J. Cent. South Univ. (2018) 25: 1409-1417

DOI: https://doi.org/10.1007/s11771-018-3836-2

Acoustic pressure simulation and experiment design in seafloor mining environment

ZHAO Hai-ming(赵海鸣)^{1, 2}, WANG Yan-li(王艳丽)¹, HAN Feng-lin(韩奉林)^{1, 2},JI Ya-qian(姬雅倩)¹, LUO Bo-wen(罗柏文)³

1. School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China;

2. State Key Laboratory of High Performance Complex Manufacturing, Central South University,Changsha 410083, China;

3. National Local Joint Engineering Laboratory of Marine Mineral Resources Exploration Equipment and Safety Technology, Hunan University of Science and Technology, Xiangtan 411201, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: Since the suspended sediments have severe influence on acoustic radiated field of transducer, it is significant for sonar system to analyze the influence of suspended sediments on acoustic pressure in the seafloor mining environment. Based on the KZK (Khokhlov–Zabolotkaya–Kuznetsov) equation, the method of sound field analysis in turbid water is proposed. Firstly, based on the analysis of absorption in clean water and viscous absorption of suspended sediments, the sound attenuation coefficient as a function of frequency in the mining environment is calculated. Then, based on the solution of KZK equation in frequency domain, the axial sound pressure of transducer in clear water as well as turbid water is simulated using MATLAB. Simulation results show that the influence of the suspended sediments on the pressure of near field is negligible. With the increase of distance, the axial sound pressures of transducer decay rapidly. Suspended sediments seriously affect the pressure in far-field. To verify the validity of this numerical method, experiment is designed and the axial sound pressure of transducer with a frequency of 200 kHz and a beam width of 7.5° is measured in simulated mining experiment. The results show that the simulation results agree well with the experiments, and the KZK equation can be used to calculate the sound field in turbid water.

Key words: seafloor mining; acoustic pressure; KZK equation; turbid seawater; sound attenuation

Cite this article as: ZHAO Hai-ming, WANG Yan-li, HAN Feng-lin, JI Ya-qian, LUO Bo-wen. Acoustic pressure simulation and experiment design in seafloor mining environment [J]. Journal of Central South University, 2018, 25(6): 1409–1417. DOI: https://doi.org/10.1007/s11771-018-3836-2.

1 Introduction

Cobalt crusts are mainly distributed in seamounts, the surface of which is uneven, and even some areas have no cobalt crusts. Thus, it is necessary to detect and recognize the micro-terrain, so that the cutting parameters of mining head can be adjusted, which can perfectly improve the mining efficiency. Compared with light and electromagnetic wave, acoustic wave is widely used in the field of underwater targets detection and recognition because the attenuation in water is smaller and the propagation distance is longer [1, 2]. However, in the mining environment, sediments like sand grain induced by the mining head are suspended in the seawater, which may affect the distribution of sound field and reduce the detection performance of sonar. Furthermore, the affected nonlinear sound field will make the signal waveform distorted, which makes it difficult to extract features and recognize seafloor materials. Hence, accurate calculation of the radiation field of transducer is essential to design the sonar detection system. The frequency, amplitude and energy of sound field can also be used as the features of objects.

Traditional analysis methods of underwater sound field assume that the medium is ideal, and there is no dissipation and dispersion. However, when we analyze the sound field in mining environment, it is necessary to consider the influence of the water medium and the suspended sediments. KZK (Khokhlov–Zabolotkaya- Kuznetsov) equation is widely used to describe the nonlinear sound field, because diffraction, nonlinearity and absorption of acoustic wave are taken into consideration [3]. KZK equation is currently used in the field of medical ultrasound to solve the problem of nonlinear sound field, and it mainly involves the analysis of high frequency focused ultrasound [4–6]. Recently, due to the development of hydroacoustics, ultrasound viscous absorption and nonlinearity caused by water medium are gradually emphasized, and KZK equation is also applied to the analysis of underwater nonlinear sound field [7–9]. There are some researchers studied the nonlinear ultrasound sound via solving the KZK equation in time domain [10]. In addition, complete algorithms for solving the equation in frequency and time domains were also studied by KHOKHLOVA et al [11], and then they studied the nonlinear sound field of planar piston source in water. WANG et al [12] simulated the sound field distribution of underwater focusing transducer via solving ZKZ equation in frequency domain, but without experimental verification.

