Abstract The stability pipeline structures are very important for offshore engineering to transfer power energy through remote area.
Thus, long pipelines or cables are one of the most popular to construct. In order to ensure that pipelines are stability on seabed, these pipelines depend on the hydrodynamic forces acting on pipeline against self-weight and line tension. This study aims to use computational fluid dynamics (CFD) to examine the oscillatory wave flow involved hydrodynamic forces on pipeline located on fixed solid boundary. In addition, the focus is relatively on small diameter of cylinders and high Keulegan-Carpenter flows. Moreover, in case of unsteady oscillatory flow, the time dependent of turbulent or laminar are role important in boundary layer.Furthermore, the ANSYS Fluent software package will be provided for user to be familiar and studying. The numerical simulations will be compared with experimental data from the Aberdeen Oscillatory flow Tunnel (AOFT) and also develop the numerical model to investigate the oscillatory flow induced forces on cylinder located on fixed bed.
Contents PageAbstract 11) Introduction 3 1.1 ) Technical Background 4-51.2 ) The wall proximity effect to seabed 5-61.3 ) The condition of hydrodynamic forces with wave boundary layer 61.4 ) Hydrodynamic forces acting on fixed cylinders on seabed 71.5 ) Forces on a cylinder in oscillatory flow 71.5.1) In line force in oscillatory flow 7-91.
5.2) The vertical line force in oscillatory flow 91.5.3) Recommended calculations for industry (DNV-RP-F109) 9 2) Literature review 102.1 ) Validation of force coefficients on cylinder 102.2 ) Numerical Simulations 112.2.1) Hydrodynamic forces and oscillatory flow 11-122.
3 ) The relation of gap flow in oscillatory flow and steady current 13-14 conditions 2.4 ) Oscillatory flow interaction in close wall proximity 15-16 3) Experimental Analysis 173.1 ) Numerical Simulation 17 4) Conclusion 185) Appendices 196) References 20 Chapter 1IntroductionSubmarine pipelines are essential mainstream of fluid and power transportation due to highly demand using of human increasing. The subsea pipelines and cables are used to transport products from one location to another, however these pipelines and cables are often construction onto the seabed without protection. In order to make stability of pipelines, hydrodynamic forces are important roles and are induced to consider by waves and currents.
Sarpkaya and Rajabi who are among first studies to measure lift, drag and inertia coefficients acting on cylinder placed at varied distance on the bottom of seabed in oscillatory flow. These force coefficients are involved in the function of Reynolds number (Re), Keulegan-Carpenter (KC), the thickness of boundary layer and the gap to diameter ratio. In deep water, the wave motion has a small effect to pipeline and the pipelines are strongly affected by the steady current. In shallow water, on the other hand, the wave-induced oscillatory motion has more heavily affected. The purpose of this study is to investigate the stability of pipelines in seabed by using the basic of Computational Fluid Dynamics (CFD) and familiarization with the ANSYS in order to analyze and simulate the oscillatory flow interaction around a cylinder on solid boundary. The other aim is focus on high Keulegan-Carpenter flows such relatively small diameter cylinders.
In additional, the numerical simulations will be involved to compare validated against force measurements that were very recently obtained in the Aberdeen Oscillatory Flow Tunnel (AOFT) as part of an ongoing research project. Background Theory1.1) Technical Background When the pipeline is resting on the seabed, the basic analysis form to consider about the stability design is shown below in the Figure 1.
The sketches illustrate the pipeline under seabed with the symbols direction to make cylinder stability. The hydrodynamic force components are defined as and where array in the horizontal and vertical directions respectively, is defined as the friction coefficient, is the submerged weight of the pipe and D is the diameter of the cylinder. The assured stability of pipeline resting on the seabed intended by purpose need to have1) The horizontal seabed resistance for pipeline on the lateral movement to pipeline on the seabed is always greater than the horizontal hydrodynamic force on the pipeline.2) The submerged weight must be higher than the lift force on pipeline.The main focus on the wave boundary layer effect is to consider only lateral stability of the pipeline. Thus, the absolute stability equation, recommended by DNV-RP-F109, can be written as As Morison’s equations illustrate that the lift and drag force are proportional to the square of fluid velocity particle and the inertia force is directly proportional to fluid acceleration particle.
