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Some Notes aboutCentrifugal Compressors

TOSI Giampiero


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2

Agenda

A LITTLE BIT OF THERMODYNAMICSIsentropic Efficiency

Polytropic Efficiency

ELEMENTS OF FLUID MECHANICS

Euler Equation

Dimensional AnalysisPerformance Curves


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A Little Bit ofThermodynamics


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4

COMPRESSOR

ENERGY

GAS GAS

PRESSURE

RATIO

What is a Compressor?


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5

The input is the energy coming from a driver, the output is the

pressure ratio, i.e. the ratio between the discharge pressure and

suction pressure.

This is the simplest possible model that take into consideration

two fundamental elements: how much we have to pay and what

we obtain.

The question is:

The pressure rat io of the gas f lowing throu gh the

compressor is the only effect of the power input?

Whatever happens in the machine it is known that a certain

amount of energy is lost.


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6

COMPRESSOR

ENERGY

GAS GAS

PRESSURE

RATIO

LOSSES


7/577

For a required pressure ratio the

absorbed energy is higher than the one

in case of no losses.

For the same duty, a compressor isbetter then another if it can achieve the

same pressure ratio with lower losses

and therefore with lower absorbedenergy.


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Efficiency

The ratio between the advantages we canobtain with the use of a certain tool and theprice we have to pay

OR

The ratio between what we would pay toobtain a needed result in a perfect world andwhat we pay to obtain the same result in thereal world


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WHICH IS THE THERMODYNAMICPROCESS INSIDETHE COMPRESSOR?


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Adiabatic Process

Gas does not exchange heat

with the external environment

First law of thermodynamics

If process is adiabatic

HW

0Q

TPfH ,

HWQ

HW

0Q

TPfH ,


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ISENTROPICPROCESS

same suction conditions Ps,Ts

same discharge pressure Pd

lower discharge temperature Tis

The isentropic process associated to the real adiabatic process has

A Further Hypothesis: No Losses


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Under the hypothesis of perfect gas

Isentropic Work

WK

KRT

P

Pis s

d

s

KK

11

1

Along vdpW


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Isentropic Efficiency

The ratio of isentropic work to the totaladsorbed energy

is

isW

W

The ratio between what we would pay to

obtain a needed result in a perfect world and

what we pay to obtain the same result in the

real world

Isentropic efficiency is a function of pressure ratio


14/5714

The heat developed by losses point by point

modifies the characteristics of the gas

TOTAL ADSORBED ENERGY

minusISENTROPIC WORK

LOSSES

More work to compress the fluid

but also

more reusable energy stored in the gas


15/5715

Losses always associated to the real process within compressor

No analytical way to describe the real process point by point

How can we simulate the real process?

Characteristics of the ideal substituteprocess reversible same discharge pressure andtemperature good estimation of reusable energy

transmitted to the gas


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Work input not influenced by heat input

First attempt of substitute process

Isoentrope from suction conditions to thefinal discharge pressure WORKINPUT ONLY

Isobar at constant discharge pressure toachieve the discharge temperature HEATINPUT ONLY

Less reusable energy stored in the gas


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17

Increase the number of steps to improve the model

The heat generated by losses in a non reversible

real process can be simulated by heat given from

the external in reversible way through a number of steps

Each step

Isoentrope

WORK INPUT ONLY

IsobarHEAT INPUT ONLY


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18

The equation define the theoretical process called

POLYTROPE

For each step the isentropic work

dw vdpis

eis the constant for which the path passes

through suction and discharge conditions

and

the isentropic efficiency of each step

It is possible to define the equation

dw vdpis

dHvdpe


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The sum of all the isentropic works

step by step along the polytrope

Polytropic Work

W vdp

pol

.

For a perfect gas

Wn

nRT

P

Pp s

d

s

n

n

11

1

W vdp

pol

.


