Rotary compressors use rotating blades to compress air. Centrifugal compressors use centrifugal force to continuously increase air pressure as it flows through an impeller and diffuser. Axial compressors increase pressure through rotating blades that accelerate air along the axis of rotation. Centrifugal compressors can achieve higher flow rates but lower pressure ratios than axial compressors. Both rotary compressor types operate at higher speeds and can supply more air than reciprocating compressors.

1. ROTARY COMPRESSORS
ROTARY COMPRESSORS: Classification, working principles of
Centrifugal compressor and Axial flow compressor, Surging, Choking
and Stalling. Comparison of Centrifugal and Axial compressor.
Comparison of Reciprocating and Rotary compressors. (7)

2. INTRODUCTION:
In a rotary compressor, the compression of air is achieved due to the
rotating blades fitted in a rotor. It requires less starting torque as compared to
reciprocating compressors because of direct coupling with the prime mover.
Usually, rotary compressors operate at high speed and supplies higher quantity of
air than reciprocating compressors.
CENTRIFUGAL COMPRESSORS:
A centrifugal compressor is of roto-dynamic type in which air flows
continuously and steadily through various parts and the rise in pressure is
primarily due to the centrifugal action. It is used to supply large quantities of air
but at a lower pressure ratio.
A centrifugal compressor consists of four elements namely, inlet buckets,
impeller, diffuser, and casing as shown in Fig. The inlet buckets are attached to the
shaft and rotate with it, which guide air on the impeller. The impeller consists of a
disc on which radial blades are attached. The diffuser surrounds the impeller and
provides diverging passages for air flow, thus increasing the air pressure. The air
coming out from the diffuser is collected in the casing and taken out from the
outlet of the compressor

3. WORKING PRINCIPLE:
The air enters the eye of the compressor at atmospheric pressure and low
velocity. The inlet buckets guide the air to the impeller where it moves radially
outward and is guided by the impeller blades. The impeller increases the
momentum of the air flowing through it, causing a rise in pressure, velocity and
temperature of the air. The air leaving the impeller enters the diffuser where its
velocity is reduced by providing more cross-sectional area for the flow of air. A part
of the kinetic energy of air is converted into pressure energy and further increases
the pressure of air.

5. VARIATION OF VELOCITY AND PRESSURE:
As the air flows through the
impeller and diffuser, there is a variation
of both velocity and pressure as shown in
Fig. Nearly half of the total pressure rise
takes place in the impeller and the
remaining half occurs in the diffuser. A
pressure ratio of 4 can be achieved in
single-stage compressors. For higher
pressure ratios, multi-stage compressors
are used. A pressure ratio of 12:1 is
possible with multi-stage compressors.

6. TYPES OF IMPELLERS:
Impellers are of two types—
single-eye type and double-eyed
type as shown in Fig. (a) and (b),
respectively. In a single-eye type, air
enters into the compressor from one
side only, whereas in a double-eyed
type, air enters from both sides. A
double-eyed type impeller sucks in
more air and has the advantage of
self-balancing over a single-eye
impeller.
In multi-stage compressors,
the output of the first stage is passed
on to the second stage and so on, as
shown in Fig.(c).

7. STATIC AND STAGNATION PROPERTIES
The velocities of air encountered in centrifugal compressors are very high as
compared to that in reciprocating compressors. Therefore, total head quantities should
be taken into account in the analysis of centrifugal compressors. The total head
quantities account for the kinetic energy of the air passing through the compressor.
Consider a horizontal passage of varying area of cross-section, as shown in Fig. ,
through which air flows from left to right. Assuming no external heat transfer and work
transfer to the system, the steady flow energy equation for one kg mass of air flow can
be written as:

8. Temperature T is called the ‘static temperature’; it is the temperature of the
air measured by a thermometer moving with the air velocity. If the moving air is
brought to rest under reversible adiabatic conditions, the total kinetic energy of the
air is converted into thermal energy, thereby increasing its temperature and
pressure. This temperature and pressure of the air are known as ‘stagnation’ or
‘total head’ temperature and pressure. The stagnation quantities are denoted by a
suffix notation o.

