CFD MODEL
URANS equations in terms of continuity, momentum and energy are given as
follows:
\(\frac{\partial\rho}{\partial t}+\frac{\partial}{{\partial x}_{j}}\left(\rho U_{j}\right)=0\)(1)
\(\frac{\partial}{\partial t}\left(\rho U_{i}\right)+\frac{\partial}{\partial x_{j}}\left(\rho U_{i}U_{j}\right)=-\frac{\partial p}{\partial x_{i}}+\frac{\partial}{\partial x_{j}}\left[\tau_{\text{ij}}-\rho\overset{\overline{}}{u_{i}u_{j}}\right]+S_{M}\)(2)
\(\frac{\partial}{\partial t}\left(\text{ρH}\right)-\frac{\partial P}{\partial t}+\frac{\partial}{\partial x_{j}}\left(\rho U_{j}H\right)=\frac{\partial}{\partial x_{j}}\left(\lambda\frac{\partial T}{\partial x_{j}}+\rho\overset{\overline{}}{u_{j}h}\right)+\frac{\partial}{\partial x_{j}}\left[U_{i}\left(\tau_{\text{ij}}-\rho\overset{\overline{}}{u_{i}u_{j}}\right)\right]+S_{E}\)(3)
Where\(\overrightarrow{\ S_{M}}=-2\overrightarrow{\Omega}\times\overrightarrow{U}+\overrightarrow{\Omega}\times(\overrightarrow{\Omega}\times\overrightarrow{r})\),\(\overrightarrow{\Omega}\) rotational velocity (rad/s),\(\overrightarrow{U}\) relative flow velocity, \(\tau_{\text{ij}}\) is
the molecular stress tensor and\(\rho\overset{\overline{}}{u_{i}u_{j}}\) is the Reynolds stresses.\(H=h+{\frac{1}{2}U}^{2}+k\) is the total enthalpy, \(S_{E}\) is
the energy source term, k is the turbulent kinetic energy and λ
is the thermal conductivity. k-ω based SST (Menter [23])
turbulence closure model is used owing to reliability in analyzing RSI
and good revelation of pressure oscillation [24].
_