Centrifugal Compressor

Taking up a characteristic of a centrifugal compressor with an adjustable inlet guide grid University Duisburg-Essen Faculty for engineering sciences Department of mechanical engineering Turbomachinery Prof. Dr.-Ing. F.-K. Benra

Table of contents 1 Introduction

2

2 Theoretical bases 3 2.1 Velocity-triangle of the compressor stage..................................................................... 3 2.2 Compressionwork, internal efficiency .......................................................................... 3 3 Characteristic curves und controlling of compressors 4 3.1 Theoretical and measured characteristic curves............................................................ 4 3.2 Regulation ..................................................................................................................... 5 3.2.1 Regulation by changing the rpm ....................................................................... 6 3.2.2 Suction throttle regulation................................................................................. 6 3.2.3 Regulation by blowing off or Umblasen?? ....................................................... 7 3.2.4 Regulation by adjustable installations within the compressor .......................... 7 4 Description of the plant 9 4.1 General operational data................................................................................................ 9 4.2 Components of the plant ............................................................................................... 9 5 Measuring instruments 11 5.1 Measuring point plan................................................................................................... 11 5.2 Measuring methods and –instruments......................................................................... 12 5.2.1 Temperature measurement .............................................................................. 12 5.2.2 Volume flow rate measurement ...................................................................... 12 5.2.3 Pressure measurement ..................................................................................... 12 5.2.4 Speed measurement......................................................................................... 13 6 Investigational procedures 7 Interpretation of test results 15 7.1 Evaluation of the measured values under test conditions ........................................... 15 7.2 Conversion on reference conditions ............................................................................ 16

1

List of used symbols Symbol

Meaning

Unit

Ad AD A* c cp g h l m M n n p P R T u V& ω& y z α ε κ η ρ π φ

Cross section of the orifice opening Tubing cross section Closest flow passage area Absolute speed Specific heat capacity Gravitation Enthalpy Height of the liquid column Aperture ratio Mach number Number of revolutions Polytropic exponent Pressure Drive power Gas constant Temperature Circumferential speed Volume flow rate Relative speed Specific flow work geodetic height Flow coefficient Expansion number Isentropic exponent Efficiency Density Pressure ratio Vapor

m2 m2 m2 m/s kJ/Kg K m/s2 kJ/kg m min-1 bar kW kJ/kg K K m/s m3/s m/s J/kg m kg/m3 %

Indices dyn m Mot ref red t u

Dynamic portion Meridional component, mechanical Drive Reference condition Reduced Total size Circumferential component

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1

Introduction

In Turbomachineries the continuous current of the fluid gets energy extracted which is supplied to the shaft as mechanical energy (Turbopowermachine). Otherwise mechanical energy is supplied by the shaft to the rotor which submits it to the fluid as pressure- or kinetic energy (Turboworkmachine). The centrifugal-compressor is a Turboworkmachine in which the pressure-heightening is achieved by converting of kinetic energy. The process of compression happens in radial streamed rotors and stators. Fig. 1.1 shows the areas in which several compressor-types are used. You can see that radialcompressors are used for volume flow rates from 1500 to 400000 m3/h and for pressures till 500 bars. In dependence of flow rate and pressure-ratio they are carried out in several arrangements, e.g. singlestaged - multistaged, singleflow - multiflow. The purpose of centrifugal-compressors in modern techniques is varied. They are used for •

Compressed-air plant

•

Charging of internal combustion engine

•

As compressors in gasturbineplants

•

As an so called process-compressor for unit-operations

•

As cooling fan

Fig. 1.1: Operative ranges of several compressor-types They are used for operative ranges, which means for several combinations of ratings like pressure-ratio, mass flow, efficiency et cetera. The relation between these parameters can be displayed in a characteristic diagram. In this experiment it is your task to determine a characteristic of a centrifugal-compressor and compare it with the one given by the manufacturer.

3

2

Theoretical bases

2.1 Velocity-triangle of the compressor stage The task of a compressor stage exists in the continuous compression of the incoming fluid..

Fig. 2.1: Velocity-triangle at the rotor The streaming fluid reaches the entry of the bladed wheel with an absolute speed c1. The current can be with or without a spin. You can adjust this by the diffuser plate (stator). The current is influenced owing to the rotation of the bladed wheel. The fluid streams into the channel with a relative speed which depends on the vectors of the velocity-triangle. (Pic. 2.1) The energy conversion in a rotary grid of turbo machinery is described with the help of the kinematic main equation.

