A Method for Enhancing the Acoustic Scattering Characteristics of Underwater Acoustic Corner Reflectors in Vacuum Cavities

To alleviate the problem of unsatisfactory target strength and scattering stability of an underwater corner refector, a method to enhance the acoustic scattering characteristics using a vacuum cavity as an acoustic refecting layer is proposed. According to the principle of acoustic impedance mismatch of a water-refecting layer, a vacuum cavity corner refector is designed to take advantage of the property that sound waves cannot propagate under vacuum conditions. Te acoustic vacuum refecting layer has a theoretical acoustic refecting coefcient of one. Comparative analyses are carried out with the single-layer metal corner refector in terms of frequency and angle of incidence. For the concave structure of the underwater corner refector, the structural fnite element software ANSYS combined with the acoustic analysis software SYSNOISE is used to simulate and analyse the acoustic scattering characteristics, and the consistency of the simulation calculations and experimental data is verifed through the pool experiments for typical cases. Te results show that under the same refection area, the vacuum cavity underwater corner refector has large scattering intensity, good antiacoustic performance, no obvious frequency characteristics, and good decoupling efects. Te target echo intensity value can be increased by 2dB for better scattering stability. Te overall weight is reduced by about 20kg, with considerable engineering practicality, proving that the true cavity corner refector is an ideal underwater acoustic counter-acoustic device.


Introduction
As a passive signal refecting device, the corner refector was frst applied in the feld of electromagnetic wave confrontation [1][2][3][4].Te device has the advantages of strong echo signals, low manufacturing cost, and simple processing [5].In contrast to radar electromagnetic wave confrontation, the use of corner refectors to simulate the acoustic refection characteristics of underwater targets and to construct acoustic decoys is a new technological way to decoy active sonar and underwater weaponry.
Te underwater corner refector is a concave structure, so the underwater acoustic wave refection process is more complex.In addition to the secondary waves caused by the vibrations refected from the elastic structure, geometric and elastic scattering waves will also be scattered from the other refecting surfaces many times, resulting in a variety of scattering waves that interact with each other [6].Te complex process of backward refection of waves is collectively referred to as the scattering wave.
Scattered waves can be detected and received at any measurement point in space, which can be used to detect and locate underwater targets.Using the excellent acoustic echo characteristics of the underwater corner refector and by simulating the underwater target sonar refection echo, the combination of multiple underwater corner refectors can be used to mark the underwater structure and simulate the underwater dummy target, so as to realise the simulation of the underwater target echo intensity value and scale characteristics [7].
Te calculation methods for determining the acoustic scattering characteristics of underwater targets are divided into analytical and numerical analysis methods [8].For the acoustic scattering calculation of complex structures, the numerical method is usually used.For complex target shapes, the fnite element solution method [9] is used, but its computational volume is large, and it cannot accurately solve the infnite-domain acoustic scattering problem.Te boundary element method [10] applies to any complex target shape and can solve the infnite-domain scattering acoustic feld problem, but it is difcult to calculate the highfrequency scattering of large-scale targets.Terefore, for such small and complex structural targets as underwater corner refectors, the fnite element coupled boundary method can be used to solve the scattered sound feld problems in infnite waters with high accuracy.
In order to improve the antiacoustic performance of a corner refector, where sound waves cannot propagate under vacuum conditions, a vacuum layer is used to act as antiacoustic material, and according to the corner refector's small concave structural characteristics, elemental coupling of the indirect boundary element method with an underwater hollow cavity corner refector body scattering acoustic feld simulation, we conduct a comparative analysis of the common metal corner refector acoustic refectivity characteristics of the law, to explore more efective ways to improve its acoustic refectivity.Trough the pool experiments in the typical conditions of the test, we provide the basis for practical engineering applications of the vacuum cavity underwater corner refector.

Acoustic Scattering Solution for Underwater Targets
Te steel surface of a typical underwater corner refector has acoustic impedance characteristics and excellent sound refection performance when the water mismatch is large.Te refection coefcient of a 0∼20 mm thick elastic steel plate within 0∼20 kHz incident sound wave is analysed in Figures 1 and 2, and it can be seen that for the metal plate at a thickness of less than 10 mm, the sound transmission is better, with very obvious elastic characteristics [11,12], which will cause the coupled vibration of the metal sheet in the water, so that the metal plate will bend with symmetrical vibration [13]; the sound wave has a large elasticity loss during the refection process, which leads to poor acoustic sound scattering characteristics.When the refective surface is 10 mm thick, the steel plate antisound coefcient of 0.9 tends to be fully refective; with the refective surface increased to a thickness of 20 mm, the antisound coefcient is infnitely close to 1, and the steel plate can be regarded as ideal.Te incident acoustic wave and the steel do not produce the acoustic vibration of the coupling efect.Restricted by the density of the steel plate of the corner refector itself, usually not more than 10 mm thick, when the incident wave frequency is 0∼15 kHz, the antisound coefcient of the steel plate composed of the corner refector is below 0.9, which is in the steel and elasticity critical point, so it is necessary to carry out coupling analysis.

