Available online at ScienceDirect. Procedia Engineering 106 (2015 ) Dynamics and Vibroacoustics of Machines (DVM2014)

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1 Available online at ScienceDirect Procedia Engineering 16 (15 ) Dynamics and Vibroacoustics of Machines (DVM14) Method develoment of the vibroacoustic characteristics calculation of the gas distribution stations elements Aleksandr A. Igolkin a, Luiza F. Musaakhunova a*, Konstantin Yu. Shabanov b a Samara State Aerosace University, Moskovskoe shosse, 34, Samara, 44386, Russian Federation b "Gazrom Transgaz Samara" LLC Novo-Sadovaya st., 16 A, Samara, 44386, Russian Federation Abstract Pressure-reducing devices such as rotective valves, control valves and chokes can create high levels of high-frequency acoustic waves at the outlet of the valve. These acoustic waves are roagated along the ie, thereby generating vibrations, which in turn lead to fatigue failures, sometimes malfunctions set in within a few hours. In this research work, we have studied the main aroaches of the vibroacoustic characteristics analysis that as a result has allowed us to develo the method of calculation of vibroacoustic characteristics, which would hel to make the assessment of ieline strength, of ies noise and vibration levels more racticable. At this method different ways could be emloyed to get the desired results deending on the kind of data (measured vibroacoustic characteristics, geometric characteristics of the element, the inut arameters) The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is an oen access article under the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under resonsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM14). Peer-review under resonsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM14) Keywords: sound ressure level; sound (acoustic) ower level;vibration velocity; vibration acceleration; fatigue life; resonant frequency; sectrum; sound reduction index;modal analysis; gas ieline; discrete throttle valve(dtv); 1. Introduction Gas distribution stations are imortant links in the gas-suly system, which erforms rearation and distribution of the gas between consumers in the country. As exloitation ractice has shown, construction of the industrial ielines of the gas distribution stations does not rovide a lengthy trouble-free oeration. Vibrations exceeding strength levels can lead to the destruction of the ieline and this factor must be taken into consideration [1]. As a result of excessive vibration in ielines, different failures occur such as cracks due to fatigue of the material, self-loosening fittings, track connections and controls valves, deressurization of ielines. * Corresonding author. Tel.: address: lu.musaakhunova@mail.ru The Authors. Published by Elsevier Ltd. This is an oen access article under the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under resonsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM14) doi:1.116/.roeng

2 31 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) Causes of vibrations occurrence Pieline vibrations by their nature of manifestation, causes, and consequently, and elimination methods, significantly differ from machine vibration. If the vibration of uming units and their foundations in most cases occurs due to the inertial forces of the moving arts of the unit and can be removed by mechanical means, then the vibration occurs in the ies as a result of inertial forces of the medium being umed (which is less significant), and also as a result of ressure ulsations in the ieline []. If the frequency of the forced vibrations of the system, usually coinciding with the cycles of oeration of the machine, close to the self-oscillation frequency of the iing system, it means that the system will resonate, which results in intense vibration mostly of the discharge ies and to a lesser extent, of the suction ies. The area of distribution of vibration is usually limited by the iing system of the uming station or of the comressor station, ressure ulsation of the medium fades raidly after reaching the straight sections of ies [3]. 3. Method of vibroacoustic characteristics calculation In this aer, different methods of determining the vibroacoustic characteristics were combined to redict the strength of the ieline. As seen in figure 1, the strength characteristics can be calculated according to several different sequences. Deending on the kind of data (measured vibroacoustic characteristics, geometric characteristics of the element, the inut arameters) different ways (solid line-calculation, dashed line-comarison) could be emloyed to get the desired results. Consider the examle of the strength calculation by known oeration mode arameters of the main gas ieline of the gas distribution station 19A in Togliatti. The lan of calculation is resented in Fig.. The first ste - it is necessary to calculate the sound ower level and ascertain if the working values conform to the standards

3 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) Fig. 1. The concet for assessing the strength of the ieline due to the vibroacoustic loads imact Fig.. The lan of the vibroacoustic characteristics calculation The sound ower level L w of the valve or orifice late can be calculated as follows: P1 P T Lw 1log M 16.1K (1) P1 W L w = sound ower level in db M = mass flow in kg/sec P 1 = ustream ressure in kpa absolute P = downstream ressure in kpa absolute T = temerature in Kelvin W = molecular weight K = zero for nonsonic flow and +6 for sonic flow conditions For comarison, we used the value taken from strength criteria develoed by V.A. Karucci and R. T. Müller [4]. Table 1. Calculated values of acoustic ower level L w The mode of oeration db Oeration mode 1 ie 5 4 Oeration mode ie 5 193,5 Oeration mode ie 6,64 Oeration mode 3 ie 6 5 Permissible values for the 7 16 mm diameter