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20


For a perfect gas

The ratio of polytropic work to the total

adsorbed energy p

pW

W

pn

n

K

K

1

1

Polytropic efficiency is not pressure ratio dependant

The ratio between the advantage we

can obtain with the use of a certain tooland the price we have to pay


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Elements ofFluid Mechanics


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22

CUSTOMER NEEDS

Different Points of View

MANUFACTURER NEEDS

A way to compare compressor of differentmanufacturers for the same service

A method to check the performance of themachine at site

Define a relationship between theperformance and the geometry

Verify the

performance

Achieve the performance


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23

A Working Impeller

Normally the tangential component of C1 is negligible


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24

The radial component of gas

velocity is associated to the flow

Multiply the inlet radial

velocity by the area at inlet to

obtain the volume flow at

impeller suction

The tangential component of

gas velocity is associated to

the work made on the fluid

Eulerequation


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25

The energy exchanged, per unit of weight of fluid, is

equal to the product of the variation of the momentum

of the fluid between impeller outlet and inlet by its

angular speed

THE LAW OF MOMENTUM CONSERVATION

Euler Equation

uu CuCuW 1122

In the hypothesis that C1u is negligible

uCuW 22

uu CuCuW 1122

uCuW 22


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26

Based on mechanical principles

FIRST LAW EQUATION

Based on thermal quantities

Wis the same!

Euler Equation

uCuW 22

HW


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27

The variables representing a physicalphenomenon are put together into groups that

are dimensionless

Dimensional Analysis

Generalise the results of experimental works

carried out on models of the real stages

independent of the actual size

of the machine independent of the actual

impellers speed

independent of gas characteristics


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28

The ratio between the radial component of the gas

velocity at inlet and impeller speed in the same point

Inlet Flow Coefficient

111

1

bDu

Qi

1 identifies gasangles at inlet

1

1

1

u

Cr

11

1

bD

QC ir

3600

42

22

1

Du

Qi

or

1

1

1

u

C r

11

1

bD

QC ir

1111 bDu

Qi

3600

42

22

1

Du

Qi


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29

The ratio between the radial component of the gas

velocity at outlet and impeller peripheral speed

Outlet Flow Coefficient

A different form

2

2

2

u

C r

22

2

bD

QC or

222

2

bDu

Qo

const

v

v

i

o12

2

2

2

u

C r

222

2 bDu

Qo

const

v

v

i

o12

22

2bD

QC or


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30

The ratio or the impeller peripheral speed to the

velocity of sound at impeller inlet

Peripheral Mach Number

A measure of gas compressibility

ina

u

Mu

2

The lower the Mach, the lower the

change of density and vice versa

ina

uMu 2


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31

Very low Re

Reynolds Number

It can be read as the ratio of inertia forces to viscous

surface forces

ubRe

Inertia forces negligible if

compared to viscous forces

gas suction density u impeller peripheral speed

b impeller exit width

dynamic viscosityubRe


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32

A measure of the impeller capacity to

energise the gas

Head Coefficient

The ratio between the tangential component of the gas

velocity at outlet and impeller peripheral speed

2

2

u

C u

22

uW

uCuW 22

Euler equation2

2

u

C u

22

uW

uCuW 22


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33

Head Coefficient andOutlet Flow Coefficient

Ideal case of infinite

number of blades22 cot1 g

22 cot g

slip factor < 1

Relative velocity at outlet withthe blades trailing direction

Real case

Head coefficient

reduced

22cot1 g

22 cot g


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34

Assuming that the change of specific volume

along the impeller vane is negligible

const12

21cot gconst

const12

Head Coefficient andInlet Flow Coefficient

21cot gconst


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35

Losses

Friction losses

Impact losses

Dissipation terms

associated with

friction phenomena

between the walls

and the gas

Entry losses associated

with incidence between

the gas and the blades

leading edge


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36

Polytropic Head Coefficient

From head coefficientsubtract the contribution of

impact and friction losses

The work contained in the fluid

under the form of potential and

kinetic energy


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37


The ratio of polytropic

head coefficient to head

coefficient


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38

Non Dimensional Performance Curves

1

f

1

gp

1

hp

1

f

1

gp

1

hp


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39

Dimensional Performance Curves

1

f

1 gp

1

hp

12

2

2

4

uDQi

Geometry and rotational speed

pp uH2

2

22

uW

Gas composition and

inlet conditions

1

1

1

n

n

ss

p

sd

RTzn

n

HPP

n

n

s

dsd

P

PTT

1

d

ddd

P

RTzv

Perfect gas

hypothesis

1

f

1

gp

1

hp

12

2

24

uDQ

i

22

uW

pp uH2

2

1

1

1

n

n

ss

p

sd

RTzn

n

HPP

n

n

s

dsd

P

PTT

1

d

ddd

P

RTzv


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40

The characteristic of standard stages have been obtained

by testing in NP fluidynamic laboratory.

