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CENTRIFUGAL COMPRESSOR
There exist a large number of fluid machines in practice which use air, steam and gas (the
mixture of air and products of burnt fuel) as the working fluids. The density of the fluids
changes with a change in pressure as well as in temperature as they pass through the
machines. These machines are called 'compressible flow machines' and more popularly
'turbo machines'
Turbo machines, including centrifugal compressors and pumps, consume a huge amount of
energy in the world, both directly and indirectly. Turbo machinery is a part of everyday life.
They are of central importance in various ways such as aeronautics, petrochemical
processing, generation of power, refrigeration, etc. They contribute to compressors,
turbochargers, pumps, turbines, and other integral equipment.
Apart from the change in density with pressure, other features of compressible flow,
depending upon the regimes, are also observed in course of flow of fluids through turbo
machines. Therefore, the basic equation of energy transfer (Euler's equation) along with the
equation of state relating the pressure, density and temperature of the working fluid and
other necessary equations of compressible flow, are needed to describe the performance
of a turbo machine.
There are three types of turbo machines: fans, blowers, and compressors.
A fan causes only a small rise in stagnation pressure of the flowing fluid. A fan consists of a
rotating wheel (called the impeller), which is surrounded by a stationary member known as
the housing. Energy is transmitted to the air by the power-driven wheel and a pressure
difference is created, providing air flow. In the analysis of the fan, the fluid will be treated
as incompressible as the density change is very small due to small pressure rise. Examples
include ceiling fans, house fans, and propellers. In blowers, air is compressed in a series of
successive stages and is often led through a diffuser located near the exit. Blower shaft
speeds are up to 30,000 rpm or more. Examples include centrifugal blowers and squirrel
cage blowers in automobile ventilation systems, furnaces, and leaf blowers.
The basic difference between the above three devices is the way they move or transmit
air/gas and induce system pressure. Compressors, Fans and Blowers are defined by ASME
(American Society of Mechanical Engineers) as the ratio of the discharge pressure over the
suction pressure. Fans have the specific ratio up to 1.11, blowers from 1.11 to 1.20 and
compressors have more than 1.20.
Compressor types can be mainly grouped into two: Positive Displacement & Dynamic.
Positive displacement compressors are again of two types: Rotary and Reciprocating.
Types of Rotary compressors are Lobe, Screw, Liquid Ring, Scroll, and Vane. Types of
reciprocating compressors are Diaphragm, Double acting, and Single acting. Dynamic
Compressors can be categorized into Centrifugal and Axial.
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Positive displacement compressors use a system which induces in a volume of air in a
chamber, and then reduce the volume of the chamber to compress the air. As the name
suggests, there is a displacement of the component that reduces the volume of the
chamber thereby compressing air/gas. On the other hand, in a dynamic compressor, there
is a change in velocity of the fluid resulting in kinetic energy which creates pressure.
Reciprocating compressors use pistons where discharge pressure of air is high, the quantity
of air handled is low and which has a low speed of the compressor. They are suitable for
medium and high-pressure ratio and gas volumes. On the other hand, rotary compressors
are suitable for low and medium pressures and for large volumes. These compressors do
not have any pistons and crankshaft. Instead, these compressors have screws, vanes, scrolls
etc. So they can be further categorized on the basis of the component they are equipped
with.
Energy Equation
The following are the notations used in the analysis of a centrifugal compressor.
α1 = Exit angle from the guide vanes at entrance = absolute angle at impeller inlet
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α2 =absolute angle at impeller outlet or inlet angle to vaneless diffuser
β1 = Inlet angle to the impeller
β2 = Outlet angle from the impeller
U1 = peripheral velocity or Mean blade velocity at inlet
U2 = peripheral velocity or Mean blade velocity at exit
V1 = Absolute velocity of air at inlet to the impeller
V2 = Absolute velocity of air at exit to the impeller
Vr1 = Relative velocity of air at inlet to the impeller blade
Vr2 = Relative velocity of air at exit to the impeller blade
Vw1 = Velocity of whirl at inlet (tangential component of absolute velocity V1)
Vw2 = Velocity of whirl at exit (tangential component of absolute velocity V2)
Vf1 = Velocity of flow or meridonal velocity at inlet (Component of V1 perpendicular to the
plane of rotation)
Vf2 = Velocity of flow or meridonal velocity at exit (Component of V2 perpendicular to the
plane of rotation)
m = Mass flow rate, kg/sec
The angles should match with vane or blade angles at inlet and outlet respectively for a
smooth, shockless entry and exit of the fluid to avoid undesirable losses.
Figure shows the velocity triangles at the inlet and outlet of a rotor. The inlet and outlet
portions of a rotor vane are only shown as a representative of the whole rotor.
Assumptions
1. Flow is steady and uniform.
2. Fluid enters and leaves the vane in a direction tangential to the vane tip at inlet and
outlet.
3. There is no flow separation anywhere along the blade surface.
Euler’s Turbine Equation
Angular Velocity of wheel (rotational Speed) (rad/sec)
Tangential Momentum of the fluid at entry
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Moment of momentum or angular momentum at entry
Similarly Angular Momentum at the outlet
T= Torque on the wheel = Rate of change of angular momentum
Work done = Rate of energy transferred per unit time = Torque х Angular velocity
But
Work done W
If
the machine is called Turbine. Energy is transferred from
fluid to rotor.
If
the machine is called pump, fan, compressor or blower.
Energy is transferred from rotor to fluid.
Euler’s Equation
If H is the head on the machine, then energy transfer can be written as
Therefore Euler’s Equation will become
Energy transfer per unit weight
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Components of Energy Transfer
It is worth mentioning in this context that either of the Equations is applicable regardless of
changes in density or components of velocity in other directions. Moreover, the shape of
the path taken by the fluid in moving from inlet to outlet is of no consequence. The
expression involves only the inlet and outlet conditions.
Now we shall apply a simple geometrical relation as follows: From the inlet velocity triangle,
Similarly from the outlet velocity triangle
Invoking the expressions of U1VW1and U2VW2 in Euler’s Eq., we get H (Work head, i.e. energy
per unit weight of fluid, transferred between the fluid and the rotor as) as
The above equation is an important form of the Euler's equation relating to fluid machines
since it gives the three distinct components of energy transfer as shown by the pair of
terms in the round brackets. These components throw light on the nature of the energy
transfer.
The first term of Eq. is readily seen to be the change in absolute kinetic energy or dynamic
head of the fluid while flowing through the impeller. The second term of Eq. represents
change in fluid energy due to the movement of the rotating fluid from one radius of
rotation to another. It shows pressure rise in the impeller due to diffusion action [as the
relative velocity changes]. The third term shows pressure rise in the impeller due to
centrifugal action [as the working fluid enters at lower diameter and comes out at higher
diameter].
The last two terms contribute to energy transferred due to static head.
The following relations are obtained from the velocity triangles at the entry and exit
Vf1 = V1sinα1 = Vr1sinβ1
Vw1 = V1cos α1 = Vf1 cot α1 = U1 - Vf1 cot β1
Vf2 = V2sinα2 = Vr2sinβ2
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Vw2 = V2cos α2 = Vf2 cot α2 = U2 - Vf2 cot β2
CENTRIFUGAL COMPRESSOR
A centrifugal compressor is a radial flow rotodynamic fluid machine that uses mostly air as
the working fluid and utilizes the mechanical energy imparted to the machine from outside
to increase the total internal energy of the fluid mainly in the form of increased static
pressure head.
The compressor, which can be axial flow, centrifugal flow, or a combination of the two
(mixed), produces the highly compressed air needed .In turbocompressors or dynamic
compressors, high pressure is achieved by imparting kinetic energy to the air in the
impeller, and then this kinetic energy converts into pressure in the diffuser. Velocities of
airflow are quite high and the Mach number of the flow may approach unity at many points
in the air stream. Compressibility effects may have to be taken into account at every stage
of the compressor. Pressure ratios of 4:1 are typical in a single stage, and ratios of 8:1 are
possible if materials such as titanium alloys are used. There is renewed interest in the
centrifugal stage, used in conjunction with one or more axial stages, for small turbofan and
turboprop aircraft engines. The centrifugal compressor is not suitable when the pressure
ratio requires the use of more than one stage in series because of aerodynamic problems.
Nevertheless, two-stage centrifugal compressors have been used successfully in turbofan
engines.
The rotating speed of a centrifugal compressor is an inverse function of diameter to
maintain a desired peripheral speed at the outer diameters of the impellers regardless of
the physical size of the compressor. Very large (i.e., high-volume) flow compressors may
operate at speeds as low as 3,000 rpm. Conversely, low-volume flow compressors may
operate at speeds up to 30,000 rpm.
