Wide flat ship type vertical vibration attached water mass calculation method

Abstract

The invention relates to a wide and flat ship type vertical vibration attached water mass calculation method, which comprises the following steps of: 1, equally dividing N parts along the length of a ship into N + 1 stations in total, and obtaining the half width and the draught of each station of a ship body; 2, calculating a transverse section water entry area of each station of the ship body, and then calculating a transverse section conformal transformation coefficient of each station of the ship body; 3, calculating the mass of vertical vibration attached water per unit length of each station through a potential flow theory; 4, calculating a three-dimensional flow dimensionless correction coefficient according to the ratio of the ship length to the ship width; and step 5, calculating the mass of the attached water of the whole ship according to the calculation results of the step 3 and the step 4. The problem that the vibration attached water mass of the wide and flat ship type cannot be calculated through vibration attached water mass calculation of a conventional ship is solved, the vertical vibration attached water mass of the wide and flat ship type can be accurately forecasted, and the vertical vibration inherent frequency calculation of the wide and flat ship type is more accurate; therefore, harmful vibration of the ship body under various excitation in the operation process is avoided.

Description

Technical Field

[0001] The invention belongs to the field of hull structure design and relates to a method for calculating the vertical vibration attached water mass of a wide and flat ship. Background Art

[0002] A wide and flat ship is a special ship type with a beam-to-draft ratio greater than 4 and a length-to-breadth ratio less than 6. It has the obvious characteristic of shallow draft. When a ship vibrates in the water, a part of the outboard water will vibrate together with the hull. Therefore, the outboard water has a great influence on the vibration of the hull. The specific influence can be divided into the following three aspects: gravity influence, damping influence and inertia influence. The influence of gravity and damping on the free vibration of the hull is very small and can generally be ignored. The inertial influence of the outboard water is reflected in the change of the equivalent mass participating in the vibration of the hull, which is equivalent to a part of the outboard water vibrating together with the hull. This part of the outboard water mass is called the attached water mass, which is of the same order of magnitude as the hull structure mass. After considering the attached water mass, the natural frequency of the hull vibration will be significantly reduced. Therefore, it is of great significance to study the calculation of the attached water mass of wide and flat ships in the prediction of hull vibration.

[0003] At present, the calculation of vibration attached water mass of conventional ships usually adopts the attached water mass calculation formula based on the spectrum proposed by FM Lewis, F HTodd and others on the basis of experimental research. The influence of factors such as attached water mass coefficient and three-dimensional flow correction coefficient on this formula is listed in the form of spectrum, which is relatively simple to use. However, this method does not give the calculation coefficient of wide and flat ships with a ratio of beam to draft greater than 4 and a ratio of length to beam less than 6, and it is impossible to calculate the vibration attached water mass of wide and flat ships. Summary of the invention

[0004] Aiming at the problem that the vibration attached water mass calculation of conventional ships cannot calculate the vibration attached water mass of wide and flat ships, a method for calculating the vertical vibration attached water mass of wide and flat ships is proposed.

[0005] The technical solution of the present invention is:

[0006] A method for calculating the mass of water attached to a wide and flat ship due to vertical vibration comprises the following steps:

[0007] Step 1: Divide the length L into N equal parts, with a total of N+1 stations. The distance between two adjacent stations is ΔL=L / N. The station numbers are numbered from 0 to N from the stern to the bow. The corresponding half-width of each station is b j (j=0,1,2…N), draft is d j (j=0,1,2…N);

[0008] Step 2: Calculate the conformal transformation coefficient of the cross section of each station on the hull;

[0009] According to step 1, the half-width and draft of each station of the hull are obtained, and the cross-sectional water entry area s of each station of the hull is calculated. j ; The conformal transformation coefficient a of the cross section of each station of the hull is obtained by the following formula: -1j 、a 1j 、a 3j :

[0010]

[0011] In the formula C j is a fixed parameter;

