阅读说明：本技术 一种子母潜器的流体动力干扰计算方法 (Fluid power interference calculation method for primary and secondary submersible vehicle ) 是由 李鹏 秦洪德 江志远 邓忠超 国瑀 于 2021-08-09 设计创作，主要内容包括：一种子母潜器的流体动力干扰计算方法,属于水动力分析领域。包括以下步骤：S1.在潜器的横剖面建立坐标系；S2.利用保角变换将大尺度的母艇曲面映射为平面；S3.结合映像法实施母艇表面边界条件,将原问题转化为无界流中物体绕流问题；S4.采用边界元法,在小尺度的子艇表面布置奇点,通过求解边界积分方程计算子艇表面速度势；S5.保角变换的逆变换,将速度势映射到原始物体表面,计算受力。本发明将原双体流体动力干扰问题简化为无界流物体绕流问题,无需将母艇表面离散,提高了计算效率。本发明提出的方法对双体流体动力干扰机理的研究具有参考价值,是子母潜器在水下发射、作业、回收的操纵和控制设计的重要依据。(A fluid dynamic interference calculation method for a primary-secondary submersible belongs to the field of hydrodynamic analysis. The method comprises the following steps: s1, establishing a coordinate system on a cross section of the submersible vehicle; s2, mapping the curved surface of the mother boat with large scale into a plane by using angle keeping transformation; s3, combining a mapping method to implement the boundary condition of the surface of the mother boat, and converting the original problem into the problem of object streaming in unbounded flow; s4, arranging singular points on the surface of the small-scale sub-boat by adopting a boundary element method, and calculating the surface speed potential of the sub-boat by solving a boundary integral equation; s5, inverse transformation of angle keeping transformation, namely mapping the velocity potential to the surface of the original object, and calculating the stress. The method simplifies the original double-body hydrodynamic interference problem into the unbounded flow object streaming problem, does not need to disperse the surface of the mother boat, and improves the calculation efficiency. The method provided by the invention has reference value for the research of the double-body hydrodynamic interference mechanism, and is an important basis for the control and control design of underwater launching, operation and recovery of the primary and secondary submersible vehicles.)

1. A fluid dynamic interference calculation method of a primary-secondary submersible vehicle is characterized by comprising the following steps: the method comprises the following steps:

s1, establishing a coordinate system on a cross section of the submersible vehicle;

s2, mapping the curved surface of the mother boat with large scale into a plane by using angle keeping transformation;

s3, combining a mapping method to implement the boundary condition of the surface of the mother boat, and converting the original problem into the problem of object streaming in unbounded flow;

s4, arranging singular points on the surface of the small-scale sub-boat by adopting a boundary element method, and calculating the surface speed potential of the sub-boat by solving a boundary integral equation;

s5, inverse transformation of angle keeping transformation, namely mapping the velocity potential to the surface of the original object, and calculating the stress.

2. The method for calculating the hydrodynamic disturbance of the primary-secondary submersible vehicle according to claim 1, wherein the method comprises the following steps: the S1 coordinate system established on the cross section of the submersible vehicle is specifically as follows: a two-dimensional Cartesian coordinate system xoy is established on the cross section of the submersible vehicle, the origin of coordinates is located at the centroid of a mother boat, the x axis is parallel to the horizontal plane, the y axis is perpendicular to the horizontal plane, and the radius of the mother boat is R.

3. The method for calculating the hydrodynamic disturbance of the primary-secondary submersible vehicle according to claim 1, wherein the method comprises the following steps: in the step S2, the surface Γ of the mother boat of large scale is transformed by conformal transformation_B1The mapping is a plane, and the transformation function is:

ζ＝f(z)＝iR(ln z-ln R)

wherein z and zeta are complex variables, z is x + iy, and z is a physical plane complex coordinate; ζ is ξ + i η, ζ is the complex coordinate of the calculation plane.

4. The method for calculating the hydrodynamic disturbance of the primary-secondary submersible as claimed in claim 3, wherein: the conformal transformation function in S2:

(＝f(z)＝iR(ln z-ln R)

separating the real part and the imaginary part to obtain the corresponding relation between the calculated plane coordinate xi, eta and the physical plane coordinate x, y as follows:

ξ＝-Rarg(x，y)

5. the method for calculating the hydrodynamic disturbance of the primary-secondary submersible vehicle according to claim 1, wherein the method comprises the following steps: in S3, the boundary conditions of the mother boat surface are implemented by using a mapping method on the calculation plane:

in the formulaIs the physical plane velocity potential, n is the object plane normal vector, gamma_B1Is the surface of a mother boat;

after transformation, the mother boat surface boundary condition is simplified to a flat bottom boundary condition:

in the formula, phi is calculated plane velocity potential; and generating a mirror image of the sub-boat about eta equal to 0 by adopting an image method, and simplifying the problem into a streaming problem of the sub-boat and the mirror image thereof in the unbounded flow.

