A method for generating a second-order Stokes wave by a plunging box type wave maker and a wave making system

Abstract

The application relates to a method for generating a second-order Stokes wave by a plunging box type wave maker and a wave making system, which is more suitable for generating deep water waves and saves horizontal space occupied by the wave maker. The method is based on high-order wave making theory. Traditional wave making theory generates free waves due to the nonlinearity of the water surface and the surface of the wave making plate. The propagation speed of the free waves is different from that of the constrained waves, thereby interfering with the propagation of the constrained waves, leading to changes in the wave propagation process. The active compensation wave making theory can eliminate the influence of the free waves on the constrained waves by controlling the displacement of the plunging box.

Description

TECHNICAL FIELD

[0001] The present application relates to the offshore, ocean engineering hydrodynamic wave tank test technical field, especially to a kind of method and wave making system for generating second-order stokes wave of impact box type wave making. BACKGROUND

[0002] Second-order stokes wave is a kind of weak nonlinear, periodic surface gravity wave, compared with the micro wave, it can reflect the nonlinear characteristics of natural wave, and compared with higher-order stokes wave, its theory is relatively simple, and it is easier to realize. In the laboratory water tank and numerical wave tank, the movement of the wave making plate is usually harmonic motion and does not consider the nonlinear effect of the wave. Although there is nonlinear existence between the free water surface and the wave making plate surface with the propagation of the wave, the wave still shows a certain degree of nonlinear characteristics, but due to the interference of second-order locking wave and free wave, the nonlinear characteristics of the wave are affected, which leads to the instability of wave propagation.

[0003] At present, most of the wave making theories are based on push plate type wave making and rocking plate type wave making, and with the implementation of the national "Maritime Power" strategy, the exploration of the ocean is also developing towards deep water, therefore, in order to meet the research needs of deep water, the depth of the laboratory water tank is gradually increased. At this time, under the condition of deep water, in order to generate relatively large wave, push plate and rocking plate wave making means that a larger power motor is needed to drive and a larger space is needed to meet the reciprocating motion of the wave making plate, so as to produce corresponding wave. Due to the nonlinear free wave generated by the water surface and the wave making plate surface in the traditional wave making theory, the propagation speed of the free wave is different from that of the constrained wave, which interferes with the propagation of the constrained wave, resulting in changes in the wave propagation process, which affects the authenticity and accuracy of the research.

[0004] Therefore, the development and application of a wave making method suitable for deep water wave generation has become a problem to be solved. SUMMARY

[0005] Therefore, the present application aims to provide a method and wave making system for generating second-order stokes wave of impact box type wave making, so as to solve the problem of the authenticity and accuracy of the research caused by the nonlinear free wave generated by the water surface and the wave making plate surface in the traditional wave making theory, which interferes with the propagation of the constrained wave, resulting in changes in the wave propagation process.

[0006] To achieve the above purpose, one of the technical solutions of the present application is: a method for generating second-order stokes wave of impact box type wave making, when using impact box type wave making machine to make wave, the method comprises:

[0007] S1, determine the second-order stokes wave expression as:

[0008]

[0009] wherein The expression is d is the water depth, k is the wave number k = 2π / L, L is the wavelength, H is the wave height, and φ is the wave phase angle;

[0010] S2, according to the principle of conservation of mass, the lowering of the tank will cause the free water surface to rise to form a wave crest, and the rising of the tank will lower the free water surface to form a wave trough, the relationship is as follows:

[0011] V t -V0 = V1 + V2 (2)

[0012] wherein V t represents the submerged volume of the tank at time t, V0 represents the submerged volume of the tank at the initial time, V1 represents the volume between the wave surface and the static water surface, and V2 represents the volume between the wet surface of the tank and the static water surface;

[0013] S3, define the X axis as the free water surface coinciding with the tank and pointing to the tank, and the Y axis as being perpendicular to the free water surface and pointing upward, V1 is obtained by integrating the wave surface equation from 0 to x c

[0014]

[0015] wherein x c is the horizontal position of the interaction between the wave surface and the tank, and η(x) is the wave surface height at position x;

[0016] V2, V0 and V t can be expressed by the following formula

[0017]