[0012] Step 3: Calculate the mass of water attached to each unit length of vertical vibration at each station: Calculate the mass of water attached to each unit length of vertical vibration at each station by potential flow theory: j ;

[0013] Step 4: Calculate the dimensionless correction coefficient of three-dimensional flow according to the ratio of ship length and ship width;

[0014] Through the three-dimensional flow dimensionless correction coefficient, two second harmonic vibration three-dimensional flow dimensionless correction coefficients for ship length / ship width less than 6 are obtained; these first harmonic vibration three-dimensional flow dimensionless correction coefficients K 1 The dimensionless correction coefficient of three-dimensional flow of attached water with n-th harmonic vertical vibration is obtained by fitting.

[0015] Step 5: Calculate the attached water mass λ of the whole ship according to the results of steps 3 and 4.

[0016] Further, step 2 is specifically as follows: take the plane z where the hull cross section is located, ox is the half-width direction, oy is the draft direction, the transformation plane is the ζ plane, oζ is the half-width direction, oη is the draft direction, and the conversion relationship between the plane z and the plane ζ is as follows:

[0017]

[0018] In the formula, z=x+iy (y≥0); ζ=ξ+iη=e iθ (0≤θ≤π), a 2p-1 is the conformal transformation coefficient; P is the number of conformal transformation coefficients; p is the counting sign of the summation formula, p is 0, 1, 2, ..., P-1; θ is the argument, and the unit semicircle boundary is expressed in a way of modulus and argument;

[0019] In this method, P = 3, and the plane z and plane ζ are converted to each other as follows:

[0020]

[0021] On the perimeter of the unit semicircle, let the real part and the imaginary part of the above formula be equal, and we get:

[0022]

[0023] When θ = 0, x = b j ;exist When y=d j , substituting into the above formula, we get

[0024]

[0025] Assume j is the water entry area of ​​the hull cross section at the jth station, then

[0026]

[0027] The above two formulas are used to obtain the conformal transformation coefficients of the cross-section of each station on the hull:

[0028]

[0029] In the formula C j is a fixed parameter.

[0030] Furthermore, step three is as follows: in the cross section of the hull in the z plane, the flow field complex potential with the vertical flow velocity V at infinity is W(z); in the unit semicircle in the ζ plane, the vertical flow velocity at infinity is V * The complex potential of the flow field is W * (ζ), according to fluid mechanics,

[0031]

[0032] According to the conversion relationship between plane z and plane ζ in step 2, the vertical flow velocity at infinity is obtained as V * for:

[0033]

[0034] So we get:

[0035]

[0036] In order to solve the attached water mass for the hull vibration, the absolute complex potential on the hull boundary is written as:

[0037]

[0038] Calculation of vertical vibration attached water mass λ per unit length at each station based on potential flow theory j :

[0039]

[0040] Where: ρ is the density of water.

[0041] Further, step 4 is specifically as follows: through the three-dimensional flow dimensionless correction coefficient, two second harmonic vibration three-dimensional flow dimensionless correction coefficients with L / B less than 6 are obtained; these first harmonic vibration three-dimensional flow dimensionless correction coefficients K 1 Perform fitting, the fitting formula is:

[0042] K 1 =-0.0064m 2 +0.14m+0.049

[0043] Where: m is the ratio of the ship length L to the ship width B, 2≤m≤6;

[0044] The distance between the nodes of the nth harmonic and the first harmonic vibration is Therefore, the dimensionless correction coefficient of the three-dimensional flow of the nth harmonic vertical vibration attached water is:

[0045]

[0046] In the formula: n=1,2,3….

[0047] Furthermore, step five is specifically as follows: calculating the mass of water attached to the vertical vibration of the entire ship;

[0048] According to the calculation results of step 3 and step 4, the attached water mass λ of the whole ship is realized by the following formula:

[0049]

[0051] Furthermore, since the hull itself is a three-dimensional spatial structure, when it floats in the water, the flow field around it is also a three-dimensional flow, which makes the actual attached water mass of the hull smaller than the value calculated in the two-dimensional flow field; Lockwood Taylor gave the ratio of the vertical vibration attached water mass of three-dimensional motion to that of two-dimensional motion based on the calculation of the bending vibration of the ellipsoid, that is, the dimensionless correction coefficient of three-dimensional flow.

