![Control volume for a generalized turbomachine](https://upload.wikimedia.org/wikipedia/commons/d/d4/Control_volume_for_a_generalized_turbomachine.png)
Centrifugal compressors, sometimes called impeller compressors or radial compressors, are a sub-class of dynamic axisymmetric work-absorbing
turbomachinery
Turbomachinery, in mechanical engineering, describes machines that transfer energy between a rotor and a fluid, including both turbines and compressors. While a turbine transfers energy from a fluid to a rotor, a compressor transfers energy from ...
.
They achieve pressure rise by adding energy to the continuous flow of fluid through the rotor/impeller. The following equation shows this specific energy input. A substantial portion of this energy is kinetic which is converted to increased potential energy/static pressure by slowing the flow through a diffuser. The static pressure rise in the impeller may roughly equal the rise in the diffuser.
Equation-0.1
:
:where the control volume nomenclature (illustrated in Figure-0.4) is:
::* subscript, is the impeller inlet location, station1
::* subscript, is the impeller discharge/exit location, station2
::* is the energy input per unit mass, units=(LP/m)
::* is the impeller's rotation speed, units=(radians/t)
::* is the radius of specified location, units=(L)
::* is velocity of fluid/gas velocity at specified location, units=(L/t)
::* is the tangential vector component in polar coordinate system
Components of a simple centrifugal compressor
![Gearbox and compressors of sectioned Rolls-Royce Dart turboprop](https://upload.wikimedia.org/wikipedia/commons/2/2b/Gearbox_and_compressors_of_sectioned_Rolls-Royce_Dart_turboprop.jpg)
A simple centrifugal compressor stage has four components (listed in order of throughflow): inlet, impeller/rotor, diffuser, and collector.
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 fluid dynamic principle plays an important role in understanding vaneless stationary components like an inlet. In engineering situations assuming adiatice flow, this equation can be written in the form:
Equation-1.1
:
where:
* is the inlet of the compressor, station 0
* is the inlet of the impeller, station 1
* is the
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
* is the
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and
indicates that it is a function of pressure
*
is the
flow speed
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
* is the
ratio of the specific heats of the fluid
Centrifugal impeller
![2 polys](https://upload.wikimedia.org/wikipedia/commons/3/33/2_polys.png)
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 0.1, 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.
[
][
][
]
A derivation of the general
Euler equations (fluid dynamics)
In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zer ...
is
Euler's pump and turbine equation
The Euler pump and turbine equations are the most fundamental equations in the field of turbo-machinery, turbomachinery. These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help ...
, 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)
:
where:
* subscript 1 is the impeller leading edge (inlet), station 1
* subscript 2 is the impeller trailing edge (discharge), station 2
* is the
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
added to the fluid
* is the acceleration due to
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
* is the impeller's circumferencal velocity, units
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
* is the velocity of flow relative to the impeller, units
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
* is the absolute velocity of flow relative to stationary, units
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
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
Diffuser
![NASA CC3 impeller and wedge diffuser](https://upload.wikimedia.org/wikipedia/commons/2/20/NASA_CC3_impeller_and_wedge_diffuser.jpg)
The next component, downstream of the impeller within a simple centrifugal compressor may the diffuser.
[
]
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 adiatice flow, this equation can be written in the form:
Equation-1.3
:
where:
* is the inlet of the diffuser, station 2
* is the discharge of the diffuser, station 4
*(see inlet above.)
Collector
![Main components of a centrifugal compressor in isometric view](https://upload.wikimedia.org/wikipedia/commons/b/bd/Main_components_of_a_centrifugal_compressor_in_isometric_view.svg)
The collector of a centrifugal compressor can take many shapes and forms.
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.
[
]
Bernoulli's fluid dynamic principle plays an important role in understanding diffuser performance. In engineering situations assuming adiatice flow, this equation can be written in the form:
Equation-1.4
:
where:
* is the inlet of the diffuser, station 4
* is the discharge of the diffuser, station 5
*(see inlet above.)
Historical contributions, the pioneers
Over the past 100 years, applied scientists including
Stodola (1903, 1927–1945),
[
] Pfleiderer (1952),
Hawthorne (1964),
[
] Shepherd (1956),
Lakshminarayana (1996),
[
] and Japikse (many texts including citations),
[
] have educated young engineers in the fundamentals of turbomachinery. These understandings apply to all dynamic, continuous-flow, axisymmetric pumps, fans, blowers, and compressors in axial, mixed-flow and radial/centrifugal configurations.
This relationship is the reason advances in turbines and axial compressors often find their way into other turbomachinery including centrifugal compressors. Figures 1.1 and 1.2 illustrate the domain of turbomachinery with labels showing centrifugal compressors.
[
][
] Improvements in centrifugal compressors have not been achieved through large discoveries. Rather, improvements have been achieved through understanding and applying incremental pieces of knowledge discovered by many individuals.
Aerodynamic-thermodynamic domain
![AeroTurboDomain](https://upload.wikimedia.org/wikipedia/commons/0/0d/AeroTurboDomain.PNG)
Figure 2.1 (shown right) represents the
aero
Aero is a Greek prefix relating to flight and air. In British English, it is used as an adjective related to flight (e.g., as a shortened substitute for aeroplane).
Aero, Ærø, or Aeros may refer to:
Aeronautics Airlines and companies
* Aero (P ...
-
thermo domain of turbomachinery. The horizontal axis represents the energy equation derivable from The
first law of thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
.
The vertical axis, which can be characterized by Mach Number, represents the range of fluid compressibility (or elasticity).
The Z-axis, which can be characterized by
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
, represents the range of fluid viscosities (or stickiness).
Mathematicians and physicists who established the foundations of this aero-thermo domain include:
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
,
Daniel Bernoulli
Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechan ...
,
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
,
Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier; ; 10 February 1785 – 21 August 1836) was a French mechanical engineer, affiliated with the French government, and a physicist who specialized in continuum mechanics.
The Navier–Stok ...