The lift force performs vertically upwards from the cylinder on seabed, whilst the drag force acts in the same way of fluid flow. The inertia force can act in the direction of flow or against flow depending on the flow in that situation is accelerating or decelerating.Chapter 2 Literature review2.1) Validation of force coefficients on cylinderThe force coefficients such as the drag force, inertia force and lift force depend mainly on KC number and Reynolds number. Most of experiments cases consider a gap ratio of a cylinder proportional to the bed in the range of 0 e/D.
From the Figure 3 represents regular and irregular wave actions which e/D = 0.25 in order to compare the rage of the gap ratio (e/D) with other published in literature. As we can see from Figure 3 that drag force ( and lift force decrease with an increase of KC number, however inertia force increases with an increase of KC number. In case of literature of Sarpkaya (1976) conducted a U-shaped tunnel to examine the effect of force coefficients and of a cylinder with regular oscillatory flow for e/D = 0.22 with the range of KC number from 1 to 34 and the range of Reynolds number from to . In addition, Bryndum et al.
(1992) presents the experimental results for force coefficients and of a cylinder for e/D = 0 with KC number ranging from 3 to 160 and Reynolds number ranging from to . The comparison of Figure 3 can be indicated that the results of e/D = 0.25 are better agreement with those gap ratio e/D = 0.
22 of Sarpkaya (1976) than those gap ratio e/D = 0 of Bryndum et al. (1992). This might be implied that for e/D = 0.
25 is reasonable and reliable, however in our case will focus on very close proximity to the bed (e/D ?0) 2.2) Numerical Simulations2.2.1) Hydrodynamic Forces and Oscillatory flow This part is about the hydrodynamic forces acting on cylinder near bed and also oscillatory flow induced vortices wave around cylinder . simulated the experimental set up the oscillatory flow around the cylinder with the diameter, the gapto diameter ratio, the Keulegan-Carpenter number and pipe Reynolds number are 9 cm, 0.4, 20 and respectively.
The pressure around a cylinder is measured immediately with oscillatory motion in water to consider the time variation of lift force acting on the cylinder. As the Figure 4 below shows about the vorticity contours with six instants in a half period of oscillatory motion. The clockwise and anti-clockwise of vortice rotating are defined as negative (dash lines) and positve (solid lines) respectively.To begin with this periodmotion, a positive vortex was evoked over the cylinder in previous period (Figure4 a,b). The mean flow of two negative vortices in left side of pipe move towardto cylinder (Figure 4 a,b). When the flow velocity increases, the cylinder isgenerated by two vortices at the upper and lower parts (Figure 4 b-d). At thesame time, the positive vortex in gap side between cylinder and wall are growsand generated (Figure 4 b-d).
Meanwhile, the plane boundary is rolled up when anegative vortex grows close to the surface. When the flow velocity decreases in(Figure 4 d-f), the positive vortex splits into two part the lower part of cylinder. One part of positive vortex is rolled up,while the other one is convected far away from cylinder. The chart above represents about timevariation of lift force acting on the pipe records the vortex shedding andvortex motion phenomena around the pipe. As mentioned previously, the liftcoefficient is calculated as. Thereare some differences between the simulated and measured lift coefficient asFigure 4.
1 shown above. This is because applied turbulence model might not beable to simulate the size and magnitude of the vortices in cases with highadverse gradient pressure (Menter, 1994). On the other hand, the results are inreasonably good agreement with the experimental data of 2.3)The relation of gap flow in oscillatory flow and steady current conditions In this section is to study the gap flowvelocities for different gap ratios in oscillatory flow and in steady currentconditions. In order to simulate the oscillatory flow conditions, the pipediameter, oscillation period flow, maximum orbital velocity, Reynolds number inpipe and Keulegan Carpenter number are 5 cm, 1.78 s, 0.197 m/s, 9500 and 7. Inpart of steady flow conditions, the pipe diameter, free stream velocity andReynolds number in pipe are 5 cm, 0.
