VIV is an important issue in the design of riser, umbilical, and dynamic power cable due to periodic vortex shedding, which causes fatigue damage on the structures. When currents exceed a certain velocity, the vortex shedding occurs on the back of the structures due to the drastic change in the gradient, leading to cyclical loadings and the occurrence of VIV through mutual interaction between the structure and vortex shedding. In particular, when the frequency of vortex shedding approaches the natural frequency of the cable, resonance can occur, resulting in large displacement oscillations known as “lock-in”. To fully develop dynamic power cables, it is necessary to assess fatigue life through VIV fatigue analysis, considering the environmental conditions measured on-site. Based on the results of VIV fatigue assessments, additional suppression systems such as strakes or fairings can be implemented for the cable.

This section provides a comprehensive overview of the research studies conducted on VIV. Wu et al. (2009) introduced a technique to derive VIV forces from collected data obtained from lengthy elastic riser models under the influence of current. Their method specifically focused on determining the first-order cross-flow force coefficients.

Soni and Larsen (2009) conducted an investigation on how to determine the hydrodynamic coefficients induced by the combined feasible motions of cross-flow and in-line flow. They extracted the force elements of higher order harmonics for each motion path, considering a combination of vortex shedding types and higher order harmonics. Zheng et al. (2011) estimated the vibrations of marine risers in the cross-flow direction under random currents using a specific program designed for VIV evaluations. They demonstrated that the insufficient number of nodes in the response of the marine risers can be attributed to a combination of standing waves and traveling waves along the length of the risers. Unlike VIV models that operate in the frequency domain, a time domain model offers the advantage of capturing the interactions between in-line and cross-flow vibrations, higher-order frequency components, structural nonlinearities, as well as simultaneous effects from other loads such as waves and imposed motions at boundaries (Maincon and Larsen, 2011). Schiller et al. (2014) provided evidence that various attributes of the current profile, including shear (du/dz), velocity (u), and direction (θ), significantly influence the development of VIV in riser models. Specifically, more intricate current profiles exhibit a discernible impact on the characteristics and stochastic behavior of VIV. Passano et al. (2016) introduced a methodology for conducting a VIV analysis of an umbilical, specifically focusing on the inclusion of slip damping. The authors presented techniques for estimating both material damping and slip damping. The findings of a case study demonstrated that the VIV response is highly sensitive to the level of damping. Pagnini et al. (2020) examined technical aspects related to VIV of structures subjected to wind excitation, specifically focusing on the spectral model commonly utilized in various codes and guidelines. The researchers highlighted that an analytical solution enables straightforward assessments, incorporating operational criteria to accurately account for both structural and flow conditions.

Experimental studies on VIV and cables have also been conducted, and some of the notable studies in this field are presented hereafter. Passano et al. (2010) conducted a comparison between VIV predictions obtained from a semi-empirical program and experimental data collected from a free span pipeline. They utilized a long elastic pipe model for their analysis, considering both combined cross-flow and in-line loading. The results indicated that the response estimates obtained from the program aligned well with the experimental data. Fu et al. (2013) conducted experimental investigations on VIV in oscillatory flow within an ocean basin. The findings revealed distinct differences between VIV in oscillatory flow compared to steady flow. Specifically, as the maximum shedding frequency increased, the lock-in region exhibited a more broad region. Additionally, cases with larger KC (Keulegan-Carpenter) numbers tended to show a pure lock-in phenomenon. According to Rao et al. (2013), an examination of VIV excitation competition between bare and buoyant segments of flexible cylinders demonstrated that the excitation occurring on the buoyant regions largely influences the VIV response across various buoyancy configurations. Wu et al. (2017) conducted experiments to acquire hydrodynamic data for a riser equipped with staggered buoyancy elements. The aim was to investigate the interaction between these buoyancy elements and the bare riser section. The findings demonstrated that this interaction had notable effects on the VIV responses and force coefficients. The extent of these influences was found to depend on the dimensions of the buoyancy element and its arrangement within the riser. Shim et al. (2021) performed physical tests to evaluate the endurance of dynamic power cables in operational environments and developed relevant testing techniques for this purpose. Wu et al. (2021) introduced a thorough experimental model that was conducted in a towing tank. The objective of the study was to investigate the hydrodynamics and motion characteristics of a tunnel-pontoon system. Kim and Rheem (2009) investigated the cross-flow VIV response in the presence of local shear flow. They confirmed the presence of common VIV characteristics, such as lock-in phenomena, through experiments conducted in uniform flow conditions.

