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The Calculating Dynamics Erosion of Support Foundations of Ocean-Technical Installations

The article discusses an approach to calculating the characteristics of soil erosion near the support foundations of ocean-technical structures under the influence of wave and constant currents. Vertical supports in the form of a circular cylinder are considered a support base. An example of the choice of the initial and boundary conditions for the calculation is given. Simulation is carried out near the cylindrical support. The results obtained were compared with empirical data. Conclusions are drawn about the displacement of the zones of maximum and minimum velocities during wave movement. The spatial distribution of the amplitudes of the wave velocities was calculated. A decrease in the amplitude in the rear part of the cylinder and immediately in front of its frontal part was revealed, and it was also determined that the zone of an increase in the amplitude was formed near the lateral surfaces of the cylinder.


Introduction
Currently, there are several methods for modeling the erosion of the support foundations of ocean engineering systems. Basically, for their application, it is necessary to calculate the three-dimensional velocity field of the flow around structural elements by wave and constant currents, and then use the obtained velocity fields to calculate turbulent stresses near the bottom surface and the conditions for the transfer of the bottom material in a suspended state or directly on the bottom surface. There are a large number of works devoted to experimental, theoretical, and numerical methods for studying the structure of a viscous fluid flow around various obstacles [1][2][3][4][5][6][7]. Nevertheless, this problem cannot be considered solved, since in a turbulent flow regime (Re >> 10 3 ), the solution of the basic hydrodynamic equations becomes unstable even with a relatively fine computational grid and a small-time step. To solve nonstationary problems associated with the interaction of various flows with streamlined objects, the averaging of the Navier-Stokes equations according to Reynolds is used [8], and at the same time, there is a well-known problem of parametrization of the subgrid stress tensor [9, 10]. In the simplest case, a hypothesis of Boussinesq is used [11,12,13]. Following the hypothesis, the tensor is expressed in terms of the gradients of the averaged components of the flow velocity and a constant value -the coefficient of turbulent viscosity . This makes it possible to formally replace the coefficient of kinematic viscosity with some constant value , which is ambiguous and, as a rule, is selected from the condition of obtaining a stable solution under given boundary conditions, computational grid, and time step. This method is still relatively widely used in solving various hydrodynamic problems and in geophysical hydrodynamics [14,15]. At the same time, relatively complex software which provides for the use of various LES methods for spatial hydrodynamic calculations is being created. These include, for   [16], COSMOSFloWorks. COSMOSFloWorks also uses Reynolds' averaging of Navier-Stokes equations, where turbulent effects are considered as flow parameters or large-scale time-dependent effects. To close the system of equations, transport equations are used for the kinetic energy of turbulence and the rate of its dissipation per unit volume (the so-called model) [17]. In this case, the same system of equations is used to describe laminar and turbulent flows. This article considers an approach to the three-dimensional hydrodynamic calculation of the velocity field when a constant current flows around vertical support (in the form of a circular cylinder) of an ocean-technical installation, and also determines the characteristics of soil erosion near the support. The results of such numerical modeling are compared with the data of known experimental studies of such flows. The considered approach is adapted for the application of COSMOSFloWorks. The solution to these problems determines the possibility and prospects of using COSMOSFloWorks as a modern tool for studying the impact of natural currents on structural elements of such ocean-technical systems as offshore drilling platforms, subsea pipelines, terminals, and others.

