Vortex Induce Vibration
INTRODUCTION 1.1. Background of Study
Vortex induced motion (VIM) or vortex induced vibration (VIV) is an object vibration influenced by the vortex shedding. When fluid flow across the blunt body, wake formed behind the bluff object and resulting in vortex shedding. Due to the long periods of motions, the vortex induced vibration will commonly refer as vortex induced motion.
Vortex-induced motion is an important source of fatigue damage for blunt cylindrical body underwater especially for production risers. When the shedding frequency matches the body Eigen frequency, the body will begin to resonate and the body’s movement becomes self-sustaining. Continuing resonating will lead to material tiredness and the materials tend to fracture or fatigue.
Vortex shedding was one of the causes proposed for the failure of the Tacoma Narrows Bridge in 1940. During the winter of 2001, a thrill ride “Vertigo” in Ohio suffered the vortex shedding result one of the three towers collapsed. On 1968, vortex shedding due to high winds caused the collapse of three towers at Ferrybridge power station.
Through countless of studies and researches, several vortex suppression methods developed designed to reduce the effects of vortex induced motion on blunt body. Commonly the fairing is used in reducing vortex shedding effect for cylindrical body. Fairing will effectively reduce the drag force and wake generated by fluid flow.
This research begins with the understanding on principles, parameters and consequence of vortex induced motion (VIM) or vortex induced vibration (VIV) then follow by conducting simulation. The analysis is simulated by CFD software which is ANSYS Fluent. The results obtained will be compared with the experimental results conducted by other researchers.
1.2. Problem Statement
In carrying out the research, several issues need to be clarified: i. The effects of waves and current on VIM ii. The effects of cylinder dimension on VIM iii. The effects fairing on vortex suppression iv. Any suppression method is more effective than fairing
1.3. Objective of Study
The objective of study as follow: i. To investigate the influences of waves and current on VIM ii. To investigate the influences of cylinder dimension on VIM iii. To identify the effects of fairing on vortex suppression iv. To develop an effective method in vortex suppression
1.4. Significant of Study
The important of this research is to develop an effective method for vortex suppression. The method will be able to suppress the vortex shedding more effectively compare to the other methods. Besides, this method will reduce the drag force and lift force generated by the vortex shedding. The forces are the main contribution to the material fracture. 1.5. Scope of Study
The scopes of study of this research are listed as follows: i. Investigate and understand the basic principles of VIM and VIV on circular cylinder ii. Analyses VIM using CFD simulation iii. Develop an effective vortex suppression method 1.6. Research Flow Chart 1.7. Research Gantt Chart
LITERATURE REVIEW (1st Draft) 2.1. Introduction
Vortex-induced motion (VIM) or vortex-induced vibration (VIV) is a phenomenon happens when fluid flow across a cylindrical body. When a fluid flow across a cylindrical body, an unsteady flow with oscillating motion formed behind the body is called shedding frequency. This shedding frequency will associated with formation of vortices. When the vortices are not formed symmetrically around the body, a time varying non-uniform pressure distribution will generate, resulting lift force acting on each side of body. As the time varying lift force continues acting on the body, the body will vibrate in inline and transverse to the flow. When the shedding frequency is close or equal to the Eigen frequency of the body, resonance occur and the vibration amplitude of the body is maximized. This phenomenon is called lock-in and fatigue tends to happen.
2.2. Vortices Shedding Formation
As the fluid approaches the front side of the tube, the fluid pressure rises from the free stream value to the stagnation point value. The high pressure forces the fluid to move along the tube surface and boundary layers develop on both sides. The pressure force is counteracted by viscous forces and the fluid cannot follow the tube surface to the rear side but separates from both sides of the tube and form two shear layers. The innermost part of the shear layers are in contact with the tube surface and moves slower than the outermost part. As a result, the shear layers roll up.[1]
A vortex is in the process of formation near the top of the cylinder surface. Below and to the right of the first vortex is another vortex which was formed and shed a short period before. Thus, the flow process in the wake of a cylinder or tube involves the formation and shedding of vortices alternately from one side and then the other. This phenomenon is of major importance in engineering design because the alternate formation and shedding of vortices also creates alternating forces, which occur more frequently as the velocity of the flow increases.[2]
Figure 2.1: Vortex formation behind a circular cylinder.[2] 2.3. Reynolds Number dependence
Generally the flow pattern around a circular cylinder can be characterized by the Reynolds number of the incident flow and by the location of points at which the flow separates from the cylinder surface which in turn depend on the state of the boundary layer (laminar or turbulent).[3]
For viscous fluids the flow pattern is much more complicated and the balance between inertia forces and viscous forces is important.[3] The relative importance is expressed by the Reynolds number Re defined as
Re =U∞Dυ≈inertial effectsviscous effects where U∞ is the free stream velocity, D is the tube diameter and υ the kinematic viscosity of the fluid.
Figure 2.2 shows the principal description of vortex shedding from a smooth circular cylinder in uniform flow for the major Reynolds number regimes.
Figure 2.2 Regimes of fluid flow across a smooth tube.[3, 4]
At Reynolds numbers below 1, no separation occurs. The shape of the streamlines is different from those in an inviscid fluid. The viscous forces cause the streamlines to move further apart on the downstream side than on the upstream side of the tube. [1]
In the Reynolds number range of 5 ≤ Re ≤ 45, the flow separates from the rear side of the tube and a symmetric pair of vortices is formed in the near wake.[1]
As the Reynolds number is further increased the wake becomes unstable and Vortex Shedding is initiated. At first, one of the two vortices breaks away and then the second is shed because of the nonsymmetrical pressure in the wake. The intermittently shed vortices form a laminar periodic wake of staggered vortices of opposite sign. This phenomenon is often called the Karman vortex street.[1]
In the Reynolds number range 150 < Re < 300, periodic irregular disturbances are found in the wake. The flow is transitional and gradually becomes turbulent as the Reynolds number is increased.[1]
The Reynolds number range 300 < Re < 1.5·105 is called subcritical (the upper limit is sometimes given as 2·105). The laminar boundary layer separates at about 80 degrees downstream of the front stagnation point and the vortex shedding is strong and periodic.[1, 3]
With a further increase of Re, the flow enters the critical regime. The laminar boundary layer separates on the front side of the tube, forms a separation bubble and later reattaches on the tube surface. Reattachment is followed by a turbulent boundary layer and the separation point is moved to the rear side, to about 140 degrees downstream the front stagnation point. As an effect the drag coefficient is decreased sharply.[1]
The range 1.5·105 Re3.5·106, referred to the literature as the transitional region, includes the critical region (1.5·105 Re3.5·105) and the supercritical region (3.5·105 Re3.5·106). In these regions, the cylinder boundary layer becomes turbulent, the separation points move aft to 140 degrees, and the cylinder drag coefficient drops abruptly.[3] Laminar separation bubbles and three-dimensional effects disrupt the regular shedding process and broaden the spectrum of shedding frequencies for smooth surface cylinders.[3, 5]
In the post-critical Reynolds number range (Re3.5·106), regular vortex shedding is re-established with a turbulent cylinder boundary layer. The vortex shedding persists at Reynolds number as high as 1011.[3, 6]
2.4. Strouhal number dependence
When the shedding frequency is near the Eigen-frequency of the structure, the resonance will occur and the structure appears to sing. A dimensionless number, the Strouhal number Sr, is commonly used as a measure of the predominant shedding frequency fs. The definition is
Sr= fsDU∞
where D is the diameter of a circular cylinder or tube in cross flow and U∞ is the free stream velocity.
The Strouhal number of a stationary tube or circular cylinder is a function of Reynolds number but less of surface roughness and free stream turbulence as shown in Figure 2.3.
Figure 2.3: Strouhal number versus Reynolds number for circular cylinders.[4]
Most of the Strouhal number data were derived from the measurements of the velocity fluctuations in the wake, while fewer data were derived from the lift force spectra. However, that lift force spectra are a more direct measure of the force characteristics than wake velocity measurements.[3]
The behavior of the Strouhal number is stable for a wide range of Reynolds numbers, except around 106(transitional region) where significant scatter occurs in the test data.[3] Vortices are frequently shed in this region and the Strouhal number is near to 0.2.
In the transitional region, the Strouhal number becomes scattered varying from 0.05-0.5. Delany & Sorensen (1953) found a sudden increase of their values of Strouhal number to 0.45 and then a decrease to 0.3 at about the same Reynolds number of 2·106. This indicates the transition to postcritical flow conditions. Bearman (1969) measured a similar value of S=0.46. [3]
Also in the transitional range, Achenbach and Heinecke (1981) found that smooth stationary cylinders had a chaotic, disorganized, high-frequency wake and Strouhal number as high as 0.5. Cylinders with some roughness (surface roughness e/D=3·10-3 or greater, where e is the characteristic surface roughness) had organized, periodic wakes with Strouhal numbers S=0.25.[3]
In the Reynolds number range 250 < Re < 2×105 the empirical formula
Sr=0.1981-19.7Re
is sometimes recommended for estimation of the Strouhal number.[2]
It has been suggested to introduce a universal Strouhal number based on the distance between the shear layers. Over a large Reynolds number range a Strouhal number of about 0.2 is then valid regardless of the body geometry.[2]
Vortex shedding from a stationary cylinder in the post-critical region does not occur at a single distinct frequency, but rather wanders over a narrow band of frequencies and it is not constant along the span. An average Strouhal number value of 0.25 is suggested.[3] 2.5. Reduced Velocity
Reduced velocity is a determination of the velocity ranges where the vortex shedding will be in resonance with Eigen frequency of the object. VR=U∞fiD where U∞ free stream velocity, fi is the ith natural frequency of the member and D is member diameter.
For low reduced velocities, there exists on initial branch associated with a 2S vortex shedding mode (two single vortices shed per cycle) and the means forces and cylinder response are in phase. For intermediate and larger reduced velocities there exists an upper and a lower branch associated with a 2P vortex shedding mode (two pairs of vortices per cycle).[7]
Figure 2.4: Sketch of the “three-branch” response model However, very few three-dimensional numerical results have been able to accurately reproduce the three-branch response model obtained from experiments. Some have successfully predicted the 2P shedding mode in the lower branch[8], but this result has only been observed at large mass-damping parameters, small aspect ratio and moderate Reynolds number. In general, the task of capturing numerically the large amplitude response of the upper branch for low mass-damping systems with large aspect ratio has remained out of reach.[7]
2.6. Lift Coefficient
Lift force is sinusoidal component and residual force. Parameter of lift force normally is used to determine the lift coefficient, CL.
CL= FL12ρDLV2 where FL is the time-average of the drag force, FL(t), ρ is the fluid mass density, D is the cylinder diameter, L is the cylinder length and V is the flow velocity.
Lift is the transverse component of force occurring at the vortex shedding frequency. Lift will be influenced by body motion, and there is considerable evidence demonstrating the influence of body on lift force frequency and correlation. But it is an applied force which owes its existence to the character and strength of the hydrodynamic wake formed by flow around the body.[3]
Lift force also can be expressed in the form of motion as equation stated below
FL=m+az+2mζωzz+Kz
where ζ is the damping factor of the cylinder, ωz is the cylinder circular natural frequency and K is the spring constant.
The time varying lift force on the oscillating cylinder may have a phase, Φ difference. Then lifting amplitude will become, z=Azsin(2πfst+Φ) where Az is maximum motion amplitude.
Concerning the fluid dynamics part of the problem the Reynolds number Re can play an important role here because flow separations are often Reynolds number dependent, even if the bodies have sharp edges. This has already been observed and explained for the approach span cross section of the Great Belt Bridge (Schewe & Larsen 1998).
High Reynolds number dependence is observed from numberless of experiments and researches. The reason for this dependence is that, the state of the boundary layer has a far-reaching influence on the entire flow field about a body. Both the state of the boundary layer and the location of transition are often responsible for the formation, length, and shape of separation bubbles.[9]
In particular when the symmetry is broken, i.e. the cross section is asymmetric or the angle of incidence α is not zero, the behavior of the separated flow that depends on the Reynolds number can be different on the upper- and the lower side of the section. Thus global values, like the lift coefficient CL, for example, can be affected by the Reynolds number. This in turn can have a large influence on the derivatives, which are differential values and thus sensitive to small variation of the underlying CL(α) curve, the latter are, in addition, typically nonlinear in case of bluff bodies. In general the derivatives and the nonlinearities are determining the type and strength of possible flow induced vibrations.[9]
Over countless experiments and researches, a large number of results had been published to attempt the relationship between the lift coefficient and Reynolds number. A tabulated and compiled test data from varies studies and data reviews is shown in Figure 2.11 and Table 1.
