A fast prediction method of Kelvin wave form for a square stern ship considering the nonlinear effect of the ship's recess

Abstract

The application discloses a Kelvin wave form rapid prediction method for a square stern ship considering the nonlinear influence of a recessed area behind the ship, S1, considering the nonlinear influence of the recessed area of the free surface behind the square stern ship, the Neumann-Michell theory is modified, and the Kelvin wave of the square stern ship is decomposed into a ship body surface contribution component ζ S and a recessed area contribution component ζ F of the free surface behind the ship; S2, the ship body surface contribution component ζ S is calculated by using the Neumann-Michell theory; the recessed area contribution component ζ F of the free surface behind the ship is considered independently; the nonlinear influence is obtained by integrating the velocity potential of the free surface on the surface of the recessed area of the free surface behind the square stern; S3, the Kelvin wave form of the square stern ship is predicted by summing the ship body surface contribution component ζ S and the recessed area contribution component ζ F of the free surface behind the ship. The Kelvin wave is decomposed into the ship body surface contribution component and the recessed area contribution component of the free surface behind the ship, independent calculation is realized, the wave system structure characteristics of the square stern ship can be more accurately revealed, and the calculation time is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship hydrodynamics, and particularly relates to a method for quickly and accurately calculating Kelvin wave of a square stern ship based on Neumann-Michell steady wave making theory, and capable of considering the nonlinear influence of the concave area of the free surface behind the square stern ship. BACKGROUND

[0002] The Kelvin wave of a square stern ship is different from that of a common ship. The Kelvin wave of a common ship is mainly determined by the hull surface. However, there is a significant concave area (with strong nonlinearity) on the free surface behind the stern plate of a square stern ship, and the Kelvin wave of the square stern ship is determined by the hull surface and the concave area. The wave system of the concave area helps to understand the characteristics of the wave system of the square stern ship and solve related engineering problems such as ship design.

[0003] The traditional CFD numerical calculation method can well calculate the complete Kelvin wave behind the square stern ship. However, on the one hand, the calculation time is long, and on the other hand, since the CFD method calculates the Kelvin wave generated by the hull surface and the concave area behind the ship, it cannot calculate the independent evolution process of the wave system of the concave area at the stern of the ship.

[0004] The Neumann-Michell (NM) theory is a potential flow method for calculating the steady wave making flow field of a ship invented by Professor Francis Noblesse in 2013, which only needs to distribute sources and sinks on the hull surface to quickly calculate the flow field of the ship. However, when calculating the square stern ship, the current theory usually chooses to directly ignore the influence of the square stern surface and only considers the influence of the two sides of the hull surface.

[0005] Therefore, although the Neumann-Michell (NM) theory can quickly predict the Kelvin wave of a common ship, the existing method cannot consider the nonlinear influence of the concave area behind the square stern ship, resulting in insufficient accuracy of the Kelvin wave prediction of the square stern ship.

[0006] Therefore, it is urgent to propose a theoretical method that can quickly predict the Kelvin wave of a square stern ship and calculate the independent contribution of the hull surface and the concave area behind the square stern to the Kelvin wave. SUMMARY

[0007] The main purpose of the present application is to propose a method for quickly predicting the Kelvin wave of a square stern ship considering the nonlinear influence of the concave area behind the ship. The method decomposes the Kelvin wave into a hull surface contribution component and a concave area behind the free surface contribution component, realizes independent calculation, and can more accurately reveal the wave system structure characteristics of the square stern ship. Compared with the numerical calculation method, the theoretical calculation method proposed in the present application greatly shortens the calculation time.

[0008] The technical scheme adopted by the present application is:

[0009] A Kelvin wave form rapid prediction method for a square stern ship considering the nonlinear influence of the ship stern depression area, comprising the following steps:

[0010] S1, considering the nonlinear influence of the square stern ship stern free surface depression area, the Neumann-Michell theory is modified, and the Kelvin wave of the square stern ship is decomposed into a ship surface contribution component ζ S and a ship stern free surface depression area contribution component ζ F ;

[0011] S2, the ship surface contribution component ζ S and the ship stern free surface depression area contribution component ζ F are calculated by using the Neumann-Michell theory; the nonlinear influence of the square stern ship stern free surface depression area is considered alone, and the nonlinear influence is obtained by integrating the free surface velocity potential on the surface of the square stern ship stern free surface depression area;

[0012] S3, the square stern ship Kelvin wave form is predicted by summing the ship surface contribution component ζ S and the ship stern free surface depression area contribution component ζ F .

