Effect of a drag-reducing polymer solution ejection on tip vortex cavitation

Experiments regarding the modification of the foil geometry and/or active or passive mass injection in the vortex core have been performed to investigate the possibility of inhibiting tip vortex cavitation. The ejection at very low flow rates of drag-reducing polymer solutions at the tip of hydrofoils and propeller blades has demonstrated effectiveness as a tip vortex cavitation inhibitor. This paper reports the results obtained with an elliptical hydrofoil, of 8cm maximum chord and 12cm haif-span, operating at Reynolds numbers, of =10⁶, much larger than those previously reported in the literature. Lift coefficients and critical cavitation numbers were determined for a variety of flow and polymer solution ejection conditions. Tangential and axial components of the mean velocity as well as velocity fluctuations along the vortex path were also measured. At 12.5 m/s free stream velocity and a variety of angles of attack, the ejection of a 500 ppm aqueous solution of a drag-reducing polymer at a flow rate of about 5 cm³/s leads to a decrease of up to 30% in the cavitation number. This occurs without modification of the lift coefficient and, hence, of the midspan bound circulation of the foil. Moreover, water injection does not cause any appreciable change in the cavitation numbers. The tangential velocity profiles along the vortex path during polymer ejection indicate that the potential region remains the same, while the viscous core dimension increases, and the maximum tangential velocity decreases substantially as compared to the no ejection or water ejection experiments. Thus, the pressure coefficients at the vortex axis are smaller than for the no ejection or water ejection cases and cause the reduction of the critical cavitation numbers. It is speculated that this inhibition effect is due only to swelling of the polymer solution when exiting the ejection orifice.List of symbols a core radius (distance to the vortex axis for maximum tangential velocity) - C ₁ lift coefficient - c _max maximum chord - Cp pressure coefficient at the vortex axis - Cp _min minimum pressure coefficient at the vortex axis - d _e diameter of the ejection port - m ejection flow rate - P reference pressure - P _v vapor pressure - V free stream velocity - V _a axial velocity - V _t tangential velocity - v _r radial component of the velocity resulting from jet swelling - x downstream distance from the tip of the foil - y, r distance to the vortex axis - angle of attack - r difference between the swollen jet and the ejection port radii - boundary layer thickness - tip vortex intensity - _d ( _de ) desinent cavitation number (with ejection) - _i ( _ie ) inception cavitation number (with ejection) - _ii normal stresses - viscosity - v kinematic viscosity - p specific mass