a wind-turbine of 120 m dia.
   6. Torque and axial thrust (Na) on the wind-turbine operating at 40 rpm and at maximum effi-
   ciency of 42%.
   Solution. 1. Air-density of wind

We use the equation ρ =

P

RT

...(1)

where P = pressure of air, Pa

T = temperature of air, K

R = gas constant 287 J/kg.k 1 atm

Pressure 1 atm = 1.01325 × 10^5 Pa

Temperature 15°C = 15 + 273.15 = 378.15 K

Substituting in Eqn. (1)

Air density ρ =

P

RT

1.01325 ×

105

287 × 378.15 = 1.226 kg/m

(^3).

2. For total power Pt

Pt

A

= 0.5ρVi^3 0.5 × 1.226 × 10^3 = 613 W/m^2.

3. Maximum possible power

Pmax

A

= (8/27)ρVi^3 = (8/27 × 1) × 1.226 × 10^3 = 363 W/m^2.

4. Assuming ηηηηη = 42%
   P/A = 0.42 (Ptot/A) = 0.42 × 613 = 257 W/m^2


5. P = 0.257 × πD^2 /4 = 0.257 × π 1202 /4 = 2906 kW.


6. Tmax =

2

27

(ρDVi^3 /Ns) =

2

27

[1.20 × 1.226 × 10^3 /(40/60)]

= 16,347 N.