Underwater towed body towing performance design method

Abstract

The invention relates to the technical field of underwater towing, in particular to an underwater towed body towing performance design method, which comprises the following steps of: performing static dynamic analysis on a towed body; carrying out dragging dynamics analysis on the towed body; constructing a towed body structure model, and performing hydrodynamic simulation calculation; establishing a dynamic coupling numerical simulation model of the towing system; and carrying out dragging attitude simulation, and obtaining an optimal design scheme. According to the invention, key indexes such as trim and rolling of the towed body in the towing system are ensured to meet the stability standard, so that the urgent requirements of marine acoustic detection on high precision and high reliability are met.

Description

TECHNICAL FIELD

[0001] The present application relates to the underwater towing technology field, and in particular to a method for designing the towing performance of an underwater towed body. BACKGROUND

[0002] The ocean covers most of the earth's surface, contains rich resources and has great scientific research value. With the increasing demand of mankind in the development of marine resources, geological exploration, disaster warning and underwater target monitoring, it is increasingly critical to develop efficient and accurate marine detection technology. The underwater towing system, as the core equipment of modern marine investigation and detection, is generally composed of a mother ship, a cable and a towed body, and is widely used in hydrological measurement, geological survey and acoustic detection.

[0003] As an integrated carrier of underwater detection equipment, the towed body is usually equipped with sensors based on optical, acoustic, magnetic field and temperature-salinity principles, and its design quality directly affects the accuracy and reliability of the detection data. Taking the underwater acoustic transducer as an example, as a key component of the acoustic signal transmission system, it undertakes the conversion function between mechanical energy and electrical signal, and its performance directly determines the effect of the whole underwater acoustic system. In the complex marine environment, the fluctuation of water pressure caused by the change of towed body depth and the noise interference caused by its own unstable attitude will change the frequency and sensitivity of the transducer, thereby increasing the difficulty of acoustic signal processing.

[0004] Towed body design is a complex system engineering covering multiple disciplines, which needs to consider many factors such as hydrodynamic characteristics, structural strength, motion stability, material corrosion resistance and equipment compatibility, especially the motion stability. In the actual towing operation process, the towed body will produce violent fluctuations in depth and attitude or even instability due to the interference of the mother ship speed change, heave motion, ocean current and wave, etc. In recent years, in order to improve the performance of the towed body, researchers have been exploring new design methods and technical means to enhance its stability and maneuverability. The use of modern design tools such as computational fluid dynamics (CFD) simulation enables designers to more accurately predict and optimize the hydrodynamic performance of the towed body. The modular design concept is also gradually adopted to quickly replace detection equipment according to task needs.

[0005] Therefore, it is necessary to provide a method for designing the towing performance of an underwater towed body, to ensure that the key indicators such as trim and roll of the towed body in the designed towing system meet the stability standards, so as to meet the urgent needs of high precision and high reliability of marine acoustic detection. SUMMARY

[0006] In order to make the key indicators such as trim and roll of the towed body in the designed towing system meet the stability standards, so as to meet the urgent needs of high precision and high reliability of marine acoustic detection, the present application provides a method for designing the towing performance of an underwater towed body to solve the existing problems.

[0007] The underwater towed body towing performance design method of the present application adopts the following technical scheme, comprising: Perform static dynamics analysis on the towed body to obtain the position relationship of the center of buoyancy, the center of gravity and the tow point of the towed body; Perform towing dynamics analysis on the towed body based on the moment balance relationship of the center of buoyancy, the center of gravity and the tow point of the towed body; Determine the basic size and weight of the towed body according to the towing dynamics analysis results and the design index, determine the towed body structure shape according to the load, and design a towed body structure model based on the towed body structure shape; Perform hydrodynamic simulation calculation on the towed body structure model to obtain the drag coefficient and the lift coefficient; Based on the drag coefficient and the lift coefficient, construct a towed cable motion mathematical model and a towed body motion mathematical model, and establish a dynamics coupling numerical simulation model of the towing system based on the towed cable motion mathematical model and the towed body motion mathematical model; Perform towing posture simulation calculation on the dynamics coupling numerical simulation model to obtain the static trim angle and the dynamic trim angle of the towed body under different centers of gravity and tow point positions, and take the center of gravity and the tow point position corresponding to the condition that the static trim angle of the towed body is less than a first angle threshold and closest to the first angle threshold, and the dynamic trim angle of the towed body is less than a second angle threshold as the best design scheme.

[0008] The further technical scheme of the present application is that the step of performing static dynamics analysis on the towed body to obtain the position relationship of the center of buoyancy, the center of gravity and the tow point of the towed body comprises: Take the tow point as the coordinate origin, point to the bow of the towed body as the x direction, point to the port side of the towed body as the y direction, and vertically upward as the z direction, to establish a fixed coordinate system; Set the center of gravity position and the center of buoyancy position based on the fixed coordinate system, and obtain the distance from the center of gravity to the tow point and the distance from the center of buoyancy to the tow point based on the center of gravity position and the center of buoyancy position; According to the distance from the center of gravity to the tow point, the distance from the center of buoyancy to the tow point, the gravity, the reverse included angle of the line connecting the tow point and the center of gravity with the z direction, and the reverse included angle of the line connecting the tow point and the center of buoyancy with the z direction, obtain the moment balance relationship of the center of buoyancy, the center of gravity and the tow point of the towed body; Determine the position relationship of the center of buoyancy, the center of gravity and the tow point of the towed body based on the moment balance relationship.