Depending on the particular application, centrifugal compressor powers can range from as
low as 500 hp (400 kW) to more than 50,000 hp (40 MW).
A centrifugal compressor essentially consists of following components.
1. A stationary casing.
Casing or housing is the pressure-containing component of the compressor. The case
houses the stationary internal components and the compressor rotor. Bearings are
attached to the case to provide both radial and axial support of the rotor. The case also
contains nozzles with inlet and discharge flange connections to introduce flow into and
extract flow from the compressor. The flange connections must be properly sized to limit
the gas velocity as necessary.
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The case is manufactured in one of three basic types: Horizontally split, vertically split
and radially split. Construction can be cast (iron or steel), forged, or fabricated by
welding.
Vertically split casing requires less sealing. They are used for medium to high pressure
applications. A vertical split compressor is easy to access the gears, bearings, seals, and
be repaired on site. However, due to the large crossing area in the splitting surface, it is
difficult to prevent gas and lubricant oil leakage.
Horizontally split casing is split along the rotor shaft and bolted at the split line. The
bearing and seal sections allow easy disassembly and assembly via the inspection cover,
without having to remove the upper casing.
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These casing are limited to low to medium pressure applications [discharge pressures
limited to 82 bar.]
2. Inlet guide vanes.
The flow enters a three-dimensional impeller through an accelerating nozzle and a row of
inlet guide vanes (IGVs). The inlet nozzle accelerates the flow from its initial conditions (at
station i) to the entry of the inlet guide vanes. Stationary inlet guide vanes are normally
positioned adjacent to the impeller inlet. The function of inlet guide vanes is to direct the
flow in the desired direction at the entry of the impeller. Variation of the inlet guide vane
angles can be employed to adjust the flow capacity of the compressor’s performance
characteristic curve. However, a variable inlet guide vane system introduces mechanical
complexity as well as additional sealing considerations. The inlet guide vanes should be
chosen so as to obtain a minimum relative Mach number at the eye tip.
3. A rotating impeller is mounted on shaft as shown in Fig. 6.1 (a) which imparts a high
velocity to the air. Inducer is the impeller entrance section where the tangential motion of
the fluid is changed in the radial direction. Inducer ensures that the flow enters the impeller
smoothly. The inducer starts at the eye and usually finishes in the region where the flow is
beginning to turn into the radial direction. Without inducers, the rotor operation would
suffer from flow separation and high noise. The inducer receives the flow between the hub
and tip diameters (der and det) of the impeller eye and passes on to the radial portion of the
impeller blades. The hub is the curved surface of revolution of the impeller A- B; the shroud
is the curved surface C - D forming the outer boundary to the flow of fluid. The flow
approaching the impeller may be with or without swirl. Double sided enables a single
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centrifugal compressor to have flow capacity similar to two compressors working in parallel
but with a smaller packaging size. It reduces inertia of the rotating group and helps improve
transient response.
The impeller may be single or double sided as shown in Fig. 6.1 (b), but the fundamental
theory is same for both. The double-sided centrifugal compressor has the advantages of
wide flow ranges and small relative volume
Fig. 6.1 a
Fig .6.1.b
Impellers can be shrouded or closed; semi-open or open. Impeller blades may be two
dimensional or three dimensional. Shroud may be attached to the blade or may be
stationery. Open impellers have the advantage of being able to operate at higher tip
speeds and thus produce greater head with lower flow than closed impellers. The
disadvantages of open impellers are their lower efficiency due to increased shroud (front
side) leakage, and increased number of blade natural frequencies. Most shrouded impellers
generate pressure ratios of 3 or less, whereas unshrouded impellers can reach pressure
ratios of 10 or higher. Semi open impellers consist of a hub and blades manufactured as a
single piece. Semi-enclosed impeller is used in single staged compressors or in the first
stage of multi-stage compressors to produce a large flow.
From the aerodynamic point of view, the cylindrical shape of blades contradicts the threedimensional character of a flow. Especially this contradiction seems important at an
impeller inlet. Inlet flow angle varies in a wide range along blade leading edge. In a 3D
impeller the blade angle from disk to shroud varies to match incoming flow field and obtain
optimum incidence angles whereas it remains constant in 2D impeller hence 3D impellers
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are preferred over 2D. Advantage is the highest durability at high blade velocity and high
flow coefficient. 3D impellers are more effective at high Mach number and big loading
factor.
Figure below shows 2D and 3D blades on left and right respectively. 2D and 3D blades are
employed for low and high flow coefficient impellers respectively.
Arrangements of shorter blades, called “1/2 blades” or “splitter blades”, are designed in
passages between the two full-length blades to reduce flow separation in the impeller. In
the passages between the full blades, a set of splitter blades is introduced symmetrically in
the mid of the channel. Conventional design approach for the splitter is to use the same
blade profile for the full and splitter blades. The splitter compressor has better
performance than that without splitter.
In multi stage compressors the number of impellers depend upon how large a pressure
increase is needed for the process, as a result compressors can have one or as many as 10
[or more impellers]. Shaft is commonly made of forged alloy with the impellers, spacers,
and the balancing drums are shrunk fitted on it.
Impeller construction can be: Riveted, Brazed, Electron beam welded and Welded
conventionally. For most applications, high-strength alloy steel is selected for the impeller
material. Stainless steel is often the material of choice for use in corrosive environments.
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Because the impellers rotate at high speeds, centrifugal stresses are an important design
consideration, and high-strength steels are required for the impeller material. In the
optimization of centrifugal compressors, the quality of the impeller optimization will play a
decisive role in the compressor stage performance.
Impeller can be of overhung or between the bearing type.
4. A diffuser consisting of a number of fixed diverging passages in which the air is
decelerated with a consequent rise in static pressure. In the diffuser, the gas velocity
decreases and dynamic pressure is converted to static pressure. Diffusers can be either
vane less, vaned or an alternating combination. Hybrid versions of vaned diffusers include:
wedge, channel, and pipe diffusers. For high performance, the design of the diffuser is
important next to that of the impeller. The vaned diffuser is composed of a sheet of equal
thickness or an airfoil blade and forces the airflow through the channel of a given geometry
to achieve effective expanding of pressure. The insight flow of the diffuser is more difficult
than the impeller because the inlet flow field of diffuser is influenced by the upstream
impeller outlet flow field and interaction of impeller and diffuser.
Pipe Diffuser
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In general, a vaneless diffuser has the widest range of flow efficiency because there are no
vanes to interfere with the flow when the gas passes through the diffuser. However, in the
vaned diffuser, the gas must flow in the direction of the blade, so the peak attainable
efficiency of the vaned diffuser is highest compared with vaneless diffuser. Flow in the
vaneless space is a free-vortex flow in which the angular momentum remains constant. To
avoid separation of flow, the divergence of the diffuser blade passages in the vaned diffuser
ring can be kept small by employing a large number of vanes. However, this can lead to
higher friction losses. Thus an optimum number of diffuser vanes must be employed. The
divergence of the flow passages must not exceed 12 degrees. It is safer to provide one third
number of diffuser blades than that of the impeller. Diffuser blade rings can be fabricated
from sheet metal or cast in cambered and uncambered shapes of uniform thickness
The diameter ratio of vaneless to impeller tip diameter [D3/D2] varies from 1.06 to 1.12.
The ratio of diffuser diameter of vaned to vaneless [D4/D3] may vary from 1.25 to 1.6.The
number of vanes in the diffuser should not coincide with number of vanes in the impeller to
avoid resonance. Design efficiency of vaned diffuser is higher than that of vaneless but it’s
off design performance is poor than that of vaneless.
5. Collector
The gas still has a high velocity after passing through the impeller, diffuser and the function
of volute is to collect and diffuse the air and make full use of the kinetic energy of the
airflow to increase the pressure. Another important function of volute is to ensure that the
impeller works in the uniform axisymmetric environment. The volute has a direct influence
on the total efficiency and stability of the compressor. The collector of a centrifugal
compressor can take many shapes and forms. When the diffuser discharges into a large
empty chamber, the collector may be termed a Plenum. When the diffuser discharges into
a device that looks somewhat like a snail shell, bull's horn or a French horn, the collector is
likely to be termed a volute or scroll. As the name implies, a collector’s purpose is to
gather the flow from the diffuser discharge annulus and deliver this flow to a downstream
pipe. Either the collector or the pipe may also contain valves and instrumentation to control
the compressor. The volute base circle radius is a little larger (1.08 times the diffuser radius)
than the impeller or diffuser exit radius.
