A turbomachine having a longitudinal axis and a flowpath, comprising a compressor, the compressor comprising: an impeller circumferentially disposed around the longitudinal axis; an impeller shroud comprising a surface having an inlet edge and an outlet edge, the impeller shroud coupled to and extending around a portion of the impeller; wherein the turbomachine further comprises: a plurality of openings formed through the impeller shroud, disposed within a region defined by the inlet edge of the impeller shroud and a substantially medial line circumferentially around the impeller shroud, wherein the medial line defines a midpoint on the shroud; each opening of the plurality of openings providing fluid communication between the flowpath and a dead-headed plenum, wherein there are no other openings in the dead-headed plenum; the openings each having a respective centerline axis and located on the impeller shroud at a respective radial distance measured perpendicular from the longitudinal axis, and wherein, for each opening, its centerline axis forms an angle in relation to the radial distance measure, characterised in that the centerline axis of each opening isnot perpendicular to the longitudinal axis, and in that each of the plurality of openings has the same dimensions, is medially located and is circumferentially aligned on the surface of the impeller shroud. an impeller circumferentially disposed around the longitudinal axis; an impeller shroud comprising a surface having an inlet edge and an outlet edge, the impeller shroud coupled to and extending around a portion of the impeller; wherein the turbomachine further comprises: a plurality of openings formed through the impeller shroud, disposed within a region defined by the inlet edge of the impeller shroud and a substantially medial line circumferentially around the impeller shroud, wherein the medial line defines a midpoint on the shroud; each opening of the plurality of openings providing fluid communication between the flowpath and a dead-headed plenum, wherein there are no other openings in the dead-headed plenum; the openings each having a respective centerline axis and located on the impeller shroud at a respective radial distance measured perpendicular from the longitudinal axis, and wherein, for each opening, its centerline axis forms an angle in relation to the radial distance measure, characterised in that the centerline axis of each opening isnot perpendicular to the longitudinal axis, and in that each of the plurality of openings has the same dimensions, is medially located and is circumferentially aligned on the surface of the impeller shroud. a plurality of openings formed through the impeller shroud, disposed within a region defined by the inlet edge of the impeller shroud and a substantially medial line circumferentially around the impeller shroud, wherein the medial line defines a midpoint on the shroud; each opening of the plurality of openings providing fluid communication between the flowpath and a dead-headed plenum, wherein there are no other openings in the dead-headed plenum; the openings each having a respective centerline axis and located on the impeller shroud at a respective radial distance measured perpendicular from the longitudinal axis, and wherein, for each opening, its centerline axis forms an angle in relation to the radial distance measure, characterised in that the centerline axis of each opening isnot perpendicular to the longitudinal axis, and in that each of the plurality of openings has the same dimensions, is medially located and is circumferentially aligned on the surface of the impeller shroud.