[0009] The further technical scheme of the present application is that the towed body reaches the moment balance when the heeling angle is , that is, the moment balance relationship formula is:

[0010] In the formula, represents the gravity; represents the buoyancy; represents the distance from the center of gravity to the tow point; represents the distance from the center of buoyancy to the tow point; represents the inverse angle between the line connecting the tow point and the center of buoyancy and the direction of z ; represents the angle of the tow body; represents the inverse angle between the line connecting the tow point of the buoyancy and the center of gravity and the direction of z ;

[0011] The further technical solution of the present application is that when the static tow body in water is disturbed initially to generate the angle of the tow body , the static restoring moment generated after the disturbance is eliminated is:

[0012] The static tow body in water is disturbed initially to generate the angle of the tow body , the static restoring moment generated after the disturbance is eliminated is:

[0013] In the formula, represents the static tow body in water is disturbed initially to generate the angle of the tow body , the static restoring moment generated after the disturbance is eliminated; represents the static tow body in water is disturbed initially to generate the angle of the tow body , the static restoring moment generated after the disturbance is eliminated; represents the gravity; represents the buoyancy; represents the longitudinal coordinate value of the center of gravity of the tow body in the fixed coordinate system; represents the longitudinal coordinate value of the center of buoyancy of the tow body in the fixed coordinate system.

[0014] The further technical solution of the present application is that the expression of the moment generated by the water dynamics on the tow point in the tow dynamics analysis is:

[0015] In the formula, represents the moment generated by the water dynamics on the tow point in the tow dynamics analysis; represents the water dynamic resistance generated by the tow body when it is subjected to the water dynamics and opposite to the direction of the speed; represents the yaw force generated by the tow body when it is subjected to the water dynamics and perpendicular to the direction of the speed; represents the horizontal coordinate value of the center of water dynamics; This indicates that the towed body generates a yaw angle after being disturbed; the towing dynamics analysis result is: from the expression of the torque generated by the hydrodynamic force on the towing point in the towing dynamics analysis, it can be seen that when the hydrodynamic center is behind the towing point, the torque generated by the lift and yaw force will reduce the yaw angle caused by the disturbance.

[0016] A further technical solution of the present invention is as follows: the basic dimensions and weight of the tow body are determined based on the results of towing dynamics analysis and design parameters, and the structural shape of the tow body is determined based on the load: The structural dimensions of the tow body are determined based on the type and size of the load equipment carried by the tow body; Based on the results of the towing dynamics analysis, the shape of the towing body structure is designed to be streamlined.

[0017] A further technical solution of the present invention is that the steps for obtaining the drag coefficient and lift coefficient by performing hydrodynamic simulation calculations on the towed body structure model are as follows: The expression for the drag coefficient is:

[0018] The expression for the lift coefficient is:

[0019] In the formula, Indicates the drag coefficient; Indicates the lift coefficient; This represents the lift force of the fluid perpendicular to the flow direction; This represents the lift force of the fluid flowing in the opposite direction. Indicates fluid density; Indicates the incoming flow velocity; This indicates the projected area of ​​the drag body.

[0020] A further technical solution of the present invention is that, based on the drag coefficient and lift coefficient, the steps for constructing the mathematical model of the towing cable motion and the mathematical model of the towing body motion are as follows: The mathematical model for cable towing motion is expressed as follows:

[0021] In the formula, Indicates the action in the The inertial force at the node corresponding to the infinitesimal element of the cable segment. Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The external hydrodynamic force experienced at the node corresponding to the micro-element of the tow cable segment; Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates the first The weight corresponding to the micro-element of the tow cable segment; Indicates the first Weight per unit length of a segment of tow cable element in a fluid; Indicates the first The length of the tow cable element after elongation;

[0022] In the formula, Indicates the first The additional mass matrix of the node corresponding to the segment drag cable micro-element; Indicates the first The acceleration vector of the node corresponding to the infinitesimal element of the cable segment; Indicates the first The diameter corresponding to the micro-element of the tow cable segment; Indicates the normal inertial force coefficient; Represents a 3×3 identity matrix; where, Indicates the first The unit vector of the tangential direction of the tow cable element divides the tow cable into N tow cable elements, and the mass of each tow cable element is concentrated on a node, so there can be N nodes. The mathematical model for dragging motion is expressed as follows:

[0023]

[0024] In the formula, Indicates inertial load; Indicates damping load; Represents the stiffness matrix; Indicates the external load on the system; Represents the moment of inertia matrix in generalized rotating coordinates; Indicates the rotational damping of the system; Indicates the rotational stiffness of the system; This represents the external torque acting on the system; Indicates the rotation angle; Indicates angular velocity; Indicates angular acceleration; Indicates the simulation time.

