Effects of Additive Ejection on Lifting Hydrofoils

Various effects of polymer additives, other than drag reduction, are discussed with an emphasis on lift effects on two-dimensional hydrofoils. In reviewing effects of additives in homogeneous solution on the pressure distributions on foils it is suggested that high strain rate phenomena which could occur near leading edges not be ruled out as a contributory cause. In connection with effects accompanying additive injection, existing data on anomalous pressures associated with slit injection into a pipe are reviewed and correlated on the basis of a slit Deborah number: De = V_iτR/t_i. The same parameter is shown to give a good correlation of lift changes measured for three different polymers, two slit velocities, and a single flow speed. Then a large amount of HYDRONAUTICS data on a single foil of 10 cm chord is correlated. These correlations show that lift changes vary as V^2.5 for De fixed, while for fixed speed the lift change grows with De, reaches a maximum for a value of De ≃ 20 and then declines and finally reaches negative values. The effects and degree of correlation are very much dependent on foil incidence and injection slit location. No physical model of the effects yet exist, but the data suggest that viscoelastic phenomena associated with the slit are involved. One possible interpretation of the correlated data is that the injected fluid forms an artificial bump whose thickness scales with V^1/2 and whose length depends upon De. The subject of polymer lift effects is of importance in connection with the performance of propellers in polymer wakes on torpedos and with the use of polymers for improvement of hydrofoil and propeller efficiency.