Studies on VIV fatigue have been conducted as follows. Jhingran et al. (2007) validated the significance of higher harmonics in estimating the fatigue life of pipes. They developed an approach to incorporate these higher harmonics into fatigue design related to VIV. The multi-mode solution, depending on the fluid riser parameters, offered valuable insights into the VIV characteristics of catenary risers. Notably, as the flow velocity increases, the presence of multiple internal resonances between higher and lower modes becomes significant. This behavior is attributed to geometric nonlinearities and cannot be captured by a linear structural model (Srinil et al., 2009). Researchers have shown great interest in obtaining information on the forces involved in VIV experiments with long elastic cylinders. This interest arises from the challenges associated with directly measuring these forces during such experiments. Marcollo et al. (2011) made meaningful contributions to the study of the occurrence and predominance of traveling wave VIV response in full-scale drilling risers. Their research revealed that fatigue damage in the drilling riser is more uniformly distributed in the upper region where traveling waves dominate, contrary to the predictions made by the classical normal mode assumption. Sodahl et al. (2011) highlighted the importance of including fatigue stress calculation and evaluating equivalent modal damping in the VIV analysis, particularly concerning the stick/slip mechanism of the helix elements in bending. These elements play crucial roles in accurately assessing the effects of VIV and ensuring the reliability of the analysis. Zhang et al. (2020) proposed the inclusion of floating body movement in the assessment of VIV of risers. They emphasized that considering the combined effect of the top-end surge caused by the movement of the floating body and the background flow is crucial for understanding the high-order harmonics of VIV frequency and the amplification of VIV amplitude at specific reduced velocities. This phenomenon has the potential to induce additional fatigue damage to the riser. Lekkala et al. (2022) performed a VIV fatigue damage analysis to examine the influence of higher harmonics. The findings revealed that higher harmonic correction factors significantly affect the performance of the riser. This suggests that considering the contribution of higher harmonics is crucial for accurate assessment and prediction of fatigue damage in VIV analysis.

As VIV fatigue analysis is still a developing research field, extensive experience and the establishment of a reliable procedure for VIV fatigue analysis are essential, particularly for dynamic power cables, which are helically wound long flexible structures consisting of various components. For these structures, stick/slip phenomenon between layers due to the tension or the compression loaded by environmental conditions, contact forces between layers, torsional moment & axial force for individual layers, and bending stiffness and curvature of whole cross-section are all must be taken into consideration. In this study, the procedure of VIV fatigue analysis for dynamic power cables is presented and the demonstration of VIV fatigue analysis cases are provided considering sheared current profiles.

The VIV fatigue analysis of a dynamic power cable has broadly been categorized into three stages by utilizing three separate programs.

The modal analysis has been performed to determine the frequency, mode type and curvature of each eigen mode of the cable system. OrcaFlex categorizes the in-line modes as the modes vibrating in the azimuth direction of laid cable and the transverse modes as vibrating 90 degrees to the in-line modes. In this study, VIV analyses only consider loadings and responses with the transverse modes assuming the response amplitudes of cross-flow VIV direction are significant compared to those of in-line VIV direction. Fig. 3 illustrates the primary mode shape (mode No. 1) of transverse modes of the first current profile calculated from OrcaFlex.

Fig. 3 
Primary mode shape (mode No. 1)

4.1 Excited modes by VIV prediction

The inputs for separate VIV analyses consist of current profiles and the static analysis results from OrcaFlex. As mode shapes to be used are different from each current profile in this study, the load cases have been applied for Shear7 repeatedly to predict the excited modes of VIV among calculated eigen modes and generate corresponding curvature time series of each node of the cable for the particular current profile. For example, the first current profile (denoted as “Profile 1.0”) and the excited modes of the cable subjected to the corresponding current are depicted in Fig. 4 and Fig. 5.