Different cross sections of volute passage
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The vaneless space before volute decreases the non-uniformities and turbulence of flow
entering the volute as well as noise level. Normally 20-30 % of the exit kinetic energy from
the impeller is recovered in the simple volute casing. Rectangular volute section is very
common in centrifugal blowers, the circular section is widely used in compressor practice.
Gas turbine compressor do not have scroll casing and the flow is given by the diffuser to the
combustion chamber. Often, in low-speed compressors and pump applications where
simplicity and low cost count for more than efficiency, the volute follows immediately after
the impeller.
Figure 6.2 is the schematic of a centrifugal compressor, where a single entry radial impeller
is housed inside a volute casing.
Principle of operation of centrifugal compressor:
Figure 6.2 Single entry and single outlet centrifugal compressor
Air is sucked into the impeller eye and whirled outwards at high speed by the impeller disc.
The static pressure of the air increases from the eye to the tip of the impeller. The
remainder of the static pressure rise is obtained in the diffuser, where the very high velocity
of air leaving the impeller tip is reduced to almost the velocity with which the air enters the
impeller eye.
Usually, about half of the total pressure rise occurs in the impeller and the other half in the
diffuser in case of radial blades. Owing to the action of the vanes in carrying the air around
with the impeller, there is a slightly higher static pressure on the forward side of the vane
than on the trailing face. The air will thus tend to flow around the edge of the vanes in the
clearing space between the impeller and the casing. This result in a loss of efficiency and
the clearance must be kept as small as possible. The straight and radial blades are usually
employed to avoid any undesirable bending stress to be set up in the blades. The choice of
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radial blades also determines that the total pressure rise is divided equally between
impeller and diffuser.
Following points are worth mentioning for a centrifugal compressor.
(i) The pressure rise per stage is high and the volume flow rate tends to be low. The
pressure rise per stage is generally limited to 4:1 for smooth operations.
(ii) Blade geometry is relatively simple and small foreign material does not affect much on
operational characteristics.
(iii) Centrifugal impellers have lower efficiency compared to axial impellers and it is not
used aircraft engine due to increased frontal area which in turn increases drag. Multistaging
is also difficult to achieve in case of centrifugal machines.
Work done and pressure rise
Since no work is done on the air in the diffuser, the energy absorbed by the compressor will
be determined by the conditions of the air at the inlet and outlet of the impeller. At the first
instance, it is assumed that the air enters the impeller eye in the axial direction, so that the
initial angular momentum of the air is zero. The axial portion of the vanes must be curved
so that the air can pass smoothly into the eye. The angle which the leading edge of a vane
makes with the tangential direction, will be given by the direction of the relative velocity of
the air at inlet, as shown in Fig. 6.3. The air leaves the impeller tip with an absolute velocity
of that will have a tangential or whirl component. Under ideal conditions, would be such
that the whirl component is equal to the impeller speed at the tip. Since air enters the
impeller in axial direction, Vw1 = 0.
The theoretical torque will be equal to the rate of change of angular momentum
experienced by the air.
Figure 6.3 Velocity triangles at inlet and outlet of impeller blades
Considering a unit mass of air, this torque is given by theoretical torque, T = Vw2 r2
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Where, Vw2 is whirl component of V2 and r2 is impeller tip radius. Let ɯ be angular velocity.
Then the theoretical work done on the air may be written as:
Theoretical work done WC = VW2 r2ɯ = Vw2 U2
Under the situation of Vw1 = 0 and Vw2 = U2, we can derive from Eq. (1.2), the energy
transfer per unit mass of air as
𝐸
The ideal work is called Euler work.
𝑚
= U22 Eq. 6.1
Due to its inertia, the air trapped between the impeller vanes is reluctant to move round
with the impeller and we have already noted that this results in a higher static pressure on
the leading face of a vane than on the trailing face. It also prevents the air acquiring a whirl
velocity equal to impeller speed. This effect is known as slip. Because of slip, we obtain
Vw2 <U2.The slip factor σ is defined as
The energy transfer per unit mass in case of slip becomes
Eq.6.2
Power Input Factor
The power input factor takes into account of the effect of disk friction, windage, etc. for
which a little more power has to be supplied than required by the theoretical expression.
Considering all these losses, the actual work done (or energy input) on the air per unit mass
becomes
Eq 7.1
Where,
is the power input factor. From steady flow energy equation and inconsideration
of air as an ideal gas, one can write for adiabatic work w per unit mass of air flow as
Eq 7.2
Where, To1 and To2 are the stagnation temperatures at inlet and outlet of the impeller, and
Cp is the mean specific heat over the entire temperature range. With the help of Eq. (6.3),
we can write
Eq7.3
The stagnation temperature represents the total energy held by a fluid. Since no energy is
added in the diffuser, the stagnation temperature rise across the impeller must be equal to
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that across the whole compressor. If the stagnation temperature at the outlet of the
diffuser is designated by To3 then To3 = To1.One can write from Eqn. (7.3)
Eq 7.4
The overall stagnation pressure ratio can be written as
Eq 7.5
Eq 7.6
Where, To3s andTo3 are the stagnation temperatures at the end of an ideal (isentropic) and
actual process of compression respectively (Figure 7.1), and
defined as
is the isentropic efficiency
Eq 7.6
Isentropic efficiency may be 0.85 in general. Equation (7.6) indicates that the pressure ratio
also depends on the inlet temperature T01 and impeller tip speed U2. Any lowering of the
inlet temperatureT01 will clearly increase the pressure ratio of the compressor for a given
work input, but it is not under the control of the designer. The centrifugal stresses in
rotating disc are proportional to the square of the rim. For single sided impellers of light
alloy, U2 is limited to about 360 m/s by the maximum allowable centrifugal stresses in the
impeller. Such speeds produce pressure ratios of about 4:1 .To avoid disc loading, lower
speeds must be used for double-sided impellers.
Since the stagnation temperature at the outlet of impeller is same as that at the outlet of
the diffuser, one can also writeTo2 in place of To3 in Eq. (7.6).
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Figure 7.1 Ideal and actual processes of compression on T-s diagram
Typical values of the power input factor lie in the region of 1.035 to 1.04. If we
know we
are able to calculate the stagnation pressure rise for a given impeller speed. The variation in
stagnation pressure ratio across the impeller with the impeller speed is shown in Figure 7.2
Figure 7.2 Variation in stagnation pressure ratio with impeller tip speed
Vaneless Diffuser
The gas in the vaneless diffuser gains static pressure rise simply due to the diffusion process
from a smaller diameter (d2) to a larger diameter (d3). The corresponding areas of crosssections in the radial direction are
A2 = ∏d2b2 = 2∏r2b2
A3 = ∏d3b3 = 2∏r3b3
Such a flow in the vane1ess space is a free-vortex flow in which the angular
momentum remains constant. This condition gives
r2Vw2 = r3 Vw3
Eqn 1
The continuity equation at the entry and exit sections of the vaneless diffuser
gives
ῤ2 Vf2A2 = ῤ3 Vf3 A3
ῤ2(2∏ r2b2)Vf2 = ῤ3 (2∏ r3b3) Vf3
ῤ2 r2b2Vf2 = ῤ3 r3b3 Vf3
For a small pressure rise across the diffuser, ῤ2 = ῤ3. Therefore,
r2b2Vf2 = r3b3 Vf3
For a constant width (parallel wall) diffuser b2 = b3
r2Vf2 = r3 Vf3
Eqn 2
The absolute velocity at the diffuser exit is given by
V32 = Vf32 +Vw32 = [r2/r3]2[Vf22 +Vw22] = [r2/r3]2 V22
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Equations (1), (2) and (3) yield
Vw3/Vw2 = Vf3/Vf2 = V3/V2 = r3/r2
Eqn 4
This relation further gives
α2 = α3 = tan -1 [Vf2/Vw2] = tan -1 [Vf3/Vw3]
It should be remembered that this equation is valid only for incompressible flow through a
constant width diffuser.
Equation (4) clearly shows that the diffusion is directly proportional to the diameter ratio
(d3/d2). This leads to a relatively large sized diffuser which is a serious disadvantage of the
vaneless type. In some cases the overall diameter of the compressor may be impractically
large. The vaneless space between the impeller exit and the diffuser entry is 0.05 to 0.1 d2.
Vaneless diffuser may not be a disadvantage in industrial applications where weight and
size may be of secondary importance compared with the cost of a vaned diffuser. A factor
in favour of vaneless diffusers is the wide operating range obtainable, vaned diffusers being
more sensitive to flow variation because of incidence effects.