,
George Stokes,
Ernst Mach
Ernst Waldfried Josef Wenzel Mach ( , ; 18 February 1838 – 19 February 1916) was a Moravian-born Austrian physicist and philosopher, who contributed to the physics of shock waves. The ratio of one's speed to that of sound is named the Mach ...
,
Nikolay Yegorovich Zhukovsky
Nikolay Yegorovich Zhukovsky ( rus, Никола́й Его́рович Жуко́вский, p=ʐʊˈkofskʲɪj; – March 17, 1921) was a Russian scientist, mathematician and engineer, and a founding father of modern aero- and hydrodyna ...
,
Martin Kutta
Martin Wilhelm Kutta (; 3 November 1867 – 25 December 1944) was a German mathematician.
Kutta was born in Pitschen, Upper Silesia (today Byczyna, Poland). He attended the University of Breslau from 1885 to 1890, and continued his studies in Mu ...
,
Ludwig Prandtl
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of ...
,
Theodore von Kármán
Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronaut ...
,
Paul Richard Heinrich Blasius
Paul Richard Heinrich Blasius (9 August 1883 – 24 April 1970) was a German fluid dynamics physicist. He was one of the first students of Prandtl.
Blasius provided a mathematical basis for boundary-layer drag but also showed as early as 1911 t ...
, and
Henri Coandă
Henri Marie Coandă (; 7 June 1886 – 25 November 1972)''Flight'' 1973 was a Romanian inventor, aerodynamics pioneer, and builder of an experimental aircraft, the Coandă-1910 described by Coandă in the mid-1950s as the world's first jet, a co ...
.
Physical-mechanical domain
Figure 2.2 (shown right) represents the physical or mechanical domain of turbomachinery. Again, the horizontal axis represents the energy equation with turbines generating power to the left and compressors absorbing power to the right.
Within the physical domain the vertical axis differentiates between high speeds and low speeds depending upon the turbomachinery application.
The Z-axis differentiates between axial-flow geometry and radial-flow geometry within the physical domain of turbomachinery.
It is implied that mixed-flow turbomachinery lie between axial and radial.
Key contributors of technical achievements that pushed the practical application of turbomachinery forward include:
Denis Papin
Denis Papin FRS (; 22 August 1647 – 26 August 1713) was a French physicist, mathematician and inventor, best known for his pioneering invention of the steam digester, the forerunner of the pressure cooker and of the steam engine.
Early lif ...
,
Kernelien Le Demour,
Daniel Gabriel Fahrenheit
Daniel Gabriel Fahrenheit FRS (; ; 24 May 1686 – 16 September 1736) was a physicist, inventor, and scientific instrument maker. Born in Poland to a family of German extraction, he later moved to the Dutch Republic at age 15, where he spent ...
, John Smeaton, Dr. A. C. E. Rateau,
John Barber,
Alexander Sablukov
Alexander Alexandrovich Sablukov (russian: Александр Александрович Саблуков; 1783–1857) was a Russian Lieutenant General, engineer and inventor. Sablukov is credited with the invention of the centrifugal fan (1832) ...
, Sir
Charles Algernon Parsons
Sir Charles Algernon Parsons, (13 June 1854 – 11 February 1931) was an Anglo-Irish engineer, best known for his invention of the compound steam turbine, and as the eponym of C. A. Parsons and Company. He worked as an engineer on dy ...
,
Ægidius Elling
Jens William Ægidius Elling (also Aegidus or Aegidius) (26 July 1861 – 27 May 1949) was a Norwegian researcher, inventor and pioneer of gas turbines who is considered to be the father of the gas turbine. He built the first gas turbine that w ...
,
Sanford Alexander Moss
Sanford Alexander Moss (August 23, 1872 – November 10, 1946) was an American aviation engineer, who was the first to use a turbocharger on an aircraft engine.
Life and career
Sanford Moss was born 1872 in San Francisco, California to Ernest ...
,
Willis Carrier
Willis Haviland Carrier (November 26, 1876 – October 7, 1950) was an American engineer, best known for inventing modern air conditioning. Carrier invented the first electrical air conditioning unit in 1902. In 1915, he founded Carrier Cor ...
,
Adolf Busemann
Adolf Busemann (20 April 1901 – 3 November 1986) was a German aerospace engineer and influential Nazi-era pioneer in aerodynamics, specialising in supersonic airflows. He introduced the concept of swept wings and, after emigrating in 1947 to t ...
,
Hermann Schlichting
Hermann Schlichting (22 September 1907 – 15 June 1982) was a German fluid dynamics engineer.
Life and work
Hermann Schlichting studied from 1926 till 1930 mathematics, physics and applied mechanics at the University of Jena, Vienne and Gö ...
,
Frank Whittle
Air Commodore Sir Frank Whittle, (1 June 1907 – 8 August 1996) was an English engineer, inventor and Royal Air Force (RAF) air officer. He is credited with inventing the turbojet engine. A patent was submitted by Maxime Guillaume in 1921 for ...
and
Hans von Ohain
Hans Joachim Pabst von Ohain (14 December 191113 March 1998) was a German physicist, engineer, and the designer of the first operational jet engine. Together with Frank Whittle he is called the "father of the jet engine". His first test unit ran ...
.
Partial timeline of historical contributions
Turbomachinery similarities
Centrifugal compressors are similar in many ways to other
turbomachinery
Turbomachinery, in mechanical engineering, describes machines that transfer energy between a rotor and a fluid, including both turbines and compressors. While a turbine transfers energy from a fluid to a rotor, a compressor transfers energy from ...
and are compared and contrasted as follows:
Similarities to axial compressor
![Turboprop T-53](https://upload.wikimedia.org/wikipedia/commons/7/7d/Turboprop_T-53.jpg)
Centrifugal compressors are similar to
axial compressor
An axial compressor is a gas compressor that can continuously pressurize gases. It is a rotating, airfoil-based compressor in which the gas or working fluid principally flows parallel to the axis of rotation, or axially. This differs from other ...
s in that they are rotating airfoil-based compressors. Both are shown in the adjacent photograph of an engine with 5 stages of axial compressors and one stage of a centrifugal compressor.
