Centrifugal compressor

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Centrifugal impeller, shown alone Compressor wheel Napier NA357.JPG
Centrifugal impeller, shown alone
Centrifugal compressor shown (in blue) as part of a turbocharger Turbocharger.jpg
Centrifugal compressor shown (in blue) as part of a turbocharger
Centrifugal compressor shown (in blue) as second stage of a axi-centrifugal jet-engine Saturn MD-120 cutaway.jpg
Centrifugal compressor shown (in blue) as second stage of a axi-centrifugal jet-engine

Centrifugal compressors, sometimes called impeller compressors or radial compressors, are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. [1]

Contents

They achieve pressure rise by adding energy to the continuous flow of fluid through the rotor/impeller. The equation in the next section 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.

Components of a simple centrifugal compressor

Figure-1.1 - 2-Stage turboshaft, 1st-stage flowpath, annular inlet, guide vanes, open impeller, vaned diffuser, vaneless return-bend Gearbox and compressors of sectioned Rolls-Royce Dart turboprop.jpg
Figure-1.1 - 2-Stage turboshaft, 1st-stage flowpath, annular inlet, guide vanes, open impeller, vaned diffuser, vaneless return-bend

A simple centrifugal compressor stage has four components (listed in order of throughflow): inlet, impeller/rotor, diffuser, and collector. [1] 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 adiabatic flow, this equation can be written in the form:

Equation-1.1

where:

Centrifugal impeller

Figure 1.2.1 - Graphic modeling of the impeller, similar to turbocharger impeller 2 polys.png
Figure 1.2.1 - Graphic modeling of the impeller, similar to turbocharger impeller

The identifying component of a centrifugal compressor stage is the centrifugal impeller rotor. Impellers are designed in many configurations including "open" (visible blades), "covered or shrouded", "with splitters" (every other inducer removed), and "w/o splitters" (all full blades). Figures 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. [2] [3] [4]

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

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

where:

Diffuser

Figure 1.3 - NASA CC3 impeller and wedge diffuser NASA CC3 impeller and wedge diffuser.jpg
Figure 1.3 - NASA CC3 impeller and wedge diffuser

The next component, downstream of the impeller within a simple centrifugal compressor may the diffuser. [5] [4] The diffuser converts the flow's kinetic energy (high velocity) into increased potential energy (static pressure) by gradually slowing (diffusing) the gas velocity. Diffusers can be vaneless, vaned, or an alternating combination. High-efficiency vaned diffusers are also designed over a wide range of solidities from less than 1 to over 4. Hybrid versions of vaned diffusers include wedge (see Figure 1.3), channel, and pipe diffusers. Some turbochargers have no diffuser. Generally accepted nomenclature might refer to the diffuser's lead edge as station 3 and the trailing edge as station 4.

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

Equation-1.3

where:

Collector

Figure 1.4 - Centrifugal compressor model illustrating the main components Main components of a centrifugal compressor in isometric view.svg
Figure 1.4 - Centrifugal compressor model illustrating the main components

The collector of a centrifugal compressor can take many shapes and forms. [5] [4] 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. [6]

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:

Historical contributions, the pioneers

Over the past 100 years, applied scientists including Stodola (1903, 1927–1945), [7] Pfleiderer (1952), [8] Hawthorne (1964), [9] Shepherd (1956), [1] Lakshminarayana (1996), [10] and Japikse (many texts including citations), [2] [11] [ citation needed ] [12] 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 2.1 and 2.2 illustrate the domain of turbomachinery with labels showing centrifugal compressors. [13] [14] 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

Figure 2.1 - Aero-thermo domain of turbomachinery AeroTurboDomain.PNG
Figure 2.1 – Aero-thermo domain of turbomachinery

Figure 2.1 (shown right) represents the aero-thermo domain of turbomachinery. The horizontal axis represents the energy equation derivable from The first law of thermodynamics. [1] [14] The vertical axis, which can be characterized by Mach Number, represents the range of fluid compressibility (or elasticity). [1] [14] The Z-axis, which can be characterized by Reynolds number, represents the range of fluid viscosities (or stickiness). [14] Mathematicians and physicists who established the foundations of this aero-thermo domain include: [15] [16] Isaac Newton, Daniel Bernoulli, Leonhard Euler, Claude-Louis Navier, George Stokes, Ernst Mach, Nikolay Yegorovich Zhukovsky, Martin Kutta, Ludwig Prandtl, Theodore von Kármán, Paul Richard Heinrich Blasius, and Henri Coandă.