Curve | # Authors | Low Re | High Re | Medium | Value | Comments | 1 | Bingham et al. (1952) | 8.0E+04 | 8.0E+04 | Air | Mean peak | Shock tube, uniform flow, few oscialltion cycles of lift force | 2 | Bishop – Hassan (1963) | 4.0E+03 | 1.2E+04 | Water | Mean peak | Rigid cylinder, strain gage measurements | 3 | Bublitz (1971) | 9.0E+04 | 7.5E+05 | Air | Rms | | 4 | Chen, Y. N. | 4.0E+01 | 5.0E+05 | Air | Peak | Smooth cylinder, uniform flow, low turbulence (calculation) | 5 | Chen, Y. N. | 4.0E+01 | 5.0E+05 | Air | Peak | Riugh cylinder, uniform flow, high turbulence (calculation) | 6 | Chen (1969) | 6.0E+03 | 6.0E+03 | Air | Rms | | 9 | Dawson – Marcus (1970) | 9.0E+01 | 9.0E+01 | Air | Mean peak | | 10 | DnV | 1.0E+04 | 8.0E+06 | Air/water | Rms | Uniform flow | 11 | Fung | 1.0E+05 | 6.0E+05 | Air | Rms | Uniform flow, strain gauges, L/D=6(overall), L/D=2 (instrum. Section) | 12 | Fung (1960) | 1.8E+05 | 1.4E+06 | Air | Rms | Uniform flow, strain gage measurements, L/D=6, L/D=2 (instrum. Section) | 14 | Goldman (1957) | 1.8E+05 | 2.5E+05 | Air | Peak | Bottom curve of Goldman curves | 15 | Goldman (1957) | 1.8E+05 | 2.5E+05 | Air | Peak | Top curve of Goldman curves | 16 | Humphreys | 4.5E+04 | 2.0E+05 | Air | Rms | Fore measurements with load cells, L/D=6.5, uniform flow | 17 | Humphreys | 4.0E+04 | 6.0E+05 | Air | Peak | Fore measurements with load cells, L/D=6.5, uniform flow | 18 | Humphreys (1960) | 2.0E+03 | 1.2E+06 | Air | Peak | Fore measurements with load cells, L/D=6.5, uniform flow | 19 | Huthloff | 3.0E+04 | 1.0E+05 | Air | Rms | Uniform flow, strain gauge and inductive transducer measurements | 20 | Jones | 4.0E+05 | 2.0E+07 | Air | Rms | Force transducers, L/D=5.33 | 21 | Jones (1968) | 2.0E+06 | 2.0E+07 | Air | Rms | Force transducers, L/D=5.33 | 22 | Jordan – Fromm (1972) | 5.0E+02 | 5.0E+02 | Air | Rms | Uniform flow (calculations) | 23 | Keefe (1962) | 1.0E+04 | 1.0E+05 | Air | Rms | Direct force transducer | 24 | King | 4.0E+04 | 4.0E+04 | Water | Rms | Uniform flow | 25 | Macovsky (1958) | 2.0E+04 | 8.0E+04 | Water | Peak | Force measurements | 26 | Macovsky (1958) | 3.7E+04 | 1.1E+05 | Water | Mean peak | Force measurements | 27 | McGregor (1957) | 4.0E+04 | 1.8E+05 | Air | Rms/mean peak | Top curve (mean peak), uniform flow, pressure measurements/integration | 28 | Moeller - Lechey | 1.9E+04 | 1.9E+04 | Water | Rms | Force measurements, rigid cylinder, U/D=28 | 29 | Phillips (1956) | 3.0E+01 | 2.0E+02 | Air | Mean peak | Uniform flow, questionable data points (from Y.N. Chenpaper) | 30 | Protos et al. (1968) | 4.5E+04 | 4.5E+04 | Water | Rms | Uniform flow, cantilever piercing free surface, L/D=6.5 | 31 | Rajaona - Sulmont | 3.0E+04 | 1.8E+05 | Water | Peak | Towed, fixed cylinder, force measurements, L/D=2.5 | 32 | Rajaona - Sulmont | 3.0E+04 | 1.8E+05 | Water | Rms | Towed, fixed cylinder, force measurements, L/D=2.5 | 33 | Rodenbusch et. Al. (Shell) | 2.0E+05 | 2.2E+06 | Water | Peak | Steady tow, smooth flow, strain gages, L/D=2.8, 1 (instrumented section) rigid cylinder, uniform flow | 34 | Ruedy | 1.0E+05 | 1.0E+05 | Air | Rms | Eigid cylinder, uniform flow | 35 | Sallet | 1.0E+02 | 1.0E+06 | Air | Peak | Theory, based on wind stationary pressure tap measurements | 36 | Schewe (1983) | 1.0E+04 | 8.0E+06 | Air | Rms | Force measurements, clamped ends, L/D=10 | 37 | Schmidt et al. (1966) | 1.0E+05 | 1.0E+07 | Air | Rms | CL0 related to infinitely thin strip pressure measurements/integration | 38 | Schmidt (1965-66) | 3.0E+05 | 7.0E+06 | Air | Rms | Uniform flow | 39 | Schwabe (1935) | 7.0E+02 | 7.0E+02 | Water | Mean peak | Uniform flow with turbulence, pressure measurements, (calculations) | 40 | Sonneville | 1.0E+04 | 3.0E+04 | Water | Mean peak | Uniform flow | 41 | Surry | 5.0E+04 | 5.0E+04 | Air | Rms | Rigid cylinder, turbulent flow | 42 | Vickery - Watkins (1962) | 4.0E+04 | 1.8E+05 | Air/water | Rms | Stationary and oscillating cylinder data | 43 | Vickery – Watkins | 1.0E+04 | 1.0E+04 | Air | Rms | Rigid cylinder, pivoted ends | 45 | Weaver (1961) | 7.0E+04 | 3.0E+05 | Air | Peak | Rigid cylinder, lu=0.5%, uniform flow, force measurements, L/D=10-15 | 46 | Whitney et al. | 1.0E+02 | 2.0E+07 | Air | Rms | Based o air stationary experiments, uniform flow (calculations) | 47 | Woodruff - Kozak | 2.0E+05 | 2.0E+05 | Air | Rms | Uniform flow |
Table 1: Compilation of Lift Coefficient from Stationary Cylinder Data[3]
Figure 2.11: Lift Coefficient Data for Stationary Cylinders[3]
2.7. Drag Fore
Drag force is another force component that acting in parallel direction on the cylinder in cross flow. Drag is the only force component that acts on a cylinder below Re=40 because all flows in that regime are symmetrical with respect to the direction of flow. Drag force normally expressed in terms of lift coefficient:
CD= FD12ρAV2 where FD is the time-average of the drag force, FD(t), ρ is the density of the fluid and A is the projected area that the cylinder presents to the flow.[10]
The drag force, FD is equal to the sum of two different kinds of force. The first is pressure drag:
FDP = A1psin∝dA where FDP is the pressure at any point on the surface of the body and ∝ is the angle between the forward stagnation streamline and a vector normal to the surface.[10]
The second component is frictional drag:
FDf = A1τ0cos∝dA where τ0 is the viscous shear stress at the surface.[10]
At very low Reynolds number (Re<5), drag will consist almost entirely of FDf . When vortices form, the pressure distribution will become more severe from the forward to the aft stagnation point and eventually it will become asymmetrical with respect to the direction of flow. As the oscillating lift force appears, FDf gradually becomes negligible in comparison with FDp .[10]
Curve | # Authors | Low Re | High Re | Medium | Cylinder | Comments | 1 | Relf – Simmons | 1.0E+02 | 2.0E+06 | Air | S | Uniform flow, based on experiments by Wieseelbrger | 2 | Sallet | 1.0E+02 | 2.0E+06 | Air | S | Uniform flow | 3 | Schewe | 1.0E+04 | 7.0E+05 | Air | S | Rigid cylinder, dampened | 4 | Kwok | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow, clamped – clamped | 5 | Achenbach | 8.4E+01 | 8.0E+05 | Air | S | Smooth, uniform flow | 6 | Rodenbusch – Gutierrez | 1.8E+05 | 3.0E+06 | Water | S | Shell experiments, uniform flow, 0.02 roughness | 7 | Farell – Blesmann | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow | 8 | Cheung – Melbourne | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow, pressure taps | 9 | NPL | 8.0E+04 | 5.0E+05 | | | Based on compiled data | 10 | Rodenbusch - Gutierrez | 1.8E+05 | 3.0E+06 | Water | S | Shell experiments, uniform flow, 0.02 roughness | 11 | Guven et al. | 2.0E+05 | 9.0E+05 | Water | S | Smooth, uniform flow | 12 | Rodenbusch – Gutierrez | 2.0E+05 | 9.0E+05 | Water | S | Shell experiments, uniform flow, smooth cylinder | 13 | Schmidt | 1.0E+06 | 6.0E+06 | Air | S | Polished surface | 14 | Jones | 5.0E+05 | 1.0E+07 | Air | S | Smooth | 15 | Rajaona – Sulmoni | 2.0E+06 | 9.0E+06 | Water | O | Forced oscillations, uniform flow, towed | 16 | Roshko | 2.0E+06 | 8.0E+06 | Air | S | Roughness = 0.0002, uniform flow |
* S = Stationary, O = Oscillating
Table 2: Compilation Drag Coefficient Data versus Reynolds Number[3]
Figure 2.13: Drag Coefficient Results for Circular Cylinders[3]
2.8. Lock-In
The presence of vibration frequency component is main factor to disrupt the lock-in or wake synchronization process. In different regions, different modes may be resonantly excited and because of shear, the shedding frequency may vary along the length. It has been experimentally demonstrated that multiple frequency components may disrupt the local, lock-in process. Thus, if one mode has been sufficient vibration energy it may prevent competing mode with lower response levels from developing wake-synchronized power-in regions.[11]
It is also known that lock-in is a very nonlinear phenomenon. If one mode is able to achieve sufficient response amplitude, then wake synchronization for other modes may be suppressed, even in regions of the cable which would appear to favor lock-in with those modes.[11]
For flow past cylinders that are free to vibrate, the phenomenon of synchronization or lock-in is observed. For low flow speeds, the vortex shedding frequency fs will be the same as that of a fixed cylinder. This frequency is fixed by Strouhal number. As the flow speed is increased, the shedding frequency approaches the vibration frequency of the cylinder fo. In this regime of flow speeds, the vortex-shedding frequency no longer follows the Strouhal relationship. Rather, the shedding frequency becomes “lock-in” to the oscillation frequency of the cylinder (i.e., fo≈ fs ). If the vortex-shedding frequency is close to the natural frequency of the cylinder fn, as is often the case, the large body motions are observed within the lock-in regime (the structure undergoes near resonance vibration).[12]
During lock-in, amplitudes of cross-flow oscillation increased markedly. The largest steady-state values correspond to peak-to-peak oscillation amplitudes of approximately 0.9D (standard deviation values of y/D are presented in Figure 2.11. The lack of exact coincidence of fo with fn during lock-in can be accounted for by a phase difference between cylinder motion and lift forces, which is known to be a function of fn/fv .[13]
Figure 2.11: Cylinder response diagram. Values along the abscissa represent the ratio of cylinder in vacuo natural frequency fn to Strouhal frequency for the fixed cylinder fv. (□) Ratio of fluctuating lift coefficients C’1/C’10; (○) ratio of mean drag coefficients Cd/Cd0; (∆) ratio of oscillation frequency to fixed-cylinder Strouhal frequency fo/fv; (−) standard deviation of cylinder cross-flow response amplitude y’/D. Shaded region indicates chaotic regime.[13]
But in later works in low mass-damping ratio, Williamson and Khalak found new branch of response, they observed that during lock-in, the ratio of two frequencies wouldn’t remain equal to unit and these frequencies match with each other near other values like 1.4. Their studies showed that the behavior of frequencies changes in different mass-damping ratios.[12]
Generally, the lock-in can be identified by using Kurtosis. Typical drilling riser response measurements are from instruments strapped to the riser at several different positions. Assume that x(t) is a zero mean, measured time series of transverse acceleration response, resulting from VIV. The kurtosis of x(t) is given by: kurtosis=x4x22 , where = time average
Kurtosis is normally used to quantify deviation from Gaussian behavior. Zero mean Gaussian processes have a kurtosis of 3.0. Multiple frequency VIV response is often Gaussian in behavior, and tends to have kurtosis values of approximately 3. The occasional occurrence of a single frequency, lock-in event is characterized by steady sinusoidal behavior. When x(t) sin(t) , the kurtosis takes on the value of 1.5.[14]
Figure 2.12 presents shedding frequency fs versus cylinder oscilating frequency fc normalized by the shedding frequncy of the stationary cylinder fo. The ordinate of each point is the ratio of shedding frequency of the oscilating cylinder to that of a stationary cylinder. Where the ordinate is 1.0, there is no differece . where the ordinate is less than 1.0, shedding on the oscilating cylinder occurs at lower frequency than that of a stationary cylinder under comparable flow conditions.[3]
The slope of the line in figure 2.12 represents change in shedding freqency with change in cylinder frequency. Note that the curve is generally flat (zero slope), but there are two areas with positive slope. The first occurs when the cylinder frequency is nearly equal to the nominal shedding frequency of a stationary cylinder (abscissa equal to 1.0), which as discussed above is an area characterized by significant organization of the wake into correlated, consistent vortex cells. The slope here is unity, indicating that the shedding frequency is equal to the cylinder frequency over a range of cylinder frequencies. The second occurs when the abscissa near 2.0, with a slope of 0.33. In the range, the shedding frequency is equal to 1/3 of the cylinder, over a range of cylinder frequencies.[3]
The explanation for this behavior is that the motion of the cylinder organizes the wake and causes the shedding frequency to abruptly jump from its nominal value fs yo a value equal to the oscillation frequency fc. At some point the shedding frequency reverts back to a constant frequency that is generally lower than of a stationary cylinder. When the cylinder motion controls the shedding frequency in this way, the frequency is said to be lock-in, locked on, or synchronized to the cylinder frequency.[3]
Figure 2.13: Frequency and amplitude response in the lock-in regime[15]
Two regions can be distinguished in the lock-in region (5 < Ur < 8):[15] * fs < fn. The vortex shedding frequency is lower than the natural frequency. The added mass coefficient in this regime is usually larger than 1. The lock-in results in a downward shift of the natural frequency, thereby adapting the natural frequency to the vortex shedding frequency. * fs > fn. The vortex shedding frequency is higher than the natural frequency. The added mass coefficient is usually smaller than 1. The lock-in results in a downward shift of the vortex shedding frequency. The vortex shedding frequency now adapts to the natural frequency.