M ⋅ω = u2 cu 2 − u1cu1 m& c22 − c12 u22 − u12 ω22 − ω12 + + 2. Shape ∆ht = a = 2 2 2

1. Shape ∆ht = a =

2.2 Compressionwork, internal efficiency The work which is converted in turbo machinery corresponds to – within the condition of an adiabatic change of state – the complete enthalpy difference between the plane in front of the first bladed wheel and behind the last one. (This derives from the 1. Axiom for stationary flow-processes) By setting ahead an isentropic change of state and looking upon the fluid as an ideal gas, the following term derives: κ −1    pt 2  κ κ   (∆ht ) s = RTt1   − 1  κ −1 p  t1   (How to derive this should be known by every student!) At a change of state, the change of the total enthalpy is given by: ∆ht1,2 = c p (Tt 2 − Tt1 )

4 The ratio between isentropic and real difference of the total enthalpy is equal to the definition of the total isentropic efficiency: ( ∆h ) ( ∆ht )s or (ηtV )s = t s = ∆ht1,2 c p (Tt 2 − Tt1 ) κ −1   κ   p  t2 Tt1  − 1  pt1     (ηtV )s = (Tt 2 − Tt1 ) Finally we get the term for the necessary output to run the machine: m& ∆ht1,2 V& ρ∆ht1,2 P= =

ηm

ηm

3 Characteristic curves und controlling of compressors 3.1 Theoretical and measured characteristic curves The theoretical curve of a compressor can be derived from the velocity triangles. A spin-free inflow is to be present. Furthermore we take the assumption of equal cm (which is characterizing for the flow rate) at entry and exit. Fig. 3.1 shows the dependence of the volume flow to the velocity triangles directly. The angle of flow β2 is decisive.

Fig. 3.1: Velocity triangle at exit of the rotor The straight line yth (Pic. 3.2), which is derived by this, is only correct for an infinite number of blades, which means it is a theoretical straight line. If you look upon a limited number of blades the lift of delivery is reduced about ∆yz. The friction losses ∆yr cause a further sinking of the characteristic curve, which becomes the larger, the higher the flow rate is. The collision losses, which result from an unfavourable incident flow of the profile nose, are considered by ∆yst. The collision losses become the larger the further away by the design point the machine is operated. Finally the clearance losses cause a further shift of the characteristic around ∆V, which causes an additional waste of the efficiency. The execution of this view for different numbers of revolutions makes predicting the characteristic diagram for a machine possible. In a characteristic diagram pressure ratio, efficiency or enthalpy characteristics are laid above massflow, volumeflow or flow rate characteristics. For this, the entrance sizes must be kept constant. A characteristic shows the dependence for constant number of revolutions, mentioned above.

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Fig. 3.2: Theoretical compressor characteristic The operating point of a machine is given by the consumer. As you can see in Fig 3.2, it’s the intersection between the compressor and plant characteristic. For practice, a stable instrument range of a compressor is from great importance.

Fig. 3.3: Compressor- and Plant-characteristics The stable work area is marked at smaller volume flow rates by the pumping border and at larger volume flow rates by the sip border.

3.2 Regulation The regulation of turbo machinery divides itself into two main areas: I. The static controller action: Here the possible regulatory interventions and their economy are examined to connection with the machine. II. The dynamic controller action: This field covers the temporal sequence of the control procedure. Of special meaning are layout and reaction as well as the stability of the controlling system. The dynamic behaviour

6 of the compressor plant and its components (Pipings, radiator, valves, etc...) at fast load changes has to be known. These changes result in the case of driving on and off as well as in the case of incidents (Breakdown of the electricity mains). If a fast switch-off takes place, the drain valve must open, in order to prevent the pumping of the compressor. In the following example (Fig. 3.4) the change of the operating points is presented as a function of the opening-time t of the valve.

Fig. 3.4: Dynamic properties of a compressor at a fast switch off As you can see, the operating points for the times t=2s and t=1,6s – for smaller volume flow rates - are beyond the stability range. To avoid a pumping of the compressor, a valve floating time t<1,6s should be taken. According to the major tasks with the regulation of compressors thereby problems have to be solved, for which also the characteristics of the consumers and power supply units should be considered. The different controlling-procedures are examined in the following terms.

3.2.1 Regulation by changing the rpm Here the rpm are adapted to the required operating point for each case. A condition for this is a drive, which is adjustable in the number of revolutions, because the drive must permit a speed-regulation. The main advantage of regulation by changing the rpm consists of the fact that the velocity-triangles in a wide field of the instrument range are similar to those, who are present at the operating point. Thus a good efficiency is ensured for nearly all operating points.

