Method for forecasting wave making and resistance of sailing ship in inter-ice channel

Abstract

The invention discloses a method for forecasting wave making and resistance of a sailing ship in an inter-ice channel, and the method comprises the steps: building different models in a channel basin and ice coverage regions at two sides, and building an ice-water coupling hydrodynamic model of a steady sailing ship in the inter-ice channel, different Green functions are adopted to construct boundary integral equations for different hydrodynamic model drainage basins for coupling solving to obtain the flow field velocity potential, and then the wave-making characteristics and the resistance of the ship sailing in the inter-ice channel are obtained. The method can provide key support for polar region ship design optimization, energy conservation and emission reduction and polar region resource development, and has remarkable academic value and application potential.

Description

Technical Field

[0001] The present invention relates to a method for predicting wave making and resistance of a sailing ship, and in particular to a method for predicting wave making and resistance of a sailing ship in an ice channel. Background Art

[0002] As the global climate warms, polar sea ice is melting at an accelerated pace, and the Arctic's ice-free passages are gradually becoming navigable. Compared to traditional passages, these passages can significantly shorten the sailing distance between the Eurasian continent, significantly reducing time and economic costs. The Arctic has also become a hotspot for international shipping and resource development. The ice-free navigation environment is complex, and the presence of ice significantly changes the flow field characteristics around the ship, resulting in significant differences in its resistance mechanism from that in conventional environments, which places higher demands on the ship's navigation performance. Existing research on ship resistance is either mainly focused on open waters and lacks a theoretical model that is adaptable to the special flow field environment of ice-free passages; or it is overly focused on icebreaking capabilities and high ice density conditions, but lacks a systematic understanding of the resistance mechanism in this high-frequency scenario of ice-free passages. As a result, polar ships often face the dual dilemma of "overdesign" or "underestimation of energy efficiency" in actual operations. Summary of the Invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a method for predicting wave and resistance for ships sailing in ice channels in order to solve the problems existing in the prior art.

[0004] Technical solution: The present invention provides a method for predicting wave generation and resistance for ships sailing in an ice channel, comprising:

[0005] (1) Different models were established in the channel basin and the ice-covered areas on both sides. The channel basin adopted nonlinear free surface conditions. The ice-water coupled dynamic equations were established in the ice-covered areas on both sides based on the continuous medium assumption and Euler-Bernoulli beam theory.

[0006] (2) By utilizing the wave-current exchange characteristics of adjacent flow fields, Dirichlet and Neumann continuity conditions of the disturbance potential are established on the control surface, and then an ice-water coupled hydrodynamic model for ships sailing steadily in ice channels is established;

[0007] (3) Constructing a Green's function system, in which the Rankine source Green's function is used in the channel basin; the ice cover areas on both sides use the Green's function that can automatically satisfy the ice-water coupling dynamic equation;

[0008] (4) Based on Green's third formula, coupled integral equations are established on the boundaries of the channel basin and the ice-covered areas on both sides;

[0009] (5) Solve the coupled integral equations to obtain the steady wave potential of the ship sailing in the ice channel, and further obtain the wave waveform and ship resistance.

[0010] Furthermore, in step (1), the nonlinear free surface condition is:

[0011]

[0012] Wherein, U represents the ship speed; represents the steady wave potential of the ship; g represents the acceleration due to gravity; x, y, and z are the three coordinate axes of the three-dimensional rectangular coordinate system, which are perpendicular to each other, with the x-axis pointing in the direction of the ship's movement, the y-axis pointing to the port side of the ship, and the z-axis pointing vertically upward.

[0013] Furthermore, the ice-water coupled dynamic equation is:

[0014]

[0015] Where ρ represents the density of water; ρ ice represents the density of the ice layer; T represents the thickness of the ice layer; E represents the elastic modulus of the ice layer; υ represents the Poisson's ratio of the ice layer.