Vaned Diffuser
In the vaned diffuser the vanes are used to remove the swirl of the fluid at a higher rate
than is possible by a simple increase in radius, thereby reducing the length of flow path and
diameter. The vaned diffuser is advantageous where small size is important.
Diffuser ring with straight (uncambered) flat blades
Radial diffuser passage with diverging walls
There is a clearance between the impeller and vane leading edges amounting to about
0:1D2 to 0:2D2 for compressors. This space constitutes a vaneless diffuser.
Area ratio of a diffuser is given by
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Some typical values of these parameters are:
d3/d2 = 1.4 to 1.8, Ar = A3/A2 = 2.5 to 3.0 α2 = 10 to 20°
b2/d2 = 0.025- 0.10
Ɵmax = 5o
If the relative velocity of a compressible fluid reaches the speed of sound in the fluid,
separation of flow causes excessive pressure losses. As mentioned earlier, diffusion is a very
difficult process and there is always a tendency for the flow to break away from the surface,
leading to eddy formation and reduced pressure rise. It is necessary to control the Mach
number at certain points in the flow to mitigate this problem. The value of the Mach
number cannot exceed the value at which shock waves occur. The relative Mach number at
the impeller inlet must be less than unity.
Altering the axial width of the impeller vanes at exit, known as Exit Trim, with respect to the
baseline design, helps the manufacturer in producing design variants to meet different
customer requirements without spending effort in carrying out a design for a new product
within a certain range of specifications. Using flow trimming, the passage area is reduced
from inlet to outlet along the entire meridional length of the impeller to reduce the flow
coefficient of the impeller while maintaining the pressure ratio of the baseline impeller.
Axial trimming is a method of trimming that reduces the blade height at the impeller exit,
while maintaining the shroud profile of the original impeller in order to reduce the head
coefficient of the impeller while maintaining the original flow range.
dt
Exit trim
dh
Figure 7.3 Inducing section of a centrifugal compressor
The velocity of flow remains constant from hub to tip of the eye. The tangential velocities of
the impeller at the hub (root) and the tip of the eye are calculated based on the
corresponding hub and tip diameters of the eye respectively. The relative blade angle at the
hub βh is slightly larger than that at the tip βt.
The mass flow rate of air entering the impeller eye can be calculated as
m = [∏/4] [dt2- dh2] Vf ῤ
The eye root diameter can be as small as possible which will be decided by the
size of shaft and bearing arrangement. Then for the given flow Q the area of the eye
flow may be large, giving a low inlet velocity V1 and a high eye tip speed U1 or it may be
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small, giving a large V1and small U1. In these two extreme cases the relative velocity Vr1 is
high and hence the minimum value is exist in between these.
The typical inlet velocity triangles for small, medium and large eye tip diameter are shown
in Figure
An expression for Vr1 can be obtained in terms of eye tip diameter dt using inlet velocity
triangle as follows.
Vr12 = V12 + U12
Vr1 = √{[∏𝑑𝑡 𝑁/60]2 + [(4𝑄/∏)/ (𝑑𝑡2 – 𝑑𝑖2)] 2}
With the di, Q and N being fixed, differentiate the above equation with respect to dt and
equate to zero for getting the value of dt for minimum value of Vr1.
If there is no possibility to reduce the relative velocity further for a given machine, the
relative Mach number can be reduced further using the pre-whirl at the inlet with the use
of inlet guide vanes preceding the impeller. Mach number at inlet may be defined as
velocity of air relative to vanes at inlet to the sound velocity. The relative velocity at the eye
tip has to be held low otherwise the Mach number (based on Vr1) given by
𝑀𝑟1 = [
𝑉𝑟1
] Will be too high causing shock losses. Mach number should be in the
(√Ÿ𝑅𝑇1)
range of 0.7- 0.9. It is not necessary to introduce prewhirl down to the hub because the
fluid velocity is low in this region, due to lower blade speed. The prewhirl is therefore
gradually reduced to zero by twisting the inlet guide vanes. Pre whirl is used only in high
pressure ratio compressor, where the inlet relative Mach number exceeds unity and
shockwaves reduce the impeller efficiency.
Advantages of pre whirl
1. It reduces curvature of impeller at inlet.
2. It reduces inlet Mach number.
Disadvantages of pre whirl
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1. Due to additional part (i.e. inlet guide vane) the weight of compressor is increased
which is not favored for jet airplane compressors.
2. There is danger of possible icing in the vanes of compressor working at high altitude.
3. The cost of additional construction is increased.
4. Pre whirl reduces the work capacity of the compressor by an amount U1Vw1.
Pressure and velocity variation across centrifugal compressor
Figure shows the pressure and velocity variation across a centrifugal compressor.
Air enters the compressor at mean radius with a low velocity C1, and atmospheric pressure
P1. It is then accelerated to a high velocity C2, and pressure P2, depending upon the
centrifugal action of the impeller, both increases along the radial direction. The air now
enters the diffuser the static pressure of the fluid rises due to the deceleration of the flow.
Therefore the velocity reduces to some value C3, and the pressure still increases to P3.In
practice, about half of the total pressure rise per stage is achieved in the impeller and the
remaining half in the diffuser.
Losses in a Centrifugal Compressor
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The power supplied to the centrifugal compressor stage is the power input at the coupling
less the mechanical losses on account of the bearing, seal and disc friction.
The losses in a centrifugal compressor are as follows
Frictional losses: A major portion of the losses is due to fluid friction in stationary and
rotating blade passages. The flow in impeller and diffuser is decelerating in nature.
Therefore the frictional losses are due to both skin friction and boundary layer separation.
The losses depend on the friction factor, length of the flow passage and square of the fluid
velocity. The variation of frictional losses with mass flow is shown in Figure. 8.1.
Incidence losses: During the off-design conditions, the direction of relative velocity of fluid
at inlet does not match with the inlet blade angle and therefore fluid cannot enter the
blade passage smoothly by gliding along the blade surface. The loss in energy that takes
place because of this is known as incidence loss. This is sometimes referred to as shock
losses.
Clearance and leakage losses: Certain minimum clearances are necessary between the
impeller shaft and the casing and between the outlet periphery of the impeller eye and the
casing. The leakage of gas through the shaft clearance is minimized by employing glands.
The clearance losses depend upon the impeller diameter and the static pressure at the
impeller tip. A larger diameter of impeller is necessary for a higher peripheral speed U2 and
it is very difficult in the situation to provide sealing between the casing and the impeller eye
tip.
The variations of frictional losses, incidence losses and the total losses with mass flow rate
are shown in Figure.8.1
Figure 8.1 Dependence of various losses with mass flow in a centrifugal compressor
The leakage losses comprise a small fraction of the total loss. The incidence losses attain
the minimum value at the designed mass flow rate. The shock losses are, in fact zero at the
designed flow rate. However, the incidence losses, as shown in Fig. 8.1, comprises both
shock losses and impeller entry loss due to a change in the direction of fluid flow from axial
to radial direction in the vane less space before entering the impeller blades. The impeller
entry loss is similar to that in a pipe bend and is very small compared to other losses. This is
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why the incidence losses show a non-zero minimum value (Figure. 8.1) at the designed flow
rate.
SLIP
In actual compressors, the angle at which fluid leaves the impeller β’ will be different from
the blade angle β. The difference being larger for a larger blade pitch or smaller number of
impeller blades. This is attributed to the internal circulation of air in the flow passages
between the impeller blades. As the air flows outwards along a rotating radius, a pressure
gradient is developed across the flow passage due to the Coriolis component of
acceleration. Due to this pressure difference, eddies form in the flow channels as shown in
Fig.21.4. As shown, these eddies rotate in a direction opposite to that of the impeller, as a
result the actual angle β’ at which the air leaves the impeller will be less. Due to this, the
tangential component of velocity Vw2 reduces, which in turn reduces the pressure rise and
also the volumetric flow rate of air. The ratio of actual tangential velocity component
(Vw2), to the tangential component without eddy formation (U2) is known as the slip factor.
The slip factor is nearly constant for any machine and is related to the number of vanes on
the impeller. Various theoretical and empirical studies of the flow in an impeller channel
have led to formulas for Slip factors. For radial vaned impellers, the formula for s is given by
Stadola
Where, z is the number of blades and
For radial blades β2 = 90o Therefore,
∅2=Vf2/U2
Stadolas formula when β2 is less than 60 0 is given by
Ơ = 1 – {[(∏/n) Cos β2] / [1-∅2tan β2]}
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Where, n is the number of vanes. As Vw2 approaches U2 the slip factor is increased.
Increasing the number of vanes may increase the slip factor but this will decrease the flow
area at the inlet.
A slip factor of about 0.9 is typical for a compressor with 19 – 21 vanes.
