What is the physics behind using smaller blades in combination with larger ones in the turbo machines. It might improve the performance, but how does the physics goes with it.
The axial flow compressor is one type of turbo machines. It has movable blades (attched to rotor) and fixed blades (attached to the stator). The pressure ratio developed by the axial flow compressor per stage (Euler's theorem).is the summation of kinetic energy component (due to change of absoulte velocites at inlet and outlet) and diffusion component (with increase of area from the base of the blade to the tip of the blade) . The profile of the blades is of aerofoil type. Size of the blades (movable and fixed) are not equal in order to keep velocity of flow constant so as to minimize the force on bearing of the shaft.
I assume the smaller blades are useful to increment the blade surface at lower radii of the rotor. Observe that the lift force that can be generated by the blades at their sections at small radii is less, because the circumferencial velocity is lower at small radii. So in order to avoid a lesser pressure change at lower radii their surface area can be increased. Increase of angle of attack is also used, but that would be limited up to the stalling angle.
There are several [papers written about this design. In radial machines the different sizes blades are necessary inorder to avoid choking at inlet especially at high gas fluid flow rate , That is why the smaller blades are a little downstream
In radial compressor rotor with large exit/inlet radius ratio th change of relative velocity in the circumferential direction of blade passage is very significant. It causes so called "jet-wake" flow structures at the rotor exit which are responsible for losses and disturbances in the diffuser, behind the rotor. In order to control the flow path we can add second row of so called "splitter vanes" which allows to improve the stage efficiency in partial loads operation.