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The Physics of Centrifugal Compressor Performance Rainer Kurz, Solar Turbines Incorporated
Copyright 2004, Pipeline Simulation Simulation Interest Group This paper was prepared for presentation at the PSIG Annual Meeting held in Palm Springs, California, 20 October – 22 October 2004. This paper was selected for presentation by the PSIG Board of Directors following review of information contained in an abstract submitted by the author(s). The material, as presented, does not necessarily reflect any position of the Pipeline Simulation Interest Group, its officers, or members. Papers presented at PSIG meetings are subject to publication review by Editorial Committees of the Pipeline Simulation Interest Group. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of PSIG is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, Pipeline Simulation Interest Group, P.O. Box 22625, Houston, TX 77227, U.S.A., fax 01-713-586-5955.
ABSTRACT This paper explains the physics of centrifugal compressor operation that are relevant to pipeline simulation. Topics include the thermodynamics of gas compression, the aerodynamics of centrifugal compressors, as well as the function of important subsystems such as seals and surge control devices. Control mechanisms for centrifugal compressors are explained and their impact on performance maps are discussed. The properties of the gas to be compressed, and its impact on relevant compressor performance parameters parameters will be analyzed. The aerodynamic components of compressors are analyzed with regards to their impact on compressor performance. The connection between the flow physics of gas compressors and the resulting performance maps, which represent the behavior of the device to be simulated, are explained.
NOMENCLATURE A c,u,w cp D F g h k M Ma m N
area velocity heat capacity diameter Force gravity acceleration enthalpy isentropic exponent momentum Mach number mass flow speed
P p Q q R s T v Wt Z z η ρ
power pressure volumetric flow heat gas constant entropy temperature specific volume work compressibility factor elevation coordinate efficiency density
INTRODUCTION The working principles of centrifugal gas compressors can be understood by applying some some basic laws of physics. Using the first and second law of thermodynamics together with basic laws of fluid dynamics, such as Bernouli’s law and Euler’s law allow to explain the fundamental working priciples, and by extension, can increase increase the understanding understanding of the operational operational behavior of centrifugal centrifugal gas compressors. compressors. Most descriptions of compressors in this paper are specifically geared towards pipeline applications. They are usually also applicable to any other gas compression application. The general description of the thermodynamics of gas compression applies to any type of compressor, independent of its detailed working principles.
THERMODYNAMICS OF GAS COMPRESSION For a compressor receiving gas at a certain suction pressure and temperature, and delivering it at a certain output pressure, the isentropic head represents the energy input required by a reversible, adiabatic (thus isentropic) compression. The actual compressor will require a higher amount of energy input than needed for the ideal (isentropic) compression (Figure 1). It is important to clarify certain properties at this time, and in particular find their connection to the first and
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RAINER KURZ
second law of thermodynamics written for steady state fluid flows. The first law , (defining the conservation of Energy) becomes:
w22 w12 h2 + + gz 2 m& − h1 + + gz 1 m& 2 2 = q12 + W t ,12 with q=0 for adiabatic processes, and gz=0 because changes in elevation are not significant for gas compressors. We can combine enthalpy and velocity into a total enthalpy by
ht
= h+
w
2
2
k −1 p 2 k ∆h s = c p T 1 − 1 p 1
For real gases (where k, and c p in the equations above, become functions of temperature and pressure), the enthalpy of a gas h(p,T) is calculated in a more complicated way using equations of state (Poling et al., 2001). These represent relationships that allow to calculate the enthalpy of gas of known composition, if any two of its pressure, its temperature, or its entropy are known. We therefore can calculate the actual head for the compression by
∆h = h( p2 , T 2 ) − h( p1 , T 1 )
