Submarine pipeline and cable stress assessment method capable of considering influence of local scour topography

Abstract

The present invention relates to the field of research on the stress and in-situ stability of submarine pipelines and cables, and relates to a submarine pipeline and cable stress assessment method capable of considering the influence of local scour topography. Submarine pipelines and cables laid on the seabed may cause serious local scour under the action of fluid, resulting in the formation of scour topography beneath the pipelines and cables. The existing research work shows that local scour topography will significantly affect the stress on submarine pipelines and cables, thereby affecting the in-situ stability thereof. For a submarine pipeline and cable stress problem considering the influence of local scour topography, related scholars mainly carry out research work on the hydrodynamic coefficients of pipelines and cables under specific parameter conditions, but at present, no parametric description method for pipeline and cable stress has been formed, and therefore, it is difficult to service actual engineering design. In the present invention, by means of a large amount of theoretical analysis and research work, the relationship between hydrodynamic coefficients of the pipelines and cables and the thickness δ / D and the Reynolds number Re of a dimensionless inflow boundary layer is found, thereby establishing a parametric description method for the hydrodynamic coefficients of the pipelines and cables, which can be directly used for accurately forecasting the stress of the pipelines and cables in actual engineering.

Description

A method for assessing the stress on submarine cables that takes into account the effects of local scour topography. Technical Field

[0001] This invention relates to the field of submarine cable stress and in-situ stability design, and to a method for evaluating submarine cable stress that can take into account the effects of local scour topography. Background Technology

[0002] Under the influence of water flow, pipelines laid on the seabed experience severe localized scouring, leading to large-scale suspension. For pipelines laid flat on the seabed, the flow field behind the pipeline is suppressed by the seabed, making vortex shedding less likely. However, as the scour pit expands, the pipeline becomes suspended, making it more susceptible to vortex shedding. Therefore, the hydrodynamic forces acting on the pipeline before and after scouring are significantly different, and the hydrodynamic coefficient changes accordingly, potentially affecting the pipeline's in-situ stability. Accurately assessing the impact of scour pits on the hydrodynamic coefficient of pipelines is crucial for the design of in-situ stability.

[0003] Regarding the influence of scour topography on the hydrodynamic characteristics of pipelines, relevant scholars have conducted research. Li et al. (2018) compared the hydrodynamic coefficients of pipelines on flat seabeds and scour equilibrium seabeds, finding that the average drag coefficient and lift coefficient of pipelines on flat seabeds were both greater than those on pipelines with the influence of scour topography. This indicates that local scour topography has a significant impact on the hydrodynamic coefficients of pipeline structures. Furthermore, Chen et al. (2020) studied the hydrodynamic characteristics of pipelines on scour equilibrium topography under different incoming boundary layer thicknesses, finding that the boundary layer thickness also has a significant impact on the flow structure and hydrodynamic coefficients around the pipeline. With the increase of the incoming boundary layer thickness, the vortex scale behind the pipeline continuously increases, but the corresponding vortex volume decreases, thus affecting the hydrodynamic coefficients. The research by Chen et al. (2020) showed that the average drag coefficient, average lift, root mean square lift coefficient, and Strouhal number significantly decrease with increasing boundary layer thickness.

[0004] The above analysis shows that after localized scouring of pipelines and cables, the surrounding seabed topography significantly affects their hydrodynamic coefficients. Furthermore, the boundary layer thickness of the incoming flow is also a crucial factor influencing the stress on the pipelines and cables. However, current research on the stress on pipelines and cables considering the influence of localized scouring topography is still incomplete. Related studies mainly consider the impact of specific parameters on the stress, but a parameterized prediction method has not yet been developed. Therefore, this invention, through numerical simulation research, deeply summarizes, generalizes, and analyzes relevant results, forming a method for assessing the stress on subsea pipelines and cables that considers the influence of localized scouring topography. This method can serve the design of subsea pipeline and cable stress and in-situ stability, thus providing a scientific basis and technical guarantee for the safe design and service of subsea pipelines and cables.

[0005] References:

[0006] [1] Li Z, Mysa RC, Jaiman RK, et al. Freely vibrating circular cylinder in the vicinity of fully developed scour holes at low Reynolds numbers. Computers&Fluids, 2018, 163: 97-120.