As we increase the number of blades, there would be lesser difference between Vw2 and
U2. Whereas for larger spacing or lesser number of blades, the variation in the relative
velocity in the tangential direction would be larger and larger leading to much larger
difference between Vw2 and U2, leading to poor values of slip factor and so, slip factor
being a strong correlation, strongly correlated to the number of blades.
THE EFFECT OF BLADE SHAPE ON PERFORMANCE
There are three types of vanes used in impellers. They are: forward-curved, backwardcurved, and radial vanes, as shown in Fig. 4.3.The impellers tend to undergo high stress
forces. Curved blades, such as those used in some fans and hydraulic pumps, tend to
straighten out due to centrifugal force and bending stresses are set up in the vanes. The
straight radial blades are not only free from bending stresses, they may also be somewhat
easier to manufacture than curved blades.
Figure 4.3 Velocity triangles at inlet and outlet of different types of blades of an impeller of
a centrifugal compressor
The mass flow rate through the impeller is given by
(39.1)
The areas of cross sections normal to the radial velocity components Vf1 and Vf2 are A1 =
𝜋𝐷1 𝑏1 and 𝐴2 = 𝜋𝐷2 𝑏2 neglecting thickness of the blades.
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(39.2)
The radial component of velocities at the impeller entry and exit depend on its width at
these sections. For small pressure rise through the impeller stage, the density change in the
flow is negligible and the flow can be assumed to be almost incompressible.
For constant radial velocity
(39.3)
Eqs. (39.2) and (39.3) give
(39.4)
The work done is given by Euler's Equation as
(39.5)
It is reasonable to assume zero whirl at the entry. This condition gives
And hence,
Therefore we can write,
(39.6)
Equation (39.5) gives
(39.7)
For any of the exit velocity triangles (Figure 4.3)
(39.8)
Eq. (39.7) and (39.8)
(39.9)
Where,
is known as flow coefficient
Head developed in meters of
air =
Ha
(39.10)
/g
H = [U22 /g] – ([U2 Vf2 cot β2] / g)
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H = [U22 /g] – [U2 cot β2 Q / π D2 b2 g]
Hence H = K1 + K2 Q
{4.8}
Eqn. (4.8) is known as the H-Q characteristic curve for the centrifugal fan, blower and
compressor. The value of constant K1 represents the kinetic energy of the fluid moving at
the tangential tip speed of the impeller and the constant K2 represents the slope of the H-Q
curve which may be positive, zero or negative for fixed value of β2. Using eqn. (4.8) the
theoretical H-Q relationship can be obtained as shown in Fig.4.12 (a).
Fig 4.12[a] H - Q curves for radial flow machines
In backward curved blades, i.e., β2 < 90o, the value of Cot β2 is positive, hence such type
machine has a negative slope (i.e., K2 is positive) & therefore H-Q curve is falling type as
shown in Fig.4.12 (a). In backward curved blades as the discharge increases, the head or the
total enthalpy rise, ∆h0, reduces as Vw2 decreases for a given value of β2 as can be seen in
Fig. (b). the dashed line shows the initial value of flow, and the solid line represents the
velocity triangle for increased flow. In radial blades i.e., β2 =90o, the value of Cot β2 is Zero.
For such type of machine for any value of flow rates, the head remains constant as shown
in Fig.4.12 (a). In forward curved blade, i.e., β2 > 90o, the value of Cot β2 is negative, and HQ curve has a positive slope as shown in Fig.4.12 (a). Hence for increased discharge, head
also increases as Vw2 increases for a given β2 as shown in Fig.4.12(c) and it has rising
characteristics.
In eqn. (4.8), if Q=0, He=Hs = U22/g. This head which is independent of vane shape is called
“Shut-off head”. The actual measured head at shut-off is much less than the value of (U22/g)
due to high turbulence and shock when pre-whirl exist as shown in inclined dash line as in
Fig.4.12(a). From Fig.4.12 (b), it seen that for large value of β2, the value of V2 is also more.
For backward curved vanes, the value of Vw2 is less and hence energy transfer is less, but
losses at exit is also less for forward curved vanes, Vw2 is large, hence it transfer more
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energy but as the value of V2 is more, the losses cannot be diffused in a fixed casing.
Hence backward curved vanes are generally used. The radial vanes are used for high
pressure rise and are a reasonable compromise between high exit K.E. and high energy
transfer, and also easy to design.
The efficiency of the backward curved vanes are considerably high and the losses are less.
In the radial vanes impeller, the efficiency is moderate and the losses are also moderate.
The forward curved vanes are unstable and less efficient. They need more input energy to
operate. The backward vanes are used where high efficiency is desired and the radial
blades are used when the high pressure rise is needed though the efficiency is not high.
Forward curved blades are used very rarely. Generally the centrifugal compressor impellers
are of radial type because of their easy manufacture and suitable for high speed. Generally
backward curved blade angle between 20 to 25 degrees are employed except in cases
where high head is the major consideration.
Type of Impeller
Radial blades
Backward
curved blades
Advantages
1. Reasonable compromise
between low energy transfer
and high absolute outlet
velocity
2. No complex bending stress
3. Ease in manufacturing
1. Low outlet kinetic energy
2. Low diffuser inlet Mach no.
3. Surge margin is widest of three
Forward curved
blades
1. High energy transfer
Disadvantages
Surge margin is narrow
1. Low energy transfer
2. Complex bending stress
3. Difficulty in manufacturing.
1. High outlet kinetic energy
2. High diffuser inlet Mach
number
3. Complex bending stress
4. Difficulty in manufacturing
Compressor characteristics
Performance characteristics are dependent on other variables such as the conditions of
pressure and temperature at the compressor inlet and physical properties of the working
fluid. To study the performance of a compressor completely, it is necessary to plot P03/P01,
against the mass flow parameter
𝑚√𝑇𝑜1
𝑃𝑜1
for fixedspeed intervals of 𝑁 / √𝑇𝑜1.
It is desirable to consider what might be expected to occur when a valve placed in the
delivery line of the compressor running at a constant speed, is slowly opened. When the
valve is shut and the mass flow rate is zero, the pressure ratio will have some value. Figure
8.2 indicates a theoretical characteristics curve ABC for a constant speed.
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The centrifugal pressure head produced by the action of the impeller on the air trapped
between the vanes is simply subjected to the churning action. The head developed
corresponding to this condition is called ‘shut-off’ head represented by the point 'A' in
Figure 8.2. As the valve is opened, flow commences and diffuser begins to influence the
pressure rise, for which the pressure ratio increases. At some point 'B', efficiency
approaches its maximum and the pressure ratio also reaches its maximum. Further increase
of mass flow will result in a fall of pressure ratio. For mass flows greatly in excess of that
corresponding to the design mass flow, the air angles will be widely different from the vane
angles and breakaway of the air will occur. In this hypothetical case, the pressure ratio
drops to unity at ‘C’, when the valve is fully open and all the power is absorbed in
overcoming internal frictional resistances.
In practice, the operating point 'A' could be obtained if desired but a part of the curve
between 'A' and 'B' could not be obtained due to surging. It may be explained in the
following way. If we suppose that the compressor is operating at a point 'D' on the part of
characteristics curve (Figure 8.2) having a positive slope, then a decrease in mass flow will
be accompanied by a fall in delivery pressure. If the pressure of the air downstream of the
compressor does not fall quickly enough, the air will tend to reverse its direction and will
flow back in the direction of the resulting pressure gradient. When this occurs, the pressure
ratio drops rapidly causing a further drop in mass flow until the point 'A' is reached, where
the mass flow is zero. When the pressure downstream of the compressor has reduced
sufficiently due to reduced mass flow rate, the positive flow becomes established again and
the compressor picks up to repeat the cycle of events which occurs at high frequency.
This surging of air may not happen immediately when the operating point moves to the left
of 'B' because the pressure downstream of the compressor may at first fall at a greater rate
than the delivery pressure. As the mass flow is reduced further, the flow reversal may occur
and the conditions are unstable between 'A' and 'B'. As long as the operating point is on the
part of the characteristics having a negative slope, however, decrease in mass flow is
accompanied by a rise in delivery pressure and the operation is stable.
