Editing Centrifugal compressor (section)

== Components of a simple centrifugal compressor ==

[[File:Gearbox and compressors of sectioned Rolls-Royce Dart turboprop.jpg|thumb|upright= 1.35|Figure-1.1 - 2-Stage turboshaft, 1st-stage flowpath, annular inlet, guide vanes, open impeller, vaned diffuser, vaneless return-bend]]
A simple centrifugal compressor stage has four components (listed in order of throughflow): inlet, impeller/rotor, diffuser, and collector.<ref name="Shepherd"/> Figure 1.1 shows each of the components of the flow path, with the flow (working gas) entering the centrifugal impeller axially from left to right. This turboshaft (or turboprop) impeller is rotating counter-clockwise when looking downstream into the compressor. The flow will pass through the compressors from left to right.

=== Inlet ===

The simplest inlet to a centrifugal compressor is typically a simple pipe. Depending upon its use/application inlets can be very complex. They may include other components such as an inlet throttle valve, a shrouded port, an annular duct (see Figure 1.1), a bifurcated duct, stationary guide vanes/airfoils used to straight or swirl flow (see Figure 1.1), movable guide vanes (used to vary pre-swirl adjustably). Compressor inlets often include instrumentation to measure pressure and temperature in order to control compressor performance.

[[Bernoulli's principle|Bernoulli's fluid dynamic principle]] plays an important role in understanding vaneless stationary components like an inlet. In engineering situations assuming [[Adiabatic process|adiabatic flow]], this equation can be written in the form:

Equation-1.1
:<math>\left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_0 = \left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_1</math>

where:
*{{mvar|0}} is the inlet of the compressor, station 0
*{{mvar|1}} is the inlet of the impeller, station 1
*{{mvar|p}} is the [[pressure]]
*{{mvar|ρ}} is the [[density]] and <math>\rho(\tilde{p})</math> indicates that it is a function of pressure
*<math>v</math> is the [[flow speed]]
*{{mvar|γ}} is the [[Heat capacity ratio|ratio of the specific heats]] of the fluid

=== Centrifugal impeller ===

[[File:2 polys.png|thumb|upright= 1.35|Figure 1.2.1 - Graphic modeling of the impeller, similar to turbocharger impeller]]
The identifying component of a centrifugal compressor stage is the centrifugal impeller rotor. Impellers are designed in many configurations including "open" (visible blades), "covered or shrouded", "with splitters" (every other inducer removed), and "w/o splitters" (all full blades). Figures 1.1, 1.2.1, and 1.3  show three different open full inducer rotors with alternating full blades/vanes and shorter length splitter blades/vanes. Generally, the accepted mathematical nomenclature refers to the leading edge of the impeller with subscript 1. Correspondingly, the trailing edge of the impeller is referred to as subscript 2.

As working-gas/flow passes through the impeller from stations 1 to 2, the kinetic and potential energy increase. This is identical to an axial compressor with the exception that the gases can reach higher energy levels through the impeller's increasing radius. In many modern high-efficiency centrifugal compressors the gas exiting the impeller is traveling near the speed of sound.

Most modern high-efficiency impellers use "backsweep" in the blade shape.<ref name="Japikse">
{{cite book|author=Japikse, David
|title=Centrifugal Compressor Design and Performance
|year=1996
|publisher=Concepts ETI .
|isbn=978-0-933283-03-9}}
</ref><ref name="Whitfield, Baines">
{{cite book|author=Whitfield, A. |author2=Baines, N. C.
|title=Design of Radial Turbomachinery
|year=1990
|publisher=Longman Scientific and Technical
|isbn=978-0-470-21667-5}}</ref><ref name="Aungier">
{{cite book|author=Aungier, Ronald H.
|title=Centrifugal Compressors, A Strategy for Aerodynamic Design and Analysis
|publisher=ASME Press
|year=2000
|isbn=978-0-7918-0093-5}}</ref>

A derivation of the general [[Euler equations (fluid dynamics)]] is [[Euler's pump and turbine equation]], which plays an important role in understanding impeller performance. This equation can be written in the form:

Equation-1.2 (see Figures 1.2.2 and 1.2.3 illustrating impeller velocity triangles)

