1 Introduction

The principle of Low Temperature Thermal Desalination (LTTD) has been adopted since the year 2006 to convert seawater to drinking water at Lakshwadeep Islands, located off the west coast of India. The LTTD utilizes the temperature difference between the warm surface water and cold water (12° C) at 350 m water depth in continental slope as per Sistla et al. [20]. High Density Poly Ethylene (HDPE) pipe is used in the desalination plant because of its leak tightness, ease in deployment, and favorable thermal conductance. Also, the irregularities of coral seabed in the location and the Coastal Regulated Zone (CRZ) norms do not allow the burial of the pipeline in the seabed. The buoyant HDPE pipe settles to an inverted catenary profile, and therefore, the pipeline keeps above the uneven surface of the seabed, adhering to the CRZ norms. An HDPE pipe with 630 mm outer diameter, 30 mm wall thickness, and 850 m length has been used to consider the desalination requirements. The pipeline is installed in the desalination plant at Agatti island Lakshwadeep, during 2009, and a schematic arrangement is shown in Fig. 1. This has been considered as the reference problem in the present work. Rajendran et al. [17] described this pipeline configuration which is exposed to nearshore current and undergoes in-line (IL) oscillation in the direction of the current flow. During initial deployment, the front portion of the pipeline, for about 200 m, was clamped with steel weights in two regions (regions A and B in Fig. 1). In region A (0 to 46 m), 17 steel clamps were attached at 4 m intervals on the pipeline’s outer periphery to increase its deadweight and reduce current-induced oscillation. To compensate for the buoyancy of the pipeline, and to avoid its pop-up to the sea surface, 4 additional steel clamps, each of weight 200 kg, were attached in region B (120 to 200 m) of the pipeline. The front end of the pipeline (see Fig. 1) as well as its far end at the bottom, which is at a depth of 450 m, are anchored. This is modeled in the analysis as simply-supported (i.e., zero z-displacement) boundary condition at both the ends.

Fig. 1
figure 1

Sectional view of HDPE pipeline (vertical plane) with the MPSC profile

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However, this setup did not mitigate pipe oscillations, and its front portion abraded with the coral seabed, and the whole pipeline was abandoned. Hence, a new pipeline configuration that consisted of a 200 m long mild steel pipe in the front portion and 650 m HDPE pipe beyond, was deployed and the desalination plant was commissioned. Rajendran et al. [17] discussed the steel pipe’s demerits and suggested alternate material (GFRP) for this pipeline configuration. However, the present paper suggests an alternative approach to mitigate pipe oscillation and recommended deployment of HDPE material for the entire pipeline.

Baarholm et al.[2] discussed the importance of fatigue due to IL oscillation and estimation of fatigue accumulation that results from it. Since the pipeline deployed at Agatti Island oscillates in IL mode, this study focuses on fatigue damage estimation due to IL VIV. Nearshore current measurement was carried out during March 2017 in the vicinity of the desalination plant [18]. These field measurements provided an opportunity to analyze, compare, and benchmark the results using numerical VIV analysis in the frequency domain as well as time domain. The VIV analysis code Shear7 [19] has been used for frequency domain VIV analysis, and the code OrcaFlex [12] has been used for time domain VIV analysis.

The objective of the present work is to estimate the Fatigue Damage Rate (FDR) of the pipeline undergoing low frequency IL VIV, substantiated with prototype measurements, numerical studies and suggest passive measures for mitigating the pipeline oscillation. This pipeline configuration is being implemented for six more desalination plants in Lakshwadeep islands, as per NIOT project report [11]. It is important to ascertain the FDR for a better understanding of the dynamic behavior and fatigue life of the pipeline. The FDR estimation has been carried out for two different configurations of the pipeline, namely, (a) HDPE pipeline with steel clamps attached in regions A and B as shown in Fig. 1, and (b) HDPE pipeline with 50% coverage of strakes excluding the clamps in region A. These two configurations are referred to as ‘bare pipe’ and ‘strake pipe’ configuration, respectively.

