An Application of Octant Analysis to Turbulent and Transitional Flow Data

Abstract

A technique called “octant analysis” was used to examine the eddy structure of turbulent and transitional heated boundary layers on flat and curved surfaces. The intent was to identify important physical processes that play a role in boundary layer transition on flat and concave surfaces. Octant processsing involves the partitioning of flow signals into octants based on the instantaneous signs of the fluctuating temperature, t′, streamwise velocity, u′, and cross-stream velocity, v′. Each octant is associated with a particular eddy motion. For example, u′ <0, v′>0, t′>0 is associated with an ejection or “burst” of warm fluid away from a heated wall. Within each octant, the contribution to various quantities of interest (such as the turbulent shear stress, −u′v′ , or the turbulent heat flux, v′t′ ) can be computed. By comparing and contrasting the relative contributions from each octant, the importance of particular types of motion can be determined. If the data within each octant are further segregated based on the magnitudes of the fluctuating components so that minor events are eliminated, the relative importance of particular types of motion to the events that are important can also be discussed. In fully developed, turbulent boundary layers along flat plates, trends previously reported in the literature were confirmed. A fundamental difference was observed in the octant distribution between the transitional and fully turbulent boundary layers, however, showing incomplete mixing and a lesser importance of small scales in the transitional boundary layer. Such observations were true on both flat and concave walls. The differences are attributed to incomplete development of the turbulent kinetic energy cascade in transitional flows. The findings have potential application to modeling, suggesting the utility of incorporating multiple length scales in transition models.