Eisinger New Method

Prediction methods for acoustic vibration

Markus Timonen

DEPARTMENT OF PROCESS AND ENVIRONMENTAL ENGINEERING

BACHELOR’S THESIS 239

2012


Markus Timonen

Supervisor: Jukka Hiltunen

DEPARTMENT OF PROCESS AND ENVIRONMENTAL ENGINEERING

BACHELOR’S THESIS 239

2012

UNIVERSITY OF OULU Abstract of thesis Faculty of technology

Department Laboratory

Department of Process and Environmental Engineering Systems Engineering Laboratory

Author Supervisor

Timonen Markus Hiltunen Jukka

Name of the thesis


Subject Level of studies Date Number of pages

Industrial engineering Bachelor’s thesis March 2012 35

Abstract An acoustic vibration or acoustic resonance in steam generators and heat exchangers is very

complex phenomenon. However, it is also a very important one, because the acoustic vibration is

known to be the main problem for undesirable loud noise in steam generators and heat exchangers.

This Bachelor’s thesis studies acoustic vibration phenomenon by concentrating mainly on the

concern in the steam generator in-line tube banks.

Over the years many researchers have tried to generate a criterion that would predict successfully

the probability of acoustic vibration phenomenon. However, the results have not been clear, and

because of that there are several quite different criteria recommended in the literature, and none of

those seems to give clear results. The chosen criterion should predict as clear as possible to the

designers whether there will be vibration or not, so that it is already known at the design stage

whether the anti-vibration baffle plates or some other prevention mechanisms are needed or not.

There are two different aims for this thesis. The first one is to explain, by using the literature, the

basics of the acoustic vibration phenomenon in steam generator in-line tube banks. The second aim

is to find and compare different acoustic vibration prediction methods by examining different

studies that can be found from literature. This thesis is also related to the larger Master thesis, and

these vibration prediction criteria are the compared more extensively with the information of

existing data from the full-size steam generators to evaluate the best possible solution for this

problem.

Library location

Additional information

OULUN YLIOPISTO Tiivistelmä opinnäytetyöstä Teknillinen tiedekunta

Osasto Laboratorio

Prosessi- ja ympäristötekniikan osasto Systeemitekniikan laboratorio

Tekijä Työn valvoja

Timonen Markus Hiltunen Jukka

Työn nimi

Akustisen värähtelyn todennäköisyyden ennustaminen

Oppiaine Työn laji Aika Sivumäärä

Tuotantotalous Kandidaatintyö Maaliskuu 2012 35

Tiivistelmä Akustinen värähtely höyrykattiloiden ja lämmönjohtimien putkipaketeissa on hyvin mutkikas ja

ongelmallinen ilmiö erityisesti koko ajan suurenevissa kattiloissa. Samalla akustinen värähtely on

myös tärkeä tutkimuskohde, sillä sen tiedetään aiheuttavan ei-toivottavaa kovaa melua sekä

pahimmassa tapauksessa jopa putkivaurioita. Tämä kandidaatintyön tarkoituksena on keskittyä

tutkimaan kirjallisuuden avulla akustisen värähtelyn ilmiötä sekä sen todennäköisyyden

arviointimenetelmiä höyrykattilan suorarivisissä (in-line) putkipaketeissa.

Useat tutkijat ovat viime vuosikymmeninä yrittäneet kehittää menetelmää, mikä ennustaisi

akustisen värähtelyn todennäköisyyden mahdollisimman tarkasti, ja minkä avulla suunnittelijat

saisivat jo suunnitteluvaiheessa selville, tarvitaanko putkipaketteihin värähdyksenestolevyjä tai

muita akustisen värähtelyn estämiseen tarkoitettuja rakenteita ja menetelmiä. Huolimatta näistä

useista tutkimuksista, tulokset eivät kuitenkaan ole tuoneet täysin selkeää ratkaisua putkipaketeissa

syntyvän akustisen värähtelyn arviointiin. Tämän työn tarkoituksena on listata ja vertailla näitä

kirjallisuudesta löytyviä erilaisia arviointimenetelmiä, jotta aiheeseen liittyvässä diplomityössä olisi

mahdollista olemassa olevan datan avulla kehittää paras mahdollinen ratkaisu höyrykattilan

takavedossa tapahtuvan akustisen värähtelyn ennustamiseen ja estämiseen.