The underwater acoustic applications of KZK equation presented above only relate to the nonlinear sound field analysis in clean water, and the influence of suspended sediments in turbid seawater is not taken into consideration. In the turbid water, not only the water, but also the suspended sediments will cause serious absorption, viscosity and scattering of sound waves, and these should be taken into account when calculating the sound field. Assuming that the seabed is flat and has no inclination, when ultrasound is applied to detect micro-terrain, according to the law of reflection, waves will reflect directly from the seafloor. In order to ensure that signals reflected from the seafloor can be received by the transducer, the target must be in the sound field, and the sound intensity must be strong enough. Therefore, it is necessary to study the axial sound pressure of transducer. In this work, KZK equation is used to simulate the axial sound field distribution of transducer in turbid water. Based on the calculation of acoustic attenuation coefficient in turbid water, the axial sound field of transducer in simulated mining environment is calculated via solving KZK equation in frequency domain. The method is verified by the designed experiment of sound pressure measurement.

2 Nonlinear sound field based on KZK equation

KZK equation is widely used in the study of nonlinear sound field. In cylindrical-coordinate system, the KZK equation for axisymmetric source geometry can be written as [13]:

              (1)

where P is the normalized sound pressure relative to the surface of sound source, and P is defined as P=p/p₀; p₀ is the surface sound pressure of transducer and p is the axial sound pressure; T=ω(t–z/c) is the retarded time which is also normalized; c is the propagation speed of sound waves in water; ω is the angular frequency of fundamental wave; Z=z/z_r, z is the coordinates of the sound propagation direction, and z_r=ka²/2 is Rayleigh distance; N=βω²a²p₀/2c⁴ρ is nonlinearity parameter, where β=1+B/2A is nonlinearity coefficient and it is usually taken as 3.5 in water; a is radius of the circular piston sound source; ρ is the density of still water; V=z_rα is sound absorption parameter, and α is the absorption coefficient; △=(1/R)(/R)+(²/R²) is the dimensionless transverse Laplace operator, and R=r/a is dimensionless transverse coordinate which is normalized.

KZK equation can be solved separately in time and frequency domains. The frequency domain solution which uses the method of Fourier series expansion is written as [11]:

                 (2)

where C_n(Z, R) is the plural amplitude of nth-degree harmonicsand it is a function associated with spatial variables. Substituting Eq. (2) into Eq. (1), we can obtain:

        (3)

where C_–n satisfies the equationis the conjugate complex number of C_n. The first term on the right side of Eq. (3) is convolution, which represents interaction between harmonics. The second term is attenuation, which is controlled by the acoustic absorption coefficient, and satisfies α₀ is the absorption coefficient at the frequency of f₀; the third term is diffraction.

In this work, we assume that the surface sound pressure of the planar piston source is equidistribution, and then parabolic approximation of the single-frequency piston source can be written as [14]:

                   (4)

where p₀ is the surface pressure of sound source, which can be obtained through experiments. Then, the boundary condition when Z=0 is as follow:

                  (5)

With the boundary conditions (4) and (5), Eq. (3) is solved by finite difference scheme, and then the modulus of each harmonic at different spatial positions can be obtained. Modulus on the frequencies which have the same subscripts are summed, and then the sound pressure p_n(Z, R) can be achieved.

Currently, when the nonlinear sound field is calculated by KZK equation, the influence on sound attenuation coefficient only considered the absorption of the water. However, in the mining environment, sediments like sand grain induced by the mining head are suspended in the seawater, which may also change the attenuation coefficient. Thus, the sound attenuation coefficient in the mining environment should be calculated before studying the nonlinear sound field.

3 Sound attenuation coefficient in simulated mining environment

In the turbid water which contains suspended sediments, the sound attenuation coefficient is associated with the scattering and absorption induced by the water medium and viscous sediments. Current study indicates that the scattering outside the acoustic propagation direction is small and it can be ignored [15]. Thus, in this work, we only calculate the absorption caused by water medium and suspended sediments as

                              (6)

where α_w is the absorption in clean water and α_s is the absorption caused by suspended sediments.