Acoustic Scattering Calculation Method.
Let the corner refector be in an ideal fuid and Q is an arbitrary point on the surface S of the structure, and according to the fuctuation equation and the Helmholtz equation of the scattered acoustic feld, the acoustic pressure can be obtained at any feld point P in space.
where G is the Green's function, σ and μ are the diference in normal pressure gradient and pressure diference on both sides of the surface, respectively, and n is the outward unit vector on the surface of the structure.Here, where ρ is the fuid density, ω is the circular frequency, v 1 and v 2 are the normal vibration velocity on both sides of the surface, and p 1 and p 2 are the acoustic pressure on both sides of the surface.
Assuming that the boundary conditions satisfy Neumann and the point P is on the boundary, the relationship between the boundary conditions and the unknown quantities can be expressed as follows: 2 Shock and Vibration where v p xx is the normal vibrational velocity at point P and n Q is the outer normal unit vector at point Q.
According to the indirect boundary element theory, after discretising the surface, the fuid pressure load can then be expressed as follows: where R e sf is the fuid-structure coupling matrix, P e 1 and P e 2 are the sound pressures at the nodes on both sides of the boundary, and δp e is the node sound pressure variance.Te fnite element equation can then be expressed as follows: where K s is the structural stifness matrix, M s is the structural mass matrix, U e is the node displacement vector, and F e s is the external force matrix on the structural nodes.By the structural vibration, equilibrium conditions can be obtained: where F a is the acoustic excitation vector function and A is the symmetry matrix.
In fuid-solid coupling, the boundary condition is v n � iωu n , and the force for the normal motion of the structure is as follows: where v n is the velocity normal to the surface of the boundary element model, u n is the displacement normal to the surface of the boundary element model, and ρ s is the structural density.
Combining equations ( 6) and ( 7), the following equation can be derived: Combining equations ( 5) and ( 8), the coupled structural fnite element and fuid boundary element equations can be obtained as follows: According to the abovementioned theory, the corner refector is modelled using the modelling software ANSYS, and the model data are imported into the acoustic analysis software SYSNOISE to analyse its underwater scattered sound feld and compare it with the steel single-layer metal plate corner refector, and the simulation process is shown in Figure 3.

Acoustic Scattering Characterisation Enhancement Method
In order to enhance the acoustic scattering characteristics of underwater corner refector, according to the principle of acoustic impedance mismatch, the greater the diference between the acoustic impedance characteristics of the acoustic refecting surface material and water, the better the antiacoustic performance of the corner refector.Domestic scholars Luo and Xin [14] used the serious mismatch between the characteristic impedance of air and water to design a kind of underwater air-cavity corner refector, and when they compared with the single-layer metal corner refector, the air-cavity corner refector showed good antiacoustic performance, and the scattering characteristics were similar to those of the steel corner refector, which is an excellent underwater corner refector; scholars Yu et al. [15] put forward a kind of underwater corner refector with a foam sandwich layer, but due to the small acoustic impedance characteristics of the foam layer, it could not signifcantly improve the acoustic performance of the underwater corner refector.Under normal temperature and pressure conditions, the acoustic impedance characteristics of water and air are seriously mismatched, so the air layer can be used as good acoustic material, but it is very difcult to make the air into an independent acoustic layer [16].Domestic scholars use rubber wrapped in metal to construct the air layer [17], but while the rubber is good at transmitting sound, it cannot achieve a high acoustic coefcient of refection, and it is complicated to process with a low costefectiveness ratio.

Shock and Vibration 3
Aiming at the abovementioned factors, we compare the acoustic refection characteristics of the corner refector with two diferent designs of a single-layer metal and air cavity.Ten, we analyse the improvement of the acoustic refection ability of the corner refector due to the vacuum cavity.

Structural Design of a Vacuum Cavity Corner Refector.
Sound waves cannot propagate in a vacuum environment; when the sound wave incident on the vacuum layer can theoretically be refected completely, the refection coefcient is 1, so the vacuum layer can be used as a good antisound material.Because of the inability to achieve an independent vacuum layer, the design of the vacuum cavity utilizes a "sandwich" structure in the metal sheet manufacturing to create a closed cavity outside the installation of the pumping valve, so this metal cavity can be pumped to a near-vacuum state.At this time, the corner of the refector has two layers of antisound material, the external metal material antisound layer and the internal vacuum antisound layer.A structure with a vacuum cavity for a right angle isosceles triangle with a side length L � 500 mm, the upper and lower layers of metal for the steel at a thickness of 2 mm, and the thickness of the internal cavity H � 10 mm is shown in Figure 4.