Wt,12 is the amount of work 1 we have to apply to affect the change in enthalpy in the gas. The work Wt,12 is related to the required power, P, by multiplying it with the mass flow. & W t ,12 P = m
Power and enthalpy difference are thus related by & (ht , 2 P = m
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− ht ,1 )
If we can find a relationship that combines enthalpy with the pressure and temperature of a gas, we have found the necessary tools to describe the gas compression process. For a perfect gas, with constant heat capacity, the relationship between enthalpy , pressures and temperatures is
and the isentropic head by
∆h = h( p 2 , s1 ) − h( p1 , T 1 ) s1 = s ( p1 , T 1 ) The performance quality of a compressor can be assessed by comparing the actual head (which directly relates to the amount of power we need to spend for the compression) with the head that the ideal, isentropic compression would require. This defines the isentropic efficiency
η s
=
∆h s ∆h
∆h = c p (T 2 − T 1 ) Because, for an isentropic compression, the discharge temperature is determined by the pressure ratio (with k= c p/cv):
T 2
p = T 1 2 p1
& ( s 2 − s1 ) = m
k −1 k
+ T 1
we can, for an isentropic compression of a perfect gas, relate the isentropic head , temperature and pressures by 1
Figure 1 shows the compression process in a Mollier diagram. The second law tells us
Physically, there is no difference between work, head, and enthalpy difference. In systems with consistent units (such as the SI system), work, head and enthalpy difference have the same unit (e.g. kJ/kg in SI units). Only in inconsistent systems (such as US customary units), we need to consider that the enthalpy difference (e.g. in BTU/lb m) is related to head and work (e.g. in ft lbf /lbm) by the mechanical equivalent of heat ( e.g. in ft lbf /BTU) .
2
dq
1
T
∫
+ s irr
For adiabatic flows, where no heat q enters or leaves, the change in entropy simply describes the losses generated in the compression process. These losses come from the friction of gas with solid surfaces and the mixing of gas of different energy levels. An adiabatic, reversible compression process therefore does not change the entropy of the system, it is isentropic. Our equation for the actual head implicitly includes the entropy rise ∆s, because:
∆h = h( p 2 , T 2 ) − h( p1 , T 1 ) = h( p 2 , s1 + ∆ s) − h( p1 , s1 ) If cooling is applied during the compression process (for example with intercoolers between two compressors in series),
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then the increase in entropy is smaller than for an uncooled process. Therefore, the power requirement will be reduced. Using the polytropic process (Beinecke and Luedtke, 1983) for comparison reasons works fundamentally the same way as using the isentropic process for comparison reasons. The difference lies in the fact that the polytropic process uses the same discharge temperature as the actual process, while the isentropic process has a different (lower) discharge temperature than the actual process for the same compression task. In particular, both the isentropic and the polytropic process are reversible (and adiabatic) processes. In order to fully define the isentropic compression process for a given gas, suction pressure, suction temperature and discharge pressure have to be known. To define the polytropic process, in addition either the polytropic compression efficiency, or the discharge temperature have to be known. The polytropic efficiency η p is defined such, that it is constant for any infinitesimally small compression step, which then allows write
∆h =
1
p2
η p
∫
vdp =
p1
∆h p η p
and p2
∆h p =
∫
vdp
p1
or, to define the polytropic efficiency :
η p
=
∆h p ∆h
The mechanical power P necessary to drive the compressor, is the gas absorbed power increased by all mechanical losses (friction in the seals and bearings), expressed by a mechanical efficiency ηm (typically in the order of 1 or 2% of the total absorbed power):
P =
Because the enthalpy definition above is on a per mass flow basis, the absorbed gas power Pg (that is, the power that the compressor transferred into the gas), can be calculated as
P g
= m& ⋅ ∆h
1
& ⋅ ∆h = m
η m
& ⋅ ∆h s m η mη s
We also encounter energy conservation on a different level in turbomachines: The aerodynamic function of a turbomachine relies on the capability to trade two forms of energy: kinetic energy (velocity energy) and potential energy (pressure energy). This will be discussed in a subsequent section.
