Hydrodynamic Forces on Partly Buried, Tandem Twin Pipelines in Coexisting Flow

Transcription

1 Journal of Coastal Research SI ICS (Proceedings) Brazil ISSN 79-8 Hydrodynamic Forces on Partly Buried, Tandem Twin Pipelines in Coexisting Flow S. Cokgor and I. Avci Istanbul Technical University, College of Civil Engineering, Division of Hydraulics, 369, Maslak, Istanbul, TURKEY ABSTRACT COKGOR, S. and AVCI, I., 6. Hydrodynamic forces on partly buried, tandem twin pipelines in coexisting flow. SI 39 (Proccendigs of e 8 International Coastal Symposium), Itajaí, SC, Brazil, ISSN This study deals wi e forces under e coexisting flow on e circular cylinder, laid on, or partly buried in e bed wi a parallel twin dummy cylinder nearby and wiout it. Forces were determined by measuring e pressure distribution on e cylinder. Force coefficients were obtained e current-to wave-velocity ratio, a, ; 3; 6; and infinity (current) for coexisting flow. The forces also determined for e various burial-dep-to-e diameter ratio between -.7 values of e cylinder. The dummy cylinder was replaced downstream and upstream of e measurement cylinder. The distance between measurement and dummy cylinders axis to diameter ratio was,.5,. The results were indicated force coefficients reduce relatively by increasing burial dep and second cylinder beside e measurement cylinder also reduces e coefficients according to e single cylinder on e bed except e gap between e cylinders are half of diameter. In is case force coefficients were taken e values close e single cylinder in e flow. ADITIONAL INDEX WORDS: Pressure distribution, inline coefficients, lift coefficient. INTRODUCTION Forces on a cylinder on or near e seabed and exposed steady current, waves and combined flows have been investigated quite extensively because importance of submarine pipelines safety. In e steady current case; BEARMAN and ZDRAVKOVICH (978) determined e pressure distributions around and e cylinder for plane wall (simulate to e bottom) mounted cylinder and near wall cylinder cases. Various auors like KIYA (968), ZDRAVKOVICH (985), JENSEN et al., (99) also defined drag force on e cylinder for wall mounted and near wall for various flow and boundary conditions. These works indicated drag coefficient reduces when e cylinder move close to wall because pressure values decreases at e wake side of e cylinder when e cylinder getting close to bottom. This behavior were presented by pressure distributions in e work of BEARMAN and ZRDAVKOVICH (978). FREDSOE et al. (985) were determined to changing e lift forces when e cylinder closes to wall in steady current experimentally. Their results indicated, mean lift force is not zero when e cylinder close or mounted e wall because of flow around e cylinder is not symmetric in is case also ey observed vortex shedding suppressed when e gap between e cylinder and bottom less en.3 diameter of e cylinder. These studies were signed lift force coefficient increase when e cylinder close to wall and during e wall mounted cylinder case it takes largest value. COKGOR and AVCI () were presented e forces on e twin pipelines wi eir different arrangements also included burial effect of e cylinders. Their results were indicated dummy cylinder reduces e forces on e measurement cylinder and also burial ratio too. In wave alone case; SARPKAYA (976), SARPKAYA (977), SARPKAYA and RAJABI (979) were published first studies about forces on e cylinder near e bed under e oscillatory flow. They were measured drag, inertia and lift coefficients on a cylinder placed at various distances from a wall were measured in ese works. The study of LUNDGREN et al.(976), was contained measurement of pressure distribution around a wall mounted cylinder. Some oer researches like JACOBSEN et al. (98), ALI and NARAYANAN (986), JUSTESEN et al. (987), SUMER et al. (99) among oers have reported measurements regarding e effect of wall on e force coefficients. All ese works reported drag, inertia and lift forces increase when e cylinder close to e wall. The largest force values are determined wall mounted cylinder case. Also ese works indicated mean lift force non-zero when e cylinder close towards to wall. The SUMER et al. (99) also reported to effect of e roughness on e forces, near/mounted cylinder on e bed. The study indicated drag, inertia and lift forces increases wi roughness of e cylinder. COKGOR and AVCI (3) were interested forces on e twin cylinders on/in e seabed wi different ratios for low Keulegean-Carpanter, KC, numbers. Results were signed dummy cylinder causes significant changes e forces on e measurement cylinder. In generally, dummy cylinder reduces e forces on e measurement cylinder except e gap between e cylinders is half diameter. In ese cases, force coefficients were taken e values close to single cylinder case. Burial dep also was investigated at e mentioned work and results indicated force coefficients reduce by increasing burial