Transition Zone In Constant Pressure Boundary Layer With Converging Streamlines

Abstract

The laminar-turbulent transition in viscous fluid flows is one of the most intriguing problems in fluid dynamics today. In view of the enormous applications it has in a variety of fields such as aircraft design, turbomachinery, etc., scientists have now realized the importance of tackling this problem effectively. Three-dimensional flows are usually associated with pressure gradient, streamline curvature, streamline convergence / divergence etc., all acting simultaneously. Towards a better understanding of the transition process and modeling the transition zone, it is important to study the effect of each of these parameters on the transitional flow. The present work aims at studying experimentally the effect of lateral streamline convergence alone on the laminar-turbulent transition zone under constant stream-wise pressure.

The experimental setup consists of a low turbulence wind tunnel with its test section modified to cause lateral streamline convergence under constant pressure. This is achieved by converging the side-walls and appropriately diverging the roof, thus maintaining a constant stream-wise pressure. The half angle of convergence is chosen as 100 , which is approximately the same as the half of the turbulent spot envelope in constant pressure two-dimensional flows.

Experiments are carried out to analyze the development of the laminar and transitional boundary layers, intermittency distribution in the transition zone and the overall characteristics of an artificially induced turbulent spot.

The laminar velocity profiles are found to be of the Blasius type for two-dimensional constant pressure flows. However, the converging streamlines are found to contribute to an increased thickness of the boundary layer as compared to the corresponding two-dimensional flow.

The intermittency distribution in the transition zone is found to follow the universal intermittency distribution for two-dimensional constant pressure flow. A simple linear-combination model for two-dimensional flows is found to perform very well in predicting the measured velocity profiles in the transition zone.

An artificially introduced turbulent spot is found to propagate along a conical envelope with an apex cone angle of 220 which is very nearly the value for a corresponding constant pressure two-dimensional flow. The spot shapes and celerities are also comparable to those in two-dimensional flow.

In summary, the present study brings out many similarities between a constant pressure laterally converging flow and a constant pressure two-dimensional flow.