Outside the lock-in regime (Ur < 5 or Ur > 8) the response follows the vortex shedding frequency, but the response is very small. Often a figure-of-eight type response is found for 2 degrees of freedom pipe motions.[15]
Generally there are some observations from most of the experiment:[3] * Lock-in can occur at the frequency of cylinder motion or at sub-harmonics of the cylinder motion, in either uniform or shear flow * Shedding behavior at the edges of the lock-in frequency range is similar for uniform and shear flow * The minimum amplitude required for initiating lock-in may increase with increasing Reynolds number * The frequency range within the shedding will lock-in to cylinder motion seems to narrow with increasing Reynolds number * At the edges of the frequency range where lock-in to the primary cylinder frequency is observed, shedding varies intermittently between the nominal frequency and the cylinder frequency
Lock-in VIV has been widely explored, and it is known to be associated with:[15] * increase of the correlation length, * increase of vortex strength, * increase of response bandwidth, * self-limiting nature at approximately 1 diameter, * increase of the in-line drag.
2.9. Inline and cross line flow
As fluid particles move close to the surface of a cylinder, vortices are shed from the structure at the separation point. Typically, the shedding process gives a vortex pattern in which the in-line excitation frequency is twice that in the cross-flow direction.[16]
Most experimental data today are based on 2D vortex induced vibrations, which means that the coupling between in-line and cross flow vibrations is not considered. These results have generally shown that amplitudes of in-line response are much lower than amplitudes in the transverse direction.[16]
These results have generally shown that amplitudes of in-line response are much lower than amplitudes in the transverse direction. Typical values for the maximum in-line VIV response are about 20 per cent of the cross-flow response. The in-line response of a pipeline span in current dominated conditions for 1.0 < UR < 4.5 is associated with either alternating or symmetric vortex shedding.[17]
Figure2.5: Vortex shedding
Symmetric vortices are shed when UR is between 1.0 and 2.2. When UR exceeds 2.2, vortices are shed alternately. This means that the oscillations depend on the vortex pattern which develops. The cross-flow natural frequency is used as reference frequency also for in-line response. Hence, the in-line curves are plotted for different frequency ratios Rf=0.5, 1.0, 1.5 and 2.0 according to the frequency ratios applied in the experiments. [17]
Diagram: In-line and cross-flow for varies reduced velocity UR and reduced amplitude A/D.
2.10. End Effects
A three-dimensional (3-D) finite cylinder in a cross-flow is one of the most basic and revealing cases in the general subject of fluid–structure interactions. Structural vibration strongly depends on the magnitude and distribution of the unsteady flow-induced forces along the span. Numerous experimental investigations have been carried out on this problem. Important findings and understanding have been achieved on the flow-induced forces, such as their variations with Reynolds numbers and free stream turbulence, and their dependence on the aspect ratio a ¼ L=D of the bluff body; and on the 3-D nature of the wake flow, such as oblique and parallel vortex shedding patterns, cellular shedding and associated vortex dislocations; and different instability modes. Here, L is the span and D is the diameter of the cylinder. Some studies generally agree that the cylinder wake is 2-D at Re ¼ U1D=n ¼, where Re is the Reynolds number, U1 is the free-stream velocity, and n is the fluid kinematic viscosity. Even in experimental visualization, three dimensionality cannot be identified for Re<15. However, in recent studies, it has been found that end conditions have a significant influence on vortex formation and their shedding from the bluff body, and on the 3-D nature of the wake flow.[18]
Generally, two methods commonly used to ensure two-dimensional flow conditions: 1)providing sufficiently long cylinders (where the force/pressure measurements are taken far from the ends) and 2) the addition of end plates to suppress the wrapping of vortices along the cylinder length.[3]
Figure 2.7: End effects on vortex shedding frequency[3]
Gouda (1975) presented the results of wind tunnel tests with cylinders of varying length, with and without end plates. The variation of vortex shedding frequency with cylinder length is illustrated in Figure 3.2. Shedding frequency is consistently lower for cylinders with three-dimensional flow effects than for cylinders with end plates except for L/D>50; for cylinders of L/D=15 the shedding frequency is 35% lower than for the infinite cylinder case. He proposed an aspect ratio of L/D=45 for no end effects without end plates. Griffin (1985) suggested conducting experiments with cylinders of sufficient length to minimize the effects of the end boundaries (length/diameter, L/D=100-120).[3]
Gouda also investigated the effects of end plate size on vortex shedding frequency and showed that for a cylinder of L/D=18, the diameter of the end plate should be at least 10D (D=cylinder diameter) to avoid all end effects.[3]
2.11. Cylinder motion (Free Oscillating)
Diagram: Sketches of force component in oscillating cylinder
For free oscillating cylinder, there are three frequencies involved[19]: * The still water eigenfrequency fo=12πkm+mao where k is the spring stiffness, m is the mass of the cylinder and mao is the added (or hydrodynamic) mass in still water
* The vortex shedding frequency fs=St∙UD where U is the flow speed, St is the Strouhal number, which is close to 0.2 in the sub-critical flow regime.
* The oscillating frequency fosc=12πkm+ma where ma is the added mass valid for the actual flow and oscillation condition.
Research Methodology (1st Draft) 3.1. Introduction
The aim of this study is to investigate the basic principles of Vortex Induced Vibration and Vortex Induced Moment and relevant parameters on circular cylinder. For this purpose, a model design and simulation was developed in (CFD) ANSYS Fluent.
ANSYS FLUENT software contains the broad physical modeling capabilities needed to model flow, turbulence, heat transfer, and reactions for industrial applications ranging from air flow over an aircraft wing to combustion in a furnace, from bubble columns to oil platforms, from blood flow to semiconductor manufacturing, and from clean room design to wastewater treatment plants. Special models that give the software the ability to model in-cylinder combustion, aero acoustics, turbo machinery, and multiphase systems have served to broaden its reach.[20]
In chapter 2, literature studies have discussed the primary parameters to analysis the Vortex Induced Motion. In this chapter, a research methodology with Computational Fluid Dynamics (CFD) method by using ANSYS Fluent is mentioned and described.
3.2. Model’s Particular Dimensions
Particular | Model | Diameter | 0.4m | Length | 1.55m | Thickness | 0.05m |
3.3. Progress Management
In conducting this methodology for model design and simulation, a procedure plan is developed to ensure the successfulness of the methodology. For this purpose, the ANYSY Workbench v14.0 is involved to manage the flow of methodology.
ANYSY Workbench is the framework upon which the industry’s broadest suite of advanced engineering simulation technology is built. An innovative project schematic view ties together the entire simulation process, guiding the user every step of the way. Even complex multi physics analyses can be performed with drag-and-drop simplicity. With bidirectional CAD connectivity, an automated project update mechanism, pervasive parameter management and integrated optimization tools, the ANSYS Workbench platform delivers unprecedented productivity that truly enables Simulation Driven Product Development.[21]
The whole simulation process is started with selecting the project system. The desired analysis system, Fluid Flow (FLUENT) is selected from the toolbox at left and it will show its progress steps in the project schematic. Complete analysis systems contain all of the necessary components as guidance through analysis process to work through the system from top to bottom.
The analysis process begin with the geometry design, followed by meshing, then problem, solution setup and finally results. For completed design or setting in each step, the software will update the information to workbench, then workbench will lead the process to next step.
3.4. Geometry Design
In Geometry Design stage, two design steps are involved which design modeling and enclosure space development. Geometry design is conducted under software named ANSYS DesignModeler.
3.5.1. Design Modeling
The design modeling started with sketching a circle with diameter, D = 0.4m and at ZX plane. The circle is then extruded about 1.5m to make it as a cylinder.
3.5.2. Enclosure Space Development
After the modeling completed, an enclosure space is developed to enclosing the meshing developing, it means that the meshing will only developed in the specified space. The meshing inside the enclosure space will input with fluid flow medium in the setup setting stage. During the simulation, the fluid flow will only present inside the enclosure space.
The enclosure dimensioning is automatically set the cylinder as reference object. Enclosure dimension is offset from the cylinder surface and enclosure surface cannot contact with the cylinder. The enclosure dimensions are set as table below: Enclosure Dimensions | Magnitude (m) | +X value | 1 | +Y value | 0.01 | +Z value | 1 | -X value | 1 | -Y value | 0.01 | -Z value | 5 |
Both +Y value and –Y value are set as 0.01m to prevent any end plate effect during the simulations. –Z value set as 5m as it prevents backflow effects and provides enough space for Vortex Induced Motion analysis especially for the shedding pattern.
In the enclosure space, the cylinder space needs to subtract to ensure the meshing will exclude the cylinder space. In order to accomplish that, Boolean is created with subtract operation and the cylinder is selected. After the subtraction is done, the space consumed by the cylinder will become hollow. As result, no fluid flow will generate inside the cylinder.
