Page History

{panel}
[Problem Specification|FLUENT - Laminar Pipe Flow Problem Specification]\\
[1. CreatePre-Analysis Geometry in GAMBIT& Start-up|FLUENT - Laminar Pipe Flow Step 1]\\
[2. Mesh Geometry in GAMBIT|FLUENT - Laminar Pipe Flow Step 2]\\
[3. Specify Boundary Types in GAMBITGeometry|FLUENT - Laminar Pipe Flow Step 3]\\
[4. Set Up Problem in FLUENTSetup (Physics)|FLUENT - Laminar Pipe Flow Step 4 *New]\\
[5. Solve\!Solution|FLUENT - Laminar Pipe Flow Step 5 *New]\\
[6. Analysis Analyze& Results|FLUENT - Laminar Pipe Flow Step 6 *New]\\
[7. Verification Refine& MeshValidation|FLUENT - Laminar Pipe Flow Step 7]\\  
{color:#ff0000}{*}Problem 1{*}{color}\\
[Problem 2|FLUENT - Laminar Pipe Flow Problem 2]
{panel}

h2. Problem 1


h4. Problem

a) Consider the problem solved in this tutorial. At the exit of the pipe,          we can define the error in the calculation of the centerline velocity          as:
{latex}
\large
$$
{\varepsilon} = {\mid U_c - U_{exact} \mid}
$$
{latex}
where _U{_}{_}{~}c{~}_ is the centerline          value from FLUENT and _U{_}{_}{~}exact{~}_ is the exact          analytical value for fully-developed laminar pipe flow. We expect the          error to take the form:
\\
{latex}
\large
$$
{\varepsilon} = {K \Delta r^p }
$$
{latex}
where the coefficient _K_ and the power _p_ depend upon the          method . Consider the solutions obtained on the 100x5, 100x10, and 100x20          meshes. Using MATLAB, perform a linear least squares fit of:

{latex}
\large
$$
{\ln \varepsilon} = {\ln K + p \ln \Delta r}
$$
{latex}
to obtain the coefficients _K_ and _p_. You can look up the          value of _U{_}{_}exact_ from any introductory textbook          in fluid mechanics such as _Fluid Mechanics_ by F. White. Explain          why your values make sense.

b) Repeat the above exercise using the "first-order upwind"          scheme for the momentum equation. Contrast the value of _p_ obtained          in this case with the previous one and explain your results briefly         (2-3 sentences).

h4. Hints

Note that the first or second order discretization applies only to the         convective terms in the Navier-Stokes equations. The viscous terms are         always second order accurate.

Go to [Problem 2|FLUENT - Laminar Pipe Flow Problem 2]\\

[See and rate the complete Learning Module|FLUENT - Laminar Pipe Flow]

[Go to all FLUENT Learning Modules|FLUENT Learning Modules]