A turbofan engine , comprising: a turbomachinery core operable to produce a flow of combustion gases; a low-pressure turbine configured to extract energy from the flow of combustion gases so as to drive a fan to produce a fan flow, the fan being configured such that at least a portion of the fan flow exits the turbofan engine without passing through a turbine; and at least one variable-cycle device operable to vary a backpressure downstream of the fan ; wherein the fan includes: a rotor comprising at least one rotor stage including a rotatable disk defining a rotor flowpath surface and an array of axial-flow rotor airfoils extending outward from the rotor flowpath surface; and at least one stator stage comprising a wall defining a stator flowpath surface, and an array of axial-flow stator airfoils extending away from the stator flowpath surface; and at least one of the rotor or stator stages includes an array of airfoil-shaped splitter airfoils extending from at least one of the rotor flowpath surface or the stator flowpath surface, wherein splitter airfoils of the array of airfoil-shaped splitter airfoils alternate with rotor airfoils of the array of axial-flow rotor airfoils or stator airfoils of the array of axial-flow stator airfoils of the corresponding stage, wherein at least one of a chord dimension of the splitter airfoils of the array of airfoil-shaped splitter airfoils and a span dimension of the splitter airfoils of the array of airfoil-shaped splitter airfoils is less than the corresponding dimension of the rotor airfoils of the array of axial-flow rotor airfoils and the stator airfoils of the array of axial-flow stator airfoils of the at least one of the rotor or stator stages. a turbomachinery core operable to produce a flow of combustion gases; a low-pressure turbine configured to extract energy from the flow of combustion gases so as to drive a fan to produce a fan flow, the fan being configured such that at least a portion of the fan flow exits the turbofan engine without passing through a turbine; and at least one variable-cycle device operable to vary a backpressure downstream of the fan ; wherein the fan includes: a rotor comprising at least one rotor stage including a rotatable disk defining a rotor flowpath surface and an array of axial-flow rotor airfoils extending outward from the rotor flowpath surface; and at least one stator stage comprising a wall defining a stator flowpath surface, and an array of axial-flow stator airfoils extending away from the stator flowpath surface; and a rotor comprising at least one rotor stage including a rotatable disk defining a rotor flowpath surface and an array of axial-flow rotor airfoils extending outward from the rotor flowpath surface; and at least one stator stage comprising a wall defining a stator flowpath surface, and an array of axial-flow stator airfoils extending away from the stator flowpath surface; and at least one of the rotor or stator stages includes an array of airfoil-shaped splitter airfoils extending from at least one of the rotor flowpath surface or the stator flowpath surface, wherein splitter airfoils of the array of airfoil-shaped splitter airfoils alternate with rotor airfoils of the array of axial-flow rotor airfoils or stator airfoils of the array of axial-flow stator airfoils of the corresponding stage, wherein at least one of a chord dimension of the splitter airfoils of the array of airfoil-shaped splitter airfoils and a span dimension of the splitter airfoils of the array of airfoil-shaped splitter airfoils is less than the corresponding dimension of the rotor airfoils of the array of axial-flow rotor airfoils and the stator airfoils of the array of axial-flow stator airfoils of the at least one of the rotor or stator stages. <EOS>