A supersonic compressor system comprising: a casing defining a cavity extending between a fluid inlet and a fluid outlet; a first drive shaft positioned within said cavity, wherein a centerline axis extends along a centerline of said first drive shaft; a supersonic compressor rotor coupled to said first drive shaft and positioned in flow communication between said fluid inlet and said fluid outlet, said supersonic compressor rotor comprising a radially outer surface and a plurality of vanes, adjacent vanes and the radially outer surface defining a flow channel with at least one supersonic compression ramp positioned within the flow channel and configured to form at least one compression wave for compressing a fluid; and a centrifugal compressor assembly positioned in flow communication between said supersonic compressor rotor and said fluid outlet, said centrifugal compressor assembly configured to compress fluid received from said supersonic compressor rotor; wherein said supersonic compressor rotor comprises: a rotor disk comprising an upstream surface, a downstream surface, and the radially outer surface that extends generally axially between said upstream surface and said downstream surface, said radially outer surface comprising an inlet surface, an outlet surface, and a transition surface extending between said inlet surface and said outlet surface; and the plurality of vanes being coupled to said radially outer surface, adjacent said vanes forming a pair and oriented such that the flow channel is defined between each said pair of adjacent vanes, said flow channel extending between an inlet opening and an outlet opening, said inlet surface extending between said inlet opening and said transition surface and oriented substantially perpendicular with respect to said centerline axis to define a radial flow path at said inlet opening, said outlet surface extending between said outlet opening and said transition surface and oriented substantially parallel with respect to said centerline axis to define an axial flow path at said outlet opening. a casing defining a cavity extending between a fluid inlet and a fluid outlet; a first drive shaft positioned within said cavity, wherein a centerline axis extends along a centerline of said first drive shaft; a supersonic compressor rotor coupled to said first drive shaft and positioned in flow communication between said fluid inlet and said fluid outlet, said supersonic compressor rotor comprising a radially outer surface and a plurality of vanes, adjacent vanes and the radially outer surface defining a flow channel with at least one supersonic compression ramp positioned within the flow channel and configured to form at least one compression wave for compressing a fluid; and a centrifugal compressor assembly positioned in flow communication between said supersonic compressor rotor and said fluid outlet, said centrifugal compressor assembly configured to compress fluid received from said supersonic compressor rotor; wherein said supersonic compressor rotor comprises: a rotor disk comprising an upstream surface, a downstream surface, and the radially outer surface that extends generally axially between said upstream surface and said downstream surface, said radially outer surface comprising an inlet surface, an outlet surface, and a transition surface extending between said inlet surface and said outlet surface; and the plurality of vanes being coupled to said radially outer surface, adjacent said vanes forming a pair and oriented such that the flow channel is defined between each said pair of adjacent vanes, said flow channel extending between an inlet opening and an outlet opening, said inlet surface extending between said inlet opening and said transition surface and oriented substantially perpendicular with respect to said centerline axis to define a radial flow path at said inlet opening, said outlet surface extending between said outlet opening and said transition surface and oriented substantially parallel with respect to said centerline axis to define an axial flow path at said outlet opening. a rotor disk comprising an upstream surface, a downstream surface, and the radially outer surface that extends generally axially between said upstream surface and said downstream surface, said radially outer surface comprising an inlet surface, an outlet surface, and a transition surface extending between said inlet surface and said outlet surface; and the plurality of vanes being coupled to said radially outer surface, adjacent said vanes forming a pair and oriented such that the flow channel is defined between each said pair of adjacent vanes, said flow channel extending between an inlet opening and an outlet opening, said inlet surface extending between said inlet opening and said transition surface and oriented substantially perpendicular with respect to said centerline axis to define a radial flow path at said inlet opening, said outlet surface extending between said outlet opening and said transition surface and oriented substantially parallel with respect to said centerline axis to define an axial flow path at said outlet opening.