REAL GAS BEHAVIOR EQUATIONS OF STATE
AND
Understanding gas compression requires an understanding of the relationship between pressure, temperature and density of a gas. An ideal gas exhibits the following behavior:
p
= RT
ρ
where R is the gas constant , and as such is constant as long as the gas composition is not changed. Any gas at very low pressures (p0) can be described by this equation. For the elevated pressures we see in natural gas compression, this equation becomes inaccurate, and an additional variable, the compressibility factor Z, has to be added:
p For designers of compressors, the polytropic efficiency has an important advantage: If a compressor has five stages , and each stage has the same isentropic efficiency ηs , then the overall compressor efficiency will be lower than ηs. If , for the same example , we assume that each stage has the same polytropic efficiency η p, then the polytropic efficency of the entire machine is also η p.
3
= ZRT
ρ
Unfortunately, the compressibility factor itself is a function of pressure, temperature and gas composition. A similar situation arises when the enthalpy has to be calculated: For an ideal gas, we find T 2
∆h = c p ⋅ ∆T = ∫ c p dT T 1
where c p is only a function of temperature. In a real gas, we get additional terms for the deviation between real gas behavior and ideal gas behavior (Poling et al, 2001):
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T 2
∆h = (h − h( p1 ))T + ∫ c p dT − (h 0 − h( p 2 ))T 0
1
2
T 1
The terms (H0-H(p1))T1 and (H0-H(p2))T2 are called departure functions, because they describe the deviation of the real gas behavior from the ideal gas behavior. They relate the enthalpy at some pressure and temperature to a reference state at low pressure, but at the same temperature. The departure functions can be calculated solely from an equation of state, while the term ∫ c pdT is evaluated in the ideal gas state. Figure 2 shows the path of a calculation using an equation of state. Equations of state are semi-empirical relationships that allow to calculate the compressibility factor as well as the departure functions. For gas compression applications, the most frequently used equations of state are Redlich-Kwong, SoaveRedlich-Kwong, Benedict-Webb-Rubin, Benedict-WebbRubin-Starling and Lee-Kessler-Ploecker (Poling et al, 2001). In general, all of these equations provide accurate results for typical applications in pipelines, i.e. for gases with a high methane content, and at pressures below about 3500 psia. Kumar et al. (1999) and Beinecke et al. (1983) have compared these equations of state regarding their accuracy for compression applications. It should be noted that the Redlich Kwong equation of state is the most effective equation from a computational point of view (because the solution is found directly rather than through an iteration).
COMPONENTS COMPRESSORS
OF
GAS
The thermodynamic considerations above treat the compressor as a black box. We want to introduce now the essential components of a centrifugal compressor that accomplish the tasks specified above (Figure 3). The gas entering the inlet nozzle of the compressor is guided (often with the help of guide vanes) to the inlet of the impeller. An impeller consists of a number of rotating vanes that impart mechanical energy to the gas. As we will see later, the gas will leave the impeller with an increased velocity and increased static pressure. In the diffuser, part of the velocity is converted into static pressure. Diffusers can be vaneless or contain a number of vanes. If the compressor has more than one impeller, the gas will be again brought in front of the next impeller through the return channel and the return vanes. If the compressor has only one impeller, or after the diffuser of the last impeller in a multi stage compressor, the gas enters the discharge system. The discharge system can either make use of a volute, which can further convert velocity into static pressure, or a simple cavity that collects the gas before it exits the compressor through the discharge nozzle.
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The rotating part of the compressor consists of all the impellers. This rotor runs on two radial bearings ( on all modern compressors, these are hydrodynamic tilt pad bearings), while the axial thrust generated by the impellers is balanced by a balance piston, and the resulting force is balanced by a hydrodynamic tilt pad thrust bearing. To keep the gas from escaping at the shaft ends, dry gas seals are used on both shaft ends. Other seal types have been used in the past, but virtually all modern centrifugal compressors in the pipeline service use dry gas seals. The sealing is accomplished by a stationary and a rotating disk, with a very small gap (about 5µm) between them. At standstill, springs press the movable seal disc onto the stationary disk. Once the compressor shaft starts to rotate, the groove pattern on one of the discs causes a separating force, making the seals run without mechanical contact of sealing surfaces. The entire assembly is contained in a casing (usually barrel type).
