Centrifugal compressor

# Centrifugal compressor

Overview
Centrifugal compressors, sometimes termed radial compressors, are a sub-class of dynamic axisymmetric work-absorbing turbomachinery
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 a rotor to a fluid...

.
The idealized compressive dynamic turbo-machine achieves a pressure rise by adding kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

/velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

to a continuous flow of fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

through the rotor or impeller
Impeller
An impeller is a rotor inside a tube or conduit used to increase the pressure and flow of a fluid.- Impellers in pumps :...

. This kinetic energy is then converted to an increase in potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

/static pressure by slowing the flow
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

through a diffuser.

Imagine a simple case where flow passes through a straight pipe to enter centrifugal compressor.
Discussion

Recent Discussions
Encyclopedia
Centrifugal compressors, sometimes termed radial compressors, are a sub-class of dynamic axisymmetric work-absorbing turbomachinery
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 a rotor to a fluid...

.
The idealized compressive dynamic turbo-machine achieves a pressure rise by adding kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

/velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

to a continuous flow of fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

through the rotor or impeller
Impeller
An impeller is a rotor inside a tube or conduit used to increase the pressure and flow of a fluid.- Impellers in pumps :...

. This kinetic energy is then converted to an increase in potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

/static pressure by slowing the flow
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

through a diffuser.

Imagine a simple case where flow passes through a straight pipe to enter centrifugal compressor. The simple flow is straight, uniform and has no swirl. As the flow continues to pass into and through the centrifugal impeller, the impeller forces the flow to spin faster and faster. According to a form of Euler's fluid dynamics equation, known as "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 many cases the flow leaving centrifugal impeller is near or above 1000 ft./s or approximately 300 m/s. It is at this point, in the simple case according to Bernoulli's principle
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy...

, where the flow passes into the stationary diffuser for the purpose of converting this velocity energy into pressure energy.

## Historical contributions, the pioneers

Over this past 100 years, applied scientists like Stodola
Aurel Stodola
Aurel Boleslav Stodola was an engineer, physicist, and inventor. He was an ethnic Slovak. He was a pioneer in the area of technical thermodynamics and its applications and published his book Die Dampfturbine in 1903...

(1903, 1927–1945), Pfleiderer (1952), Hawthorne (1964), Shepard (1956), Lakshminarayana (1996), and Japikse (many texts including, 1997), have tried to educate 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 why 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.

Figure 1.1 represents the aero
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

-thermo
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

domain of turbomachinery. The horizontal axis represents the energy equation derivable from The First Law of Thermodynamics. The vertical axis, which can be characterized by Mach Number, represents the range of fluid compressibility (or elasticity). The Zed axis, which can be characterized by Reynolds Number, represents the range of fluid viscosities (or stickiness). Mathematicians
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and Physicists
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

that established the foundations of this aero-thermo domain include: Sir Isaac Newton, Daniel Bernoulli
Daniel Bernoulli
Daniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

, Leonard Euler, Claude-Louis Navier
Claude-Louis Navier
Claude-Louis Navier born Claude Louis Marie Henri Navier , was a French engineer and physicist who specialized in mechanics.The Navier–Stokes equations are named after him and George Gabriel Stokes....

, Sir George Gabriel Stokes, Ernst Mach
Ernst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...

, Nikolay Yegorovich Zhukovsky, Martin Wilhelm Kutta
Martin Wilhelm Kutta
Martin Wilhelm Kutta was a German mathematician.Kutta was born in Pitschen, Upper Silesia . He attended the University of Breslau from 1885 to 1890, and continued his studies in Munich until 1894, where he became the assistant of Walther Franz Anton von Dyck. From 1898, he spent a year at the...

, Ludwig Prandtl, Theodore von Karman
Theodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...

, Paul Richard Heinrich Blasius
Paul Richard Heinrich Blasius
Paul Richard Heinrich Blasius was a German fluid dynamics engineer.He was one of the first students of Prandtl who provided a mathematical basis for boundary-layer drag but also showed as early as 1911 that the resistance to flow through smooth pipes could be expressed in terms of the Reynolds...

, and Henri Coandă
Henri Coanda
Henri Marie Coandă 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 controversial claim disputed by some and supported by others...

.

