CN110080931A - The poly- wave device of ripples - Google Patents

Abstract

The invention discloses a water wave condenser, which relates to the technical field of water wave energy utilization and is applied to a water wave field. The extension line intersects the central axis of the annular base plate, and any two adjacent baffles form an equal-sized radial slot, and the effective depth of the radial slot is gradually reduced from the outside to the inside of the annular base plate. . The beneficial effect of the present invention is that there are only waves propagating in a specific direction in the designed water wave condenser. The radial slits of the wave condenser help reduce scattering at the inner and outer boundaries, and it can maintain the phase of the wave while maintaining perfect transmission. The centrality and invisibility of the two devices are verified by experimental measurements and simulation results.

Description

water wave condenser

technical field

The invention relates to the technical field of water wave energy utilization, in particular to a water wave condenser.

Background technique

In marine engineering, the concentration of water waves is crucial for coastal protection and the harvesting of wave energy. The current utilization of water wave energy is not ideal. One reason is that waves at sea level are dispersed, which requires many energy conversion devices to be deployed over large areas to harvest energy. In this regard, a collector device for water waves that simply inherits the concept of conversion optics might help. The key properties of these devices are often non-uniform and anisotropic. The concept of using non-uniform properties to control water waves dates back to those early devices with variable depth profiles that could simulate the refractive index profile of the mirage effect. Anisotropic responses to water waves are difficult to achieve. Using alternating strips of a step depth profile, waves experience different propagation velocities in directions parallel and perpendicular to the strips. To obtain such an anisotropic effective depth tensor, the wavelength usually needs to be much larger than the width of each strip. However, even with such inhomogeneity and anisotropy, coordinate transformation-based water wave collectors are almost impossible to construct, since they not only require a strong anisotropic water depth distribution, but also need to be significantly different from the natural environment gravitational acceleration.

SUMMARY OF THE INVENTION

The purpose of the present invention is to design a water wave condenser by applying the design of the Fabry-Perot (FP) resonance anisotropic extreme value collector to the water wave field based on the similarity between the water wave field equation and the two-dimensional electromagnetic wave field equation.

In order to achieve the above purpose, the technical solution of the present invention is that a water wave condenser is applied to a water wave field, comprising: an annular base plate; and at least three baffle plates, which are arranged on the annular base plate, and the baffle plates The extension line intersects the central axis of the annular bottom plate, and any two adjacent baffles form radial slits of equal size.

Further, the outer diameter of the annular base plate is r ₀ and the inner diameter is r _i , and the annular base plate satisfies the following relationship:

Among them, r is the radius of the annular base plate; λ is the wavelength of the water wave in the water wave field, a constant; m is a positive integer.

Further, the effective depth of the radial slot is gradually decreased from the outer side to the inner side of the annular bottom plate.

Further, the outer diameter of the annular bottom plate is r ₀ =70mm, and the inner diameter _ri =35mm.

Further, the outer diameter of the annular bottom plate is r ₀ =42.888mm, and the inner diameter ri = _24.761mm .

Further, the number of the baffles is 50.

Further, the width of the baffle plate gradually decreases from the outside to the inside.

Further, widened plates are connected to the outer sides of at least two of the baffles, and both sides of the widened plates are flush with the two sides of the adjacent baffles.

The beneficial effect of the present invention is that only waves propagating in a specific direction exist in the designed water wave condenser. The radial slits of the wave condenser help reduce scattering at the inner and outer boundaries, and it can maintain the phase of the wave while maintaining perfect transmission. The centrality and invisibility of the two devices are verified by experimental measurements and simulation results.

Description of drawings

Fig. 1 is the structural representation of the water wave condenser of the present application;

Fig. 2 is the top view of Fig. 1;

Fig. 3 is the front view of Fig. 1;

Fig. 4 is the partial enlarged view of A place in Fig. 3;

Fig. 5 is the experimental measurement value and simulation result of the small wave condenser;

Fig. 6 is the amplitude simulation diagram of the large wave condenser;

Fig. 7 is a screenshot of the experiment video of the large-scale wave condenser of the present application;

FIG. 8 is a schematic diagram of a variant design of the wave condenser of the present application, wherein the outer diameter of the annular base plate is larger than the outer side of the baffle;

FIG. 9 is a schematic diagram of a variant design of the wave condenser of the present application, wherein a widened plate is added to the outer side of the baffle.

