Cfd modelling of h-darrieus vertical axis wind turbine

4.6.4 Reference Values and Power Coefficient 
The reference values used for computing normalized flow field variables such as moment, moment 
coefficient etc. can be set in Fluent: [61] 
𝐶
𝑝
=
𝑃
𝑡
𝑃
𝑎
=
𝑀𝜔
1
2 𝜌𝐴𝑣
3
 
Eq (4.4) 
The total moment M is calculated in Fluent using the moment coefficient Cm, which is stated as: 
𝐶
𝑚
=
𝑀
1
2 𝜌𝐴𝑣
2
𝐿
 
Eq (4.5) 
A is the reference area, and L is the reference length in the equation above. 
With these considerations in mind, the power coefficient equation can be reduced to the following: 
𝐶
𝑝
=
𝐶
𝑚
1
2 𝜌𝑣
2
𝐴𝐿𝜔
1
2 𝜌𝐴𝑣
3
= 𝐶
𝑚
𝜔𝐿
𝑣
 
Eq (4.6) 
In 2D simulations of turbines, the value of A is equal to the diameter of the turbine, while the value 
of L is equal to the radius of the turbine, as detailed in [85]. When these adjustments are applied to 
equation 4.6, the following equation is obtained:

---

44 
𝐶
𝑝
= 𝐶
𝑚
𝜔𝑅
𝑣
 
Eq (4.7) 
Lastly, a simple statement can be derived that links the power coefficient with the tip speed ratio and 
the moment coefficient extracted by the Fluent models by applying the definition of the tip speed 
ratio from in equation 4.7: 
𝐶
𝑝
= 𝐶
𝑚
λ 
Eq (4.8) 
Apart from the geometric reference values, which are only dependent on the turbine size, there are 
other fluid-related characteristics such as density and viscosity. All of the reference values in the 
simulations were calculated using the inlet boundary condition, which forces the value of the free 
stream velocity. The primary reference values for the Vertical axis wind turbine simulations are 
listed in Table 7. Once the fluid is established in the Materials dialog box in the Problem Setup 
menu, these values can be set automatically or manually by the Fluent materials database. 
Table 7: Reference Values 
Parameters 
Values (a) 
Velocity
10 (m/s) 
Viscosity 
1.7894e-5 (kg/m-s) 
Density
1.225 (kg/m