Akıntılı Deniz Ortamında Tabana Oturan Silindirlere Etkiyen Kuvvetler

Abstract

Akım ortamında yeralan cisimler, akım ile etkileşimleri sonucu hidrodinamik kuvvetlerin etkisinde kalırlar. Günümüzde yaygın olarak kullanılan petrol, doğalgaz veya su iletimi, atıksu deşarjı, ulaşım amaçlı büyük nehir veya denizaltı tüp (körfez boğaz) geçişi gibi değişik amaçlarla deniz veya nehir altında inşa edilen yapılar da bu tip kuvvetlerden etkilenmektedir. Bu çalışmanın ilk bölümünde, deniz ortamında görülebilecek kararlı akım, salt dalga ve akıntı ile dalganın birlikte oluşması durumlarında bir yapı etrafındaki akım alanı ve akımın yapı üzerindeki etkisi ile, yapıya gelen kuvvetlerle ilgili literatür çalışması yapılmıştır. Literatür çalşmasına, olayın mekaniğinin açıklanması açısından, çok sayıda araştırıcı tarafından detaylı olarak incelenen sonsuz kararlı akım veya salınımlı akım ortamında yeralan tek bir silindir etrafındaki akım alanı ve bu silindire etkiyen kuvvetler incelenerek başlanmıştır. Bu konudaki çalışmalar, incelenecek konuya yakın katı cidar yakınındaki silindir etrafındaki akım alanı ve silindire etkiyen kuvvetlerin belirlenmesine ait sınırlı sayıda çalışma ile birleştirilmiştir. Çalışmanın ikinci bölümünde, deniz tabanına oturan bir silindire etkiyen kuvvetlerin belirlenmesi amacıyla İ.T.Ü. İnşaat Fakültesi Hidrolik Laboratuvannda oluşturulan deney düzeneği, ölçme ve değerlendirme sistemi açıklanmıştır. Hazırlanan deney sisteminden yararlanarak, deniz tabanına oturan ve "kararlı akım", "düzenli dalga" ve "akım+dalga" etkileri altında bulunan bir silindir üzerindeki basınç değerleri ölçülmüş ve basınç dağılımları belirlenmiştir. Tek silindirin tabana oturması veya değişik gömülme oranlan ile, çift silindir olma durumları için ayrı ayrı belirlenen bu basınç dağılımları kullanılarak silindire gelen kuvvetler hesaplanmıştır. Silindire etkiyen bu kuvvetler CD,CM ve CL kuvvet katsayıları ile ifade edilmiş ve bu kuvvet katsayılarının olay üzerinde etkili olan Re ve KC sayıları gibi boyutsuz sayılarla değişimi grafikler halinde gösterilmiştir. Tabana oturan tek silindire ait değişik akım koşullarında elde edilen sonuçlar, literatür çalışmasında verilen diğer araştırmacıların benzer koşullarda elde ettikleri sonuçlarla karşılaştırılmıştır. Çalışmanın son kısmında, elde edilen deneysel sonuçlar değerlendirilmiş, çalışmanın sağlayacağı yararlar ve bilgi birikimi tartışılmış ve çalışmanın gelişmesi için gelecekte yapılması gereken konularda önerilerde bulunulmuştur.

The effect of close proximity of a wall on the flow around a cylinder has been the subject of several investigations in recent decades. Various authors have developed theoretical models of potential flows around a cylinder, such as MILNE and THOMSON, (1962) for a cylinder on a plane boundary, and YAMOMOTO et al. (1974) for a cylinder close to a plane wall. FREDSOE and HANSEN (1987) gave modified description of the potential flow in which the lift force on the cylinder was evaluated. Various authors, reported qualitative and quantitative observations of the flow around a circular cylinder placed near a wall where the cylinder was towed at constant velocity in stili fluid. BEARMAN and ZDRAVKOVICH (1978) measured pressure distribution around a circular cylinder on and near a wall and also along the wall in steady currents. They also conducted a spectral analysis of hot-wire signals received from both sides of the cylinder wake. From their spectral analysis, they found out that regular vortex shedding persisted for cylinder on the bottom. This result was later confirmed by the measurement of GRASS et al. (1984). The case where the cylinder is subjected to an oscillatory flow has also attracted much attention, in view of its application to marine pipelines exposed to waves. The first investigation was the research work of SARPKAYA (1976). Drag, inertia and lift coefficients on the cylinder placed at wall were the measured studies. Recently JACOBSEN et al (1987), JUSTESEN et al. (1987) and SÜMER et al. (1991) have reported measurements regarding the efiect of the wall on force coefficients on a cylinder exposed to oscillatory flow. The studies of SARPKAYA and STORM (1985) and SÜMER et al. (1992) are related to the determination of the forces on a cylinder, if both the wave and current exist. in both studies, the coexisting flow is obtained with the sinusoidally oscillating motion of the cylinder. in these studies, the forces on a cylinder are determined by obtaining the pressure distribution with the pressure transducers placed on the cylinder. On the other hand, the study of SÜMER et al. (1992), covers the determination of the forces on a structure such as the cylinder on the wall ör at various distances from the wall. in this study, the forces on a cylinder, laid just on the ground are determined by measuring the pressure distribution on the cylinder in the case of steady current, püre wave and both together. The bottom of the cyünder is buried at different burying ratios with a dummy cyünder nearby and without it. in these two cases the variations of the forces on the cylinder are measured. Esperimental Set-up Experiments were reaüzed in a water flume; having 26 m. length, l m. width and 0.85 m height. The closed water circuit