Säilytyspaikka

Muita tietoja

Table of contents

Abstract

Tiivistelmä

Table of contents ............................................................................................................... 5

Nomenclature..................................................................................................................... 6

1 Introduction ................................................................................................................ 7

2 Acoustic vibration phenomenon ............................................................................... 8

2.1 Excitation frequency and Strouhal number ........................................................ 10

2.2 Standing wave frequency.................................................................................... 11

2.3 Acoustic vibration .............................................................................................. 13

3 Prediction methods for acoustic vibration ............................................................... 16

3.1 The Grotz & Arnold Criterion ............................................................................ 16

3.2 The Y.N. Chen Criterion .................................................................................... 18

3.3 The Fitzpatrick Criterion .................................................................................... 20

3.4 Blevins’ Acoustic Resonance Map ..................................................................... 23

3.5 The Ziada et al. Criterion .................................................................................... 24

3.6 Eisinger’s old method ......................................................................................... 26

3.7 Eisinger’s new method ....................................................................................... 28

4 Summary ..................................................................................................................... 32

References... ………………………………………………………………………………33

Nomenclature

c speed of sound, [m/s]

D tube diameter, [m]

fa acoustic frequency, [Hz]

fe excitation frequency, [Hz]

fn acoustic frequency (in the n:th mode), [Hz]

fsw,i standing wave frequency (in the i:th mode), [Hz]

G Ziada resonance parameter, [-]

i,j acoustic mode number, (i,j = 1,2,3, …), [-]

L longitudinal tube pitch/spacing, [m]

M Mach number, [-]

Pmax maximum acoustic pressure, [Pa]

∆p pressure drop through the tube bank, [Pa]

Re Reynolds number, [-]

Recr critical Reynolds number, [-]

S Strouhal number, [-]

T transverse tube pitch/spacing, [m]

v gas flow velocity, [m/s]

W width of the flow channel, [m]

XL longitudinal tube pitch/spacing ratio, [-]

XT transverse tube pitch/spacing ratio, [-]

Г Grotz and Arnold dimensionless number, [-]

∆, ∆* Fitzpatrick damping parameters, [-]

δ Chen damping parameter, [-]

ρ flow mass density, [kg/m3]

σ tube bank solidity ratio, [-]

ν kinematic viscosity, [m2/s]

Ψ Chen dimensionless number, [-]

7

1 Introduction

Flow-induced vibrations can cause harmful vibration and noise, and therefore they are

commonly recognized as a major concern in steam generators and heat exchangers.

Generally, there are several possible excitation mechanisms for the flow-induced vibration;

however, the most important ones are fluid-elastic instability, turbulence buffeting, vortex

shedding and acoustic resonance. This thesis concentrates only on acoustic resonance

(vibration) phenomenon which is the main problem for undesirable loud noise in steam

generators.

The aims of this thesis are to explain the basics of the acoustic vibration phenomenon in

steam generators and heat exchangers, and also to find and compare different acoustic

vibration prediction criteria by examining the studies from the literature. These prediction

methods have been generated to give an important evaluation about the possibility of

acoustic vibration, so that the designers can use the chosen criterion as a design guide when

doing the prediction process of acoustic vibration.

8

2 Acoustic vibration phenomenon

An acoustic vibration or acoustic resonance, especially in steam generator tube banks, is

very complex phenomenon. However it is also a very important one since the acoustic

vibration is commonly recognized as a major concern in steam generators and heat

exchangers by causing the harmful vibration and noise. For example Blevins & Bressler

(1987) measured in their tests that during the acoustic vibration, the highest acoustic levels

were as high as 173 dB. The basics of acoustic vibration phenomenon are explained in this

next chapter.

The study in this thesis is based mainly on the acoustic vibration phenomenon in the tube

banks of circulating fluidized bed (CFB) boilers (see Figure 1). The tube banks, which are

composed of for example superheaters, reheaters, economizers and air heaters, are usually

located in the flow channels of rectangular cross section at the backpass of boiler. Typical

lay-out of superheater and economizer tube banks are presented in the Figure 2.

Figure 1: The backpass of circulating fluidized bed (CFB) boiler (Foster Wheeler).

9

Figure 2: Typical lay-out of boiler superheater and economizer tube banks (Steam/its

generation and use, 2005).