The first part of the centrifugal impeller looks very similar to an axial compressor. This first part of the centrifugal impeller is also termed an ''inducer''. Centrifugal compressors differ from axials as they use a significant change in radius from inlet to exit of the impeller to produce a much greater pressure rise in a single stage (e.g. 8 in the
Pratt & Whitney Canada PW200
The Pratt & Whitney Canada PW200 is a family of turboshaft engines developed specifically for helicopter applications. It entered service in the 1990s.
Variants
;PW205B
:First run 1987. Flown in twin-engine MBB BO105 for demonstration only.
;PW ...
series of helicopter engines) than does an axial stage. The 1940s-era German
Heinkel HeS 011
The Heinkel HeS 011 or Heinkel-Hirth 109-011 ''(HeS - Heinkel Strahltriebwerke)'' was an advanced World War II jet engine built by Heinkel-Hirth. It featured a unique compressor arrangement, starting with a low-compression impeller in the intak ...
experimental engine was the first aviation turbojet to have a compressor stage with radial flow-turning part-way between none for an axial and 90 degrees for a centrifugal. It is known as a mixed/diagonal-flow compressor. A diagonal stage is used in the
Pratt & Whitney Canada PW600
The Pratt & Whitney Canada PW600 series is a family of small turbofan engines developed by Pratt & Whitney Canada producing between of thrust and powering the Eclipse 500/550, the Cessna Citation Mustang and the Embraer Phenom 100.
Development
...
series of small turbofans.
Centrifugal fan
![CentrifugalCompressor](https://upload.wikimedia.org/wikipedia/commons/f/f5/CentrifugalCompressor.jpg)
Centrifugal compressors are also similar to
centrifugal fan
A centrifugal fan is a mechanical device for moving air or other gases in a direction at an angle to the incoming fluid. Centrifugal fans often contain a ducted housing to direct outgoing air in a specific direction or across a heat sink; such a ...
s of the style shown in the neighboring figure as they both increase the energy of the flow through the increasing radius.
In contrast to centrifugal fans, compressors operate at higher speeds to generate greater pressure rises. In many cases, the engineering methods used to design a centrifugal fan are the same as those to design a centrifugal compressor, so they can look very similar.
For purposes of generalization and definition, it can be said that centrifugal compressors often have density increases greater than 5 percent. Also, they often experience relative fluid velocities above
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \frac ...
0.3
when the working fluid is air or nitrogen. In contrast, fans or blowers are often considered to have density increases of less than five percent and peak relative fluid velocities below Mach 0.3.
Squirrel-Cage fan
![CentrifugalFan](https://upload.wikimedia.org/wikipedia/commons/9/95/CentrifugalFan.png)
Squirrel-Cage fans are primarily used for ventilation. The flow field within this type of fan has internal recirculations. In comparison, a centrifugal fan is uniform circumferentially.
Centrifugal pump
Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic ...
Centrifugal compressors are also similar to centrifugal pumps
of the style shown in the adjacent figures. The key difference between such compressors and pumps is that the compressor working fluid is a gas (compressible) and the pump working fluid is liquid (incompressible). Again, the engineering methods used to design a centrifugal pump are the same as those to design a centrifugal compressor. Yet, there is one important difference: the need to deal with
cavitation
Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, cal ...
in pumps.
Radial turbine
Centrifugal compressors also look very similar to their turbomachinery counterpart the
radial turbine A radial turbine is a turbine in which the flow of the working fluid is radial to the shaft. The difference between axial and radial turbines consists in the way the fluid flows through the components (compressor and turbine). Whereas for an axial ...
as shown in the figure. While a compressor transfers energy into a flow to raise its pressure, a turbine operates in reverse, by extracting energy from a flow, thus reducing its pressure. In other words, power is input to compressors and output from turbines.
Turbomachinery using centrifugal compressors
Standards
As turbomachinery became more common, standards have been created to guide manufacturers to assure end-users that their products meet minimum safety and performance requirements. Associations formed to codify these standards rely on manufacturers, end-users, and related technical specialists. A partial list of these associations and their standards are listed below:
*
American Society of Mechanical Engineers
The American Society of Mechanical Engineers (ASME) is an American professional association that, in its own words, "promotes the art, science, and practice of multidisciplinary engineering and allied sciences around the globe" via "continuing ...
:
BPVC,PTC.
*
American Petroleum Institute
The American Petroleum Institute (API) is the largest U.S. trade association for the oil and natural gas industry. It claims to represent nearly 600 corporations involved in production, refinement, distribution, and many other aspects of the pet ...
: API STD 617 8TH ED (E1), API STD 672 5TH ED (2019).
*
American Society of Heating, Refrigeration, and Airconditioning Engineers: Handbook Fundamentals.
*
Society of Automotive Engineers
SAE International, formerly named the Society of Automotive Engineers, is a United States-based, globally active professional association and standards developing organization for engineering professionals in various industries. SAE Internatio ...
*
Compressed Air and Gas Institute
Compressed Air and Gas Institute or CAGI is the industry association located in Cleveland, Ohio, USA. It was founded in 1915. CAGI represents manufacturers of compressed air system equipment, including air compressor
An air compressor is a pn ...
*
International Organization for Standardization
The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Ar ...
ISO 10439, ISO 10442, ISO 18740, ISO 6368, ISO 5389
Applications
Below, is a partial list of centrifugal compressor applications each with a brief description of some of the general characteristics possessed by those compressors. To start this list two of the most well-known centrifugal compressor applications are listed; gas turbines and turbochargers.