AERODYNAMICS COMPRESSORS
OF
CENTRIFUGAL
In the last chapter, we talked about the impeller which ‘impart[s] mechanical energy to the gas’ and the diffuser, where ‘part of the velocity is converted into static pressure’. In this section, we describe in more detail how this works. Bernoullis law (which is strictly true only for incompressible flows, but which can be modified for the subsonic compressible flows we find in gas compressors) describes the interchangeability of two forms of energy : static pressure and velocity. The incompressible formulation of Bernoullis law for a frictionless, stationary, adiabatic flow without any work input is:
pt
= p +
ρ
2
c2
= const
For compressible flows, the equation becomes
ht
= h+
c2 2
= const
Another requirement is, that mass cannot appear or disappear, thus for any flow from a point 1 to a point 2
= ρ 1Q1 = m& 2 = ρ 2 Q2 ρ ⋅ Q = ρ ⋅ c ⋅ A &1 m
This requirement is valid for compressible and incompressible flows, with the caveat that for compressible flows the density is a function of pressure and temperatures, and thus ultimately a function of the velocity.
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These two concepts explain the working principles of the vanes and diffusers used. Due to requirement for mass conservation, any flow channel that has a wider flow area at its inlet and a smaller flow area at its exit will require a velocity increase from inlet to exit. If no energy is introduced to the system, Bernoulli’s law requires a drop in static pressure (Figure 4a). Examples for flow channels like this are turbine blades and nozzles, inlet vanes in compressors and others (Figure 4b). Conversely, any flow channel that has a smaller flow area A at its inlet and a larger flow area at its exit will require a velocity decrease from inlet to exit. If no energy is introduced to the system, Bernoulli’s law requires a increase in static pressure (Figure 4c). Examples for flow channels like this are vaned or vaneless diffusers, flow channels in impellers, rotor and stator blades of axial compressors volutes and others (Figure 4d). If these flow channels are in a rotating system (for example in an impeller), mechanical energy is added to or removed from the system. Nevertheless, if the velocities are considered in a rotating system of coordinates, above principles are applicable as well. Another important concept is the conservation of momentum. The change in momentum M of gas flowing from a point 1 to a point 2 is its mass times its velocity (m c), and is also the sum of all forces F acting. The change in momentum is r
d M dt
r
r
r
= m& (c2 − c1 ) = F
To change the momentum of this gas, either by changing the velocity or the direction of the gas (or both), a force is necessary. Figure 5 outlines this concept for the case of a bent, conical pipe. The gas flows in through the area A 1 with w1, p1, and out through the flow area A 2 with w2, p 2. The differences in the force due the pressure (p 1A1 and p2A2, respectively), and the fact that a certain mass flow of gas is forced to change its direction generates a reaction force FR . Split into x and y coordinates, and considering that & = ρ 1 A1 w1 m
= ρ 2 A2 w2
we get (due to the choice of coordinates, w1y=0)
x : y :
(w2 x − w1 ) = p1 A1 − ( p 2 A2 ) x + F Rx ρ A1 w1 (w2 y ) = −( p 2 A2 ) y + F Ry
ρ A1 w1
It should also be noted that this formulation is also valid for viscous flows, because the friction forces become internal forces. All these concepts are applied in a very similar way in pipeline flows. For a rotating row of vanes in order to change the velocity of the gas, the vanes have to exert a force upon the gas. This is
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fundamentally the same force that F Ry that acts in the previous example for the pipe. This force has to act in direction of the circumferential rotation of the vanes in order to do work on the gas. According to the conservation of momentum, the force that the blades exert is balanced by the change in circumferential velocity times the associated mass of the gas. This relationship is often referred to as Euler’s Law: & ⋅ ∆h = m & ⋅ (u 2 cu 2 P = m
− u1cu1 )
where u is the circumferential blade velocity at the inlet (1) and exit (2) of the impeller, and c u is the circumferential component of the gas velocity, taken in an absolute reference frame at the inlet (1) and exit (2) (Figure 6). At this point, one of the advantages of centrifugal compressors over axial compressors becomes apparent: In the axial compressor, the entire energy transfer has to come from the turning of the flow imposed by the blade (cu2-cu1), while the centrifugal compressor has added support from the centrifugal forces on the gas while flowing from the diameter at the impeller inlet (u1=π D N) to the higher diameter at the impeller exit (u 2=π i Dtip N) . The importance of Euler’s law lies in the fact that it connects aerodynamic considerations (i.e the velocities involved) with the thermodynamics of the compression process.
