Experimental and numerical study of sink flow turbulent boundary layers

Abstract

Sink flow turbulent boundary layers (TBLs) develop in the incompressible flow be- tween two convergent, plane smooth walls and represent a family of favorable pres- sure gradient TBLs. These are the only smooth wall TBLs known to be in perfect equilibrium/self-preservation. The present thesis reports an experimental and numerical investigation of these sink flow TBLs. Particle Image Velocimetry (PIV) measurements were used to analyze the outer region of the boundary layer and it is shown that these TBLs possess a laminar-like outer region while maintaining the near-wall turbulence structure just as in any other wall-bounded turbulent flow. The implications of this for the inner/outer interaction and the absence of mean entrainment into the boundary layer are discussed. Two perturbation experiments were performed to understand the equilibrium state of the sink flow. In the first exercise, surface roughness effects on the sink flow are studied. Roughness while destroying the equilibrium in wall scaling, admits self-similarity in laminar-like coordinates. The effect of roughness on turbulence fluctuations of sink flow is shown to be the opposite of pressure gradient effects. Roughness increased turbulent stresses in the outer region while favorable pressure gradient attenuated the stresses. The second perturbation exercise involved introducing a thin spanwise cylinder into the sink ow TBL. The perturbation decays down with distance and the relaxation process back to original equilibrium state was found to occur at about 10 boundary layer thicknesses downstream. Direct Numerical Simulations (DNS) of five different sink flow cases were performed to investigate those aspects of the ow inaccessible to experimental techniques. The physical processes behind the zero mean entrainment behaviour in sink flow TBLs are studied. The turbulent kinetic energy budget showed that all the terms in the budget are an order of magnitude smaller than in a zero-pressure-gradient turbulent boundary layer (ZPG TBL) with a comparable Reynolds number. The large eddy structure of sink flow in the outer region is seen to be much weaker than in a ZPG TBL which plays an important role in explaining the zero mean entrainment. It is shown that the skewness of wall-normal fluctuations near the wall are negative in sink flow TBLs. This result combined with a quadrant analysis indicates that sink flow TBLs contain minimal `inactive' motion compared to a ZPG TBL with similar Reynolds number. In light of the present results, it is argued that the sink flow TBL presents a canonical case to study near- wall turbulence without the complicating features present in other near-equilibrium/non- equilibrium ows. The utility of studying sink flow TBLs towards modeling other general TBLs is outlined.