[0016] Furthermore, in step (3), the Green's function that can automatically satisfy the ice-water coupled dynamic equation is:

[0017]

[0018] Among them, G p,q is the Green's function that automatically satisfies the ice-water coupled dynamic equation; r' p,q represents the distance between the field point p and the source point q about the symmetrical point of the still water surface; r p,q represents the distance between the field point p and the source point q; k represents the integrated wave number; θ represents the polar angle; (ξ, η, ζ) are the coordinates of the source point q; i is the imaginary unit.

[0019] Furthermore, in step (4), the coupled integral equation is:

[0020]

[0021] in, Indicates the normal derivative; represents the steady wave potential at the field point p; σ p represents the source intensity at the field point p; σ q represents the source intensity at the source point q; represents the integral over the hull surface, the free surface, and the interface between the channel flow domain and the ice-covered domain; represents the integral over the interface between the channel basin and the ice-covered domain; S q represents the integration about the source point q.

[0022] Furthermore, in step (5), solving the coupled integral equation includes:

[0023] The coupled integral equations are discretized using a panel grid. The discretized coupled integral equations in the ice channel in equation (4) are processed in the same way as the solution to the steady wave problem in open waters. The discretized coupled integral equations in the ice-covered domains on both sides in equation (4) are written as:

[0024]

[0025] Among them, N I Represents the number of discrete surface elements on the interface between the channel basin and the ice cover domain; Indicates the integration of the nth surface element; m is the number of the field point; σ qn represents the source intensity at the nth surface element; n1 represents the component of the surface element normal along the ship's forward direction;

[0026] The key to solving equation (5) lies in the influence coefficient The calculation of the influence coefficient The calculation depends on the G pm,q Calculate the surface integral of the x, y, and z partial derivatives of G using a semi-analytical method. pm,q The surface integral of the x, y, and z partial derivatives of x , I y , I z .

[0027] Furthermore, the discrete boundaries of the ice channel include the hull surface, the free surface, and the interface between the channel basin and the ice-covered area; the discrete boundaries of the ice-covered areas on both sides only have the interface.

[0028] Furthermore, the semi-analytical method calculates The surface integral of the x, y, and z partial derivatives of x , I y , I z When , the numerical Gauss integral formula is used in the vertical direction, and the following analytical formula is used in the horizontal direction:

[0029]

[0030] Among them, J m (·) is the first kind m-order Bessel function, m=0,1,2…; R1 is the horizontal distance between the field point and the starting point of the horizontal line segment source; R2 is the horizontal distance between the field point and the end point of the horizontal line segment source;

[0031]

[0032] Among them, ρ I is the density of ice.

[0033] Furthermore, the wave shape is calculated:

[0034] After obtaining the steady wave potential of a ship sailing in an ice channel, the free surface rise η in the channel is obtained using the dynamic boundary conditions:

[0035]

[0036] in, yes gradient;

[0037] The deformation of the ice surface on both sides caused by the ship motion is obtained by integrating the kinematic boundary conditions:

[0038]

[0039] in, represents the integral on the hull surface; the pressure distribution of the flow field is obtained according to the Bernoulli equation: take a point on the streamline at infinity, whose velocity is 0, then the pressure p at any point in the flow field at the same depth as the infinite point is expressed as:

[0040]

[0041] Furthermore, the ship resistance is calculated:

[0042] The pressure is obtained by integrating the fluid pressure along the wet surface of the hull. The component of this pressure in the x direction is the wave resistance R w :

[0043]

[0044] The total resistance acting on the hull can be obtained by adding wave-making resistance to friction resistance and viscous pressure resistance.