Figure 1.2 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 Zed 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
Denis Papin was a French physicist, mathematician and inventor, best known for his pioneering invention of the steam digester, the forerunner of the steam engine and of the pressure cooker.-Life in France:...

, Kernelien Le Demour, Daniel Gabriel Fahrenheit, John Smeaton, Dr. A. C. E. Rateau, John Barber
John Barber (engineer)
John Barber was an English coalmaster and inventor. He was born in Nottinghamshire, but moved to Warwickshire in the 1760s to manage collieries in the Nuneaton area. For a time he lived in Camp Hill House, between Hartshill and Nuneaton, and later lived in Attleborough...

, Alexander Sablukov
Alexander Sablukov
Alexander Alexandrovich Sablukov was a Russian Lieutenant General, engineer and inventor. Sablukov is credited with invention of the centrifugal fan and contribution to the development of centrifugal pump.-References:*...

, Sir Charles Algernon Parsons
Charles Algernon Parsons
Sir Charles Algernon Parsons OM KCB FRS was an Anglo-Irish engineer, best known for his invention of the steam turbine. He worked as an engineer on dynamo and turbine design, and power generation, with great influence on the naval and electrical engineering fields...

, Ægidius Elling
Ægidius Elling
Jens William Ægidius Elling was a Norwegian researcher, inventor and pioneer of gas turbine who is considered to be the father of the gas turbine. He built the first gas turbine that was able to produce more power than needed to run its own components.Elling was born in and grew up in Oslo, Norway...

, Sanford Alexander Moss
Sanford Alexander Moss
Sanford Alexander Moss was an aviation engineer, he was the first to use a turbocharger on an aircraft engine.-Biography:...

, Willis Carrier
Willis Carrier
Willis Haviland Carrier was an American engineer and inventor, and is known as the man who invented modern air conditioning....

Adolph Busemann was a German aerospace engineer and influential early pioneer in aerodynamics, specialising in supersonic airflows...

, Hermann Schlichting
Hermann Schlichting
Hermann Schlichting 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 Göttingen...

, and Frank Whittle
Frank Whittle
Air Commodore Sir Frank Whittle, OM, KBE, CB, FRS, Hon FRAeS was a British Royal Air Force engineer officer. He is credited with independently inventing the turbojet engine Air Commodore Sir Frank Whittle, OM, KBE, CB, FRS, Hon FRAeS (1 June 1907 – 9 August 1996) was a British Royal Air...

.

### Partial timeline

| <1689
| Early turbomachines
| Pumps, blowers, fans
|-
| 1689
| Denis Papin
| Origin of the centrifugal compressor
|-
| 1754
| Leonhard Euler
| Euler's "Pump & Turbine" equation
|-
| 1791
| John Barber
| First gas turbine patent
|-
| 1899
| Dr. A. C. E. Rateau
| First practical centrifugal compressor
|-
| 1927
| Aurel Boleslav Stodola
| Formalized "slip factor"
|-
| 1928
| Derived "slip factor"
|-
| 1937
| Frank Whittle
| First gas turbine using centrifugal compressor
|-
| >1970
| Modern turbomachines
| 3D-CFD, rocket turbo-pumps, heart assist pumps, turbocharged fuel cells
|}

## Turbomachinery similarities

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Centrifugal compressors are similar to axial compressor
Axial compressor
Axial compressors are rotating, airfoil-based compressors in which the working fluid principally flows parallel to the axis of rotation. This is in contrast with other rotating compressors such as centrifugal, axi-centrifugal and mixed-flow compressors where the air may enter axially but will have...

s in that they are rotating airfoil based compressors as shown in Figure 2.1. It should not be surprising that 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 greater change in radius from inlet to exit of the rotor/impeller.

Centrifugal compressors are also similar to centrifugal blowers
Centrifugal fan
A centrifugal fan is a mechanical device for moving air or other gases. It has a fan wheel composed of a number of fan blades, or ribs, mounted around a hub. As shown in Figure 1, the hub turns on a driveshaft that passes through the fan housing...

of the style shown in Figure 2.2 as they both increase pressure with the benefit of increasing radius. In contrast to centrifugal blowers, compressors operate at higher speeds to generate greater pressure rises. In many cases the engineering methods used to design a centrifugal blower are the same as those to design a centrifugal compressor. As a result they can at times look very similar. This relationship is less true in comparison to a squirrel-cage fan
Centrifugal fan
A centrifugal fan is a mechanical device for moving air or other gases. It has a fan wheel composed of a number of fan blades, or ribs, mounted around a hub. As shown in Figure 1, the hub turns on a driveshaft that passes through the fan housing...

as shown in Figure 2.3. 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
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...