3.5. Meshing
After the geometry design is completed, the workbench will lead the process to mesh development. In this stage, the involved software is ANSYS ICEM CFD. ANSYS ICEM CFD offer the capability to parametrically create volume or surface meshes from geometry or mesh in multi-block structured, unstructured hexahedral, Cartesian, tetrahedral, tetra/prism hybrid, hex hybrid and unstructured quad/tri shell formats.[22]
3.6.3. Mesh Control
Mesh control is important to determine the quality of meshing and the accuracy of the results. Mesh control in ANSYS ICEM CFD is consists of several settings and inputs in controlling the meshing smoothness, mesh sizing, suppression effects etc. 3.6.4.1. Physics Based Setting
Different types of analysis require different meshing properties. In this study, fluid flow analysis involved, the meshing requirements is finer, smoothly varying mesh, boundary layer resolution. To fulfill these requirements, first the physics preference option is chosen as CFD. The physics preference will auto fulfill the majority of the requirements in mesh settings. 3.6.4.2. Relevance Center * Function : Control the smoothness of the meshing, further affects the quality of meshing * Default : Coarse (Lowest smoothness) * Selected : Fine (Highest smoothness)
3.6.4.3. Initial Size Seed * Function : Control the initial mesh seeding for each part * Default: Active Assembly (The mesh could change as part are suppressed or unsuppressed) * Selected : Full Assembly (The mesh never changes due to the part suppression) 3.6.4.4. Smoothing * Function : Improve element quality by moving locations of nodes with respect to surrounding nodes and elements * Selected : Medium (Medium number of smoothing iterations along with the threshold metric) 3.6.4.5. Transition * Function : Control the rate at which adjacent elements will grow * Selected : Slow (Produces a smooth transition)
3.6.4.6. Span Center Angle * Function : Sets the goal for curvature based refinement for edges * Selected : Fine (The mesh will subdivide in curved regions until the individual elements span between 36o to 12o) 3.6.4.7. Growth Rate
Growth rate can be assumed as the sizing of the meshing. The value of growth rate is decreasing for each simulation until obtain consistence results.
3.6.4. Component Grouping
In the system, different position of the components will have different function and different settings in the Boundary Conditioning. For this purpose, all the components like surface of enclosure box and cylinder is group into different category according to their position. These groups are defined as boundary zone. Boundaries are inlet, outlet, wall and cylinder. All this setups are the preparation in preprocessing phase. 3.6.5.8. Inlet * Components : Enclosure surface +Z * Function : As the inlet surface for fluid flow to enter the enclosure space
3.6.5.9. Outlet * Components : Enclosure surface –Z * Function : As the outlet surface for fluid flow to exit the enclosure space
3.6.5.10. Wall * Components : Enclosure surface +X, -X, +Y, -Y * Function : To bounder the fluid flow in the designed space
3.6.5.11. Cylinder * Components : Hollow with cylinder shape * Function : To experience the forces generated by fluid flow on the cylinder
3.6. Problem Setup
Problem setup is the setup step for flow condition and properties setting before compute the simulation. ANSYS Fluent will be involved for setup setting, simulations and results.
3.7.5. Turbulence Modeling
The first step in setup setting is to determine the turbulence modeling. Turbulence is an inherently unsteady, three dimensional and periodic swirling motions (fluctuations). The instantaneous are random in space and time, in addition, vortices and eddies always exist in the turbulence flows.
In ANSYSY Fluent, RNG k-ɛ and Realizable k-ɛ are the model specialized for simulation involved vortices shedding. The applications and usage of both model is similar. But in term of accuracy and converge, Realizable k-ɛ will shows better performance.
Realizable k-ɛ allows mathematical constraints to be obeyed which ultimately improve the performance of the model. For this purpose, Realizable k-ɛ is selected as the turbulent model.
3.7.6. Mesh Material Design
Mesh material is determined based on type of analysis. For this fluid flow analysis, the mesh material is water liquid with density, 998.2 kgm-3, specific heat, 4182j/kg-k, thermal conductivity, 0.6 w/m-k and viscosity, 0.001003 kg/m-s.
3.7.7. Boundary Conditioning
Boundary conditioning is the information specified process on the variables flow at the boundary which is necessary to obtain an accurate solution. Defining the boundary condition involves identifying the boundary location which is done in the preprocessing phase, and supplying the boundary information. 3.7.8.12. Inlet
Velocity specification method is applied for Inlet boundary condition. Velocity specification method will apply a uniform velocity profile at the boundary and is intended for use in incompressible flows.
In this case, the velocity specification is applied as magnitude, normal to boundary. The velocity magnitude is equal to 2ms-1. For turbulence specification method, intensity and viscosity ratio is selected. 3.7.8.13. Outlet
Pressure Outlet is the only mode of boundary condition for outlet boundary. Input requirements for Pressure Outlet are leave as default but the gauge pressure needs to be zero. 3.7.8.14. Wall
For wall boundary setting, the setup only done on defining the wall boundary to symmetry boundary, then ANSYS Fluent will generate the input for wall boundary. 3.7.8.15. Cylinder
In the boundary conditioning for cylinder, the cylinder is assume as no movements and rotations. For this reason, all the movement and rotation are null. 3.7.8. References Value Setup
Basically ANSYS Fluent will input the value from the setup done from the previous phase. The optional inputs are the flow direction and contact area. The inlet boundary is selected as flow direction and the area contact is equal to cylinder diameter multiple with cylinder height, 0.62m2.
3.7. Solution Setup
3.8.9. Output parameter determination
In solution setup, the output parameter can be determined in monitor option. In this simulation, lift force and drag force are decided to become the output parameter with print to console function and plot function for graph displaying.
3.8.10. Solution initialization
Solution initialization is the conclusion step to all the set up and design done. In solution initialization, ANSYS Fluent will ensure all the require input are inserted and it will input them into the calculation. 3.8.11. Run calculation
Deciding the number of iterations is the final step before compute the simulation. The accuracy of result depended on the number of iterations. In this study, at the specified growth rate of meshing, the number of iterations will start with 100000 times and increase 50000 times for every following simulations.
1. Sundén, B. Tubes, Crossflow over. Fluid Flow Fundamentals - External Flows 2011 16 March 2011 2 February 2011]; Available from: http://www.thermopedia.com/content/1216/?tid=104&sn=1410.
2. Sundén, B. Vortex Shedding. Fluid Flow Fundamentals - External Flows 2011 16 March 2011 [cited 2011 2 February 2011]; Available from: http://www.thermopedia.com/content/1247/?tid=104&sn=1410.
3. Pantazopoulos, M.S., Vortex-Induced Vibration Parameters: Critical Review. Offshore Technology, ASME OMAE 1994, 1994. Vol. 1 & 2: p. 199 - 255.
4. Blevins, R.D., Flow Induced Vibration, 2nd Edition, 1990, Van Nostrand Reinhold Co.
5. W., B.P., On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number Regime. Fluid Mechanics, 1969. Vlo. 37: p. 577-586.
6. O. M. Griffin, S.E.R., Some Recent Studies of Vortex Shedding with Application to Marine Tubulars and Risers. Journal of Energy Resources Technology, 1982. Vol. 104: p. 2-13.
7. D. Lucor, J.F., G.E. Karniadakis, Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping. Journal of Fluids and Structures, 2005. Vol. 20: p. 483-503.
8. H. M. Blackburn, R.N.G., D C. H. K. Williamson, A complementary numerical and physical investigation of vortex-induced vibration. Journal of Fluids and Structures, 2000. Vol. 15: p. 481-488.
9. Schewe, G., Reynolds-Number-Effects in Flow around a rectangular Cylinder with Aspect Ratio 1:5, in European-African Conference on Wind Engineering (EACWE) 52009, Institut für Aeroelastik: Florence, Italy.
10. Lienhard, J.H., SYNOPSIS OF LIFT, DRAG, AND VORTEX FREQUENCY DATA FOR RIGID CIRCULAR CYLINDERS. BULLETIN 300, 1966: p. 1 - 32.
11. J.K. Vandiver, D.A., L. Li, The Occurrence Of Lock-In Under Highly Sheared Conditions. Journal of Fluids and Structures, 1996. Vol. 10: p. 555-561.
12. A. Farshidianfar, H.Z., The Lock-in Phenomenon in VIV using A Modified Wake Oscillator Model for both High and Low Mass-Damping Ratio. Iranian Journal of Mechanical Engineering, 2009. Vol. 10: p. 6-28.
13. Hugh Blackburn, R.H., Lock-In Behavior in Simulated Vortex-Induced Vibration. Experimental Thermal and Fluid Science 1996, 1995. Vol. 12: p. 184-189.
14. Vandiver, J.K., Predicting Lock-in on Drilling Risers in Sheared Flows, in Proceedings of the Flow-Induced Vibration 2000 Conference2000: Lucerne, Switzerland.
15. Jaap de Wilde, A.S.a.H.C., N. Willis and C. Bridge, Cross Section VIV Model Test For Novel Riser Geometries, in DOT Conference2004: New Orleans. p. 1-19.
16. Søreide, M. Experimental Investigation of In-line and Cross-flow VIV. in Proceedings of The Thirteenth (2003) International Offshore and Polar Engineering Conference. 2003. Honolulu, Hawaii, USA: The International Society of Offshore and Polar Engineers.
17. Veritas, D.N., Free spanning pipelines, in DNV-RP-F1052002: Norway.
18. R.M.C. So, Y.L., Z.X. Cui, C.H. Zhang, X.Q. Wang, Three-dimensional wake effects on flow-induced force. Journal of Fluids and Structures, 2005. Vol. 20: p. 373-402.
19. Larsem, C.M., Vortex Induced Vibrations - A Short and Incomplete Introduction to Fundamental Concepts, D.o.M. Tachnology, Editor 2006, NTNU: Trondheim, Norway.
20. ANSYS, I., ANSYS FLUENT Tutorial Guide. Vol. Release 14.0. 2011, Canonsburg, PA 15317: ANSYS, Inc.
21. ANSYS, I., ANSYS Workbench Platform. ANSYS WORKBENCH Manual, 2009. Release 12.1: p. 1 - 4.
22. ANSYS, I., ANSYS ICEM CFD. ANSYS ICEM CFD Introduction, 2009. Release 13.0: p. 1 - 2.
References: 3. Pantazopoulos, M.S., Vortex-Induced Vibration Parameters: Critical Review. Offshore Technology, ASME OMAE 1994, 1994. Vol. 1 & 2: p. 199 - 255. 4. Blevins, R.D., Flow Induced Vibration, 2nd Edition, 1990, Van Nostrand Reinhold Co. 5. W., B.P., On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number Regime. Fluid Mechanics, 1969. Vlo. 37: p. 577-586. 6. O. M. Griffin, S.E.R., Some Recent Studies of Vortex Shedding with Application to Marine Tubulars and Risers. Journal of Energy Resources Technology, 1982. Vol. 104: p. 2-13. 7. D. Lucor, J.F., G.E. Karniadakis, Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping. Journal of Fluids and Structures, 2005. Vol. 20: p. 483-503. 8. H. M. Blackburn, R.N.G., D C. H. K. Williamson, A complementary numerical and physical investigation of vortex-induced vibration. Journal of Fluids and Structures, 2000. Vol. 15: p. 481-488. 10. Lienhard, J.H., SYNOPSIS OF LIFT, DRAG, AND VORTEX FREQUENCY DATA FOR RIGID CIRCULAR CYLINDERS. BULLETIN 300, 1966: p. 1 - 32. 11. J.K. Vandiver, D.A., L. Li, The Occurrence Of Lock-In Under Highly Sheared Conditions. Journal of Fluids and Structures, 1996. Vol. 10: p. 555-561. 12. A. Farshidianfar, H.Z., The Lock-in Phenomenon in VIV using A Modified Wake Oscillator Model for both High and Low Mass-Damping Ratio. Iranian Journal of Mechanical Engineering, 2009. Vol. 10: p. 6-28. 13. Hugh Blackburn, R.H., Lock-In Behavior in Simulated Vortex-Induced Vibration. Experimental Thermal and Fluid Science 1996, 1995. Vol. 12: p. 184-189. 18. R.M.C. So, Y.L., Z.X. Cui, C.H. Zhang, X.Q. Wang, Three-dimensional wake effects on flow-induced force. Journal of Fluids and Structures, 2005. Vol. 20: p. 373-402. 20. ANSYS, I., ANSYS FLUENT Tutorial Guide. Vol. Release 14.0. 2011, Canonsburg, PA 15317: ANSYS, Inc. 21. ANSYS, I., ANSYS Workbench Platform. ANSYS WORKBENCH Manual, 2009. Release 12.1: p. 1 - 4. 22. ANSYS, I., ANSYS ICEM CFD. ANSYS ICEM CFD Introduction, 2009. Release 13.0: p. 1 - 2.