6. The method for calculating the hydrodynamic disturbance of the primary-secondary submersible vehicle according to claim 1, wherein the method comprises the following steps: in the step S4, the surface of the submarines is discretized into N surface elements delta Q on the calculation plane by adopting a boundary element method_jCalculating bin centroids p, q and normal vectorsAnd solving the boundary integral equation:

in the formulaA_ii＝π，

Solving the equation to calculate the velocity potential phi (zeta) of the surface of the plane sub-boat, and writing a complex potential omega (zeta) ═ phi (zeta) + i psi (zeta), wherein psi (zeta) is a flow function of the calculation plane.

7. The method for calculating the hydrodynamic disturbance of the primary-secondary submersible vehicle according to claim 1, wherein the method comprises the following steps: in S5, the complex potential Ω (ζ) is mapped to the complex potential of the surface of the original object by the inverse transformation of the conformal transformationWhere ψ (z) is a flow function of the physical plane;

the transformation function is:

the surface velocity potential of the boat can be obtainedAnd further obtaining the surface speed, pressure distribution and stress information of the submarines according to the surface speed potential of the submarines.

8. The method for calculating the hydrodynamic disturbance of a mother-son submersible as claimed in claim 7, wherein: in S5, transforming the calculated plane velocity potential to a physical plane using an inverse transform function, the steps specifically include:

separating the real part and the imaginary part to obtain the corresponding relation between the physical plane coordinates x and y and the calculation plane coordinates xi and eta as follows:

Technical Field

The invention belongs to the field of hydrodynamic analysis, and particularly relates to a hydrodynamic interference calculation method of a primary-secondary submersible vehicle.

Background

Compared with a large-scale submersible vehicle, the small-scale unmanned submersible vehicle has the characteristics of low manufacturing cost, low energy consumption and flexible movement, has more advantages in the fields of navigation measurement, underwater rescue and the like, can be carried by a mother boat and distributed underwater, and can complete specified tasks through multi-boat cooperative operation. The submersible vehicle is different from the movement characteristics in the unbounded flow, and can be influenced by the fluid interference force of objects such as a mother ship and the like in the processes of laying, recovering and underwater operation, so that the operation control stability and the positioning precision are adversely affected. In order to reduce the influence of the hydrodynamic interference effect, the stress condition in the motion process of the device needs to be accurately researched. The traditional boundary element method for calculating the fluid power needs to disperse all object boundaries into grids and calculate the speed potential in the grids, and when the fluid power borne by the primary boat and the secondary boat is calculated, the calculation cost is high due to the large difference of the scales and the large number of the grids, so that a simple, convenient and efficient double-body fluid power interference calculation method is needed.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a fluid dynamic interference calculation method of a primary-secondary submersible vehicle.

The technical scheme adopted by the invention is as follows: a fluid dynamic interference calculation method of a primary-secondary submersible vehicle is characterized by comprising the following steps: the method comprises the following steps:

s1, establishing a coordinate system on a cross section of the submersible vehicle;

s2, mapping the curved surface of the mother boat with large scale into a plane by using angle keeping transformation;

s3, combining a mapping method to implement the boundary condition of the surface of the mother boat, and converting the original problem into the problem of object streaming in unbounded flow;

s4, arranging singular points on the surface of the small-scale sub-boat by adopting a boundary element method, and calculating the surface speed potential of the sub-boat by solving a boundary integral equation;

s5, inverse transformation of angle keeping transformation, namely mapping the velocity potential to the surface of the original object, and calculating the stress.

Compared with the prior art, the invention has the following beneficial effects:

the method simplifies the original double-body hydrodynamic interference problem into the unbounded flow object streaming problem, does not need to disperse the surface of the mother boat, and improves the calculation efficiency. The method provided by the invention has reference value for the research of the double-body hydrodynamic interference mechanism, and is an important basis for the control and control design of underwater launching, operation and recovery of the primary and secondary submersible vehicles.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic cross-sectional coordinate system for the submersible of the present invention;

FIG. 3 is a schematic view of a physical plane of the hybrid submersible of the present invention;

FIG. 4 is a schematic view of a plane of the present invention obtained by conformal transformation of a physical plane;

FIG. 5 is a schematic diagram of a plane of calculation obtained by mapping according to the present invention;

Detailed Description

The method is based on the hydrodynamic potential flow theory, utilizes conformal transformation to map the surface of a large-scale mother boat into a flat bottom, implements boundary conditions of the surface of the mother boat by combining with a mapping method, and converts the original problem into the problem of object streaming in unbounded flow; arranging singular points on the surface of the small-scale sub-boat by adopting a boundary element method, and calculating the surface speed potential of the sub-boat by solving a boundary integral equation; and finally, mapping the velocity potential to the surface of the original object through inverse transformation of conformal transformation, and calculating the stress.