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 5 percent and peak relative fluid velocities below Mach 0.3.

Centrifugal compressors are also similar to centrifugal pump
Centrifugal pump
A centrifugal pump is a rotodynamic pump that uses a rotating impeller to create flow by the addition of energy to a fluid. Centrifugal pumps are commonly used to move liquids through piping...

s of the style shown in Figure 2.4. 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
Cavitation is the formation and then immediate implosion of cavities in a liquidi.e. small liquid-free zones that are the consequence of forces acting upon the liquid...

in pumps.

Centrifugal compressors also look very similar to their turbomachinery counterpart the radial-inflow turbine as shown in Figure 2.5. 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.

## Components of a simple centrifugal compressor

A simple centrifugal compressor has four components: inlet, impeller/rotor, diffuser, and collector. Figure 3.1 shows each of the components of the flow path, with the flow (working gas) entering the centrifugal impeller axially from right to left. As a result of the impeller rotating clockwise when looking downstream into the compressor, the flow will pass through the volute's discharge cone moving away from the figure's viewer.

### Inlet

The inlet to a centrifugal compressor is typically a simple pipe. It may include features such as a valve, stationary vanes/airfoils (used to help swirl the flow) and both pressure and temperature instrumentation. All of these additional devices have important uses in the control of the centrifugal compressor.

### Centrifugal impeller

The key component that makes a compressor centrifugal is the centrifugal impeller, Figure 01. It is the impeller's rotating set of vanes (or blades) that gradually raises the energy of the working gas. This is identical to an axial compressor with the exception that the gases can reach higher velocities and 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.

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). Both Figures 0.1 and 3.1 show open impellers with splitters. Most modern high efficiency impellers use "backsweep" in the blade shape.

Euler’s pump and turbine equation plays an important role in understanding impeller performance.

### Diffuser

The next key component to the simple centrifugal compressor is the diffuser. Downstream of the impeller in the flow path, it is the diffuser's responsibility to convert the kinetic energy (high velocity) of the gas into 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, channel, and pipe diffusers. There are turbocharger applications that benefit by incorporating no diffuser.

Bernoulli's fluid dynamic principal
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy...

plays an important role in understanding diffuser performance.

### Collector

The collector of a centrifugal compressor can take many shapes and forms. When the diffuser discharges into a large empty chamber, the collector may be termed a Plenum. When the diffuser discharges into a device that looks somewhat like a snail shell, bull's horn or a French horn, the collector is likely to be termed a volute or scroll. As the name implies, a collector’s purpose is to gather the flow from the diffuser discharge annulus and deliver this flow to a downstream pipe. Either the collector or the pipe may also contain valves and instrumentation to control the compressor. For example, a turbocharger blow-off valve.

## 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.

• In gas turbine
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

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 turboshaft, turboprop, auxiliary power units, and micro-turbines. The industry standards applied to all of the centrifugal compressors used in aircraft applications are set by the FAA and the military to maximize both safety and durability under severe conditions.

• In automotive engine and diesel engine
Diesel engine
A diesel engine is an internal combustion engine that uses the heat of compression to initiate ignition to burn the fuel, which is injected into the combustion chamber...

turbocharger
Turbocharger
A turbocharger, or turbo , from the Greek "τύρβη" is a centrifugal compressor powered by a turbine that is driven by an engine's exhaust gases. Its benefit lies with the compressor increasing the mass of air entering the engine , thereby resulting in greater performance...

s and supercharger
Supercharger
A supercharger is an air compressor used for forced induction of an internal combustion engine.The greater mass flow-rate provides more oxygen to support combustion than would be available in a naturally aspirated engine, which allows more fuel to be burned and more work to be done per cycle,...

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
SAE or Sae may refer to:* Soviet Antarctic Expedition* Scientific Audio Electronics* 3GPP System Architecture Evolution* Space Age Electronics* Supervised agricultural experience* a serious adverse event in a clinical trial...

. Ideal gas properties often work well for the design, test and analysis of turbocharger centrifugal compressor performance.

