Construction :
The arrangement of Roots Blower , which is simply a development of gear pump. To get higher pressure ratio, three or four lobes are used. It consists of two rotors called lobes which are aligned in different parallel axis. One of the rotors is connected to the drive and the second rotor is driven from the first. The two rotors rotates in opposite directions i.e one in clockwise direction and the other in anti clockwise direction. The lobes of the rotors are of epicycloids, hypocycloids, or involute profile to ensure correct matching. There match must be a small clearance between the lobe and casing to reduce the wear of moving parts.
Working :
When the power is given to the roots blower, rotors rotate and the air at atmospheric pressure is trapped between the lobe and casing. The trapped air moves along the casing and discharged into the receiver. The flow area from entry to exit remains constant. So, there is no developing in pressure. When the exit port opens, some high pressure air from receiver will rush back and mixed up with entrapped air until the pressure is equalized. Thus, The pressure of the entrapped air is increased by back flow of air. The p-V diagram for this type of compressor.
For p-V diagram, we infer that the pressure rise takes place at the irreversible constant volume.
Work done per cycle = V(p2-p1).
But Work done per revolution = 4V( p2 - p1 ) [ Two lobes ]
We know that the ideal compression of takes place at reversible adiabatic process.
Roots Efficiency = Ideal Work done / Actual Work done
Therefore, The roots blower efficiency decreases with increase in pressure ratio.
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