Vortex induced motion (VIM) or vortex induced vibration (VIV) is an object vibration influenced by the vortex shedding. When fluid flow across the blunt body, wake formed behind the bluff object and resulting in vortex shedding. Due to the long periods of motions, the vortex induced vibration will commonly refer as vortex induced motion.
Vortex-induced motion is an important source of fatigue damage for blunt cylindrical body underwater especially for production risers. When the shedding frequency matches the body Eigen frequency, the body will begin to resonate and the body’s movement becomes self-sustaining. Continuing resonating will lead to material tiredness and the materials tend to fracture or fatigue.
Vortex shedding was one of the causes proposed for the failure of the Tacoma Narrows Bridge in 1940. During the winter of 2001, a thrill ride “Vertigo” in Ohio suffered the vortex shedding result one of the three towers collapsed. On 1968, vortex shedding due to high winds caused the collapse of three towers at Ferrybridge power station.
Through countless of studies and researches, several vortex suppression methods developed designed to reduce the effects of vortex induced motion on blunt body. Commonly the fairing is used in reducing vortex shedding effect for cylindrical body. Fairing will effectively reduce the drag force and wake generated by fluid flow.
This research begins with the understanding on principles, parameters and consequence of vortex induced motion (VIM) or vortex induced vibration (VIV) then follow by conducting simulation. The analysis is simulated by CFD software which is ANSYS Fluent. The results obtained will be compared with the experimental results conducted by other researchers.
1.2. Problem Statement
In carrying out the research, several issues need to be clarified: i. The effects of waves and current on VIM ii. The effects of cylinder dimension on VIM iii. The effects fairing on vortex suppression iv. Any suppression method is more effective than fairing
1.3. Objective of Study
The objective of study as follow: i. To investigate the influences of waves and current on VIM ii. To investigate the influences of cylinder dimension on VIM iii. To identify the effects of fairing on vortex suppression iv. To develop an effective method in vortex suppression
1.4. Significant of Study
The important of this research is to develop an effective method for vortex suppression. The method will be able to suppress the vortex shedding more effectively compare to the other methods. Besides, this method will reduce the drag force and lift force generated by the vortex shedding. The forces are the main contribution to the material fracture. 1.5. Scope of Study
The scopes of study of this research are listed as follows: i. Investigate and understand the basic principles of VIM and VIV on circular cylinder ii. Analyses VIM using CFD simulation iii. Develop an effective vortex suppression method 1.6. Research Flow Chart 1.7. Research Gantt Chart
LITERATURE REVIEW (1st Draft) 2.1. Introduction
Vortex-induced motion (VIM) or vortex-induced vibration (VIV) is a phenomenon happens when fluid flow across a cylindrical body. When a fluid flow across a cylindrical body, an unsteady flow with oscillating motion formed behind the body is called shedding frequency. This shedding frequency will associated with formation of vortices. When the vortices are not formed symmetrically around the body, a time varying non-uniform pressure distribution will generate, resulting lift force acting on each side of body. As the time varying lift force continues acting on the body, the body will vibrate in inline and transverse to the flow. When the shedding frequency is close or equal to the Eigen frequency of the body, resonance occur and the vibration amplitude of the body is maximized. This phenomenon is called lock-in and fatigue tends to happen.
2.2. Vortices Shedding Formation
As the fluid approaches the front side of the tube, the fluid pressure rises from the free stream value to the stagnation point value. The high pressure forces the fluid to move along the tube surface and boundary layers develop on both sides. The pressure force is counteracted by viscous forces and the fluid cannot follow the tube surface to the rear side but separates from both sides of the tube and form two shear layers. The innermost part of the shear layers are in contact with the tube surface and moves slower than the outermost part. As a result, the shear layers roll up.[1]
A vortex is in the process of formation near the top of the cylinder surface. Below and to the right of the first vortex is another vortex which was formed and shed a short period before. Thus, the flow process in the wake of a cylinder or tube involves the formation and shedding of vortices alternately from one side and then the other. This phenomenon is of major importance in engineering design because the alternate formation and shedding of vortices also creates alternating forces, which occur more frequently as the velocity of the flow increases.[2]
Figure 2.1: Vortex formation behind a circular cylinder.[2] 2.3. Reynolds Number dependence
Generally the flow pattern around a circular cylinder can be characterized by the Reynolds number of the incident flow and by the location of points at which the flow separates from the cylinder surface which in turn depend on the state of the boundary layer (laminar or turbulent).[3]
For viscous fluids the flow pattern is much more complicated and the balance between inertia forces and viscous forces is important.[3] The relative importance is expressed by the Reynolds number Re defined as
Re =U∞Dυ≈inertial effectsviscous effects where U∞ is the free stream velocity, D is the tube diameter and υ the kinematic viscosity of the fluid.
Figure 2.2 shows the principal description of vortex shedding from a smooth circular cylinder in uniform flow for the major Reynolds number regimes.
Figure 2.2 Regimes of fluid flow across a smooth tube.[3, 4]
At Reynolds numbers below 1, no separation occurs. The shape of the streamlines is different from those in an inviscid fluid. The viscous forces cause the streamlines to move further apart on the downstream side than on the upstream side of the tube. [1]
In the Reynolds number range of 5 ≤ Re ≤ 45, the flow separates from the rear side of the tube and a symmetric pair of vortices is formed in the near wake.[1]
As the Reynolds number is further increased the wake becomes unstable and Vortex Shedding is initiated. At first, one of the two vortices breaks away and then the second is shed because of the nonsymmetrical pressure in the wake. The intermittently shed vortices form a laminar periodic wake of staggered vortices of opposite sign. This phenomenon is often called the Karman vortex street.[1]
In the Reynolds number range 150 < Re < 300, periodic irregular disturbances are found in the wake. The flow is transitional and gradually becomes turbulent as the Reynolds number is increased.[1]
The Reynolds number range 300 < Re < 1.5·105 is called subcritical (the upper limit is sometimes given as 2·105). The laminar boundary layer separates at about 80 degrees downstream of the front stagnation point and the vortex shedding is strong and periodic.[1, 3]
With a further increase of Re, the flow enters the critical regime. The laminar boundary layer separates on the front side of the tube, forms a separation bubble and later reattaches on the tube surface. Reattachment is followed by a turbulent boundary layer and the separation point is moved to the rear side, to about 140 degrees downstream the front stagnation point. As an effect the drag coefficient is decreased sharply.[1]
The range 1.5·105 Re3.5·106, referred to the literature as the transitional region, includes the critical region (1.5·105 Re3.5·105) and the supercritical region (3.5·105 Re3.5·106). In these regions, the cylinder boundary layer becomes turbulent, the separation points move aft to 140 degrees, and the cylinder drag coefficient drops abruptly.[3] Laminar separation bubbles and three-dimensional effects disrupt the regular shedding process and broaden the spectrum of shedding frequencies for smooth surface cylinders.[3, 5]
In the post-critical Reynolds number range (Re3.5·106), regular vortex shedding is re-established with a turbulent cylinder boundary layer. The vortex shedding persists at Reynolds number as high as 1011.[3, 6]
2.4. Strouhal number dependence
When the shedding frequency is near the Eigen-frequency of the structure, the resonance will occur and the structure appears to sing. A dimensionless number, the Strouhal number Sr, is commonly used as a measure of the predominant shedding frequency fs. The definition is
Sr= fsDU∞
where D is the diameter of a circular cylinder or tube in cross flow and U∞ is the free stream velocity.
The Strouhal number of a stationary tube or circular cylinder is a function of Reynolds number but less of surface roughness and free stream turbulence as shown in Figure 2.3.
Figure 2.3: Strouhal number versus Reynolds number for circular cylinders.[4]
Most of the Strouhal number data were derived from the measurements of the velocity fluctuations in the wake, while fewer data were derived from the lift force spectra. However, that lift force spectra are a more direct measure of the force characteristics than wake velocity measurements.[3]
The behavior of the Strouhal number is stable for a wide range of Reynolds numbers, except around 106(transitional region) where significant scatter occurs in the test data.[3] Vortices are frequently shed in this region and the Strouhal number is near to 0.2.
In the transitional region, the Strouhal number becomes scattered varying from 0.05-0.5. Delany & Sorensen (1953) found a sudden increase of their values of Strouhal number to 0.45 and then a decrease to 0.3 at about the same Reynolds number of 2·106. This indicates the transition to postcritical flow conditions. Bearman (1969) measured a similar value of S=0.46. [3]
Also in the transitional range, Achenbach and Heinecke (1981) found that smooth stationary cylinders had a chaotic, disorganized, high-frequency wake and Strouhal number as high as 0.5. Cylinders with some roughness (surface roughness e/D=3·10-3 or greater, where e is the characteristic surface roughness) had organized, periodic wakes with Strouhal numbers S=0.25.[3]
In the Reynolds number range 250 < Re < 2×105 the empirical formula
Sr=0.1981-19.7Re
is sometimes recommended for estimation of the Strouhal number.[2]
It has been suggested to introduce a universal Strouhal number based on the distance between the shear layers. Over a large Reynolds number range a Strouhal number of about 0.2 is then valid regardless of the body geometry.[2]
Vortex shedding from a stationary cylinder in the post-critical region does not occur at a single distinct frequency, but rather wanders over a narrow band of frequencies and it is not constant along the span. An average Strouhal number value of 0.25 is suggested.[3] 2.5. Reduced Velocity
Reduced velocity is a determination of the velocity ranges where the vortex shedding will be in resonance with Eigen frequency of the object. VR=U∞fiD where U∞ free stream velocity, fi is the ith natural frequency of the member and D is member diameter.
For low reduced velocities, there exists on initial branch associated with a 2S vortex shedding mode (two single vortices shed per cycle) and the means forces and cylinder response are in phase. For intermediate and larger reduced velocities there exists an upper and a lower branch associated with a 2P vortex shedding mode (two pairs of vortices per cycle).[7]
Figure 2.4: Sketch of the “three-branch” response model However, very few three-dimensional numerical results have been able to accurately reproduce the three-branch response model obtained from experiments. Some have successfully predicted the 2P shedding mode in the lower branch[8], but this result has only been observed at large mass-damping parameters, small aspect ratio and moderate Reynolds number. In general, the task of capturing numerically the large amplitude response of the upper branch for low mass-damping systems with large aspect ratio has remained out of reach.[7]
2.6. Lift Coefficient
Lift force is sinusoidal component and residual force. Parameter of lift force normally is used to determine the lift coefficient, CL.
CL= FL12ρDLV2 where FL is the time-average of the drag force, FL(t), ρ is the fluid mass density, D is the cylinder diameter, L is the cylinder length and V is the flow velocity.
Lift is the transverse component of force occurring at the vortex shedding frequency. Lift will be influenced by body motion, and there is considerable evidence demonstrating the influence of body on lift force frequency and correlation. But it is an applied force which owes its existence to the character and strength of the hydrodynamic wake formed by flow around the body.[3]
Lift force also can be expressed in the form of motion as equation stated below
FL=m+az+2mζωzz+Kz
where ζ is the damping factor of the cylinder, ωz is the cylinder circular natural frequency and K is the spring constant.
The time varying lift force on the oscillating cylinder may have a phase, Φ difference. Then lifting amplitude will become, z=Azsin(2πfst+Φ) where Az is maximum motion amplitude.
Concerning the fluid dynamics part of the problem the Reynolds number Re can play an important role here because flow separations are often Reynolds number dependent, even if the bodies have sharp edges. This has already been observed and explained for the approach span cross section of the Great Belt Bridge (Schewe & Larsen 1998).
High Reynolds number dependence is observed from numberless of experiments and researches. The reason for this dependence is that, the state of the boundary layer has a far-reaching influence on the entire flow field about a body. Both the state of the boundary layer and the location of transition are often responsible for the formation, length, and shape of separation bubbles.[9]
In particular when the symmetry is broken, i.e. the cross section is asymmetric or the angle of incidence α is not zero, the behavior of the separated flow that depends on the Reynolds number can be different on the upper- and the lower side of the section. Thus global values, like the lift coefficient CL, for example, can be affected by the Reynolds number. This in turn can have a large influence on the derivatives, which are differential values and thus sensitive to small variation of the underlying CL(α) curve, the latter are, in addition, typically nonlinear in case of bluff bodies. In general the derivatives and the nonlinearities are determining the type and strength of possible flow induced vibrations.[9]
Over countless experiments and researches, a large number of results had been published to attempt the relationship between the lift coefficient and Reynolds number. A tabulated and compiled test data from varies studies and data reviews is shown in Figure 2.11 and Table 1.
