Why do we need stators in compressors or turbines?

One way to look at what happens in a turbine: At the first rotor, the blade can move due to pressure of the moving gas and gets energy transferred from the moving gas and momentum is transferred. Power transferred will be 'pressure times blade speed'. At the first stator, because the stator is attached to the 'Earth' it will not move so Pressure times speed is zero. Conservation of Momentum means there is a finite motion but the moving gas has the same speed ('bounces' with equal opposite velocity). It retains all (most ) of the Kinetic energy and is moving in the right direction for the next rotor.

At the second rotor, the moving gas can give additional KE to the blades (pressure times speed). Same for second stator; no energy transferred and for the second rotor; more KE transferred. Each layer of rotating blades can acquire more energy but none goes to the stators. The shapes and pressures are chosen to maximise this because the pressures / gas speed decreases along the turbine.

Without the stators, the angle of gas flow would need to change from rotor to rotor. The gas would end up 'chasing' the subsequent blades and the leading edges would have to be angled more and more. A pretty smart piece of non-intuitive design imo.

One way to look at what happens in a turbine: At the first rotor, the blade can move due to pressure of the moving gas and gets energy transferred from the moving gas and momentum is transferred. Power transferred will be 'pressure times blade speed'. At the first stator, because the stator is attached to the 'Earth' it will not move so Pressure times speed is zero. Conservation of Momentum means there is a finite motion but the moving gas has the same speed ('bounces' with equal opposite velocity). It retains(most ) of the Kinetic energy and is moving in the right direction for the next rotor.At the second rotor, the moving gas can give additional KE to the blades (pressure times speed). Same for second stator; no energy transferred and for the second rotor; more KE transferred. Each layer of rotating blades can acquire more energy but none goes to the stators. The shapes and pressures are chosen to maximise this because the pressures / gas speed decreases along the turbine.Without the stators, the angle of gas flow would need to change from rotor to rotor. The gas would end up 'chasing' the subsequent blades and the leading edges would have to be angled more and more. A pretty smart piece of non-intuitive design imo.