dep of e cylinder. In coexixting flow case; several auors were interested forces on e cylinder, such as MOE and VERLEY (98), SARPKAYA and STORM (985), JUSTESEN et al., (987), BEARMAN and OBAJASU (989), SUMMER et al., (99). The study of SUMER et al. (99) covers e determination of e forces on a structure such as e cylinder on e wall or at various distances from e wall under e combined flow. Their results showed drag coefficient generally decreases wi e current-to wave-velocity ratio, inertia forces is not very sensitive except low KC numbers and lift forces (for max. value of e lift forces) decreases markedly when e current is superimposed on e wave motion. When e current-to wavevelocity ratio increases force coefficients might be expected to approach its asymptotic value obtained for e steady current case. JACOBSEN et al. (989) have focused on forces on e partly buried pipelines, pipelines in open trenches and pipelines sliding on e seabed under e waves and combined flows. They signed force coefficients decreases wi increasing e burial-dep-to-e diameter ratio. The results of eir measurements were indicated force coefficients reduced gradually when burial-dep-to-e diameter ratio is increased for waves and coexisting flow case. COKGOR and AVCI (998), COKGOR () were investigated effect of e burial dep on e forces under e waves, steady current and combined flow. Results were indicated; increasing of e burial dep reduced e forces on e cylinder but is changing was not determined gradually. and.5 values of e burial dep to diameter

2 78 Cokgor and Avci ratios almost same force coefficient values were signed. The aim of e presented study is experimentally determined, e forces exposing e pipeline laid just on, or partly buried in e seabed for cases of combined waves and various tandem arrangements. EXPERIMENTAL SETUP Experiments were achieved in a water flume wi 6 m leng, m wid and.85 m height wi a smoo bed and plexiglass side walls. Regular waves were generated wi a palette of flap type (Figure.a.). The dummy and measurement cylinders had a diameter of 8.9 cm, wi a leng of m and uniform surface roughness (k) of.5 mm by generated to scraping e PVC pipe using a knife of lae. The cylinders were flush mounted to e base of e water flume. Different burial ratios (e/d) were obtained false bottom by raising e water flume base by steel plates (Figure.b.). Seepage under e cylinder was prevented. Eleven transducers (Endevco Model 85B- wi range of. psi and wi a sensitivity of 5 ± 5 o mv psi at V d.c and C) were flush mounted on e surface o of e measurement cylinder at 3 intervals (except e bottom point of e cylinder);(figure.c). They were also mounted at e same cross section in e measurement cylinder. Nixon Instrumentation Stream Flow Velocity Meter, Type, Model 3 micro propeller was mounted in symmetry axis of e cross section, far enough to e flow was not effected by cylinder(s) for measuring e maximum horizontal value of wave velocity which is based on KC number calculations. For determining e KC Re and current to wave-velocity ratio, velocity was determined at e top level of e cylinder. Two HBM P inductive type pressure transducers were used by wave probe. One of ese transducers was flush mounted on e flume wall at e axis of e cylinder; e oer was replaced at e same cross-section wi e propeller on e sidewall. The signals received from transducers have been regulated wi an ampflicator and ey were transmitted to e computer in e form of analog signals wi e help ofad card and are saved in e computer TEST CONDITIONS The experiments cover e determination of e forces on e cylinder in e case of different boundary conditions (wall mounted and partly buried cylinder and various twin, tandem cylinder arrangements) and coexisting flow condition. Dummy cylinder replaced upstream and downstream of e measurement wi D,.5 D, D distances between cylinders axis. Here D referred to diameter of e cylinders. The forces on e cylinder is a function of e Re number due to e steady flow condition at is given by; U c D Re () Where D, v and Uc are diameter of e cylinder, kinematic viscosity of fluid and e maximum measured flow velocity at e top level of e cylinder respectively. During e wave alone case, Re number is defined on e basis of reference velocity, U w, e maximum value of e orbital velocity at e top level of e cylinder. In is case, e variation of e forces depend not only on Re, but also e Keulegan Carpenter number, KC, is defined by, U wt KC () D where U w, T are e maximum horizontal wave velocity at e top of e cylinder level and e wave period, respectively. When e steady current and wave combined in e flow, e reference velocity component U m, in e KC and Re numbers is considered as "U C+U w". In combined flow condition, e current-velocity-to-wave-velocity ratio ( ) is e key parameter regarded to Re, KC. is given by, U c (3) U w The text matrix is given for experiments in Table. Figure. Experimental setup.