Figure 8.2. Theoretical characteristic curve
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There is an additional limitation to the operating range, between 'B' and 'C'. As the mass
flow increases and the pressure decreases, the density is reduced and the radial component
of velocity must increase. At constant rotational speed this means an increase in resultant
velocity and hence an angle of incidence at the diffuser vane leading edge. At some point
say 'E', the position is reached where no further increase in mass flow can be obtained no
matter how wide open the control valve is. This point represents the maximum delivery
obtainable at the particular rotational speed for which the curve is drawn. This indicates
that at some point within the compressor sonic conditions have been reached, causing the
limiting maximum mass flow rate to be set as in the case of compressible flow through a
converging diverging nozzle. Choking is said to have taken place. Prolonged operation of a
compressor at its choke point can lead to damaging the compressor parts. To prevent the
compressor choke or stonewall from happening it is needed to maintain a certain level of
flow resistance in the compressor outlet line. Anti-choke valves can be used for this
purpose in the compressor outlet line. Anti-choke valves close to restrict the flow to keep
compressor from stonewalling. When flow resistance in compressor outlet falls and flow
begins to increase, the anti-choke valves close to develop resistance to the increasing flow.
Other curves may be obtained for different speeds, so that the actual variation of pressure
ratio over the complete range of mass flow and rotational speed will be shown by curves
such as those in Figure. 8.3. The left hand extremities of the constant speed curves may be
joined up to form surge line, the right hand extremities indicate choking (Figure 8.3).
Figure 8.3 Variations of pressure ratio over the complete range of mass flow for different
rotational speeds
Surge, can result both in severe vibration and damage to compressor units and in reduced
efficiency. Violent flows of compressor surge repeatedly hit blades in the compressor,
resulting in blade fatigue or even mechanical failure. Surging can cause the compressor to
overheat to the point at which the maximum allowable temperature of the unit is
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exceeded. Also, surging can cause damage to the thrust bearing due to the rotor shifting
back and forth from the active to the inactive side. Choke line [stonewall line] is the line
joining the choke points on different constant speed lines. The operation on right side of
choke line is very inefficient.
Turndown is the percentage below full load flow the compressor can run without
experiencing surge. For example, 15% turndown means the unit can run at 85% flow or
higher, as equipped without hitting surge. At greater turndown, it will be close to or at
surge. Turndown is defined as the relative difference between the maximum flow (at the
design point) and minimum flow before blow-off (on the surge line) or difference between
the requested flow and minimum flow before blow-off.
STALL
Stalling of a stage will be defined as the aerodynamic stall, or the breakaway [separation] of
the flow from the suction side of the blade airfoil. Stall propagates in a direction opposite to
blade rotation relative to the blades from channel to channel. A multistage compressor
may operate stably in the unsurged region with one or more of the stages stalled, and the
rest of the stages unstalled. Stall, in general, is characterized by reverse flow near the blade
tip, which disrupts the velocity distribution and hence adversely affects the performance of
the succeeding stages. Rotating stall may lead to vibrations resulting in fatigue failure in
other parts of the gas turbine.
Compressor operation with speed and flow control can have extended zone of operation
abcd. Speed lines are bounded by maximum and minimum speed line nmax and nmin
respectively. Efficiency lines are bounded by maximum and minimum efficiency.
Bearings and seals
Centrifugal compressors are equipped with two radial (journal) bearings to support the
rotor weight and position the rotor concentrically within the stationary elements of the
compressor. One thrust bearing also is used to ensure that the compressor rotor is
maintained in its desired axial position. The thrust bearing usually is a “double-acting,”
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tilt-pad design installed at both sides of a rotating thrust disc. Proper rotor axial position is
thereby assured regardless of the direction of the net axial pressure forces acting on the
rotor.
Two distinct categories of compressor seals are used: Internal seals and Shaft seals
Internal seals minimize internal recirculation losses between stages and across the thrust
balance drum. Labyrinth type seals are customarily used for this purpose to maximize
operating efficiency.
Shaft seals are required to seal the gas inside the compressor at the point where the
compressor rotor shaft penetrates the case. This vital sealing function is necessary to
prevent escape of process gas to the environment surrounding the compressor. Dry gas
seals are the most commonly used type of shaft seal. Liquid film seals are sometimes used.
Air film bearings or active magnetic bearings can be used for a completely oil-free machine.
The balancing drum is attached to the shaft at the discharge end of the compressor. One
end of the drum is vented to the suction end of the compressor. The pressure on the
vented end is the same as the suction pressure. The non-vented side of the drum is
exposed to the gas at discharge pressure.
Capacity control:
The capacity of a centrifugal compressor is normally controlled by adjusting inlet guide
vanes (pre-rotation vanes). Adjusting the inlet guide vanes provide a swirl at the impeller
inlet and thereby introduces a tangential velocity at the inlet to the impeller, which gives
rise to different refrigerant flow rates. Use of inlet guide vanes for capacity control is an
efficient method as long as the angle of rotation is high, i.e., the vanes are near the fully
open condition. When the angle is reduced very much, then this method becomes
inefficient as the inlet guide vanes then act as throttling devices.
In addition to the inlet guide vanes, the capacity control is also possible by adjusting the
width of a vaneless diffuser or by adjusting the guide vanes of vaned diffusers. Using a
combination of the inlet guide vanes and diffuser, the capacities can be varied from 10
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percent to 100 percent of full load capacity. Capacity can also be controlled by varying the
compressor speed using gear drives.
Enthalpy-entropy diagram for flow through a centrifugal compressor stage
Figure 12. 10 shows an enthalpy-entropy diagram for a centrifugal compressor stage (Figs.
12.1 and 12.2).
Flow process occurring in the accelerating nozzle (i-1), impeller (1-2), diffuser (2-3) and the
volute (3-4) are depicted with values of static and stagnation pressures and enthalpies.
W, C and Cr are relative velocity, Absolute and Flow velocities respectively.
The fluid is accelerated from velocity Ci to velocity C1 and the static pressure falls from Poi
to P1 as indicated in Figure 7.3. Since the stagnation enthalpy is constant in steady,
adiabatic flow without shaft work then hoi= ho1.
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Fig. 12.10 Enthalpy-entropy diagram for flow through a centrifugal compressor stage
On account of the losses and increase in the entropy the stagnation pressure loss is
Poi– Po1, but the stagnation enthalpy remains constant:
hoi = ho1
(12.25a)
hi+[1/2]ci2 = h1 +[1/2 ] c12
(12.25b)
The isentropic compression is represented by the process 1-2s-4ss.
This process does not suffer any stagnation pressure loss:
Po2s = Po3ss = Po4ss
(12.26)
The stagnation enthalpy remains constant.
ho2s = ho3ss = ho4ss
(12.27)
The energy transfer (and transformation) occurs only in the impeller blade passages. The
actual (irreversible adiabatic) process is represented by 1-2. The stagnation enthalpies in
the relative system at the impeller entry and exit are
ho1rel = h1+ [1/2] w12
(12.28)
ho2rel = h2+ [1/2] w22
(12.29)
The corresponding stagnation pressures are Po1rel and Po2rel
The fluid is decelerated adiabatically from velocity C2 to a velocity C3, the static pressure
rising from P2 to P3 in diffuser, similarly the fluid is decelerated adiabatically from velocity C3
to a velocity C4, the static pressure rising from P3 to P4. The stagnation enthalpy remains
constant from station 2 to 4 but the stagnation pressure decreases progressively.
ho2 = ho3 = ho4
(12.30)
Po2> Po3> Po4
(12.31)
The actual energy transfer (work) appears as the change in the stagnation enthalpy.
Therefore, from Eq. (12.16)
wa= ho2- ho1= [1/2] (c22- c12) + [1/2] (w12- w22) +[ 1/2 ] (u22- u12)
This on rearrangement gives
h2 - h1+ [1/2] (W22- W12) – [1/2] (u22 - u12) = 0
(h2 + [1/2] W22) – [1/2] U22 = (h1 + [1/2] W12) – [1/2] U12
ho2rel – [1/2] U22 = ho1rel – [1/2] U12
This relation is also shown on the h-s diagram (Fig. 12.10).
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Flow coefficient
Flow coefficient is defined as the ratio between the inlet volumetric flow rate and the
product of the tip speed and some characteristic area.
Flow coefficient Ø =
m
ρ2U2A2
m = Mass flow rate of air = ∏ {D1 b1 – nt} Vf1ῤ1 =∏ {D2 b2 – nt} Vf2 ῤ2
Neglecting thickness of blade (t) for n number of blades.
m = Mass flow rate of air = ∏ D1 b1 Vf1ῤ1 =∏ D2 b2 Vf2 ῤ2
A2 is flow area at the tip of impeller and
Using continuity equation the flow coefficient becomes
Ø = = ∏ D2 b2 Vf2 ρ2/ρ2U2A2
Ø = Vf2 /U2
This dimensionless parameter not only allows comparisons between compressors operating
at different pressure and density levels, variations in gas molecular weight, differences in
rotational speed, and different impeller diameters, but it also provides insight into the
geometric relationships that exist between the designs of different impellers. The flow
coefficient is directly related to the relative amount of volumetric flow that the impeller
must accept. Very low flow coefficients are characterized by a flow path through the
impeller that incorporates an almost right angle turn downstream of the impeller eye.