[0045] Beneficial Effects: Compared with existing technologies, this invention offers the following significant advantages: It approximates the ice sheets on both sides of the channel as deformable elastic thin plates. Different Green's functions are used to construct boundary integral equations in the channel flow area and the ice-covered areas on both sides, and the velocity potential of the flow field is coupled to solve them. This in turn derives the wave-making characteristics and resistance of ships navigating the ice channel. This invention can provide key support for polar ship design optimization, energy conservation and emission reduction, and polar resource development, and has significant academic value and application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flowchart of a method for predicting wave generation and resistance for ships sailing in an ice channel provided by an embodiment of the present invention;

[0047] Figure 2 This is a model of a ship sailing in an ice channel according to an embodiment of the present invention;

[0048] Figure 3 Schematic diagram of grid discretization in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described below with reference to the accompanying drawings.

[0050] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting wave making and resistance for a ship sailing in an ice channel, comprising the following steps:

[0051] (1) Figure 2 The model of a ship sailing in an ice channel is shown. Because the waters on both sides are covered by ice, the waves generated by the ship will undergo different changes when propagating into the ice-covered area than in the open water. To reflect the different propagation characteristics of ship waves within the channel and in the ice-covered area, different models are established for these two watersheds. Specifically:

[0052] In the free surface area within the ice channel, the following free surface conditions are adopted considering the influence of nonlinear effects:

[0053]

[0054] Wherein, U represents the ship speed; represents the steady wave potential of the ship; g represents the acceleration due to gravity; x, y, and z are the three coordinate axes of the three-dimensional rectangular coordinate system, which are perpendicular to each other, with the x-axis pointing in the direction of the ship's movement, the y-axis pointing to the port side of the ship, and the z-axis pointing vertically upward.

[0055] In the ice-covered areas on both sides, considering the ice deformation caused by the steady waves generated by the ship, the following ice-water coupled dynamic equations are established based on the continuum assumption and Euler-Bernoulli beam theory;

[0056]

[0057] Where ρ represents the density of water; ρ ice represents the density of the ice layer; T represents the thickness of the ice layer; E represents the elastic modulus of the ice layer; υ represents the Poisson's ratio of the ice layer.

[0058] (2) In order to achieve cross-domain coupling between the ice channel and the ice-covered areas on both sides, the wave-current exchange characteristics of adjacent flow fields are utilized to establish Dirichlet and Neumann type continuity conditions of the disturbance potential on the control surface, and then an ice-water coupled hydrodynamic model for ships sailing steadily in the ice channel is established.

[0059] (3) A Green's function system is constructed for the above-mentioned basins with different hydrodynamic models: for the channel basin (ice channel), the Rankine source Green's function that can handle complex nonlinear boundary conditions is used; for the ice-covered domain on both sides, the Green's function that can automatically satisfy the ice-water coupled dynamic equation is used:

[0060]

[0061] Among them, G p,q is the Green's function that automatically satisfies the ice-water coupled dynamic equation; r' p,q represents the distance between the field point p and the source point q about the symmetrical point of the still water surface; r p,q represents the distance between the field point p and the source point q; k represents the integrated wave number; θ represents the polar angle; (ξ, η, ζ) are the coordinates of the source point q; i is the imaginary unit.

[0062] (4) Based on the Green's function system constructed above, coupled integral equations are established on the boundaries of the channel basin and the ice-covered areas on both sides based on Green's third formula:

[0063]

[0064] in, Indicates the normal derivative; represents the steady wave potential at the field point p; σ p represents the source intensity at the field point p; σ q represents the source intensity at the source point q; represents the integral over the hull surface, the free surface, and the interface between the channel flow domain and the ice-covered domain; represents the integral over the interface between the channel basin and the ice-covered domain; S q represents the integration about the source point q.

[0065] (5) Solve the coupled integral equations to obtain the steady wave potential of the ship sailing in the ice channel, and further obtain the wave waveform and ship resistance.

[0066] In order to solve the coupled integral equation (4), the surface element grid is used to discretize it. Figure 3 As shown in Figure 3, the discrete boundaries of the ice channel include the hull surface, the free surface, and the interface between the channel flow area and the ice-covered area. The ice-covered areas on both sides have only the interface as the Green's function used can automatically satisfy the ice-water coupled dynamic equations.