system was used for the case of steady current. Regular wave produced with a palette of flop type was connected to the direct current (DC) motor. The experiment cylhıder, where pressure measurements were reaüzed, and the dummy cyünder have a diameter of 8.9 cm, with a length of l m and a surface roughness (k) of 0.5 mm. The measurement cyünder was fixed to the base of the water flume. in the water flume, different bury ratios (e/D) were obtained by raising the water flume base by steel plates. Eleven transducers (Endevco Model 8510B-2 with range of 0.2 psi and with a sensitivity of 150±50 mV psi at 10 V d.c and 24 °C) vvere mounted on the surface of the cyünder at 30° intervals (except the bottom point of the cyünder); (Fiğ. 1). They were mounted at the same cross section. in the water flume, "Nkon Instrumentation Stream Flow Velocity Meter, Type 400, Model 403" muüne was mounted in the cross section, where the flow was not under the effect of the cyünder, to determine the wave characteristics and two HBM Pil transducers were mounted in the same section to determine the wave characteristics on the cylinder axis. The signals received from transducers have been regulated with an ampflicator and they were transmitted to the computer in the form of analog signals with the help of AD card and are saved in the ASCII format with the EASYEST LX data acquisition program. The distribution of the measured pressure values on the cylinder, exposed to steady flow, were presented in Fiğ 2. for different bury ratios of the cyünder. The pressure values in the Fiğ 2. have been made dimensionless with a pressure coefficient. The pressure coeffıcient is defined as C, = f*- (!) jPUj Where p, po, p and Uç are the measured pressure value, the hydrostatic pressure, the density of the fluid and the steady flow velocity at the top level of the cyünder respectively. AMPLIFIER A/I) CON. (DAS 1601) DATA ACQ. SYS. AND ANALYZER HARDWARE SOFTWARE (EASYEST LX) GRAPHICS PRINTER Figure 1. Measurement and evaluation system XX11 Re = 8949 Uc = 9-94 cm^ Flow direction //£&/ CP Re = 6244 Uc = 9.32 cm/s Flow direction wvava "K^c Re = 4725 U = 10.5 cm/s c Flow direction \^f/w\ e/D=0.48 Figure 2. Pressure distribution around a cylinder; buried and unburied position The force components affecting on the in line and lift directions are determined by the integration of the measured pressures on the cylinder surface. For a wall mounted cylinder under the wave, the variation of the forces on the in line and lift directions with the angular frequency are presented in Figure 3. Test Conditions The study covers the determination of the forces on the cylinder in the case of different boundary conditions (wall mounted, partly buried and parallel twin cylinders) and for different flow conditions (steady flow, coexisting flow and wave). The forces on the cylinder change with the Reynolds number for the steady current. Re number is defined as follows: Re UCD (2) XX111 In the above equation, Uc, D and v represent the flow velocity at the top level of the cylinder, the diameter of the cylinder and the kinematic viscosity respectively. In the experiment conditions, where wave effect is investigated, Re number is determined by considering the maximum horizontal velocity (Um), which is due to the wave effect at the same level. In the flow condition, "Uc+Um" is considered as the velocity component for the case of coexisting flow. In the case of wave, the variation of the forces does not depend only on the Re number but also on the Keulegan Carpenter number. KC is defined as KC=UmT/D where T is the wave period. For coexisting flow condition, the velocity component in the equation is considered as "Uc+Um". In the coexisting flow, also dimensionless Uc/Um value has to be taken into account together with Re and KC numbers. In this study, the forces on the cylinder are determined in the case of the different bury positions for one cylinder and parallel twin cylinders. (x/D) and their variations with Re, KC and Uc/Um are investigated. Different cylinder configurations, considered in the experiment are presented in Fig. 3. a. Single Cylinder b. Twin Cylinders Figure 3. Definition sketch of test conditions In the steady current case, the force on the cylinder in the flow direction can be defined as: Fs=|pCDDU* (3) The drag coefficient, (Cd), can be determined from Eq. 3. since the Fx force is obtained from the measured pressure values. The lift force (Fy), which is in the vertical direction with respect to flow, is obtained by; 1 F=-pCLDU2 (4) Here, O, is obtained by the help of determining Fy by the measured force. XXIV The acting force on the cylinder in the flow direction under the wave condition can be determined by MORRISON et al (1950) equation. MORRISON equation is as follows; Fx = Ip CD U(t)|U(t)| + p CM A U(t) (5) In the Eq. 5. Cm is the inertia force coefficient. Co and Cm can be determined with the least squares method. The lift force on the cylinder under wave condition is obtained by Eq. 4. In the coexisting flow condition, the hydrodynamic forces are found using Eq. 4. and Eq. 5. As an example for the variation of the force coefficients with the flow conditions and their variation with KC for a wall mounted cylinder is presented in