[0013] In the above scheme, the calculation method of the ship stern free surface depression area contribution component ζ F is:

[0014]

[0015] In the formula, the x-direction partial derivative of the free surface velocity potential of the field point position is represented, and its expression is:

[0016]

[0017] In the formula, is the x-direction partial derivative of the x component of the free surface velocity potential Local item of the field point position, is the x-direction partial derivative of the y component of the free surface velocity potential Local item of the field point position, is the x-direction partial derivative of the z component of the free surface velocity potential Local item of the field point position, is the x-direction partial derivative of the x component of the free surface velocity potential Wave item of the field point position, is the x-direction partial derivative of the y component of the free surface velocity potential Wave item of the field point position, is the x-direction partial derivative of the free-surface velocity potential Wave term z component at the field point; the x-direction is the longitudinal direction of the ship, pointing from the stern to the bow; the field point represents the position point affected by the ship's wave making.

[0018] In the above scheme, the expression of the x-direction partial derivative of the free-surface velocity potential at each field point is:

[0019]

[0020] where n x , n y , n z respectively represent the x, y, z direction components of the ship's stern free-surface depression surface normal vector; L, W respectively represent the Local term and the Wave term of the Green function, L x , W x respectively represent the x-direction partial derivatives of L, W, L xx , L xy , L xz respectively represent the x, y, z direction partial derivatives of L x , W xx , W xy , W xz respectively represent the x, y, z direction partial derivatives of W x ; ψ H is the Hogner velocity potential at the source point, is the y-direction partial derivative of the Hogner velocity potential at the source point, is the z-direction partial derivative of the Hogner velocity potential at the source point; η0 is the ship's stern free-surface depression height; F r is the Froude number of the square stern ship; represents the square stern free-surface depression area, the shape of which is determined by the size of η0; the y-direction represents the ship's width direction, pointing from the left side to the right side; the z-direction represents the draft direction, pointing from the ship's bottom to the deck; the source point is a concept opposite to the field point, representing the position point exciting the ship's wave making.

[0021] In the above scheme, the calculation formula of the ship's stern free-surface depression height η0 is:

[0022] η0 = y * x * with -0.5 < x < -0.5, |y| < b h

[0023] where y * is the transverse variation coefficient of the depression area shape, x * is the longitudinal variation coefficient of the depression area shape, l h ​is the length of the recessed area, b is the dimensionless beam, x represents the coordinate in the x direction, and y represents the coordinate in the y direction.

[0024] In the above scheme, y * is expressed as:

[0025]

[0026] In the formula, r is the approximate circular arc radius of the width direction of the recessed area of the ship, η dry represents the dimensionless wet height of the transom plate of the transom stern ship;

[0027] x * is expressed as:

[0028] x * =-1-(x+0.5) / l h .

[0029] In the above scheme, the expression of the length l h of the recessed area is:

[0030]

[0031] In the above scheme, the calculation formula of the dimensionless wet height η dry of the transom plate of the transom stern ship is:

[0032] η dry =(E dry / T r )×(T r / L s )

[0033] Wherein:

[0034]

[0035] In the formula, E dry represents the dimensionless wet height of the transom plate of the transom stern ship, T r represents the draft height of the stern, L S represents the length of the ship, F T represents the Froude number of the transom stern, represents the critical value of the Froude number of the transom stern (which can be approximately taken as 2.6), V s represents the ship speed, and g represents the acceleration of gravity.

[0036] In the above scheme, the calculation method of the ship surface contribution component ζ S is:

[0037]

[0038] In the formula, x-direction partial derivative of the Hogner velocity potential representing the position of the field point, x-direction partial derivative of the NM velocity potential representing the position of the field point.

[0039] In the above scheme, The expression of is:

[0040]

[0041] In the formula, n x x-direction component of the surface normal vector of the concave surface of the free surface at the stern of the ship, x-direction component of the surface normal vector considering the influence of the turbulent vortex zone at the stern of the square stern, and is taken as 0.25n x ; L and W respectively represent the Local term and the Wave term of the Green function, L x and W x respectively represent the x-direction partial derivatives of L and W; da represents a microelement of the hull surface, and ∑ wet represents the wet surface of the hull.