OPERATING REGIMES OF CENTRIFUGAL COMPRESSOR
A
The general behavior of any gas compressor can be gauged by some additional, fundamental relationships: The vanes of the rotating impeller ‘see’ the gas in a coordinate system that rotates with the impeller. The transformation of velocity coordinates from an absolute frame of reference ( c ) to the a frame of reference rotating with a velocity u is by: r
r
r
w = c −u
where, for any diameter D of the impeller u=πDN. The impeller exit geometry (‘backsweep’) determines the direction of the relative velocity w2 at the impeller exit. The basic 'ideal' slope of head vs. flow is dictated by the kinematic flow relationship of the compressor, in particular the amount of backsweep of the impeller. Any (Figure 6) increase in flow at constant speed causes a reduction of the circumferrential component of the absolute exit velocity (cu2) . It follows from Eulers equation above, that this causes a reduction in head. Adding the influence of various losses to this basic relationship shape the head-flow-efficiency characteristic of a compressor (Figure 7): Whenever the flow deviates from the flow the stage was designed for, the components of the stage operate less efficient. This is the
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reason for incidence losses. Figure 8 illustrates this, using an airfoil as an example: At the 'design flow' the air follows the contours of the airfoil. If we change the direction of the incoming air, we see increasing zones where the airflow ceases to follow the contours of the airfoil, and create increasing losses. Furthermore, the higher the flow, the higher the velocities, and thus the friction losses . A compressor, operated at constant speed, is operated at its best efficiency point (Figure 7). If we reduce the flow through the compressor (for example, because the discharge pressure that the compressor has to overcome is increased), then the compressor efficiency will be gradually reduced. At a certain flow, stall, probably in the form of rotating stall, in one or more of the compressor components will occur. At further flow reduction, the compressor will eventually reach its stability limit, and go into surge. If, again starting from the best efficiency point, the flow is increased, then we also see a reduction in efficiency, accompanied by a reduction in head. Eventually the head and efficiency will drop steeply, until the compressor will not produce any head at all. This operating scenario is called choke. (For practical applications, the compressor is usually considered to be in choke when the head falls below a certain percentage of the head at the best efficiency point).
Surge At flows lower than the flow at the stability limit, practical operation of the compressor is not possible. At flows to the left of the stability limit, the compressor cannot produce the same head as at the stability limit. It is therefore no longer able to overcome the pressure differential between suction and discharge side. Because the gas volumes upstream (at discharge pressure) is now at a higher pressure than the compressor can achieve, the gas will follow its natural tendency to flow from the higher to the lower pressure: The flow through the compressor is reversed. Due to the flow reversal, the system pressure at the discharge side will be reduced over time, and eventually the compressor will be able to overcome the pressure on the discharge side again. If no corrective action is taken, the compressor will again operate to the left of the stability limit and the above described cycle is repeated: The compressor is in surge. The observer will detect strong oscillations of pressure and flow in the compression system. It must be noted that the violence and the onset of surge are a function of the interaction between the compressor and the piping system.
