Improved forecasting method for stress of submarine suspended pipe cable

Abstract

The invention belongs to the field of research on stress and in-situ stability of submarine suspended pipe cables, and discloses an improved forecasting method for stress of submarine suspended pipe cables. According to the method, through a large amount of theoretical analysis and research work, the defects that in existing research work, the influence of the incoming flow boundary layer thickness delta / D on the stress of the suspended pipe cable is difficult to avoid, the drag force coefficient Cd and the lift coefficient Cl are highly discrete, and a unified experience forecasting formula is difficult to carry out parameterized description are overcome. According to the method, the flow velocity at the center height of the pipe cable is adopted to carry out dimensionless processing on the stress of the pipe cable, the influence of an incoming flow boundary layer on the stress of the pipe cable can be eliminated, and therefore the parameterized description method of the hydrodynamic coefficient of the pipe cable is established and can be directly used for accurately forecasting the stress of the pipe cable in actual engineering.

Description

Technical Field

[0001] The invention belongs to the research field of the stress and in-situ stability of a submarine suspended umbilical cable, and relates to an improved prediction method for the stress of a submarine suspended umbilical cable. Background Art

[0002] Submarine cable structures are widely used in the fields of marine oil and gas resource transportation, offshore wind farm power transmission, and underwater communications. Their routes are often tens of kilometers long and require huge investments. The above-mentioned cable structures are often laid directly on the seabed. Under the action of the fluid, the cables will be locally scoured, and the scour pits will continue to expand along the axis of the cables, forming a suspended span of a certain length. In addition, there are often various complex seabed conditions on the seabed, such as gravel, sand waves and sand ridges. These seabed terrains often cause the submarine cables laid on them to form suspended spans. Once the submarine cable forms a suspended span, the fluid force it is subjected to will change, causing it to become unstable and damaged in situ. Once the above-mentioned cable structure is damaged, it will not only cause huge economic losses, but even difficult-to-repair marine ecological and environmental disasters. Therefore, the prediction of the force on the suspended cable has important scientific significance and engineering application value for ensuring the in-situ stability and safe operation of the submarine cable.

[0003] At present, the design of the stress and in-situ stability of submarine cables is mainly based on the DNV-RP-F109 specification issued by the Norwegian Classification Society. This specification is applicable to the stress and in-situ stability assessment of cables directly laid on the seabed, and cannot be applied to the situation where cables are suspended. For cables directly laid on the seabed, it is difficult to remain static due to the effect of fluid forces, that is, instability in situ will occur. Therefore, additional weight, such as a concrete outer layer, is required to maintain its in-situ stability. According to the DNV-RP-F109 specification, the following conditions must be met for cables to maintain in-situ stability:

[0004]

[0005] Among them, s g It represents the weight coefficient of the stability of the cable in place. Its physical meaning is the ratio of the density of the cable after adding weight to the density of the water body; U represents the flow velocity of the fluid outside the flow boundary layer; C d and C lThey represent the drag coefficient and lift coefficient of the umbilical cable respectively; μ represents the friction coefficient between the umbilical cable structure and the seabed; g represents the acceleration of gravity; and D represents the diameter of the umbilical cable. It can be seen from the above formula that the stability weight coefficient of the umbilical cable is closely related to the fluid force it is subjected to. As mentioned earlier, the DNV-RP-F109 specification can only be used to evaluate the stress and stability of umbilical cables laid flat on the seabed. The current specifications are difficult to consider the stress of umbilical cables with a suspended height. Therefore, it is necessary to develop a stress assessment method that can consider the suspended effect of umbilical cables to improve the in-situ stability design of the submarine umbilical cable structure and ensure its service safety.

[0006] At present, many scholars at home and abroad have carried out relevant research on the stress of suspended cables, and studied the influence of dimensionless suspension height e / D on the stress of suspended cables under different flow conditions. Representative research works include "Vortex shedding suppression for flow over a circular cylindernear a plane boundary." published by Lei et al., "Numerical modeling of flow and scourbelow a pipeline in currents: partⅡ. Scour simulation." published by Liang et al., "Numerical simulation of flow around a circular cylinder close to a flatseabed at high Reynolds numbers using a k-εmodel" published by Ong et al. In their research work, the influence of the thickness of the flow boundary layer δ / D on the stress of the cable was considered. At the same time, the velocity U outside the boundary layer was used to non-dimensionalize the velocity force on the cable structure, and the drag coefficient C was obtained. d and lift coefficient C l The above research work shows that for unidirectional flow conditions, the obtained drag coefficient C d and lift coefficient C lThe relationship between the Reynolds number Re is very discrete, and it is difficult to use a unified empirical prediction formula for parameterization, so it cannot be directly applied to actual engineering design. The definition of Reynolds number Re is Re = UD / υ, where υ represents the viscosity coefficient of the fluid. The research work "Vortexshedding suppression for flow over a circular cylinder near a plane boundary" published by Lei et al. shows that different incoming flow boundary layer thickness δ / D has a great influence on the force on the cable, which is the cause of the drag force coefficient C d and lift coefficient C l The main reason for discretization.