3.2.2 Suction throttle regulation Through attach a throttle organ in the intake of the compressor the operating point can be varied at constant number of revolutions. The intake pressure is lowered and behind the compressor a lower pressure is automatically adjusted. Due to volume shifts, which can be derived from the continuity equation, the separation phenomena at the pumping border are shifted to smaller flow rates.

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Fig. 3.5: Regulation by suction throttle control 3.2.3 Regulation by blowing off or blowing back A further possibility of the regulation can be achieved by blowing a subset off at the compressor-exit. If this subset is led back to the intake, then one speaks of blowing back regulation. Both procedures are strongly inefficient. 3.2.4 Regulation by adjustable installations within the compressor Here losses are strongly reduced, by trying to adapt the machine to the operating-conditions. This happens e.g. through: a) By sliding a ring into the rotor inlet opening: The current separates at the ring edge, and the available delivery volume is equivalent to a smaller rotor.

Fig. 3.6: Regulation by adjustable ring Although this procedure does not work loss-free, the inset is more economical than the suction throttle control. b) Pre-diffuser plate adjustment With the help of an entrance control device the compressor is adapted to the operating conditions in each case. The stator causes a change of the blow direction. On the basis of the velocity triangles at the entrance the effect for the case of a current within a positive spin should be described now. (Fig. 3.7)

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Fig. 3.7: Velocity triangles at the rotor inlet On the assumption cm=const. the influence of the absolute speed c1 on the specific shovelwork is clearly. The circumferential-component of c1´ becomes positive (positive spin), so that the specific shovel-work a = u2cu2 – u1cu1 becomes smaller. This has the consequence that also the compression of the stage becomes smaller. Fig. 3.7 shows also the reverse effect for an incident flow with negative spin (cu1’’<0). A throttle procedure is connected with dissipation, which has to be avoided as far as possible. In the practical course attempt the regulation of the throughput takes place with the help of an entrance control device as well as a throttle lying on the pressure-site of the piping. The flow rate can be reduced or increased (in certain borders) by use of a pre-diffuser plate, whereby the stability range is extended. Fig. 3.8 shows the characteristic diagram of a compressor with an entrance control device.

Fig. 3.8: Diagram of a compressor with entrance control device 0°-position: The guide vanes stand parallel to the incident-flow direction of the fluid. Positive Spin: This range extends from 0° to +80°. Here the flow rate can be reduced e.g. with constant final pressure depending upon compressor-type up to 50% of the nominal quantity. Negative Spin: The usable range extends from 0° to for instance -30°. The flow rate and/or the pressure can be reduced in limited extent. During over-regulation the current at the guide vanes tears off.

9 This develops a turbulence, which leads to a substantial volume and pressure reduction which reduces the efficiency.

4 Description of the plant 4.1 General operational data The practical course attempt is done at a radial compressor of the type KG 3.32 of the company DEMAG. Design data of the compressor Intake volume flow Sucking in temperature Intake pressure Final pressure Relative dampness Clutch performance Number of revolutions

: 6500 m3/h : 20° C : 0,985 bar : 2,11 bar : 70% : 233 kw : 22340 U/min (=100%)

Speed ratio of the transmission

: i = 7,446

As drive engine an electric motor of the company GARBE, LAHMEYER & CO. AG with the following data is used: Voltage Power input Number of revolutions Year of construction

: 400 V - DC voltage : 1070 / 1092 A : 0 – 1500 / 3000 U/min : 1980

4.2 Components of the plant Fig. 4.1 is to illustrate how the individual components work together. Fig. 4.2 illustrates the structure of the compressor.

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Fig. 4.1: Components of the plant

Fig. 4.2: Structure of the compressor-type KG 7

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5 Measuring instruments 5.1 Measuring point plan In Fig. 5.1 the test range and the measuring point plan are represented. In the measuring point plan of the plant the levels are registered, which should be measured. Level 1 marks the condition of the air in the compressor entrance, Level 2 the condition in the compressor exit. In level 3 an orifice plate (effect pressure procedure) for the determination of the flow rate is used.

Fig 5.1: Test range and measuring point plan In the levels specified above the following sizes are measured: Level 1:

- static pressure p1 - total temperature Tt1

Level 2:

- static pressure p2 - total temperature Tt2

Level 3:

- effect pressure ∆pBl

In addition the following sizes are necessary for interpretation of test results:

•

Outside temperature T∞

•

Ambient pressure p∞

•

Engine speed n

The measuring instruments which are necessary for the collection of these sizes are described in the next section.