• In pipeline compressors
Pipeline transport
Pipeline transport is the transportation of goods through a pipe. Most commonly, liquids and gases are sent, but pneumatic tubes that transport solid capsules using compressed air are also used....

of natural gas
Natural gas
Natural gas is a naturally occurring gas mixture consisting primarily of methane, typically with 0–20% higher hydrocarbons . It is found associated with other hydrocarbon fuel, in coal beds, as methane clathrates, and is an important fuel source and a major feedstock for fertilizers.Most natural...

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 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 an API-style. The power needed to drive these compressors is most often in the thousands of horsepower (HP). Use of real gas properties is needed to properly design, test and analyze the performance of natural gas pipeline centrifugal compressors.

• In oil refineries, natural gas processing
Natural gas processing
Natural-gas processing is a complex industrial process designed to clean raw natural gas by separating impurities and various non-methane hydrocarbons and fluids to produce what is known as pipeline quality dry natural gas.-Background:...

, petrochemical
Petrochemical
Petrochemicals are chemical products derived from petroleum. Some chemical compounds made from petroleum are also obtained from other fossil fuels, such as coal or natural gas, or renewable sources such as corn or sugar cane....

and chemical plant
Chemical plant
A chemical plant is an industrial process plant that manufactures chemicals, usually on a large scale. The general objective of a chemical plant is to create new material wealth via the chemical or biological transformation and or separation of materials. Chemical plants use special equipment,...

s.
Centrifugal compressors for such uses are often one-shaft multi-stage and driven by large steam or gas turbines. Their casings are often termed horizontally split or barrel. Standards set by the industry (ANSI/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 power needed to drive these compressors is most often in the thousands of HP. Use of real gas properties is needed to properly design, test and analyze their performance.

• Air-conditioning and refrigeration
Refrigeration
Refrigeration is a process in which work is done to move heat from one location to another. This work is traditionally done by mechanical work, but can also be done by magnetism, laser or other means...

and HVAC
HVAC
HVAC refers to technology of indoor or automotive environmental comfort. HVAC system design is a major subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics, and heat transfer...

: Centrifugal compressors quite often supply the compression in water chillers
Vapor-compression refrigeration
Vapor-compression refrigeration is one of the many refrigeration cycles available for use. It has been and is the most widely used method for air-conditioning of large public buildings, offices, private residences, hotels, hospitals, theaters, restaurants and automobiles...

cycles.
Because of the wide variety of vapor compression cycles (thermodynamic cycle
Thermodynamic cycle
A thermodynamic cycle consists of a series of thermodynamic processes transferring heat and work, while varying pressure, temperature, and other state variables, eventually returning a system to its initial state...

, thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

) and the wide variety of workings gases (refrigerant
Refrigerant
A refrigerant is a substance used in a heat cycle usually including, for enhanced efficiency, a reversible phase change from a liquid to a gas. Traditionally, fluorocarbons, especially chlorofluorocarbons, were used as refrigerants, but they are being phased out because of their ozone depletion...

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
Pneumatic tool
A pneumatic tool or air tools is a tool driven by a gas, usually compressed air supplied by a gas compressor. Pneumatic tools can also be driven by compressed carbon dioxide stored in small cylinders allowing for portability...

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. Note that the road repair crew and the local automobile repair garage 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
Oil field
An oil field is a region with an abundance of oil wells extracting petroleum from below ground. Because the oil reservoirs typically extend over a large area, possibly several hundred kilometres across, full exploitation entails multiple wells scattered across the area...

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, casing 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. Use of real gas properties is needed to properly design, test and analyze their performance.

## Performance

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. Studying these two plots further we see that the pressure rises between the compressor inlet (station 1) and compressor exit (station 2). At the same time, it is easy to see that the specific volume decreases or similarly the density increases. Studying the temperature-entropy plot we see the temperature increase with increasing entropy (loss). If we assume dry air, and ideal gas equation of state and an isentropic process, we have enough information to define the pressure ratio and efficiency for this one point. Unfortunately, we are missing several other key pieces of information if we wish to apply the centrifugal compressor to another application.

Figure 5.2, a centrifugal compressor performance map (either test or estimated), shows 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 (i.e. PTC–10, Fluid Meters Handbook, PTC-19.x), ASHRAE (ASHRAE Handbook
ASHRAE Handbook
The ASHRAE Handbook is the four-volume flagship publication of the nonprofit technical organization American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc....