![Turbojet operation-centrifugal flow-en](https://upload.wikimedia.org/wikipedia/commons/1/19/Turbojet_operation-centrifugal_flow-en.svg)
* In
gas turbine
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directi ...
s and auxiliary power units. Ref. Figures 4.1–4.2 In their simple form, modern gas turbines operate on the Brayton cycle. (ref Figure 5.1) Either or both axial and centrifugal compressors are used to provide compression. The types of gas turbines that most often include centrifugal compressors include small aircraft engines (i.e. turboshafts, turboprops, and turbofans), auxiliary power units, and micro-turbines. The industry standards applied to all centrifugal compressors used in aircraft applications are set by the relevant civilian and military certification authorities to achieve the safety and durability required in service. Centrifugal impellers used in gas turbines are commonly made from titanium alloy forgings. Their flow-path blades are commonly flank milled or point milled on 5-axis milling machines. When running clearances have to be as small as possible without the impeller rubbing its shroud the impeller is first drawn with its high-temperature, high-speed deflected shape and then drawn in its equivalent cold static shape for manufacturing. This is necessary because the impeller deflections at the most severe running condition can be 100 times larger than the required hot running clearance between the impeller and its shroud.
* In automotive engine and
diesel engine
The diesel engine, named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is a so-call ...
turbocharger
In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to pro ...
s and
supercharger
In an internal combustion engine, a supercharger compresses the intake gas, forcing more air into the engine in order to produce more power for a given displacement.
The current categorisation is that a supercharger is a form of forced induct ...
s.
[
] Ref. Figure 1.1 Centrifugal compressors used in conjunction with reciprocating internal combustion engines are known as turbochargers if driven by the engine's exhaust gas and turbo-superchargers if mechanically driven by the engine. Standards set by the industry for turbochargers may have been established by
SAE
SAE or Sae may refer to:
Science and technology
:
* Selective area epitaxy, local growth of epitaxial layer through a patterned dielectric mask deposited on a semiconductor substrate
* Serious adverse event, in a clinical trial
* Simultaneous Auth ...
.
Ideal gas properties often work well for the design, test and analysis of turbocharger centrifugal compressor performance.
* In
pipeline compressors of
natural gas
Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbo ...
to move the gas from the production site to the consumer.
Centrifugal compressors for such uses may be one- or multi-stage and driven by large gas turbines. Standards set by the industry (ANSI/API, ASME) result in thick casings to achieve a required level of safety. The impellers are often if not always of the covered style which makes them look much like pump impellers. This type of compressor is also often termed an ''API-style''. The power needed to drive these compressors is most often in the thousands of horsepower (HP). The use of real gas properties is needed to properly design, test, and analyze the performance of natural gas pipeline centrifugal compressors.
* In
oil refineries
An oil refinery or petroleum refinery is an industrial process plant where petroleum (crude oil) is transformed and refined into useful products such as gasoline (petrol), diesel fuel, asphalt base, fuel oils, heating oil, kerosene, liquefie ...
,
natural-gas processing
Natural-gas processing is a range of industrial processes designed to purify raw natural gas by removing impurities, contaminants and higher molecular mass hydrocarbons to produce what is known as ''pipeline quality'' dry natural gas. Natural gas ...
,
petrochemical
Petrochemicals (sometimes abbreviated as petchems) are the chemical products obtained from petroleum by refining. Some chemical compounds made from petroleum are also obtained from other fossil fuels, such as coal or natural gas, or renewable sou ...
and
chemical plant
A chemical plant is an industrial process plant that manufactures (or otherwise processes) chemicals, usually on a large scale. The general objective of a chemical plant is to create new material wealth via the chemical or biological transform ...
s.
Centrifugal compressors for such uses are often one-shaft multi-stage and driven by large steam or gas turbines. Their casings are termed ''horizontally split'' if the rotor is lowered into the bottom half during assembly or ''barrel'' if it has no lengthwise split-line with the rotor being slid in. Standards set by the industry (ANSI/API, ASME) for these compressors result in thick casings to achieve a required level of safety. The impellers are often of the covered style which makes them look much like pump impellers. This type of compressor is also often termed ''API-style''. The power needed to drive these compressors is usually in the thousands of HP. Use of real gas properties is needed to properly design, test and analyze their performance.
*
Air-conditioning
Air conditioning, often abbreviated as A/C or AC, is the process of removing heat from an enclosed space to achieve a more comfortable interior environment (sometimes referred to as 'comfort cooling') and in some cases also strictly controlling ...
and
refrigeration
The term refrigeration refers to the process of removing heat from an enclosed space or substance for the purpose of lowering the temperature.International Dictionary of Refrigeration, http://dictionary.iifiir.org/search.phpASHRAE Terminology, ht ...
and
HVAC
Heating, ventilation, and air conditioning (HVAC) is the use of various technologies to control the temperature, humidity, and purity of the air in an enclosed space. Its goal is to provide thermal comfort and acceptable indoor air quality. HV ...
: Centrifugal compressors quite often supply the compression in
water chillers cycles.
Because of the wide variety of vapor compression cycles (
thermodynamic cycle
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventuall ...
,
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
) and the wide variety of workings gases (
refrigerant
A refrigerant is a working fluid used in the heat pump and refrigeration cycle, refrigeration cycle of air conditioning systems and heat pumps where in most cases they undergo a repeated phase transition from a liquid to a gas and back again. Ref ...
s), centrifugal compressors are used in a wide range of sizes and configurations. Use of real gas properties is needed to properly design, test and analyze the performance of these machines. Standards set by the industry for these compressors include ASHRAE, ASME & API.
* In industry and manufacturing to supply compressed air for all types of
pneumatic tool
A pneumatic tool, air tool, air-powered tool or pneumatic-powered tool is a type of power tool, driven by compressed air supplied by an air compressor. Pneumatic tools can also be driven by compressed carbon dioxide () stored in small cylinders al ...
s.
Centrifugal compressors for such uses are often multistage and driven by electric motors. Inter-cooling is often needed between stages to control air temperature. Road-repair crews and automobile repair garages find screw compressors better adapt to their needs. Standards set by the industry for these compressors include ASME and government regulations that emphasize safety. Ideal gas relationships are often used to properly design, test, and analyze the performance of these machines. Carrier's equation is often used to deal with humidity.
* In air separation plants to manufacture purified end product gases.
