MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION Hisao Izuchi, Pricipal Egieerig Cosultat, Egieerig Solutio Uit, ChAS Project Operatios Masato Nishiguchi, Egieerig Solutio Uit, ChAS Project Operatios Toshio Mabuchi, Egieerig Cosultat, Pipig Egieerig Uit Moritaka Nakamura, Fellow, Techology & Egieerig Divisio Chiyoda Corporatio Yokohama, Japa KEYWORDS: Flow Iduced Vibratio, Turbulece, Flare Pipig System, 45 Degree Combiig Tee, Vibratio Aalysis, Vibratio Velocity Number ABSTRACT I recet baseload LNG plats of larger capacity, the risk of vibratio for large diameter pipes icreases, especially for a flare system with relatively high velocity. Oe such kid of pipig vibratio is FIV (Flow Iduced Vibratio) caused by turbulece. It is kow that FIV occurs at locatios where high turbulece is preset such as dowstream of a combiig tee. However, o paper has yet bee published that focuses i detail o the characteristics of this FIV at the tee. I this paper, a study is preseted o FIV, dowstream of a 45 degree combiig tee. Experimets ad a CFD / FEA approach were used to ivestigate the characteristics of FIV. The results of the experimets show that the shell mode vibratio of the pipe is larger tha the beam mode vibratio. This fidig cotradicts the previous uderstadig that FIV geerally iitiates beam mode vibratio. The CFD results show that large turbulece eergy occurs a little dowstream from the combiig poit. Radom vibratio aalysis was executed with FEA based o the experimetal ad CFD results, which demostrated that the CFD/FEA approach is practical method to evaluate the overall vibratio characteristics of FIV. I cosideratio of the basic characteristics of FIV, a idex is proposed, called Vibratio Velocity Number,which expresses the magitude of the vibratio velocity. The experimetal results show that this idex is effective i evaluatig the vibratio risk of FIV for wide rage of brach area ratios to the mai. INTRODUCTION I recet baseload LNG plats of larger capacity, the risk of vibratio for large diameter pipes icreases, especially for a large diameter flare system with relatively high velocity. Oe such kid of pipig vibratio is FIV (Flow Iduced Vibratio) caused by turbulece. It is kow that the FIV occurs at locatios where high turbulece is preset such as dowstream of a combiig tee [1]-[3] or dowstream of a bed [4]. For FIV dowstream of a bed, Hirota et al. ivestigated the o-dimesioal relatioship betwee pressure fluctuatio ad fluid mometum eergy with experimets ad vibratio aalysis [4]. However, there is o publicatio which expresses i detail the characteristics of the vibratio pheomea of FIV dowstream of a combiig tee. The author has recetly ivestigated this FIV by aalytical ad experimetal methods [], [3], ad foud that the shell mode vibratio of the pipe is larger tha the beam mode vibratio with large diameter ad relatively thier wall pipes. This fidig cotradicts the previous uderstadig that FIV geerally iitiates beam mode vibratio [1]. The author has also demostrated that CFD (Computatioal Fluid Dyamics) / FEA (Fiite Elemet Aalysis) aalysis is effective i ivestigatig the characteristics of FIV ad itroduced a idex called Vibratio Velocity Number which expresses the magitude of the vibratio velocity. 1