[0018]

[0019]

[0020] wherein S is the vertical displacement of the tank, ds is the initial submerged water depth of the tank, and θ is the bottom angle;

[0021] S4, substituting the formula (3) to the formula (6) in S3 into the formula (2), to obtain

[0022]

[0023] In the formula, S and x c are two unknown variables about time;

[0024] ​S5, define the wedge free surface equation as

[0025] f(y) = c-t-(y+S) tan θ (8)

[0026] In the formula, c is the wave propagation speed, t is the time, y is the variable;

[0027] Put (x c , η x＝xc ) into equation (8) to get:

[0028] c-t-x c = |S+η(x c )| tan θ (9)

[0029] Equations (7) to (9) constitute the real-time displacement expression of the ram tank;

[0030] S6, substitute equation (1) into equations (7) and (9), and the displacement of the ram tank to generate a second-order Stokes wave is obtained by the following equation:

[0031]

[0032] S7, load equation (10) into the wave making system of the ram tank wave maker, and a second-order Stokes wave can be generated in the flume.

[0033] Further, the capacity of the ram tank restricts the generation of waves and the quality of waves, and the total constraint condition formula of the ram tank wave generation of the second-order Stokes wave is:

[0034]

[0035] Further, the ram tank motion does not exceed the bottom of the flume, and the specific expression is:

[0036] S < d-d s (12)

[0037] When the ram tank immersion depth increases from the initial value to the maximum value, a 1 / 2 period wave volume is generated, and the specific expression is:

[0038]

[0039] In order to obtain the first constraint condition, solve equations (12) and (13), and the following expression is obtained:

[0040]

[0041] Further, when the ram tank drops to the lowest position, a second-order Stokes wave volume is generated, and the specific expression is:

[0042]

[0043] V2 is omitted in formula (15), V2 is proportional to η(x), when x c = L / 2, η(x) ≈ 0, according to the calculation expression (4) of V2, V2 = 0

[0044] By solving formula (12) and formula (15), the first constraint condition formula is obtained as follows:

[0045]

[0046] Further, the slope of the wedge-shaped impact box is less than the minimum slope of the wave front, and the specific expression is as follows:

[0047] k p <k wmin (17)

[0048] In the formula, k p is the slope of the wedge-shaped impact box, k wmin is the minimum slope of the wave front; wherein the slope k p of the wedge-shaped impact box in formula (17) is calculated as follows

[0049]

[0050] On the contrary, the impact box will cover the generated wave, affecting the quality of the wave.

[0051] Further, the slope k w of the wave front in formula (17) can be:

[0052]

[0053] The minimum slope position of the impact box can be derived by taking the derivative of x in formula (19)

[0054]

[0055] By derivation, the second constraint condition formula is obtained as follows:

[0056]

[0057] Further, the volume of the second-order Stokes wave in a period is less than zero, and the average water level in the tank will drop. In order to balance the dropped water level, the impact box needs to rise by a certain amount to ensure that the impact box will not rise out of the water when the second-order Stokes wave spreads to the entire tank, therefore, there is another constraint condition, and its formula is

[0058]

[0059] where w is the length of the flume, and substituting The third constraint condition is derived from the expression.

[0060] Further, according to the constraint condition of various wave theories, the fourth constraint condition formula of the second-order Stokes wave is:

[0061]

[0062] Another technical solution of the present application is a piston-type wave generation system, which is suitable for the piston-type wave generation method of the second-order Stokes wave.

[0063] Further, the system at least includes a set of driving systems, a piston connected with the driving systems, and a control system for feedback and control signals.

[0064] The present application has the following beneficial effects:

[0065] 1. Compared with the push plate wave generation method and the swing plate wave generation method, the present application is more suitable for deep water wave generation and saves the horizontal space occupied by the wave generator.