Centrifugal compressors for such uses are often multistage using inter-cooling to control air temperature. Standards set by the industry for these compressors include ASME and government regulations that emphasize safety. Ideal gas relationships are often used to properly design, test, and analyze the performance of these machines when the working gas is air or nitrogen. Other gases require real gas properties.
* In
oil field
A petroleum reservoir or oil and gas reservoir is a subsurface accumulation of hydrocarbons contained in porous or fractured rock formations.
Such reservoirs form when kerogen (ancient plant matter) is created in surrounding rock by the presence ...
re-injection of high-pressure natural gas to improve oil recovery.
Centrifugal compressors for such uses are often one-shaft multi-stage and driven by gas turbines. With discharge pressures approaching 700 bar, casings are of the barrel style. Standards set by the industry (API, ASME) for these compressors result in large thick casings to maximize safety. The impellers are often if not always of the covered style which makes them look much like pump impellers. This type of compressor is also often termed ''API-style''. The use of real gas properties is needed to properly design, test, and analyze their performance.
Theory of operation
In the case where flow passes through a straight pipe to enter a centrifugal compressor, the flow is axial, uniform, and has no vorticity, i.e. swirling motion. As the flow passes through the centrifugal impeller, the impeller forces the flow to spin faster as it gets further from the rotational axis. According to a form of
Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
's fluid dynamics equation, known as the ''
pump and turbine equation'', the energy input to the fluid is proportional to the flow's local spinning velocity multiplied by the local impeller
tangential velocity
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. ...
.
In many cases, the flow leaving the centrifugal impeller is traveling near the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...
. It then flows through a stationary compressor causing it to decelerate. The stationary compressor is ducting with increasing flow-area where energy transformation takes place. If the flow has to be turned in a rearward direction to enter the next part of the machine, e.g. another impeller or a combustor, flow losses can be reduced by directing the flow with stationary turning vanes or individual turning pipes (pipe diffusers). As described in
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematici ...
, the reduction in velocity causes the pressure to rise.
Performance
![Cent comp map](https://upload.wikimedia.org/wikipedia/commons/a/a6/Cent_comp_map.PNG)
While illustrating a gas turbine's Brayton cycle,
Figure 5.1 includes example plots of pressure-specific volume and temperature-entropy. These types of plots are fundamental to understanding centrifugal compressor performance at one operating point. The two plots show that the pressure rises between the compressor inlet (station 1) and compressor exit (station 2). At the same time, the specific volume decreases while the density increases. The temperature-entropy plot shows that the temperature increases with increasing entropy (loss). Assuming dry air, and the ideal gas equation of state and an isentropic process, there is enough information to define the pressure ratio and efficiency for this one point. The compressor map is required to understand the compressor performance over its complete operating range.
Figure 5.2, a centrifugal compressor performance map (either test or estimated), shows the flow, pressure ratio for each of 4 speed-lines (total of 23 data points). Also included are constant efficiency contours. Centrifugal compressor performance presented in this form provides enough information to match the hardware represented by the map to a simple set of end-user requirements.
Compared to estimating performance which is very cost effective (thus useful in design), testing, while costly, is still the most precise method.
[
]
Further, testing centrifugal compressor performance is very complex. Professional societies such as
ASME
The American Society of Mechanical Engineers (ASME) is an American professional association that, in its own words, "promotes the art, science, and practice of multidisciplinary engineering and allied sciences around the globe" via "continuing ...
(i.e. PTC–10, Fluid Meters Handbook, PTC-19.x),
[
] ASHRAE
The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE ) is an American professional association seeking to advance heating, ventilation, air conditioning and refrigeration (HVAC&R) systems design and constructio ...
(
ASHRAE Handbook
The ASHRAE Handbook is the four-volume flagship publication of the nonprofit technical organization ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers). This Handbook is considered the most comprehensive and author ...
) and
API
An application programming interface (API) is a way for two or more computer programs to communicate with each other. It is a type of software Interface (computing), interface, offering a service to other pieces of software. A document or standa ...
(ANSI/API 617–2002, 672–2007)
have established standards for detailed experimental methods and analysis of test results. Despite this complexity, a few basic concepts in performance can be presented by examining an example test performance map.
Performance maps
Pressure ratio and flow are the main parameters
needed to match the Figure 5.2 performance map to a simple compressor application. In this case, it can be assumed that the inlet temperature is sea-level standard. This assumption is not acceptable in practice as inlet temperature variations cause significant variations in compressor performance. Figure 5.2 shows:
* Corrected mass flow: 0.04 – 0.34 kg/s
*
Total pressure In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure:
For compressible flow the Isentropic nozzle flow#Supersonic flow, isentropic relations can be used (also valid for incompressible ...
ratio, inlet to discharge (PR = P/P): 1.0 – 2.6
As is standard practice, Figure 5.2 has a horizontal axis labeled with a flow parameter. While flow measurements use a variety of units, all fit one of 2 categories:
Mass flow per unit time
Mass flow units, such as kg/s, are the easiest to use in practice as there is little room for confusion. Questions remaining would involve inlet or outlet (which might involve leakage from the compressor or moisture condensation). For atmospheric air, the mass flow may be wet or dry (including or excluding humidity). Often, the mass flow specification will be presented on an equivalent Mach number basis,
. It is standard in these cases that the equivalent temperature, equivalent pressure, and gas is specified explicitly or implied at a standard condition.
Volume flow per unit time
In contrast, all volume flow specifications require the additional specification of density. Bernoulli's fluid dynamic principle is of great value in understanding this problem. Confusion arises through either inaccuracies or misuse of pressure, temperature, and gas constants.
Also as is standard practice, Figure 5.2 has a vertical axis labeled with a pressure parameter. There is a variety of pressure measurement units. They all fit one of two categories:
* ''A △pressure, ie increase from inlet to exit'' (measured with a manometer)
* ''A discharge pressure''
The pressure rise may alternatively be specified as a ratio that has no units:
* ''A pressure ratio'' (exit/inlet)
Other features common to performance maps are:
Constant speed-lines
The two most common methods for producing a map for a centrifugal compressor are at constant shaft speed or with a constant throttle setting. If the speed is held constant, test points are taken along a constant speed line by changing throttle positions. In contrast, if a throttle valve is held constant, test points are established by changing speed and repeated with different throttle positions (common gas turbine practice). The map shown in Figure 5.2 illustrates the most common method; lines of constant speed. In this case, we see data points connected via straight lines at speeds of 50%, 71%, 87%, and 100% RPM. The first three speed-lines have 6 points each while the highest speed line has five.
