# Flow Between Concentric Cylinders

In this application, AcuSolve is used to simulate the flow of water between concentric cylinders. The outer cylinder is held stationary while the inner cylinder rotates with a constant speed. AcuSolve results are compared with analytical results as described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases containing thin annular gaps with flow induced by rotating walls.

## Problem Description

The problem consists of two concentric pipes with water filling the void between them, as shown in the following image, which is not drawn to scale. The radius of the outer pipe is 0.0468 m and the radius of the inner pipe is 0.0178 m. The inner cylinder rotates at 1 rad/sec and the outer cylinder is fixed. The induced flow is laminar and exhibits a steady state behavior. The rotation of the inner cylinder causes the fluid to rotate due to viscous shearing near the wall. As the outer cylinder is fixed, a velocity gradient is generated as a function of radius within the flow domain.
The simulation was performed as a two dimensional problem by restricting flow in the out-of-plane direction through the use of a mesh that is one element thick.

## AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. The velocity of the fluid within the cavity is greatest near the rotating inner cylinder. There is a nonlinear decrease in velocity as a function of distance away from the inner cylinder.
Analytical tangential velocity at four distances away from the center of the rotating inner cylinder are presented with the corresponding AcuSolve results in the following table.
Table 1.
Distance from the center of rotating cylinder (m) Analytical tangential velocity (m/s) AcuSolve tangential velocity (m/s) Percent deviation from analytical
0.020 0.01514 0.01514 0.04
0.025 0.01059 0.01058 0.10
0.030 0.00727 0.00727 0.06
0.035 0.00466 0.00466 0.10

## Summary

The AcuSolve solution compares well with analytical results for the flow between concentric cylinders. In this application, the velocity in the annular fluid region is driven by the viscous stresses on the rotating wall. The AcuSolve tangential velocity is within 0.1 percent of the analytical solution at all radial locations.

## Simulation Settings for Flow Between Concentric Cylinders

HyperWorks CFD database file: <your working directory>\annulus_rotating\annulus_rotating.hm

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Laminar
• Auto Solution Strategy
• Relaxation Factor - 0.2
• Material Model
• Water
• Density - 1000.0 kg/m3
• Viscosity - 0.001 kg/m-sec
• Reference Frame
• Rotating_Cylinder
• Rotation center
• X-coordinate - 0.0 m
• Y-coordinate - 0.0 m
• Z-coordinate - 0.0 m
• Angular velocity

Model

• Volumes
• Volume
• Element set
• Material model - Water
• Surfaces
• Boundary1
• Simple Boundary Condition
• Type - Symmetry
• Boundary2
• Simple Boundary Condition
• Type - Symmetry
• Inner
• Simple Boundary Condition
• Type - Wall
• Reference Frame - Rotating_Cylinder
• Outer
• Simple Boundary Condition
• Type - Wall
• Nodes
• Fixed
• Pressure
• Type - Zero

## References

F. M. White. "Viscous Fluid Flow". Section 3-2.3. McGraw-Hill Book Co., Inc. New York. 1991.