) and API (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. Making this assumption in a real case would be a significant error. A detailed inspection of Figure 5.2 shows:
• Flow — kg/s (range: 0.04 - 0.34 kg/s)
• Pressure — pressure ratio (t-t) (range 1.0 - 2.6 PR_t-t)
"t-t" implies the discharge total pressure is divided by the inlet total pressure (Pt_discharge/Pt_inlet).

As is standard practice, Figure 5.2 has a horizontal axis labeled with a flow parameter. While flow measurements use a wide variety unit specifications, all fit one of 2 categories:
• Mass flow per unit time
• Volume flow per unit time

Mass flows, 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.

In contrast, all volume flow specifications require the additional specification of density. Bernoulli's fluid dynamic principal 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. The variety of pressure measurement units is also vast. In this case, they all fit one of three categories:
• The delta increase or rise from inlet to exit (Manometer style)
• The measured discharge pressure (force)
• The force ratio (ratio, exit/inlet)

• Constant speed lines
The two most common methods used for testing centrifugal compressors is to test along lines of constant shaft speed or along lines of constant throttle. If the shaft 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 (common gas turbine practice). The map shown in Figure 5.2 illustrate 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 as 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 point(s) 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 compressors 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 by 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 the point at which the compressor cannot add enough energy to overcome the system resistance or backpressure.

This causes a rapid flow reversal (i.e. surge). As a result, high vibration, temperature increases, and rapid changes in axial thrust can occur. 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, the cycles/processes that they are used within can be far less robust.

• Surge Line
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 backpresuure. 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.
• Choke
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.

• Maximum flow line
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 use 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.

• Stonewall
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 (mu) 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 Buckingham's Pi-Therom 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 examples below Head will be substituted for pressure and sonic velocity will be substituted for elasticity.

### 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:

| Flow:
|
|
| ex. = m^3/s
|-
|
|
| ex. = kg*m/s^2
|-
| Speed:
|
|
| ex. = m/s
|-
| Power:
|
|
| ex. = kg*m^2/s^3
|-
| Density:
|
|
| ex. = kg/m^3
|-
| Viscosity:
|
|
| ex. = kg/(m*s)
|-
| Diameter:
|
|
| ex. = m
|-
| Speed of sound:
|
|
| ex. = m/s
|}

### 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 of the 5 Pi-parameters are equivalent. This of course would mean the two turbomachines being compared are geometrically similar and running at the same operating point.

| Flow coefficient:
|
|
|-
|
|
|-
| Speed coefficient:
|
|
|-
| Power coefficient:
|
|
|-
| Reynolds coefficient:
|
|
|}

Turbomachinery analysts gain tremendous insight into performance by comparisons of these 5 parameters with 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 velocity coefficient is of secondary importance while the Reynolds coefficient is of tertiary importance. In contrast, as expected for pumps, the Reynolds number becomes of secondary importance and the velocity coefficient almost irrelevant. It may be found interesting that the speed coefficient is used to define the y-axis of Figure 1.1, while at the same time the Reynolds coefficient is used to define the zed 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.

|
| Corrected mass flow coefficient:
|
|
|-
|
| Alternate#1 equivalent Mach form:
|
|
|-
|
| Alternate#2 simplified dimensional form:
|
|
|-
|
| Specific speed coefficient:
|
|
|-
|
| Specific diameter coefficient:
|
|
|}

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 zed axis.

### Affinity laws

The following "affinity laws" are derived from the five Pi-parameters shown above. They provide a simple basis for scaling turbomachinery from one application to the next.

| From flow coefficient:
|
|
|-
|
|
|-
| From power coefficient:
|
|
|-
| From flow coefficient:
|
|
|-
|
|
|-
| From power coefficient:
|
|
|}

## 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, this fundamental is derivable from Newton's second law  when applied to fluid motion
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

. Written in compressible form for a Newtonian fluid, this equation may be written as follows:

### Conservation of energy

The First Law of Thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

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
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

and is entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. 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.

### Equation of state

The classical ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

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
Heat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...

), 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 the 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 gas
Real gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behaviour of real gases, the following must be taken into account:* compressibility effects;...

equation of state
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...

rather than ideal gases. The Wikipedia entry for equations of state is very thorough.