The Figure 3 represents the typical definitions for tube diameter, longitudinal/transverse

pitch, and the difference between in-line and staggered tube banks. This thesis is focused

only on the acoustic vibration phenomenon in in-line tube banks, and therefore, the

different prediction methods explaining in this thesis also intend to predict acoustic

vibration only for in-line tube banks. There are a number of different factors and conditions

that can affect an acoustic vibration, and the tube spacing ratios are one of the most

significant ones. For example Blevins & Bressler (1987) have found out that the tightly

spaced tube banks (pitch/diameter ratio ≤ 1.5) are generally quieter than the ones which are

more widely spaced.

10

Figure 3: The definitions for the longitudinal (XL) and transverse (XT) tube pitch/spacing

ratios in in-line and staggered tube banks (Ziada et al. 1989).

2.1 Excitation frequency and Strouhal number

The tube banks which are located in the flow channels of steam generators are exposed to

(excited) the crossflow of hot gas flowing in a vertical direction to tube axes (Eisinger et al.

1996). When the gas flows, alternately varying vortex shedding waves will come into being

downstream of tubes, and then generates periodic changing exciting forces, which direction

is vertical to flow direction (Dong & Liu 2004). The excitation (vortex shedding)

frequency, fe, is given by

(1)

where

fe excitation frequency, [Hz]




The Strouhal number, S, is a dimensionless function of the tube geometry. This number can

be defined from the Fitzhugh’s Strouhal number map (Figure 4) by knowing the

longitudinal and transverse pitches and the tube diameter. Although the Strouhal number is

one of the most significant factors when analyzing the probability of flow-induced

11

vibrations, there are still many unclear points when using the available maps. However,

Blevins & Bressler (1987) and Eisinger et al. (1994) have represented that the Fitzhugh’s

map is probably the closest one.

Figure 4: Fitzhugh’s Strouhal number map for in-line tube banks represented by

longitudinal and transverse pitch/spacing ratios (Fitzhugh 1973).

2.2 Standing wave frequency

Vortex shedding phenomenon can excite the standing waves within the tube banks located

in flow channels. The direction of standing waves is vertical to both tubes and the flow

direction. (Eisinger et al. 1996)

12

The standing wave frequency, fsw,i, of the gas column within a tube bank is given by

(2)

where

fsw,i standing wave frequency (in the i:th mode), [Hz]

i acoustic mode number, (i = 1,2,3, …), [-]




The dimensionless tube bank solidity ratio, σ, is the fraction of volume occupied by the

tubes reducing the speed of sound (Eisinger et al. 1996). Tube bank solidity ratio depends

on the tube bank geometry and is given by

(3)

where


T transverse tube pitch/spacing, [m]

L longitudinal tube pitch/spacing, [m]

Figure 5 shows an example of the occurrence of the first four acoustic standing wave

modes inside the flow channel; in this case acoustic mode number i=1,2,3,4. In this figure

the x-axis explains the width of flow channel, and the acoustic standing wave frequencies

in different modes can be calculated from the Equation 2.

13

Figure 5: The presentation of first four acoustic modes.

2.3 Acoustic vibration

An acoustic vibration/resonance can occur only when the shellside fluid is vapor or gas

(Dong & Liu 2004). The acoustic vibration phenomenon in tube banks is very similar to

vortex shedding phenomenon that occurs with single tubes; however, in this case, it is the

gas, not the tube, that makes the vibration. The acoustic vibration may occur inside the flow

channel when the excitation (vortex shedding) frequency, fe, approaches to the standing

wave frequency, fsw. If these two frequencies fall into the range of 80% to 120%, the

acoustic vibration may start. The phenomenon is called as a lock-in effect and it is

presented in Figure 6. (Goyder 2002)

This generated resonance can lead to either only a mild vibration with no clearly developed

standing wave or even a strong acoustic vibration with well developed standing wave at a

single frequency (Eisinger et al. 1996). Eisinger & Sullivan (2010) presented also that

resonance by itself is not sufficient enough to cause the vibration. Therefore, there have to

be two different conditions that must occur at the same time for the excitation of acoustic

vibration. Firstly, an acoustic resonance or coincidence of frequencies must occur and

secondly, the input energy vibration thresholds must be reached or exceeded. (Eisinger &

Sullivan 2010)

14

Figure 6: A presentation for acoustic vibration lock-in phenomenon (Mohany & Ziada

2005).