[0007] The present invention analyzes the influence of the thickness of the incoming flow boundary layer on the stress of the cable through a large number of numerical simulation studies. Through a large number of theoretical analysis studies, it is found that the influence of the incoming flow boundary layer on the stress of the cable can be eliminated by using the flow velocity at the center height of the cable to perform dimensionless processing on the stress of the cable, thereby establishing a parameterized description method for the hydrodynamic coefficient of the cable. This method can be directly used for the accurate prediction of the stress of the cable in actual engineering. Summary of the invention

[0008] In order to solve the above problems existing in the prior art and provide a scientific basis and technical guarantee for the stress evaluation and in-situ stability design of suspended cables, the purpose of the present invention is to provide an improved prediction method for the stress of submarine suspended cables, so as to overcome the influence of the thickness of the incoming boundary layer δ / D on the stress of suspended cables, which is difficult to avoid in the existing research work, resulting in the drag force coefficient C d and lift coefficient C l The defect is that it is highly discrete and difficult to describe parameterized using a unified empirical prediction formula.

[0009] The technical solution of the present invention:

[0010] An improved prediction method for submarine suspended cable stress comprises the following steps:

[0011] (1) Determination of characteristic flow rate

[0012] Since the thickness of the incoming flow boundary layer δ / D is an important factor affecting the stress on the cable, it is also the factor causing the drag force coefficient C d and lift coefficient C l The fundamental reason why the Reynolds number Re presents a discrete characteristic; for this reason, a method is proposed to non-dimensionalize the fluid force based on the flow velocity at the center height of the cable, thereby eliminating the influence of the boundary layer thickness. The core problem that needs to be solved is how to conveniently and quickly calculate the flow velocity U at the center height of the cable. c; In addition, in order to facilitate the comparison and verification of the superiority of the proposed method, it is also necessary to know the flow velocity U outside the boundary layer; for unidirectional flow, the horizontal flow velocity along the water depth velocity profile satisfies the logarithmic rate distribution law, which is described by the following equation:

[0013]

[0014] Where u(z) represents the horizontal flow velocity at height z; u * represents the bottom friction velocity; κ=0.42 represents the Karman constant coefficient; k s =2.5d 50 represents the roughness height of the seabed, d 50 represents the median particle size of sediment in a sandy seabed;

[0015] For actual marine engineering, according to the boundary layer theory, the flow velocity U at different water depths outside the boundary layer is equal. It is obtained by field measurement. By formula (2), assuming that the spatial coordinate z = H, where H represents the water depth, the bottom friction velocity u caused by the fluid flow can be calculated. * According to formula (2), the velocity at any water depth z is obtained; assuming that the suspension height of the cable is e, which represents the distance from the seabed to the lowest point of the cable, the spatial coordinates corresponding to the center height of the cable are z = e + 0.5D. Substituting this spatial coordinate into formula (2), combined with the known bottom friction velocity u * , the flow velocity U at the center height of the cable can be calculated c , and then use this flow velocity to make the fluid force on the cable dimensionless;

[0016] (2) Parametric description method of the forces on suspended cables

[0017] For the suspended cable span formed by local scouring of the cable and complex seabed conditions, such as gravel or sand waves and ridges, the suspension height is often low, and the flow field around the cable will be strongly affected by the seabed, so that the tail vortex shedding behind it is suppressed, resulting in the corresponding horizontal drag force and vertical lift force often being dominated by the average value, while the pulsation value is small and can be ignored. Therefore, this method mainly focuses on the average value of the lift coefficient C Lm and the average value of the drag coefficient C Dm ;

[0018] Based on the fluid velocity at the center height of the cable obtained by formula (2), combined with theoretical analysis and numerical simulation, the average value of the drag force coefficient C is obtained by least squares fitting. Dm and the average value of the lift coefficient C Lm The following empirical formula can be used to evaluate the stress of submarine cables:

