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• Turbulent Pipe Flow (LES) - Numerical Solution

# Turbulent Pipe Flow (LES) - Numerical Solution

Author: Ranjith Tirunagari, Cornell University

# Numerical Solution

#### Solution Methods

Click on Solution Methods then click on Momentum and select Bounded Central Differencing as shown in the image below. Also choose, Second order for Pressure and Second Order Implicit under Transient Formulation.  as

#### Set Initial Guess

Here, the flow field will be initialized to the values at the inlet. In order to carry out the initialization click on Solution Initialization then click on Compute from and select inlet as shown below.

Then click initialize to initialize the domain with an initial guess. This completes the initialization.

#### Set Convergence Criteria

FLUENT reports a residual for each governing equation being solved. The residual is a measure of how well the current solution satisfies the discrete form of each governing equation. We'll iterate the solution until the residual for each equation falls below 1e-6. In order to specify the residual criteria (Click) Monitors > Residuals > Edit..., as shown in the image below.

Next, change the residual under Convergence Criterion for continuityx-velocity,and y-velocity, all to 1e-6, as can be seen below.

Lastly, click OK to close the Residual Monitors menu.

#### Execute Calculation

Note that, we have to run the transient simulation to a statistically stationary state and then collect statistics. Click on Run Calculation then choose the Time Step Size(s) as 1e-05 and the Number of Time Steps  as 20000. Also choose Extrapolate Variables option (refer to FLUENT documentation for information) and leave the Max Iterations/Time Step as 20 (default). The corresponding image is shown below.

As a safeguard save the project now. Now, click on Calculate in order to run the calculation. The residuals for each iteration are printed out as well as plotted in the graphics window as they are calculated. The residuals decrease during the inner iterations and jump again when we advance by one time step as shown in image below.

From the above inputs, it is clear that 20 inner iterations are carried out to advance the simulation by one time step and we requested for 20,000 time steps. So, typically these simulations are very long even if we use 4 processors. To reduce the simulation time one can opt to High Performance Computing (HPC) resources. The calculations performed for this tutorial are based on the simulations run on an HPC cluster using 48 cores.