Investigating the Turbulent Flow Inside the Pipe Using the Large Eddy Simulation Method

Abstract

In this project, the numerical simulation of the turbulent flow inside the pipe with the method of large eddies is discussed. In this project, after the simulation using the large eddies method, the simulation with the k-ε method is done and the results of these two simulations are compared. The average speed obtained from these two simulations is consistent with each other.

1. Introduction

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.

2. Methodology & Solution

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) \( f = 4C_f = \frac{8 \tau_w}{\rho u_m^2} = \frac{64}{Re_D} \)

3. Results

The simulation was done in Fluent and the geometry is a pipe with \( L = 0.0635 \, m \) and \( D = 0.0127 \, m \). In short, the results are:

• The results obtained from the simulation of large eddies and the k-ε model are consistent with each other.
• Data sampling is used for time averaging in the model of large eddies.
• The instantaneous speed, which is actually the actual speed at any moment of the range.
• Average speed is obtained by collecting data related to speed and time interval on instantaneous speeds (performed by sampling).