Cooling systems for high pressure compressor systems are provided. The cooling systems may comprise tangential on board injectors (“TOBIs”). The TOBIs may comprise one or more fluid channels configured to conduct cooling fluid flow to components of the compressor, including, for example, disk-hub portions of the compressor. In this regard, the TOBI may be configured to exhaust cooling air in a manner such that the exhausted air has a similar linear velocity of the disk-hub portion. The cooling air may also be exhausted in a manner that is substantially parallel to the disk-hub portion.