This paper is organized as follows: Sect. 2 details the field measurements associated with the actual underwater pipeline. Numerical modeling and comparison with field measurements are discussed in Sects. 3 and 4 respectively. The estimation of Fatigue damage is entailed in Sect. 5 and possible mitigation measures are included in Sect. 6, with the last Sect. 7 highlights the important conclusions from the present study.

2 Field measurements

2.1 Oscillation of the pipeline

To know the magnitude and frequency of oscillation of the bare pipe, an underwater video was taken with experienced divers during November 2009. The video was analyzed using video analysis and modeling code developed by Brown [5], a open source physics project. It allows the user to track the pipe undergoing oscillation and measure the oscillation parameters, such as frequency and amplitude. The oscillation amplitude (A) with respect to time (t), extracted from the video, is shown in Fig. 2 at the location x = 108 m highlighted in Fig. 1. The spectral density of this time series, which is shown in Fig. 3, indicates the pipeline oscillates at the dominant frequency (f) of 0.08 Hz (period 12.5 s). Thus, the pipeline IL mode oscillation occurs at a low frequency. This result gave an opportunity to carry out numerical analysis and validation of VIV results and also to estimate the fatigue damage due to VIV.

Fig. 2
figure 2

Oscillation of coldwater pipeline at x = 108 m based on field observations

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Fig. 3
figure 3

Spectral density of pipeline oscillation at x = 108 m (see Fig. 1)

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2.2 Current profile

Vandiver [21] mentioned that good current data is must to estimate the fatigue life of risers oscillating due to VIV and suggested that Acoustic Doppler Current Profilers (ADCP) provide better current measurement. Figure 1 shows that the front portion of the inverted catenary pipeline configuration has about 200 m free span, and hence, it is important to measure the current magnitude and direction in this shallow region. Rajendran et al. [17] had used a 75 kHz ADCP to measure the magnitude (V) and direction (θ) of sheared current profile at this shallow region. The maximum depth up to which the current flow could be measured was up to 40 m. The navigation software connected with ADCP had been utilized to record the current with respect to the geographic coordinate system. The data processing indicated that the surface current speed (V) is around 0.4 m/s and the dominant direction (θ) with respect to the north is about 15°, which is almost perpendicular to the pipeline. The current profile V recorded up to 40 m depth is shown as a dotted line in Fig. 1, and the current data beyond 40 m depth is referred from Amol et al. [1] and Prakash et al. [16]. The profile in Fig. 1 has been considered as the Most Probable Sheared Current (MPSC) profile in the VIV analysis.

2.3 Deflected profile of the pipeline

McCormack and Andersen [10] reported a study of a Clathrate desalination plant that uses a large diameter HDPE pipeline configuration. They reported that the pipeline moves 152 m horizontally and 76 m vertically under excitation by the current. In the present study, therefore, it is important to ascertain the deflected profile of the 850 m long coldwater pipeline that is exposed to nearshore current. The prototype measurement of the deflected pipeline profile can be used to validate numerical VIV analysis.

The Side ScanSonar (SSS) is widely used for mapping the seafloor and also to identify objects lying on it. The alignment of the deployed pipeline was also done using SSS. Hence, SSS is used to measure the deflected profile of the cold water pipeline. A 120 kHz, Edgetech 4200 SSS model had been used as tow fish to conduct the survey. The tow fish is lowered and towed at 4.8 knots at an altitude of 8 m from the sea surface in grids with required swath coverage. The SSS data had been processed by mosaic method, which is used to make continuous and accurate sonar images of the pipeline on the seabed. Based on the mosaic method, the imagery of the pipeline lying on the seabed is processed and superimposed on the satellite earth imagery, with real time GPS coordinates, and is shown in Fig. 4. The SSS image of the deflected bare pipeline can be identified on the white colored mosaic panel in Fig. 4, along with the aerial view of the trestle and seashore of the Agatti Island. It was intended to lay the pipeline on the extended alignment of the trestle. The maximum deflected offset distance of the HDPE pipeline was100 m at 300 m from the front end of the pipeline.

