Simulated and Experimental Study of Sediments Sampling Parameters Based on the VOF Method

: Sediments in the seabed hold vital clues to the study of marine geology, microbial communities and history of ocean life, and the remote operated vehicle (ROV) mounted tubular sampling is an important way to obtain sediments. However, sampling in the seabed is a particularly difficult and complicated task due to the difficulty accessing deep water layers. The sampling is affected by the sampler’s structural parameters, operation parameters and the interaction between the sampling tube and sediments, which usually results in low volume and coring rate of sediments obtained. This paper simulated the soft viscous seabed sediments as non-Newtonian Herschel-Bulkley viscoplastic fluids and established a numerical model for the tubular sampling based on the volume of fluid (VOF) method. The influence rules of the sampling tube diameter, drainage area rate, penetration velocity, and sediments dynamic viscosity on coring rate and volume were studied. The results showed that coring volume was negatively correlated with all the parameters except the sampling tube diameter. Furthermore, coring rate decreased with increases in penetration velocity, drainage area rate, and sediments dynamic viscosity. The coring rate first increased and then decreased with increasing of the sampling tube diameter, and the peak value was also influenced by penetration velocity. Then, based on the numerical simulation results, an experimental sampling platform was set up and real-world sampling experiments were conducted. The simulation results tallied with the experimental results, with a maximum absolute error of only 4.6%, which verified that the numerical simulation model accurately reflected real-world sampling. The findings in this paper can provide a theoretical basis for facilitating the optimal design of the geometric structure of the seabed sediments samplers and the parameters in the sampling process.


Introduction
Deep-sea sediments hold evolutionary records of the oceanic environment, records of great significance for scientific fields investigating marine sedimentary processes, structural evolution, paleoceanography, paleomagnetism, seabed mineral resource exploration, and history of marine life. However, the acquisition of original samples from deep-sea sediments is completely dependent on advanced seabed sediments collection methods and technical equipment [1][2][3][4]. Among them, the ROV-mounted tubular sampling is one of the important ways to obtain seabed sediments. However, sampling in the seabed is a particularly difficult and complicated task due to the difficulty accessing deep water layers. The sampling is affected by the sampler's structural parameters, operation parameters and the interaction between the sampling tube and sediments, which usually results in low volume and coring rate of sediments obtained [5][6][7][8]. For example, Emery and Dietz et al. [9] found that the sediments entering the tube was compressed to about 50% of the penetration depth by measuring the sampling rate of an open gravity sampler. Therefore, it is particularly important to study the influence rules of key parameters such as the sampling tube diameter, drainage area rate, penetration velocity, and sediments dynamic viscosity on coring volume and rate based on the dynamic sampling process, which can provide a basis for the design of samplers with high sampling volume and coring rate.
Many researchers ignored the high pressure in seabed, and they used the pipe pile theory to assume that the sampling process of deep-sea sediments was approximately equivalent to the process of pipe piles driving into soft clay, and the sediments sampling process was theoretically modeled and analyzed. For example, Carret et al. [10] regarded the sampling process as the expansion of a cylindrical hole in soil. Axisymmetric elastoplastic theory was used to study the change characteristics of stress and pore water stress during pile sinking in viscous soil, and a change rule for the stress field with depth was obtained. Tatsvnovi [12] regarded the soil plug as a series of spring units connected in series with mass points using stress wave theory, and carried out dynamic and static mechanical analyses of the pile penetration process. L.C. Skinner et al. [13] established a mathematical model of the sampling process based on the principle of soil mechanics, and analyzed the effects of a gravity corer and a piston sampler on the coring volume and rate of marine sediments samples.
Based on the principle of soil mechanics, the study of sampling process by using pipe pile theory lacks the understanding of the physical mechanism determining sediments strain and stress characteristics in the sampling process, and sampling dynamic process is not visually clear. Therefore, some researchers have turned to numerical methods to analyze the coring process. For example, Chopra et al. [14] used the finite element method to establish a time-dependent, large-deformation consolidation analysis. They believed that the sediments followed the revised Cambridge model, and the principle of effective stress was used to derive the large deformation finite element consolidation equations, which were later applied to simulate the sampling process. Randolph et al. [15] conducted a one-dimensional simplified analysis of soil plugs of pipe piles during penetration, discussing the soil plug problem only in drained conditions and not in undrained conditions. Zhou et al. [16] applied a nonlinear finite element analysis method to establish a two-dimensional axisymmetric finite element model of the contact between the sampling tube and the sediments, and selected the Drucker-Prager elastoplastic model to simulate the sediments. By assessing disturbance to the sediments during the sampling process, the results confirmed that a tubular sampler would cause the shortening of sediments samples. However, this method also ignored the effect of hydrostatic pressure. Qin et al. [17] proposed a numerical method for simulating gravity coring in which the sediments model was a modified Drucker-Prager constitutive model. They established a three-dimensional finite element model based on ABAQUS, and the sampling effect was analyzed using the Euler-Lagrange coupling method. Obvious phenomena of sample shortening were captured in this model. Guo et al. [18] used the discrete element model (DEM) to simulate the clogging of soil inside a large-diameter pipe pile, comprehensively simulating the interactions between the soil particles and between the soil particles and the pipe pile. The influence of parameters such as the length of the soil column, inner diameter of the pile was studied, but the soil did not conform to the mechanical characteristics of seabed sediments.
In the above-mentioned researches, the elastic-plastic model based on the principle of soil mechanics was usually used to characterize the seabed sediments, which is different from the actual situation of deep-sea environment which is characterized by ultrahigh pressure. Moreover, the influences of hydrostatic pressure and sampling velocity on the coring volume and rate were ignored in research processes. In this paper, the sampling process of sediments was studied from the perspective of fluid mechanics, and the influence rules of key parameters such as the sampling tube diameter, drainage area rate, penetration velocity, sediments dynamic viscosity on coring rate and volume were studied. The simulation results tallied with the experimental results, which proved that this method is more suitable for the actual seabed sampling. The findings in this paper can provide a theoretical basis for facilitating the optimal design of the geometric structure of the seabed sediments samplers and the parameters in the sampling process.

