Streamwise development of turbulent boundary-layer drag reduction with polymer injection

Zero-pressure-gradient turbulent boundary-layer drag reduction by polymer injection has been studied with particle image velocimetry. Flow fields ranging from low to maximum drag reduction have been investigated. A previously developed technique - the (1 - y1 delta) fit to the total shear stress profile - has been used to evaluate the skin friction, drag reduction and polymer stress. Current results agree well with the semi-log plot of drag reduction vs. normalized polymer flux which has been used by previous workers and can be used as a guide to optimize the use of polymer from a single injector. Detailed flow-field statistics show many special features that pertain to polymer flow. It is shown that the mean velocity responds quickly to the suddenly reduced wall shear stress associated with polymer injection. However, it takes a much longer time for the entire Reynolds shear stress profile to adjust to the same change. The Reynolds shear stress profiles in wall units can be higher than unity and this unique feature can be used to further judge whether the flow is in equilibrium. The streamwise evolution of drag reduction magnitude is used to divide the flow into three regions: development region; steady-state region; and depletion region. The polymer stress is estimated and found to be proportional to drag reduction in the depletion region, but not necessarily so in the other regions. The interaction between injected polymer and turbulent activity in a developing boundary-layer flow is dependent upon the flow history and it produces an equally complex relationship between polymer stress and drag reduction. The stress balance in the boundary layer and the dynamical contribution of the various stresses to the total stress are evaluated and it is seen that the polymer stresses can account for up to 25% of the total stress. This finding is in contrast to channel flows with homogeneous polymer injection where the polymer stress is found to account for up to 60% of the total stress.