Experiences with the numerical solution of the 3-D laminar boundary layer equations in streamline coordinates

1987 ◽  
Vol 15 (1) ◽  
pp. 93-118 ◽  
Author(s):  
W. Schónauer ◽  
K. Háfele
1959 ◽  
Vol 63 (588) ◽  
pp. 722-722
Author(s):  
R. L. Dommett

It has been found that there is a critical height for “sandpaper” type roughness below which no measurable disturbances are introduced into a laminar boundary layer and above which transition is initiated at the roughness. Braslow and Knox have proposed a method of predicting this height, for flow over a flat plate or a cone, using exact solutions of the laminar boundary layer equations combined with a correlation of experimental results in terms of a Reynolds number based on roughness height, k, and local conditions at the top of the elements. A simpler, yet more general, method can be constructed by taking additional advantage of the linearity of the velocity profile near the wall in a laminar boundary layer.


Author(s):  
Ahmad Fakheri

In thermal science courses, flow over curved objects, like cylinders or spheres are generally discussed qualitatively, followed by the presentation of numerical or experimental results for the drag coefficient, Nusselt number, and flow separation. Rarely, there is much discussion of how solutions are obtained. In this paper the flow separation is first introduced by solving the Falkner-Skan flow. The process for numerical solution of equations is presented to show that the flow separates at a plate angle of about −18°. Comparisons are drawn between this and flow over a cylinder. The non-similar boundary layer equations are then solved flow over a cylinder, using potential flow results for the velocity outside of the boundary layer. This solution shows that the flow separates at 103.5°, which is significantly more than the experimental value of 80°. Using a more realistic velocity for flow outside of the boundary layer, the numerical solution obtained predicts flow separation at an angle of 79°, which is close to the experimental results. All the solutions are obtained using spreadsheets that greatly simplify the analysis.


Author(s):  
S. N. Brown ◽  
K. Stewartson

An analysis is made of the response of a laminar boundary layer to a perturbation, either in the mainstream, or of the boundary conditions at the wall. The disturbance propagates with the mainstream velocity, and the manner in which it decays at large distances downstream is determined by eigensolutions of the boundary-layer equations. The elucidation of the structure of these eigensolutions requires division of the boundary layer into three regions. Comparison of the asymptotic formula obtained for the displacement thickness is made with the numerical results of Ackerberg and Phillips (1).


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