Stall If the flow through a compressor at constant speed is reduced, the losses in all aerodynamic components will increase. Eventually the flow in one of the aerodynamic components, usually in the diffuser, but sometimes in the impeller inlet, will separate (The last picture in Figure 8 shows such a flow
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separation for an airfoil). It should be noted that stall usually appears in one stage of a compressor first. Flow separation in a vaneless diffuser means, that all or parts of the flow will not exit the diffuser on its discharge end, but will form areas where the flow stagnates or reverses its direction back to the inlet of the diffuser (i.e. the impeller exit; Figure 3). Stall in the impeller inlet or a vaned diffuser is due to the fact, that the direction of the incoming flow (relative to the rotating impeller changes with the flow rate through the compressor. Usually, vanes in the diffuser reduce the operating range of a stage compared to a vaneless diffuser. Therefore, a reduction in flow will lead to an increased mismatch between the direction of the incoming flow the impeller was designed for and the actual direction of the incoming flow. At one point this mismatch becomes so significant that the flow through the impeller breaks down. Flow separation can take on the characteristics of a rotating stall. When the flow through the compressor stage is reduced, parts of the diffuser experience flow separations. Rotating stall occurs if the regions of flow separation are not stationary, but move in the direction of the rotating impeller (typically at 15-30% of the impeller speed). Rotating stall can often be detected from increasing vibration signatures in the subsynchronous region. Onset of stall does not necessarily constitute an operating limit of the compressor. In fact, in many cases the flow can be reduced further before the actual stability limit is reached.
Choke At high flow the head and efficiency will drop steeply, until the compressor will not produce any head at all. This operating scenario is called choke. However, for practical applications, the compressor is usually considered to be in choke when the head falls below a certain percentage of the head at the best efficiency point. Some compressor manufacturers do not allow opration of their machines in deep choke. In these cases, the compressor map has a distinct high flow limit for each speed line. The efficiency starts to drop off at higher flows, because a higher flow causes higher internal velocities, and thus higher friction losses. The head reduction is a result of both the increased losses and the basic kinematic relationships in a centrifugal compressor: Even without any losses, a compressor with backwards bent blades (as they are used in virtually every industrial centrifugal compressor) will experience a reduction in head with increased flow (Figure 7). 'Choke' and 'Stonewall' are different terms for the same phenomenon. Surge Margin and Turndown Any operating point A can be characterized by its distance from the onset of surge.Two definitions are widely used: The surge margin
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SM (%) =
The Physics of Centrifugal Compressor Performance
Q A
− Q B
Q A
PERFORMANCE CHARACTERISTICS OF CENTRIFUGAL COMPRESSORS
⋅100
Which is based on the flow margin between the operating point and the surge point at constant speed, and the turndown
Turndown(%) =
Q A − QC Q A
⋅100
Which is based on on the flow margin between the operating point and the surge point at constant head.
Surge Control Surge Control systems are by nature surge avoidance systems. In general, the control system measures the gas flow through the compressor and the head it generates. The knowledge of head and flow allows to compare the present operating point of the compressor with the predicted surge line (Figure 9). If the process forces the compressor to approach the surge line, a recycle valve in a recycle line is opened. This allows the actual operating point of the compressor to move away from surge ( Kurz and White, 2004). Similarity Law (Fan Law) Under certain simplifying conditions, operating points of a compressor at different speeds can be compared (Kurz and Ohanian, 2003). This fact is captured in the fan law, which is strictly only true for identical Mach numbers in all stages, but which is still a good approximation for cases where the machine Mach number
M N
u
=
k 1 Z 1 RT 1
changes by less than 10% (for single and two stage compressors). The more stages the compressor has, the less deviation is acceptable (Kurz and Fozi, 2002). The fan law is based on the fact that if for two opearing points A and B all velocities change by the same factor (which in particular means that none of the flow angles change), then the compressor will show the following relations between two different operating points :
Q A
=
N A H sA N A2 η A
Q B N B
=
H sB N B2
= η B
7
Process Control with Centrifugal Compressors Driven by Two Shaft Gas Turbines Centrifugal Compressors, when driven by two shaft gas turbines, are usually adapted to varying process conditions by means of speed control. This is the most natural way of controlling a system, because both the centrifugal compressor and the power turbine of a two shaft gas turbine can operate over a wide range of speeds without any adverse effects. A typical configuration can operate down to 50% of its maximum continuous speed, and in many cases even lower. Reaction times are very fast, thus allowing a continuous load following using modern, PLC based controllers.