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5.2 Measuring methods and measuring instruments 5.2.1 Temperature measurement For the measurement of the temperatures 2 thermocouples are intended in the practical course attempt. The thermocouples are attached to an electronic measurer version plant, which converts the measured thermovoltage into appropriate centigrades. These are brought on the screen of a computer. 5.2.2 Volume flow rate measurement The measurement of the flow rate takes place with the help of the effect pressure procedure according to DIN 1952. A schematic representation for the measurement of the effect pressure is given in fig. 5.2.

Fig. 5.2: Flow measurement by the effect compression procedure. To the relationship between the flow and the measured effect pressure the equation applies: 2∆pOr V& = αε Ad (5.1)

ρ

ε : Expansion number α : Flow coefficient ∆pBl : Effect pressure Ad : Cross section of the opening ρ : Density The effect pressure ∆pBl is measured with the help of one u-pipe-manometer filled with water. The necessary data for the inserted standard orifice you can find in chapter 7. 5.2.3 Pressure measurement

The static pressure is measured in conventional way with the help of a Prandtlrohr and a upipe-manometer downstream. With the help of the u-pipe-manometer the difference between the static pressure and the ambient pressure is measured. To the static pressure applies thus:

13 p = (p - p∞) + p∞ = ∆p + p∞ (Note during the evaluation that ∆p1 is negative!) The total pressure pt results from the following relationship: pt = p + pdyn

(5.2)

It shows up that the dynamic pressure pdyn is comparatively small at the speeds arising in the practical course, so that total pressure and static pressure in good approximation can be equated. Pt = p U-pipe-manometer: The measured difference of pressure amounts for an equal-leg u-pipe-manometer, if the density of air is neglected in relation to the density of the measuring liquid ρFl. ∆p = g l ρFl

(5.3)

In the practical course attempt the u-pipe-manometers for the static pressure measurement are filled with mercury. By the higher density of mercury opposite of water a larger pressure range can be seized. For the conversion of the read off liquid column in units of pressure see chapter 7. 5.2.4 Speed measurement

The engine speed nM is measured on optical way at the clutch between transmission and electric motor. For this a giver and a counting device are available. For calculating of the compressor number you need the following formula: nV = nM ·i

; i = 7,446

Here i is the speed ratio of the transmission.

6 Investigational procedures For the practical course a reference characteristic diagram is given, which was measured with the following suction conditions: Tref = 291 K

pref = 1.1013 bar

nM,ref = 2700 min-1

Since these conditions are present only in a few cases at the time of the execution of the practical course attempts, it is, in order to receive comparable conditions in the compressor, necessary, to keep some demands from the similitude theory. Under the condition that the isentropic exponents at attempt- and reference conditions are equal, the change in status in the compressor can be kept alike. Additional the demand after same Mach numbers and same Reynolds numbers has to be fulfilled. For a practical course all these demands don’t have to

14 be fulfilled except the Mach-similarity. The influence of the change of the Reynolds-number has to be neglected. Mach-similarity is present, if with the circumferential speed of the impeller formed Mach number at test conditions agrees with that of the reference condition. M 1uV = M 1uref

=

u = konst. κ ⋅ R ⋅ T1

(T1 ≈ T2 )

or transformed

uV Tt1V i ⋅ nM = = uref i ⋅ nM ,ref Tt1ref Thus the compressor number of nV results in the case of test conditions as reduced number of revolutions to: Tt1V nV = i ⋅ nM = i ⋅ nM , ref Tt1ref The appropriate engine speed nM = nV must be determined before beginning of the attempt i

(pocket calculator !!!). Switching on of the engine on as well as the controlling of the engine speed takes place at the control desk. After starting the plant short time must be waited, until a stationary condition adjusted itself. The adjusting of the operating points (Intersection of compressor characteristic and plant characteristic) takes place via adjustment of the entrance control device and the throttle attached on the pressure site. The control device can be adjusted directly at the blower (manually) or by a by hand steered motor drive. Each group has the task during the attempt to determine the measured values for the examination of the throttle characteristic with a firm position of the entrance control device. The position of the entrance control device and the throttle positions which are necessary for the determination of the throttle characteristic are given before the attempt. For the later determination of the compressor characteristic the following sizes must be measured and be registered into the prepared measurement-table. Level 1:

- static pressure p1 - total temperature Tt1

Level 2:

- static pressure p2 - total temperature Tt2

Level 3:

- effect pressure ∆pBl for calculating the volume flow.

In addition: • Ambient pressure • Intake pressure must be measured.

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7 Interpretation of test results 7.1 Evaluation of the measured values under test conditions • Temperatures The total temperatures Tt1 and Tt2 are indicated on the screen of a computer directly in centigrade.