Fig. 4
figure 4

Side scan sonar image of the pipeline

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3 Numerical VIV analysis

The VIV parameters such as natural frequency and amplitude are estimated using codes Shear7 (in frequency domain) and OrcaFlex (in time domain). These two codes can be interfaced so that the structural natural frequencies and mode shapes can be generated in OrcaFlex and exported to Shear7 for VIV analysis.

The frequency domain VIV analysis is based on the mode superposition. It calculates the natural frequencies and corresponding mode shapes of the pipeline under consideration. The governing equation of motion for a tensioned beam without damping is

$$(m + m_{a} )\frac{{\partial^{2} y}}{{\partial t^{2} }} + EI\frac{{\partial^{4} y}}{{\partial x^{4} }} - T\frac{{\partial^{2} y}}{{\partial x^{2} }} = 0$$
(1)

where m and ma are the mass added mass per unit length, respectively, E is the Young’s modulus, I is the second moment of area of the cross-section, EI is the bending stiffness, T is the constant axial tension, t is time, x represents the centroidal axis of the pipeline, and y is the pipe deflection. Considering a deflection pattern, \(y = Ae^{i(kx + \omega t)}\), where A is the amplitude of vibration, k the wave number, and \(\omega\) the circular frequency; and substituting it in Eq. (1), one gets

$$- m\omega^{2} + EIk^{4} + Tk^{2} = 0$$
(2)

Defining a parameter \(\alpha = T/(EIk^{2} )\), one can estimate if the pipeline behaves like a taut string (α >  > 1). If it does not behave like a taut string, the bending stiffness needs to be accounted for as in Eq. (1), else it can be neglected. If α > 30, the bending stiffness (EI) will not affect the natural frequency of the structure and T is dominant, then the taut string model can be chosen in the numerical analysis [19]. Solution for k from Eq. (2) is the dispersion relation (it is quadratic in k2)

$$k^{2} = \frac{{ - T \pm \sqrt {T^{2} + 4EI\omega^{2} (m + m_{a} )} }}{2EI}$$
(3)

Substituting Eq. (3) in the expression for α, one obtains α in terms of frequency as

$$\alpha = \frac{2}{{ - 1 + \sqrt {1 + \frac{{4EI(m + m_{a} )}}{{T^{2} }}\omega^{2} } }}$$
(4)

Pavlou [15] shown that the buckling effect of inner flow in a FRP riser model, induce dynamic instability and this can be simulated equivalent to the dynamic buckling model of an Euler column. In our case it turns out that the pipeline parameters are such that it behaves like a taut string (i.e., α > 30) and hence omitting the bending stiffness term in Eq. (1), but including damping in the model, one has, under current-induced excitation

$$(m + m_{a} )\frac{{\partial^{2} y}}{{\partial t^{2} }} + R\frac{\partial y}{{\partial t}} - T\frac{{\partial^{2} y}}{{\partial x^{2} }} = P(x,t)$$
(5)

where R is the damping per unit length (structural and hydrodynamic damping) and P(x,t) is the excitation force per unit length, which is essentially the lift force distribution.

For a particular mode of vibration, the lift force distribution (per unit length) is taken as [3]

$$P(x,t) = \frac{1}{2}\rho_{f} DV^{2} (x)C_{L} (x;\omega_{r} )\sin (\omega_{r} t)$$
(6)

where ρf is seawater density, D is pipeline diameter, V(x) is the flow velocity normal to the pipeline, CL(x; ωr) is the lift coefficient for mode r for which the natural frequency is ωr. The code utilizes smoothed CL, which are developed using experiments, and the VIV is estimated using semi-empirical lift coefficient curves [19] as a function of non-dimensional amplitudes (A/D) by considering the balance between vortex-shedding force and damping of the member for each mode. The smoothened lift coefficient curve shown in Fig. 5, has been used to predict the amplitude of oscillations due to VIV. In frequency domain analysis, [19] when the oscillation of the object due to VIV, is excited up to mode 3, the IL parameters have to be used, for fatigue damage estimation. In this study, the excited modes are more than 3, and hence, the cross flow parameters are used to predict the modes in IL for fatigue damage calculation. Wu et al. [22] also suggested for adopting a reliable combined IL and cross-flow load model for the empirical VIV prediction programs. They mentioned that combined IL and cross-flow response analysis gives less conservative estimation than the pure cross-flow or IL model analysis.