A simple case is flow control: The flow into the machine is sensed by a flow metering element (such as a flow orifice, a venturi nozzle or a ultrasonic device). A flow set point is selected by the operator. If the discharge pressure increases due to process changes, the controller will increase the fuel flow into the gas turbine. As a result the power turbine will produce more power and cause the powerturbine, together with the driven compressor, to accelerate. Thus, the compressor flow is kept constant ( Mode constant Flow in Figure 9). From Figure 1, it can be seen that both the power turbine speed and the power increase in that situation. If the discharge pressure is reduced, or the suction pressure is increased due to process changes, the controller will reduce the fuel flow into the gas turbine. As a result the power turbine will produce less power and cause the power turbine, together with the driven compressor, to decelerate. Thus, the compressor flow is kept constant (Mode constant flow in Figure 9). Similar control mechanisms are available to keep the discharge pressure constant, or to keep the suction pressure constant (Mode constant discharge pressure in Figure 1). Another possible control mode is to run the unit at maximum available driver power (or any other, constant driver output). In this case, the operating points are on a line of constant power in Figure 9. The control scheme works for one or more compressors, and can be set up for machines operating in series as well as in parallel. If speed control is not available, the compressor can be equipped with a suction throttle, or with variable guide vanes. The latter, if available in front of each impeller is rather effective, but the mechanical complexity proves usually to be prohibitive in pipeline applications. The former is a mechanically simple means of control, but it has a detrimental effect on the overall efficiency.
8
RAINER KURZ
Interaction of the Compressor and the Compression System The operating point of a compressor is determined by the interaction between the system it operates in and the compressor operating characteristics. For example, if a compressor operates at steady state in a pipeline, then an increase in flow through that pipeline with require an increase of the pressure ratio (thus the head) of the compressor station, due to the increased friction losses in the pipeline. Any operating point of the compressor would thus lie on a curve that can approximately described by
H ∝ Q 2 The maximum flow is limited by either the maximum allowable speed of the compressor train, or the maximum available driver power. If more than one compressor operates at a station, they can either operate in parallel or in series . Ohanian et al. (2003) report on considerations to use either of the two approaches. Control strategies can be set to attempt to run all compressors at the station at the same surge margin. Additionally, with multiple units available at a station, it is often advantageous to shut one or more units down, rather than operate all of them in deep part load.
CONCLUSIONS The working principles of centrifugal gas compressors have been been explained by applying some basic laws of physics. Using the first and second law of thermodynamics together with basic laws of fluid dynamics, such as Bernouli’s law and
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Euler’s law were used to explain the fundamental working priciples, and by extension, can increase the understanding of the operational behavior of centrifugal gas compressors.
REFERENCES 1.
2.
3.
4. 5. 6. 7.
8.
Beinecke, D., Luedtke, K., 1983, ‘Die Auslegung von Turboverdichtern unter Beruecksichtigung des realen Gasverhaltens, VDI Berichte 487. Kumar,S., Kurz,R., O’Connell, J.P., 1999, ‘Equations of State for Compressor Design and Testing’, ASME Paper 99-GT-12. Ohanian, S., Kurz, R., 2003, Transient Simulation of the Effects of Compressor Outage, Pipeline Simulation Interest Group. Poling, B.E., Prausnitz, J.M, O’Connell,J.P., 2001, The Properties of Gases and Liquids, McGraw-Hill. Kurz,R., Fozi, A.A., 2002,’Acceptance Criteria for Gas Compression Systems ’, ASME GT2002-30282. Nakajama, Y., 1988,’Visualized Flow’, Pergammon. Kurz, R., Ohanian, S., 2003, ‘Modeling Turbomachinery in Pipeline Simulations’, Pipeline Simulation Interest Group. Kurz, R., White, R.C., 2004, ’Surge Avoidance in Gas Compression Systems’, ASME Paper GT2004-53066.