[0067] The discretized coupled integral equations in equation (4) for the ice channel are processed in the same way as the solution to the steady wave problem in open waters. The discretized coupled integral equations in equation (4) for the ice-covered domains on both sides are written as:

[0068]

[0069] Among them, N I Represents the number of discrete surface elements on the interface between the channel basin and the ice cover domain; Indicates the integration of the nth surface element; m is the number of the field point; σ qn represents the source intensity at the nth surface element; n1 represents the component of the surface element normal along the ship's forward direction;

[0070] The key to solving equation (5) lies in the influence coefficient The calculation of the influence coefficient The calculation depends on the G pm,q The surface integral of the x, y, and z partial derivatives of G is calculated. In order to improve stability and efficiency when calculating these integrals, this embodiment adopts a semi-analytical method. pm,q The surface integral of the x, y, and z partial derivatives of x , I y , I z When , the numerical Gauss integral formula is used in the vertical direction, and the following analytical formula is used in the horizontal direction:

[0071]

[0072] Among them, J m (·) is the first kind m-order Bessel function, m=0,1,2…; R1 is the horizontal distance between the field point and the starting point of the horizontal line segment source; R2 is the horizontal distance between the field point and the end point of the horizontal line segment source;

[0073]

[0074] Among them, ρ I is the density of ice.

[0075] Calculate wave shapes and ship resistance:

[0076] After the steady wave potential of a ship sailing in an ice channel is obtained using the aforementioned method, the free surface rise η in the channel is obtained using the dynamic boundary conditions:

[0077]

[0078] in, yes gradient.

[0079] The deformation of the ice surface on both sides caused by the ship motion is obtained by integrating the kinematic boundary conditions:

[0080]

[0081] in, represents the integral on the hull surface; the pressure distribution of the flow field is obtained according to the Bernoulli equation: take a point on the streamline at infinity, whose velocity is 0, then the pressure p at any point in the flow field at the same depth as the infinite point is expressed as:

[0082]

[0083] The pressure is obtained by integrating the fluid pressure along the wet surface of the hull. The component of this pressure in the x direction is the wave resistance:

[0084]

[0085] Among them, R w To create resistance to waves;

[0086] The total resistance acting on the hull can be obtained by adding the wave resistance to the friction resistance and the viscous pressure resistance. The methods for obtaining the friction resistance and the viscous pressure resistance are well known in the art and will not be described in detail here.

Claims

1. A method for predicting wave and resistance for ships sailing in ice channels, characterized by: include: (1) Different models were established in the channel basin and the ice-covered areas on both sides. The channel basin adopted nonlinear free surface conditions. The ice-water coupled dynamic equations were established in the ice-covered areas on both sides based on the continuous medium assumption and Euler-Bernoulli beam theory. (2) By utilizing the wave-current exchange characteristics of adjacent flow fields, Dirichlet and Neumann continuity conditions of the disturbance potential are established on the control surface, and then an ice-water coupled hydrodynamic model for ships sailing steadily in ice channels is established; (3) Constructing a Green's function system, in which the Rankine source Green's function is used in the channel basin; the ice cover areas on both sides use the Green's function that can automatically satisfy the ice-water coupling dynamic equation; (4) Based on Green's third formula, coupled integral equations are established on the boundaries of the channel basin and the ice-covered areas on both sides; (5) Solve the coupled integral equations to obtain the steady wave potential of the ship sailing in the ice channel, and further obtain the wave waveform and ship resistance.

2. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 1, characterized in that: In step (1), the nonlinear free surface condition is: Wherein, U represents the ship speed; represents the steady wave potential of the ship; g represents the acceleration due to gravity; x, y, and z are the three coordinate axes of the three-dimensional rectangular coordinate system, which are perpendicular to each other, with the x-axis pointing in the direction of the ship's movement, the y-axis pointing to the port side of the ship, and the z-axis pointing vertically upward.

3. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 2, characterized in that: The ice-water coupled dynamic equation is: Where ρ represents the density of water; ρ ice represents the density of the ice layer; T represents the thickness of the ice layer; E represents the elastic modulus of the ice layer; υ represents the Poisson's ratio of the ice layer.

4. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 3 is characterized in that: In step (3), the Green's function that can automatically satisfy the ice-water coupled dynamics equation is: Among them, G p,q is the Green's function that automatically satisfies the ice-water coupled dynamic equation; r' p,q represents the distance between the field point p and the source point q about the symmetrical point of the still water surface; r p,q represents the distance between the field point p and the source point q; k represents the integrated wave number; θ represents the polar angle; (ξ, η, ζ) are the coordinates of the source point q; i is the imaginary unit.

5. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 4 is characterized in that: In step (4), the coupled integral equation is: in, Indicates the normal derivative; represents the steady wave potential at the field point p; σ p represents the source intensity at the field point p; σ q represents the source intensity at the source point q; represents the integral over the hull surface, the free surface, and the interface between the channel flow domain and the ice-covered domain; represents the integral over the interface between the channel basin and the ice-covered domain; S q represents the integration about the source point q.

6. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 5 is characterized in that: In step (5), solving the coupled integral equation includes: The coupled integral equations are discretized using a panel grid. The discretized coupled integral equations in the ice channel in equation (4) are processed in the same way as the solution to the steady wave problem in open waters. The discretized coupled integral equations in the ice-covered domains on both sides in equation (4) are written as: Among them, N I Represents the number of discrete surface elements on the interface between the channel basin and the ice cover domain; Indicates the integration of the nth surface element; m indicates the number of the field point; represents the source intensity at the nth surface element; n1 represents the component of the surface element normal along the ship's forward direction; The key to solving equation (5) lies in the influence coefficient The calculation of the influence coefficient The calculation depends on Calculate the surface integral of the x, y, and z partial derivatives of ; use the semi-analytical method to calculate The surface integral of the x, y, and z partial derivatives of x , I y , I z .

7. The method for predicting wave generation and resistance of ships sailing in ice channels according to claim 6, characterized in that: The discrete boundaries of the ice channel include the hull surface, free surface, and the interface between the channel basin and the ice-covered area; the discrete boundaries of the ice-covered areas on both sides only include the interface.

8. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 6, characterized in that: Semi-analytical calculation method The surface integral of the x, y, and z partial derivatives of x , I y , I z When , the numerical Gauss integral formula is used in the vertical direction, and the following analytical formula is used in the horizontal direction: Among them, J m (·) is the first kind m-order Bessel function, m=0,1,2…; R1 is the horizontal distance between the field point and the starting point of the horizontal line segment source; R2 is the horizontal distance between the field point and the end point of the horizontal line segment source; Among them, ρ I is the density of ice.

9. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 8, characterized in that: Calculate the wave shape: After obtaining the steady wave potential of a ship sailing in an ice channel, the free surface rise η in the channel is obtained using the dynamic boundary conditions: in, yes gradient; The deformation of the ice surface on both sides caused by the ship motion is obtained by integrating the kinematic boundary conditions: in, represents the integral on the hull surface; the pressure distribution of the flow field is obtained according to the Bernoulli equation: take a point on the streamline at infinity, whose velocity is 0, then the pressure p at any point in the flow field at the same depth as the infinite point is expressed as:

10. The method for predicting wave making and resistance for ships sailing in ice channels according to claim 9, characterized in that: Calculate ship resistance: The pressure is obtained by integrating the fluid pressure along the wet surface of the hull. The component of this pressure in the x direction is the wave resistance R w : The total resistance acting on the hull can be obtained by adding wave-making resistance to friction resistance and viscous pressure resistance.

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