# Laminar Couette Flow with Imposed Pressure Gradient

In this application, AcuSolve is used to simulate the viscous flow of water between a moving and a stationary plate with an imposed pressure gradient. AcuSolve results are compared with analytical results described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with imposed pressure gradients.

## Problem Description

## AcuSolve Results

## Summary

The velocity profile computed by AcuSolve agrees well with the analytical solution for this application. The velocity profile arises due to the combination of the imposed pressure gradient and the constant upper-wall velocity. Note that the combination of these effects results in the asymmetric velocity profile that is reflected in the results.

## Simulation Settings for Laminar Couette Flow with Imposed Pressure Gradient

AcuConsole database file: <your working directory>\couette_flow\couette_flow.acs

Global

- Problem Description
- Analysis Type - Steady State
- Turbulence equation - Laminar

- Auto Solution Strategy
- Relaxation factor -
`0.2`

- Relaxation factor -
- Material Model
- Air
- Density -
`1.0`kg/m3 - Viscosity -
`1.0`kg/m-sec

- Density -

- Air
- Body Force
- DP/DL
- Gravity
- Z-component -
`18.0`m/sec2

- Z-component -

- Gravity

Model

- DP/DL
- Volumes
- Fluid
- Element set
- Material model - Air
- Body force - DP/DL

- Element set

- Fluid
- Surfaces
- Max_X
- Simple Boundary Condition
- Type - Symmetry

- Simple Boundary Condition
- Max_Y
- Simple Boundary Condition
- Type - Wall
- Wall velocity type - Cartesian
- Z-velocity -
`3.0`m/s

- Simple Boundary Condition
- Max_Z
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)

- Min_X
- Simple Boundary Condition
- Type - Symmetry

- Simple Boundary Condition
- Min_Y
- Simple Boundary Condition
- Type - Wall

- Simple Boundary Condition
- Min_Z
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)

- Max_X
- Periodics
- Periodic 1
- Periodic Boundary Conditions
- Type - Periodic

- Periodic Boundary Conditions

- Periodic 1

## References

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