In the above figures, 1. annular bottom plate; 2. baffle plate; 3. widened plate.

Detailed ways

In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, below in conjunction with the accompanying drawings and preferred embodiments, the specific embodiments, structures, features and effects according to the present invention are described in detail as follows:

1. Structural design of wave condenser

A water wave condenser is applied to a water wave field, as shown in Figures 1 to 4, comprising an annular base plate 1 and a baffle plate 2.

The outer diameter of the annular base plate 1 is r ₀ and the inner diameter is r _i . The baffle plate 2 is arranged on the annular base plate 1; the extension line of the baffle plate 2 intersects the central axis (concentric) of the annular base plate 1, and the central axis here is the axis of the through hole in the middle of the annular base plate 1, and any two phase The adjacent baffles 2 form radial slits of equal size, that is, the baffles 2 are evenly distributed on the annular base plate 1 , the sides of the radial slot are the sides of the baffle 2 , and the bottom surface is the top surface of the annular base plate 1 .

Preferably, the annular base plate 1 satisfies the following relationship:

Among them, r is the radius of the annular base plate 1; λ is the wavelength of the water wave in the water wave field, a constant; m is a positive integer. In the above formula, after the annular base plate 1 is designed, r ₀ and _ri are fixed values, and the fixed value λ can be obtained, that is to say, after the design of the annular base plate 1 is completed, the wavelength collected by the wave condenser is a fixed value. value. In addition, the corresponding annular base plate 1 can also be produced according to the wavelength λ.

Preferably, assuming a horizontal liquid level, as shown in Fig. 4 B, the water wave condenser is placed in it, the liquid level intersects the side of the baffle 2, and the effective depth refers to the liquid level and the top of the annular bottom plate 1. height between faces. Defining the effective height, the height of the baffle 2 can be increased without limit, and the heights between different baffles 2 can also be different.

Preferably, the effective depth of the radial slit is gradually decreased from the outer side to the inner side of the annular base plate 1, so as to enhance the wavelength concentration effect.

Preferably, the width of the baffle plate 2 gradually decreases from the outside to the inside, so as to conform to the design of the radial slit and enhance the wavelength concentration effect.

2. Manufacture of wave condenser

When in use, the wave condenser is placed in the water wave field. As shown in Figure 2 and Figure 4, the area outside the radius r ₀ is the environment with the water depth h ₀ , and the area within the radius _ri has the water depth _hi , that is, the water depth. h(r ₀ )=h ₀ , h(r _i )= _hi . The region between r ₀ and _ri is based on the Fabry-Perot resonance, which is extremely anisotropic. Here, h(r) is defined as the effective height of the liquid within a series of radial slits. The height of the baffle 2 is greater than the height of the liquid surface (wave surface), so the wave can only propagate in the radial direction, which is what we call extreme anisotropy. The main characteristic of this structure is that the selected depth is continuous at each point.

It is easier to realize the continuous longitudinal section of the water wave. Before modeling the actual wave condenser, we take the shallow water approximation, so that the linear dispersion relation can be written as

Among them, ω is the angular frequency; g is the acceleration of gravity; h is the water depth; k is the wave number of the water wave.

Assuming that the wave number of the water wave in the area outside the radius r ₀ is _{k 0} , the effective refractive index of the area inside the radius ri is

n _i =k/k ₀ (2)

From equations (1) and (2), we get

Here we assume that the refractive index of the region outside the radius of r ₀ is 1, that is, n ₀ =1. Therefore, based on the design of the wave condenser, the refractive index of the region within the radius _{ri is ni =} r ₀ / _ri . In the region between ri and _r0 , the choice of refractive index _n is very flexible, i.e.