This paper presets the study results of FIV dowstream of a 45 degree combiig tee usig experimets ad CFD / FEA aalysis. It also demostrates the cocepts of the Vibratio Velocity Number idex which is derived from the basic radom vibratio theory ad expresses the magitude of the vibratio severity. The experimetal results show that this idex is effective i evaluatig the vibratio stress of FIV for a wide rage of process coditios ad the brach flow area ratios to the mai pipe. METHOD OF EXPERIMENT Figures 1 ad show the experimetal facility which has a air chamber at the upstream ed. The pipig system is coected to the air chamber through a ball valve ad a RO (Restrictio Orifice) ad there is a 45 degrees tee dowstream of the orifice. After opeig the ball valve, air will flow from the pressurized air chamber ito the tee sectio. Two types of sesor, strai gage type (TP1-TP4) ad piezoelectric type (TPA1-TPA5), are used to measure the absolute pressure ad pressure fluctuatio, respectively. Twety oe stai gages for the circumferetial directio are attached dowstream of the combiig poit, as show i Figure 3, i order to measure the shell mode vibratio i detail. Table 1 shows the five experimetal cases that were executed to ivestigate the effect of the brach flow area ratio to the mai pipe. To Atmosphere 6 ich ) TP4 TPA5 TPA4 TPA3 Restrictio Orifice TP1 Ball Valve ( 6 ich PG Air 3,311 4ich 11.6 11.6 TPA TP3 Flow Air Chamber TP : Pressure Sesor (Strai Gage Type) TPA : Pressure Sesor (Piezoelectric Type) 5.8 5 5.8 Figure 1. Experimetal Facility (4 x1.5 ) Strai Measuremet Sectio Tap for Pressure Sesor (TPA4) 1 9deg 3 4 5 6 7 8 9 1 11 4ich 1 13 14 TPA5 TPA4 TPA3 TPA 15 11.6 11.6 5.8 Figure. Experimetal Facility aroud Combiig Tee (4 x1.5 ) 1 19 18 17 16 Figure 3. Measurig Poits for Strai
Table 1. Experimetal Cases Case Defiitio Mai Pipe Brach Pipe Brach Area O.D. Wall. Thick. D/t O.D. Wall Thick. Ratio to Mai 4 x 4 114.3 mm.1 mm 54.4 114.3 mm.1 mm 1. 4 x 3 114.3 mm.1 mm 54.4 89.1 mm.1 mm.6 4 x 1. 5 114.3 mm.1 mm 54.4 48.6 mm 1.65 mm.17 4 x 3/4 114.3 mm.1 mm 54.4 7. mm 1.65 mm.47 4 x 1/4 114.3 mm.1 mm 54.4 13.8 mm 1. mm.11 METHOD OF NUMERICAL ANALYSIS Figure 4 shows the aalytical model for the 4 x 1.5 case. First, CFD aalysis is executed usig the commercial code STAR-CCM+ V5. to obtai a area of high turbulece where high pressure fluctuatios occur. The CFD results i Figure 5 show that the area of high turbulece occurs a little dowstream of the combiig poit ad this idicates that the high turbulece is caused by the jet flow from the brach impigig o the mai pipe wall. Correspodig to this area of high turbulece, the excitig force area is determied i the FEA model. Figure 6 shows the PSD (power spectrum desity) of the pressure fluctuatio at TPA4 (refer to Figure ) for the 4 x1.5 case with 6 bara at the RO upstream. This pressure fluctuatio is treated as the excitig force actig o the area of high turbulece as explaied above ad the radom vibratio aalysis is executed by usig the commercial FEA code, ABAQUS V6.1. 1-1/ich brach pipe (beam model) Fix Boudary Coditio Fix Boudary Coditio Tap for Sesor Blid Flage (Fix Boudary Coditio) 4ich Paret pipe (Shell model) Figure 4. Aalytical Model (4 x1.5 ) Turb. Kietic Eergy [m /s ] 65 433 17 Figure 5. Turbulece Eergy Obtaied by CFD Aalysis (Upstream Pressure of RO (TP1) is 6 bara, 4 x1.5 ) 3
Power Spectrum Desity of Pressure Fluctuatio [kpa /Hz].5. 1.5 1..5. 5 5 Frequecy [Hz] Figure 6. Power Spectrum Desity of Pressure Fluctuatios at TPA4 (Upstream Pressure of RO (TP1) is 6 bara, 4 x1.5 ) RANDOM VIBRATION THEORY Statistical processig is required [5] i order to evaluate the radom vibratio i which the overall RMS (Root Mea Square) of the vibratio is equivalet to the stadard deviatio. For simplicity a simple vibratio model is cosidered with a radom excitatio force, F, expressed by equatio (1). m x + cx + kx = F(t) (1) Here, m, c ad k ad F are the mass, dampig costat, sprig costat ad displacemet, respectively. PSD (Power Spectrum Desity) of the vibratio displacemet, S x ca be writte by equatio (). S ( ω) = H( ω) S ( ω) () x w Here, ω, H