Boru hatlarında akışın yarattığı titreşimler
Flow-induced vibrations in pipelines
Yazar: SUAT CANBAZOĞLU
Danışman: DOÇ.DR. HALUK KARADOĞAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Ana Bilim Dalı
Derece: Doktora, 1989
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Boru hatları = Pipelines ; Titreşim = Vibration

Özet:
ÖZET Petrol, doğal gaz, su v.b. boru hatlarında; akışı kontrol amacıyla kullanılan vanalar ile geometrik nedenlerle konulan genişleme, daralma elemanları, dirsek gibi elemanlar ve debi ölçümü için kullanılan diyafram (ori- fis) v.b. elemanlar akış açısından birer aykırılık (sürek sizlik) yüzeyleridir. Bu elemanlar sınır tabaka ayrılmaları nedeniyle, akışa, sürekli olarak yaklaşık-periyodik bir yapıda vorteksler üretmektedirler. Bu vortekslerin boru sisteminin akustik, mekanik veya termik yapısı ile akuple olması halinde mühendisleri tedirgin eden, ciddî titreşim problemleri ortaya çıkabilmektedir. Bu çalışmada; çalpara tipi çek valf ve sürgülü vana halleri için ortaya çıkabilecek vortekslerin yapısı ve çek valf, sürgülü vana ve diyafram ihtiva eden boru hatlarında akış ile sistemin (boru hattının) akustik yapısının akuple olması sonucu ortaya çıkan titreşimler, kurulan bir boru hattı modeliyle deneysel olarak incelenmiştir. Yapılan deneyler sonucunda vortekslerin kopma frekanslarının boru hattının akustik frekanslarına veya tam katlarına eşit olması hallerinde akış-akustik akuplajının ortaya çıktığı görülmüştür. Ayrıca çek valfin kendi geometrisinin de bir vorteks (titreşim) kaynağı olduğu gözlenmiştir. Kurulan matematik modelle akış-akustik akuplajı gösterilmiş ve debi çalkantıları için tanımlanan amplifikasyon faktörünün küçük vana açılma oranlarında (kısmî debilerde) büyüdüğü ve rezonans halinde debi çalkantıları için tanımlanan faz farkının sıfır olduğu yani titreşimlerin aynı fazda olduğu da belirtilmiştir. Ayrıca matematik model yardımı ile küçük Mach sayılarında ve sıvı akımlarında amplifikasyonun büyüdüğü ifade edilmiştir. Matematik modelde vana bir diyafram olarak modellenmiş ve model sonuçları diyaframlı boru sisteminde yapılan deneylerle uyum sağlamıştır. Yapılan bir boyut analizi sonucunda amplifikasyon faktörünün; Reynolds, Strouhal, Mach sayılarıyla birlikte hızlar oranına, frekanslar oranına, vana açılma oranına ve boru boyunun boru çapma olan oranına bağlı olduğu da gösterilmiştir. Elde edilen akış-akustik akuplajı düşüncesini; boru hatlarının tasarımında proje kontrol hesaplarının bir aşaması olarak, ya da titreşim problemi işletme aşamasında ortaya çıktığında, olayın çözümlenip titreşimlerin zarar sız hale getirilmesinde bir araç olarak kullanmak mümkün dür. VII

Abstract:
SUMMARY FLOW- INDUCED VIBRATIONS IH PIPELINES Control valves, orifices, fitting elements used on pipelines have discontinuity surfaces for flow. These surfaces generate almost-periodic vortices. Vortical structures coupled with acoustics or mechanics of pipe system cause forced vibrations which is called as "Flow- induced vibrations". Because of extra energy losses, vibration, noise and errors on measurements, flow- induced vibrations are not wanted in pipelines. In the present study, flow-acoustic coupling phenomenon in pipelines has been investigated. The mathematical model which shows amplification is developed. When this operation is performed in an unsteady flow, generalised Bernoulli equation, continuity equation, generalised momentum equation and sound equation have been used. In addition, the following hypothesis proposed for velocity fluctuations by YAZICI [30] which agrees with experimental data is employed. ~ ~ ~ ~ x2 V = Vi + (Vi - Vi) (1) L2 where i and j show respectively the pipe inlet and exit cross-sections, x shows the distance of cross-sections from section i and V^ shows the velocity fluctuation at cross-section i. Assuming that the average velocities are small with respect to the sound velocity c and the fluid is more or less incompressible and all energy losses is neglected; the generalised Bernoulli equation, generalised momentum equation and continuity equation are applied between several points, pressure differance (po - p4) is obtained. Sound equation for isentropic state changing of perfect gases is written (p4 = constant). dp d(po - p4) do = = C2 - L_ (2) dt dt dt VIIIwhere p, c, p and t shows respectively pressure, sound propogation velocity in fluid, fluid density and time. Pulsating flow is occured due to vortices induced by flow seperation. For the purpose of modelling, the valve is represented as an orifice. Flow rate varying with respect to time as: Q3 = Q (1 + a3sinwvt) = Q(l+a3sin2n:f vt) (3) is proposed due to periodic structure of vortices induced by vortical structure at cross-section 3. Where as shows relative amplitute of flow rate fluctuation at cross-sec tion 3 and wv shows angular vortex shedding frequency. Assuming that the flow rate fluctuations are very small with respect to the time average value of Q and after the necessary operations are performed d2Q4 dQ.4 4" d2Q.3 dQ3 a^ A4 4B4 4waQ4=A3 +B3 +WaQs (4) dtz dt dt.2 dt is obtained. The right side of this equation