Constant efficiency islands
The next feature to be discussed is the oval-shaped curves representing islands of constant efficiency. In this figure we see 11 contours ranging from 56% efficiency (decimal 0.56) to 76% efficiency (decimal 0.76). General standard practice is to interpret these efficiencies as isentropic rather than polytropic. The inclusion of efficiency islands effectively generates a 3-dimensional topology to this 2-dimensional map. With inlet density specified, it provides a further ability to calculate aerodynamic power. Lines of constant power could just as easily be substituted.
Design or guarantee point(s)
Regarding gas turbine operation and performance, there may be a series of guaranteed points established for the gas turbine's centrifugal compressor. These requirements are of secondary importance to the overall gas turbine performance as a whole. For this reason, it is only necessary to summarize that in the ideal case, the lowest specific fuel consumption would occur when the centrifugal compressor's peak efficiency curve coincides with the gas turbine's required operation line.
In contrast to gas turbines, most other applications (including industrial) need to meet a less stringent set of performance requirements. Historically, centrifugal compressors applied to industrial applications were needed to achieve performance at a specific flow and pressure. Modern industrial compressors are often needed to achieve specific performance goals across a range of flows and pressures; thus taking a significant step toward the sophistication seen in gas turbine applications.
If the compressor represented in Figure 5.2 is used in a simple application, any point (pressure and flow) within the 76% efficiency would provide very acceptable performance. An "End User" would be very happy with the performance requirements of 2.0 pressure ratio at 0.21 kg/s.
Surge
Surge - is a low flow phenomenon where the impeller cannot add enough energy to overcome the system resistance or backpressure. At low flow rate operation, the pressure ratio over the impeller is high, as is back system backpressure. Under critical conditions, the flow will reverse back over the tips of the rotor blades towards the impeller eye (inlet). This stalling flow reversal may go unnoticed as the fraction of mass flow or energy is too low. When large enough, rapid flow reversal occurs(i.e., surge). The reversed flow exiting the impeller inlet exhibits a strong rotational component, which affects lower radius flow angles (closer to the impeller hub) at the leading edge of the blades. The deterioration of the flow angles causes the impeller to be inefficient. A full flow reversal can occur. (Therefore, surge is sometimes referred to as axisymmetric stall.) When reversed flow reduces to a low enough level, the impeller recovers and regains stability for a short moment at which point the stage may surge again. These cyclic events cause large vibrations, increase temperature and change rapidly the axial thrust. These occurrences can damage the rotor seals, rotor bearings, the compressor driver, and cycle operation. Most turbomachines are designed to easily withstand occasional surging. However, if the machine is forced to surge repeatedly for a long period of time, or if it is poorly designed, repeated surges can result in a catastrophic failure. Of particular interest, is that while turbomachines may be very durable, their physical system can be far less robust.
Surge line
![StallFormation](https://upload.wikimedia.org/wikipedia/commons/8/8d/StallFormation.svg)
The surge-line shown in Figure 5.2 is the curve that passes through the lowest flow points of each of the four speed-lines. As a test map, these points would be the lowest flow points possible to record a stable reading within the test facility/rig. In many industrial applications, it may be necessary to increase the stall line due to the system backpressure. For example, at 100% RPM stalling flow might increase from approximately 0.170 kg/s to 0.215 kg/s because of the positive slope of the pressure ratio curve.
As stated earlier, the reason for this is that the high-speed line in Figure 5.2 exhibits a stalling characteristic or positive slope within that range of flows. When placed in a different system those lower flows might not be achievable because of interaction with that system. System resistance or adverse pressure is proven mathematically to be the critical contributor to compressor surge.
Maximum flow line versus choke
Choke occurs under one of 2 conditions. Typically for high speed equipment, as flow increases the velocity of the flow can approach sonic speed somewhere within the compressor stage. This location may occur at the impeller inlet "throat" or at the vaned diffuser inlet "throat". In contrast, for lower speed equipment, as flows increase, losses increase such that the pressure ratio eventually drops to 1:1. In this case, the occurrence of choke is unlikely.
The speed-lines of gas turbine centrifugal compressors typically exhibit choke. This is a situation where the pressure ratio of a speed line drops rapidly (vertically) with little or no change in flow. In most cases the reason for this is that close to Mach 1 velocities have been reached somewhere within the impeller and/or diffuser generating a rapid increase in losses. Higher pressure ratio turbocharger centrifugal compressors exhibit this same phenomenon. Real choke phenomena is a function of compressibility as measured by the local Mach number within an area restriction within the centrifugal pressure stage.
The maximum flow line, shown in Figure 5.2, is the curve that passes through the highest flow points of each speed line. Upon inspection it may be noticed that each of these points has been taken near 56% efficiency. Selecting a low efficiency (<60%) is the most common practice used to terminate compressor performance maps at high flows. Another factor that is used to establish the maximum flow line is a pressure ratio near or equal to 1. The 50% speed line may be considered an example of this.
The shape of Figure 5.2's speed-lines provides a good example of why it is inappropriate to use the term choke in association with a maximum flow of all centrifugal compressor speed-lines. In summary; most industrial and commercial centrifugal compressors are selected or designed to operate at or near their highest efficiencies and to avoid operation at low efficiencies. For this reason there is seldom a reason to illustrate centrifugal compressor performance below 60% efficiency.
Many industrial and commercial multistage compressor performance maps exhibits this same vertical characteristic for a different reason related to what is known as stage stacking.
Other operating limits
;Minimum operating speed: The minimum speed for acceptable operation, below this value the compressor may be controlled to stop or go into an "idle" condition.
