Lesson
21 Centrifugal Compressors
The specific objectives of this lesson are to:
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1. Explain the working principle of a centrifugal compressor (Section 21.1)
2. Prent the analysis of centrifugal compressors (Section 21.2)
3. Discuss the lection of impeller diameter and speed of a centrifugal
compressor using velocity diagrams (Section 21.3)
4. Discuss the effect of blade width on the capacity of centrifugal compressor
炒鸭肠的做法(Section 21.4)
5. Discuss the methods of capacity control of a centrifugal compressor
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(Section 21.5)
6. Discuss the performance aspects and the phenomenon of surging in
centrifugal compressors (Section 21.6)
7. Compare the performance of a centrifugal compressor with a reciprocating
compressor vis-á-vis condensing and evaporator temperatures and compressor speed (Section 21.6)
8. Describe commercial refrigeration systems using centrifugal compressors
(Section 21.7)
At the end of the lecture, the student should be able to:
1. Explain the working principle of a centrifugal compressor with suitable
diagrams
2. Analy the performance of a centrifugal compressor using steady flow
energy equation and velocity diagrams
3. Calculate the required impeller diameter and/or speed of a centrifugal
compressor
4. Explain the limitations on minimum refrigeration capacity of centrifugal
compressors using velocity diagrams
5. Explain the methods of capacity control of centrifugal compressor
6. Explain the phenomenon of surging
7. Compare the performance aspects of centrifugal and reciprocating
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21.1. Introduction:
Centrifugal compressors; also known as turbo-compressors belong to the roto-dynamic type of compressors. In the compressors the required pressure ri takes place due to the continuous conversion of angular momentum imparted to the refrigerant vapour by a high-speed impeller into st
atic pressure. Unlike reciprocating compressors, centrifugal compressors are steady-flow devices hence they are subjected to less vibration and noi.
Figure 21.1 shows the working principle of a centrifugal compressor. As shown in the figure, low-pressure refrigerant enters the compressor through the eye of the impeller (1). The impeller (2) consists of a number of blades, which
form flow passages (3) for refrigerant. From the eye, the refrigerant enters the flow passages formed by the impeller blades, which rotate at very high speed. As the refrigerant flows through the blade passages towards the tip of the impeller, it gains momentum and its static pressure also increas. From the tip of the impeller, the refrigerant flows into a stationary diffur (4). In the diffur, the refrigerant is decelerated and as a result the dynamic pressure drop is converted into static pressure ri, thus increasing the static pressure further. The vapour from the diffur enters the volute casing (5) where further conversion of velocity into static pressure takes place due to the divergent shape of the volute. Finally, the pressurized refrigerant leaves the compressor from the volute casing (6).
The gain in momentum is due to the transfer of momentum from the high-speed impeller blades to the refrigerant confined between the blade passages. The increa in static pressure is due to the
lf-compression caud by the centrifugal action. This is analogous to the gravitational effect, which caus the fluid at a higher level to press the fluid below it due to gravity (or its weight). The static pressure produced in the impeller is equal to the static head, which would be produced by an equivalent gravitational column. If we assume the impeller blades to be radial and the inlet diameter of the impeller to be small, then the static head, h developed in the impeller passage for a single stage is given by:
g
V h 2
= (21.1)
where h = static head developed, m
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鱼肉用英语怎么说V = peripheral velocity of the impeller wheel or tip speed, m/s
g = acceleration due to gravity, m/s 2
Hence increa in total pressure, ΔP as the refrigerant flows through the passage is given by:
2V gh P ρ=ρ=Δ (21.2)
Refrigerant
out
3
Refrigerant
伤感情诗
in
Thus it can be en that for a given refrigerant with a fixed density, the pressure ri depends only on the peripheral velocity or tip speed of the blade. The tip speed of the blade is proportional to the rotational speed (RPM) of the impeller and the impeller diameter. The maximum permissible tip speed is limited
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by the strength of the structural materials of the blade (usually made of high speed chrome-nickel steel) and the sonic velocity of the refrigerant. Under the limitations, the maximum achievable pressure ri (hence maximum achievable temperature lift) of single stage centrifugal compressor is limited for a given refrigerant. Hence, multistage centrifugal compressors are ud for large temperature lift applications. In multistage centrifugal compressors, the discharge
of the lower stage compressor is fed to the inlet of the next stage compressor
and so on. In multistage centrifugal compressors, the impeller diameter of all stages remains same, but the width of the impeller becomes progressively narrower in the direction of flow as refrigerant density increas progressively.
The blades of the compressor or either forward curved or backward curved or radial. Backward curved blades were ud in the older compressors, whereas the modern centrifugal compressors u mostly radial blades.
The stationary diffur can be vaned or vaneless. As the name implies, in vaned diffur vanes are ud in the diffur to form flow passages. The vanes
can be fixed or adjustable. Vaned diffurs are compact compared to the vaneless diffurs and are commonly ud for high discharge pressure applications. However, the prence of vanes in the diffurs can give ri to shocks, as the refrigerant velocities at the tip of the impeller blade could reach sonic velocities in large, high-speed centrifugal compressors. In vaneless diffurs the velocity of refrigerant in the diffur decreas and static pressure increas as the radius increas. As a result, for a required pressure ri, the required size of the vaneless diffur could be large compared to vaned diffur. However, the problem of shock due to supersonic velocities at the tip does not ari with vaneless diffurs as the velocity can be diffud smoothly.
Generally adjustable guide vanes or pre-rotation vanes are added at the inlet (eye) of the impeller for capacity control.
21.2. Analysis of centrifugal compressors:
Applying energy balance to the compressor (Fig.24.2), we obtain from steady flow energy equation:
)gZ 2
V h (m W )gZ 2V h (m Q e 2e e c i 2
i i +++−=+++− (21.3)
where Q = heat transfer rate from the compressor
W = work transfer rate to the compressor
m = mass flow rate of the refrigerant
V i ,V e = Inlet and outlet velocities of the refrigerant
Z i ,Z e = Height above a datum in gravitational force field at inlet and outlet
Neglecting changes in kinetic and potential energy, the above equation becomes:
e c i mh W mh Q +−=+− (21.4)
In a centrifugal compressor, the heat transfer rate Q is normally negligible (as the area available for heat transfer is small) compared to the other energy terms, hence the rate of compressor work input for adiabatic compression is given by:
)h h (m W i e c −=
(21.5)
The above equation is valid for both reversible as well as irreversible adiabatic compression, provided the actual enthalpy is ud at the exit in ca of irreversible compression. In ca of reversible, adiabatic compression, the power input to the compressor is given by:
in i e in ,c )h h (m W −= (21.6)