Fig. 5
figure 5

Lift coefficient as function of A/D (from Shear7)

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During VIV analysis, the code assigns initial values of lift and damping coefficients, and these values are analyzed for equilibrium state through iteration. The converged lift and damping coefficients are used to estimate the response amplitude of the member. Table 1 shows the parameters that are considered in the analysis for both bare and strake pipes. The physical properties of the pipeline are given in Table 2. The cold sea water flow by siphon action, in the pipeline also contributes to the dynamic behavior of the pipeline. Pavlou [14] derived, motion equation for curved FRP pipe and discussed the importance of Coriolis and centrifugal forces caused due to inner fluid flow, in which Coriolis force, acts in direction opposing the motion and dominates the dynamic response for small values of inner fluid flow and centrifugal force dominates for higher values of inner fluid flow. Methodology to estimate the Critical inner flow velocities and its natural frequencies were presented and suggested, that the suction pump parameters can be optimized to create safe inner flow velocities, to have better control on the dynamic instability. Considering the importance of inner fluid effect, coldwater flow rate for 0.15 ton/s is given as external user input while modeling of pipeline in time domain to consider centrifugal and Coriolis force [12].

Table 1 Parameters used in Shear7 for the VIV analysis
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Table 2 Properties of the HDPE pipeline
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4 VIV analysis vs. field measurements

The bare pipe has been modeled, including the steel clamps (17 in region A and 4 in region B as stated earlier), and analyzed for frequency domain response with parameters listed in Tables 1 and 2. The rms (root mean square) amplitude (Arms) of deflection estimated along the pipeline exposed to the MPSC profile is shown in Fig. 6. In general, if the time series of VIV response amplitude, measured at any one particular node of the member, the node displacement from amplitude spectrum can be correlated with the numerically obtained Arms profile at that particular node. Also based on the response amplitude observed from the time series data at various nodes, the Arms profile can be constructed along the length of the member. In this method, Lie et al. [9] experimentally measured the time series response amplitude of the model, using sensors at various nodes and used modal approach to construct the Arms profile along the depth of the model.

Fig. 6
figure 6

Arms (deflection amplitudes) along the pipeline for the MPSC profile (frequency domain analysis)

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In frequency domain the Arms is in displacement units, obtained based on mode superposition method, is comparable with experimental or field measurements results. From Fig. 6, Arms ≈ 0.32 m at x = 108 m (see Fig. 1 that highlights this location). This correlates well with the field observation at the same location shown in Fig. 2, where the deflection is about 0.3 m. The data of the excited modes obtained from this analysis are shown in Table 3. This table shows that the mode number 17, with a natural frequency of 0.089 Hz (period = 11.23 s), dominates the mode superposition analysis. The modes 15 to 19 are significant in this analysis, and the effect of other modes is negligibly small. The computed natural frequency (= 0.089 Hz) agrees well with field measurements (= 0.082 Hz) as shown in Fig. 3.

Table 3 Parameters of the excited modes
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The bare pipe with steel clamps has been also analyzed in the time domain with parameters listed in Table 2. The Iwan and Blevins [6] model of VIV analysis has been used. The deflection (A) time history of the pipeline exposed to the MPSC profile at x = 108 m is shown in Fig. 7, where the comparison with field measurements is also shown. The spectral density from this time history is shown in Fig. 8, showing a natural frequency of 0.09 Hz. The deflection estimated along the pipeline exposed to the MPSC profile is shown in Fig. 9, where the deflected pattern obtained from field measurements is also shown for comparison. The comparisons between time domain analysis and field measurements are good for the frequency (i.e., 0.09 Hz vs. 0.082 Hz), deflection amplitude (i.e., 0.31 m vs. 0.3 m) and overall deflected shape. Both frequency domain and time domain analyses are in good agreement with field measurements, and this is brought out in Table 4.