Fig. 4 
Current Profile 1.0 (0.07 ~ 0.21m/s)

Fig. 5 
Excited modes by VIV (Profile 1.0)

There is a “Zone 1” legend in Fig.5 that is the independent time series of excited modes. Although real field tests found that several frequencies were manifest simultaneously, Shear7 allows only one particular frequency to be excited in a certain interval which is called time sharing method. Shear7 allows up to three independent time zone on the structure which is the concept of space sharing of some mode. These zones are made independently by allowing the time sharing probabilities to add up to one (Shear7, 2021). The excited modes in Fig. 5 demonstrate that approximately between 0 and ~550s, mode No. 6 is excited while between ~550 to ~600s, mode No. 7 is excited, then mode No. 4 and mode No. 5 are excited in consecutive order. Relatively lower number of modes were excited due to subtle current speeds along the cable length. For instance, below Fig. 6 and Fig. 7 illustrate 4^th and 7^th excited mode shapes of Profile 1.0 respectively.

Fig. 6 
4th mode shape of Profile 1.0

Fig. 7 
7^th mode shape of Profile 1.0

4.2 Higher modes excitation by VIV

When the velocity of sheared current profile becomes stronger, the higher mode numbers tends to be excited by VIV prediction. For example, when Profile 28.0 (Fig. 8) was applied for the excited modes prediction, higher mode numbers, specifically from No. 9 to No. 25 were excited as illustrated in Fig. 9.

Fig. 8 
Current Profile 28.0 (0.10 ~ 0.71m/s)

Fig. 9 
Excited higher modes by VIV (Profile 28.0)

The mode superposition method is commonly employed to predict the response of uniform or nearly uniform structures that exhibit low mode numbers and has proven to be successful in such cases. However, when dealing with structures that respond at high mode numbers (greater than the tenth mode), resulting in traveling waves rather than standing waves, the mode superposition method may encounter limitations. To account for traveling wave behavior, the method requires the inclusion of a significant number of non-resonant modes, as discussed by Jaiswal and Vandiver(2007). In this context, the traveling wave seemed to arise along the cable due to strong sheared current profile. Below figures (Fig. 10 & Fig. 11) are excited mode shapes i.e. the 9th mode and the 25th mode of Profile 28.0.

Fig. 10 
9th mode shape of Profile 28.0

Fig. 11 
25th mode shape of Profile 28.0

In this research, the procedure of VIV fatigue analysis for dynamic power cables or umbilicals have been established by utilizing three commercial programs, specifically OrcaFlex, Shear7 and Helica. This calculation method could be applied to any helically wound long flexural structures that consist of various components. The VIV fatigue damage evaluation of helical structures greatly depends on the intensity of sheared current profiles, and the static analysis results of the cable line configurations and mode shapes. VIV prediction has mainly been made by the empirical force based model and the time sharing method from which the excited modes and frequencies, curvature time series, and cycle counting have been obtained. Cross-sectional properties of the cable can be estimated for the capacity curve, bending stiffness, torsional moment, and contact forces in layers, etc. The accumulated long-term fatigue life has been assessed by fatigue damages of each node of the cable and probabilities of % occurrence of current profiles. The dynamic power cable developed for this study showed 3,800,000 years of the minimum fatigue life for cross-flow VIV occurred at 132.25m of the arc length at which the inflection point of sag bend and hog bend is located. Furthermore, the most severe current loading condition can be identified, for instance, in this study the 410th loading condition contributed maximally to the lowest fatigue life which showed relatively high mode numbers excited in cross-flow VIV direction. Finally, sensitivity studies have been performed to check the design parameters, specifically, structural damping ratio, higher order harmonics, and lift coefficients tables. When the structural damping ratio for the dynamic power cable was increased from 0.01 to 0.03 (3% of critical damping), the curvature amplitudes decreased by 26% compared to the initial case. The fatigue life would be expected to increase accordingly. In the case of activating higher order harmonics, the fatigue life has been forecasted to be reduced due to 219% of magnified curvature variations by the resonant behavior between the closely spaced natural frequencies and 3x frequency response components. In terms of shifting the lift coefficient tables, the CL Type 2 presented the less conservative results. As a result, the maximum curvature has been reduced by approximately 35% when the initial CL Type 1 of the lift coefficient table was replaced by CL Type 2. The VIV response of Shear7 stems from the assumption that it complies with a narrow-banded Gaussian process with a standard deviation derived from the VIV amplitudes. This approach is consistent with the material and guidance of the industries. The other approach to obtain the VIV responses is based on time-domain results which will be reported by deterministic signals with the constant amplitude of curvature. In the future, more research on the potential errors between the Gaussian process and the deterministic time series will be carried out to confirm their level of consistency and verify one of the fundamental assumptions using time sharing method.