Additionally, the ratio between the diameters of the eye of the impeller at the shroud to
the outer diameter is relatively small. As the flow coefficient increases, this eye-to-outer
diameter ratio approaches unity since the eye diameter increases to accommodate larger
volumetric flows. At higher flow coefficients, the flow path through the impeller transitions
from a radial exit to one at a lower angle relative to the axis of the shaft. These are
commonly known as mixed flow impeller designs. Ultimately, the flow coefficient can rise
to levels where the impeller changes from a radial to an axial design.
Order of magnitude of the flow coefficient:
Centrifugal flow impeller: 0.04 to 0.2
Mixed flow: 0.2 to 0.6
Axial flow impeller: 0.8 to 1.2
Peripheral flow impeller: 0.04
Head Coefficient λ
Head Coefficient is defined as the ratio of enthalpy increase in a stage to the kinetic energy
corresponding to tip peripheral velocity. It depends upon number of blades. The head
coefficient, relates the specific work of compression to the specific kinetic energy of the
gas. High head coefficient also provide lower rise- to- surge than lower head coefficient
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designs. Rise- to- surge is a measure of how much the pressure increases between the
design flow rate and the flow rate at which surge will occur.
Pressure coefficient Ψ
Pressure coefficient is defined as the ratio of isentropic enthalpy increase to the kinetic
energy corresponding to tip peripheral velocity.
Ψ = λ ɳi
It is a measure of the pressure raising capacities of various types of centrifugal compressor
impellers of different sizes running at different speeds. The lower the flow coefficient, the
higher will be the pressure coefficient.
Order of magnitude of the Pressure coefficient:
Centrifugal flow impeller: 0.5 to 0.6
Mixed flow: 0.35
Axial flow impeller: 0.05 to 0.25
Peripheral flow impeller: 1.8
Degree of Reaction
A large proportion of energy in the gas at the impeller exit is in the form of kinetic energy.
This is converted into static pressure rise by the energy transformation process in the
diffuser and volute casing. The division of static pressure rise in the stage between the
impeller and the stationary diffusing passages is determined by the degree of reaction. This
can be defined either in terms of pressure changes or enthalpy changes in the impeller and
the stationary diffusing passages.
Degree of reaction or reaction ratio (R) is defined as the ratio of change in static enthalpy in
the impeller to the change in stagnation enthalpy in the stage.
R = [h2- h1]/ [ho2-ho1]
[h2 - h1]= [1/2] (U22- Vr22) + [1/2] (Vr12 - U12)
If there is no prewhirl [Vw1 =0]
ho2-ho1 = U2Vw2
R = [(U22- Vr22) + (Vr12 - U12)]/ [Vw2U2]
For the constant radial velocity component, V1 = Vr1 = Vr2
With these conditions, the following expressions are obtained from the entry
and exit velocity triangles:
Vr12- U12 = Vf12- Vf22
Vr22 = Vf22 + [U2 – Vw2]2
Vr22 = Vf22 + U22 – 2U2Vw2 + Vw22
U22 – Vr22 = 2u2Vw2 – Vw22 – Vf22
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R = 1 – (1/2) [Vw2/ U2]
1
𝑅 = [1 + ∅2cotβ2]
2
The degree of reaction of the radial-tipped impeller remains constant at all values of the
flow coefficient. Degree of Reaction increases with flow coefficient for backward-swept
impeller blades and decreases for forward swept type.
Ψ = 2[1-R]
Equation above shows that the higher the degree of reaction, the lower is the stage
pressure coefficient and vice versa. The backward-swept impeller blades gives a higher
degree of reaction and a lower pressure coefficient compared to the radial and forward
swept blades.
Degree of reaction (R) is an important factor in designing the blades of a turbine,
compressors, pumps and other turbo-machinery. It also tells about the efficiency of
machine and is used for proper selection of a machine for a required purpose.
Specific speed or shape parameter (Ns).
Ns = N √𝑄/(𝑔𝐻)3/4
Where,
N in rps or radians per second, Q in m3/s, g in m/s2, H in metres, P in watts and ῤ in kg/m3.
It should also be noted that the head included in these relations is the adiabatic, or
isentropic, head per stage.
The value of the specific speed at the maximum efficiency point is a useful guide in
designing and selecting turbomachines for given conditions. Thus the use of the specific
speed places various types of turbomachines in different brackets of distinct ranges. This is
a very useful guide in selecting the type (axial, radial and mixed) of pumps, turbines,
compressors, fans and blowers because each type has almost a well-defined range on the
specific speed scale. Large specific speeds are associated with axial compressors, which
handle large flow and low heads and modest speeds.
If a compressor develops comparatively higher pressure (Δp or H) and handles smaller flow
rates (Q), it must have lower values of the specific speed.
Specific diameter Ds
𝐷𝑠 = 𝐷 [𝑔𝐻]0.25 /√𝑄
Number of blades in the impeller
In case of a small number of blades which is identical to too high a blade loading, the fluid
may break away at the discharger edge especially at lower than design flow conditions.
Thus due to separation losses, the efficiency and pressure developed will be lower than
theoretically calculated. If the number of blades are too many [i.e. too much blade surface]
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the frictional loss becomes high which lowers the pressure rise and efficiency. Hence the
optimum number of blades which gives the best efficiency can be chosen by the experience
for a particular requirement.
The inlet blade angle within the reasonable limit does not affect the performance and, its
optimum value is 30 to 35 o. The optimum outlet bade angle β2 is about 45 o.
Compressors configuration
In a series setup, the discharge of the first compressor feeds into the suction line
of the next. The compressed gas that enters the second compressor is at a higher
pressure than when it entered the first compressor.
The gas flow is divided so that all the gas does not flow through both
compressors. Parallel compressors draw to their full capacity from a common
source of gas increasing overall flow.
COMPARISON OF CENTRIFUGAL COMPRESSOR AND AXIAL COMPRESSOR
Sr.
No.
Centrifugal Compressor
Axial Compressor
1.
Flow at inlet is axial and flow
outlet is radial.
Fluid flows parallel to the axis of
rotation—Inlet and outlet axial.
2.
Motion to the gas is imparted
with inertia forces by the
rotating impellers.
Further, velocity is converted
into pressure rise in the diffuser
Motion to the gas is imparted with
torque exerted by the rotor blades
and uses several rows of airfoils to
achieve pressure rise. It makes these
complex and expensive.
3.
Higher stage pressure ratio [4.5]
Lower stage pressure ratio[1.2]
4.
Simple in construction
Complex in construction
5.
Strong in construction
Less strong in construction
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6.
Shorter in length and larger in
diameter. Large frontal area.
Larger in length and smaller in
diameter. Small frontal area suitable
for jet engines.
7.
More resistant to foreign
materials
Less resistant to foreign particles
8.
Less chances of blockade
More chances of blockade
9.
Handles large volume flow
Handles larger volume flow
10.
Improved matching
characteristics
Average matching characteristics
11.
Less cost of construction
More cost of construction
12.
Lower isentropic efficiency [80
to 82 %] and less flow rate
Higher isentropic efficiency [86 to 88
%] and more flow rate
13.
Less weight
More weight
14.
Less starting power requirement
More starting power requirement
15.
Number of stages are less but
the pressure rise per stage is
high
Number of stages are more but the
pressure rise per stage is low, thus
requiring large of stages for certain
pressure and hence becomes
complex.
16.
Less Flow rate is up to 5663cmm
High Flow rate is 850 to 14150 cmm
17.
Discharge pressure up to 690
bar
Discharge pressure up to 17.2 bar
18.
Efficiency 70 to 85 %
Efficiency 85 to + 90 %
19.
Operating speed up to 50000
RPM
Operating speed up to 10000 RPM
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20.
Overall Less pressure rise
because of limited or less
number of stages
More pressure rise because of large
number of stages
21.
More stresses and life is less
Relatively less stresses and more life
22.
These supply relatively less
continuous flow of air.
These supply a continuous flow of
compressed air
23.
Centrifugal compressors are
used with gas turbines, turbo
shaft, turboprop, auxiliary
power units, and microturbines.
Axial compressors are used with
large gas turbines in jet engines, high
speed ships small power stations,
blast furnaces and aerospace
engines.
COMPARISON OF CENTRIFUGAL COMPRESSOR AND RECIPROCATING
COMPRESSOR
Sr.No
Reciprocating
1
Presence of reciprocating
masses makes the machine
poorly balanced and hence
vibration problems are greater.