Physical-mechanical domain

Figure 2.2 - Physical domain of turbomachinery PhysTurboDomain.PNG
Figure 2.2 – Physical domain of turbomachinery

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. [1] [14] Within the physical domain the vertical axis differentiates between high speeds and low speeds depending upon the turbomachinery application. [1] [14] The Z-axis differentiates between axial-flow geometry and radial-flow geometry within the physical domain of turbomachinery. [1] [14] It is implied that mixed-flow turbomachinery lie between axial and radial. [1] [14] Key contributors of technical achievements that pushed the practical application of turbomachinery forward include: [15] [16] Denis Papin, [17] Kernelien Le Demour, Daniel Gabriel Fahrenheit, John Smeaton, Dr. A. C. E. Rateau, [18] John Barber, Alexander Sablukov, Sir Charles Algernon Parsons, Ægidius Elling, Sanford Alexander Moss, Willis Carrier, Adolf Busemann, Hermann Schlichting, Frank Whittle and Hans von Ohain.

Partial timeline of historical contributions

Table 2.1
<1689Early turbomachinesPumps, blowers, fans
1689Denis PapinOrigin of the centrifugal compressor
1754Leonhard EulerEuler's "Pump & Turbine" equation
1791John BarberFirst gas turbine patent
1899A. C. E. RateauFirst practical centrifugal compressor
1927Aurel Boleslav StodolaFormalized "slip factor"
1928Adolf BusemannDerived "slip factor"
1937Frank Whittle and Hans von Ohain, independentlyFirst gas turbine using a centrifugal compressor
>1970Modern turbomachines3D-CFD, rocket turbo-pumps, heart assist pumps, turbocharged fuel cells

Turbomachinery similarities

Centrifugal compressors are similar in many ways to other turbomachinery and are compared and contrasted as follows:

Similarities to axial compressor

Cutaway showing an axi-centrifugal compressor gas turbine Turboprop T-53.jpg
Cutaway showing an axi-centrifugal compressor gas turbine

Centrifugal compressors are similar to axial compressors 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. [10] 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 [19] in the Pratt & Whitney Canada PW200 series of helicopter engines) than does an axial stage. The 1940s-era German Heinkel HeS 011 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 series of small turbofans.

Centrifugal fan

A low speed, low-pressure centrifugal compressor or centrifugal fan, with upward discharging cone used to diffuse the air velocity CentrifugalCompressor.jpg
A low speed, low-pressure centrifugal compressor or centrifugal fan, with upward discharging cone used to diffuse the air velocity

Centrifugal compressors are also similar to centrifugal fans of the style shown in the neighboring figure as they both increase the energy of the flow through the increasing radius. [1] 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 0.3 [20] 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

A low-speed, low-pressure blower used for HVAC ventilation CentrifugalFan.png
A low-speed, low-pressure blower used for HVAC ventilation

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 Pump-mod.jpg
A 3D-solids model of a type of centrifugal pump
Centrifugal Pump.png
Cut-away of a centrifugal pump

Centrifugal compressors are also similar to centrifugal pumps [1] 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 in pumps.

Radial turbine

Centrifugal compressors also look very similar to their turbomachinery counterpart the radial turbine 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.[ citation needed ] 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:

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. [10]

Figure 4.1 - Jet engine cutaway showing the centrifugal compressor and other parts DH Goblin annotated colour cutaway.png
Figure 4.1 – Jet engine cutaway showing the centrifugal compressor and other parts
Figure 4.2 - Jet engine cross section showing the centrifugal compressor and other parts Turbojet operation-centrifugal flow-en.svg
Figure 4.2 – Jet engine cross section showing the centrifugal compressor and other parts

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'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 many cases, the flow leaving the centrifugal impeller is traveling near the speed of sound. 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, the reduction in velocity causes the pressure to rise. [1]