The difference between the resonant and non-resonant flow structure associated with the

excitation of vortex shedding is compared in Figure 7. When acoustic resonance occurs

(Figure 7 (a)), the resonant flow structure is symmetric and can couple with a fluid

resonance. On the other hand, Figure 7 (b) shows that when acoustic resonance does not

occur, the neighboring columns are 180˚ out of phase. Therefore the resultant excitation

produced by this vortex shedding in the transverse direction is practically zero. (Oengören

& Ziada 1992)

Figure 7: The vortex shedding within the tube bank when acoustic resonance occurs (a)

and when acoustic resonance does not occur (b) (Oengören & Ziada 1992).

15

Most of these acoustic vibration studies are made in small scale laboratory environment. A

problem, which may occur due to these laboratory conditions, is that how well these

smaller models agreed in reality with the actual full-size steam generators. Eisinger &

Sullivan (2007) defined the acoustic vibration phenomenon also in full-size units. They

found out that acoustic pressure levels at resonance are typically much higher in full-size

scale than in predictions based on laboratory tests. Therefore, when decided the method to

use, it is important to remember that acoustic vibration phenomenon might behaved in a

totally different way at the full scale steam generators.

The main problem due to acoustic vibration is the undesirable loud noise. However,

sometimes it may even cause some structural vibration inside the flow channel. If acoustic

vibration is sustained it may lead to the significant tube damages. (Weaver & Fitzpatrick

1987) While acoustic vibration phenomenon is quite well understood for the case of

isolated cylinders, the more complex cases with close proximities have still many

unresolved questions. (Mohany & Ziada 2005)

Therefore, if acoustic vibration is predicted, it is required to make necessary modifications

to eliminate this problem. The most common mechanism to prevent acoustic vibration is

the arrangement of acoustic vibration (anti-vibration) baffle plates, which disturb acoustic

waves by preventing the lock-in effect. Because the baffle plates are more difficult and

more expensive to install after the boiler construction, it is important to make an attempt to

find the necessary adjustments to prevent the predicted acoustic vibration already during

the design stage.

16

3 Prediction methods for acoustic vibration

Many researchers have tried to formulate a criterion that would predict successfully the

probability of acoustic vibration phenomenon. However, the results have not been clear,

and because of that there are several quite different criteria recommended in the literature.

This chapter lists and gives some comparisons for the most common prediction methods for

in-line tube banks by using among others Ziada’s et al. (1989) and Eisinger’s et al. (1994)

studies as a help. The chosen criterion should predict as clear as possible to the designers

whether there will be vibration or not, so that it is already known at the design stage

whether the anti-vibration baffle plates or some other prevention mechanisms are needed or

not. However, none of the earlier criteria seems to give the results clear enough for the

prediction of acoustic vibration (Ziada et al. 1989).

In this thesis these different available criteria that can be found in literature have been listed

and compared using mainly the results of Eisinger et al. (1994) study as a help. Eisinger et

al. tested 66 tube banks (27 vibrating and 39 non-vibrating) and presented the results in

graphical form for each of the chosen, and the most common prediction criteria. All the

following Eisinger’s et al. evaluation processes are based on Fitzhugh’s Strouhal number

map (Figure 4), which seems best to represent tube banks vibration behavior. (Eisinger et

al. 1994)

3.1 The Grotz & Arnold Criterion

Grotz & Arnold (1956) investigated one of the earliest studies of acoustic vibration. They

also produced the first parameter for prediction process of acoustic vibration. This

parameter is known as the Grotz & Arnold resonance parameter Г, and it is given by for in-

line tube banks

(4)

17

where

Г Grotz & Arnold dimensionless number, [-]


XL longitudinal tube spacing ratio, [-]


j acoustic mode number, (j = 1,2,3, …), [-]

According to this parameter, a strong acoustic vibration is the most probable when Г < 62-

80. However, Eisinger et al. (1994) showed in their study that this original region is not a

good estimation scale, because there are a relatively wide “mixed region” (Г = 80-320)

between the vibration and non-vibration regions. This “mixed region” can be seen in the

Figure 8. (Eisinger et al. 1994)

As can be seen from the equation of the Grotz & Arnold resonance parameter, it has a lack

of flow parameters and is based on geometry only. Besides of that lack of flow parameters,

the wide “mixed region” can also lead to the doubtful results. Therefore, it can be said that

Grotz & Arnold criterion is less useful when predict the acoustic vibration at the design

stage.