[0025] A further technical solution of the present invention is that the expression for the external hydrodynamic force acting on each node is:

[0026] In the formula, Indicates the first The external hydrodynamic forces acting on the nodes of the cable segment micro-element; The density of seawater; This represents the tensile strain of the i-th cable element; For the first The normal resistance coefficient corresponding to the micro-element of the tow cable segment; For the first The tangential resistance coefficient corresponding to the micro-element of the tow cable; Indicates the water flow relative to the first The normal velocity vector of the tow cable element. Water flow relative to the first The tangential velocity vector of the infinitesimal element of the tow cable segment. For the first The normal inertial force coefficient corresponding to the micro-element of the tow cable segment; Indicates the first The acceleration vector of water particles at the nodes of the cable segment element.

[0027] A further technical solution of the present invention is that the shear force expression at each node is:

[0028] In the formula, Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates tensile strain The next The length of the cable segment micro-element; This indicates the elastic modulus of the cable material; Indicates the first The moment of inertia of the cross section of the tow cable element; Indicates tensile strain The next The length of the cable segment micro-element; Indicates the first Shear force at the node corresponding to the micro-element of the cable segment.

[0029] The beneficial effects of this invention are: Through dynamic analysis of the towed body, the relative positions of the center of buoyancy, center of gravity, and towing point were determined, laying the foundation for motion stability. The towed body's structural shape was designed with a low-resistance streamlined shape to improve hydrodynamic performance. Computational fluid dynamics (CFD) was used to perform hydrodynamic simulation calculations of the towed body, and the STAR-CCM+ software platform was used to obtain accurate drag and lift coefficients. OrcaFlex software was used to simulate the impact of different center of gravity positions and towing point configurations on towing attitude under sea state 5 conditions, optimizing design parameters to ensure the pitch angle is controlled within ±7.5°, ultimately determining the optimal center of gravity and towing point positions. This design scheme supports modular integration and mounting of acoustic components, ensuring that key indicators such as pitch and roll of the towed body in the towing system meet stability standards, thus satisfying the urgent need for high precision and high reliability in marine acoustic detection. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart illustrating an embodiment of the underwater towing performance design method of the present invention; Figure 2 This is a schematic diagram of the force analysis projected onto the longitudinal section in an embodiment of the present invention; Figure 3 This is a schematic diagram of hydrodynamic analysis projected onto a cross-section in an embodiment of the present invention; Figure 4 This is a schematic diagram of hydrodynamic analysis projected onto a longitudinal section in an embodiment of the present invention; Figure 5 This is a schematic diagram of hydrodynamic analysis projected onto a horizontal plane in an embodiment of the present invention; Figure 6 This is a schematic diagram of the dynamic coupling numerical simulation model of the towing system in an embodiment of the present invention; Figure 7 This is a schematic diagram of the OrcaFlex dynamic simulation time history in an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] An embodiment of the underwater towing performance design method of the present invention is as follows: Figure 1 As shown, it includes: S1. Perform static dynamic analysis on the towed body; Specifically, a static dynamic analysis is performed on the towed body to obtain the positional relationship between the towed body's center of buoyancy, center of gravity, and towing point.

[0034] For example, in one specific embodiment, the step of performing static dynamic analysis on the towed body to obtain the positional relationship between the towed body's center of buoyancy, center of gravity, and towing point is as follows: taking the towing point as the origin of the coordinate system, and pointing towards the head of the towed body as... x Direction, pointing towards the port side of the towing hull. y Direction, vertically upwards. z Direction, establish a fixed coordinate system; based on the fixed coordinate system, set the position of the center of gravity and the position of the center of buoyancy; based on the positions of the center of gravity and the center of buoyancy, obtain the distances from the center of gravity to the towing point and from the center of buoyancy to the towing point; based on the distances from the center of gravity to the towing point, the distances from the center of buoyancy to the towing point, gravity, buoyancy, and the line connecting the towing point and the center of gravity... z The opposite angle of the direction and the line connecting the drag point and the center of buoyancy. z The opposite angle of the direction is used to obtain the torque balance relationship between the center of buoyancy, center of gravity and towing point of the towed body; based on the torque balance relationship, the positional relationship between the center of buoyancy, center of gravity and towing point of the towed body is determined.

[0035] Step S11: Establish a fixed coordinate system: Because the towed body is subjected to three forces when it is suspended statically in the water, one of which is gravity. G Secondly, buoyancy. B Thirdly, the drag force acting on the drag point. T The center of buoyancy is the centroid of the towed body structure; the center of gravity and towing point are adjustable. When the towed body is in a state of zero roll and zero pitch, the coordinate origin is the towing point, pointing towards the bow of the towed body. x Direction, pointing towards the port side of the towing hull. y Direction, vertically upwards. z Direction, establish a fixed coordinate system.