[0042] In the above scheme, The expression of is:

[0043]

[0044] In the formula, A ij represents the configuration matrix coefficient, (A ij ) x represents the x-direction partial derivative of A ij , φ j represents the velocity potential of the node, i represents the number of the field point, and j represents the number of the source point.

[0045] The present application has the beneficial effects that:

[0046] The present application considers the nonlinear influence of the concave zone at the stern of the square stern, decomposes the Kelvin wave of the square stern into a contribution component of the hull surface and a contribution component of the concave zone of the free surface at the stern of the ship, realizes independent calculation, and can more accurately reveal the wave system structure characteristics of the square stern ship; compared with the numerical calculation method, the theoretical calculation method proposed in the present application greatly shortens the calculation time. The present application is verified by numerical calculation, and it is shown that the method proposed in the present application can accurately and quickly calculate the Kelvin wave of the square stern ship.

[0047] In order to more accurately calculate the Kelvin wave form of the square stern ship, the present application describes the shape expression of the concave zone of the free surface at the stern of the square stern through a second-order precision mode, and also gives a more accurate expression of the non-wet height of the stern transom of the square stern ship. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative effort.

[0049] Figure 1 is the meaning of each parameter in the method of the present application and the schematic diagram of the ship's recessed area behind the ship;

[0050] Figure 2 is the comparison between the Kelvin wave of the square stern ship predicted in the embodiment of the method of the present application and the CFD calculation result;

[0051] Figure 3 is the hull surface contribution component ζ of the Kelvin wave predicted in the embodiment of the method of the present application S and the contribution component ζ of the free surface recessed area behind the ship F . DETAILED DESCRIPTION

[0052] In order to make the objects, technical solutions and advantages of the present application clearer, the following will further describe the present application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0053] The present application proposes a fast prediction method of Kelvin wave form of square stern ship considering the nonlinear influence of the recessed area behind the ship, including the following steps:

[0054] S1, considering the nonlinear influence of the recessed area of the free surface behind the square stern ship, modifying the Neumann-Michell theory, and decomposing the Kelvin wave of the square stern ship into the hull surface contribution component ζ S and the contribution component ζ of the recessed area of the free surface behind the ship F .

[0055] S2, calculating the hull surface contribution component ζ S using the Neumann-Michell theory; and calculating the contribution component ζ of the recessed area of the free surface behind the ship F considering the nonlinear influence of the recessed area of the free surface behind the square stern ship alone, and the nonlinear influence is obtained by integrating the velocity potential of the free surface on the surface of the recessed area of the free surface behind the square stern ship.

[0056] S3, summing the hull surface contribution component ζ S and the contribution component ζ of the recessed area of the free surface behind the ship F to predict the Kelvin wave form of the square stern ship.

[0057] The present embodiment takes NPL-4a ship type as the object, and calculates the Kelvin wave form of the ship type by using the method. The following is one of the specific implementation steps of the method:

[0058] First step, according to the given ship type, determine the ship speed V s , ship length L s , stern draft height T r , calculate the ship F r and F T :

[0059]

[0060] Second step, according to F T , calculate E dry / T r and η dry :

[0061]

[0062] η dry =(E dry / T r )×(T r / L S )

[0063] Third step, according to F r , calculate the length of the free surface depression area behind the ship l h :

[0064]

[0065] Further obtain the free surface depression height η0 behind the ship:

[0066] η0=y * x * with-0.5-l h ≤x≤-0.5,|y|<b

[0067] Wherein:

[0068]

[0069] x * =-1-(x+0.5) / l h

[0070] Non-dimensional square stern width b=B s / L S , B s represents the dimensional square stern width.