ad S w are the agular frequecy, trasfer fuctio ad PSD of excitig force, respectively. Trasfer fuctio, H ca be writte by equatio (3). H(ω) = 1 (3) (k mω ) + (cω) Itegratig of equatio () derives equatio (4) [5]. x W = Sx ( ω) dω = H( ω) Sw ( ω)dω = 4kc Here, x is the root mea square of the displacemet ad W is a coefficiet which shows the PSD of the excitig force at a certai frequecy ad is assumed to be costat. k ad c ca be writte as follows; k = (π f ) m, c = ζ mk = ζ mω = 4πζ mf (5) Here, f, ω ad ζ are the atural frequecy, atural agular frequecy ad dampig ratio, respectively. From equatios (4) ad (5), equatio (6) is derived. (4) x W f Wfg (6) m f m f I equatio (6), ζ is assumed to be costat ad f g which expresses the frequecy rage of the excitatio force is used istead of f. Geerally From the vibratio velocity, V is equal to πf x. Ad the vibratio stress is basically proportioal to the vibratio velocity. Therefore, the followig equatio ca be derived; Wfg s V = π fx (7) m f 4
Here, s is the root mea square of the vibratio stress. The excitatio force is geerally proportioal to the product of the pressure fluctuatio ad excitatio area which would be proportioal to the total fluid mometum r g AV at the ed of the brach just before the combiig poit, here, r g, A ad V are the fluid desity, flow area of brach ad velocity at the brach, respectively. Therefore, r g AV ca be used istead of W f g i equatio (7). The mass of the pipe, m ca be expressed as πr p D t, here, r p, D ad t are the desity of the pipe material, the outside diameter of the mai pipe ad the wall thickess of the mai pipe, respectively. Thus the equatio (8) ca be derived. r AV s = (8) g V prpd tf I equatio (8), a idex, V expresses the magitude of the vibratio velocity which would show the vibratio stress, i.e. the vibratio severity. From this poit of view, the idex V is amed as Vibratio Velocity Number. Where critical flow occurs with soic speed at the ed of the brach pipe just before eterig the mai pipe, there would be a pressure discotiuity at the combiig poit with a rapid expasio of air. This rapid expasio of air would have the effect of icreasig the turbulece eergy at the combiig poit. The turbulece eergy, icludig this rapid expasio effect, could be assumed to be proportioal to the total pressure chage (1/)r g V +Dp at the combiig poit; here, Dp is the pressure discotiuity at the combiig tee for the critical flow coditio. From this assumptio, equatio (8) ca be modified to equatio (9) i case of the critical flow occurrece at the ed of the brach. s r AV + DpA (9) tf g V = prpd RESULTS AND DISCUSSION Figures 7 ad 8 show typical examples of the measured time histories of pressure fluctuatio ad strai respectively. As show i these figures the time history data seem to have radom vibratio characteristics with o periodic vibratio characteristics. Figure 9 shows the probability distributio of the measured strai. Figure 9 shows that the measured probability distributio is almost close to the ormal probability distributio. This is oe of the typical characteristics of radom vibratio [5]. Pressure Fluctuatio [kpa] 15 1 5-5 -1..4 Time [Sec] Figure 7. Time History of Measured Pressure Fluctuatio (TPA4: Upstream Pressure of RO is 8 bara, 4 x1.5 ) Strai [µst] 5-5 -1-15 - -5-3..4 Time [Sec] Figure 8. Time History of Measured Strai (ST: Upstream Pressure of RO is 8 bara, 4 x1.5 ) 5
