Multistage compressor and method for operating a multistage compressor

A multi-stage compressor comprising:

• a rotor comprising a plurality of axially stacked impellers;
• a tie rod extending through the stacked impellers and holding the stacked impellers together;
• a gas compression path extending from a compressor inlet to a compressor outlet and through the stacked impellers;
• and
• a flow channel between the tie rod and the stacked impellers, the flow channel developing along at least a portion of the tie rod,
• wherein the flow channel is in fluid communication with a first location along the gas compression path and a second location along the gas compression path, a pressure difference between the first location and the second location in the gas compression path generating a gas flow along the flow channel.