3.1 Absorption in clean water

Absorption in clean water mainly includes two parts. The first is pure water absorption. The second is the absorption caused by ions relaxation. The main ions in water are B(OH)₃ and Mg(SO₄). The sound attenuation of clean water is calculated by the formula of Francois and Garrison [16]:

    (7)

where the three terms in the right of equation are absorption of B(OH)₃, Mg(SO₄) and pure water; f (kHz) is the frequency of transmitting signal; A_i (i=1, 2, 3) is the parameter related to temperature and salinity; P_i (i=1, 2, 3) is associated with pressure; f₁ and f₂ are the relaxation frequencies of B(OH)₃ and Mg(SO₄), respectively. Expression for each parameter is as follows [17]:

where c is sound velocity in water. When the impact of suspended sediments is ignored, we can let c=1500 m/s. pH, S and t₀ are acid/alkaline balance, salinity and temperature in water, respectively; z is the depth of water.

3.2 Viscous absorption of suspended sediments

Viscous sound absorption of the suspended sediments is caused by viscous drag between fluid and the particles in water. Because the density of particles is greater than the surrounding water, velocity of the suspended particles is not synchronized with the surrounding water molecules when the sound wave propagates. Thus, velocity gradients will exist in the boundary layer of particles. Because of the viscosity of sediments, the velocity gradient will make acoustic energy change into heat energy and the acoustic energy will be weakened, the process of which is called viscous sound absorption. The model of calculating viscous absorption coefficient is based on the theory of energy conservation [18]. The model assumes that particles are hard spheres and volume concentration of suspended particles is less than 8%–9% of the turbid water. Then, the interaction between particles and multiple scattering can be ignored. So viscous absorption coefficient indicates approximate linear relationship with the suspended sediments concentration. For quartz particles, when the volume concentration of the suspended seston is 8%, the mass concentration of it is 200 kg/m³. Viscous absorption of suspended sediments can be written as [19]:

        (8)

where a_s is the average particle radius of the suspended sediments;Here, ω is the angular frequency of transmitted wave and v is viscosity coefficient of the moving water; ε=m_s/ρ_s is volume fraction of suspended sediments; m_s is mass concentration of sediments; k is the number of incident waves. k=2π/λ, λ is the wavelength; σ=ρ_s/ρ_o is the density ratio of suspended particles in surrounding water.

3.3 Sound attenuation coefficient in simulated mining environment

In the mining environment, when the seafloor to be mined is detected and recognized, ultrasonic transducer is required to be installed at the front of the mining vehicle, and it needs to be 1–2 m from seafloor. Because the operating distance of ultrasonic is short, temperature, salinity and pressure of water can be taken as constants in the sound propagation domain, and the sound attenuation coefficient is assumed to have a constant value. Form Eq. (8), it can be seen that viscous absorption of suspended sediments is related to the radius of particles. Analysis of polymetallic nodule and marine geologic survey in the cobalt-rich crust region of the Pacific showed that the average radius of particles is 0.85–2.43 μm [20]. In this work, the radius is taken as the average a_s=1.6 μm. From formulae (6) and (7), when the mass concentration of the suspended sediments is 10 kg/m³, as a function of frequency in clean water and turbid water, attenuation coefficients are calculated. The results are shown in Figure 1. We can see that, for the attenuation coefficients at a particle concentration of 10 kg/m³, turbid water is to be 1–2 orders of magnitude higher than it in clean water. While the concentration increases, the coefficient will continue to increase, so the impact of suspended sediments on sound field distribution can not be ignored. When sound field of turbid water is analyzed, the viscous absorption of suspended sediment needs to be taken into account. The sum of viscous absorption α of sediments and the absorption of water medium are shown in Figure 1. The absorption coefficient α increases with the increasing frequency, but does not strictly increase with square. So it can not be directly used for KZK equation calculation. As a function of frequency at different concentration, the absorption coefficient must be fitted using quadratic polynomial.

Figure 1 Attenuation coefficient as a function of frequency at particle concentration of 10 kg/m³

4 Calculation of acoustic pressure in simulated mining environment

Based on the solution of KZK equation in frequency domain, the sound pressures in clean water and the concentration of 63 g/L and 114.3 g/L were calculated respectively. The axial sound pressures of transducer were normalized to the surface pressure p₀. Sound absorption coefficients at different concentration were calculated using Eq. (6), the results of which were fitted using quadratic polynomial. The fitting results are shown in Table 1.In formula (6), temperature, salinity and PH were obtained by experiment. Axial and radial steps were taken as ΔZ=(λ/1200) μm and ΔR= (λ/800) μm. Here, λ is the wavelength.

