Analysis Characteristics
- Transient Fluid Flow
- Two Dimensional Axisymmetric Internal Flow
- Incompressible Flow
Reference
White, F. M., “Viscous Fluid Flow,” McGraw-Hill, Inc., New York, 1974, pp. 141-143.
Problem Description
For this case, fluid in a long pipe is initially. A uniform, constant pressure gradient is instantaneously applied. Axial flow starts, and gradually approaches Poiseuille flow. The results are compared to an analytic solution from the reference.
Geometry and Boundary Conditions
Initial Condition: u(x,r,t=0)=v(x,r,t=0)=0.0, 
= 4.0
Boundary Conditions: v(x,r=0,t>0)=0.0, u(x,r=1,t>0)=v(x,r=1,t>0)=0.0, p(x=0) = 40, p(x=L) = 0
Results
In the table below the u (axial) velocity versus time (sec) at the pipe inlet on the centerline is compared between Autodesk Simulation CFD and the analytical results
| Benchmark | 2013: Build 20120131 | % Error | 2014: Build 20130102 | % Error | |
| u(x=0,r=0,t=0.05) | 0.1995 | 0.1986 | 0.412 | 0.1989 | 0.287 |
| u(x=0,r=0,t=0.10) | 0.3851 | 0.3838 | 0.325 | 0.3844 | 0.166 |
| u(x=0,r=0,t=0.20) | 0.6517 | 0.659 | 1.089 | 0.660 | 1.275 |
| u(x=0,r=0,t=0.30) | 0.8045 | 0.822 | 2.172 | 0.823 | 2.339 |