Methodology
The sampling device, as an important part of the sampler, is used to collect deep-sea sediments. The studied sampling device's major components included a handle, a sampling tube, a high-pressure valve, a gas-tight coupler, and a piston. A number of holes were evenly spaced around the proximal end of the sampling tube for drainage. The outer side of the top of the sampling tube was connected via threading with the gas-tight coupler, tightening onto an O-ring to guarantee the seal and ensure constant pressure retaining the sediments once sampling was completed, until being fixed to the pressure-retaining cylinder. The sampler is mounted on an ROV. When the sampler reaches the sampling point, the mechanical arm grabs the handle of the sampling device and inserts it vertically into the sediments with a certain velocity. Then, the sampling device is pulled vertically upward and is fixed to the sampler until it is locked and sealed. In order to meet the requirements of modeling, the sampling tube length is marked as L , the sampling tube diameter as D , and the drain hole diameter as d , as shown in Fig. 1. In order to simplify the model, it is imperative to make reasonable assumptions. The specific assumptions are as follows: (1) The sediments and water are not mixed with each other during the sampling process because the velocity during penetration is relatively low (According to the requirements of the on-site ROV's mechanical arm, the penetration velocity is usually set at less than 200 mm /s.), in each controlled volume, the sum of the volume fractions of water and sediments is 1; (2) The flow of sediments and water in the tube is continuous during the sampling process; (3) Any changes in temperature or sediments water content have no influence on the sediments dynamic viscosity; (4) The thickness of the sampling tube wall is zero and the sampling tube sediments catchers have no influence on sampling.
The continuity equation is as follows: Where q is the physical density of phase q ; q v is the velocity of phase q ; pq m is the mass transfer from phase q to p ; qp m is the mass transfer from phase p to q ; and q S is the source item with a default value of zero. The basic phase volume fraction is calculated with the constraint that the sum of the volume fractions of all phases is 1 without solving the volume fraction equation: Unit density: Where the seawater density is 1 . In this paper, 3 Where is the dynamic viscosity; and F is the source item of the momentum equation caused by surface tension and wall adhesion. Assuming that the penetration depth of the sampling tube into the sediments is L , the height of the sediments entering the sampling tube is , and the coring volume is Q , then: At the same time, in order to further evaluate the sampling performance of the sampler, the concept of coring rate is introduced. The coring rate is : The coring rate is an important index of deep-sea sediments sampling equipment. The larger is, the better the sampling performance is; the lower is, the worse the sampling performance is. Therefore, the research focus of this paper was to determine how to effectively increase the coring volume and rate of the sampler. The grid quality directly affects the accuracy of the computational results. In order to obtain more accurate computational results while also reducing computational costs, the structural grid was adopted, which is mainly tetrahedron. However, because higher numbers of the grid cell benefit computational accuracy but also increase computational cost, an acceptable degree of error must be determined. In order to find a balance between error and cost, it is necessary to verify the grid independence to determine the grid size. Under the conditions of sampling tube length