[0036] Step S12, Still Water Stance: Let the centroid coordinates be... Floating center coordinates The static force analysis of the towed body projected onto the mid-longitudinal section is as follows: Figure 2 As shown, the distance from the center of gravity to the drag point is... The distance from the center of buoyancy to the drag point .

[0037] If the towing body's pitch angle is 0, then according to the moment balance: (1) In the formula, Represents gravity; Indicates buoyancy; Indicates the distance from the center of gravity to the drag point; Indicates the distance from the center of buoyancy to the drag point; The line connecting the drag point and the center of buoyancy is... z The angle between the opposite directions; The line connecting the buoyancy fulcrum and the center of gravity is... z The angle between the opposite directions.

[0038] The horizontal distance between the center of gravity and the center of buoyancy is: (2) In the formula, The x-coordinate representing the centroid. The x-coordinate represents the center of buoyancy.

[0039] To ensure the towed body is in a head-up position when stationary in the water, the towing point needs to be moved towards the bow of the towed body. Let the distance between the center of buoyancy and the leading edge of the towed body be... The horizontal distance between the towing point and the center of buoyancy. Therefore, the horizontal distance between the center of gravity and the center of buoyancy When the body was dragged and the head was raised When the angle reaches torque balance, it can be seen from the torque balance that when the towing body raises its head at the following angle... When torque equilibrium is reached, the torque equilibrium equation is: (3) In the formula, Represents gravity; Indicates buoyancy; Indicates the distance from the center of gravity to the drag point; Indicates the distance from the center of buoyancy to the drag point; The line connecting the drag point and the center of buoyancy is... z The angle between the opposite directions; Indicates the angle at which the body lifts its head; The line connecting the buoyancy fulcrum and the center of gravity is... z The angle between the opposite directions.

[0040] Then we have: (4) In order to ensure that the towed body has good roll stability, the structure of the towed body is generally designed to be symmetrical along the mid-longitudinal section. Therefore, the roll angle of the towed body when it is stationary in the water can be approximately 0. As can be seen from equation (4), the lower the center of gravity of the towed body and the higher the center of buoyancy, the smaller the static roll angle of the towed body.

[0041] Step S13, Static restoring torque: If an initial disturbance is applied to a towed body stationary in the water, causing its nose-up angle to be... The static restoring torque generated after the disturbance is eliminated is: (5) The derivation yields: (6) The static forces of the towed body projected from back to front onto the cross-section are as follows: Figure 3 As shown. The distance from the center of gravity to the drag point at this time is... The distance from the center of buoyancy to the drag point .

[0042] If an initial disturbance is applied to a towed body stationary in the water, causing it to tilt to the right... The static restoring torque generated after the disturbance is eliminated is: (7) The derivation yields: (8) In the formula, This indicates that a towed body at rest in the water experiences a head-up angle due to an initial disturbance. At that time, the static restoring torque generated after the disturbance is eliminated; This indicates that a towed body at rest in the water tilts to the right due to an initial disturbance. At that time, the static restoring torque generated after the disturbance is eliminated; Represents gravity; Indicates buoyancy; This represents the ordinate value of the center of gravity of the drag body in a fixed coordinate system; This represents the ordinate value of the center of buoyancy of the towed body in a fixed coordinate system.

[0043] Thus, from equations (6) and (8), it can be seen that the lower the center of gravity of the towed body, the higher the center of buoyancy, and the greater the net weight, the greater the restoring torque and the higher the stability when suspended at rest. Therefore, in this embodiment, the positional relationship between the center of gravity, center of buoyancy, and towing point of the towed body should be as follows: in the longitudinal direction, the center of gravity is closer to the head of the towed body than the center of buoyancy, and in the vertical direction, the center of gravity is closer to the bottom of the towed body than the center of buoyancy.

[0044] S2. Perform towing dynamics analysis on the towed body; Specifically, towing dynamics analysis of the towed body is performed based on the torque balance relationship between the center of buoyancy, center of gravity, and towing point of the towed body.

[0045] For example, in one specific embodiment, during towing operations, in addition to buoyancy, gravity, and towing force, the towing body is also subjected to velocity-related hydrodynamic forces under the influence of water flow. If the towing body experiences additional attitude angles due to disturbances during towing, the static restoring torque still plays a role in stabilizing the towing body, but whether the towing body can remain stable in this case depends on the effect of the hydrodynamic torque. Figure 4 As shown, Figure 4This describes the forces acting on the towed body in the longitudinal section. Let the coordinates of the hydrodynamic center be... If the towing body's tilt angle is 0, then according to the moment balance: (9) Due to structural and other performance design limitations, the towing point is usually located above the hydrodynamic center. As shown in equation (9), when the hydrodynamic center is below the towing point, the hydrodynamic resistance... This consistently results in the bow of the towed hull being submerged. If the hydrodynamic center is behind the towing point, the hydrodynamic lift... The resulting torque reduces the submerged angle caused by the disturbance; that is, the lift generates a trim-restoring moment. Conversely, if the hydrodynamic center is ahead of the towing point, the hydrodynamic lift... The generated torque increases the submerged angle caused by the disturbance.

