Instability and transition estimates of laminar boundary layers
A rough estimate of the location of the point of instability (critical point) or transition can be obtained from semi–empirical correlations, such as e.g.:
– for the point of instability: ,Re exp(26.3 8 )crit H (after Wieghardt)
– for the point of transition: 0.4, , Re 2.9(Re )trans x trans (after Michel)
a. Apply these correlations to determine the point of instability and the point of transition for the following self–similar boundary layer flows.
Give in both cases the values for Rex as well as Reθ.
–i– flat plate flow: 1/ 22.591 0.664 RexH x
–ii– stagnation point flow: 1/ 22.216 0.292 RexH x
b. Based on these estimates, what can you conclude about the effect of the pressure gradient on the stability of a laminar boundary layer?
c. The velocity profile of the asymptotic suction boundary layer is given by the exponential function: 1 with: w
e
yvu eu
where wv is the normal velocity at the wall (for suction wv is negative).
Determine with the given correlation for the instability point, how large the suction velocity w must be chosen, in order to keep the boundary layer on the margin of stability.