Fig. 7
figure 7

Deflection of the pipeline at x = 108 m for the MPSC profile (time domain analysis)

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Fig. 8
figure 8

Spectral density of pipeline oscillation at x = 108 m

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Fig. 9
figure 9

Deflection (A) along the pipeline for the MPSC profile (Time domain analysis vs. field measurement)

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Table 4 Pipeline oscillation parameters at x = 108 m (see Fig. 1)
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5 Estimation of fatigue damage

5.1 Methodology

The code Shear7 has been widely used for the prediction of fatigue damage due to cross-flow and IL VIV of risers in sheared current. Yang et al. [23] had validated the fatigue life results of a riser, and Loentgen et al. [8] had carried out VIV fatigue analysis of a hybrid riser tower using this code and validated the results with other VIV prediction codes such as Subsea7, OrcaFlex, etc. In the present work, Shear7 and OrcaFlex codes are used in the estimation of VIV induced fatigue damage. This exercise has been carried out for surface current velocity ranging from 0.05 to 0.8 m/s, including the MPSC profile shown in Fig. 1. The results from both codes are compared. The shape of the current profile is assumed constant, however in other words, the ordinates of the current profile for a surface current of 0.8 m/s is 16 times the ordinates of that for 0.05 m/s surface current. At the end of each static analysis, the equilibrium shape of the pipeline is different, when the current velocity is different and with this static convergence solution, the mode shapes are generated and considered for analysis.

Pavlou [13] has developed a non linear isodamage model based on curved shape of the S–N curve diagram, which covers the full range of stresses unlike the existing nonlinear isodamage straight line models, available in the literature. In line with this, Bjørheim et al. [4] proposed non linear fatigue damage accumulation model with respect to S–N fatigue envelope and they suggested the following equation.

$$D = \left( {\frac{n}{{N_{f} }}} \right)^{{q\left( {\sigma ,{\text{m}}} \right)}}$$
(7)

where D is non linear fatigue damage, n is the number of loading cycle and N is the number of loading at failure. The exponent \(q(\sigma ,\mathrm{m})\) is the function of the stress amplitude and material property, interpolated using S–N curve damage model as given below.

$$q\left( {\sigma , m} \right) = \frac{{a\left( {S_{u} - S_{e} } \right)}}{{\left( {\sigma - S_{e} } \right)}}$$
(8)

where \({S}_{u}\) is ultimate stress, \({S}_{e}\) fatigue endurance limit, \(\sigma\) applied stress amplitude and a is the parameter using the damage model interpolation. In our work, VIV fatigue damage of HDPE pipe is to be estimated. Khelif et al. [7] reported that unlike steel, no horizontal asymptote is available from literature to define \({S}_{e}\) for HDPE. The results may not be accurate due to the insufficient S–N curve data to arrive non linear fatigue. Hence, the standard Miner rule approach is adopted to compute the fatigue damage rate (FDR), which is the damage ratio accumulated for 1 year.

The stress amplitudes (S) are assumed to follow Rayleigh distribution. Khelif et al. [7] had carried out a fatigue study on HDPE material in the axial direction and developed a S–N curve of form NS8.5 = 1.6 × 1014 (N is the number of cycles to failure at stress amplitude S) using statistical analysis by a two-parameter Weibull distribution for design against fatigue. This S–N curve has been considered for the VIV fatigue analysis in the present work. The expression for damage rate Dr, which is the damage caused by mode r in one year, is given by [19].

$$D_{r} = \frac{{\omega_{r} T}}{2\pi C}(\sqrt 2 \,S_{{{\text{rms}}}} )^{b} \Gamma \left( {\frac{b + 2}{2}} \right)$$
(9)

where Srms is the rms value of the stress amplitude, constants b and C define the S–N curve as \(NS^{b} = C\), ωr is the natural frequency in mode r, and T is one year in seconds (= 365 × 24 × 3600 s).

