In this project, the numerical simulation of the turbulent flow inside the pipe is discussed. The grid generation and solution of this problem have been done with the Prick code based on the k-ε turbulent model for two low Reynolds models (Model 1 and Lander model) and the outputs have been compared with the results of the Fluent software as well as the k-ε model for high Reynolds. Also, during this project, it has been tried to point out important and significant points in CFD and evaluate their impact on this issue.
Internal flow is a flow in which the fluid is enclosed by a surface and viscous effects develop and are observed throughout the flow (such as flow in a pipe). Therefore, the boundary layer cannot expand without limits. When examining external flow, the only question is whether the flow is laminar or turbulent. But for the internal flow, the presence of the entrance area or the completely inclusive area should also be checked.
Reynolds number is the only parameter that affects the inlet length:
(1) \( Re = \frac{\rho U_m d}{\mu} \)
Also, for the average velocity inside the tube, we can write:
(2) \( u_m = \frac{1}{\pi r_0^2} \int_0^{r_0} 2\pi r u \, dr \)
Also, using the \( C_f \) relation, it is concluded that:
(3) \( f = 4C_f = \frac{8 \tau_w}{\rho u_m^2} = \frac{64}{Re_D} \)
In flows with high Reynolds numbers, using the wall function saves time and the volume of calculations because they do not need to be solved for the areas near the wall where the gradient is strong, and from the semi-empirical relations, in order to apply the boundary conditions of the rest of the computational domain far from the wall is used.
In low Reynolds numbers, it is tried to mesh the geometry in such a way that the first node is placed under the viscous layer. As a result, we seek to resolve the nodes near the wall, and it is no longer necessary to use the wall functions in the first node.
The results of the developed codes agree with the results of simulation with Fluent.