3 Hydrodynamic Forces 785 Table. Test Conditions. Re KC Cylinder k/d e/d Configuration 3 Single - x, 3, and 5 3 X/D = +, +.5, + 55x. 3 -, -.5 and EXPERIMENTAL RESULTS AND DISCUSSIONS Pressure Distributions The distribution of e measured pressure values on e cylinder, which is unburied (e/d = ), and semi buried (e/d =.5) position, exposed to coexisting flow, was presented in Fig.. for evolve during e course of one flow cycle where KC =, value of e parameter a = 3 and Re = x. The pressure values in e Figure, were presented at dimensionless manner wi a pressure coefficient. Here, pressure coefficient is defined as. p p c p () ( U c U w ) Where p, p, and (u c +u w) are e time average measured pressure, e hydrostatic pressure, e density of e fluid and e steady flow velocity at e top level of e cylinder respectively. From e mentioned figure, pressure distribution around a cylinder was almost uniform in e half period 8 36 an in e previous half period (wave crest) 8 for unburied position (Figure. A). Also magnitude of e pressure at e cylinder experiences in at period 8 36 is significantly reduced wi respect an e previous (wave crest) period. Same behavior at e pressure distributions around e cylinder also occur for e/d =.5 case. But at e second cycle of e wave, pressures are taken negative values on e wake side of e cylinder because steady current is dominant. Hydrodynamic Forces The force components, e in line and lift forces are determined by e integration of e measured pressures on e surface of e cylinder. The lift force (F y), is obtained by; F ( ) DU y t CL m( t) (5) Here, lift coefficient C L, is obtained by e help of determining Fy by e measured force. In e following chapter of e article, lift force coefficient obtained by maximum measured lift force value so at lift force coefficient named by C Lmax. The force acting on e cylinder in e flow direction under e wave condition case can be determined by MORISON et al. (95) equation. Morison equation is as follows; Fx ( t) CDU ( t) U ( t) CM AU ( t) Here, CM is e inertia force coefficient. CD and CM can be determined wi e least squares meod between measured and predicted forces (for details of e meod see SUMER and FREDSOE 997). In e presented study mean values are focused by mentioned inline coefficients in coexisting flow condition. Inline Force Coefficients For Single Cylinder In line coefficient CD calculated from Eq. 6 was presented in Fig. 3 as a function of KC numbers for various burial ratios of single cylinder by Re = x and current to wave velocity ratio, a =3. Drag force coefficient CD gets to increase wi increasing KC for each burial condition. When e cylinder begins to bury in e bed, CD values decrease. The significant changing observed from e/d =. to e/d =.5 because of e geometric condition of e cylinder in e flow. The stagnation point, which is characterized by e maximum positive value of pressure, moves towards to top of e cylinder and is reduce in line direction force. The least C values were determined for D (6) Figure.Pressure distributions around e flush mounted (e/d=) and semi buried (e/d=.5) cylinder for coexisting flow case ( =3, KC=5, Re=x ).

4 786 Cokgor and Avci C D.8.6. e/d= e/d =. e/d =.5 e/d =.7.6 C Lmax e/d= e/d =. e/d =.5 e/d = KC Figure 3. Variation of e drag force coefficient wi KC at single cylinder case for different burial ratios. e/d=.7 positions for single cylinder (Figure 3). The CD values increase towards to steady current case by increasing KC at given in e literature by ZDRAVKOVICH 985), KALGATHI and SAYER (997), COKGOR and AVCI (998) and () as.85. The variation of inertia coefficient, C M, for single cylinder wi KC number is given in Figure. for unburied and different burial ratios of cylinder. CM rapidly decreases wi KC at all e/d ratios because flow conditions close to steady current case. CM values also decrease wi increasing e/d values almost linearly (Figure.and 7). When e cylinder gets to bury into e bottom (e/d increase), structural geometry is getting suitable for stream lines as a result of it added mass getting reduces around e cylinder, it causes to reducing inertia forces on e cylinder. The smallest CM values are determined for e/d =.7 case. Lift Force Coefficients for Single Cylinder Variation of e lift force coefficients, CL, wi KC is given in e Figure 5 for single cylinder case for different e/d ratios. In e figure, CL is given regarding maximum lift force