[0046] Therefore, from the perspective of tow body structural design, the tow body should be designed with a low-resistance shape to reduce hydrodynamic resistance. At the same time, the projected area of ​​the tail section on the horizontal plane should be reasonably increased to enhance hydrodynamic lift. Considering the arrangement of the hydrodynamic center and towing point, the vertical distance between the towing point and the hydrodynamic center should be reasonably reduced to lower hydrodynamic resistance. The resulting submerged moment; appropriately increasing the horizontal distance between the towing point and the hydrodynamic center to increase hydrodynamic lift. The resulting longitudinal restoring moment.

[0047] Due to the increase in towing speed, the hydrodynamic resistance As the submerged moment increases rapidly, the submerged angle also increases. Therefore, the initial attitude of the towed body is designed as a head-up attitude, which reduces hydrodynamic resistance at low speeds. With water lift The restoring torque generates a restoring moment that causes the towed body to approach a horizontal attitude. At high speeds, as the bow angle decreases... As the hydrodynamic center shifts upward, the hydrodynamic resistance increases. Lever arm of the drag point As the angle of retraction decreases rapidly, the torque generated by the resistance also decreases rapidly. When it increases, the hydrodynamic lift Increase the lever arm of the hydrodynamic lift on the towing point. This also increases. Therefore, there exists a critical pitch angle that allows the towed body to maintain a stable attitude. The magnitude of this critical pitch angle is related to the hydrodynamic restoring moment and requires further simulation analysis.

[0048] Dynamic analysis of the towed body in the horizontal plane, such as Figure 5 As shown. Assume the towed body experiences a yaw angle after being disturbed. (Right yaw is positive, left yaw is negative), then the hydrodynamic force on the towed body is the hydrodynamic drag in the opposite direction of the velocity. and yaw force perpendicular to the velocity direction The torque generated by the hydrodynamic force on the towing point is: (10) In the formula, This represents the torque generated by hydrodynamic forces on the towing point in the towing dynamics analysis; This represents the resistance generated in the opposite direction to the velocity when the towed body is subjected to hydrodynamic forces. This refers to the yaw force perpendicular to the velocity direction generated when the towed body is subjected to hydrodynamic forces. The x-coordinate value represents the hydrodynamic center; This indicates that the towed body generates a yaw angle after being disturbed; therefore, the towing dynamics analysis result is: From the expression of the torque generated by the hydrodynamic force on the towing point in the towing dynamics analysis, it can be seen that when the hydrodynamic center is behind the towing point, the torque generated by the lift and yaw force will reduce the yaw angle caused by the disturbance. From equation (10), it can be seen that when the hydrodynamic center is behind the towing point, the yaw force and hydrodynamic resistance The generated torque will affect the yaw angle caused by the disturbance. β The reduction generates a yaw restoring moment, making the towed body towed and stable.

[0049] S3. Construct a towed body structure model and perform hydrodynamic simulation calculations; Specifically, based on the results of towing dynamics analysis and design parameters, the basic dimensions and weight of the tow body are determined, and the shape of the tow body structure is determined according to the load. Based on the shape of the tow body structure, a tow body structure model is designed. Hydrodynamic simulation calculations are performed on the tow body structure model to obtain the drag coefficient and lift coefficient.

[0050] For example, in one specific embodiment, the steps of designing a tow body structural model based on the tow dynamics analysis results and design specifications, determining the basic dimensions and weight of the tow body, and determining the tow body structural shape based on the load, are as follows: The tow body structural dimensions are determined according to the type and size of the load equipment carried by the tow body. Typical tow body structural types include open-frame structures, closed streamlined bodies, and composite functional structures. Based on the tow dynamics analysis results, this invention designs the tow body structural shape as a closed streamlined body to reduce drag and improve stability. Furthermore, the tail fin size is reasonably increased within the limits of available dimensions.

[0051] For example, in one specific embodiment, the steps for performing hydrodynamic simulation calculations on the towed body structure model to obtain the drag coefficient and lift coefficient are as follows: In the simulation calculation of towed body attitude, the hydrodynamic drag and lift coefficient of the towed body are required as input parameters, and their accuracy directly affects the simulation analysis of towed attitude. Therefore, it is necessary to use professional hydrodynamic simulation software to simulate and calculate the hydrodynamic drag and lift of the towed body.

[0052] drag coefficient It comprehensively reflects both the drag caused by the shape of the object (pressure drag) and the surface friction drag. A lower value indicates higher aerodynamic efficiency, which is defined as: (11) In the formula, Indicates the drag coefficient; This represents the lift force of the fluid flowing in the opposite direction. Indicates fluid density; Indicates the incoming flow velocity; Represents the projected area of ​​the drag body, where, The input settings are affected by factors such as object shape, surface roughness, and Reynolds number (Re), therefore, it is necessary to select appropriate settings. As input, the drag body in this embodiment is a teardrop-shaped object. The settings are too small.