Result
Let us consider the numerical calculation of the structure of the velocity field and the characteristics of soil erosion near the vertical support of the ocean-technical installation under the influence of constant and wave currents with the help of COSMOSFloWorks.
Vertical cylindrical supports are widely used in installations for offshore development, as well as for studying the dynamics of the bottom topography under the action of waves and currents in controlled laboratory conditions. The design diagram of the flow around the cylinder is shown in Figure 1. To solve a three-dimensional non-stationary problem, the dimensions of the computational domain are set along the axes , which are 10 ... 15 times larger than the dimensions of the streamlined cylinder.
The boundary conditions are defined as follows: 1. The geometry of the streamlined cylinder -the coordinates of its surface in the base coordinate system are determined. The adhesion condition is set on a solid surface of the streamlined object.
2. On the boundary planes AA'CC ', ABCD and A'D'C'B', a constant flow velocity (along the axis) is set. 3. At the boundary of the outflowing stream (plane BB'DD '), the Sommerfeld condition [18] is set for the normal components of the velocity.
As the initial conditions, a uniform flow with a constant velocity directed along the axis is  The calculation results showed that within an hour the depth changes do not exceed one centimeter. In 12 hours, the amount of washout reaches 5.5 cm, and the washout -1.5 cm. Over the first day, the washout increases to 7 cm, for the second -up to 10 cm, and for the third -up to 16 cm. Maximum washout for the same intervals time is 4, 6, and 10 cm, respectively. Areas of soil washout are located in the frontal and rear parts of the cylinder, areas of washout are located near the side surfaces. An interesting feature of the bottom structure is the formation of zones of erosion and soil reclamation in the wake of the flow around the cylinder at a distance of 5 ... 8 m from its center.

Discussion
Comparison of simulation results with empirical data based on the SRICOS-EFA method [20]. Following this method, the time dependence of the erosion depth is calculated by the formula , where; ; -the coefficient of the shape of the streamlined object, for a cylinder its value is equal to 1; -Reynolds number; is the initial erosion rate, which corresponds to the turbulent stress near the bottom . The comparison results showed that the difference between the calculations does not exceed 5%. As mentioned above, the flow around the cylinder is shown in Figure 1. The wave propagates along the axis . The boundary conditions for calculating the wave velocity are determined as follows. 1. On the plane AA'CC ' the wave velocity field is set in the following form: , , , .
The wave propagates along the axis The pressure field is set on the free surface (plane ABCD) , , where -circular frequency of wave vibrations; -wave number; -wave amplitude.
2. On the plane DBB'D', the Sommerfeld radiation condition is set for the normal components of the flow velocity, i.e. .
3. On the surface of the cylinder and the bottom , the condition of equality to zero of the flow velocity is satisfied, i.e. . The boundary conditions for calculating mean flow disturbances are determined as follows. 1. On the sea surface (plane ABCD) and the plane, the drift velocity of the current m/s is set. The bottom boundary layer is not taken into account in this problem, since the solution uses the vertical average flow velocity .
2. On the plane DBB'D', the Sommerfeld radiation condition is set in the following form .
3. On the surface of the cylinder and the bottom , the condition of equality to zero of the flow velocity is satisfied, i.e. . Since the phase velocity of the wave is approximately 10 m/s, and the velocity of the constant flow is 0.2 m/s, there is practically no interaction between the constant and the wave velocity and these fields can be considered independently, i.e. solve two problems -one for wave velocity, the other for constant flow. Figure 3 shows the results of the distribution of the wave velocity of the flow around the cylinder with the indicated interval. Figure 4 shows the results of calculations of erosion and washout of bottom material near the vertical cylinder, calculated for the above conditions and for different time intervals.    The shift of the zones of maximum and minimum velocities during wave movement is noticeable. Having the data on the wave velocity field at each point of the calculation scheme, the spatial distribution of the wave velocity amplitudes was calculated. Its feature is a decrease in amplitude in the rear of the cylinder and immediately in front of its frontal part. Zones of increasing amplitude are formed near the lateral surfaces of the cylinder.
Based on the results of calculations, conclusions can be drawn. Within an hour, changes in depth do not exceed one centimeter. In 12 hours, the amount of washout reaches 5.5 cm, and the washout -1.5 cm. Over the first day, the washout increases to 7 cm, for the second -up to 10 cm, and for the thirdup to 16 cm. Maximum washout for the same time intervals is 4, 6, and 10 cm respectively. Areas of