[0066] 2. The method is based on the high-order wave generation theory. The traditional wave generation theory generates free waves due to the nonlinearity of the water surface and the surface of the wave plate. The propagation speed of the free wave is different from that of the constrained wave, which further interferes with the propagation of the constrained wave, resulting in changes in the wave propagation process. The active compensation wave generation theory can eliminate the influence of the free wave on the constrained wave by controlling the displacement of the piston. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a schematic diagram of the initial moment of the piston-type wave generation to generate waves;

[0068] Figure 2 is a schematic diagram of the moment of forming a wave crest of the piston-type wave generation to generate waves;

[0069] Figure 3 is a schematic diagram of the moment of forming a wave trough of the piston-type wave generation to generate waves;

[0070] Figure 4 is a constraint condition diagram of various wave theories;

[0071] Figure 5 is a comparison diagram of the second-order Stokes wave generated by the piston-type wave generation and the analytical solution when the water depth is 15m;

[0072] Figure 6 is a comparison diagram of the second-order Stokes wave generated by the piston-type wave generation and the analytical solution when the water depth is 200m. DETAILED DESCRIPTION

[0073] For better understanding of the present application, the present application is further described below in conjunction with specific embodiments and drawings.

[0074] Embodiment 1

[0075] A method for generating second-order Stokes wave by using a plunger-type wave maker, the method comprising:

[0076] S1, determining the expression of the second-order Stokes wave as:

[0077]

[0078] wherein the expression is d is the water depth, k is the wave number k = 2π / L, L is the wavelength, H is the wave height, and φ is the wave phase angle;

[0079] As shown in Figures 1-3 S2, according to the principle of mass conservation, the lowering of the plunger will cause the lifting of the free water surface to form a wave crest, and the rising of the plunger will lower the free water surface to form a wave trough, and the relationship is as follows:

[0080] V t -V0 = V1 + V2 (2)

[0081] wherein V t represents the submerged volume of the plunger at time t, V0 represents the submerged volume of the plunger at the initial time, V1 represents the volume between the wave surface and the static water surface, and V2 represents the volume between the wet surface of the plunger and the static water surface;

[0082] S3, defining the X axis as the free water surface coinciding with the plunger and pointing to the plunger, and the Y axis as the vertical to the free water surface and pointing upward, V1 is obtained by integrating the wave surface equation from 0 to x c

[0083]

[0084] wherein x c is the horizontal position of the wave surface and the plunger interaction, and η(x) is the wave surface height at position x;

[0085] V2, V0 and V t can be expressed by the following formula

[0086]

[0087]

[0088]

[0089] wherein S is the vertical displacement of the plunger, ds is the initial submerged water depth of the plunger, and θ is the bottom angle.​

[0090] S4, substituting formula (3) to formula (6) in S3 into formula (2), get

[0091]

[0092] In the formula, S and x c are two unknown variables about time;

[0093] S5, define the wedge free surface equation as

[0094] f(y)=c·t-(y+S)tanθ (8)

[0095] In the formula, c is the generation wave propagation speed, t is the time, y is the variable;

[0096] Put (x c ,η| x＝xc ) into equation (8) to get:

[0097] c·t-x c =|S+η(x c )|tanθ (9)

[0098] Formula (7) to formula (9) constitute real-time displacement expression of the tank;

[0099] S6, substituting formula (1) into formula (7) and formula (9), the displacement of the tank to generate second order Stokes wave is obtained by the following equation:

[0100]

[0101] S7, formula (10) is loaded into the wave making system of the tank type wave maker, and the second order Stokes wave can be generated in the water tank.

[0102] Further, the capacity of the tank restricts the generation of the wave and the quality of the wave, and the total constraint condition formula of the tank wave making to generate second order Stokes wave is:

[0103]

[0104] Further, the tank movement does not exceed the bottom of the water tank, and the specific expression is:

[0105] S<d-d s (12)

[0106] When the tank immersion depth increases from the initial value to the maximum value, 1 / 2 cycle wave volume is generated, and the specific expression is:

[0107]

[0108] To get the first constraint condition, solve equation (12) and equation (13), then get the following expression:

[0109]

[0110] Specifically, when the ram drops to the lowest position, it generates a second-order Stokes wave volume of half, the specific expression is:

[0111]

[0112] V2 is omitted in equation (15), V2 is proportional to η(x), when x c =L / 2, η(x)≈0, according to the calculation expression (4) of V2, V2=0

[0113] By solving equation (12) and equation (15), the first constraint condition formula is obtained as:

[0114]

[0115] Further, where the slope of the wedge-shaped ram is less than the minimum slope of the wave front, the specific expression is:

[0116] k p <k wmin (17)

[0117] In the formula, k p is the slope of the wedge-shaped ram, k wmin is the minimum slope of the wave front; wherein the slope k p of the wedge-shaped ram in equation (17) is calculated as follows

[0118]

[0119] Conversely, the ram will cover the generated wave, affecting the quality of the wave.