[0053] Lift coefficient The efficiency of an object in generating lift is directly related to airfoil design and angle of attack, and directly affects the lift of the towed body. Its definition is as follows: (12) In the formula, Indicates the lift coefficient; This represents the fluid lift force perpendicular to the flow direction. The input settings are affected by the angle of attack, airfoil parameters, and fluid state (Reynolds number, Mach number).

[0054] In the professional computational fluid dynamics (CFD) simulation software STARCCM+, the drag coefficient With lift coefficient These are core indicators for evaluating the hydrodynamic performance of a towed body. Their accurate acquisition is crucial throughout the entire numerical simulation process, including geometric modeling, computational domain creation, mesh generation, physical model setup, solution calculation, and post-processing analysis.

[0055] In this embodiment, the Reynolds-averaged Navier-Stokes (RANS) method is used as the turbulence model. After solver setup and parameter monitoring, the surface of the towed body is selected as the domain of action, and the drag direction (along the X-axis) and lift direction (along the Z-axis) are clearly defined. The optimal balance solution between drag and lift coefficients is obtained through iterative system calculation. Based on the teardrop-shaped towed body configuration used in this study, its streamlined shape contributes to superior hydrodynamic characteristics. The final simulation results show that, under the specified operating conditions, the drag coefficient of this towed body is... The lift coefficient is 0.38. The value is 1.8. This result is consistent with the general rule that teardrop-shaped structures have lower drag and relatively significant lift effects in fluids.

[0056] S4. Establish a dynamic coupling numerical simulation model of the towing system; Specifically, the dynamic simulation of the towed body involves the coupled motion of the tow cable and the towed body. In this embodiment, based on the drag coefficient and lift coefficient, mathematical models of the tow cable motion and the towed body motion are constructed. Based on the mathematical models of the tow cable motion and the towed body motion, a dynamic coupling numerical simulation model of the towing system is established. The marine engineering hydrodynamic analysis software OrcaFlex is used to simulate and calculate the dynamic process of the towed body.

[0057] Step S41, the steps for constructing the mathematical model of the towing cable motion are as follows: In this embodiment, the towing cable model is considered as a slender, flexible cylindrical cable. A discrete condensed mass model is used to solve the nonlinear boundary value problem. The basic idea of ​​this model is to divide the towing cable into N segments of cable elements, and the mass of each segment is concentrated at a single node, thus resulting in N nodes. The tension acting at the end of each segment... and shear force This can be viewed as a concentrated action on a single node, with any external hydrodynamic load considered as acting concentrated on a node of each tow cable segment. Therefore, the mathematical model of the tow cable motion is expressed as: (13) In the formula, Indicates the action in the The inertial force at the node corresponding to the infinitesimal element of the cable segment. Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The external hydrodynamic force experienced at the node corresponding to the micro-element of the tow cable segment; Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates the first The weight corresponding to the micro-element of the tow cable segment; Indicates the first Weight per unit length of a segment of tow cable element in a fluid; Indicates the first The length of the tow cable element after elongation; (14) In the formula, Indicates the first The additional mass matrix of the node corresponding to the segment drag cable micro-element; Indicates the first The acceleration vector of the node corresponding to the infinitesimal element of the cable segment; Indicates the first The diameter corresponding to the micro-element of the tow cable segment; Indicates the normal inertial force coefficient; Represents a 3×3 identity matrix; where, Indicates the first The unit vector of the tangential direction of the tow cable element divides the tow cable into N tow cable elements, and the mass of each tow cable element is concentrated on a node, so there can be N nodes. The external hydrodynamic force is calculated using the Morrison formula: (15) In the formula, Indicates the first The external hydrodynamic forces acting on the nodes of the cable segment micro-element; The density of seawater; This represents the tensile strain of the i-th cable element; For the first The normal resistance coefficient corresponding to the micro-element of the tow cable segment; For the first The tangential resistance coefficient corresponding to the micro-element of the tow cable; Indicates the water flow relative to the first The normal velocity vector of the tow cable element. Water flow relative to the first The tangential velocity vector of the infinitesimal element of the tow cable segment. For the first The normal inertial force coefficient corresponding to the micro-element of the tow cable segment; Indicates the first The acceleration vector of water particles at the nodes of the cable segment element.

[0058] The shear force expression at each node is as follows: (16) In the formula, Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates the application of tensile strain The next The length of the cable segment micro-element; This indicates the elastic modulus of the cable material; Indicates the first The moment of inertia of the cross section of the tow cable element; Indicates the application of tensile strain The next The length of the cable segment micro-element; Indicates the first Shear force at the node corresponding to the micro-element of the cable segment.

[0059] Step S42, the steps for constructing the mathematical model of the dragged body motion are as follows: During the movement of the towing system, the towing cable and the underwater towed body interact and influence each other. The towing cable provides tension to tow the towed body forward, while the resistance of the towed body also affects the movement of the towing cable, especially its original shape and tension distribution.