[0007] [2] Chen L, Wang Y, Sun S, et al. The effect of boundary shear flow on hydrodynamic forces of a pipeline over a fully scoured seabed. Ocean Engineering, 2020, 206: 107326. Summary of the Invention

[0008] The technical solution of the present invention:

[0009] To address the aforementioned problems in existing technologies and to provide a scientific basis and technical support for assessing the stress and in-situ stability of submarine cables under the influence of scour pit topography, the objective of this invention is to provide a method for assessing the stress of submarine cables that can take into account the influence of local scour topography. This overcomes the technical deficiency of existing research, which has only conducted partial parametric studies and has not yet formed a parametric prediction method for assessing the stress of submarine cables.

[0010] To achieve the above objectives, the technical solution of the present invention is as follows: A method for assessing the stress on submarine cables that takes into account the influence of local scour topography, comprising the following steps:

[0011] Determination of boundary layer thickness under different inflow conditions

[0012] The thickness of the incoming boundary layer significantly affects the local scour development process, and consequently the stress on submarine cables. Therefore, the first step is to determine the boundary layer thickness δ under different incoming flow velocities. This invention primarily addresses the influence of local scour topography on the stress on submarine cables under unidirectional flow conditions. Under unidirectional flow conditions, the distribution of horizontal velocity along water depth satisfies the logarithmic law formula, which is as follows:

[0013] MERGEFORMAT (1)

[0014] Where u(z) represents the horizontal flow velocity at a water depth of z; κ is the Karman constant, which can be taken as 0.42; z s =d 50 / 12 represents the roughness length of the seabed, and d50 represents the median grain size of sediment in sandy seabeds, which can be obtained from sediment gradation curves; u f This represents the bottom friction velocity. In practical engineering, marine hydrological surveys are typically conducted to measure the velocity at a single point in space. Substituting this velocity into formula (1), u can be calculated. f For unidirectional flow, the velocity at the boundary layer edge is 0.99U, where U represents the free flow velocity. The water depth z at the boundary layer edge can be calculated from this velocity, and thus the boundary layer thickness δ can be obtained.

[0015] B. Evaluation method for submarine cable stress considering the influence of local scour topography

[0016] Combining theoretical analysis and numerical simulation studies, a method for evaluating the stress on submarine cables considering the influence of local scour topography was established using least squares fitting. The relevant average drag force coefficient C... dm Average lift coefficient C lm and the root mean square lift coefficient C lrms The following formula can be used for forecasting:

[0017] MERGEFORMAT (2)

[0018] MERGEFORMAT (3)

[0019] MERGEFORMAT (4)

[0020] MERGEFORMAT (5)

[0021] MERGEFORMAT (6)

[0022] As can be seen from the above formula, once the thickness of the incoming boundary layer is determined, the empirical formula proposed in this invention can be used to evaluate the stress on submarine cables under different Reynolds number conditions.

[0023] The beneficial effects of this invention are:

[0024] This invention enables accurate prediction of the hydrodynamic coefficients of submarine cables under the influence of local scour topography. The relevant empirical formula comprehensively considers the influence of the incoming boundary layer thickness and Reynolds number on the hydrodynamic coefficients of the cables, thereby enabling the assessment of the in-situ stability of submarine cables. This overcomes the shortcomings of existing research, which has not yet developed empirical prediction formulas for the hydrodynamic coefficients of submarine cables that take into account the influence of local scour topography, making it difficult to serve engineering design and practice. Attached Figure Description

[0025] Figure 1 is a schematic diagram of numerical simulation calculation of the stress on submarine cables considering local scour pits;

[0026] Figure 2 shows the comparison between the average drag coefficient of submarine cables and the empirical prediction formula;

[0027] Figure 3 shows the comparison between the average lift coefficient of the submarine cable and the empirical prediction formula.

[0028] Figure 4 shows the comparison between the root mean square lift coefficient of submarine cables and the empirical prediction formula.

[0029] [Corrected according to Rule 91 09.01.2026] Figure 5 shows the validity verification of the numerical analysis model, including the average drag coefficient, average lift coefficient, root mean square lift coefficient, and Strouhal number. Detailed Implementation

[0030] To enable those skilled in the art to better understand the technical solution of the present invention, the following description will be based on the numerical simulation work carried out by the present invention, and the effectiveness of the method proposed in the present invention will be discussed.