Performance

Figure 5.1 - Illustration of the Brayton cycle as applied to a gas turbine Brayton cycle.svg
Figure 5.1 – Illustration of the Brayton cycle as applied to a gas turbine
Figure 5.2 - Example centrifugal compressor performance map Cent comp map.PNG
Figure 5.2 – Example centrifugal compressor performance map

While illustrating a gas turbine's Brayton cycle, [15] 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. [12] Further, testing centrifugal compressor performance is very complex. Professional societies such as ASME (i.e. PTC–10, Fluid Meters Handbook, PTC-19.x), [34] ASHRAE (ASHRAE Handbook) and API (ANSI/API 617–2002, 672–2007) [31] [33] 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 [15] [31] [33] [34] 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:

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, . [35] 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. [36] 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). [37] 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

Figure-6.2.1 Stall formation StallFormation.svg
Figure-6.2.1 Stall formation

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. [1] [ citation needed ] [16] 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:

According to the theorem each of the eight main parameters are equated to its independent dimensions as follows:

Flowex. = m3/s
Headex. = kg·m/s2
Speedex. = m/s
Powerex. = kg·m2/s3
Densityex. = kg/m3
Viscosityex. = kg/m·s
Diameterex. = m
Speed of soundex. = 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. [1] 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.

Table of Classic dimension-less similitude parameters
1Flow-coefficient
Head-coefficient
3Speed-coefficient
4Power-coefficient
5Reynolds-coefficient

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. [38]

1Corrected mass flow coefficient
2Alternate#1 equivalent Mach form
3Alternate#2 simplified dimensional form
4Specific speed coefficient
5Specific 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 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.

From flow coefficient
From head 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. [10] [39] 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. Written in compressible form for a Newtonian fluid, this equation may be written as follows:

Conservation of energy

The first law of thermodynamics 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 and is entropy. 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 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), 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 equation of state rather than ideal gases. The Wikipedia entry for equations of state is very thorough.

Pros and cons

Pros
Cons

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.[ clarification needed ]

From the very start of the aero-thermodynamic design process, the aerodynamic considerations and optimizations [29,30] are 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. [40] [41]

See also

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A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor.

<span class="mw-page-title-main">Axial compressor</span> Machine for continuous flow gas compression

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 rotating compressors such as centrifugal compressor, axi-centrifugal compressors and mixed-flow compressors where the fluid flow will include a "radial component" through the compressor.

<span class="mw-page-title-main">Turbomachinery</span> Machine for exchanging energy with a fluid

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. It is an important application of fluid mechanics.

<span class="mw-page-title-main">Centrifugal pump</span> Pump used to transport fluids by conversion of rotational kinetic energy

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 axisymmetric work-absorbing turbomachinery. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from which it exits.

<span class="mw-page-title-main">Axial-flow pump</span> Type of pump consisting of a propeller in a pipe

An axial-flow pump, or AFP, is a common type of pump that essentially consists of a propeller in a pipe. The propeller can be driven directly by a sealed motor in the pipe or by electric motor or petrol/diesel engines mounted to the pipe from the outside or by a right-angle drive shaft that pierces the pipe.

In a hydraulic circuit, net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation:

  1. The Available NPSH (NPSHA): a measure of how close the fluid at a given point is to flashing, and so to cavitation. Technically it is the absolute pressure head minus the vapour pressure of the liquid.
  2. The Required NPSH (NPSHR): the head value at the suction side required to keep the fluid away from cavitating.

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 compressor. A map is created from compressor rig test results or predicted by a special computer program. Alternatively the map of a similar compressor can be suitably scaled. This article is an overview of compressor maps and their different applications and also has detailed explanations of maps for a fan and intermediate and high-pressure compressors from a three-shaft aero-engine as specific examples.

A jet engine performs by converting fuel into thrust. How well it performs is an indication of what proportion of its fuel goes to waste. It transfers heat from burning fuel to air passing through the engine. In doing so it produces thrust work when propelling a vehicle but a lot of the fuel is wasted and only appears as heat. Propulsion engineers aim to minimize the degradation of fuel energy into unusable thermal energy. Increased emphasis on performance improvements for commercial airliners came in the 1970s from the rising cost of fuel.

