Starting Flow in a Circular Pipe

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® CFD and the analytical results