2. You are working for a glider manufacturer and have been asked to analyse the laminar boundary layer at a certain point on the smooth wing. The velocity profile at this point, u(y), is given by: น Us 2 3 3 (15)²³ – ² (3) ³ - + A + B where & is the boundary-layer thickness and us is the velocity at the edge of the boundary layer. A and B are constants. a) Determine the values of A and B such that the primary boundary conditions for the velocity profile are satisfied. Is it necessary to apply any auxiliary boundary conditions? b) Evaluate the boundary-layer shape factor, H. c) At the point of separation, the wall shear stress goes from positive to negative. Thus, show that the boundary layer at this location is on the point of separating. d) Show that the pressure on the wing surface is increasing with downstream distance. Is this consistent with your calculations showing that the boundary layer is approaching separation? Explain your reasoning.
You are working for a glider manufacturer and have been asked to analyse the laminar boundary layer at a certain point on the smooth wing. The velocity profile at this point, ?(?), is given by:
? =3A?C" −2A?C# +?A?C+? ?! δ δ δ
where δ is the boundary-layer thickness and ?$ is the velocity at the edge of the boundary layer. ? and ? are constants.
Determine the values of ? and ? such that the primary boundary condi9ons for the velocity profile are sa9sfied. Is it necessary to apply any auxiliary boundary condi9ons?
Evaluate the boundary-layer shape factor, H.
At the point of separa9on, the wall shear stress goes from posi9ve to nega9ve. Thus, show that the boundary layer at this loca9on is on the point of separa9ng.
Show that the pressure on the wing surface is increasing with downstream distance. Is this consistent with your calcula9ons showing that the boundary layer is approaching separa9on? Explain your reasoning.
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