[0060] In the marine engineering hydrodynamic analysis software OrcaFlex, the solution for the system's motion attitude is divided into two processes: static analysis and dynamic analysis. Static analysis is a nonlinear equilibrium solution process, the ultimate goal of which is to find the position and orientation of each element in the model so that all forces and moments are in equilibrium. Dynamic analysis is a time-domain integration and coupled solution process, based on the multi-system Newton-Euler equations to solve for the system's motion.

[0061] The equation of translational motion is: (17) The equation of rotational motion is: (18) In the formula, Indicates inertial load; Indicates damping load; Represents the stiffness matrix; Indicates the external load on the system; Represents the moment of inertia matrix in generalized rotating coordinates; Indicates the rotational damping of the system; Indicates the rotational stiffness of the system; This represents the external torque acting on the system; Indicates the rotation angle; Indicates angular velocity; Indicates angular acceleration; Indicates the simulation time.

[0062] At the start of the dynamic analysis, the initial positions and orientations of all objects in the model (including all nodes in all lines) are obtained from the static calculation results. The forces and moments acting on each free body and node are calculated, and the equations of motion are formed for each free body and each line node. During the calculation, the velocity and position quantities are obtained using the semi-implicit Euler integral method.

[0063] For equations (17) and (18), the damping load term is contributed by the damping and damping torque of the towed body; while the external load term mainly corresponds to the resistance and resistance torque generated by the towed body moving in the fluid.

[0064] The specific formula for calculating the damping applied to the towed body using the OrcaFlex software in marine engineering hydrodynamic analysis is as follows: (19) in, The value represents humidity; UDF represents the unit damping in each direction relative to the local coordinate system of the towed body, which is used as an input parameter. This represents the x-axis velocity component of the towed body in its local coordinate system; This represents the y-axis velocity component of the towed body in its local coordinate system; This represents the z-axis velocity component of the towed body in its local coordinate system.

[0065] The formula for calculating the damping torque is as follows: (20) Where UDM represents the unit damping in each direction relative to the local coordinate system of the towed body, and is also used as an input parameter. This represents the x-axis angular velocity component of the towed body in its local coordinate system; This represents the y-axis angular velocity component of the towed body in its local coordinate system; This represents the z-axis angular velocity component of the towed body in its local coordinate system. In this embodiment, the vibration motion of the towed body during movement is relatively small, so UDF and UDM are set to zero.

[0066] OrcaFlex applies the Morrison formula to the resistance applied to the tow body, as follows: (twenty one) in, Indicates humidity. The density of seawater, Let S be the translational drag coefficient in each direction, and S be the drag area in each direction. The drag coefficients in each direction are set as described above and are calculated using the professional computational fluid dynamics (CFD) simulation software STARCCM++.

[0067] The formula for calculating the drag torque is as follows: (twenty two) in, The rotational drag coefficients in each direction; This refers to the drag area torque in each direction. In this embodiment, the rotational motion of the towed body in each direction is relatively small during the motion, therefore the angular velocity... Since it is close to zero, the rotational drag coefficient is also set to be close to zero.

[0068] Step S42: Based on the mathematical model of the towing cable motion and the mathematical model of the towing body motion, establish a dynamic coupling numerical simulation model of the towing system. For example... Figure 6 As shown, the towing system consists of a surface vessel, a fiber optic composite cable, and a towing body. The dynamic coupling numerical simulation model of the towing cable system was modeled using the marine engineering hydrodynamic analysis software OrcaFlex.

[0069] Step S421: Establishing Basic Parameters and Model In terms of environmental configuration, the Pierson-Mosocowitz spectrum was used as the sea state wave spectrum (PM spectrum). The PM spectrum is a single-parameter spectrum calculated based on the sea wind speed. When the wind speed is 22 knots, the meaningful wave height is 2.735 m, the average wave period is 6.388 s, the zero crossing period is 5.909 s, and it corresponds to sea state 5.

[0070] In the OrcaFlex simulation environment, three basic model elements—Vessel, Line, and 6D buoy—were used to construct a surface tugboat, a fiber optic composite cable, and an underwater towing body, respectively, integrating a dynamic coupled numerical simulation model of the underwater towing system. The surface tugboat was represented by Vessel elements, and its motion mode was set as uniform straight-line travel along the positive X-axis of the global coordinate system, with a towing speed ranging from 2 to 20 knots (kN). The fiber optic composite cable was numerically simulated using Line elements, and its structural mechanical parameters are detailed in Table 1. Table 1

[0071] The tow body is characterized by 6D buoy elements, and its structural mechanical parameters are detailed in Table 2.

[0072] Table 2

[0073] Regarding the hydrodynamic drag and lift coefficient of the towed body, calculations were performed using the professional computational fluid dynamics (CFD) simulation software STARCCM++. Under the specified operating conditions, the drag coefficient of the towed body was... The lift coefficient is 0.38. It is 1.8.