The technical scheme of the invention will be clearly and completely described below with reference to the accompanying drawings 1-4.

A fluid dynamic interference calculation method of a primary-secondary submersible vehicle comprises the following steps:

s1, establishing a coordinate system on a cross section of the submersible vehicle;

the method specifically comprises the following steps: based on the assumption of the elongated body, the problem is simplified into two dimensions, a two-dimensional Cartesian coordinate system xoy is established on the cross section of the submersible vehicle, the origin of coordinates is located at the centroid of a mother boat, the x axis is parallel to the horizontal plane, the y axis is vertical to the horizontal plane, the radius of the mother boat is R, and the shape and the position of a child boat are arbitrary, as shown in the attached figure 2;

s2, mapping the curved surface of the mother boat with large scale into a plane by using angle keeping transformation;

the method specifically comprises the following steps: gamma on surface of mother boat with large scale by using conformal transformation_B1The mapping is a plane, and the transformation function is:

ζ＝f(z)＝iR(ln z-ln R)

wherein z and zeta are complex variables, z is x + iy, and z is the physical section complex coordinate; zeta is xi + i eta, zeta is complex coordinate of calculation plane, and the transformation function is the circumference gamma of the mother boat surface of the physical plane_B1Mapping to calculate the xi axis of the plane, shape gamma of the sub-boat_B2The physical plane area S is mapped into an upper half plane area S' of the calculation plane after a certain change occurs; taking the motion of the physical plane sub-boat around the mother boat as an example, according to the principle of relative motion, the fluid can be regarded as flowing around the mother boat at an angular velocity ω and mapped into the flow for calculating the plane velocity U, as shown in fig. 4;

s3, combining a mapping method to implement the boundary condition of the surface of the mother boat, and converting the original problem into the problem of object streaming in unbounded flow;

specifically, the method comprises the following steps of; and (3) adopting a mapping method on a calculation plane to implement the boundary conditions of the mother boat surface:

in the formulaIs the physical plane velocity potential, n is the object plane normal vector, gamma_B1Is the surface of a mother boat;

after transformation, the mother boat surface boundary condition is simplified to a flat bottom boundary condition:

in the formula, phi is calculated plane velocity potential; and generating a mirror image of the sub-boat about eta equal to 0 by adopting an image method, and simplifying the problem into a streaming problem of the sub-boat and the mirror image thereof in the unbounded flow.

S4, arranging singular points on the surface of the small-scale sub-boat by adopting a boundary element method, and calculating the surface speed potential of the sub-boat by solving a boundary integral equation;

the method specifically comprises the following steps: discretizing the surface of the submarines into N surface elements delta Q on a calculation plane_jCalculating bin centroids p, q and normal vectorsAnd solving the boundary integral equation:

in the formulaA_ii＝π，

Solving the equation to calculate the surface velocity potential phi (zeta) of the plane sub-boat, and writing a complex potential omega (zeta) ═ phi (zeta) + i psi (zeta), wherein psi (zeta) is used for calculating the plane flow function.

S5, inverse transformation of angle keeping transformation, namely mapping the velocity potential to the surface of the original object, and calculating the stress.

The method specifically comprises the following steps: mapping the complex potential omega (zeta) to the complex potential of the surface of the original object by inverse transformation of the conformal transformationWhere ψ (z) is a physical plane flow function;

the transformation function is:

the surface velocity potential of the boat can be obtainedAccording to the surface speed potential of the sub-boat, required information such as the surface speed, the pressure distribution, the stress and the like of the sub-boat can be further obtained.

Taking the complex velocity as an example, the mapping relation of the complex velocity of the plane and the physical plane is calculated as follows:

aiming at the hydrodynamic interference problem of the primary and secondary submersible vehicles, the invention maps the curve boundary complex potential W (z) on the physical plane into the simple boundary complex potential omega (zeta) on the calculation plane through the angle preserving transformation function f (z), and the simple boundary complex potential omega (zeta) is solved and then is subjected to f^-1(ζ) inverse transformation to physical plane, resulting in velocity potential on physical planeThe required physical quantities can be further solved.

In S2, transforming the circular cross section of the mother boat to a plane using a conformal transformation function, the steps specifically include:

ζ＝f(z)＝iR(lz z-ln R)

separating the real part and the imaginary part to obtain the corresponding relation between the calculated plane coordinate xi, eta and the physical plane coordinate x, y as follows:

ξ＝-Rarg(x，y)

in S5, transforming the calculated plane velocity potential to a physical plane using an inverse transform function, the steps specifically include:

separating the real part and the imaginary part to obtain the corresponding relation between the physical plane coordinates x and y and the calculation plane coordinates xi and eta as follows:

it is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.