GOVERNING EQUATIONS

In this study, CFD has been used to carry out aerodynamic analysis of a wind turbine blade in which Navier-Stokes equations are used to accomplish the simulations. Navier-stokes equation encompasses three conservation laws; known as the conservation of mass, conservation of energy and conservation of momentum as mentioned in the following[20]
\(\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x}\left(\text{ρu}\right)+\frac{\partial}{\partial y}\left(\text{ρv}\right)+\frac{\partial}{\partial z}\left(\text{ρw}\right)=0\)(1)
\(\rho\frac{\text{Du}}{\text{Dt}}=\frac{\partial\left(-p+\tau_{\text{xx}}\right)}{\partial x}+\frac{\partial\tau_{\text{yx}}}{\partial y}+\frac{\partial\tau_{\text{zx}}}{\partial z}+S_{\text{Mx}}\)(2)
\(\rho\frac{\text{Dv}}{\text{Dt}}=\frac{\partial\tau_{\text{xy}}}{\partial x}+\frac{\partial\left(-p+\tau_{\text{yy}}\right)}{\partial y}+\frac{\partial\tau_{\text{zy}}}{\partial z}+S_{\text{My}}\)(3)
\(\rho\frac{\text{Dw}}{\text{Dt}}=\frac{\partial\tau_{\text{xz}}}{\partial x}+\frac{\partial\tau_{\text{yz}}}{\partial y}+{\frac{\partial\left(-p+\tau_{\text{zz}}\right)}{\partial z}+S}_{\text{Mz}}\)(4)
Where
u, v and w =components of the velocity in the x, y and z-direction respectively.
P = pressure
\(\tau_{\text{ij}}\) = the normal and shear stress that affects the 3D fluid particles.
\(S_{\text{Mx}},S_{\text{My}},and\ S_{\text{Mz}}=\) Body forces per unit of mass in the x, y, and z-direction.