Specific speedNs, is used to characterize turbomachinery speed. Common commercial and industrial practices use dimensioned versions which are of equal utility. Specific speed is most commonly used in pump applications to define the suction specific speed —a quasi non-dimensional number that categorizes pump impellers as to their type and proportions. In Imperial units it is defined as the speed in revolutions per minute at which a geometrically similar impeller would operate if it were of such a size as to deliver one gallon per minute against one foot of hydraulic head. In metric units flow may be in l/s or m3/s and head in m, and care must be taken to state the units used.

<span class="mw-page-title-main">Centrifugal fan</span> Mechanical fan that forces fluid to move radially outward

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 fan is also called a blower, blower fan, or squirrel-cage fan. Tiny ones used in computers are sometimes called biscuit blowers. These fans move air from the rotating inlet of the fan to an outlet. They are typically used in ducted applications to either draw air through ductwork/heat exchanger, or push air through similar impellers. Compared to standard axial fans, they can provide similar air movement from a smaller fan package, and overcome higher resistance in air streams.

<span class="mw-page-title-main">Radial turbine</span> Type of 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. Whereas for an axial turbine the rotor is 'impacted' by the fluid flow, for a radial turbine, the flow is smoothly orientated perpendicular to the rotation axis, and it drives the turbine in the same way water drives a watermill. The result is less mechanical stress which enables a radial turbine to be simpler, more robust, and more efficient when compared to axial turbines. When it comes to high power ranges the radial turbine is no longer competitive and the efficiency becomes similar to that of the axial turbines.

In fluid dynamics, flow can be decomposed into primary flow plus secondary flow, a relatively weaker flow pattern superimposed on the stronger primary flow pattern. The primary flow is often chosen to be an exact solution to simplified or approximated governing equations, such as potential flow around a wing or geostrophic current or wind on the rotating Earth. In that case, the secondary flow usefully spotlights the effects of complicated real-world terms neglected in those approximated equations. For instance, the consequences of viscosity are spotlighted by secondary flow in the viscous boundary layer, resolving the tea leaf paradox. As another example, if the primary flow is taken to be a balanced flow approximation with net force equated to zero, then the secondary circulation helps spotlight acceleration due to the mild imbalance of forces. A smallness assumption about secondary flow also facilitates linearization.

Cheng Xu is a Chinese American aerodynamic design engineer and engineering manager. He is a Fellow of the American Society of Mechanical Engineers and a member of the Technical Committee on Energy and Power Systems, IASTED. He also served as a guest editor of International Journal of Rotating Machinery.

In turbomachinery, degree of reaction or reaction ratio (R) is defined as the ratio of the static pressure rise in the rotating blades of a compressor (or drop in turbine blades) to the static pressure rise in the compressor stage (or drop in a turbine stage). Alternatively it is the ratio of static enthalpy change in the rotor to the static enthalpy change in the stage.

Compressor characteristic is a mathematical curve that shows the behaviour of a fluid going through a dynamic compressor. It shows changes in fluid pressure, temperature, entropy, flow rate etc.) with the compressor operating at different speeds.

In turbomachinery, the slip factor is a measure of the fluid slip in the impeller of a compressor or a turbine, mostly a centrifugal machine. Fluid slip is the deviation in the angle at which the fluid leaves the impeller from the impeller's blade/vane angle. Being quite small in axial impellers, slip is a very important phenomenon in radial impellers and is useful in determining the accurate estimation of work input or the energy transfer between the impeller and the fluid, rise in pressure and the velocity triangles at the impeller exit.

An axial fan is a type of fan that causes gas to flow through it in an axial direction, parallel to the shaft about which the blades rotate. The flow is axial at entry and exit. The fan is designed to produce a pressure difference, and hence force, to cause a flow through the fan. Factors which determine the performance of the fan include the number and shape of the blades. Fans have many applications including in wind tunnels and cooling towers. Design parameters include power, flow rate, pressure rise and efficiency.

An axial turbine is a turbine in which the flow of the working fluid is parallel to the shaft, as opposed to radial turbines, where the fluid runs around a shaft, as in a watermill. An axial turbine has a similar construction as an axial compressor, but it operates in the reverse, converting flow of the fluid into rotating mechanical energy.

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 where mathematical complexity is substantially less.

<span class="mw-page-title-main">Blade solidity</span>

Blade solidity is an important design parameter for the axial flow impeller and is defined as the ratio of blade chord length to spacing.

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