According to equations (3) and (4), the water depth distribution can be obtained

Under the condition of Fabry-Perot resonance, the condition of the water wave condenser to reflect the invisibility is that the wavelength λ of the water wave should meet the following conditions

That is, the length of the radial slit is an integer multiple of half a wavelength. Therefore, the waves can pass through each small channel perfectly, with no phase delay. Using these parameters, we can construct water wave condensers of different sizes to demonstrate the concentration and invisibility of water waves. specific:

The small annular wave condenser is made by a 3D printer, and the dimensions are as follows: outer diameter r ₀ =70mm, inner diameter _ri =35mm, and environmental water depth h ₀ =8mm. The gradient index varies from 1 to 2 in the region between radii r ₀ and _ri . At the same time, 50 thin baffles with a thickness of 1.1 mm are evenly arranged on the annulus to form a slot array. The slit width near radius r ₀ is _7.7 mm, and the slit width near radius ri is 3.3 mm. We put a piece of plastic with a thickness of 6mm into the area within the radius _ri , and the depth is _hi = 2mm. At this time, the effective refractive index can be calculated as 2 according to formula (3).

The large annular wave condenser is configured in a deep water tank, and its parameters are the outer radius r ₀ =42.888cm, the inner radius ri = _24.761cm , and the ambient water depth h ₀ =10cm. Similarly, we evenly arrange 50 thin baffles with a thickness of 0.5mm on the annulus to form a slot array. The slit width near radius r ₀ is _5.34 cm, and the slit width near radius ri is 3.06 cm. The thickness of the cylinder is _6.667 cm, located in the region within the radius ri, and the effective refractive index is 1.732.

The above two devices are designed with shallow water approximation, so that the field equations are the same as Maxwell's equations in two dimensions. However, the wavelength should be more than 20 times the water depth. For both cases, we remodeled the device during simulation using the following dispersion relation beyond equation (7) to obtain the effective water depth or effective refractive index profile.

ω ² =gktanh(kh) (7)

For the small ring condenser, emphasis is placed on demonstrating its invisibility effect. The device was measured according to the previous description. The frequency is 4.95 Hz, which is suitable for the Fabry-Perot resonance of m=2, the amplitude profile is shown in Fig. 5(a), and the background wavelength is 50 mm. The visible water waves are plane waves both inside and outside the condenser, which explains its invisibility: basically no scattering. The wave attenuates after passing through the condenser due to the fluid-solid interaction.

Using the software (COMSOL Multiphysics), the wave amplitude is simulated using the linear dispersion relation (1) and the transcendental dispersion relation (7), and Figure 5 is obtained. In Figure 5, for m=2, (a) is the experimental measurement, and the background wavelength is 50 mm; (b) is the simulation result of linear dispersion, and the background wavelength is 52.5 mm; (c) is the simulation result of transcendence dispersion, and the background wavelength is is 48.5mm. For m=3, (d) is the experimental measurement, and the background wavelength is 31 mm; (e) is the simulation result of linear dispersion, and the background wavelength is 35 mm; (f) is the simulation result of the prior dispersion, and the background wavelength is 29.7 mm.