[0071] Fourth step, according to the x direction component n of the normal of the free surface depression surface of the stern of the shipx , the x-direction partial derivative of the Local term L and the Wave term W of the Green function x , W x , the x-direction partial derivative of the Hogner velocity potential of the field point position:

[0072]

[0073] According to the hull surface shape, the x-direction partial derivative of the configuration matrix coefficient (A ij ) x and the hull surface velocity potential φ j , further calculate the x-direction partial derivative of the NM velocity potential of the field point position:

[0074]

[0075] Fifth step, according to the calculated and Calculate the hull surface contribution component ζ S of the Kelvin wave:

[0076]

[0077] Sixth step, according to the x-direction partial derivative of the x, y, z components of the free surface velocity potential Local term of the field point position And the x-direction partial derivative of the x, y, z components of the free surface velocity potential Wave term of the field point position The x-direction partial derivative of the free surface velocity potential of the field point position can be calculated:

[0078]

[0079] Seventh step, according to the calculated x-direction partial derivative of the free surface velocity potential of the field point position, the contribution component ζ F of the Kelvin wave of the free surface depression area behind the ship is obtained:

[0080]

[0081] Eighth step, the complete Kelvin wave height of the square stern ship is calculated as:

[0082] ζ = ζ S + ζ F

[0083] According to the above steps, develop the corresponding program. Based on the hull shape, ship speed, transom height, and transom width, the wave height distribution of the Kelvin wave of the transom stern ship can be directly calculated. It should be noted that when programming according to the fast prediction method of the Kelvin wave form of the transom stern ship proposed in this invention, it is not limited to the above specific implementation steps. In other embodiments, it is also possible to first solve the contribution component of the sunken area of the free liquid surface behind the ship, and then solve the contribution component of the hull surface (i.e., place steps six and seven before steps four and five).

[0084] Using the method of this invention, the Kelvin wave form calculated by the developed program (displaying the two-dimensional wave height distribution with Tecplot) is compared with the CFD calculation results. See Figure 2 . From Figure 2 , it can be seen that the method of this invention is in good agreement with the CFD method. The CFD method uses the commercial software StarCCM+, the control equation uses the SIMPLE algorithm, the free liquid surface is captured using the VOF method, and the flow field (X, Y, Z) range is 2.5Ls < X < -4Ls, 0 < Y < 2Ls, -2Ls < Z < 1.5Ls. The y+ range within the boundary layer is 30 < y+ < 100, and the time step is 0.005s. The calculation grid is approximately 1.96 million. The traditional CFD method takes more than several hours to calculate, while this method takes less than 30s.

[0085] Figure 3 [[ID=ID=11]]These are the two components of the Kelvin wave of the transom stern ship calculated by this method, namely the contribution component ζ S ( Figure 3 upper part) and the contribution component ζ F ( Figure 3 lower part) of the sunken area of the free liquid surface behind the ship.From Figure 3 , it can be seen that the contribution component ζ F of the sunken area of the free liquid surface behind the ship only exists behind the ship, and its contribution to the Kelvin wave of the transom stern ship is significant. Moreover, there is a certain phase difference between ζ F and the contribution component ζ S of the hull surface. All these can reveal the wave system structure characteristics of the transom stern ship.

[0086] It should be pointed out that according to the needs of implementation, each step / component described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0087] The size of the serial numbers of each step in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of this application.

[0088] It is to be understood that all such modifications and variations that can occur to those skilled in the art in the light of the foregoing description are to be considered within the scope of the application as defined in the claims appended hereto.

Claims

1. A method for rapid prediction of Kelvin waveforms of a square-stern ship considering the nonlinear effects of the stern depression region, characterized in that, Includes the following steps: S1. Considering the nonlinear influence of the free surface depression region behind the stern-shaped ship, the Neumann-Michell theory is modified to decompose the Kelvin wave of the stern-shaped ship into the contribution component ζ of the hull surface. S The contribution component ζ of the free surface depression area behind the ship F ; S2. Calculate the hull surface contribution component ζ using Neumann-Michell theory. S The contribution component ζ of the free liquid surface depression area behind the ship F The nonlinear effect of the free liquid surface depression region behind the square stern is considered separately. The nonlinear effect is obtained by integrating the free liquid surface velocity potential over the surface of the free liquid surface depression region behind the square stern. S3, by contributing the component ζ to the hull surface S The contribution component ζ of the free surface depression area behind the ship F Summation is performed to predict the Kelvin waveform of the stern ship.

2. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 1, characterized in that, The contribution component ζ of the free surface depression area at the stern of the ship. F The calculation method is as follows: In the formula, The partial derivative of the free surface velocity potential at the location of the field point in the x-direction is expressed as follows: In the formula, Let x be the x-direction partial derivative of the local component of the free surface velocity potential at the field point. Let be the x-direction partial derivative of the y-component of the local term of the free surface velocity potential at the field point. Let be the x-direction partial derivative of the z-component of the local term of the free surface velocity potential at the field point. Let be the x-direction partial derivative of the wave term of the free surface velocity potential at the field point location. Let be the x-direction partial derivative of the y-component of the Wave term, representing the free surface velocity potential at the field point. The x-direction partial derivative of the z-component of the free surface velocity potential Wave term at the field point location; the x-direction is the longitudinal direction of the hull, pointing from the stern to the bow; the field point represents the location affected by the wave-making effect of the hull.

3. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear influence of the stern depression region according to claim 2, characterized in that, The expression for the partial derivative of the free surface velocity potential in the x-direction at each field point is: In the formula, n x n y n z Let x, y, and z represent the x, y, and z directional components of the normal vector to the surface of the free liquid depression at the stern; L and W represent the Local and Wave terms of the Green's function, respectively. x W x Let L and W represent the partial derivatives of L and W in the x-direction, respectively. xx L xy L xz L respectively x The partial derivatives in the x, y, and z directions, W xx W xy W xz W x Partial derivatives in the x, y, and z directions; ψ H The Hogner velocity potential at the source point is... Let be the y-direction partial derivative of the Hogner velocity potential at the source point. Let be the z-direction partial derivative of the Hogner velocity potential at the source point; η0 is the height of the free surface depression at the stern of the ship; F r For the Froude number of square stern ships; The stern free surface depression is defined by the size of η0; the y-direction represents the ship's beam direction, pointing from left to right; the z-direction represents the draft direction, pointing from the bottom to the deck; the source point is a concept relative to the field point, representing the location where the ship's waves are generated.

4. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 3, characterized in that, The formula for calculating the height η0 of the free surface depression at the stern of the ship is: In the formula, y * x is the lateral variation coefficient of the shape of the depression region. * This is the longitudinal variation coefficient of the shape of the depression region. Let be the length of the concave region, b be the dimensionless stern width, x represent the coordinate in the x-direction, and y represent the coordinate in the y-direction.

5. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 4, characterized in that, y * The expression is: In the formula, r is the approximate radius of the circular arc in the width direction of the stern depression area, and η dry This represents the dimensionless unwetted height of the stern sealing plate of a square stern ship; x * The expression is:

6. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 4 or 5, characterized in that, Length of the depression area The expression is:

7. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 5, characterized in that, The dimensionless unwetted height η of the stern sealing plate of a square stern ship dry The calculation formula is: η dry =(E dry / T r )×(T r / L S ) in: In the formula, E dry T represents the dimensionless unwetted height of the stern sealing plate of a square stern ship. r Indicates the stern draft, L S Indicates the captain, F T Represents the Froude number, V represents the critical value of the Froude number at the stern. s The speed of the ship is represented by g, and the acceleration due to gravity is represented by g.

8. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 1, characterized in that, The contribution component ζ of the hull surface S The calculation method is as follows: In the formula, The x-direction partial derivative of the Hogner velocity potential at the field point location is represented by... The x-direction partial derivative of the NM velocity potential at the field point location is represented by this derivative.

9. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 8, characterized in that, The expression is: In the formula, n x This represents the x-direction component of the normal vector to the surface of the free liquid depression at the stern. The x-direction component of the normal vector of the object surface, considering the influence of the turbulent swirling region behind the stern, is taken as 0.25n. x ; L and W represent the Local and Wave terms of the Green function, respectively. x W x Let L and W represent the partial derivatives in the x-direction, respectively; da represents the infinitesimal element of the hull surface, ∑ wet This refers to the wetted surface of the ship's hull.

10. The method for rapid prediction of Kelvin waveforms for square-stern ships considering the nonlinear effects of the stern depression region according to claim 8, characterized in that, The expression is: In the formula, A ij Represents the configuration matrix coefficients, (A ij ) x A represents ij The partial derivative in the x-direction, φ j Let i represent the velocity potential of the node, i represent the field point number, and j represent the source point number.

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