A method of attenuating fluid dynamic pulsations that propagate through a flow of fluid at a convective velocity of the fluid, the pulsations having an organized vortical structure includes directing the flow to a pulsation dampener inlet having a first area and transitioning the organized vortical structure to a small-scale turbulent structure by squeezing the vorticies by passing the flow of fluid through a passage having a second area that is smaller than the first area, then rapidly expanding the flow of fluid by passing it into a chamber having a third area measured at an inlet of the chamber that is substantially larger than the second area. The method also includes discharging the flow of fluid from the chamber. The flow of fluid includes substantially attenuated fluid dynamic pulsations and acoustic pulsations that travel through the flow of fluid at the speed of sound.