9. ADIABATIC AND ISENTROPIC PROCESSES
For an adiabatic compression process, there is no heat
exchange with the surroundings. If the adiabatic process is
reversible (frictionless), then the process is called isentropic
process in which the entropy of the system does not change.
However, in an actual compressor, during adiabatic compression,
there are losses due to friction in air and blade passages, eddies
formation, and shocks at entry and exit. These factors cause
internal heat generation and consequently, the maximum
temperature reached would be higher than that for adiabatic
compression. This results in a progressive increase in entropy.
Such a process, although adiabatic, is not reversible adiabatic or
isentropic.
The isentropic and adiabatic processes for the static and
stagnation values are shown in Fig. on the T-s diagram. Process
1-2 is the isentropic process for the static temperature and 01-02
for the total head temperature. Processes 1-2′ and 01-02′ are the
adiabatic processes for the static and total head temperatures,
respectively.

10. Isentropic Efficiency
Definition: Isentropic efficiency may be defined as the ratio of isentropic
temperature rise to actual temperature rise.
During compression process, work has to be done on the impeller. The energy
balance then gives,

11. COMPARISON OF CENTRIFUGAL AND RECIPROCATING COMPRESSORS

13. Velocity triangle Nomenclature:
Suffix ‘1’ denotes parameters at inlet and ‘2’ at
outlet.
β1 = Angle of the rotor blade at inlet
β2 = Angle of the rotor blade at outlet
α1 = Angle made by entering air or exit angle of
guide blade
α2 = Angle made by the outgoing air from rotor
blade
V1 and V2 = Absolute velocity of air at inlet and
outlet of rotor, m/s
Vr1 and Vr2 = Relative velocity of air at inlet and
outlet of rotor, m/s
Vf1 and Vf2 = Velocity of flow at inlet and outlet
of rotor, m/s
Vw1 and Vw2 = Velocity of whirl at inlet and outlet of rotor, m/s
Vb1 and Vb2 = Mean peripheral velocity of blade tip at inlet and outlet, m/s
R1 and R2 = Inner and outer radii of rotor, m
m = Mass flow rate of air, kg/s
At the inlet to rotor, air enters with absolute velocity V1 making an angle α1
to the direction of motion of blade (usually α1 = 90°), without any shock and
its whirl component Vw1 = 0.

14. Work Requirement (Euler’s Work) for a Centrifugal
Compressor:
The work required/kg of air in a stage of a centrifugal compressor
can be found by applying the moment of momentum theorem.
As per the Newtonian equation, force is given by rate of change of
momentum.
Similarly, rate of change of moment of momentum about the centre
of rotation gives torque.

15. Work Requirement (Euler’s Work) for a Centrifugal Compressor:

16. Different vane shape
• The impellers may be classified depending on the exit angle β2 into (i)
Backward curved vanes, (ii) Radial vanes and (iii) Forward curved
blades.
16

17. Slip Factor of Centrifugal Compressors:
Under ideal conditions, fluid particles follow exactly the same path
of blade profile such that relative velocity at impeller outlet tip is
inclined with the tangential direction at blade tip angle β2 only,
irrespective of mass flow rate, speed etc.
Such an ideal flow is possible when impeller has infinite number of
blades of no thickness.
In actual practice, when impeller has finite number of blades, fluid
is trapped between the impeller vanes due to its inertia and the fluid
is reluctant to flow over the impeller.
This causes a pressure difference across the blades. There is a high
pressure at the leading face and low pressure at the trailing face.
This pressure difference generates a relative velocity gradient and
formation of eddies.
The fluid is thus discharged at a certain average angle β’2 which is
less than β2.
Therefore fluid is said to have slipped with respect to impeller during
its flow across it.

18. Slip and Slip Co-efficient
• It is assumed that the velocities are constant over the cross sectional
area.
• But in actual practice this assumption is not correct as shown if fig,

19. Slip factor depends upon number of blades and is usually 0.9. It does not
reduces the efficiency but only reduces the head developed.

20. Pre-rotation or Pre-whirl
• We know that the velocity at inlet
have more effect on Mach number
at inlet.
• The relative velocity at the inlet
should be minimum, which
reduces the Mach number for a
given eye tip diameter.
• For a fixed eye tip diameter the
Mach number can be reduced by
providing pre-whirl at the inlet
using guide vanes.

21. Pressure coefficient

22. Effect of blade shape on impeller performance