[0120] Specifically, the slope k w of the wave front in equation (17) can be:

[0121]

[0122] The minimum slope position of the ram can be derived by taking the derivative of x in equation (19)

[0123]

[0124] By derivation, the second constraint condition formula is obtained as:

[0125]

[0126] Further, the volume of the second-order Stokes wave in a period is less than zero, so the average water level in the tank will drop. In order to balance the drop in water level, the impact box needs to rise by a certain amount, so as to ensure that the impact box does not rise out of the water when the second-order Stokes wave spreads to the entire tank. Therefore, there is also a constraint condition, and the formula is:

[0127]

[0128] where w is the length of the tank, and substituting into the expression, the third constraint condition is derived.

[0129] Further, according to the constraint condition of various wave theories, the fourth constraint condition formula of the second-order Stokes wave is:

[0130]

[0131] Test Example

[0132] Based on the method described in Embodiment 1 above, a numerical wave tank with different water depths is established to carry out tests. First, it is assumed that the water depth of the tank is d = 15 m, the target wave height H = 2 m, and the period is 8.05 s. At this time, the corresponding wavelength L = 82.49 m, and according to Figure 2 calculation, at this time H / d = 0.133 < 0.3, 0.05 > H / L = 0.024 > 0.006, and the wave is a second-order Stokes wave. The impact box is a wedge-shaped body with a bottom angle of 45° and an initial immersion depth of 4 m. A wave height instrument is arranged at a distance of 206.23 m from the impact box to monitor the wave height, and compared with the analytical solution, as shown in Figure 5 .

[0133] Further, the water depth is deepened to d = 200 m, and the target wave height and period remain unchanged, H = 5 m and T = 8.94 s. At this time, the corresponding wavelength L = 124.91 m, and according to Figure 4 calculation, at this time H / d = 0.025 < 0.3, 0.05 > H / L = 0.04 > 0.006, and the wave is a second-order Stokes wave. The impact box size remains unchanged, and is also a wedge-shaped body with a bottom angle of 45° and an initial immersion depth of 4 m. A wave height instrument is arranged at a distance of 312.26 m from the impact box to monitor the wave height, and compared with the analytical solution, through Figure 5 and Figure 6 comparison results can be found that the second-order Stokes wave generated by the impact box type wave making system is in good agreement with the analytical solution, which proves the correctness and accuracy of the method recorded in Embodiment 1.

[0134] Embodiment 2

[0135] An impact box type wave making system is suitable for the method of generating a second-order Stokes wave by an impact box type wave making system recorded in Embodiment 1 above.

[0136] Further, the system comprises at least a set of drive systems, a plunger connected with the drive systems and a control system for feedback and control signals.

[0137] Single plunger wave making, double plunger synchronous wave making and double plunger pulse wave making can be realized.

[0138] The above has described one embodiment of the present application in detail, but the content is only the preferred embodiment of the present application and cannot be considered to limit the implementation range of the present application. Any equivalent changes and improvements made according to the application scope of the present application should still belong to the patent coverage range of the present application.