[0031] This invention verifies the effectiveness of the proposed cable stress prediction method through numerical simulation. The numerical calculations were performed using the open-source software OpenFOAM. The governing equations for fluid flow are Reynolds-averaged Navier-Stokes equations. To account for the influence of submarine cable stress under high Reynolds number conditions, a two-equation model (SSTk-ω) was used for turbulent closure. The relevant numerical calculation model is shown in Figure 1, where 1 represents the cable, with a non-slip boundary condition applied in the numerical calculation, i.e., both the horizontal velocity u and the vertical velocity v are zero, and the normal derivative of pressure ∂p / ∂n = 0; 2 represents the seabed with local scour pits, with a non-slip boundary condition applied in the numerical calculation; 3 represents the inlet, using a well-developed boundary layer as the velocity inlet, thus enabling numerical simulation of different boundary layer thicknesses; 4 represents the outlet, using a free outflow boundary condition; and 5 represents the upper boundary of the numerical calculation domain, with a symmetric boundary condition applied in the numerical model.

[0032] [Corrected according to Rule 91, 09.01.2026] To verify the effectiveness of the numerical analysis model established by this invention, Figure 5 shows the average drag coefficient C calculated by the numerical analysis model established by this invention. dm Average lift coefficient C lm Root mean square lift coefficient C lrms A comparison of the Strouhal number (St) with the physical experimental results of Jensen et al. (1990). In the experiment of Jensen et al. (1990), the submarine cable was placed on a sandy seabed that could be scoured, and the variation law of the above coefficients during the scour process was studied. The present invention selects the data at scour equilibrium to verify the numerical analysis model. As can be seen from the comparison results in Figure 5, the hydrodynamic coefficients calculated by the present invention are in good agreement with the experimental results, which verifies the reliability of the numerical analysis model established by the present invention. Figures 2, 3 and 4 respectively show the comparison between the numerical simulation results of the average drag coefficient, average lift coefficient and root mean square lift coefficient of the submarine cable and the prediction results of the empirical formulas (2) to (5) established by the present invention. As can be seen from the comparison results, the empirical prediction formulas established by the present invention are in very good agreement with the numerical simulation results, which verifies the reliability of the empirical prediction formulas proposed by the present invention.

[0033] [Corrected from Rule 91, 2026]

Claims

1. A method for assessing the stress on submarine cables that takes into account the effects of local scour topography, comprising the following steps: Determination of boundary layer thickness under different inflow conditions The thickness of the incoming boundary layer significantly affects the local scour development process, and consequently the stress on submarine cables. Therefore, the first step is to determine the boundary layer thickness δ under different incoming flow velocities. This invention mainly addresses the influence of local scour topography on the stress on submarine cables under unidirectional flow conditions. Under unidirectional flow conditions, the distribution of horizontal velocity along water depth satisfies the logarithmic law formula, which is as follows: MERGEFORMAT (1) Where u(z) represents the horizontal flow velocity at a water depth of z; κ is the Karman constant, which can be taken as 0.42; z s =d 50 / 12 represents the roughness length of the seabed, and d50 represents the median grain size of sediment in sandy seabeds, which can be obtained from sediment gradation curves; u f The velocity represents the bottom friction velocity. For practical engineering projects, marine hydrological surveys are generally conducted to measure the velocity at a single point in space. Substituting this velocity into formula (1), u can be calculated. f For unidirectional flow, the velocity at the boundary layer edge is 0.99U, where U represents the free flow velocity. The water depth z at the boundary layer edge can be calculated from this, and then the boundary layer thickness δ can be obtained. B. Evaluation method for submarine cable stress considering the influence of local scour topography Combining theoretical analysis and numerical simulation studies, a method for evaluating the stress on submarine cables considering the influence of local scour topography was established using least squares fitting. The relevant average drag force coefficient C... dm Average lift coefficient C lm and the root mean square lift coefficient C lrms The relationship between boundary layer thickness and Re number was investigated. Based on this, a method for assessing the stress on subsea cables that can consider the influence of local scour topography was established through least squares fitting. The cable stress was assessed using the average drag coefficient C. dm Average lift coefficient C lm and the root mean square lift coefficient C lrms The empirical prediction formula for the hydrodynamic coefficient of the pipe cable, obtained by fitting using the least squares method, is as follows: MERGEFORMAT (2) MERGEFORMAT (3) MERGEFORMAT (4) MERGEFORMAT (5) MERGEFORMAT (6) Where δ represents the thickness of the incoming boundary layer, D represents the diameter of the pipe / cable, Re=UD / v represents the Reynolds number, U represents the free flow velocity, and v represents the kinematic viscosity of the fluid.

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