Table 1 Fitting results of sound attenuation coefficient as a function of frequency

The results of sound absorption coefficient in Table 1 were adopted when calculating the axial sound pressure at different concentrations. The results of pressure are shown in Figure 2. We can see that influence of the suspended sediments on the pressure of near field is negligible. The main reason is that absorption of suspended sediments is not obvious near the surface of transducer. The pressure near surface is oscillatory under the impact of diffraction. With the increase of distance, absorption of turbid water is strengthened. So the axial sound pressures of transducer decay rapidly. In clean water, attenuation is only caused by water medium, so the pressure decays slowly. While in turbid water, the attenuation is caused by water and suspended sediments, which makes the pressure decay sharply and the attenuation slope increase. At a distance of 1.5 m from the transducer, compared with clean water, the pressure of turbid water whose concentration is 63 g/L decreases to 0.85p₀. While for the concentration of 114.3 g/L, the sound pressure nearly decayed to 0.05p₀. It can be seen that serious attenuation of the axial sound pressure of transducer will be caused by suspended sediments. So when we design the sonar detection system which is used in the mining environment, the impact of suspended sediments can not be ignored.

Figure 2 Pressure in different particle concentrations

5 Experimental verification of acoustic pressure in simulated mining environment

In order to verify the applicability of the KZK equation in simulated mining environment, experiment was designed to measure the axial sound pressure of transducer. The experimental results are compared with the results calculated by KZK equation.

5.1 Measuring system of sound pressure in simulated mining environment

The experiment was performed in a water- filled tank, the dimension of which was 5 m×3 m× 1.8 m. The experiment apparatus is shown in Figure 3. In the experiment, the bottom of the tank was covered with sediments which were mixtures of sand and cement fragments. Helical blades were used to stir up water and sediments. The sediments near the mining head will move along with the water flow. Software of FLUENT simulations shows that the concentration field and velocity field o.8 m away from the helical blades are equivalent. So the transducer is positioned 1–1.5 m in front of the helical blades. The distance far away from the seafloor is adjustable. Plane piston transducer, centre frequency and beam angle of which are 200 kHz and 7.5°, are used to send signals. The pumping signal is four high-voltage pulses and it transmits vertically to the bottom. The stepping motor is activated, and then the sediments are stirred up by the helical blades, which can simulate the mining environment. The movement of the transducer in the directions of x and y is controlled by the stepping motor. While the direction of z was adjusted by the bracing piece. The movement step of the bracing piece was 100 mm [21].

Figure 3 Experimental apparatus of sound pressure measurement in simulated seafloor mining environment:

In the experimental apparatus, the receiving transducer was fastened on the bottom of tank. The position of transmitting transducer was adjusted to make it aligned with the receiving transducer axis. Initial distance between the two transducers is 40 cm. Sound pressure is measured at 10 cm interval. Direction of the energy propagation is vertical. So the received signal may be affected by the bottom reflection. In order to prevent the bottom reflection, the receiving transducer is surrounded by a layer of sound absorber. In addition, to decrease the impact of surrounding walls, transducers are placed in the center of the pool. Because of vertical propagation, short propagation distance and small beam angle of the transmitted wave, it is assumed that there is no reflection from the walls. In the experiment, tap water is poured into the tank. The salinity and PH of the water are 1.0 g/kg and 8. To reduce error, the sound pressure is measured three times at each point, and the average of which is taken as the final result. A sample of receiving signal is shown as Figure 4.

Calculation of sound pressure is defined as:

P²=I×ρ×c                               (9)

where P is sound pressure; I is sound intensity; ρ is the density of medium; c is sound velocity. The sound pressure is normalized to the surface pressure p₀. Then the normalized pressure is

Figure 4 Receiving signal

The measurement of sound pressure is carried out as follows:

1) After adjusting the position of two transducers, tap water is poured into the tank.