Curve | # Authors | Low Re | High Re | Medium | Value | Comments | 1 | Bingham et al. (1952) | 8.0E+04 | 8.0E+04 | Air | Mean peak | Shock tube, uniform flow, few oscialltion cycles of lift force | 2 | Bishop – Hassan (1963) | 4.0E+03 | 1.2E+04 | Water | Mean peak | Rigid cylinder, strain gage measurements | 3 | Bublitz (1971) | 9.0E+04 | 7.5E+05 | Air | Rms | | 4 | Chen, Y. N. | 4.0E+01 | 5.0E+05 | Air | Peak | Smooth cylinder, uniform flow, low turbulence (calculation) | 5 | Chen, Y. N. | 4.0E+01 | 5.0E+05 | Air | Peak | Riugh cylinder, uniform flow, high turbulence (calculation) | 6 | Chen (1969) | 6.0E+03 | 6.0E+03 | Air | Rms | | 9 | Dawson – Marcus (1970) | 9.0E+01 | 9.0E+01 | Air | Mean peak | | 10 | DnV | 1.0E+04 | 8.0E+06 | Air/water | Rms | Uniform flow | 11 | Fung | 1.0E+05 | 6.0E+05 | Air | Rms | Uniform flow, strain gauges, L/D=6(overall), L/D=2 (instrum. Section) | 12 | Fung (1960) | 1.8E+05 | 1.4E+06 | Air | Rms | Uniform flow, strain gage measurements, L/D=6, L/D=2 (instrum. Section) | 14 | Goldman (1957) | 1.8E+05 | 2.5E+05 | Air | Peak | Bottom curve of Goldman curves | 15 | Goldman (1957) | 1.8E+05 | 2.5E+05 | Air | Peak | Top curve of Goldman curves | 16 | Humphreys | 4.5E+04 | 2.0E+05 | Air | Rms | Fore measurements with load cells, L/D=6.5, uniform flow | 17 | Humphreys | 4.0E+04 | 6.0E+05 | Air | Peak | Fore measurements with load cells, L/D=6.5, uniform flow | 18 | Humphreys (1960) | 2.0E+03 | 1.2E+06 | Air | Peak | Fore measurements with load cells, L/D=6.5, uniform flow | 19 | Huthloff | 3.0E+04 | 1.0E+05 | Air | Rms | Uniform flow, strain gauge and inductive transducer measurements | 20 | Jones | 4.0E+05 | 2.0E+07 | Air | Rms | Force transducers, L/D=5.33 | 21 | Jones (1968) | 2.0E+06 | 2.0E+07 | Air | Rms | Force transducers, L/D=5.33 | 22 | Jordan – Fromm (1972) | 5.0E+02 | 5.0E+02 | Air | Rms | Uniform flow (calculations) | 23 | Keefe (1962) | 1.0E+04 | 1.0E+05 | Air | Rms | Direct force transducer | 24 | King | 4.0E+04 | 4.0E+04 | Water | Rms | Uniform flow | 25 | Macovsky (1958) | 2.0E+04 | 8.0E+04 | Water | Peak | Force measurements | 26 | Macovsky (1958) | 3.7E+04 | 1.1E+05 | Water | Mean peak | Force measurements | 27 | McGregor (1957) | 4.0E+04 | 1.8E+05 | Air | Rms/mean peak | Top curve (mean peak), uniform flow, pressure measurements/integration | 28 | Moeller - Lechey | 1.9E+04 | 1.9E+04 | Water | Rms | Force measurements, rigid cylinder, U/D=28 | 29 | Phillips (1956) | 3.0E+01 | 2.0E+02 | Air | Mean peak | Uniform flow, questionable data points (from Y.N. Chenpaper) | 30 | Protos et al. (1968) | 4.5E+04 | 4.5E+04 | Water | Rms | Uniform flow, cantilever piercing free surface, L/D=6.5 | 31 | Rajaona - Sulmont | 3.0E+04 | 1.8E+05 | Water | Peak | Towed, fixed cylinder, force measurements, L/D=2.5 | 32 | Rajaona - Sulmont | 3.0E+04 | 1.8E+05 | Water | Rms | Towed, fixed cylinder, force measurements, L/D=2.5 | 33 | Rodenbusch et. Al. (Shell) | 2.0E+05 | 2.2E+06 | Water | Peak | Steady tow, smooth flow, strain gages, L/D=2.8, 1 (instrumented section) rigid cylinder, uniform flow | 34 | Ruedy | 1.0E+05 | 1.0E+05 | Air | Rms | Eigid cylinder, uniform flow | 35 | Sallet | 1.0E+02 | 1.0E+06 | Air | Peak | Theory, based on wind stationary pressure tap measurements | 36 | Schewe (1983) | 1.0E+04 | 8.0E+06 | Air | Rms | Force measurements, clamped ends, L/D=10 | 37 | Schmidt et al. (1966) | 1.0E+05 | 1.0E+07 | Air | Rms | CL0 related to infinitely thin strip pressure measurements/integration | 38 | Schmidt (1965-66) | 3.0E+05 | 7.0E+06 | Air | Rms | Uniform flow | 39 | Schwabe (1935) | 7.0E+02 | 7.0E+02 | Water | Mean peak | Uniform flow with turbulence, pressure measurements, (calculations) | 40 | Sonneville | 1.0E+04 | 3.0E+04 | Water | Mean peak | Uniform flow | 41 | Surry | 5.0E+04 | 5.0E+04 | Air | Rms | Rigid cylinder, turbulent flow | 42 | Vickery - Watkins (1962) | 4.0E+04 | 1.8E+05 | Air/water | Rms | Stationary and oscillating cylinder data | 43 | Vickery – Watkins | 1.0E+04 | 1.0E+04 | Air | Rms | Rigid cylinder, pivoted ends | 45 | Weaver (1961) | 7.0E+04 | 3.0E+05 | Air | Peak | Rigid cylinder, lu=0.5%, uniform flow, force measurements, L/D=10-15 | 46 | Whitney et al. | 1.0E+02 | 2.0E+07 | Air | Rms | Based o air stationary experiments, uniform flow (calculations) | 47 | Woodruff - Kozak | 2.0E+05 | 2.0E+05 | Air | Rms | Uniform flow |
Table 1: Compilation of Lift Coefficient from Stationary Cylinder Data[3]
Figure 2.11: Lift Coefficient Data for Stationary Cylinders[3]
2.7. Drag Fore
Drag force is another force component that acting in parallel direction on the cylinder in cross flow. Drag is the only force component that acts on a cylinder below Re=40 because all flows in that regime are symmetrical with respect to the direction of flow. Drag force normally expressed in terms of lift coefficient:
CD= FD12ρAV2 where FD is the time-average of the drag force, FD(t), ρ is the density of the fluid and A is the projected area that the cylinder presents to the flow.[10]
The drag force, FD is equal to the sum of two different kinds of force. The first is pressure drag:
FDP = A1psin∝dA where FDP is the pressure at any point on the surface of the body and ∝ is the angle between the forward stagnation streamline and a vector normal to the surface.[10]
The second component is frictional drag:
FDf = A1τ0cos∝dA where τ0 is the viscous shear stress at the surface.[10]
At very low Reynolds number (Re<5), drag will consist almost entirely of FDf . When vortices form, the pressure distribution will become more severe from the forward to the aft stagnation point and eventually it will become asymmetrical with respect to the direction of flow. As the oscillating lift force appears, FDf gradually becomes negligible in comparison with FDp .[10]
Curve | # Authors | Low Re | High Re | Medium | Cylinder | Comments | 1 | Relf – Simmons | 1.0E+02 | 2.0E+06 | Air | S | Uniform flow, based on experiments by Wieseelbrger | 2 | Sallet | 1.0E+02 | 2.0E+06 | Air | S | Uniform flow | 3 | Schewe | 1.0E+04 | 7.0E+05 | Air | S | Rigid cylinder, dampened | 4 | Kwok | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow, clamped – clamped | 5 | Achenbach | 8.4E+01 | 8.0E+05 | Air | S | Smooth, uniform flow | 6 | Rodenbusch – Gutierrez | 1.8E+05 | 3.0E+06 | Water | S | Shell experiments, uniform flow, 0.02 roughness | 7 | Farell – Blesmann | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow | 8 | Cheung – Melbourne | 8.0E+04 | 8.0E+05 | Air | S | Smooth, uniform flow, pressure taps | 9 | NPL | 8.0E+04 | 5.0E+05 | | | Based on compiled data | 10 | Rodenbusch - Gutierrez | 1.8E+05 | 3.0E+06 | Water | S | Shell experiments, uniform flow, 0.02 roughness | 11 | Guven et al. | 2.0E+05 | 9.0E+05 | Water | S | Smooth, uniform flow | 12 | Rodenbusch – Gutierrez | 2.0E+05 | 9.0E+05 | Water | S | Shell experiments, uniform flow, smooth cylinder | 13 | Schmidt | 1.0E+06 | 6.0E+06 | Air | S | Polished surface | 14 | Jones | 5.0E+05 | 1.0E+07 | Air | S | Smooth | 15 | Rajaona – Sulmoni | 2.0E+06 | 9.0E+06 | Water | O | Forced oscillations, uniform flow, towed | 16 | Roshko | 2.0E+06 | 8.0E+06 | Air | S | Roughness = 0.0002, uniform flow |
* S = Stationary, O = Oscillating
Table 2: Compilation Drag Coefficient Data versus Reynolds Number[3]
Figure 2.13: Drag Coefficient Results for Circular Cylinders[3]
2.8. Lock-In
The presence of vibration frequency component is main factor to disrupt the lock-in or wake synchronization process. In different regions, different modes may be resonantly excited and because of shear, the shedding frequency may vary along the length. It has been experimentally demonstrated that multiple frequency components may disrupt the local, lock-in process. Thus, if one mode has been sufficient vibration energy it may prevent competing mode with lower response levels from developing wake-synchronized power-in regions.[11]
It is also known that lock-in is a very nonlinear phenomenon. If one mode is able to achieve sufficient response amplitude, then wake synchronization for other modes may be suppressed, even in regions of the cable which would appear to favor lock-in with those modes.[11]
For flow past cylinders that are free to vibrate, the phenomenon of synchronization or lock-in is observed. For low flow speeds, the vortex shedding frequency fs will be the same as that of a fixed cylinder. This frequency is fixed by Strouhal number. As the flow speed is increased, the shedding frequency approaches the vibration frequency of the cylinder fo. In this regime of flow speeds, the vortex-shedding frequency no longer follows the Strouhal relationship. Rather, the shedding frequency becomes “lock-in” to the oscillation frequency of the cylinder (i.e., fo≈ fs ). If the vortex-shedding frequency is close to the natural frequency of the cylinder fn, as is often the case, the large body motions are observed within the lock-in regime (the structure undergoes near resonance vibration).[12]
During lock-in, amplitudes of cross-flow oscillation increased markedly. The largest steady-state values correspond to peak-to-peak oscillation amplitudes of approximately 0.9D (standard deviation values of y/D are presented in Figure 2.11. The lack of exact coincidence of fo with fn during lock-in can be accounted for by a phase difference between cylinder motion and lift forces, which is known to be a function of fn/fv .[13]
Figure 2.11: Cylinder response diagram. Values along the abscissa represent the ratio of cylinder in vacuo natural frequency fn to Strouhal frequency for the fixed cylinder fv. (□) Ratio of fluctuating lift coefficients C’1/C’10; (○) ratio of mean drag coefficients Cd/Cd0; (∆) ratio of oscillation frequency to fixed-cylinder Strouhal frequency fo/fv; (−) standard deviation of cylinder cross-flow response amplitude y’/D. Shaded region indicates chaotic regime.[13]
But in later works in low mass-damping ratio, Williamson and Khalak found new branch of response, they observed that during lock-in, the ratio of two frequencies wouldn’t remain equal to unit and these frequencies match with each other near other values like 1.4. Their studies showed that the behavior of frequencies changes in different mass-damping ratios.[12]
Generally, the lock-in can be identified by using Kurtosis. Typical drilling riser response measurements are from instruments strapped to the riser at several different positions. Assume that x(t) is a zero mean, measured time series of transverse acceleration response, resulting from VIV. The kurtosis of x(t) is given by: kurtosis=x4x22 , where = time average
Kurtosis is normally used to quantify deviation from Gaussian behavior. Zero mean Gaussian processes have a kurtosis of 3.0. Multiple frequency VIV response is often Gaussian in behavior, and tends to have kurtosis values of approximately 3. The occasional occurrence of a single frequency, lock-in event is characterized by steady sinusoidal behavior. When x(t) sin(t) , the kurtosis takes on the value of 1.5.[14]
Figure 2.12 presents shedding frequency fs versus cylinder oscilating frequency fc normalized by the shedding frequncy of the stationary cylinder fo. The ordinate of each point is the ratio of shedding frequency of the oscilating cylinder to that of a stationary cylinder. Where the ordinate is 1.0, there is no differece . where the ordinate is less than 1.0, shedding on the oscilating cylinder occurs at lower frequency than that of a stationary cylinder under comparable flow conditions.[3]
The slope of the line in figure 2.12 represents change in shedding freqency with change in cylinder frequency. Note that the curve is generally flat (zero slope), but there are two areas with positive slope. The first occurs when the cylinder frequency is nearly equal to the nominal shedding frequency of a stationary cylinder (abscissa equal to 1.0), which as discussed above is an area characterized by significant organization of the wake into correlated, consistent vortex cells. The slope here is unity, indicating that the shedding frequency is equal to the cylinder frequency over a range of cylinder frequencies. The second occurs when the abscissa near 2.0, with a slope of 0.33. In the range, the shedding frequency is equal to 1/3 of the cylinder, over a range of cylinder frequencies.[3]
The explanation for this behavior is that the motion of the cylinder organizes the wake and causes the shedding frequency to abruptly jump from its nominal value fs yo a value equal to the oscillation frequency fc. At some point the shedding frequency reverts back to a constant frequency that is generally lower than of a stationary cylinder. When the cylinder motion controls the shedding frequency in this way, the frequency is said to be lock-in, locked on, or synchronized to the cylinder frequency.[3]
Figure 2.13: Frequency and amplitude response in the lock-in regime[15]
Two regions can be distinguished in the lock-in region (5 < Ur < 8):[15] * fs < fn. The vortex shedding frequency is lower than the natural frequency. The added mass coefficient in this regime is usually larger than 1. The lock-in results in a downward shift of the natural frequency, thereby adapting the natural frequency to the vortex shedding frequency. * fs > fn. The vortex shedding frequency is higher than the natural frequency. The added mass coefficient is usually smaller than 1. The lock-in results in a downward shift of the vortex shedding frequency. The vortex shedding frequency now adapts to the natural frequency.