Comparative Analysis of Acoustic Scattering
Characteristics Simulation. Figure 5 shows the schematic diagram of the sound wave incident to the angular refector, where φ is the angle between the incident sound wave and the plane Oxz, and θ is the angle between the incident sound wave and the axis.We defne the incident sound wave as a plane wave, θ � 90 °, φ � 0∼90 °, frequency of 5 kHz, 10 kHz, 15 kHz, with an amplitude of 1 Pa, the sound source from the centre of the target at 100 m, where the feld point and the location of the sound source are the same.To meet the conditions of the farfeld and send/receive the joint position, the fow medium for water is set at room temperature and the pressure to a density of 1,000 kg/m 3 , the sound wave propagation velocity of 1,500 m/s in the water, and the acoustic wave angle of incidence is φ � 0 °∼90 °, every 5 °for a calculation.
Te metal material of the refector is defned as steel, with modulus of elasticity E � 2.1e11 Pa, Poisson's ratio of 0.3, density of 7800 kg/m 3 , and side length L � 500 mm.Te thickness of the refecting surface of the single-layer metal corner refector is H � 10 mm; the thickness of the metal refecting surface of the vacuum cavity corner refector is H � 2 mm, and that of the vacuum cavity is 10 mm, with vacuum conditions inside the cavity.Under diferent incident frequencies and incident angles, the simulation results of the target strength (TS) curves of the corner refector are shown in Figure 6.
As can be seen from Figure 6, the characteristic curve of the target intensity value of the single-layer steel corner refector with the frequency change of the incident wave is symmetric along φ � 45 °; the maximum target intensity value is achieved when the incident acoustic wave is 15 kHz, which shows obvious frequency characteristics; the scattering width is small, which can only maintain a high target intensity value in a small acoustic wave incident angle.
True cavity three-sided angular refector target intensity value with the incident wave frequency with the horizontal angle of incidence change law curve along the φ � 45 °symmetry; frequency characteristics are obvious in the incident acoustic wave for 15 kHz to achieve the maximum target intensity value, the incident acoustic wave frequency is reduced, the target intensity value of the attenuation of the faster, scattering width range is large, and the angle of incidence within the higher target intensity value, the return of the stability of the wave is strong.
Comparative analysis shows that the frequency characteristics of the corner refector are obvious and compared with the single-layer steel three-sided corner refector, the vacuum cavity corner refector has a larger target intensity value and a wider range of scattering width, which can achieve more excellent acoustic scattering characteristics under the same dimensions and has an improved efect on the acoustic scattering characteristics.
Te air cavity corner refector has strong frequency characteristics [14], and when comparing and analysing with the true air cavity corner refector, the rest of the parameters of the incident source remain unchanged; the incident wave frequency is 15 kHz, the rest of the simulation parameters remain unchanged, and the results are shown in Figure 7.
Te two types of corner refectors have the same trend of target intensity change, and the comparative analysis shows that the target intensity curve of the vacuum cavity corner refector is smooth, and there are high target intensity values in 0-90 °with large scattering width and good decoupling efects, proving the vacuum cavity corner refector has better acoustic scattering performance.

Experimental Verification
In order to verify the ability of the vacuum layer to improve the acoustic scattering characteristics of the angular refector, the experimental prototype of the vacuum cavity three-sided angular refector processing is shown in Figure 8. Te vacuum cavity corner refector consists of three independent metal cavities perpendicular to each other.Te cavity is connected to a one-way pumping ball valve, which is connected to the air pressure gauge.Te air compressor is used to pump out the internal air of the cavity to 0.06 Pa, close to the state of a vacuum.Compared with the steel three-sided angle refector, the hollow cavity angle refector with a single cavity mass of 3.9 kg and an overall mass of 11.7 kg, not counting the cavity bracket, is much smaller than the single layer of the steel three-sided angle refector at 30 kg, so it has a better engineering practicality.
Te parameters are shown for a 6 m * 4 m * 4 m reverberation pool, equipped with two skids as fxed devices.Te fxtures are used to suspend the experimental equipment in the reverberation pool, and the distance between the experimental equipment is adjusted by means of the skids.
In the test device layout shown in Figure 9, the corner refector with a cable connection is suspended in the water, ignoring the infuence of the thin rope on the sound scattering; the standard hydrophone and transmitting transducer external PVC tube is suspended into the water to