5.2 Analysis for the MPSC profile

The rms values of stress (Srms) along the pipeline, under the MPSC profile, are shown in Fig. 10. The computed FDR, which includes the damage rates of all significant vibration modes based on Eq. (9) along the pipeline, is shown in Fig. 11 using both codes. The agreement between both codes is good. The stress fluctuations are high in the front 300 m length of the pipeline submerged below 40 m water depth because of high current speeds in this region, and as a result, this region determines the fatigue life of the pipeline system. The maximum FDR is 1.6 × 10−4 at about x = 300 m, and hence the fatigue life, assuming critical fatigue damage of 0.1 that is allowable, yields a fatigue life of 625 years (= 0.1/1.6 × 10− 4).

Fig. 10
figure 10

RMS stress along pipeline exposed to the MPSC profile using Shear7

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Fig. 11
figure 11

FDR (log10 scale) along pipeline exposed to MPSC profile using Shear7 and OrcaFlex

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5.3 Analysis for a range of current profiles

The maximum FDR values for the pipeline subjected to surface current speed varying between 0.05 to 0.6 m/s using both analysis methods are compared in Fig. 12. The FDR rate beyond 0.4 m/s increases exponentially, but it follows the same trend in both methods. The results are under estimated by the time domain approach [12] in comparison to the frequency domain approach [19] for a surface current velocity beyond 0.4 m/s.

Fig. 12
figure 12

Comparison of fatigue damage assessment using OrcaFlex and Shear7

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The cold water pipeline is the main component of the desalination process, and mild variations in temperature of the coldwater would impact the desalination process. Hence, a critical VIV fatigue value, i.e., Critical Fatigue Damage (CFD) of 0.1 has been considered to avoid the initiation of fatigue damage due to VIV. As shown in Fig. 12, the FDR per year for each current profile is below 0.1. Table 5 shows the number of years to reach CFD = 0.1 for each surface current velocity against its maximum FDR. The FDR of 0.011 per year corresponding to 0.8 m/s surface current velocity will result in critical damage of 0.1 in about 9 years.

Table 5 Critical fatigue life for various current profiles
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Considering the design life of 25 years of the desalination plant, it becomes essential to mitigate the FDR to avoid CFD = 0.1 within 9 years. Even though the attachment of clamps in region B of the HDPE pipeline is counteracting the buoyancy of the pipeline, it does not help mitigate VIV oscillation in a bare pipe.

6 Mitigation of fatigue damage

Suppression devices for mitigating fatigue damage have been developed through experiments since 1971 [3]. Shear7 has the provision to model helical strakes in pipes to mitigate fatigue damage due to VIV. The parameters developed for the pipeline with strakes from the field testing [19] shown in Table 1 have been considered for VIV mitigation analysis.

In previous sections, the response amplitude, stress, and FDR are high for the front 300 m of the pipeline. Hence the strakes along the pipeline are proposed for the front 50% length (from the shore). The default geometry of the helical strakes having pitch and height of 17.5 D and 0.25 D are considered, respectively for modeling the strakes in the analysis, but without the attachment of 17 steel clamps in region A. However, 4 clamps attached in the region B has been retained in the mitigation analysis to compensate the pipeline buoyancy.

The Arms magnitudes along the bare and strake pipe are compared in Fig. 13. Due to introduction of strakes, Arms is reduced very significantly all along the strake pipe. It is observed that the maximum Arms for the strake pipe is around 0.06 m as compared to a maximum value of 0.355 m for the bare pipe.

Fig. 13
figure 13

Arms along X for the bare pipe and strake pipe

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Similarly, the FDR distributions for the bare and strake pipes along the length are compared in Fig. 14. The FDR with strakes reduces substantially as compared to the bare pipe. The maximum FDR of 1.6 × 10−4 that occurs in the bare pipe reduces to 3.08 × 10−13 for the strake pipe, which is almost a 100% reduction. Thus, by introducing helical strake in the first 50% length (from shore) of the pipeline, the maximum response amplitude reduces by about 85%, and FDR by close to 100%.

Fig. 14
figure 14

FDR (log 10 scale) along X for the bare pipe and strake pipe

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The VIV mitigation analysis with strakes on pipe is carried out using shear 7, while Orcaflex does not have the option to perform the strakes modeling. The mitigation analysis has been carried out further for a range of current speeds starting from 0.05 to 0.6 m/s. In Fig. 15, the maximum FDR for the bare pipe for each current profile, estimated by Shear7 and OrcaFlex, are shown, as was presented in Fig. 12. Now, in the same figure, the maximum FDR for the strake pipe is also shown for comparison. The introduction of strakes has almost nullified the FDR for all current profiles considered in the VIV mitigation analysis.