[0052] Furthermore, the dimensionless correction coefficient for three-dimensional flow is as follows:

[0053] When the ship length / breadth is 6-10 respectively, the three-dimensional flow dimensionless correction coefficients of the first harmonic vertical vibration are 0.674, 0.724, 0.764, 0.797, and 0.825 respectively, and the three-dimensional flow dimensionless correction coefficients of the second harmonic vertical vibration are 0.564, 0.633, 0.682, 0.723, and 0.760 respectively.

[0054] Furthermore, the dimensionless correction coefficients of the three-dimensional flow of the first harmonic and the second harmonic are different, mainly due to the different distances between the vibration nodes. The ratio of the distances between the nodes of the second harmonic and the first harmonic vibration in Table 1 is 0.78. Therefore, the dimensionless correction coefficient of the three-dimensional flow of the second harmonic vibration with ship length / ship width = 10 is the same as the dimensionless correction coefficient of the three-dimensional flow of the first harmonic vibration with ship length / ship width = 10*7.8, and the rest is similar.

[0055] Furthermore, using the second harmonic vibration three-dimensional flow dimensionless correction coefficients 0.564 and 0.633, these two coefficients should be the first harmonic vibration three-dimensional flow dimensionless correction coefficient of ship length / ship width = 6*0.78 = 4.7 and ship length / ship width = 7*0.78 = 5.5.

[0056] Furthermore, the conformal transformation technology transforms an area on the Z plane into an area on the ζ plane, and transforms the boundary of this area on the Z plane into the boundary of the corresponding area on the ζ plane, while maintaining the direction of passage; the shape of the hull cross-section is very complex, and it is difficult to solve the fluid motion on the cross-section. Therefore, the conformal transformation method is used to transform the moving hull cross-section into a unit semicircle, and transform the external domain of the cross-section into the external domain of the unit semicircle, and then solve the fluid motion problem on the unit circle.

[0057] The beneficial effects of the present invention are:

[0058] The mass of attached water for hull vibration is of the same order of magnitude as the mass of the hull structure. After considering the mass of attached water, the natural frequency of hull vibration will be significantly reduced. The calculation of attached water mass is of great significance in the prediction of hull vibration. The present invention provides a method for calculating the mass of attached water for vertical vibration of a wide and flat ship, which can accurately predict the mass of attached water for vertical vibration of a wide and flat ship, making the calculation of the natural frequency of vertical vibration of the wide and flat ship more accurate, thereby avoiding harmful vibration of the hull under various excitations during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a typical cross-sectional schematic diagram of the present invention;

[0060] Figure 2 It is a schematic diagram of the conformal transformation between the cross section of the hull and the unit semicircle of the present invention. DETAILED DESCRIPTION

[0061] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0062] A method for calculating the mass of water attached to a wide and flat ship due to vertical vibration comprises the following steps:

[0063] Step 1: Divide the length L into N equal parts, with a total of N+1 stations. The distance between two adjacent stations is ΔL=L / N. The station numbers are numbered from 0 to N from the stern to the bow. The corresponding half-width of each station (referring to half of the corresponding ship width) is b j (j=0,1,2…N), draft is d j (j=0,1,2…N).

[0064] Step 2: Calculate the conformal transformation coefficient of the cross-section of each station on the hull.

[0065] The conformal transformation technique transforms an area on the Z plane into an area on the ζ plane, and transforms the boundary of this area on the Z plane into the boundary of the corresponding area on the ζ plane, while maintaining the direction of passage. The cross-section of the hull is very complex, and it is difficult to solve the fluid motion on the cross-section. Therefore, the conformal transformation method is used to transform the moving hull cross-section into a unit semicircle, and transform the external domain of the cross-section into the external domain of the unit semicircle, and then solve the fluid motion problem on the unit circle.