;Maximum allowable speed: The maximum operating speed for the compressor. Beyond this value stresses may rise above prescribed limits and rotor vibrations may increase rapidly. At speeds above this level the equipment will likely become very dangerous and be controlled to lower speeds.
Dimensional analysis
To weigh the advantages between centrifugal compressors it is important to compare 8 parameters classic to turbomachinery. Specifically, pressure rise (p), flow (Q), angular speed (N), power (P), density (ρ), diameter (D), viscosity (μ) and elasticity (e). This creates a practical problem when trying to experimentally determine the effect of any one parameter. This is because it is nearly impossible to change one of these parameters independently.
The method of procedure known as the Buckingham π theorem can help solve this problem by generating 5 dimensionless forms of these parameters.
These Pi parameters provide the foundation for "similitude" and the "affinity-laws" in turbomachinery. They provide for the creation of additional relationships (being dimensionless) found valuable in the characterization of performance.
For the example below Head will be substituted for pressure and sonic velocity will be substituted for elasticity.
Buckingham Π theorem
The three independent dimensions used in this procedure for turbomachinery are:
*
mass (force is an alternative)
*
length
*
time
According to the theorem each of the eight main parameters are equated to its independent dimensions as follows:
Classic turbomachinery similitude
Completing the task of following the formal procedure results in generating this classic set of five dimensionless parameters for turbomachinery.
Full-similitude is achieved when each one of the 5 Pi-parameters is equivalent when comparing two different cases. This of course would mean the two turbomachines being compared are similar, both geometrically and in terms of performance.
Turbomachinery analysts gain tremendous insight into performance by comparisons of the 5 parameters shown in the above table. Particularly, performance parameters such as efficiencies and loss-coefficients, which are also dimensionless. In general application, the Flow-coefficient and Head-coefficient are considered of primary importance. Generally, for centrifugal compressors, the Speed-coefficient is of secondary importance while the Reynolds-coefficient is of tertiary importance. In contrast, as expected for pumps, the Reynolds-coefficient becomes of secondary importance and the Speed-coefficient of tertiary importance. It may be found interesting that the Speed-coefficient may be chosen to define the y-axis of Figure 1.1, while at the same time the Reynolds coefficient may be chosen to define the z-axis.
Other dimensionless combinations
Demonstrated in the table below is another value of dimensional analysis. Any number of new dimensionless parameters can be calculated through exponents and multiplication. For example, a variation of the first parameter shown below is popularly used in aircraft engine system analysis. The third parameter is a simplified dimensional variation of the first and second. This third definition is applicable with strict limitations. The fourth parameter, specific speed, is very well known and useful in that it removes diameter. The fifth parameter, specific diameter, is a less often discussed dimensionless parameter found useful by Balje.
It may be found interesting that the specific speed coefficient may be used in place of speed to define the y-axis of Figure 1.2, while at the same time, the specific diameter coefficient may be in place of diameter to define the z-axis.
Affinity laws
The following ''affinity laws'' are derived from the five Π-parameters shown above. They provide a simple basis for scaling turbomachinery from one application to the next.
Aero-thermodynamic fundamentals
The following equations outline a fully three-dimensional mathematical problem that is very difficult to solve even with simplifying assumptions.
[
] Until recently, limitations in computational power, forced these equations to be simplified to an Inviscid two-dimensional problem with pseudo losses. Before the advent of computers, these equations were almost always simplified to a one-dimensional problem.
Solving this one-dimensional problem is still valuable today and is often termed ''mean-line analysis''. Even with all of this simplification it still requires large textbooks to outline and large computer programs to solve practically.
Conservation of mass
Also termed ''continuity'', this fundamental equation written in general form is as follows:
:
Conservation of momentum
Also termed the ''
Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
'', this fundamental is derivable from
Newton's second law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
when applied to
fluid motion
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
. Written in compressible form for a Newtonian fluid, this equation may be written as follows:
:
Conservation of energy
The
first law of thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
is the statement of the conservation of energy. Under specific conditions, the operation of a Centrifugal compressor is considered a reversible process. For a reversible process, the total amount of heat added to a system can be expressed as
where
is
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
and
is
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. Therefore, for a reversible process:
:
Since U, S and V are thermodynamic functions of state, the above relation holds also for non-reversible changes. The above equation is known as the
fundamental thermodynamic relation
In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentiall ...
.
Equation of state
The classical
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
may be written:
:
The ideal gas law may also be expressed as follows
:
where
is the density,
is the adiabatic index (
ratio of specific heats
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...
),
is the internal energy per unit mass (the "specific internal energy"),
is the specific heat at constant volume, and
is the specific heat at constant pressure.
With regard to the equation of state, it is important to remember that while air and nitrogen properties (near standard atmospheric conditions) are easily and accurately estimated by this simple relationship, there are many centrifugal compressor applications where the ideal relationship is inadequate. For example, centrifugal compressors used for large air conditioning systems (water chillers) use a refrigerant as a working gas that cannot be modeled as an ideal gas. Another example are centrifugal compressors design and built for the petroleum industry. Most of the hydrocarbon gases such as methane and ethylene are best modeled as a
real gas
Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law.
To understand the behaviour of real gases, the following must be taken into account:
*compressibility effects ...
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
rather than ideal gases. The Wikipedia entry for equations of state is very thorough.
Pros and cons
;Pros
* Centrifugal compressors offer the advantages of simplicity of manufacturing and relatively low cost. This is due to requiring fewer stages to achieve the same pressure rise.
* Centrifugal compressors are used throughout industry because they have fewer rubbing parts, are relatively energy efficient, and give higher and non-
oscillating
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
constant
airflow
Airflow, or air flow, is the movement of air. The primary cause of airflow is the existence of air. Air behaves in a fluid manner, meaning particles naturally flow from areas of higher pressure to those where the pressure is lower. Atmospheric a ...
than a similarly sized
reciprocating compressor
A reciprocating compressor or piston compressor is a positive-displacement compressor that uses pistons driven by a crankshaft to deliver gases at high pressure. Pressures of up to 5,000 PSIG are commonly produced by multistage reciprocating ...
or any other
positive displacement pump
A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they u ...