Computational parameters and boundary conditions
The multiphase model and the realizable k-ε turbulence model were used to simulate the flow field in the computational domain. The calculation uses 3D single precision, and the dynamic grid change is controlled by a dynamic layering method, which activates the size function control to prevent the occurrence of excessively distorted grids during the calculation process. The convection term is discretized by a first order upwind scheme that easily converges. The pressure solver was also used, and the PISO algorithm was applied for pressure-velocity coupling.
Outlet boundary conditions: the boundary conditions of pressure outlet were adopted, with a gauge pressure of zero.
Wall boundary conditions: the lower boundary of the computational domain adopted rigid boundary, and for the cylindrical surface of the computational domain a symmetric boundary was adopted.

Settings of parameters 2.4.1 Sampling tube diameter
Laboratory sampling experiments and research data have shown that coring volume and rate are related to the sampling tube diameter. To select the sampling tube diameter, the index requirements must be met, such as the coring volume requirements and the weight requirements of the sampler for ROV on-board operation. In this paper, the sampling tube diameter was set to within the range of 20 mm to 80 mm to best meet the research goals.

Penetration velocity
Literature [12] shows that coring volume and rate are affected by penetration velocity. Therefore, the penetration velocity should be chosen to maximize sampling performance. Too high a sampling speed velocity during penetration may hinder the flow of water in the sampling tube or exceed the capacity of the drain holes, and the upper surface of the sediments in the sampling tube may generate water pressure which will reduce the coring rate. At the same time, according to the sampling operation requirements of the on-site ROV's mechanical arm, the penetration velocity is usually set at less than 200mm /s. In order to study the influence of the penetration velocity on coring volume and rate, the simulated velocities of penetration ranged from 20 mm/s to 200 mm/s in this paper.

Drainage area rate
In the actual sampling process, if the drainage from the sampling tube is not smooth or becomes completely closed, the flow of water in the sampling tube will be blocked, and the upper surface of sediments in the sampling tube may generate water pressure which will reduce the sampling rate. In order to overcome this "hydraulic effect", drain holes with a certain diameter are arranged around the upper circumference of the sampling tube to reduce the hydrostatic pressure on the upper surface of the sediments. In this paper, drain holes for the upper circumference of the sampling tube were proposed, and the number and the diameter of drain holes must meet the requirements of the sampling tube. Therefore, the drainage area rate of the fluid in the sampling tube was introduced, and is defined as follows:

Where in
S is the total inlet area of the sampling tube; and out S is the outlet area of the sampling tube. Where D is the sampling tube diameter. Where N is the number of drain holes ( 8 N ); and d is the drain hole diameter. Under the same tube diameter condition, setting 12 0 , the influence of different drainage area rates on the coring volume and rate was studied.

Sediments dynamic viscosity
Previous research data has shown that the sediments located on the seabed surface has a high water content and high viscosity, which conforms to the characteristics of a non-Newtonian fluid. The Herschel-Bulkley model is one of the simplest viscoplastic models for non-Newtonian fluids. The model is described using the following parameters: Where 0 is the yield stress; is the shear strain rate; K is the consistency coefficient; and n is the shear-thinning index. The above formula is simplified to n=1. The shear stress changes linearly with shear strain rate, thus K is the dynamic viscosity . In the experiments part of section 4, the sediments dynamic viscosity was measured, and the value was within 100 s m / kg under different temperature conditions. The sediments dynamic viscosity is directly related to its water content and the temperature and pressure of the environment, so the sediments at different depths and in different sea areas will have different dynamic viscosities. Therefore, this paper set the sediments dynamic viscosity to range from 10 -2 to 10 2 kg/m•s to study the influence of dynamic viscosity on coring volume and coring rate.
The specific calculation parameters of the model are shown in Table 1:

Results and discussion
The sampling tube length (L), diameter (D), and drain hole diameter (d) will affect the sediments entering the tube, which needs to overcome its own viscous resistance, interfacial surface tension, and water resistance during sampler penetration. When sampling is finished, the height of sediments that has entered the tube can be clearly observed, and the height of the sediments in the sampling tube was always less than the sampling tube's penetration depth, as shown in Fig. 5. In order to further study the relationship between sampling efficiency and the influential parameters, this paper studied the influence of different velocities of penetration, different inner diameters of the sampling tube, different drainage area rate, and different dynamic viscosities of sediments on coring volume and coring rate. In this section, the study on influence rules of the sampling tube diameter on the coring volume and coring rate is reported and discussed. For this examination, the length of the sampling tube was 500 mm, the viscosity of the sediments was 10 kg/ m•s, the drain holes diameter was 5 mm, the sampler diameter ranged from 20 to 80 mm, and six different velocities of penetration were used. Fig.  6 shows the coring volume increased linearly with increases in sampling tube diameter. The lower the penetration velocity, the more obvious the increasing trend in coring volume. Fig. 7 shows the coring rate first increased and then decreased with increases in the sampling tube diameter. When the penetration velocity was 200 mm/s and the sampling tube diameter was 40 mm, the coring rate was about 0.33. When the penetration velocity was 20 mm/s and the sampling tube diameter was 70 mm, the coring rate was around 0.8.
The comparison between Fig. 6 and Fig. 7 shows that the changing trends of the sampling tube diameter on the coring volume and rate are completely different. Increasing the sampling tube diameter can improve the coring volume, but the coring rate first increases and then decreases, indicating there is an inflection point at which an optimal coring rate is achieved. When designing the sampling tube, increasing the sampling tube diameter can increase the sampling volume, but an unlimited increase in the sampling tube diameter means an increase in the weight of the sampler, which is definitely not desirable for ROV with a weight limit on the sampler. Therefore, under the condition of a known penetration velocity, a reasonable sampling tube diameter is an important guarantee for obtaining samples with a high coring rate. Fig. 6 The influence curve of the sampling tube diameter on the coring volume Fig. 7 The influence curve of the sampling tube diameter on the coring rate 3. 2 Influence of drainage area rate Drainage area rates determine the flow of the water in the sampling tube and whether it can be drained smoothly or not. Therefore, in this section, numerical simulations were conducted for drainage area rates of 1, 2, 3, 4, 6, 8, and 12, and the influence rules of different drainage area rates on coring volume and rate were assessed. For these simulations, the sampling tube length was 500 mm, sediments viscosity was 10 kg/ m•s, and the penetration velocity was 100 mm/s. Fig. 8 shows the influence rules of drainage area rate of the sampling tube on the coring volume. Under the condition of the sampling tube diameters of 20 mm, 30 mm, 40 mm, the coring volume remains constant with the drainage area rate. While, under the condition of the sampling tube diameters of 50 mm, 60 mm, 70 mm, 80 mm, when the drainage area rate was less than or equal to 3, the coring volume remained basically unchanged. When the drainage area rate was greater than 3, the Coring rate λ Sampling tube diameter / mm v=20 mm/s v=30 mm/s v=40 mm/s v=50 mm/s v=100 mm/s v=200 mm/s coring volume decreased with increasing drainage area rate, this trend became more pronounced as the sampling tube diameter increased. Fig. 9 shows the influence of drainage area rate of the sampling tube on the coring rate. When the drainage area rate was less than or equal to 3, the coring rate remained basically unchanged; when the drainage area rate was greater than 3, the coring rate decreased with increasing drainage area rate. This trend became more pronounced as the sampling tube diameter increased. Therefore, both coring volume and rate are related to drainage area rate. This important finding showed that as long as the inlet area was less than or equal to 3 times the outlet area, drainage would not be hindered and optimal sampling could be achieved, providing an important reference for the design of drainage discharge in samplers. Fig. 8 The influence curve of the drainage area rate on the coring volume Fig. 9 The influence curve of the drainage area rate on the coring rate