2) The temperature of water is measured using sampler. The axial sound pressure of transducer in clean water is measured. Initial distance between the two transducers is 40 cm. The pressure is measured at 10 cm interval. There are 11 points totally.

3) Steeping motor is activated and the sediments are stirred up by the helical blades. We need to wait for 1 min to form a stable state.

4) The axial sound pressure of transducer in turbid water is measured, which is similar to Eq.(2). The initial distance is 40 cm, the pressure is measured at 10 cm interval. There are 11 points totally. At the same time, water surrounding the measuring point is obtained by the sampler. The sample is filtered and air-dried to obtain the concentration of the measuring point.

5) The axial sound pressure of transducer is measured three times using the same method as in Eq. (4).

5.2 Analysis of experiment results

The calculating results using KZK equation and the experimental results are shown in Figure 5. Figure 5(a) shows the results in clean water. Figures 5 (b) and (c) show the results in simulated mining environment. All of the pressures are normalized to the surface pressure. Concentration values denoted in the figure are the average value of all points in z axis. Because the pressures of near-filed are fluctuant, only sound pressures of far-filed are measured.

From Figure 5, it can be seen that, within a given range of error, the experimental results of the axial sound pressure are in good agreement with the numerical predictions of the KZK equation. The application of KZK equation in simulated mining environment is verified by the experimental results. KZK solution in frequency domain can perfectly describe the nonlinear sound filed in turbid water. The main reason for small fluctuation in the experimental results is that there is operational error when the height of transducer is adjusted. For the experimental results in simulated mining environment, the vertical distribution of suspended sediment concentration is uneven and there may be some particles with larger diameter, which will make the acoustical impedances of measuring points different. Thus, in addition to the existence of operational error, also there is calculation error. However, there is not much difference among the concentrations of measuring points, so the fluctuation of sound pressure is not severe. Furthermore, because of the stir of helical blades, state of the turbid water is changeable in an experimental period, which will attenuate and distort signals. The unstable signals are also the reason for the fluctuation of sound pressure. Concentration of the measuring point is obtained by filtering and air-drying the samples, which may lead to the measuring concentration lower than actual concentration. Therefore, the KZK solutions are higher than the experimental results.

Figure 5 Normalized sound pressure along z axis in different particle concentrations:

6 Conclusions

The sound attenuation coefficient in turbid water is calculated, and then the solution of KZK equation in frequency is used to simulate the axial sound pressure of transducer in the seafloor mining environment. Experiment is designed to measure the axial sound pressure of transducer. The experimental results are consistent with the numerical predictions of KZK equation. The application of KZK equation in nonlinear sound field analysis is verified by the experiment. KZK equation can be used to guide the designation of sonar system. Suspended sediments seriously affect the pressure in far-field. Before designing sonar system, sound field need to be calculated via KZK equation.

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(Edited by FANG Jing-hua)

中文导读

海底采矿环境下声场建模及实验设计

摘要：针对海底采矿环境下，悬浮泥沙对换能器声场分布影响严重的问题，基于KZK （Khokhlov–Zabolotkaya–Kuznetsov）方程，提出了混浊水域中声场分析方法。首先，对清洁水域声吸收和悬浮泥沙引起的粘滞声吸收进行分析，并由此建立采矿环境下声衰减系数随频率变化的规律曲线。然后，利用MATLAB，通过KZK方程的频域求解方法，对清洁水域和混浊水域中换能器轴向声场进行数值计算。仿真结果表明，悬浮泥沙对近场距离内轴向声压的影响不大，而随着距离的增大，换能器轴向声压幅值很快衰减，悬浮泥沙使远场区声压幅值严重降低。模拟采矿实验测量频率为200 kHz，波束角为7.5°换能器的轴向声压分布，结果表明，仿真结果与实验结果的一致性较好，KZK方程可以有效描述混浊水域中的声场分布。

关键词：海底采矿；声压；KZK方程；混浊海水；声衰减

Foundation item: Project(51374245) supported by the National Natural Science Foundation of China; Project(10C0681) supported by Education Department of Hunan Province, China

Received date: 2016-12-29; Accepted date: 2018-03-10

Corresponding author: HAN Feng-lin, PhD; Tel: +86–13332510097; E-mail: hanfl@csu.edu.cn; ORCID: 0000-0003-4392-9752