:<math>E=\left(\frac {u_2}{2g}-\frac {u_1}{2g}\right)+\left(\frac {w_2}{2g}-\frac {w_1}{2g}\right)+\left(\frac {c_2}{2g}-\frac {c_1}{2g}\right)</math>
where:
*{{mvar|1}} subscript 1 is the impeller leading edge (inlet), station 1
*{{mvar|2}} subscript 2 is the impeller trailing edge (discharge), station 2
*{{mvar|E}} is the [[energy]] added to the fluid
*{{mvar|g}} is the acceleration due to [[gravity]]
*{{mvar|u}} is the impeller's circumferential velocity, units [[velocity]]
*{{mvar|w}} is the velocity of flow relative to the impeller, units velocity
*{{mvar|c}} is the absolute velocity of flow relative to stationary, units velocity
<gallery>
Impeller inlet meridional triangles.PNG|Figuer1.2.2 -Inlet velocity triangles for centrifugal compressor impeller
Impeller exit meridional trianges.PNG|Figuer1.2.3 - Exit velocity triangles for centrifugal compressor impeller
</gallery>

=== Diffuser ===

[[File:NASA CC3 impeller and wedge diffuser.jpg|thumb|upright= 1.35|Figure 1.3 - NASA CC3 impeller and wedge diffuser]]
The next component, downstream of the impeller within a simple centrifugal compressor may the diffuser.<ref name="Japikse&Baines">
{{cite book|author=Japikse, David |author2=Baines, N.C.
|title=Diffuser Design Technology
|year=1998
|publisher=Concepts ETI .
|isbn=978-0-933283-01-5}}</ref><ref name="Aungier"/> The diffuser converts the flow's kinetic energy (high velocity) into increased potential energy (static pressure) by gradually slowing (diffusing) the gas velocity. Diffusers can be vaneless, vaned, or an alternating combination. High-efficiency vaned diffusers are also designed over a wide range of solidities from less than 1 to over 4. Hybrid versions of vaned diffusers include wedge (see Figure 1.3), channel, and pipe diffusers. Some turbochargers have no diffuser. Generally accepted nomenclature might refer to the diffuser's lead edge as station 3 and the trailing edge as station 4.

Bernoulli's fluid dynamic principle plays an important role in understanding diffuser performance. In engineering situations assuming adiabatic flow, this equation can be written in the form:

Equation-1.3
:<math>\left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_2 = \left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_4</math>

where:
*{{mvar|2}} is the inlet of the diffuser, station 2
*{{mvar|4}} is the discharge of the diffuser, station 4
*(see inlet above.)

=== Collector ===
[[File:Main components of a centrifugal compressor in isometric view.svg|thumb|upright= 1.35|Figure 1.4 - Centrifugal compressor model illustrating the main components]]
The collector of a centrifugal compressor can take many shapes and forms.<ref name="Japikse&Baines"/><ref name="Aungier"/> When the diffuser discharges into a large empty circumferentially (constant area) 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''.

When the diffuser discharges into an annular bend the collector may be referred to as a ''combustor inlet'' (as used in jet engines or gas turbines) or a ''return-channel'' (as used in an online multi-stage compressor). As the name implies, a collector's purpose is to gather the flow from the diffuser discharge annulus and deliver this flow downstream into whatever component the application requires. The collector or discharge pipe may also contain valves and instrumentation to control the compressor. In some applications, collectors will diffuse flow (converting kinetic energy to static pressure) far less efficiently than a diffuser.<ref name="Heinrich&Schwarze">
{{cite journal
| last1 = Heinrich | first1 = Martin| author-link1 = Martin Heinrich
| last2 = Schwarze | first2 = Rüdiger| author-link2 = Rüdiger Schwarze
| title = Genetic Algorithm Optimization of the Volute Shape of a Centrifugal Compressor
| journal = International Journal of Rotating Machinery| date = January 2016
| volume = 2016| pages = 1–13| doi = 10.1155/2016/4849025| doi-access = free}}</ref>

Bernoulli's fluid dynamic principle plays an important role in understanding diffuser performance. In engineering situations assuming adiabatic flow, this equation can be written in the form:

Equation-1.4
:<math>\left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_4 = \left(\left(\frac {v^2}{2}\right)+\left(\frac {\gamma}{\gamma-1}\right)\frac {p}{\rho}\right)_5</math>

where:
*{{mvar|4}} is the inlet of the diffuser, station 4
*{{mvar|5}} is the discharge of the diffuser, station 5
*(see inlet above.)