## Pros and cons

• Pros
Centrifugal compressors are used throughout industry because they have fewer rubbing parts, are relatively energy efficient, and give higher airflow than a similarly sized reciprocating compressor
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....

or positive-displacement compressor.

• Cons
Their main drawback is that they cannot achieve the high compression ratio
Compression ratio
The 'compression ratio' of an internal-combustion engine or external combustion engine is a value that represents the ratio of the volume of its combustion chamber from its largest capacity to its smallest capacity...

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.

• Pros
Centrifugal compressors are often used in small gas turbine
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

engines like APUs (auxiliary power units) and smaller aircraft gas turbines. A significant reason for this is that with current technology, the equivalent flow axial compressor
Axial compressor
Axial compressors are rotating, airfoil-based compressors in which the working fluid principally flows parallel to the axis of rotation. This is in contrast with other rotating compressors such as centrifugal, axi-centrifugal and mixed-flow compressors where the air may enter axially but will have...

will be less efficient due primarily to a combination of rotor and variable stator tip-clearance losses. Further, they offer the advantages of simplicity of manufacture and relatively low cost. This is due to requiring fewer stages to achieve the same pressure rise.

• Cons
Centrifugal compressors are less practical than axial turbines for propelling large aircraft, due to the resulting weight and stress, and to the frontal area presented by the diffuser.

## Turbomachinery

Many types of dynamic continuous flow turbomachinery are treated in Wikipedia. Below is a partial list of these topics. What is notable about this set is that the fundamentals that apply to centrifugal compressors also apply to each of these topics. Certainly there are significant differences between these machines and between the types of analysis that are typically applied to specific cases. This does not negate that they are unified by the same underlying physics of fluid dynamics, gas dynamics, aerodynamics, hydrodynamics, and thermodynamics.

• Axial compressor
Axial compressor
Axial compressors are rotating, airfoil-based compressors in which the working fluid principally flows parallel to the axis of rotation. This is in contrast with other rotating compressors such as centrifugal, axi-centrifugal and mixed-flow compressors where the air may enter axially but will have...

• Axial fan

• Centrifugal fan
Centrifugal fan
A centrifugal fan is a mechanical device for moving air or other gases. It has a fan wheel composed of a number of fan blades, or ribs, mounted around a hub. As shown in Figure 1, the hub turns on a driveshaft that passes through the fan housing...

• Centrifugal pump
Centrifugal pump
A centrifugal pump is a rotodynamic pump that uses a rotating impeller to create flow by the addition of energy to a fluid. Centrifugal pumps are commonly used to move liquids through piping...

• Centrifugal type supercharger
Centrifugal type supercharger
The centrifugal-type supercharger is an engine-driven compressor used to increase the power output of an internal-combustion engine by increasing the amount of available oxygen by compressing air that is entering the engine...

• Francis turbine
Francis turbine
The Francis turbine is a type of water turbine that was developed by James B. Francis in Lowell, Massachusetts. It is an inward-flow reaction turbine that combines radial and axial flow concepts....

• Gas turbine
Gas turbine
A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....

• Industrial fans
Industrial fans
Industrial fans and blowers are machines whose primary function is to provide a large flow of air or gas to various processes of many industries. This is achieved by rotating a number of blades, connected to a hub and shaft, and driven by a motor or turbine. The flow rates of these fans range from...

• Jet engine
Jet engine
A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...

• Mechanical fan
• Mixed flow compressor
Mixed flow compressor
A mixed flow compressor combines the axial and radial components to produce a diagonal flow unit. The exit mean radius is greater than at the inlet, but the flow tends to exit in an axial rather than radial direction...

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 air flows through the components...

• Steam turbine
Steam turbine
A steam turbine is a mechanical device that extracts thermal energy from pressurized steam, and converts it into rotary motion. Its modern manifestation was invented by Sir Charles Parsons in 1884....

• Turbocharger
Turbocharger
A turbocharger, or turbo , from the Greek "τύρβη" is a centrifugal compressor powered by a turbine that is driven by an engine's exhaust gases. Its benefit lies with the compressor increasing the mass of air entering the engine , thereby resulting in greater performance...

• Turboexpander
Turboexpander
A turboexpander, also referred to as a turbo-expander or an expansion turbine, is a centrifugal or axial flow turbine through which a high pressure gas is expanded to produce work that is often used to drive a compressor....