[0066] (Reference: Zhang Teng et al., Simulation of ship heave and pitch motion based on multi-coefficient conformal transformation method [J]. Journal of Dalian Maritime University, 2019, 40(3): 51-56)

[0067] like Figure 1 , 2 As shown, the plane where the hull cross section is located is taken as the z plane, ox is the half-width direction, and oy is the draft direction; the transformation plane is the ζ plane, oζ is the half-width direction, and oη is the draft direction. The conversion relationship between the z plane and the ζ plane is as follows:

[0068]

[0069] In the formula, z=x+iy (y≥0); ζ=ξ+iη=e iθ (0≤θ≤π), a 2p-1 is the conformal transformation coefficient; P is the number of conformal transformation coefficients. p is the counting sign of the summation formula, p takes 0, 1, 2, ..., P-1. θ is the argument, and the unit semicircle boundary is expressed in a way of modulus (modulus = 1) and argument.

[0070] In the present invention, P=3, then plane z and plane ζ are converted to each other as follows:

[0071]

[0072] On the perimeter of the unit semicircle, let the real part and the imaginary part of the above equation be equal, and we get:

[0073]

[0074] When θ = 0, x = bj , (b j is the half width of the hull at the jth station in step 1); When y=d j , (d j is the hull draft of the jth station in step 1), substitute it into the above formula, and we get

[0075]

[0076] Assume j is the water entry area of ​​the hull cross section at the jth station, then

[0077]

[0078] The above two formulas are used to obtain the conformal transformation coefficients of the cross-section of each station on the hull:

[0079]

[0080] In the formula C j is a fixed parameter.

[0081] Step 3: Calculate the vertical vibration attached water mass per unit length at each station.

[0082] In the cross section of the hull in the z plane, the flow field complex potential with the vertical flow velocity V at infinity is W(z). In the unit semicircle in the ζ plane, the vertical flow velocity at infinity is V * The complex potential of the flow field is W * (ζ), according to fluid mechanics (Zhang Zhaoshun et al., Fluid Mechanics, Beijing: Tsinghua University Press, 2006),

[0083]

[0084] According to the conversion relationship between plane z and plane ζ in step 2, the vertical flow velocity at infinity is obtained as V * for:

[0085]

[0086] So we get:

[0087]

[0088] In order to solve the attached water mass for the hull vibration, the absolute complex potential on the hull boundary is written as:

[0089]

[0090] Calculation of vertical vibration attached water mass λ per unit length at each station based on potential flow theory j :

[0091]

[0092] Where: ρ is the density of water.

[0093] Step 4: Calculate the dimensionless correction coefficient for three-dimensional flow based on the ratio of ship length to ship width (this coefficient remains unchanged for each station profile).

[0094] Since the hull itself is a three-dimensional structure, when it floats in the water, the flow field around it is also a three-dimensional flow, which makes the actual attached water mass of the hull smaller than the value calculated in the two-dimensional flow field. Lockwood Taylor gave the ratio of the vertical vibration attached water mass of three-dimensional motion to that of two-dimensional motion based on the calculation of the bending vibration of the ellipsoid, that is, the dimensionless correction coefficient of three-dimensional flow, see Table 1.

[0095] Table 1 Dimensionless correction coefficients for three-dimensional flow

[0096]

[0097] The dimensionless correction coefficients of the three-dimensional flow of the first harmonic and the second harmonic are different, mainly due to the different distances between the vibration nodes. The ratio of the distances between the nodes of the second harmonic and the first harmonic vibration in Table 1 is 0.78. Therefore, the dimensionless correction coefficient of the three-dimensional flow of the second harmonic vibration with L / B=10 in Table 1 is the same as the dimensionless correction coefficient of the three-dimensional flow of the first harmonic vibration with L / B=10*7.8, and the rest are similar.