2
Presence of numerous sliding or
bearing members lowers its
mechanical efficiency.
3
Higher installed first cost
4
5
6
7
8
Pressure ratio per stage is high,
about 5 to 8.
Capability of delivering high
pressure. By multi staging, high
delivery pressure up to 5000
atm may be achieved
Capable of delivering small
volume. By using multi cylinders
the volume may be increased
Greater flexibility in capacity
and pressure range.
Higher maintenance expense.
Mir Aqueel Ali
Centrifugal
Absence of reciprocating masses
makes the machine better balanced
Absence of numerous sliding or
bearing members improves its
mechanical efficiency
Lower installed first cost where
pressure and volume conditions are
favourable.
Pressure ratio per stage is about 4.5.
Capable of delivering medium
pressure. By multi staging, the
delivery pressure up to 400 atm may
be achieved.
Capable of delivering greater
volumes per unit of building space.
No flexibility in capacity and
pressure range.
Lower maintenance expense.
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9
Lesser continuity of service.
10
Higher compression efficiency
at compression ratio above 2.
Adaptability to low speed drive
11
12
13
14
Greater continuity of service and
dependability
Higher compression efficiency at
compression ratio less than 2.
Adaptability to high speed, low
maintenance cost drivers such as
turbines.
Less operating attention
No chance of mixing of working fluid
with lubricating oil
More operating attention
There is always a chance of
mixing working fluid with
lubricating oil
Suitable for low, medium and
high pressure and low and
medium gas volumes
Suitable for low and medium
pressure and large gas volume
Advantages of Centrifugal Compressor
High efficiency approaching two stages reciprocating compressor
Can reach pressure up to 83 bar.
Completely package for plant or instrument air up through 500 hp.
Relatives first cost improves as size increase
Designed to give lubricant free air
Does not require special foundations
Disadvantages of Centrifugal Compressor
High initial cost
Complicated monitoring and control systems
Limited capacity control modulation, requiring unloading for reduced capacities
High rotational speed require special bearings and sophisticated vibration and clearance
monitoring
Specialized maintenance considerations
Advantages of Axial flow compressor
High peak efficiency
Small frontal area for given airflow
Straight-through flow, allowing high ram efficiency
Increased pressure rise due to increased number of stages with negligible losses
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Disadvantages of Axial flow compressor
Good efficiency over narrow rotational speed range
Difficulty of manufacture and high cost.
Relatively high weight
High starting power requirements
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CENTRIFUGAL FANS AND BLOWERS
A large number of fans and blowers for high pressure applications are of the centrifugal
type. Figure 15.1 shows an arrangement employed in centrifugal machines. It consists of an
impeller which has blades fixed between the inner and outer diameters. The impeller can
be mounted either directly on the shaft extension of the prime mover or separately on a
shaft supported between two additional bearings. The latter arrangement is adopted for
large blowers in which case the impeller is driven through flexible couplings.
Fig. 15.1 A centrifugal fan or blower
Air or gas enters the impeller axially through the inlet nozzle which provides slight
acceleration to the air before its entry to the impeller. The action of the impeller swings the
gas from a smaller to a larger radius and delivers the gas at a high pressure and velocity to
the casing. Thus unlike the axial type, here the centrifugal energy also contributes to the
stage pressure rise. The flow from the impeller blades is collected by a spirally-shaped
casing known as scroll or volute. It delivers the air to the exit of the blower. The scroll
casing can further increase the static pressure of air. The outlet passage after the scroll can
also take the form of a conical diffuser.
The centrifugal fan impeller can be fabricated by welding curved or almost straight metal
blades to the two side walls (shrouds) of the rotor or it can be obtained in one piece by
casting. Such an impeller is of the enclosed type. The open types of impellers have only one
shroud and are open on one side. A large number of low pressure centrifugal fans are made
out of thin sheet metal. The casings are invariably made of sheet metal of different
thicknesses and steel reinforcing ribs on the outside. In some applications, if it is necessary
to prevent leakage of the gas, suitable sealing devices are used between the shaft and the
casing. Large capacity centrifugal blowers sometimes employ double entry for the gas.
Centrifugal Fan Stage Parameters
The mass flow rate through the impeller is given by
m = ῤ1Q1 = ῤ2Q2
The areas of cross-section normal to the radial velocity components vf1 and vf2 are
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A1 = ∏d1b1 and A2 = ∏d2b2
Therefore,
M = ῤ1 vf1 [∏d1b1] = ῤ2 vf2 [∏d2b2]
The radial components of velocities at the impeller entry md exit depend on its width at
these sections. For a small pressure rise through the stage, the density change in the flow is
negligible and can be assumed to be almost incompressible. Thus for constant radial
velocity
vf1 = vf2 = vf
M = ῤ1 vf [∏d1b1] = ῤ2 vf [∏d2b2]
[b1/d2] = [b2/d1]
Design Parameters
Impeller Size
On account of the much lower pressure rise in fans, their peripheral speeds are much below
the maximum permissible values. Fan speeds can vary from 360 to 2940 rpm for ac motor
drives at 50 c/s, though much lower speeds have been used in some applications. With
other drives, considerably higher speeds can be obtained if desired.
The diameter ratio (d1/d2) of the impeller determines the length of the blade passages: the
smaller this ratio, the longer is the blade passage.
d1/d2 ≈ Ø 0.33
With a slight acceleration of the flow from the impeller eye to the blade entry, the following
relation for the blade width to diameter ratio is recommended
b1 /d1 = 0.2
Impellers with backward-swept blades are narrower, i.e. b1/d1 < 0.2.
Blade Shape
Straight or curved sheet metal blades or aerofoil-shaped blades have been used in
centrifugal fans and blowers. Sheet metal blades are circular arc shaped or of a different
curve. They can either be welded or rivetted to the impeller disc. The blade exit angles
depend on whether they are backward-swept, radial or for forward··swept. The optimum
blade angle at the entry is found to be about 35°.
Backward-swept blade impellers are employed for lower pressure and lower flow rates. The
width to diameter ratio of such impellers is small (b / D = 0.05 - 0.2) and the number of
blades employed is between 6 and 17.
When the blades are inclined in the direction of motion, they are referred to as forwardswept blades. These blades have a larger hub-to-tip diameter ratio which allows large area
for the flow entering the stage. However, on account of the shorter length of blade
passages, the number of blades required is considerably larger to be effective.
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For backward-swept blades the degree of reaction is always less than unity.
For radial-tipped blades the degree of reaction is equal to 0.5.
For forward-swept blades the degree of reaction is always less than 0.5.
Number of Blades
The number of blades in a centrifugal fan can vary from 2 to 64 depending on the
application, type and size. Too few blades are unable to fully impose their geometry on the
flow, whereas too many of them restrict the flow passage and lead to higher losses. Most
efforts to determine the optimum number of blades have resulted in only empirical
relations given below: Pfleirderer has recommended the following relation:
𝑑2 + 𝑑1
𝑍 = 6.5 [
] sin [(𝛽1 + 𝛽2) /2 ]
𝑑2 − 𝑑1
From data collected for a large number of centrifugal blowers, Stepanoff suggests
Z≈ [β2/3]
For smaller-sized blowers, the number of blades is lesser than this.
The provision of a vaned diffuser in a blower can give a slightly higher efficiency than a
blower with only a volute casing. However, for a majority of centrifugal fans and blowers,
the higher cost and size that result by employing a diffuser outweigh its advantages.
Therefore, most of the single stage centrifugal fan impellers discharge directly into the
volute casing. Some static pressure recovery can also occur in a volute casing
There is a small vaneless space between the impeller exit (Fig. 15.1) and the volute base
circle. The base circle diameter is 1.1 to 1.2 times the impeller diameter. The volute width is
1.25 and 2.0 times the impeller width at the exit.
NUMERICAL ON BLOWER
A centrifugal blower with a radial impeller produces a pressure equivalent to 100 cm
column of water. The pressure and temperature at its entry are 0.98 bar and 310 K. The
electric motor driving the blower runs at 3000 rpm. The efficiencies of the fan and drive are
82% and 88% respectively. The radial velocity remains constant and has a value of 0.2U2.
The velocity at the inlet eye is 0.4U2. If the blower handles 200 m3 /min of air at the entry
conditions,
Determine:
(a) Power required by the electric motor, (b) Impeller diameter, (c) Inner diameter of the
blade ring, (d) Air angle at entry, (e) Impeller widths at entry and exit, (f) Number of
impeller blades, and (g) Specific speed.
Solution:
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