at observed on e cylinder. C L, decrease by increasing KC number and also decreases regularly wi increasing cylinder burial dep (e/d). Inline Force Coefficients for Tandem, Twin Cylinders The inline forces on e cylinder is effected by dummy cylinder at replaced near e measurement cylinder. The variations of e CD wi e burial ratio for KC for e various dummy cylinder (x/d =,.5,, -.5 and, -) around e measurement cylinder are presented in Figure 6 (for KC =, Re = x and a = 3). Single cylinder data is also plotted in is KC Figure 5. Variation of e maximum lift force coefficient wi KC at single cylinder case for different burial ratios. figure for comparison. CD values drop dramatically en after e/d =. and after at, CD values reduced linearly for all twin cylinder arrangement such as single cylinder. For various twin pipeline arrangements, CD values are always smaller an e single cylinder case. During e twin pipeline positions, e larger CD values are determined at x/d = + and +.5 ratios. In ese configurations negative pressure zone at e wake side of e cylinder does not significantly effect from dummy cylinder. When e measurement cylinder takes e place behind e dummy cylinder, positive pressures around e stagnation point greatly reduce at cause to reducing e CD values and ese configuration measurement cylinder hide from flow effect behind e dummy cylinder. The smallest CD values observed when e cylinders to be tangent position to each oer. During ese configurations, dummy cylinder prevents positive pressures (x/d = ) or negative pressures disappear at e wake side of e measurement cylinder (x/d = ). When e cylinders replaced tangent each oer is body has more suitable wi streamlines an e oer x/d ratios so at CD values dropped in at cases (Figure 6). From e Figure 7, CM values almost linearly decrease wi decreasing e/d at all tandem twin cylinder configurations like single cylinder case. CM takes smaller values in all tandem arrangement cases an single cylinder case such as oer inline coefficient C D. When e measurement cylinder replace at upstream of dummy cylinder (positive x/d values), CM is taken greater values an e negative x/d values except e tangent position (x/d = +). When e measurement cylinder takes a place behind e dummy cylinder added mass around it added mass significantly reduces. For x/d = +.5 case water column between two cylinder increase added mass so at Cm values take larger values even an e single cylinder case (Figure 7). C M.5.5 e/d= e/d =. e/d =.5 e/d =.7 C D Single x/d=+ x/d = -.5 x/d=+ x/d=- x/d = -.5 x/d= KC Figure. Variation of e inertia force coefficient wi KC at single cylinder case for different burial ratios e/d Figure 6. Drag force coefficient as a function of e/d (Re=x, KC=, =3).

5 Hydrodynamic Forces 787 CM Figure 7. Inertia force coefficient as a function of e/d (Re=x, KC=, =3). Lift Force Coefficient for Tandem Twin Cylinders The variation of lift force coefficients wi burial ratios (e/d) is given in Figure 8 for various tandem arrangements. All lift coefficient values for tandem-twin cylinder arrangements are smaller an single cylinder case for each e/d ratios. Positive x/d ratios lager CL values observed because negative pressures at supplied major contribution to lift force always greater in ose cases. When e measurement cylinder hides behind e dummy cylinder, flow does not penetrate on it so at negative pressure zone reduces relatively to positive x/d ratios. The largest values determined at x/d = + position and close to single cylinder. CONCLUSIONS In single cylinder case, e drag force coefficient CD decreases wi increasing KC and e/d ratios and close to steady current values wi increasing KC. CM values suddenly decrease wi increasing and close to zero like steady current case. Lift force coefficients decrease wi increasing KC and e/d almost linearly. In twin cylinder case, CDvalues reduce to be parallel to single cylinder case wi increasing e/d after e plateau between and.. Positive values of x/d ratios greater C D's determine an e negative except tangent position. In tangent configurations drag force coefficients takes smaller values an oers for bo tangent positions. (x/d = + and ). CM values for twin cylinders reduce almost linearly wi increasing e/d for each arrangement. When e measurement cylinder replace incoming wave side (positive x/d values) CM values have greater an oers except tangent positions, x/d = +.5 and + values