The static temperatures result from the kinetic energies

c2 T = Tt − 2c p Since the flow rates are relatively low in sucking and pressure pipe, these differences are neglected during the further evaluation (T1 ≈ Tt1; T2≈Tt2). • Pressure The static pressure is determined for the respective level (chapter 5.2.3). To the total pressure P applies:

pi = ∆pi + p∞ i=1,2 pti = pi i=1,2

• Flow rate For the determination of the characteristics the flow rate at the compressor entrance (Level 1) is needed. In addition first the flow rate in level 3 is determined. Here it is to be presupposed that the thermodynamic condition is identical in the levels 2 and 3 (p2=p3; T2=T3). The flow rate V3 can be calculated by: 2∆pOr V&3 = V&2 = αε Ad

ρ2

For the following effect pressure measurement in the practical course attempt a standard orifice with the following values is used: α = 0,70673 ε = 0,99568 Ad = (0,1892406 m)2 π/4 The density ρ2 before the orifice can be calculated with the help of the equation of state for ideal gases: p ρ3 = ρ 2 = 2 , R=287 J/kgK RT2 The flow rate at the compressor entrance Vt1 is determined according to the following formula: p ⋅T V&t1 = V&2 ⋅ 2 t1 T2 ⋅ pt1 • Polytropic flow work To the specific flow work applies under the condition of a polytropic change in status: n y polV = ⋅ R ⋅ (T2 − T1 ) , n −1

16 Whereby the polytropic exponent should be constant and can be calculated by the following formula: ln ( p2 / p1 ) n= ln ( p2 / p1 ) − ln (T2 / T1 ) • Polytropic efficiency The polytropic efficiency η polV can be approximated by:

η polV =

y polV ∆h

n = n −1

mit κ=1,4

κ

κ −1 7.2 Conversion on reference conditions • State of reference

Tref = 291 K ;

nM,ref = 2700 min-1

pref = 1,013 bar;

• Polytropic shovel work n  = y polV  M ,ref   nM 

y polref

2

• Volume flow rate V&ref

• Efficiency

n  = V&t1 ⋅  M , ref   nM 

2

ηref = η polV

• Pressure ratio from

y polref

 nn−1  n = ⋅ R ⋅ Tref π ref − 1 n −1  

the pressure ratio derives to 

π ref =  y polref ⋅ 

 n −1 + 1 nR ⋅ Tref 

n n −1

•Required power PKref ≈ V&ref ρ ref ⋅

with:

ρ ref =

pref R ⋅ Tref

y polref 1

ηref ηm

; nM=0,98; R=287 J/kgK

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Bibliography 1. 2. 3. 4. 5. 6.

Adolph, Max: Strömungsmaschinen, Springer Verlag, Berlin/Hagen 1965 Prospects of the company GHH Sterkrade Prospects of the company DEMAG: “Turboverdichter radialer Bauart” Grahl, K.: Vorlesung Strömungsmaschinen I und II, Duisburg 1983 Dietzel, Fritz: Turbinen, Pumpen und Verdichter, Vogel Verlag Würzburg Traupel, W.: Thermische Turbomaschinen, Regelverhalten, Festigkeit und dynamische Probleme, Zürich 1986 7. Prospects of the company DEMAG, Einstufige Getriebe-Turbogebläse Typ KG 8. Bohl/Mathieu: Laborversuche an Kraft- und Arbeitsmaschinen Hanser Verlag, München 1975

∆p = p - p∞ t∞ = Level 1 ELAPosition [°]

ThrottlePositiom [°]

1 2 3 4 5 6 7 8 9 10 11 12

Table 6.1: Measured values

Level 2

Rpm [min-1]

Tt1 [°C]

∆p1 [mbar]

Tt2 [°C]

∆p2 [mbar]

∆pOr [mbar]

Not.

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Evaluation lab test “CC” The evaluation happens according to the data in chapter 7 of the practical course script. With the help of the relations indicated there the table 7.1 can be filled out and thus the characteristic can be drawn in illustration 7.1. (ypolref(V) and/or ηpolV(V)) p∞ = Tt1 Tt2 [K]

p1

p2

∆pOr

V2

[mbar] Vt1

ypolV

[K] [mbar] [mbar] [mbar] [m3/h] [m3/h] [kJ/kg]

1 2 3 4 5 6 7 8 9 10 11 12

Table 7.1: Calculated values

n

ηpolV Ypolref

Vref

[kJ/kg] [m3/h]

Kref

Pkref [kW]

Fig 7.1: Spin characteristic diagram for radial compressors