Figure 5(b) presents the results of the linear dispersion relationship, illustrating the perfect stealth effect (with a background wavelength of 52.5mm). Figure 5(c) is a transcendental dispersion relationship, in which case the invisible effect is compromised (the background wavelength is 48.5 mm). For superdispersion, the effective refractive index of the region within radius _ri changes from 2 to around 1.8. According to the corresponding principle in transformation optics, the device is treated by the wave as an object with an effective index of refraction of about 0.9, thus producing slight scattering. At the operating frequency of 7.05 Hz, corresponding to the Fabry-Perot resonance of m=3, the measured amplitude distribution is shown in Figure 5(d), and the background wavelength is 31 mm. Figure 5(e) and Figure 5(f) are the linear dispersion relationship and the transcendental dispersion relationship, respectively. Their background wavelengths were shifted to 35mm and 29.7mm, respectively. When the wavelength is much larger than the crack width, the effective refractive index tensor (or depth tensor) is more accurate in the region between r _i and r ₀ , so the invisibility effect of Fig. 5(e) is not ideal. And for Fig. 5(f) the scattering becomes stronger. This is because for superdispersion, the effective refractive index of the region within the radius _ri has changed to around 1.6, corresponding to an illusion that the effective refractive index is around 0.8. Therefore, the simulation results show that the effective refractive index tensor theory is more accurate because the effective refractive index of the illusion is closer to that of the background, and therefore, the device appears to have better invisibility at larger wavelengths. In order to obtain the amplitude amplification factor inside the condenser, pixel analysis was performed on the experimental photos. When m=2 and m=3, the amplitude amplification factors within the radius ri are _2.21 and 1.94, respectively, which are consistent with the simulation results (which we normalize to the amplitude of the incident wave). Furthermore, the measured background wavelength is between linear dispersion and transcendental dispersion, due to the consideration of the effect of dispersion (d _c is the length of the capillary with 2.7 mm of water in the capillary).

3. Invisibility and concentration of water wave collectors

For the larger type of collector, a large water tank with a length of 60 meters, a width of 1.2 meters and a depth of 2 meters was used for the test test. One end of the slot is provided with a push rod type wave generator, and the other end is provided with a wave elimination device. In order to demonstrate the wave-gathering effect of the large wave condenser, the amplitude around the wave condenser was measured with a wavemeter instead of a photographic method.

In Fig. 6, when (a) is the incident amplitude of 1.2 mm, the experimental amplitude amplification factor of the wave condenser with and without baffles is between 1.1 and 1.75 Hz; (b) is the single-point simulation amplitude amplification factor; (c) is the average amplitude amplification factor of the internal simulation; (d) is the incident amplitude of the large wave condenser is 1.2 (black), 1.7 (red), 2mm (blue), and its internal amplitude amplification factor is 1.1-1.75Hz ; (e) is the simulated amplitude profile of the baffle collector at 1.5Hz; (f) is the simulated amplitude profile of the unbaffled collector at 1.5Hz.

First, for the wave condensers with and without baffle 2, we plotted the amplitude amplification factor of a point within the radius ri to be _1.1-1.75 Hz when the incident amplitude is 1.2 mm, as shown in Fig. 6(a) . In the corresponding simulations, we plot the single-point amplitude amplification factor and the average area within the radius _ri from 1.1 to 1.75 Hz, as shown in Fig. 6(b) and Fig. 6(c), respectively. At a frequency of 1.5 Hz, the large collector has the largest amplitude within the radius _ri , which illustrates the concentrating effect of the above design at a Fabry-Perot resonance. The amplitude amplification coefficients at different frequencies are basically consistent with the simulation results. This is because the incident amplitude of the water wave is 1.2mm, which approximately satisfies the condition of a linear amplitude wave: the nonlinearity can be ignored. The amplitude amplification factor within the radius _ri is about 2, which is close to the theoretical value. However, when the incident amplitude increases to 1.7 and 2 mm, the nonlinear effect increases, and the amplitude amplification factor within the radius _ri increases, which deviates from the theoretical value. When the water wave incident amplitude is 1.2, 1.7 or 2 mm, respectively, we plot the amplitude amplification factor within the collector radius ri as _1.1–1.75 Hz, as shown in Fig. 6(d). The nonlinear effect here is beneficial because it enables the amplification factor to be larger over the entire frequency range. Furthermore, we plotted the simulation graphs of the wave condenser with and without baffle 2, as shown in Fig. 6(e) and 6(f), with an incident amplitude of 1.2 mm and a frequency of 1.5 Hz. This invisibility and concentration effect is again well documented.