Fig. 15
figure 15

Variation of maximum FDR for a range of current profiles

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7 Conclusion

The safety of the buoyant HDPE pipeline installed to draw coldwater for the LTTD plant poses challenge to limit its vortex induced oscillations because of its 850 m long inverse catenary profile that is exposed to sheared current. The field observations on the response of the prototype pipeline provided an opportunity to benchmark the VIV response analysis and to carry out the fatigue damage assessment based on current flow measurements in field and SSS data. Some of the important conclusions of this study are summarized below.

  1. (a)

    The shallow sheared current profile measurements in the vicinity of the deployed cold water pipeline indicate that the current velocity has a magnitude of 0.4 m/s with a direction of current almost perpendicular to the pipeline. This has been considered as the MPSC profile that act on the cold water pipeline in the shallow water region for the VIV study.

  2. (b)

    The deflected view of the prototype pipeline based on the real time SSS imagery is very close to the time domain numerical analysis results.

  3. (c)

    The observed oscillation frequency and deflection amplitude of the bare prototype pipeline at X = 108 m are 0.08 Hz and 0.32 m, respectively. The VIV numerical analysis results in both frequency domain and time domain indicate very close oscillation frequency and response characteristics as observed for the prototype pipeline. Thus, using the VIV analysis tools for the assessment of the FDR of the prototype is justifiable.

  4. (d)

    The FDR variation along the pipeline by the frequency domain analysis can be much higher than that by the time domain analysis. The same was observed by Zhang and Tan [24] for a flexible riser. This large difference is seen for the part of the pipeline that is exposed to higher currents in shallow region. However, the trends are in agreement by both methods. The FDR by Shear7 has been considered for VIV mitigation analysis as it has the provision for helical strakes.

  5. (e)

    For the MPSC profile (surface current of 0.4 m/s), the maximum FDR along the pipeline is 1.6 × 10−4 from the frequency domain analysis, resulting in a fatigue life of about 625 years corresponding to CFD = 0.1. Hence, the pipeline is considered safe for the MPSC profile. However, for a surface current speed of 0.8 m/s, the maximum FDR is 0.011, yielding a fatigue life is 9 years, and hence VIV mitigation is proposed since the design life of the desalination plant is 25 years.

  6. (f)

    Helical strakes have been considered for the front one-half of the pipeline, and it results in substantial FDR reduction along the pipeline for a sheared current profile with 0.8 m/s surface current. It is found that the attachment of 17 steel clamps in region A is redundant since addition of the helical strakes reduces the oscillation of the pipeline substantially. Nevertheless, in region B, the attachment of 4 steel clamps is retained to avoid the pop-up of the pipelineto the sea surface due to its buoyancy.

In the VIV research domain, there is lack of measurements in prototype environment for validation of numerical results. To the best of authors knowledge there is no field measurements reported. The measurement of oscillation response parameters and the deflected shape of long flexible prototype pipeline is the basis for bench marking of VIV numerical analysis in this study. Prototype measurements and recording of external loads for the purpose of validating with numerical studies are highly expensive than validating with experimental studies. The basis for bench marking with experimental studies is prone to scale model errors, but comparing with the prototype field measurements is the real bench marking for numerical studies, with which one can proceed further with reliability of using the numerical analysis. This study may be fine-tuned by carrying out the fatigue test on HDPE pipe to establish the accurate S–N curve parameters in flexure. The present study considers the fatigue parameters of HDPE material in the axial direction. Also, measurement of the sheared current profile up to 400 m water depth would enhance the accuracy of the response characteristics of the inverse catenary HDPE cold water pipeline. The present VIV study includes the dynamic effect of inner fluid flow. However, the estimation of critical inner fluid flow velocity is the scope for further study, to optimize the suction pumps specifications and to have control on pipe dynamics due to inner fluid flow.