4 31 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) The next ste is to calculate the level of the internal sound ressure according to the method roosed by the IEC () [5]. The total internal sound ressure level (in db) downstream of the valve exit is given by: 9 X 3.91 W in d c d LP 1log () 1 Di W=acoustic ower, W ρ d = density of the medium kg/m 3 с = seed of sound in the medium, the subscrit "d" signifies downstream (normally assumed to be 1m from the valve exit) m/s D i = internal ie diameter of the downstream ie m X = factor to account for et exit angle. The factor (3. 1 9) comes from converting sound ower into sound ressure [1] with a reference ressure of 1-6 Pa. For further calculations we need to get the external sound ressure level, however we cannot obtain it in a straightforward manner by converting the internal sound ressure level, that is why we need to find out the value of transmission loss coefficient T l. Knowledge of the eak internal sound frequency f is crucial for a roer rediction of the ie transmission loss coefficient T l. The coefficient T l does not vary significantly between the first cutoff frequency f and the ring f r of the ie, but variations can be large at other frequencies. The sloe of T l about -6dB er octave below f and +6dB er octave above f r [5]. For Mach numbers in the ie less than about.3 and for relatively heavy ies it may be assumed that the minimum transmission loss occurs at f and is given by (3) [6]. rt 6 P TLf 1log (3) Di Pa r distance from ie wall to observer, m t thickness of ie wall, m D i internal ie diameter, m P internal static ressure downstream of the valve, Pa P a external static ressure at the same downstream of the valve, Pa The total transmission loss coefficient is now exressed in the form (4) [6]: T T T (4) L Lf Lf where the correction log f f f f log f TLf 13 f 4 f f log f 7.8 f f 4 f T Lf (in decibels) is determined by the eak noise frequency according to (5) [6]: The eak frequency is determined from (6)[6]: (5)

5 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) M c M 4 D f.8c M 4 D M 1 c - seed of sound at vena contracta, m/s D - et diameter at valve orifice 1 1 P P M The external sound level ressure (measured at 1 m from the wall) is given by (8) [6]: ex in L 5L T (8) P P L (6) (7) L, db Allowed L L(external.) calculated L(external.) calculated at the oeration mode 1 ie 5 L(external.) calculated at the oeration mode ie 5 L(external.) calculated at the oeration mode ie 6 L(external.) calculated at the oeration mode 3 ie D, inch Fig. 3. Calculated sound ressure level at 1 m from the ieline To further comare calculated and measured values of vibration velocity, it is necessary to exand the obtained values of the acoustic ower level into the range. Calculation of frequency correction begins with determination of the frequency, which corresonds to the highest level of sound ower (9) [6]: V f (9) 5 D f р maximum acoustic ower frequency for the free flow of gas, Hz; V the outut seed of the gas flow in m / s; D ie internal diameter, m.

6 314 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) L, db Calculated external L Measured external L f, Hz Fig. 4. The level of external calculated and measured sound ressure Sound ower level is determined by the frequency at which the correction is erformed for various maximum frequencies f according to the Strouhal coefficient, as result we obtain the level of acoustic ower decomosed into the sectrum. Next, it is required to convert the acoustic characteristics onto vibration characteristics using formulas (1, 11) [7]. The basis of this conversion method is the relationshi between acoustic ower and radiation efficiency [7]. ex D f ( LP 1lg 1lg 13.7 ) r fc v f f с (1) ex D ( LP 1lg 13.7 ) r v f f с (11) Then using Watchel's method [8], the ieline stresses are calculated. During the research, it was discovered that the most loaded ie is 6. For ieline 6, the safety factor was calculated (Table ). Table - Calculated safety factor of the ie 6 at oeration mode 3 vibrodislacement σ, MPа η (the rms value), m,6 11 1,65 4. Conclusion The main aroaches to the analysis of vibroacoustic characteristics have been examined. These include estimation of the sound ower level according to the methodology develoed by Carucci and Mueller; sound ressure level calculation according rocedure described in the L.L. Beranek method and stress analysis by the method develoed by D.S. Watchel. In this research work, the method of vibroacoustic characteristics calculation was develoed. Usage of this method makes an estimation of ieline strength, noise and vibration levels more racticable. At this method an alication of different ways, deending on the kind of data you obtain (measured vibroacoustic characteristics, geometric characteristics of the element, the inut arameters), allows getting the desired results.

7 Aleksandr A. Igolkin et al. / Procedia Engineering 16 ( 15 ) References [1]Tolokonnikov, I.S., Karmanova, V.V., Oleynikov, A.Yu., Petrov, S.K., Polyakh, I.I. (11) Snizhenie urovney shuma i vibracii na gazorasredelitel'nykh unktakh energeticheskikh ob"ektov. Sbornik dokladov. P. 45-6, (in Russian) [] Makaryants, G.M., Gafurov, S.A., Zubrilin, I.A., Kruchkov, A.N., Prokofiev, A.B., Shakhmatov, E.V. (13) Design methodology of hydrodynamic noise silencer, ICSV 13, Volume 3, 13, Pages [3]Bolotin, V.V. Prognozirovanie resursa mashin i konstrukci. Moskva: Mashinostroenie; 1984, 31., (in Russian). [4]Bruce, D.R., Bommer, A.S., Leage, T.E. (13) Solving acoustic-induced vibration roblems in the design stage, Sound and Vibration. [5]Singh, G.M., Rodarte, E., Miller, N. R., Hrnak, P. () Modification of a standard aero acoustic valve noise model to account for friction and two-hase flow, ACRC Proect 7. [6]Beranek, L.L. (6) Noise and Vibration Control Engineering: Princiles and Alications, Second Edition, Istvan. [7]Fagerlund, A.C. Use of iewall vibrations to measure valve noise, Technical monograh 33. [8]Wachel, J.C. (1995) Dislacement method for determining accetable iing vibration amlitudes, International ressure vessels and iing codes ans standarts: Volume current ersectives.