An implicit numerical solution of the turbulent three-dimensional incompressible boundary-layer equations

A method of solving the three-dimensional, incompressible turbulent boundary-layer equations was developed using a Crank-Nicholson implicit finite-difference technique, with the turbulent stress terms modeled with an eddy-viscosity model obtained from mixing length theory. The method was applied to two three-dimensional flow geometries for which experimental data exists and a comparison with this data showed excellent agreement. The complete computer program was sufficiently generalized for application to two-dimensional laminar and turbulent flows with arbitrary pressure gradients. The method was applied to several such test cases and the solutions agreed well with both theory and experiment. An analysis was presented to determine the conditions for which the finite difference equations were stable and convergent. The results of this analysis demonstrated that the equations are generally stable and convergent. However, care must be exercised when writing the finite difference approximation to the continuity equation, because certain finite difference formulations of the continuity equation can lead to an instability when the initial values for the distribution of the velocity normal to the bounding surface cannot be accurately specified.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mechanical Engineering

Department dc:contributor.department

Mechanical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1971

Author dc:creator

• Klinksiek, William Frederick

Chair dc:contributor.committeechair

• Pierce, Felix J.

Committee members dc:contributor.committeemember

• Jones, J. B.
• Wood, Henry L.
• Comparin, Robert A.
• Martin, Charles K.

• turbulent stress terms

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-05192010-020209

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/37827