Figure 8: Grotz & Arnold number Г versus acoustic vibration mode number (based on

Eisinger et al. 1994).

18

3.2 The Y.N. Chen Criterion

The Chen (1968) acoustic vibration criterion Ψ for in-line tube banks is given by

(5)

where

Ψ Chen dimensionless number, [-]



XL, XT longitudinal and transverse tube spacing ratios, [-]

The Reynolds number is given by

(6)

where




According to the Chen’s (1968) own investigations, the value which separates the vibration

and non-vibration cases from each other seemed to be about 600. However, later this value

was raised to 2000 for the industrial non-ideal flow conditions, when 600 can only be used

in laboratory condition (Rodarte & Miller 2001). Therefore it can be said that based on the

Chen’s criterion, the acoustic vibration is not likely when Ψ < 600...2000.

Before generating their own acoustic vibration evaluation method Eisinger et al. reported in

1994 that the Chen criterion gave the best results for in-line tube banks when separating the

vibration cases from the non-vibration cases. However, they recommended also that instead

19

of the Chen number Ψ = 2000, the criterion should be 1300 < Ψ < 2700. So that if Ψ <

1300, there is always no vibration, and if Ψ > 2700, there is always vibration. The region

between these two limits is called again “the mixed region”, and it can be seen in a Figure

9. (Eisinger et al. 1994)

Figure 9: Chen number Ψ versus acoustic vibration mode number (based on Eisinger et al.

1994).

The Chen criterion takes into account also the flow parameters; and therefore it should

evaluate the acoustic vibration better than the earlier criterion from Grotz & Arnold.

However, due to Eisinger’s et al. study and its quite large mixed region, it is showed that

Chen’s criterion has also some unclearness. The best solution would be that when utilizes

the Chen criterion for industrial conditions the designers should use their own critical Chen

number limits depending on their investigation from earlier boiler plants (Kaneko et al.

2008, 93).

20

3.3 The Fitzpatrick Criterion

Fitzpatrick (1986) introduced a damping criterion ∆, which is a modified version of the

previous Grotz & Arnold’s and the Chen’s acoustic vibration criterions. Later Fitzpatrick

modified this criterion and introduce a new damping criterion ∆*. These two damping

criteria are given by

1) The Fitzpatrick damping criterion, ∆

(7)

2) The Fitzpatrick modified damping criterion, ∆*

(8)

where

∆, ∆* Fitzpatrick damping parameters, [-]


M Mach number, [-]


XL, XT longitudinal and transverse tube spacing ratios, [-]

21

Figures 10 & 11: Fitzpatrick’s damping criterion ∆ and the modified version ∆* versus

1/XL (Fitzpatrick 1986).

Figures 10 and 11 gives the results based on these damping parameters versus 1/XL.

Fitzpatrick (1986) considered that there is a central region (between the lines) that contains

all the acoustic vibration cases, and below and above that region all the cases are the non-

vibration cases. It has been represented that below this central region, the acoustic

frequency is so high that the turbulent energy cannot cause acoustic vibration. On the other

hand, above this central region, the damping effect is high enough to prevent acoustic

vibration phenomenon. (Ziada et al. 1989)

As can be seen from the Figures 12 and 13, Eisinger et al. (1994) expanded these limits due

to their own acoustic vibration research. However, the scatter in these studied cases is so

significant that it is obvious that either of these criterion has no clear results in a large

number of cases. The Fitzpatrick criterion is based on small scale tests on laboratory

models and appears to be less reliable for large size industrial cases (VDI Heat Atlas 2010).

This important notice can be seen also quite clearly from the results of Eisinger’s et al.

study.

22

Figure 12: The Fitzpatrick damping criterion ∆ versus 1/XL (based on Eisinger et al. 1994).

Figure 13: The Fitzpatrick modified damping criterion ∆* versus 1/XL (based on Eisinger

et al. 1994).