.
* Centrifugal compressors are mostly used as
turbocharger
In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to pro ...
s and in small
gas turbine
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directi ...
engines like in an APU (
auxiliary power unit
An auxiliary power unit (APU) is a device on a vehicle that provides energy for functions other than propulsion. They are commonly found on large aircraft and naval ships as well as some large land vehicles. Aircraft APUs generally produce 115&n ...
) and as main engine for smaller aircraft like
helicopter
A helicopter is a type of rotorcraft in which lift and thrust are supplied by horizontally spinning rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and laterally. These attributes ...
s. A significant reason for this is that with current technology, the equivalent airflow
axial compressor
An axial compressor is a gas compressor that can continuously pressurize gases. It is a rotating, airfoil-based compressor in which the gas or working fluid principally flows parallel to the axis of rotation, or axially. This differs from other ...
will be less efficient due primarily to a combination of rotor and variable stator tip-clearance losses.
;Cons
*Their main drawback is that they cannot achieve the high
compression ratio
The compression ratio is the ratio between the volume of the cylinder and combustion chamber in an internal combustion engine at their maximum and minimum values.
A fundamental specification for such engines, it is measured two ways: the stati ...
of reciprocating compressors without multiple stages. There are few one-stage centrifugal compressors capable of pressure ratios over 10:1, due to stress considerations which severely limit the compressor's safety, durability and life expectancy.
*Centrifugal compressors are impractical, compared to axial compressors, for use in large
gas turbine
A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directi ...
s and
turbojet
The turbojet is an airbreathing jet engine which is typically used in aircraft. It consists of a gas turbine with a propelling nozzle. The gas turbine has an air inlet which includes inlet guide vanes, a compressor, a combustion chamber, and ...
engines propelling large aircraft, due to the resulting weight and stress, and to the frontal area presented by the large diameter of the radial diffuser.
Structural mechanics, manufacture and design compromise
Ideally, centrifugal compressor impellers have thin air-foil blades that are strong, each mounted on a light rotor. This material would be easy to machine or cast and inexpensive. Additionally, it would generate no operating noise, and have a long life while operating in any environment.
From the very start of the aero-thermodynamic design process, the aerodynamic considerations and optimizations
9,30are critical to have a successful design. during the design, the centrifugal impeller's material and manufacturing method must be accounted for within the design, whether it be plastic for a vacuum cleaner blower, aluminum alloy for a turbocharger, steel alloy for an air compressor or titanium alloy for a gas turbine. It is a combination of the centrifugal compressor impeller shape, its operating environment, its material and its manufacturing method that determines the impeller's structural integrity.
[Xu, C. and R.S. Amano, The Development of a Centrifugal Compressor Impeller, International Journal for Computational Methods in Engineering Science and Mechanics, Volume 10 Issue 4 2009, Pages 290 – 301.][Xu, C., Design experience and considerations for centrifugal compressor development., J. of Aerospace Eng. 2007]
See also
*
Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
*
Axial compressor
An axial compressor is a gas compressor that can continuously pressurize gases. It is a rotating, airfoil-based compressor in which the gas or working fluid principally flows parallel to the axis of rotation, or axially. This differs from other ...
*
Centrifugal force
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
*
Centripetal force
A centripetal force (from Latin ''centrum'', "center" and ''petere'', "to seek") is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous c ...
*
Coandă effect
The Coandă effect ( or ) is the tendency of a fluid jet to stay attached to a convex surface. ''Merriam-Webster'' describes it as "the tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to ent ...
*
Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate th ...
*
Compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fl ...
*
Compressor map A compressor map is a chart which shows the performance of a turbomachinery compressor. This type of compressor is used in gas turbine engines, for supercharging reciprocating engines and for industrial processes, where it is known as a dynamic comp ...
*
Coriolis force
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
*
Darcy–Weisbach equation
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation ...
*
Enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
*
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
*
Euler equations (fluid dynamics)
In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zer ...
*
Finite element method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
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Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
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Gas laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
Boyle ...
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Gustaf de Laval
Karl Gustaf Patrik de Laval (; 9 May 1845 – 2 February 1913) was a Swedish engineer and inventor who made important contributions to the design of steam turbines and centrifugal separation machinery for dairy.
Life
Gustaf de Laval was born a ...
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Ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
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Kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...
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Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \frac ...
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Multiphase flow
In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve s ...
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Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
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Real gas
Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law.
To understand the behaviour of real gases, the following must be taken into account:
*compressibility effects ...
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Reynolds-averaged Navier–Stokes equations
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged
equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged ...
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Reynolds transport theorem
In differential calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds (1842–1912), is a three-dimensional generalization of the Leibniz int ...
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Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
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Rossby number
The Rossby number (Ro), named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial force to Coriolis force, terms , \mathbf \cdot \nabla \mathbf, \sim U^2 / L and \Omega ...
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Three-dimensional losses and correlation in turbomachinery
Three-dimension losses and correlation in turbomachinery refers to the measurement of flow-fields in three dimensions, where measuring the loss of smoothness of flow, and resulting inefficiencies, becomes difficult, unlike two-dimensional losses w ...
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Turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
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Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
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von Karman Institute for Fluid Dynamics
The von Karman Institute for Fluid Dynamics (VKI) is a non-profit educational and scientific organization which specializes in three specific fields: aeronautics and aerospace, environment and applied fluid dynamics, turbomachinery and propulsi ...
References
External links
MIT Gas Turbine Laboratory(1948), First Marine Gas Turbine in Service. Journal of the American Society for Naval Engineers, 60: 66–86.
A history of Chrysler turbine cars To find API codes, standards & publicationsTo find ASME codes, standards & publicationsTo find ASHRAE codes, standards & publicationsHydrodynamics of Pumps, by Christopher Earls BrennenCtrend website to calculate the head of centrifugal compressor online
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Gas compressors
pt:Compressor#Compressores Dinâmicos
ru:Лопастной компрессор#Центробежный компрессор