3 Influence of the penetration velocity
The sediments sampling process is regarded as the flow of fluid in a tube. Then, the penetration velocity directly affects surface tension, wall adhesion, and fluid friction loss, thus affecting the coring volume and coring rate according to the relevant knowledge of fluid mechanics. Therefore, the influence rules of different velocities of penetration on the coring volume and rate were examined in this study. Numerical simulations were carried out for the penetration velocities of 20 mm/s, 30 mm/s, 40 mm/s, 50 mm/s, 100 mm/s, and 200 mm/s. For these calculations, the sampling tube length was 500 mm, the drain holes diameter was 5 mm, and the sampling tube diameter was 40 mm.
When the sediments dynamic viscosity was 1, 10, 100( s m / kg ), the coring volume and rate decreased with increasing penetration velocity, and the trend of decrease was basically the same. When the sediments dynamic viscosity was 0.  Similarly, the sediments dynamic viscosity also affects surface tension, wall adhesion, and fluid friction loss, thus affecting the coring volume and coring rate according to the relevant knowledge of fluid mechanics. This section, the influence rules of different sediments dynamic viscosities (0.01 to 100 kg/m•s ) on coring volume and rate under different the velocities of penetration were studied. Fig. 12 and 13 show the influence rules of the different sediments dynamic viscosities on the coring volume and rate, respectively. For these simulations, the sampling tube length was 500 mm, the drain holes diameter was 5 mm, and the sampling tube diameter was 40 mm. When the viscosity was less than 0.1, the decreasing trend observed in coring volume and coring rate as viscosity increased was not obvious. It can be seen from the figures, that when the dynamic viscosity was 0.1 and 0.01, the corresponding curves of coring volume and rate coincided. When the viscosity was 1, 10, 100( s m / kg ), the decreasing trends in coring volume and rate as viscosity increased were obvious. Before sampling, it was necessary to measure or estimate the characteristic parameters of sediments, such as dynamic viscosity, so as to facilitate the optimal design of structural parameters of the sampler using realistic values.

Experimental study
In this section, in order to verify the correctness of the model and the results, a sampling experimental platform was set up to conduct the sampling experiments on the basis of the simulation results analyzed in the previous section.

Experimental principles
According to the simulation results, when the drainage area rate was less than or equal to 3 in the water environment, smooth drainage can be ensured, thus ignoring the influence of drainage pressure. Since the order of magnitude of the dynamic viscosity of air is 10 -5 , which is much smaller than that of water (10 -3 ), it is feasible to use the laboratory air environment to replace the water environment for sampling experiments as long as the drainage area rate is less than or equal to 3. Then, a sampling experimental platform was set up for sampling experiments.
The platform is shown in Fig. 14, its major components include: the platform body, a tank, an operational platform, control assembly, and hydraulic and electrical control piping. The platform body comprised a base, a circular hydraulic oil cylinder, a displacement sensor, a proximity switch, fixed Through simulation analysis, the influences rules of various influencing parameters on the coring volume and rate of the sampler were studied. Based on these simulations and taking the sampler as the experimental object, with a known sediments dynamic viscosity, the actual coring volumes and coring rates under specific conditions were obtained at different velocities of penetration and different tube diameters. The measurement principle for experimental data is shown in Fig. 16. For each velocity, when the sampling tube had been penetrated into the sediments to a depth of 500 mm, the height of the sediments that had entered the sampler was measured, only the height (Ha) from the upper end of the sampling tube to the upper surface of the sediments needed to be measured. During the experiments, when the sampling tube penetrated to the specified depth (H = 500 mm), as shown in Fig. 17(a), the clamping device was loosened and the top piston was removed as shown in Fig. 17(b, c) at which point the value of Ha was measured, as shown in Fig 17(d). The height of the sediments that had entered the sampling tube was calculated as Ht = 500 -Ha, and the experimental data (Ht) were recorded.