Cm values almost idendical wi single cylinder. Variation of CL wi KC is almost linear at e range of e experiments for all e/d ratios. Lift force coefficients for each period of wave reduce wi increasing e/d like single cylinder. CL changed all x/d ratios parallel to single cylinder case wi e/d. The smallest values determined for tangent arrangements for each coefficient. Positive x/d ratios except tangent case (x/d = + and +.5) lift force coefficient takes greater values. LITERATURE CITED Single x/d=+ x/d = -.5 x/d=+ x/d=- x/d=-.5 x/d= e/d ALI, N. ;NARAYANAN, R., 986. Forces on cylinders oscillating near a plane boundary. In Proc. 5 Intl. Offshore Mechanics & Arctic Engineering (OMAE) Symp., Tokyo, Japan, 3, BEARMAN, PW. ; ZDRAVKOVICH, M.M., 978. Flow around a circular cylinder near a plane boundary. J. Fluid Mech., l 89,, COKGOR, S. ; AVCI I., 998. Hydrodynamic forces on partly CD Single x/d=+ x/d=+.5 x/d=+ x/d=- x/d=-.5 x/d= e/d Figure 8. Maximum value of e lift force coefficient as a function of e/d (Re=x, KC=, á=3) buried pipelines in waves/current. International Offshore and Polar Engineering Conference, ISOPE'98,, Montreal, Canada. COKGOR, S. ; AVCI, I.,. Hydrodynamic forces on partly buried tandem, twin pipelines in current. Ocean Eng., 8, COKGOR, S.,. Hydrodynamic forces on partly buried cylinder exposed to combined waves and current. Ocean Eng., 9, COKGOR, S. and AVCI, I., 3. Forces on partly buried, tandem twin cylinders in waves at low Keulegan-Carpenter numbers. Ocean Eng., 3, FREDSFE, J. ; SUMER, B.M. ; ANDERSEN, J. and HENSEN, E.A., 985. Transverse vibrations of a cylinder very close to a plane wall, OMAE Dallas, Texas, JACOBSEN, V. ; BRYNDUM, M.B. and FREDSFE, J., 98. Determination of flow kinematics close to marine pipelines and eir use in stability calculations. Proc. 6. Annual Offshore Technology Conf. Paper OTC, 833, 3, 8-9. JACOBSEN, V. ; BRYNDUM, M.B. and BONDE C., 989. Fluid loads on pipelines: sheltered or sliding. Proc..st Annual Offshore Technology Conf., Paper OTC, 656, 3, JENSEN, B.L. ; SUMER, B.M. ; JENSEN, H.R. and FREDSFE, J., 99. Flow around and forces on a pipeline near a scoured bed in steady current. Trans. of e ASME, Journal of Offshore Mech. and Arctic Eng.,, 6-3. JUSTESEN, P. ; HANSEN, E.A. ; FREDSFE, J. ; BRYNDUM, M.B. and JACOBSEN, V.,987. "Forces on and Flow Around Near-Bed Pipelines in Waves and Current", Proc. 6 Int. Offshore Mechanics and Arctic Engrg. Symp., ASME, Houston, TX,, KALGHATGI, S.G. and SAYER, P.G., 997. Hydrodynamic forces on piggyback pipeline configurations. J. of Waterway, Port, Coastal, and Ocean Eng., ASCE, 3,, 6-. KIYA, M., 968. Study on e turbulent shear flow past a circular cylinder. Bulletin Faculty of Eng., Hokkaido University, 5, -. LUNDGUREN, H. ; MATHISEN, B. and GRAVSEN, H. (976). st Wave Loads on Pipelines on e Seafloor. Proc. International Conference on e Behavior of offshore Structures, BOSS 76,, MOE, G. and VERLEY, R.L.P., 98. Hydrodynamic damping of offshore structures in waves and current. Annual Offshore Technology Conference, Paper No OTC 3798, Houston, TX, May 5-8, 98. MORISON, J.R. ; O'BRIEN, M.P. ; JHONSON, J.W. and SCHAAF, S.A., 95. The forces exerted by surface wave on piles. J. of Petrol. Technology, Petroleum Transactions, AIME (American Inst. Mining Engrs.), 89, 9-5 SARPKAYA, T., 976. "In-line And Transverse Forces on Smoo and Sand-Roughened Cylinders in Oscillatory Flow at High Reynolds Numbers", Naval Postgraduate School, Monterey, CA, Tech. Rep. NPS-69SL766.

6 788 Cokgor and Avci SARPKAYA, T., 977. In-line and Transverse Forces on Cylinders Near a Wall in Oscillatory Flow at High Reynolds Numbers, Proc. 9 Annual Offshore Technology Conference, Houston, TX, Paper OTC 898, 3, SARPKAYA, T. and RAJABI, F. (979) Hydrodynamic Drag on Bottom Mounted Smoo and Rough Cylinders in Periodic Flow. Proc. Annual Offshore Technology Conference, Houston, TX, Paper OTC 376,, 9-6. SARPKAYA, T. and STORM, M., 985. In line force on a cylinder translating in oscillatory flow. Applied Ocean Research, 7,, SUMER, B.M. ; JENSEN, B.L. and FREDSFE, J. (99). "Effect of a Plane Boundary on Oscillatory Flow Around a Circular Cylinder", J. Fluid Mech., 5, 7-3. SUMER, B.M. ; JENSEN, B.L. and FREDSFE, J., 99. Pressure measurement around a pipeline exposed to combined waves and current. OMAE, Calgary. ZDRAVKOVICH, M.M., 985. Forces on a circular cylinder near a plane wall. Applied Ocean Research, 7, 97-.