[0098] According to the above rules, we use the second harmonic vibration three-dimensional flow dimensionless correction coefficients 0.564 and 0.633. These two coefficients should be L / B = 6*0.78 = 4.7 and L / B = 7*0.78 = 5.5. In this way, we get two second harmonic vibration three-dimensional flow dimensionless correction coefficients with L / B less than 6. These first harmonic vibration three-dimensional flow dimensionless correction coefficients K 1 Perform fitting, the fitting formula is:

[0099] K 1 =-0.0064m 2 +0.14m+0.049

[0100] In the formula: m is the ratio of the ship length L to the ship width B, 2≤m≤6.

[0101] The distance between the nodes of the nth harmonic and the first harmonic vibration is Therefore, the dimensionless correction coefficient of the three-dimensional flow of the nth harmonic vertical vibration attached water is:

[0102]

[0103] In the formula: n=1,2,3...

[0104] Step 5: Calculate the mass of water attached to the vertical vibration of the entire ship.

[0105] According to the calculation results of step 3 and step 4, the attached water mass λ of the whole ship is realized by the following formula:

[0106]

[0107] The above-mentioned embodiment only expresses one implementation mode of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A method for calculating the mass of water attached to a wide flat ship due to vertical vibration, characterized in that: The following steps are involved: Step 1: Divide the length L into N equal parts, with a total of N+1 stations. The distance between two adjacent stations is ΔL=L / N. The station numbers are numbered from 0 to N from the stern to the bow. The corresponding half-width of each station is b j (j=0,1,2…N), draft is d j (j=0,1,2…N); Step 2: Calculate the conformal transformation coefficient of the cross section of each station on the hull; According to step 1, the half-width and draft of each station of the hull are obtained, and the cross-sectional water entry area s of each station of the hull is calculated. j ; The conformal transformation coefficient a of the cross section of each station of the hull is obtained by the following formula: -1j 、a 1j 、a 3j : In the formula C j is a fixed parameter; Step 3: Calculate the mass of water attached to each unit length of vertical vibration at each station: Calculate the mass of water attached to each unit length of vertical vibration at each station by potential flow theory: j ; Step 4: Calculate the dimensionless correction coefficient of three-dimensional flow according to the ratio of ship length and ship width; Through the three-dimensional flow dimensionless correction coefficient, two second harmonic vibration three-dimensional flow dimensionless correction coefficients for ship length / ship width less than 6 are obtained; these first harmonic vibration three-dimensional flow dimensionless correction coefficients K1 are fitted to obtain the three-dimensional flow dimensionless correction coefficient of the nth harmonic vertical vibration attached water; Step 5: Calculate the attached water mass λ of the whole ship according to the results of steps 3 and 4.

2. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 1 is characterized in that: Step 2 is as follows: take the plane z where the hull cross section is located, ox is the half-width direction, oy is the draft direction, transform the plane to the ζ plane, oζ is the half-width direction, oη is the draft direction, and the conversion relationship between plane z and plane ζ is as follows: In the formula, z=x+iy (y≥0); ζ=ξ+iη=e iθ (0≤θ≤π), a 2p-1 is the conformal transformation coefficient; P is the number of conformal transformation coefficients; p is the counting sign of the summation formula, p is 0, 1, 2, ..., P-1; θ is the argument, and the unit semicircle boundary is expressed in a way of modulus and argument; In this method, P = 3, and the plane z and plane ζ are converted to each other as follows: On the perimeter of the unit semicircle, let the real part and the imaginary part of the above formula be equal, and we get: When θ = 0, x = b j ;exist When y=d j , substituting into the above formula, we get Assume j is the water entry area of ​​the hull cross section at the jth station, then The above two formulas are used to obtain the conformal transformation coefficients of the cross-section of each station on the hull: In the formula C j is a fixed parameter.

3. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 2 is characterized in that: Step 3 is as follows: for the cross section of the hull in the z plane, the flow field complex potential with the vertical flow velocity V at infinity is W(z); for the unit semicircle in the ζ plane, the vertical flow velocity at infinity is V * The complex potential of the flow field is W * (ζ), according to fluid mechanics, According to the conversion relationship between plane z and plane ζ in step 2, the vertical flow velocity at infinity is obtained as V * for: So we get: In order to solve the attached water mass for the hull vibration, the absolute complex potential on the hull boundary is written as: Calculation of vertical vibration attached water mass λ per unit length at each station based on potential flow theory j : Where: ρ is the density of water.

4. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 3 is characterized in that: Step 4 is specifically as follows: using the three-dimensional flow dimensionless correction coefficient, two second harmonic vibration three-dimensional flow dimensionless correction coefficients with L / B less than 6 are obtained; these first harmonic vibration three-dimensional flow dimensionless correction coefficients K1 are fitted, and the fitting formula is: K1=-0.0064m 2 +0.14m+0.049 Where: m is the ratio of the ship length L to the ship width B, 2≤m≤6; The distance between the nodes of the nth harmonic and the first harmonic vibration is Therefore, the dimensionless correction coefficient of the three-dimensional flow of the nth harmonic vertical vibration attached water is: In the formula: n=1,2,3….

5. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 4 is characterized in that: Step 5 is specifically as follows: calculate the mass of water attached to the vertical vibration of the entire ship; According to the calculation results of step 3 and step 4, the attached water mass λ of the whole ship is realized by the following formula:

6. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 4 is characterized in that: Since the hull itself is a three-dimensional spatial structure, when it floats in the water, the flow field around it is also a three-dimensional flow, which makes the actual attached water mass of the hull smaller than the value calculated in the two-dimensional flow field; Lockwood Taylor gave the ratio of the vertical vibration attached water mass of three-dimensional motion to that of two-dimensional motion based on the calculation of the bending vibration of the ellipsoid, that is, the dimensionless correction coefficient of three-dimensional flow.

7. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 4 is characterized in that: The dimensionless correction coefficients for three-dimensional flow are as follows: When the ship length / breadth is 6-10 respectively, the three-dimensional flow dimensionless correction coefficients of the first harmonic vertical vibration are 0.674, 0.724, 0.764, 0.797, and 0.825 respectively, and the three-dimensional flow dimensionless correction coefficients of the second harmonic vertical vibration are 0.564, 0.633, 0.682, 0.723, and 0.760 respectively.

8. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 7 is characterized in that: The dimensionless correction coefficients of the three-dimensional flow of the first harmonic and the second harmonic are different, mainly due to the different distances between the vibration nodes. The ratio of the distances between the nodes of the second harmonic and the first harmonic vibration in Table 1 is 0.

78. Therefore, the dimensionless correction coefficient of the three-dimensional flow of the second harmonic vibration with ship length / ship width = 10 is the same as the dimensionless correction coefficient of the three-dimensional flow of the first harmonic vibration with ship length / ship width = 10*7.8, and the rest are similar.

9. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 8, characterized in that: Using the second harmonic vibration three-dimensional flow dimensionless correction coefficients of 0.564 and 0.633, these two coefficients should be ship length / ship width = 6*0.78 = 4.7 and ship length / ship width = 7*0.78 = 5.5, the first harmonic vibration three-dimensional flow dimensionless correction coefficient.

10. The method for calculating the water mass attached to the vertical vibration of a wide and flat ship according to claim 1, characterized in that: The conformal transformation technology transforms an area on the Z plane into an area on the ζ plane, and transforms the boundary of this area on the Z plane into the boundary of the corresponding area on the ζ plane, while maintaining the direction of passage; the shape of the hull cross-section is very complex, and it is difficult to solve the fluid motion on the cross-section. Therefore, the conformal transformation method is used to transform the moving hull cross-section into a unit semicircle, and transform the external domain of the cross-section into the external domain of the unit semicircle, and then solve the fluid motion problem on the unit circle.

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