Outside the lock-in regime (Ur < 5 or Ur > 8) the response follows the vortex shedding frequency, but the response is very small. Often a figure-of-eight type response is found for 2 degrees of freedom pipe motions.[15]
Generally there are some observations from most of the experiment:[3] * Lock-in can occur at the frequency of cylinder motion or at sub-harmonics of the cylinder motion, in either uniform or shear flow * Shedding behavior at the edges of the lock-in frequency range is similar for uniform and shear flow * The minimum amplitude required for initiating lock-in may increase with increasing Reynolds number * The frequency range within the shedding will lock-in to cylinder motion seems to narrow with increasing Reynolds number * At the edges of the frequency range where lock-in to the primary cylinder frequency is observed, shedding varies intermittently between the nominal frequency and the cylinder frequency
Lock-in VIV has been widely explored, and it is known to be associated with:[15] * increase of the correlation length, * increase of vortex strength, * increase of response bandwidth, * self-limiting nature at approximately 1 diameter, * increase of the in-line drag.
2.9. Inline and cross line flow
As fluid particles move close to the surface of a cylinder, vortices are shed from the structure at the separation point. Typically, the shedding process gives a vortex pattern in which the in-line excitation frequency is twice that in the cross-flow direction.[16]
Most experimental data today are based on 2D vortex induced vibrations, which means that the coupling between in-line and cross flow vibrations is not considered. These results have generally shown that amplitudes of in-line response are much lower than amplitudes in the transverse direction.[16]
These results have generally shown that amplitudes of in-line response are much lower than amplitudes in the transverse direction. Typical values for the maximum in-line VIV response are about 20 per cent of the cross-flow response. The in-line response of a pipeline span in current dominated conditions for 1.0 < UR < 4.5 is associated with either alternating or symmetric vortex shedding.[17]
Figure2.5: Vortex shedding
Symmetric vortices are shed when UR is between 1.0 and 2.2. When UR exceeds 2.2, vortices are shed alternately. This means that the oscillations depend on the vortex pattern which develops. The cross-flow natural frequency is used as reference frequency also for in-line response. Hence, the in-line curves are plotted for different frequency ratios Rf=0.5, 1.0, 1.5 and 2.0 according to the frequency ratios applied in the experiments. [17]
Diagram: In-line and cross-flow for varies reduced velocity UR and reduced amplitude A/D.
2.10. End Effects
A three-dimensional (3-D) finite cylinder in a cross-flow is one of the most basic and revealing cases in the general subject of fluid–structure interactions. Structural vibration strongly depends on the magnitude and distribution of the unsteady flow-induced forces along the span. Numerous experimental investigations have been carried out on this problem. Important findings and understanding have been achieved on the flow-induced forces, such as their variations with Reynolds numbers and free stream turbulence, and their dependence on the aspect ratio a ¼ L=D of the bluff body; and on the 3-D nature of the wake flow, such as oblique and parallel vortex shedding patterns, cellular shedding and associated vortex dislocations; and different instability modes. Here, L is the span and D is the diameter of the cylinder. Some studies generally agree that the cylinder wake is 2-D at Re ¼ U1D=n ¼, where Re is the Reynolds number, U1 is the free-stream velocity, and n is the fluid kinematic viscosity. Even in experimental visualization, three dimensionality cannot be identified for Re<15. However, in recent studies, it has been found that end conditions have a significant influence on vortex formation and their shedding from the bluff body, and on the 3-D nature of the wake flow.[18]
Generally, two methods commonly used to ensure two-dimensional flow conditions: 1)providing sufficiently long cylinders (where the force/pressure measurements are taken far from the ends) and 2) the addition of end plates to suppress the wrapping of vortices along the cylinder length.[3]
Figure 2.7: End effects on vortex shedding frequency[3]
Gouda (1975) presented the results of wind tunnel tests with cylinders of varying length, with and without end plates. The variation of vortex shedding frequency with cylinder length is illustrated in Figure 3.2. Shedding frequency is consistently lower for cylinders with three-dimensional flow effects than for cylinders with end plates except for L/D>50; for cylinders of L/D=15 the shedding frequency is 35% lower than for the infinite cylinder case. He proposed an aspect ratio of L/D=45 for no end effects without end plates. Griffin (1985) suggested conducting experiments with cylinders of sufficient length to minimize the effects of the end boundaries (length/diameter, L/D=100-120).[3]
Gouda also investigated the effects of end plate size on vortex shedding frequency and showed that for a cylinder of L/D=18, the diameter of the end plate should be at least 10D (D=cylinder diameter) to avoid all end effects.[3]
2.11. Cylinder motion (Free Oscillating)
Diagram: Sketches of force component in oscillating cylinder
For free oscillating cylinder, there are three frequencies involved[19]: * The still water eigenfrequency fo=12πkm+mao where k is the spring stiffness, m is the mass of the cylinder and mao is the added (or hydrodynamic) mass in still water
* The vortex shedding frequency fs=St∙UD where U is the flow speed, St is the Strouhal number, which is close to 0.2 in the sub-critical flow regime.
* The oscillating frequency fosc=12πkm+ma where ma is the added mass valid for the actual flow and oscillation condition.
Research Methodology (1st Draft) 3.1. Introduction
The aim of this study is to investigate the basic principles of Vortex Induced Vibration and Vortex Induced Moment and relevant parameters on circular cylinder. For this purpose, a model design and simulation was developed in (CFD) ANSYS Fluent.
ANSYS FLUENT software contains the broad physical modeling capabilities needed to model flow, turbulence, heat transfer, and reactions for industrial applications ranging from air flow over an aircraft wing to combustion in a furnace, from bubble columns to oil platforms, from blood flow to semiconductor manufacturing, and from clean room design to wastewater treatment plants. Special models that give the software the ability to model in-cylinder combustion, aero acoustics, turbo machinery, and multiphase systems have served to broaden its reach.[20]
In chapter 2, literature studies have discussed the primary parameters to analysis the Vortex Induced Motion. In this chapter, a research methodology with Computational Fluid Dynamics (CFD) method by using ANSYS Fluent is mentioned and described.
3.2. Model’s Particular Dimensions
Particular | Model | Diameter | 0.4m | Length | 1.55m | Thickness | 0.05m |
3.3. Progress Management
In conducting this methodology for model design and simulation, a procedure plan is developed to ensure the successfulness of the methodology. For this purpose, the ANYSY Workbench v14.0 is involved to manage the flow of methodology.
ANYSY Workbench is the framework upon which the industry’s broadest suite of advanced engineering simulation technology is built. An innovative project schematic view ties together the entire simulation process, guiding the user every step of the way. Even complex multi physics analyses can be performed with drag-and-drop simplicity. With bidirectional CAD connectivity, an automated project update mechanism, pervasive parameter management and integrated optimization tools, the ANSYS Workbench platform delivers unprecedented productivity that truly enables Simulation Driven Product Development.[21]
The whole simulation process is started with selecting the project system. The desired analysis system, Fluid Flow (FLUENT) is selected from the toolbox at left and it will show its progress steps in the project schematic. Complete analysis systems contain all of the necessary components as guidance through analysis process to work through the system from top to bottom.
The analysis process begin with the geometry design, followed by meshing, then problem, solution setup and finally results. For completed design or setting in each step, the software will update the information to workbench, then workbench will lead the process to next step.
3.4. Geometry Design
In Geometry Design stage, two design steps are involved which design modeling and enclosure space development. Geometry design is conducted under software named ANSYS DesignModeler.
3.5.1. Design Modeling
The design modeling started with sketching a circle with diameter, D = 0.4m and at ZX plane. The circle is then extruded about 1.5m to make it as a cylinder.
3.5.2. Enclosure Space Development
After the modeling completed, an enclosure space is developed to enclosing the meshing developing, it means that the meshing will only developed in the specified space. The meshing inside the enclosure space will input with fluid flow medium in the setup setting stage. During the simulation, the fluid flow will only present inside the enclosure space.
The enclosure dimensioning is automatically set the cylinder as reference object. Enclosure dimension is offset from the cylinder surface and enclosure surface cannot contact with the cylinder. The enclosure dimensions are set as table below: Enclosure Dimensions | Magnitude (m) | +X value | 1 | +Y value | 0.01 | +Z value | 1 | -X value | 1 | -Y value | 0.01 | -Z value | 5 |
Both +Y value and –Y value are set as 0.01m to prevent any end plate effect during the simulations. –Z value set as 5m as it prevents backflow effects and provides enough space for Vortex Induced Motion analysis especially for the shedding pattern.
In the enclosure space, the cylinder space needs to subtract to ensure the meshing will exclude the cylinder space. In order to accomplish that, Boolean is created with subtract operation and the cylinder is selected. After the subtraction is done, the space consumed by the cylinder will become hollow. As result, no fluid flow will generate inside the cylinder.