23

3.4 Blevins’ Acoustic Resonance Map

Eisinger et al. (1994) presented their studies also in the Figure 14 that represents the

acoustic vibration data in a Blevins-type acoustic resonance map (Blevins & Bressler

1987). The figure shows five modes for the non-vibration cases and four modes for the

vibration cases. Although the Blevins map is simple and quite informative, it lacks of data

and does not give clear separation between the vibration and non-vibration cases. Eisinger

et al. (1994) gave some observations that can be made from the Figure 14: 1) for XL > 2.2,

acoustic vibration occurred in all cases; 2) for XL < 2.0 and XT > 2.8, no acoustic vibration

occurred and 3) for XL < 2.3 and XT < 2.8, the region is mixed. Although the Blevins’ map

is not very usable for the designers, it gives some confirmation that if longitudinal tube

spacing ratio is large, the acoustic vibration will more likely occurs.

Figure 14: Blevins’ acoustic resonance map (based on Eisinger et al. 1994).

24

It is also good to keep in mind that the Blevins’ acoustic resonance map does not take into

account for example the Reynolds number or the gas properties. It is based on the idea that

whether the vibration will happen or not depends simply on the tube’s longitudinal and

transverse spacing ratios. (Ziada et al. 1989)

3.5 The Ziada et al. Criterion

The Ziada’s et al. resonance parameter (1989) for in-line tube banks is given by

(9)

where

G Ziada resonance parameter, [-]

Recr critical Reynolds number, [-]

XT transverse tube spacing ratio, [-]




The critical Reynolds number is based on the critical gap velocity, vcr, and it can be

calculated from the Equation 6 (Ziada et al. 1989). Because other parameters are constant

during the calculation process at different acoustic modes, it can be seen from the Equation

9, that the higher the critical Reynolds number is, the higher is the Ziada’s resonance

parameter and, therefore, the acoustic vibration will more likely occur.

Ziada et al. showed the resonance parameter, G, in graphical presentation, G versus (XL)2

(Figure 15). In this presentation two regions were separated by a curve, which showed the

separation of vibrating and non-vibrating cases. It also showed that vibration is more likely

when the tube banks are not so closely packed (i.e. higher XL). (Ziada et al. 1989)

25

Figure 15: Ziada’s acoustic resonance parameter G versus (XL)2 for in-line tube banks

(Ziada et al. 1989).

Once again Eisinger et al. (1994) gave the new vibration/non-vibration limits based on their

own research. These limits are showed in Figure 16. It can be seen from the figure based on

the Eisinger’s et al. study that the acoustic vibration data is scattered throughout a wide

area, and because of that it does not provide a clear solution to separate the vibration cases

from the non-vibration ones. (Eisinger et al. 1994)

In the same way like the earlier two Fitzpatrick’s criteria, the Ziada’s criterion is also based

on small scale model tests and it appears to be less reliable for large size industrial cases

(VDI Heat Atlas 2010). Like the Eisinger’s et al. research shows, the Ziada’s criterion

seems not be either very usable at the design stage.

26

Figure 16: Ziada’s acoustic resonance parameter G versus (XL)2 (based on Eisinger et al.

1994).

3.6 Eisinger’s old method

After the studies and evaluations of the previous methods from the literature, Eisinger et al.

(1996) developed their own criterion that can be used in design stage to free steam

generator and heat exchanger tube banks from the acoustic vibration. The criterion is based

on acoustic particle velocity, acoustic pressure, pressure drop and the Mach number of the

gas flow through the tube bank. This criterion was generated by using the data from 60 full

size operating steam generators in-line tube banks. 25 of those were vibrating and 35 were

the non-vibrating ones. In addition, they utilize data from 60 laboratory tests with cold air

flow, complemented by 8 cases of operating narrow-channel steam generator tube banks.

(Eisinger et al. 1996)

Eisinger’s et al. method has two different input energy criteria that can be utilized for an

acoustic vibration prediction process. The first one is based on acoustic pressure and the

other is based on acoustic particle velocity.

