Cfd modelling of h-darrieus vertical axis wind turbine

Eq (3.10) 
𝜁
𝑧𝑧
= 2𝜇
𝜕𝑤
𝜕𝑧
+ 𝜆 𝑑𝑖𝑣 𝒖 
Eq (3.11) 
 
𝜁
𝑥𝑦
= 𝜁
𝑦𝑥
= 𝜇 (
𝜕𝑢
𝜕𝑦
+
𝜕𝑣
𝜕𝑥
), 
Eq (3.12) 
𝜁
𝑥𝑧
= 𝜁
𝑧𝑥
= 𝜇 (
𝜕𝑢
𝜕𝑧
+
𝜕𝑤
𝜕𝑥
), 
Eq (3.13) 
𝜁
𝑦𝑧
= 𝜁
𝑧𝑦
= 𝜇 (
𝜕𝑣
𝜕𝑧
+
𝜕𝑤
𝜕𝑦
). 
Eq (3.14) 
By substituting the equations 3.12 to 3.14 to equations 3.4 to 3.6 we will reach to the Navier-
Stokes equations: 
𝜕(𝜌𝑢)
𝜕𝑡
+ div(ρu𝐮) = −
𝜕𝑝
𝜕𝑥
+ 𝑑𝑖𝑣 (𝜇 𝑔𝑟𝑎𝑑 𝑢) + 𝑆
𝑀𝑥
 
Eq (3.15) 

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24 
𝜕(𝜌𝑣)
𝜕𝑡
+ div(ρv𝐮) = −
𝜕𝑝
𝜕𝑦
+ 𝑑𝑖𝑣 (𝜇 𝑔𝑟𝑎𝑑 𝑣) + 𝑆
𝑀𝑦
 
Eq (3.16) 
𝜕(𝜌𝑤)
𝜕𝑡
+ div(ρw𝐮) = −
𝜕𝑝
𝜕𝑧
+ 𝑑𝑖𝑣 (𝜇 𝑔𝑟𝑎𝑑 𝑤) + 𝑆
𝑀𝑧
 
Eq (3.17) 
 
3.2.2 Finite Volume Method 
One of the most popular discretization method used in CFD is the Finite Control Volume 
Method which is commonly known as the Finite Volume Method. In this method, first the main
domain is discretized into finite control volumes and then over each of the control volumes, 
integration is done. The finite volume method has some similarity with finite difference and 
finite element methods where the discretization part is very similar to that of the finite element 
method. However, finite volume method’s computational effort is higher than that of finite 
difference method but less than that of the finite element method when accuracy is almost 
similar. Besides, the FVM offers some advantages over the other two methods. FVM is based on 
cell average value. This is why, it provides some advantages like conservation of momentum, 
mass and energy is maintained at local scales. In addition, this can enable to work with geometry 
with complex shapes. [60]
The general conservation equation is equal to: 
𝜕(𝜌𝜑)
𝜕𝑡
+ div(ρφ𝐮) = div(Γ grad φ) + 𝑆
𝜑