Fig. 4. Water displacement Fx: In line force Figure 4. Sample records of drag and lift force under the wave condition (KC = 4) Results In line force coefficients Steady current case: In line coefficient Cd was determined from Eq. 2. The results of the experiments show that Cd values change between 0.6~0.9. These Cd values are very close to the result of (ZDRAVKO VICH 1985);(KALGATHI and SAYER 1987) under the same flow conditions. When the cylinder, begins to bury in the base, Cd values decrease. The least Cd values were determined for e/D=0.48 positions for single cylinder. Generally, Cd values decrease when the parallel dummy cylinder is replaced near the measurement cylinder. For +1.5 and +2 x/D values the larger Cd values were determined than the other x/D ratios. Cd values are small when the x/D ratio is negative. XXV Wave alone: In line force coefficient Cd and CM were determined from Eq. 5. by using least square method. The Cd values which are determined from the experiments are very similar to experiment results of YAMOMOTO 1974, SARPKAYA and STORM 1989. When the cylinder starts to bury, Cd values decrease. Generally, in parallel twin cylinder position Cd values are smaller than the single cylinder case. For positive x/D ratios (especially +1.5 and +2) Cd values are bigger than the negative x/D ratios. When the cylinders are tangent to each other (x/D=+l and -1 positions) Cd takes the smallest values. Generally, when the KC number increases, Cd values decrease. The other in line coefficient Cm also can be determined from Eq. 5. with least square method. CM values decrease with increasing burying ratios e/D like the Co values. The twin cylinder condition for the negative x/D ratios, Cm values are larger than the positive values and also single cylinder case. Also, a decrease in Cd values is seen for the positive values of x/D. The reason of this is the addition of hydrodynamic mass of the dummy cylinder which is placed at inlet, on the hydrodynamic mass of the measurement cylinder. Since the dummy cylinder is placed in the hydrodynamic mass of the measurement cylinder, it diminishes the hydrodynamic mass of the measurement cylinder. The largest Cm values were determined for -1.5 and -2 values of x/D. Generally, for all boundary conditions, CM values decrease with increasing KC numbers. Coexisting flow case: In line force coefficients were determined for approximately Uc/Um=5 and two different Re numbers. Drag force coefficient Co takes small values at the large Re number. As a result of the movement of the separation point towards the wake with increasing Re numbers, the negative pressures behind the cylinder decrease and at large Re numbers Co also decrease. Cd values decrease with the increasing cylinder bury ratio. Twin cylinder conditions; sometimes larger values can occur at +1.5 and 2 x/D values compared to single cylinder position. For all other twin cylinder positions Cd values generally are small than single cylinder Cd's under same flow conditions. The other in line coefficient Cm decrease with the increasing e/D values for the single cylinder position. Inertia coefficient Cm takes larger values for negative x/D ratios with respect to positive values. The reason of this is similar to the steady current case. Lift force coefficient Steady current case: Lift force coefficient Cl can be determined by Eq. 4. An increase was seen in the values of Cl with the increase of bury ratios for the single cylinder case. The reason of this can be seen from Fig.2. In Fig. 2. it can also be seen that with the burying of cylinder to the base, negative pressure values under the horizontal axis which is in the opposite direction to the lift force, diminish. Pressure values opposite to the lift force are also small in e/D=0.48 case. Hence, the increase in Cl is high for e/D=0.48. The Cl in case of twin cylinders is generally smaller than the single cylinder case. Also, higher CL values were seen from time to time for x/D=+1.5 XXVI value. For x/D=-2 and +2 values and in some current conditions, similar Cl values were obtained like the single cylinder results. Wave alone: Cl values under the wave effect increase with burying the cylinder to the base like the single cylinder case under steady flow condition. In twin cylinder case, an increase has been seen for positive x/D values but also a decrease has been observed for negative x/D values compared to the single cylinder results. Similar single cylinder Cl values have been obtained in some flow conditions. With x/D=+2 and -2 values. This shows that the measuring cylinder has not been affected from the dummy cylinder. Generally, CL values for x/D=+1.5 value are higher compared to single cylinder results. Coexisting flow: The variation of Cl for the single cylinder settled on the base case is like the steady flow and wave alone case. Cl values increase with the increase of bury ratios. In examining Cl values with two different Re number flow conditions, small Cl values were observed in high KC numbers. When the variation of Cl is examined in twin cylinder case, generally there is an increase for positive x/D values compared to single cylinder results. Higher Cl values than the single cylinder case were obtained from time to time at x/D=+l.5.