Shock and Vibration
ensure that the acoustic centre of the three test equipment parts are at the same depth.Te direction of the transmitting transducer emitting sound waves is directly opposite from the acoustic centre of the angular refector to ensure the accuracy of the angle of incidence of the sound source.Te test equipment pool layout is shown in Figure 10, where the angle of incidence of the sound source is 0 °, and the sound wave is vertically incident on the corner refector of the refective surface.
Te side length of the corner refector was 0.5 m.Based on the equation L 2 /λ, when the incident acoustic source was 15 kHz, the corner refector was 2.5 m away from the standard hydrophone and 3 m away from the transmitting transducer, which satisfed the far-feld conditions.Te incident sound waves were continuous wave pulse signals with a pulse cycle of 2 s, a pulse width of 1 ms, and a frequency of 15 kHz.Te scattering target intensity was stabilized by no less than ten waves of a narrow pulse width passed within a unit pulse cycle.In this way, the reverberation waves generated by incident pulse signals exerted the minimum efect on the target refected waves.When the acoustic centers remained unchanged, data were collected at every 5 °rotation of the corner refector.Tis was intended to measure the infuence of angle variation on the target intensity value of the corner refector.Te hydrophone was connected to the oscilloscope.Te target intensity echo variation was observed on the oscilloscope, then recorded and analysed.
Te hydrophone converted acoustic signals into electrical signals and then displayed them as voltage.Te target intensity value is calculated by the following equation: where d 1 is the distance from the transmitting transducer to the standard hydrophone; d 2 is the distance from the hydrophone to the target corner refector; U b stands for the of the echo signals from the corner refector; and U d is the voltage of the direct waves.Among them, d 1 and d 2 have been determined in Figure 9, while U b and U d are read from the oscilloscope.
In the case of a vacuum cavity, the internal cavity is pumped to make the air pressure inside the cavity as close to a vacuum as possible.Diferent types of corner refectors are suspended in the reverberation pool by cables, the corner refectors are rotated, and measurements are taken once every 5 °, the target intensity values change with the incident angle, as shown in Figure 11.
As can be seen from Figure 11, the simulation results of the target intensity of the corner refector of the vacuum cavity in the real measurement of the reverberant pool are basically the same as the experimental results, thus verifying the correctness of the calculation results and also proving the contribution of the vacuum cavity to increase the echo intensity of the corner refector.
Te target intensity value of the corner refector of the vacuum cavity under the experimental conditions is about 0.6 dB higher than that of the simulation calculation, and this error is caused by the fact that the reverberant pool is small, and the wall reverberation cannot be completely avoided, which results in the superposition of the reverberant wave and the scattered wave of the corner refector of the vacuum cavity.Compared with the simulation results, the characteristic curve of the target intensity test value of   the vacuum cavity three-sided corner refector is sharper, which is due to the fact that in the actual test, the corner refector in the underwater rotation of the human error is larger, and the acoustic wave incidence angle sampling points are fewer.In summary, it can be seen that, due to the serious mismatch of acoustic impedance characteristics between the cavity and the water medium layer, the acoustic scattering characteristics of the vacuum cavity corner refector are better than those of the single-layer metal and air cavity three-face corner refector under the actual experimental conditions, and the acoustic scattering characteristics of the three-face corner refector can be greatly improved, so the reasonableness of the design of the vacuum cavity corner refector has been proven.

Conclusion
According to the characteristics of the acoustic properties of the serious mismatch of air and water impedance, this paper ofers a design for a true air cavity three-sided corner refector.Comparative analyses of acoustic scattering characteristics are carried out with single-layer steel and air-cavity corner refectors, and the simulation results are experimentally verifed in a typical pool.Te results show that the hollow cavity corner refector has good antiacoustic performance, no obvious frequency characteristics, a large scattering width, and good decoupling efect and at the same time, the overall weight is reduced by about 20 kg, which is of strong value for engineering applications, because the hollow cavity can be used as an ideal method to improve the acoustic scattering characteristics of the underwater corner refector.
Due to time limitations, this paper studies and analyses only the acoustic scattering characteristics of a typical threesurface vacuum cavity corner refector and leaves the collapse problem of a vacuum cavity under deep water conditions for future studies.Further research is needed to determine the acoustic scattering characteristics of the multigrid refector composed of multiple corner refectors as well as the rationality of the structural design.

Figure 1 : 9 |A|Figure 2 :
Figure 1: Variation of an elastic metal plate with incident wave angle and frequency.

Figure 10 :
Figure 10: Layout of experimental instruments in the water tank.

Figure 11 :
Figure 11: Comparison of experimental results of a vacuum cavity trihedral corner refector.