Perspectives in Science (2016) 7, 287—291

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Using scaled physical model for assessmentof mechanical damping of power plantboiler structure�

Jirí Protivínsky ∗, Martin Krejsa

VSB — Technical University of Ostrava, Faculty of Civil Engineering, Department of Structural Mechanics,Ludvika Podeste 1875/17, 708 33 Ostrava-Poruba, Czech Republic

Received 23 October 2015; accepted 19 November 2015Available online 12 December 2015

KEYWORDSPhysical model;Scaling law;Boiler;Modal analysis;

Summary To determine dynamic response of mechanical system is always a complex issue.One of the core inputs for such a task is a coefficient of logarithmic damping decrement. Thereis no way how to determine this coefficient analytically; it needs to be measured on the finalproduct. There has been a large amount of dynamic tests carried out on common structures andthe results have been incorporated in design codes. Nevertheless, power plant boiler structure

Experiment differs significantly from common structures. To provide a large number of dynamic tests onreal facility is very difficult for many reasons. Using a scaled model is a way how to achieverelevant data based on repeatable experiment.© 2015 Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license

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Foreword

Structural conception of power plant boiler structure isdriven by its technological purpose. According to boilertype there is a variety of types of boiler power plantstructures. This article focuses to heat recovery steam boil-

ers with vertical direction of flue gas (Fig. 1). This typeof boiler is commonly known as a vertical HRSG boiler.Structural system of vertical HRSG boilers is quite simple and

� This article is part of a special issue entitled ‘‘Proceedings ofthe 1st Czech-China Scientific Conference 2015’’.

∗ Corresponding author.E-mail address: jiri.protivinsky@vsb.cz (J. Protivínsky).

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http://dx.doi.org/10.1016/j.pisc.2015.11.0442213-0209/© 2015 Published by Elsevier GmbH. This is an open access artlicenses/by-nc-nd/4.0/).

censes/by-nc-nd/4.0/).

he differences compared to the common structure are wellecognizable.

The majority of mass in structural system is madey tube modules and boiler casing. Either modules oroiler casing slang from boiler upmost part called ‘‘boilereiling’’. Boiler ceiling is created by massive beams cominghrough the flue gas duct. These beams are in full contactith hot flue gas and that is why they cannot be fixed to

he supporting structure. The suspended boiler body isxed in its position by a system of vertical guiding and sidetoppers. The detail of guiding allows thermal dilatation.

his brief summary of boiler structure specifics shows thatechanical damping properties could have been bigger inRSG structure compared to the common steel structure

Carpinteri et al., 2011).

icle under the CC BY-NC-ND license (http://creativecommons.org/

288 J. Protivínsky, M. Krejsa

ity o

oOccbmroatmtrpt(

S

FptKttoitp

M

Mm

2mq(e

soderttnRthe formula (1) solving unknown exponents x1 to x9. Sincethere are just three quotations for estimating nine unknownswe are choosing six linear independent choices for the six

Table 1 Relevant physical quantities applicable for modalanalysis.

Symbol Scaled unit Dimensionin LTM

l Characteristic length L� Specific weight ML−3

E Modulus of elasticity ML−1T−2

t Characteristic time Tω Characteristic frequency T−1

� Stress ML−1T−2

Fig. 1 Vertical HRSG boiler (real facil

Mechanical damping assessment is possible only by meansf experimental testing (Cajka and Krejsa, 2013; Li, 2010).rganizing this type of dynamic test on real facility is practi-ally hardly feasible (Dusicka and Iwai, 2007). Moreover, theorresponding value of one unique dynamic test would haveeen limited. For that reason the solution on scaled physicalodel was chosen (Graczyk and Moan, 2011). Subject of the

esearch was an experimental modal analysis carried out onne scaled physical model. This model was modified into fivelternative designs during the testing. Three of the modifica-ions represented one isolated specific in view. First and fifthodification represented simple steel structure without any

echnology. Logarithmic damping decrement applicable foreal vertical HRSG boilers was determined on base of pro-ortional change of property in view assessed for model withechnology compared to a model without any technologyMaheedhara Reddy and Diwakar Reddy, 2014).