[0019]

[0020] Among them, F Dm and F Lm Respectively represent the average drag force and the average lift; From the above formula, it can be seen that the prediction method of the hydrodynamic coefficient of the submarine cable is only related to the dimensionless suspension height e / D of the cable. In engineering practice, the suspension conditions of the cable at different positions are conveniently obtained through side-scan sonar, and then the force is predicted. The above prediction formula uses the flow velocity at the center height of the cable to non-dimensionalize the fluid force, and eliminates the influence of the incoming flow boundary layer in the prediction formula, thereby avoiding the defect that the force of the cable due to the boundary layer is discretely distributed with the flow control parameters.

[0021] Beneficial effects of the present invention:

[0022] 1) The present invention uses the flow velocity at the center height of the cable to non-dimensionalize the hydrodynamic force on the cable, and then establishes a parameterized description method for the hydrodynamic coefficient of the suspended cable. Through the above-mentioned non-dimensionalization method, the influence of the incoming flow boundary layer can be effectively avoided, overcoming the major defect that the existing scholars use the free flow velocity to non-dimensionalize the cable force, which cannot avoid the influence of the incoming flow boundary layer, resulting in the corresponding hydrodynamic coefficient showing a highly discrete feature with the flow control parameter, and it is difficult to use a unified quantitative method to accurately predict the cable force.

[0023] 2) The prediction formula established in the present invention can accurately predict the stress of suspended cables and pipes, and can provide a scientific basis and technical guarantee for the stress and in-situ stability design of cables and pipes. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a schematic diagram of numerical simulation calculation of the forces on suspended cables under the action of fluid;

[0025] Figure 2 To verify the validity of the numerical analysis model, the average drag force coefficient;

[0026] Figure 3 To verify the validity of the numerical analysis model, the average lift coefficient;

[0027] Figure 4 is the calculation result of dimensionlessizing the force on the cable using the velocity U outside the boundary layer;

[0028] Figure 5 The calculation result of non-dimensionalizing the force on the cable using the flow velocity at the cable center height;

[0029] Figure 6 Comparison between the average drag coefficient predicted by formula (3) and the numerical simulation results;

[0030] Figure 7 Comparison between the average lift coefficient predicted by formula (4) and the numerical simulation results. DETAILED DESCRIPTION

[0031] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0032] The effectiveness of the proposed method for predicting the stress of the cable is verified by numerical simulation. The numerical calculation uses the open source software OpenFOAM. The control equation of the flow is the Reynolds-averaged Navier-Stokes equation, and the turbulence is closed by the SST k-ω two-equation model. The relevant numerical calculation models are as follows: Figure 1 As shown, 1 represents the cable, and the non-slip boundary condition is applied in the numerical calculation, that is, the horizontal flow velocity u and the vertical flow velocity v are both equal to zero, and the normal derivative of the pressure is 2 represents the suspension height, which is defined as the height of the bottom of the umbilical cable from the seabed; 3 represents the inlet, and a mature boundary layer is used as the velocity inlet, so that the hydrodynamic force on the umbilical cable under different inlet boundary layer thickness conditions can be obtained; 4 is the outlet, and a free outflow boundary condition is adopted; 5 is the seabed boundary, and a non-slip boundary condition is applied in the numerical calculation; 6 is the top boundary of the calculation model, and a symmetric boundary condition is adopted.

[0033] The calculation parameters of the above numerical analysis model are: Reynolds number Re = 1×10 4 , gap ratio e / D=0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1.0, 1.5, 2.0, and the incoming boundary layer thickness δ / D=0.5, 0.7, 1.0, 1.5, 2.0, 2.5 and 3.0. In the numerical calculation, the effects of boundary layer thickness δ / D and gap ratio e / D on the stress of cable are analyzed.

[0034] In order to verify the accuracy of the numerical analysis model established by the present invention, Figure 2 The average drag coefficient C calculated by the numerical analysis model established by the present invention is given. Dm Comparison with the experimental results of Jensen et al. (1990) and the numerical simulation results of Kazeminezhad et al. (2010); Figure 3 The average lift coefficient C calculated by the numerical model is given Lm Compared with the experimental results of Jensen et al. (1990), the numerical results of Kazeminezhad et al. (2010) and the numerical simulation results of Tang et al. (2018), Figure 2 and Figure 3It can be seen from the comparison results that the numerical analysis model established in the present invention is in good agreement with the physical experiments and numerical simulation results of others, which verifies the reliability of the established numerical analysis model.