Claims

1. A method of generating a second order Stokes wave when using a plunging-piston wave maker, characterized in that, The method comprises: S1, determining the second-order Stokes wave expression as: wherein The expression is d is the water depth, k is the wave number k = 2π / L, L is the wavelength, H is the wave height, and φ is the wave phase angle. S2, according to the principle of conservation of mass, the lowering of the impact box will cause the lifting of the free water surface to form a wave crest, and the rising of the impact box will lower the free water surface to form a wave trough, and the relationship is as follows: V t -V0 = V1 + V2 (2) where V t V0 represents the submerged volume of the tank at the initial time, V1 represents the volume between the wave front and the calm water surface, and V2 represents the volume between the wet surface of the tank and the calm water surface. S3, define the free water surface coincides with the X axis and points to the X axis, and the Y axis is perpendicular to the free water surface and points to the upper V1 through from 0 to x c wave surface equation integral where x c is the horizontal position of the wave surface and the impact of the tank, η(x) is the wave surface height at position x; V2, V0 and V t may be expressed by the following equation Where S is the vertical displacement of the impact box, ds is the initial submerged water depth of the impact box, and θ is the bottom angle; S4, substituting formula (3) to formula (6) in S3 into formula (2), to obtain where S and x c are two unknown variables with respect to time; S5, the wedge free surface equation is defined as f(y)=c·t-(y+S)tanθ (8) In the formula, c is the generated wave propagation speed, t is the time, and y is the variable; Substitute (x c , η x＝xc ) into equation (8) to obtain: Formula (7) to formula (9) constitute the real-time impact box displacement expression; S6, substituting formula (1) into formula (7) and formula (9), the displacement of the impact box generating the second-order Stokes wave is obtained through the following equation: S7, loading formula (10) into the wave making system of the impact box wave maker, the second-order Stokes wave can be generated in the water tank.

2. A method of generating a second order Stokes wave by a plunging-piston type wave maker according to claim 1, wherein The capacity of the impact box restricts the generation of the wave and the quality of the wave, and the total constraint condition formula of the impact box wave making to generate the second-order Stokes wave is:

3. A method of generating a second order Stokes wave by a plunging plate type wave maker as claimed in claim 2, wherein Wherein, The movement of the impact box does not exceed the bottom of the water tank, and the specific expression is: S < d - d s (12) When the immersion depth of the impact box increases from the initial value to the maximum value, a 1 / 2 period wave volume is generated, and the specific expression is: In order to obtain the first constraint condition, formula (12) and formula (13) are solved, and the following expression is obtained:

4. A method of generating a second order Stokes wave by a plunging plate type wave maker according to claim 3, wherein When the impact box is lowered to the lowest position, a half of the second-order Stokes wave volume is generated, and the specific expression is: V2 is omitted in equation (15), V2 is proportional to η(x), when x c = L / 2, η(x) ~ 0, according to equation (4) for calculating V2, V2 = 0 By solving formula (12) and formula (15), the first constraint condition formula is obtained:

5. A method of generating a second order Stokes wave by a plunging plate type wave maker as claimed in claim 2, wherein, Wherein, The slope of the wedge-shaped impact box is less than the minimum slope of the wave front, and the specific expression is: k p <k wmin (17) where k p is the slope of the wedge-shaped bore, k wmin is the minimum slope of the wave front; where the wedge-shaped bore slope k p is calculated as follows Otherwise, the impact box will cover the generated wave, affecting the quality of the wave.

6. A method of generating a second order Stokes wave by a plunging plate type wave maker as claimed in claim 5, wherein, Slope k of wave front w In formula (17) can be written as The minimum slope position of the impact box can be derived by formula (19) to x Through derivation, the second constraint condition formula is obtained:

7. A method of generating a second order Stokes wave by a plunging plate type wave maker as claimed in claim 2, wherein, The volume of the second-order Stokes wave in a period is less than zero, and the average water level in the water tank will drop. In order to balance the dropped water level, the impact box needs to rise a certain amount to ensure that the impact box will not rise out of the water when the second-order Stokes wave spreads to the entire water tank, so there is also a constraint condition, and its formula is: where w is the water channel length, and substituting The expression, from which the third constraint is derived.

8. A method of generating a second order Stokes wave by a plunging plate type wave maker as claimed in claim 2, wherein, According to the restriction condition of various wave theories, the third constraint condition formula of the second-order Stokes wave is:

9. A fluming box wave maker system characterized by, The system is suitable for any one of the claims 1-8.

10. A flume-type wave generator as claimed in claim 9, characterized in that The system at least comprises a set of driving systems, an impact box connected with the driving system, and a control system for feedback and control signal.

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