imilitude and dimensional analysis

undamental principle of theory of similitude between realroduct and its scaled model is a conversion of the technicalask in view into its non-dimensional expression (Melcer anducharova, 2014). This way we can derive so called simili-ude invariant numbers which take the same value for bothhe product and its scaled model. The dimensional analysisf the specific task needs to be provided to perform thesenvariants. So the solution is not universal. There is a needo provide this type of analysis for every type of technicalroblems (Protivinsky and Krejsa, 2015).

odal analysis on a scaled model

odal analysis of mechanical systems is defined by nineutually independent physical quantities (Merczel et al.,

n the left, 3D FEM model on the right).

013). By means of these quantities we can express theodal analysis problem in a perfect way. All nine relevantuantities with their expression in technical system LTMlength, time and mass) are provided in Table 1 (Salajkat al., 2013).

On base of relevant quantities we can make up dimen-ional matrix of its exponents in LTM system. Determinantf sub-matrix composed from last three matrix columns isifferent from zero. Therefore the rank of the matrix isqual to three. In agreement with PI-Buckingham’s theo-em, the number of similitude invariant numbers is equalo the difference between the number of relevant quan-ities and the rank of dimensional matrix. Therefore theumber of final similitude invariant numbers is equal to six.epresentation of �-parameters will be provided by using

F Force MLT−2

a Characteristic acceleration LT−2

c Coefficient of viscous damping MT−1

Using scaled physical model for assessment of mechanical damping of power plant boiler structure 289

recti

ihiaP

T

E

Aipertiswere six accelerometric single-axial sensors fixed to themodel. Location of fixing points was designed for evaluatingboth flexural shapes of natural vibration (Kralik, 2013).

Table 2 PMMA material properties.

Symbol Physical quantity Value Unit

Fig. 2 Physical model (on the left — X di

redundant exponents x4 to x9.

⎡⎣

0 1 11 −3 −10 0 −2

⎤⎦ ×

⎛⎜⎜⎝

x1

...x3

⎞⎟⎟⎠

= (−1) ×

⎡⎣

0 0 1 1 0 10 0 −1 1 1 01 −1 −2 −2 −2 −1

⎤⎦ ×

⎛⎜⎜⎝

x4

...x9

⎞⎟⎟⎠ (1)

By solving the Eq. (1) for i = 6 exponent choices x4 to x9

we receive six dimensionless parameters �1 to �6. Since the�-parameters are compound by relevant quantities and atthe same time their numerical representation shall be equalfor the original product, its scaled model can derive scalinglaws for every relevant physical quantity just knowing �-parameters. Unfortunately the scaling laws computed fromparticular �-parameters contradict each other very often. Itis on a researcher to neglect the weak laws not significantfor main focus of his research. The contradiction comes fromthe fact that we choose a limited number of scales equal tothe rank of dimensional matrix only. Moreover, choosing thelength scale and model material we run out of all selectscales. The rest of scales are computed.

Physical scaled model

PMMA material was chosen as the most suitable material fora physical model (Fig. 2). PMMA is a commonly used material

on view, on the right — Y direction view).

n modeling practice (Protivinsky and Krejsa, 2012). PMMAas linear response to loading, quite small internal damp-ng, and connections provided by the PMMA glue behavings basic material (Pospisil et al., 2014). A brief summary ofMMA material properties is shown in Table 2.