In order to visually see the concentrated effect of the large collector, we placed a small boat on the water surface and inside the collector in the environment. Figure 7 is obtained. In Figure 7, (a) is the ship with the incident wave amplitude of 2 mm; (b) is the ship inside the collector when the incident frequency is 1.1 Hz; (c) is the ship inside the collector when there is a wave with a frequency of 1.2 Hz ; (d) is the ship inside the collector when there is an incident wave with a frequency of 1.3Hz; (e) is the ship inside the collector when there is an incident wave with a frequency of 1.5Hz; (f) is collected when there is an incident wave with a frequency of 1.6Hz ship inside the collector; (g) is the ship inside the collector when there is an incident wave with a frequency of 1.7 Hz.

The amplitude of the water wave can be represented by the vertical motion of the ship, while the horizontal motion of the ship is limited by the ropes fixed to the bottom of the ship, as shown in Fig. 7(a). Position the sensor at the position of the boat to obtain the position of the vertical motion amplitude of the boat. In the environment shown in Fig. 7(a), the amplitude of the water wave is 2 mm, which is indicated by the black arrow. When an incident wave with a frequency of 1.1-1.7 Hz is incident inside the wave condenser, the amplitude is shown in Fig. 7(b)-(g), which corresponds to the blue curve (the uppermost broken line) in Fig. 6(d) .

The present application successfully designs and manufactures a ring-shaped water wave collector device based on the gradient depth profile of Fabry-Perot resonance, and the wave gathering and invisibility of the wave collector are verified through experimental measurements and simulation results. Furthermore, the results show that the slit array structure under Fabry-Perot resonance can be used to control water waves.

4. Variation design of wave condenser structure

Different from FIG. 1 , referring to FIG. 8 , the outer diameter of the annular base plate 1 is larger than that of the outer side of the baffle plate 2 , and the design is convenient for gathering wavelengths.

For another example, referring to FIG. 9, a widening plate 3 is designed, the widening plate 3 is arranged on the outer side of the baffle 2, and the two sides of the widening plate 3 are flush with the two sides of the adjacent baffle 2, so that the The widening plate 3 is oriented towards the direction with stronger wavelength intensity to improve the collection effect.

The present invention has been described above with reference to preferred embodiments, but the scope of protection of the present invention is not limited thereto, and various improvements may be made and equivalents may be substituted therein without departing from the scope of the present invention. As long as there is no structural conflict, the technical features mentioned in each embodiment can be combined in any way, and any reference signs in the claims should not be construed as limiting the claims involved, regardless of In all respects, the embodiments should be considered as exemplary and not restrictive. Therefore, any technical solutions falling within the scope of the claims are within the protection scope of the present invention.

Claims (8)

1. a water wave condenser, is characterized in that, comprises: an annular base plate (1); and At least three baffle plates (2) are arranged on the annular base plate (1), the extension line of the baffle plate (2) intersects the central axis of the annular base plate (1), and any two adjacent The baffles (2) form radial slits of equal size. 2. The water wave condenser according to claim 1, wherein the outer diameter of the annular bottom plate (1) is r ₀ and the inner diameter is r _i , and the annular bottom plate (1) satisfies the following relationship Mode: Among them, r is the radius of the annular base plate (1); λ is the wavelength of the water wave in the water wave field, a constant; m is a positive integer. 3 . The water wave condenser according to claim 1 , wherein the effective depth of the radial slit is gradually reduced from the outer side to the inner side of the annular bottom plate ( 1 ). 4 . The water wave condenser according to claim 2, characterized in that, the outer diameter of the annular bottom plate (1) is r ₀ =70mm, and the inner diameter _ri =35mm. 5 . The water wave condenser according to claim 2 , wherein the outer diameter of the annular bottom plate ( 1 ) is r ₀ =42.888 mm, and the inner diameter r _i =24.761 mm. 6 . 6 . The water wave condenser according to claim 1 , wherein the number of the baffles ( 2 ) is 50. 7 . 7. The water wave condenser according to claim 1, characterized in that, the thickness of the baffle plate (2) gradually decreases from the outside to the inside. 8. The water wave condenser according to claim 1, characterized in that, widened plates (3) are connected to the outer sides of at least two of the baffles (2), and both sides of the widened plates (3) It is flush with the two sides of the adjacent baffles (2).