Experimental procedures
The specific operation steps of the experiments were as follows: (1) First, in order to produce the best model and results, the sediments dynamic viscosity (which was actual sediments taken from the seabed under the "Hainiu" drilling rig) was measured by viscometer. Fig. 18(a) shows the curves of the sediments dynamic viscosity over time at several different temperatures. As can be seen from Fig. 18(b), the sediments dynamic viscosity increased with increases in temperature. The sediments dynamic viscosity tended to stabilize as time progressed. The ambient temperature in the laboratory for the sampling experiments was about 25°C. According to the curves, after stabilizing, the viscosity value of the experimental sample was about 80 kg/m•s. (2) The actual sediments were transferred to the sediments tank and an appropriate amount of water was added to bring the sediments to a state close to that in the seabed, as shown in Fig. 14(f); (3) Before starting, the displacement sensor was checked for proper installation, and the data acquisition software was checked to see it was reading correctly; (4) In order to facilitate sampling observation and collection of experimental data, a transparent circular tube of a given thickness was used for the sampling tube in this experiments. The exact dimensions are shown in Fig. 15. The sampling assembly with an inner diameter (D1) of 40 mm, drain hole diameters (d) of 8 mm, and a length of 500 mm was installed on the clamping device so that the transparent circular tube was oriented vertically downwards, as shown in Fig. 14(d); (5) The penetration velocity was adjusted and the sampling experiments were conducted. Penetration velocities of approximately 20 mm/s, 40 mm/s, 50 mm/s, and 100 mm/s were tested. Three experiments were carried out under the same velocity and the average value was recorded.
(6) The sampling tube with an inner diameter (D2) of 60 mm, drain hole diameters of 12 mm, and a length of 500 mm was then installed on the clamping device so that the sampling tube was oriented vertically downward; (7) The operations in step (5) were repeated for the second sampling tube.

Experimental results
Using sampling tube diameters of 40 mm and 60 mm, sampling experiments were carried out at different velocities. The height of the sediments in the sampling tube Ht can be obtained, and then the corresponding coring volumes and rates were calculated. The experimental results are shown in Table  2, where: Ht represents the experimental value of sediments height in the sampling tube; Hs represents the simulated calculation value of sediments height in the sampling tube; and the last row provides the absolute error between the experimental results and the computational results. In order to compare the experimental results with the simulated results more clearly, curves were constructed (Fig. 19): the blue curves are the simulation computational results and the red curves are the experimental results; (a) and (c) show the relationships between coring volume and the penetration velocity for D1 (40 mm) and D2 (60 mm) sampling tubes, respectively; and (b) and (d) show the relationships between coring rate and the penetration velocity for D1 and D2, respectively. From the comparison of the results, it appeared that the simulated results satisfactorily matched the experimental results as the maximum absolute error was only 4.6%. This shows that the sediments sampling model established in this paper was reliable and produced results that accurately reflected real-world observations.
Due to the limitations of the experimental equipment, there was no way to accurately control the penetration velocity. Similarly, the sediments dynamic viscosity may have also changed with changes in the sediments water content and laboratory ambient temperature. Also, due to the difficulty in obtaining deep-sea sediments, the simulated sediments from which experimental sediments cores were extracted was small and may not accurately reflect natural sediments substrates, which are deep and unconstrained. These limitations will inevitably produce some degree of error between the computational results and the experimental results.

Conclusions
In this paper, the sediments on the seabed were simulated as a non-Newtonian Herschel-Bulkley viscoplastic fluid. A numerical model for sediments sampling was established and the influence rules of various key parameters on the coring rates and the volumes were particularly studied. The findings in this paper can provide a theoretical basis for facilitating the optimal design of the geometric structure of the seabed sediments samplers and the parameters in the sampling process. The following conclusions were obtained: (1) Coring volume increased with increases in the sampling tube diameter, but decreased with increased penetration velocity, drainage area rate, and sediments dynamic viscosity. Coring rate decreased with increased penetration velocity, drainage area rate, and sediments dynamic viscosity. The coring rate first increased and then decreased with increasing sampling tube diameter, and the peak value was also related to the penetration velocity.
(2) When the drainage area rate was less than or equal to 3, the coring volume and coring rate remained basically unchanged; but when the drainage area rate was greater than 3, the coring volume and coring rate decreased with increasing drainage area rate. The larger the sampling tube diameter,

Simulation result
Test result the more pronounced this decreasing trend was. These relationships provide important guidelines for the design of drainage discharge ports in similar samplers.
(3) A sampling experimental platform was set up to conduct physical experiments. The simulation results tallied with the experimental results, with a maximum absolute error of only 4.6%, which verified that the numerical simulation model accurately reflected real-world sampling.