Scaling laws of relevant physical quantities are shown inable 3. The gravity law was considered as weak law.

xperimental modal analysis

complete set of dynamic tests was carried out in the exper-mental research center in ITAM Prague. Modal analysis waserformed using industrial computer Dewetron DW 2010 andxciter Brüel&Kjaer, type 8202. The tests were carried outepeatedly on one single model in five particular modifica-ions. A brief description of the model modifications is shownn Table 4. There were twelve measurement tests for everyingle modification in each of horizontal directions. There

� Specific weight 1190 kgm−3

E Modulus of elasticity 3200 MPafy Yield point 60 MPa

290 J. Protivínsky, M. Krejsa

Table 3 Applicable scaling laws.

Symbol Physical quantity Scaling law (scale) Note

L Characteristic length 1:20 = 0.05 Geometry scaleP Specific weight 1.19:7.85 = 0.15159 Determined by the material choiceE Modulus of elasticity 3.2:210 = 0.015238 Determined by the material choiceT Characteristic time 1:6.341 = 0.15770 Computed field

Characteristic frequency 6.341:1 = 6.341 Computed fieldA Characteristic acceleration 1:2 = 0.5

Table 4 Model modifications.

Modificationnumber

Model description

K1 Unloaded model — structure onlyK2 Hanging technology fixed to structure by

springsK3 Hanging technology — no springsK4 Hanging technology — no springs, beams

supporting slung technology fixed onball-bearing

K5 Unloaded model — structure only

Table 5 Logarithmic damping decrement.

Modificationnumber

Logarithmicdampingdecrement

Rate to modificationK1 (rate to commonstructure)

K1 0.059 1.0K2 0.135 2.3K3 0.154 2.6

R

Ettaoo

p2

�

v(

C

Tt

stscfobetsmfssiasB2

veait

ti

C

T

A

Tptbi

R

B

K4 0.48 8.1K5 0.065 1.1

esults and evaluations

valuation of the data recording of tail vibration shows thathe PMMA scaled model is applicable for the specified task. Inhe first phase of tail there is significant mutual influence ofdjacent natural shapes in evidence. Nevertheless, dampingf the PMMA system is low enough to get in the late phasef tail where only the first dominant natural shape occurs.

Logarithmic decrement was determined from the latehase of tail according to formula (2) (Melcer and Kucharova,014).

= 1n

× ln�0(t)

�0(t + n × Td)(2)

The n in (2) formula represents number of periods and the0 represents amplitude of the measured physical quantityTable 5).

onclusion

his paper brings results of the first part of the experimen-al research on mechanical damping of power plant boiler

C

Computed field, considered as weak law

tructure. Time data recording of the vibration tail showswo phases of vibration tail. In the first phase there is visibleignificant mutual influence of the adjacent natural frequen-ies. In the second phase there is only one dominant naturalrequency visible. All the evaluation was done on the basisf this second phase. The cardinal task for every researchased on scaled physical models is how to converse thexperimental results gained on scaled model to a real struc-ural design. The methodology used in this case was veryimple. The damping decrement gained for every particularodel modification was divided by the decrement pertained

or modification K1. This modification represents commonteel structure. Every other modification represents somepecific of vertical HRSG steel structure. This methodologys clear and universal. Results determined in this way arepplicable for structural design of real vertical HRSG boilertructures (Brozovsky and Dufka, 2014; Jendzelovsky andalaz, 2014; Protivinsky and Krejsa, 2014; Vican and Janik,014; Protivinsky and Krejsa, 2015).

In next steps of this research it is planned to evaluate theibrating tail from harmonic force with frequency of loadingqual to first dominant natural ones. These measurementsre to give countercheck of the recent conclusion. Moreover,t will be possible to evaluate the damping even based onhe first phase of vibration tail.

Although there are some more tests ahead we can claimhat vertical HRSG structures have significantly bigger damp-ng than that applicable for common steel structures.

onflict of interest

he authors declare that there is no conflict of interest.

cknowledgements

his paper has been completed thanks to the financial sup-ort provided to VSB — Technical University of Ostrava byhe Czech Ministry of Education, Youth and Sports from theudget for conceptual development of science, research andnnovations for the year 2015.

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