Probability of Occurrece 15% 1% 5% % -6 ~ -4 - ~ - -18 ~ -16-14 ~ -1-1 ~ -8-6 ~ -4 - ~ ~ 4 6 ~ 8 Figure 9. Probability Distributio of Measured Strai (ST: Upstream Pressure of RO (TP1) is 8 bara, 4 x1.5 ) Figure 1 shows typical examples of PSD of the pressure fluctuatios upstream (TPA1) ad dowstream (TPA4) of the combiig poit. As show i this figure, the pressure fluctuatio dowstream of the tee (TPA4) is cosiderably larger tha that upstream of the tee (TPA1). This meas the most of the large pressure fluctuatio would be geerated by the turbulece just after the combiig poit. PSD of Pressure Fluctuatio [kpa /Hz] 3.5 1.5 1.5 Upstream of Tee coectio (TPA1) Dowstream of Tee coectio (TPA4) 1 3 4 5 Frequecy [Hz] Figure 1. Power Spectrum Desity of Pressure Fluctuatios at Upstream ad Dowstream of Tee (Upstream Pressure of RO (TP1) is 6 bara, 4 x1.5 ) Figures 11 ad 1 show the shapes of the vibratio modes obtaied by measuremet ad aalysis, respectively. I Figure 11 the vibratio strais at the poits from to 4 are assumed to be equal to the measured vibratio strais at the poits from 1 to 1. These figures show that the aalysis agrees well with the measured data, ot oly for the vibratio mode shapes but also vibratio frequecies. Figure 13 shows the overall vibratio stresses obtaied by the measuremet ad aalysis. From this figure the aalytical vibratio stress has good agreemet with the measured oe though the aalytical vibratio stress is a little larger tha that of the measured oe. 6
d mode (4Hz) d mode (375Hz) 3rd mode (117Hz) Figure 11. Vibratio Modes (Measuremet, 4 x1.5 ) (Upstream Pressure of RO (TP1) is 6 bara) 3rd mode (1163Hz) Figure 1. Vibratio Modes (Aalysis, 4 x1.5 ) Vibratio Stress [MPa ] 15 1 5 Numerical Aalysis Experimet 1 3 Upstream Pressure of RO (TP1) [barg] Figure 13. Compariso of Vibratio Stresses betwee Aalysis ad Experimet (4 x1.5 ) Figure 14 shows the relatioship betwee the measured vibratio stress ad vibratio velocity umber, V. I this figure Ab/Am is the brach flow area ratio to the mai pipe, ad the maximum measured strai amog the 1 measurig poits is depicted. The proposed vibratio idex V, Vibratio Velocity Number, is quite effective to evaluate the order of the vibratio stress for wide rage of process coditios icludig the occurrece of critical flow ad a brach area ratio from.11 to 1.. 7
Vibratio Strai (microstrais, ) 1 9 8 7 6 5 4 3 1 4" x 4" Ab/Am=1. 4" x 3" Ab/Am=.6 4" x 1.5" Ab/Am=.17 4" x 3/4" Ab/Am=.47 4" x 1/4" Ab/Am=.11 4 6 8 1 V (m/s) Figure 14. Relatioship betwee Measured Vibratio Stress ad Vibratio Velocity Number (V ) CONCLUSION The FIV (Flow Iduced Vibratio caused by turbulece) at 45 degree combiig tee was ivestigated by measuremet ad aalysis. The results drew the followig coclusios: (1) The turbulece geerated at the combiig poit creates the large pressure fluctuatio ad results i shell mode vibratio i the case of relatively thier wall pipes. () The vibratio has radom characteristics ad CFD/FEA approach with radom vibratio aalysis is effective to evaluate the vibratio pheomea. (3) The proposed vibratio idex called Vibratio Velocity Number, V is quite effective to evaluate the order of the vibratio stress for a wide rage of process coditios icludig the occurrece of critical flow ad a brach area ratio from.11 to 1.. REFERENCES [1] Guidelies for Avoidace of Vibratio Iduced Fatigue Failure i Process Pipework, Eergy Istitute - d Editio, 8 [] H. Izuchi, T. Mabuchi & I. Hayashi, Pipig Itegrity Desig for Flare System o Acoustically Iduced Vibratio ad Flow Iduced Vibratio, th World Petroleum Cogress, 11 [3] M. Nishiguchi, H. Izuchi, I. Hayashi & G. Miorikawa, Flow Iduced Vibratio of Pipig Dowstream of Tee Coectio, FIV1, 1 [4] K. Hirota, Y. Ishitai, T. Nakamura, T. Shiraishi & H. Sago, Flow-Iduced Vibratio of a Large-Diameter Elbow Pipig i High Reyolds Number Rage; Radom Force Measuremet ad Vibratio Aalysis, FIV8, 8 [5] Paul H. Wirschig et al., Radom Vibratios Theory ad Practice, DOVER Books 8