is known. This equation is a second order linear differential equation with constant coefficients. A 4 and A3 coefficients depend only on the geometric dimensions of the system, and B4 and Bs coefficients depend both on the geometric parameters and the mean flow rate Q. Since the inlet flow rate to the pipe of length L2 is taken to vary as in equation (3), we may seek a solution to equation (4) as: Q4 = Q [(1 + a4sin(wvt - 0)] (5) Giving wv B3 wv [1 - A3( )2]2+( )2( )2 a4 wa Wa wa Y=(- )2 = _ (6) a3 wv B4 wv [1 - A4( )2]2+( )2( )2 Wa Wa Wa and IXWV WV WV _ Wv [ 1-As ( )2 ]B4 C1-A4 ( ) 2]B3- Wa Wa Wa Wa tan 0 = - : (7) Wv Wv B3 B4 a. [1_A3( )2][1-A4( )2]+- r __- WV Wa Wa Wa Wa is obtained. Where Y shows amplification factor for flow rate fluctuations, wa fundamental angular acoustic frequency of pipeline and 0 phase lag. When equation (6) is examined, it can be seen that amplification factor Y has a maximum value which indicates the resonance phenomenon when the angular frequency of the vortices becomes wv * Wa //IT ( 8 ) Amplification factor Y depends on the system's geometry and its geometric dimensions, the vortex shedding frequency and acoustic frequency, the Mach number and the Strouhal number of flow. Especially, when Mach number decreases, the maximum value of amplification factor Y increases. Amplification factor Y at liquid flows has greater values than at the gas flows. Resonance frequencies calculated by mathematical model have been agreed with results of experiments done for two orifices. Amplification factor found for flow rate fluctuations are increased at small orifice-pipe diameters ratio, in other words vibrations are being more violent in small valve opening ratios. Amplification factor equals to approximately sero at direct atmosphere disharging conditions of jet. Phase lag for relative flow rate fluctuations in resonance has reached to approximately sero. That is, vibrations are occured in same phase at resonance state. Dimensional analysis is done for the defined flow. Found diroensionless numbers are Reynolds, Strouhal and Mach numbers, vortex shedding-acoustic frequencies ratio, velocities ratio, valve opening ratio and pipe length-pipe diameter ratio. In addition, vortex structure of 68 mm 0 (2 1/2") swing check valve and gate valve has been obtained with experiments. Experimental results have been shown almost- periodic structure of vortices. Vibrations according to valve opening ratio and mean flow velocity of vortex shedding frequency have given. For swing check valve andgate valve Re-St relations are presented too, Experimental results have shown that model valve is working as an oscillator due to its own geometric structure of swing check valve. Because of this reason, valve body and seat space must be modified. Acoustic frequencies of pipe system have been obtained by experiments. The natural acoustic frequencies of pipelines can be calculated with teorethical method for three different boundary conditions. Experimental method is more convenient for the complex structures. Flow -acoustic coupling phenomenon has been shown by experiments. All experiments have been carried out with air. Experiments with flow-acoustic coupling have been shown that vibrations are controlled by acoustic of pipe system. Vortices shed at the nearest acoustic frequency. Resonance frequencies have been increased linearly with mean flow velocity. To run experiments on vortex- induced vibrations, the plate of swing valve has held stationary. In practice, natural mechanical frequencies of valve plate must be calculated. Because flow-mechanic structure coupling can be occured. Vortices can be more periodic and more violent when two orifices (or valve) are located in one after another on the pipeline. Because of this reason, in the case of two gate valves following each other (or in the case of two orifices), flow-acoustic coupling phenomenon occurs more stronger. A whistling sound has been heared during the experiments as a result of resonance in model pipeline system. Orifice- induced vortices for same conditions have been appeared by experiments more periodic, stronger and with higher shedding fequencies according to vortices induced by gate valve and swing check valve. When three orifices used in experiments, third orifice has been made a little attenuation effect. Vortex generators, complient boundaries, acoustic silencers and changing of acoustic frequencies can attenuate vibrations which occures as a result of flow- acoustic coupling. For attenuation of such vibrations, the almost-periodic structure of vortices should be disturbed. XIFlow-acoustic coupling phenomenon occurs, when fv = n fa ; n = 1,2,3,... (9) Where fv and fa shows respectively vortex shedding frequency and acoustic frequency in Hs. Because of this reason, the attenuation of vibrations can be made by changing either vortex shedding frequency or natural acoustic frequency of pipeline. Vortices are more periodic (organised) and stronger in low mean flow velocities. Valves must not be operated at small openings to avoid from dangerous vibrations. XII