A Finite Difference Solution of the Two and Three-Dimensional Incompressible Turbulent Boundary Layer Equations

1973 ◽  
Vol 95 (3) ◽  
pp. 445-458 ◽  
Author(s):  
W. F. Klinksiek ◽  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Three Dimensional ◽  
Mixing Length ◽  
Mean Velocity ◽  
Boundary Layer Equations ◽  
Incompressible Turbulent Boundary Layer ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Transverse Stresses

A modified Crank-Nicholson implicit finite difference formulation is presented for two and three-dimensional turbulent boundary layers. The turbulent stresses are treated after Prandtl’s early mixing length model. “Boundary layer like” assumptions result in only the streamwise and transverse stresses remaining. The specific empirical input is the Maise and McDonald mixing length model. Excellent agreement with two independent experiments is obtained for mean velocity field data. Both experiments included a plane of symmetry to provide a transverse coordinate initial condition.

Application of a General Finite-Difference Method to Boundary Layer Flows

1972 ◽  
Vol 1 (3) ◽  
pp. 146-152
Author(s):  
S. D. Katotakis ◽  
J. Vlachopoulos
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Boundary Layer Flows ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Temperature Boundary ◽  
Dimensional Boundary ◽  
Finite Difference Solution ◽  
Suction Or Injection ◽  
Layer Problem

A straight-forward and general finite-difference solution of the boundary layer equations is presented. Several problems are examined for laminar flow conditions. These include velocity and temperature boundary layers over a flat plate, linearly retarded flows and several cases of suction or injection. The results obtained are in excellent agreement with existing accurate solutions. It appears that any kind of steady, two-dimensional boundary layer problem can be solved thus with accuracy and speed.

Solution of the Incompressible Turbulent Boundary-Layer Equations With Heat Transfer

1970 ◽  
Vol 92 (1) ◽  
pp. 133-141 ◽  
Author(s):  
T. Cebeci ◽  
A. M. O. Smith ◽  
G. Mosinskis
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Incompressible Flows ◽  
Reynolds Shear Stress ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Incompressible Turbulent Boundary Layer ◽  
Implicit Finite Difference ◽  
Stress Term ◽  
Made In

The boundary-layer equations for laminar and turbulent incompressible flows about two-dimensional and axisymmetric flows are solved by an implicit finite-difference method. An eddy-viscosity concept is used to eliminate the Reynolds shear-stress term, and an eddy-conductivity concept is used to eliminate the time mean of the product of fluctuating velocity and temperature. Several flows have been computed by this method, and comparisons with experimental data and with the Bradshaw-Ferriss method are made. In general, the agreement is quite good.

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