3.5. Meshing
After the geometry design is completed, the workbench will lead the process to mesh development. In this stage, the involved software is ANSYS ICEM CFD. ANSYS ICEM CFD offer the capability to parametrically create volume or surface meshes from geometry or mesh in multi-block structured, unstructured hexahedral, Cartesian, tetrahedral, tetra/prism hybrid, hex hybrid and unstructured quad/tri shell formats.[22]
3.6.3. Mesh Control
Mesh control is important to determine the quality of meshing and the accuracy of the results. Mesh control in ANSYS ICEM CFD is consists of several settings and inputs in controlling the meshing smoothness, mesh sizing, suppression effects etc. 3.6.4.1. Physics Based Setting
Different types of analysis require different meshing properties. In this study, fluid flow analysis involved, the meshing requirements is finer, smoothly varying mesh, boundary layer resolution. To fulfill these requirements, first the physics preference option is chosen as CFD. The physics preference will auto fulfill the majority of the requirements in mesh settings. 3.6.4.2. Relevance Center * Function : Control the smoothness of the meshing, further affects the quality of meshing * Default : Coarse (Lowest smoothness) * Selected : Fine (Highest smoothness)
3.6.4.3. Initial Size Seed * Function : Control the initial mesh seeding for each part * Default: Active Assembly (The mesh could change as part are suppressed or unsuppressed) * Selected : Full Assembly (The mesh never changes due to the part suppression) 3.6.4.4. Smoothing * Function : Improve element quality by moving locations of nodes with respect to surrounding nodes and elements * Selected : Medium (Medium number of smoothing iterations along with the threshold metric) 3.6.4.5. Transition * Function : Control the rate at which adjacent elements will grow * Selected : Slow (Produces a smooth transition)
3.6.4.6. Span Center Angle * Function : Sets the goal for curvature based refinement for edges * Selected : Fine (The mesh will subdivide in curved regions until the individual elements span between 36o to 12o) 3.6.4.7. Growth Rate
Growth rate can be assumed as the sizing of the meshing. The value of growth rate is decreasing for each simulation until obtain consistence results.
3.6.4. Component Grouping
In the system, different position of the components will have different function and different settings in the Boundary Conditioning. For this purpose, all the components like surface of enclosure box and cylinder is group into different category according to their position. These groups are defined as boundary zone. Boundaries are inlet, outlet, wall and cylinder. All this setups are the preparation in preprocessing phase. 3.6.5.8. Inlet * Components : Enclosure surface +Z * Function : As the inlet surface for fluid flow to enter the enclosure space
3.6.5.9. Outlet * Components : Enclosure surface –Z * Function : As the outlet surface for fluid flow to exit the enclosure space
3.6.5.10. Wall * Components : Enclosure surface +X, -X, +Y, -Y * Function : To bounder the fluid flow in the designed space
3.6.5.11. Cylinder * Components : Hollow with cylinder shape * Function : To experience the forces generated by fluid flow on the cylinder
3.6. Problem Setup
Problem setup is the setup step for flow condition and properties setting before compute the simulation. ANSYS Fluent will be involved for setup setting, simulations and results.
3.7.5. Turbulence Modeling
The first step in setup setting is to determine the turbulence modeling. Turbulence is an inherently unsteady, three dimensional and periodic swirling motions (fluctuations). The instantaneous are random in space and time, in addition, vortices and eddies always exist in the turbulence flows.
In ANSYSY Fluent, RNG k-ɛ and Realizable k-ɛ are the model specialized for simulation involved vortices shedding. The applications and usage of both model is similar. But in term of accuracy and converge, Realizable k-ɛ will shows better performance.
Realizable k-ɛ allows mathematical constraints to be obeyed which ultimately improve the performance of the model. For this purpose, Realizable k-ɛ is selected as the turbulent model.
3.7.6. Mesh Material Design
Mesh material is determined based on type of analysis. For this fluid flow analysis, the mesh material is water liquid with density, 998.2 kgm-3, specific heat, 4182j/kg-k, thermal conductivity, 0.6 w/m-k and viscosity, 0.001003 kg/m-s.
3.7.7. Boundary Conditioning
Boundary conditioning is the information specified process on the variables flow at the boundary which is necessary to obtain an accurate solution. Defining the boundary condition involves identifying the boundary location which is done in the preprocessing phase, and supplying the boundary information. 3.7.8.12. Inlet
Velocity specification method is applied for Inlet boundary condition. Velocity specification method will apply a uniform velocity profile at the boundary and is intended for use in incompressible flows.
In this case, the velocity specification is applied as magnitude, normal to boundary. The velocity magnitude is equal to 2ms-1. For turbulence specification method, intensity and viscosity ratio is selected. 3.7.8.13. Outlet
Pressure Outlet is the only mode of boundary condition for outlet boundary. Input requirements for Pressure Outlet are leave as default but the gauge pressure needs to be zero. 3.7.8.14. Wall
For wall boundary setting, the setup only done on defining the wall boundary to symmetry boundary, then ANSYS Fluent will generate the input for wall boundary. 3.7.8.15. Cylinder
In the boundary conditioning for cylinder, the cylinder is assume as no movements and rotations. For this reason, all the movement and rotation are null. 3.7.8. References Value Setup
Basically ANSYS Fluent will input the value from the setup done from the previous phase. The optional inputs are the flow direction and contact area. The inlet boundary is selected as flow direction and the area contact is equal to cylinder diameter multiple with cylinder height, 0.62m2.
3.7. Solution Setup
3.8.9. Output parameter determination
In solution setup, the output parameter can be determined in monitor option. In this simulation, lift force and drag force are decided to become the output parameter with print to console function and plot function for graph displaying.
3.8.10. Solution initialization
Solution initialization is the conclusion step to all the set up and design done. In solution initialization, ANSYS Fluent will ensure all the require input are inserted and it will input them into the calculation. 3.8.11. Run calculation
Deciding the number of iterations is the final step before compute the simulation. The accuracy of result depended on the number of iterations. In this study, at the specified growth rate of meshing, the number of iterations will start with 100000 times and increase 50000 times for every following simulations.
1. Sundén, B. Tubes, Crossflow over. Fluid Flow Fundamentals - External Flows 2011 16 March 2011 2 February 2011]; Available from: http://www.thermopedia.com/content/1216/?tid=104&sn=1410.
2. Sundén, B. Vortex Shedding. Fluid Flow Fundamentals - External Flows 2011 16 March 2011 [cited 2011 2 February 2011]; Available from: http://www.thermopedia.com/content/1247/?tid=104&sn=1410.
3. Pantazopoulos, M.S., Vortex-Induced Vibration Parameters: Critical Review. Offshore Technology, ASME OMAE 1994, 1994. Vol. 1 & 2: p. 199 - 255.
4. Blevins, R.D., Flow Induced Vibration, 2nd Edition, 1990, Van Nostrand Reinhold Co.
5. W., B.P., On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number Regime. Fluid Mechanics, 1969. Vlo. 37: p. 577-586.
6. O. M. Griffin, S.E.R., Some Recent Studies of Vortex Shedding with Application to Marine Tubulars and Risers. Journal of Energy Resources Technology, 1982. Vol. 104: p. 2-13.
7. D. Lucor, J.F., G.E. Karniadakis, Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping. Journal of Fluids and Structures, 2005. Vol. 20: p. 483-503.
8. H. M. Blackburn, R.N.G., D C. H. K. Williamson, A complementary numerical and physical investigation of vortex-induced vibration. Journal of Fluids and Structures, 2000. Vol. 15: p. 481-488.
9. Schewe, G., Reynolds-Number-Effects in Flow around a rectangular Cylinder with Aspect Ratio 1:5, in European-African Conference on Wind Engineering (EACWE) 52009, Institut für Aeroelastik: Florence, Italy.
10. Lienhard, J.H., SYNOPSIS OF LIFT, DRAG, AND VORTEX FREQUENCY DATA FOR RIGID CIRCULAR CYLINDERS. BULLETIN 300, 1966: p. 1 - 32.
11. J.K. Vandiver, D.A., L. Li, The Occurrence Of Lock-In Under Highly Sheared Conditions. Journal of Fluids and Structures, 1996. Vol. 10: p. 555-561.
12. A. Farshidianfar, H.Z., The Lock-in Phenomenon in VIV using A Modified Wake Oscillator Model for both High and Low Mass-Damping Ratio. Iranian Journal of Mechanical Engineering, 2009. Vol. 10: p. 6-28.
13. Hugh Blackburn, R.H., Lock-In Behavior in Simulated Vortex-Induced Vibration. Experimental Thermal and Fluid Science 1996, 1995. Vol. 12: p. 184-189.
14. Vandiver, J.K., Predicting Lock-in on Drilling Risers in Sheared Flows, in Proceedings of the Flow-Induced Vibration 2000 Conference2000: Lucerne, Switzerland.
15. Jaap de Wilde, A.S.a.H.C., N. Willis and C. Bridge, Cross Section VIV Model Test For Novel Riser Geometries, in DOT Conference2004: New Orleans. p. 1-19.
16. Søreide, M. Experimental Investigation of In-line and Cross-flow VIV. in Proceedings of The Thirteenth (2003) International Offshore and Polar Engineering Conference. 2003. Honolulu, Hawaii, USA: The International Society of Offshore and Polar Engineers.
17. Veritas, D.N., Free spanning pipelines, in DNV-RP-F1052002: Norway.
18. R.M.C. So, Y.L., Z.X. Cui, C.H. Zhang, X.Q. Wang, Three-dimensional wake effects on flow-induced force. Journal of Fluids and Structures, 2005. Vol. 20: p. 373-402.
19. Larsem, C.M., Vortex Induced Vibrations - A Short and Incomplete Introduction to Fundamental Concepts, D.o.M. Tachnology, Editor 2006, NTNU: Trondheim, Norway.
20. ANSYS, I., ANSYS FLUENT Tutorial Guide. Vol. Release 14.0. 2011, Canonsburg, PA 15317: ANSYS, Inc.
21. ANSYS, I., ANSYS Workbench Platform. ANSYS WORKBENCH Manual, 2009. Release 12.1: p. 1 - 4.
22. ANSYS, I., ANSYS ICEM CFD. ANSYS ICEM CFD Introduction, 2009. Release 13.0: p. 1 - 2.
References: 3. Pantazopoulos, M.S., Vortex-Induced Vibration Parameters: Critical Review. Offshore Technology, ASME OMAE 1994, 1994. Vol. 1 & 2: p. 199 - 255. 4. Blevins, R.D., Flow Induced Vibration, 2nd Edition, 1990, Van Nostrand Reinhold Co. 5. W., B.P., On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number Regime. Fluid Mechanics, 1969. Vlo. 37: p. 577-586. 6. O. M. Griffin, S.E.R., Some Recent Studies of Vortex Shedding with Application to Marine Tubulars and Risers. Journal of Energy Resources Technology, 1982. Vol. 104: p. 2-13. 7. D. Lucor, J.F., G.E. Karniadakis, Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping. Journal of Fluids and Structures, 2005. Vol. 20: p. 483-503. 8. H. M. Blackburn, R.N.G., D C. H. K. Williamson, A complementary numerical and physical investigation of vortex-induced vibration. Journal of Fluids and Structures, 2000. Vol. 15: p. 481-488. 10. Lienhard, J.H., SYNOPSIS OF LIFT, DRAG, AND VORTEX FREQUENCY DATA FOR RIGID CIRCULAR CYLINDERS. BULLETIN 300, 1966: p. 1 - 32. 11. J.K. Vandiver, D.A., L. Li, The Occurrence Of Lock-In Under Highly Sheared Conditions. Journal of Fluids and Structures, 1996. Vol. 10: p. 555-561. 12. A. Farshidianfar, H.Z., The Lock-in Phenomenon in VIV using A Modified Wake Oscillator Model for both High and Low Mass-Damping Ratio. Iranian Journal of Mechanical Engineering, 2009. Vol. 10: p. 6-28. 13. Hugh Blackburn, R.H., Lock-In Behavior in Simulated Vortex-Induced Vibration. Experimental Thermal and Fluid Science 1996, 1995. Vol. 12: p. 184-189. 18. R.M.C. So, Y.L., Z.X. Cui, C.H. Zhang, X.Q. Wang, Three-dimensional wake effects on flow-induced force. Journal of Fluids and Structures, 2005. Vol. 20: p. 373-402. 20. ANSYS, I., ANSYS FLUENT Tutorial Guide. Vol. Release 14.0. 2011, Canonsburg, PA 15317: ANSYS, Inc. 21. ANSYS, I., ANSYS Workbench Platform. ANSYS WORKBENCH Manual, 2009. Release 12.1: p. 1 - 4. 22. ANSYS, I., ANSYS ICEM CFD. ANSYS ICEM CFD Introduction, 2009. Release 13.0: p. 1 - 2.
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