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FIGURES
Figure 1 – Compression Process in the Mollier Diagram
Figure 2 – Calculation Path for Equations of State
9
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Figure 3 – Centrifugal Compressor Components
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Figure 4 – Acceleration and Diffusion
Figure 5 – Conservation of Momentum
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RAINER KURZ
Figure 6 – Velocity vectors in a Centrifugal Impeller
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Figure 7 – Head versus Flow Relationship at Constant Speed
Figure 8 – Unseparated (a,b), Partially Separated (c), and Fully Separated (d) Flow over an Airfoil at increasing angle of attack (Nakajama(1988))
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Figure 9 – Centrifugal Compressor Performance Map
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PSIG 0408
The Physics of Centrifugal Compressor Performance
Appendix A – Definitions Pressure ABSOLUTE PRESSURE is the pressure measured from an absolute vacuum. It equals the algebraic sum of barometric pressure and gage pressure. STATIC PRESSURE is the pressure in the gas measured in such a manner that no effect is produced by the velocity of the gas stream. It is the pressure that would be shown by a measuring instrument moving at the same velocity as the moving stream and is the pressure used as a property in defining the thermodynamic state of the fluid. STAGNATION (Total) PRESSURE is the pressure which would be measured at the stagnation point when a moving gas stream is brought to rest and its kinetic energy is converted to an enthalpy rise by an isentropic compression from the flow condition to the stagnation condition. It is the pressure usually measured by an impact tube. In a stationary body of gas, the static and stagnation pressures are numerically equal. VELOCITY PRESSURE (DYNAMIC PRESSURE) is the stagnation pressure minus the static pressure in a gas stream. It is the pressure generally measured by the differential pressure reading of a Pitot tube
Temperature ABSOLUTE TEMPERATURE is the temperature above absolute zero. It is equal to the degrees Fahrenheit plus 459.69 and is stated as degrees Rankine. STATIC TEMPERATURE is the temperature that would be shown by a measuring instrument moving at the same velocity as the fluid stream. It is the temperature used as a property in defining the thermodynamic state of the gas. STAGNATION (Total) TEMPERATURE is that temperature which would be measured at the stagnation point if a gas stream were brought to rest and its kinetic energy converted to an enthalpy rise by an isentropic compression process from the flow condition to the stagnation condition.
Flow CAPACITY (Actual Flow) of a compressor is the volume rate of flow of gas compressed and delivered referred to conditions of pressure, temperature and gas composition prevailing at the compressor inlet. STANDARD or NORMAL FLOW is the rate of flow under certain ‘standard’ conditions, for example 60 °F and 30”Hg (US Standard) or 0 °C and 101.325 kPa (SI Normal).
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MASS FLOW is the rate of flow in mass units
Work,Power, Efficiency ISENTROPIC COMPRESSION as used here refers to the reversible adiabatic compression process. ISENTROPIC WORK (Head) is the work required to compress a unit mass of gas in an isentropic compression process from the inlet pressure and temperature to the discharge pressure. ISENTROPIC POWER is defined as the power required to compress isentropically and deliver the capacity of the compressor from the compressor inlet conditions to the compressor discharge pressure. ISENTROPIC EFFICIENCY is the ratio of the isentropic work to the work required for the compression process. POLYTROPIC COMPRESSION is a reversible compression process between the compressor inlet and discharge conditions, which follows a path such that, between any two points on the path, the ratio of the reversible work input to the enthalpy rise is constant. POLYTROPIC WORK (Head) is the reversible work required to compress a unit mass of the gas in a polytropic compression process.