197 m/s and 9500 respectively. Thesimulations are investigated in different gap ratios where are 0.1, 0.2, 0.3,0.
5 and 0.7 respectively. Figure 5a represents the variation of the maximum gap flowvelocity against different gap ratios in both flows oscillatory flow and steadycurrent flow conditions.
To beginwith oscillatory flow conditions, the maximum gap flow velocity decreases whenthe gap increases. On the other hand, in case of steady current condition themaximum gap flow velocity slightly rises up as the gap increases also. We cannotice that the maximum gap flow velocity of oscillatory flow is higher thansteady current flows. Sumer and Fredse (2002) also indicated that the waterdischarge in oscillatory flow is much larger than in steady currents.
This maybe because the large pressure gradient that attribute from incoming flow. Figure 5billustrates the mean gap flow velocity against the different gap ratios. Thiscan be clearly seen that the oscillatory flow condition is also higher thansteady current flow. In addition, Figure 5b shows that the oscillatory flow inboth mean and maximum gap flow velocities exceed the amplitude of free streamvelocity.
So, this can be pointed out that in case of small KC number theinertia is dominated while the KC number become larger, the drag force isdominated because the flow pattern is similar to the steady flow conditions.Thus, we can mention that if KC number increases, the small range of the gapratios the decreases. 2.4) Oscillatory flow interaction in close wallproximity The purpose ofthis section is to examine the effect of wall proximity on flow regimes arounda cylinder. In addition, who conclude the visualization study of theflow around a cylinder on fixed bed for the half of the wave period in Figure 6. Ineach sequence is involved variety of KC and Re for the flow regime around thecylinder where the flow can be separated to five different regimes as shown onthe table 2 below. Regime KC range Reynold number (Re) 1 < 2 2 2 3 4 4 10 5 15 Note that when KC is very small, the flow separation behindthe cylinder might not occur.
1) In the first regime, the flow separations don’t occur but the flowparticles behind the cylinder are similar to elliptical movement.2) In the second regime, the flow is first time occuring with small voticesunder downstream of the cylinder3) In the third regime, the flow is stronger than the the second regime and two small votices occur behind a cylinderwhile other large two occur downstream.4) In the fourth regime, there are two different flow behaviours areillustrated.
The first flow separation is symmetric vortices. The second flowrepresents that the larger vortex shedding happening at the downstream of acylinder.5) The last regime, the votex shedding is no more occuring but there is thelarge vortex form at the upper area downstream of a cylinder. Chapter33) Experimental analysis 3.
1) Numerical Simulation The chart above represents the simulationabout the vertex maximum of X velocity against flow time as in this example isapproximately 3,000 time-step running, which is around 30 flow cycles. Inaddition, the oscillatory flow and orbital amplitude of this modelsimulation set up are 5 second and 0.1 meter respectively. As we can see thatafter 1200 time-steps, the flow becomes repeatable. Thus, this can be impliedthat it has converged and can stop the simulation.
The chart showing above is using the datafrom CFD simulation and applies to Matlab code on appendices (1). 4.Conclusion In this reportis to analyze the oscillatory flow interaction by the Morison’s equations arerelative to the pipeline by hydrodynamic forces including with lift, drag andinertia forces. These equations represents that the drag and lift forces areproportional to x-direction and y-direction respectively, and the inertia forceis directly relative to fluid particle acceleration. In order to ensure thatpipeline is stable, the submerged weight must be higher thanthe lift force on pipeline. Meanwhile, the frictional force needs to exceed thedrag and inertia forces combining. In addition, the hydrodynamic coefficientsin oscillatory flow depend on Reynolds number (Re), Keulegan-Carpenter number (KC)and the position of the pipe. Furthermore, Most of experiments cases consider agap ratio of a cylinder proportional to the bed in the range of 0 e/D.
In addition, if KC number increases,the small range of the gap ration will decrease. This reportwill continue in Computational Fluid Dynamics (CFD) by using AberdeenOscillatory Flow Tunnel (AOFT) experimental data to analyze and ANSYS Fluentsoftware package will be used more in the spring term also. This report is notaffected any risk assessment because I use computer from University of Aberdeenand VMware Horizon to get access at home.