STAGE CODE:

A letter that identifies the family

A number that identifies the subfamily

The external impeller diameter

Standard Stages


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Test rig for standard stages


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Stage in the test rig


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FAMILY SUBFAMILY *104L

2445

432350L 57 40 316256L 710 30 231187B 112 58 1120190A 112 3730 1180145D 18 30 27580

Q 111 45 535195F 313 16 22050G 513 16 18040H 512 16 18050W 214 40 856463V 214 40 856463

= exit blade angle = suction flow coefficient


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Each FAMILY-SUBFAMILY of performance curves has

been memorized as a function of non dimensional

variables.

= suction flow coefficient

Q (m3/h) suction volumetric flowU2 (m/s) peripheral speed

D2 (m) impeller diameter

36004

2

2

2

1

UD

Q


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Suction flow coefficient corrected with specific

volumes ratio:

Peripheral Mach number:

a2 (m/s) = sonic velocity at inlet condition

01

06

V

V

2

2

a

UMU


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46

POLYTROPIC EFFICIENCY

p = f ()

HEAD COEFFICIENT

= f [(V06/V01)]

Performance Non Dimensional Curves


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47

Standard Stage Selection Range


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48

The performance non dimensional curves of each

single stage are stored in a computer program andthey can be managed through a proper equation of

the state for the real gasses.

The curves of the single stages are achieved by

testing.

The computer code can select the stage for flow

coefficient values near to the design one and then

compose the machine to obtain the total requiredcurves.


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49

Knowing

Inlet conditions in terms ofpressure,

temperature and suction flow

Gas composition

Impellers characteristics

State equation

It is possible to calculate the conditions at stage outlet

which are the inlet condition of the next stage.

For all the compressor stages the procedure is thesame as for the first one until final conditions are

reached.


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50

Compressor performance curves consist of a plot showing

at various constant RPM and different suction flow the

variation of the following characteristics:

Polytropic Head

Polytropic efficiency

Pressure Ratio Power

Discharge temperature

Discharge pressure

To reach the total performance curves of a machine it isnecessary to gather the curves of the various stages.


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Performance Curves


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52

Performance CurvesDifferent Parameters


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Typical Expected Performance Curves


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54

Significant improvements in the efficiency of acentrifugal compressor stage can be obtained

using vaned diffuser

Normally a vaned diffuser reduces the extension ofthe operating region of the compressor

The diffuser vanes (number and position) must be

selected considering the structural interference

with the other components of the stage

Vaned Diffuser Characteristics


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Vaned Diffuser


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At relatively low flow rates, 60 70% of those of maximum

efficiency (design conditions), instability in operation can arises,which can be noted from the outside since it results in very

pronounced flow pulsation, shaft vibrations, instability in axial

thrust, abnormal noise level (typical whistling), which can vary

highly depending on the case. This phenomenon, known as

surge, occurs when the machine is required to operate at acompression ratio close the maximum that the compressor can

furnish at the speed at which it is running.

Slightly less severe phenomena can be noted even before

reaching the maximum of the characteristic curve (pressure

pulsation at frequency much lower than the speed of rotation ofthe compressor (10 30%). They are due to rotating stall, i.e.

detachment of the fluid stream from some blades of an impeller

or a diffuser.

Surge and Rotating Stall


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If the flow rate is increased beyond the design valueat constant speed, the pressure drops due the friction

on the fixed and mobile ducts and the pressure drops

due the high incidence increase substantially,

resulting in an enormous reduction in efficiency.

It may happen that in some duct the speed of the

sound is reached and in this case there is an almost

vertical drop in the characteristic curve operation.

This phenomenon should be taken into consideration

especially in compressors which process very heavygases that have low speed of sound.

Choking or Stonewall

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