27

The first input energy criterion, which is based on acoustic pressure, is given by

(10)

where

M Mach number, [-]

∆p pressure drop through the tube bank, [Pa]




The Mach number for a tube bank is given by

(11)

where




The second input energy criterion, which is based on acoustic particle velocity, is given by

(12)

where the Chen damping parameter δ is given by

(13)

28

These two criteria (Equations 10 and 12) can be combined into one criterion by

representing the greater of the two values at each acoustic mode. This upper limit value is

called (MΔp)upper,j. Figure 17 shows the stability boundary for vibration and non-vibration

cases at different acoustic vibration modes. After the calculation of the upper limit value, it

is necessary to determine an input energy parameter (MΔp)j at each acoustic mode has as

well. The acoustic vibration is then predicted at mode j when (MΔp)j (MΔp)upper,j and not

predicted when (MΔp)j < (MΔp)upper,j. (Eisinger et al. 1996, Sullivan et al. 1998)

Figure 17: Stability boundary (upper) limit diagram based on acoustic pressure and

acoustic particle velocity (Eisinger & Sullivan 2003)

3.7 Eisinger’s new method

In 2010 Eisinger & Sullivan presented a new criterion for the predicting the acoustic

vibration. The data for this evaluation process is derived from the 55 full size steam

generator and tubular heat exchanger tube banks, 20 of them were the vibrating cases and

35 of them were the non-vibrating ones. They did also some small scale cold air laboratory

29

tests to get further evidence for the criterion. This new method makes the difference from

the previous method in that it is based on dimensionless acoustic particle velocity, which

Eisinger & Sullivan show in their study to be the decisive parameter of acoustic vibration

prediction. This new method can be used directly or together with the Eisinger’s et al.

previously published method in order to reach the best results in the evaluation process of

acoustic vibration. (Eisinger & Sullivan 2010)

The dimensionless acoustic particle velocity is given by

(14)

where

Pmax maximum acoustic pressure, [Pa]

ρ flow mass density, [kg/m3]


fn acoustic frequency (in the n:th mode), [Hz]


For the determination of the dimensionless acoustic particle velocity, the maximum

acoustic pressure Pmax needs to be calculated. The most conservative (the lowest) value for

the maximum acoustic pressure at resonance is given by

(15)

Although the parameter M∆p has also an important role in the prediction method, the

evaluation is ultimately done through the dimensionless acoustic particle velocity parameter

vp/fnD. The results from this study are showed in the Figures 18 & 19. In these figures the

dimensionless acoustic particle velocity is showed as a function of the dimensionless input

energy parameter (M∆p/p0) and the Mach number (M). The utilized data is from the full

size steam generator and tubular heat exchanger in-line tube banks. However, also the data

30

from the laboratory tests for the in-line and staggered tube banks show the same clear

difference between the vibration and non-vibration cases. The figures of the laboratory tests

can be found from that same article. (Eisinger & Sullivan 2010)

As can be seen from the Figures 18 & 19, the acoustic particle velocity separates the

vibrating cases from the non-vibrating ones a much clearer than any of those previous

prediction methods. The equations which represent the placed lines that separate the

vibration region from the non-vibration region can be utilized in each specific case to

predict if the acoustic vibration will occur or not.

Figure 18: Dimensionless acoustic particle velocity versus dimensionless input energy

parameter (Eisinger & Sullivan 2010).

31

Figure 19: Dimensionless acoustic particle velocity versus Mach number (Eisinger &

Sullivan 2010).

32

4 Summary

An acoustic vibration or acoustic resonance in steam generators and heat exchangers is very

complex phenomenon. However, it is also the main problem for undesirable loud noise, and

therefore, it is significant concern to the designers. This Bachelor’s thesis explains the

basics of acoustic vibration phenomenon and compares different acoustic vibration

prediction methods by concentrating mainly on this concern to the steam generators in-line

tube banks.

Over the years many researchers have tried to generate the damping criteria that would

predict the probability of acoustic vibration as successfully as possible. However, none of

those previous criteria seem to give results clear enough. Although the Eisinger’s et al.

(2010) new method seems to predict acoustic vibration quite clearly, and much clearer than

the other criteria, it is important to remember that all those introduced methods need still

some proper researches with full-size boilers. It is also important to remember that each

boiler is a case-specific, so that one working solution is not necessary usable in other cases.

Therefore, the designers should use the criterion that gives the best results depending on

their information and data from their own previous vibrating and non-vibrating boiler cases.

The most common mechanism to prevent the lock-in phenomenon of acoustic vibration is

to disturb acoustic waves by installing the acoustic vibration baffle plates inside the tube

banks. However such baffle plates are more difficult and expensive to install after the boiler

construction. Therefore, a proper prediction method would be very significant benefit

because then the necessary adjustments could be made already during the design stage to

prevent the possibly predicted acoustic vibration.

33

References

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Documents

Eisinger New Method