[0035] Figure 4 The average drag coefficient under different suspension height conditions is obtained by non-dimensionalizing the fluid force on the suspended cable using the velocity outside the boundary layer. It can be seen from the figure that the thickness of the boundary layer has a greater impact on the force on the cable. Under the same suspension height e / D, the distribution of the hydrodynamic coefficient of the cable under different boundary layer thickness δ / D conditions shows a certain bandwidth, and the data is relatively discrete. Figure 5 The hydrodynamic coefficient is given after the fluid force on the suspended cable is dimensionless using the flow velocity at the center height of the cable. It can be seen from the figure that for the same cable suspension height e / D, the hydrodynamic coefficients under different boundary layer thicknesses δ / D are almost the same, which means that the dimensionless method of the force on the cable using the flow velocity at the center height of the cable can eliminate the influence of the boundary layer thickness, which lays a theoretical foundation for the establishment of relevant empirical prediction formulas.

[0036] Figure 6 and Figure 7 The comparison between the empirical prediction formulas of the average drag coefficient and the average lift coefficient proposed in the present invention and the numerical simulation results is given respectively. It can be seen from the figure that the empirical prediction formula of the hydrodynamic coefficient of the cable proposed in the present invention is almost consistent with the numerical calculation results, and has a high prediction accuracy, which proves the effectiveness and accuracy of the method for predicting the hydrodynamic coefficient of the suspended cable proposed in the present invention.

Claims

1. An improved prediction method for the stress of submarine suspended cables, characterized in that: The following steps are involved: (1) Determination of characteristic flow rate The thickness of the incoming flow boundary layer δ / D is a factor that affects the stress on the cable and is also the factor that causes the drag force coefficient C. d and lift coefficient C l The reason why the Reynolds number Re presents a discrete characteristic; To this end, a method based on the flow velocity at the center height of the cable is proposed to non-dimensionalize the fluid force to eliminate the influence of the boundary layer thickness, and then calculate the flow velocity U at the center height of the cable. c ; In addition, it is also necessary to obtain the flow velocity U outside the boundary layer; for unidirectional flow, the horizontal flow velocity along the water depth velocity profile satisfies the logarithmic rate distribution law, which is described by the following equation: Where u(z) represents the horizontal flow velocity at height z; u * represents the bottom friction velocity; κ=0.42 represents the Karman constant coefficient; k s =2.5d 50 represents the roughness height of the seabed, d 50 represents the median particle size of sediment in a sandy seabed; According to the boundary layer theory, the flow velocity U at different water depths outside the boundary layer is equal, which is obtained by field measurement. According to formula (2), assuming that the spatial coordinate z = H, where H represents the water depth, the bottom friction velocity u caused by the fluid flow is calculated. * According to formula (2), the velocity at any water depth z is obtained; Assuming that the suspension height of the cable is e, which represents the distance from the seabed to the lowest point of the cable, the spatial coordinates corresponding to the center height of the cable are z = e + 0.5D. Substituting this spatial coordinate into formula (2), combined with the known bottom friction velocity u * , that is, calculate the flow velocity U at the center height of the cable c , and then use this flow velocity to make the fluid force on the cable dimensionless; (2) Parametric description method of the forces on suspended cables For the suspended cable span formed by local scouring of the cable and complex seabed conditions, the suspension height is often low, and the flow field around the cable will be strongly affected by the seabed, which suppresses the shedding of the wake vortex behind it, resulting in the corresponding horizontal drag force and vertical lift force often being dominated by the average value, while the pulsation value is small and negligible; therefore, this method mainly focuses on the average value of the lift coefficient C Lm and the average value of the drag coefficient C Dm ; Based on the fluid velocity at the center height of the cable obtained by formula (2), combined with theoretical analysis and numerical simulation, the average value of the drag force coefficient C is obtained by least squares fitting. Dm and the average value of the lift coefficient C Lm The following formula is used to obtain the force assessment of the submarine cable: Among them, F Dm and F Lm They represent the average drag force and the average lift respectively. As can be seen from the above formula, the prediction method of the hydrodynamic coefficient of the submarine cable is only related to the dimensionless suspension height e / D of the tube and cable. The suspension conditions of the tube and cable at different positions are obtained through the side-scan sonar, and then the force prediction is carried out.

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