• Turbofans
• Turbojet
• Turbomachinery
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 a rotor to a fluid...

• Turboprop
Turboprop
A turboprop engine is a type of turbine engine which drives an aircraft propeller using a reduction gear.The gas turbine is designed specifically for this application, with almost all of its output being used to drive the propeller...

• Turbopump
Turbopump
A turbopump is a gas turbine that comprises basically two main components: a rotodynamic pump and a driving turbine, usually both mounted on the same shaft, or sometimes geared together...

• Turboshaft
Turboshaft
A turboshaft engine is a form of gas turbine which is optimized to produce free turbine shaft power, rather than jet thrust...

• Turbines

• Water turbine
Water turbine
A water turbine is a rotary engine that takes energy from moving water.Water turbines were developed in the 19th century and were widely used for industrial power prior to electrical grids. Now they are mostly used for electric power generation. They harness a clean and renewable energy...

• Aircraft engine
Aircraft engine
An aircraft engine is the component of the propulsion system for an aircraft that generates mechanical power. Aircraft engines are almost always either lightweight piston engines or gas turbines...

• Angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

• Coandă effect
Coanda effect
The Coandă effect is the tendency of a fluid jet to be attracted to a nearby surface. The principle was named after Romanian aerodynamics pioneer Henri Coandă, who was the first to recognize the practical application of the phenomenon in aircraft development....

• Computational Fluid Dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...

• Compressibility
• Compressors
• Compressor map
Compressor map
Each compressor in a gas turbine engine has an operating map. Complete maps are either based on compressor rig test results or are predicted by a special computer program...

• Corrected speed
Corrected speed
Corrected Speed is the speed a component would rotate at if the inlet temperature corresponded to ambient conditions at Sea Level, on a Standard Day Corrected Speed is the speed a component would rotate at if the inlet temperature corresponded to ambient conditions at Sea Level, on a Standard Day...

• Darcy–Weisbach equation
• Gustaf de Laval
Gustaf de Laval
Karl Gustaf Patrik de Laval was a Swedish engineer and inventor who made important contributions to the design of steam turbines and dairy machinery.-Life:De Laval was born at Orsa in Dalarna...

• Enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

• Entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

• Euler equations (fluid dynamics)
• Finite element analysis
• Fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

• Gas compressor
Gas compressor
A gas compressor is a mechanical device that increases the pressure of a gas by reducing its volume.Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe. As gases are compressible, the compressor also reduces the volume of a gas...

• Gas laws
Gas laws
The early gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases...

• History of the internal combustion engine
History of the internal combustion engine
Although various forms of internal combustion engines were developed before the 19th century, their use was hindered until the commercial drilling and production of petroleum began in the mid-1850s...

• Ideal gas law
Ideal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

• Pumps
• Real gas
Real gas
Real gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behaviour of real gases, the following must be taken into account:* compressibility effects;...

• HVAC
HVAC
HVAC refers to technology of indoor or automotive environmental comfort. HVAC system design is a major subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics, and heat transfer...

• List of mechanical engineering topics
• List of aerospace engineering topics
• List of engineering topics
• Mach number
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...

• Multiphase flow
Multiphase flow
In fluid mechanics, multiphase flow is a generalisation of the modelling used in two-phase flow to cases where the two phases are not chemically related or where more than two phases are present In fluid mechanics, multiphase flow is a generalisation of the modelling used in two-phase flow to...

• Navier-Stokes equations
Navier-Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous...

• Reynolds-averaged Navier–Stokes equations
• Reynolds transport theorem
Reynolds transport theorem
Reynolds' transport theorem , or in short Reynolds theorem, is a three-dimensional generalization of the Leibniz integral rule which is also known as differentiation under the integral sign....

• Osborne Reynolds
Osborne Reynolds
Osborne Reynolds FRS was a prominent innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design.-Life:...

• Reynolds number
• Refineries
• Turbine map
Turbine map
Each turbine in a gas turbine engine has an operating map. Complete maps are either based on turbine rig test results or are predicted by a special computer program. Alternatively, the map of a similar turbine can be suitably scaled.-Description:...

• Turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

• Viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

• Vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

• Von Karman Institute for Fluid Dynamics (VKI)