[0074] S5. Perform dragging attitude simulation and obtain the optimal design solution; Specifically, the towing attitude simulation calculation of the dynamic coupling numerical simulation model is performed to obtain the static pitch angle and dynamic pitch angle of the towing body under different center of gravity and towing point positions. The center of gravity and towing point position corresponding to the towing body static pitch angle being less than the preset first angle threshold and closest to the first angle threshold, and the towing body dynamic pitch angle being less than the second angle threshold, are taken as the optimal design scheme.

[0075] For example, in one specific embodiment, the marine engineering hydrodynamic analysis software OrcaFlex is used to perform simulation calculations on the dynamic coupling numerical simulation model of the towed cable system.

[0076] The OrcaFlex numerical solution process involves two methods: frequency domain analysis and time domain analysis. Frequency domain analysis, based on linear system theory, approximates nonlinear variables using modal superposition and constructs a frequency domain transfer function to solve for the system response. However, this method is limited by the assumption of a linear time-invariant system and struggles to handle highly nonlinear problems such as large geometric deformations and abrupt changes in contact states, thus limiting its engineering applicability. Time domain analysis employs a fully nonlinear numerical framework, enabling the calculation of parameters such as mass, damping, stiffness, and load at any time step, as well as instantaneous, time-varying geometry. For time domain analysis, the main output is the time-varying response variable; this study primarily utilizes time domain analysis. Figure 7 As shown, the time-domain calculation is in seconds (s) and adopts a three-time-axis independent control mechanism: system simulation time axis, environmental load time axis, and variable measurement time axis. The negative time period is the static analysis stage, i.e. the force balance stage, and the positive time period is the dynamic calculation stage.

[0077] This embodiment employs a globally unified time reference, aligning the origins of the environmental load time axis, variable measurement time axis, and system simulation time axis to the zero point of the time coordinate system (t0=0), ensuring complete synchronization between the acquisition range of all time series data and the dynamic simulation time domain. The dynamic calculation time domain is set to 1800 seconds (s), covering the entire process of the towing system from initial transient response to steady-state evolution. Output variables include: tow body heave displacement (characterizing depth change), cable end drag force, and tow body pitch angle. Specifically, in this embodiment, for the operating condition of a cable length of 450 m and a towing speed of 20 kN, parametric analysis of the tow body's center of gravity position and towing point position is conducted: the x-coordinate of the center of gravity is sequentially set to 0.3, 0.4, and 0.5, and the towing point position is adjusted synchronously to match the changes in the center of gravity. The following key indicators were calculated through numerical simulation: static pitch angle of the towed body, depth of the towed body, dynamic stable pitch angle of the towed body, and towing force of the winch end cable. The specific simulation results of the static pitch of the towed body under different centers of gravity and towing points are detailed in Table 3, and the simulation results of the towing attitude prediction under different centers of gravity and towing points at a towing speed of 20kN are detailed in Table 4.

[0078] Table 3

[0079] Table 4

[0080] The calculation results in Tables 3 and 4 show that there are corresponding optimized towing point positions under different center of gravity configurations, which can enable the towed body to maintain a basic horizontal equilibrium attitude. As the horizontal distance between the center of gravity and the center of buoyancy increases, the horizontal distance between the towing point and the center of gravity and the center of buoyancy also increases in order to keep the towed body in a horizontal attitude. This is beneficial for providing a greater restoring torque for the towed body under the influence of hydrodynamics.

[0081] In this embodiment, the first angle threshold is set to 0° and the second angle threshold is set to 10°. When the static pitch angle of the towed body is less than the first angle threshold and the dynamic pitch angle of the towed body is less than the second angle threshold, the corresponding center of gravity and towing point positions are taken as the optimal design scheme. That is, according to Tables 3 and 4, when the center of gravity coordinates are selected as (0.3, 0, 0.2), the towing point coordinates are determined to be (0.10, 0, 0.60) by the static pitch angle of the towed body. Under this configuration, the pitch angle of the towed body in still water is -4.44°, which meets the first angle threshold of 0° and satisfies the requirement that the dynamic pitch angle of the towed body is less than the second angle threshold of 10°. In summary, this study adopts the center of gravity position (0.3, 0, 0.2) and towing point coordinates (0.10, 0, 0.60) as the final design scheme.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing the towing performance of an underwater towed body, characterized in that, include: Static dynamic analysis of the towed body is performed to obtain the positional relationship between the towed body's center of buoyancy, center of gravity, and towing point; The towing dynamics analysis of the towed body is based on the torque balance relationship between the center of buoyancy, center of gravity and towing point of the towed body; Based on the results of towing dynamics analysis and design parameters, the basic dimensions and weight of the towing body are determined, and the shape of the towing body structure is determined according to the load. Based on the shape of the towing body structure, the towing body structure model is designed. Hydrodynamic simulation calculations were performed on the towed body structure model to obtain the drag coefficient and lift coefficient; Based on the drag coefficient and lift coefficient, a mathematical model of the towing cable motion and a mathematical model of the towing body motion are constructed. Based on the mathematical models of the towing cable motion and the towing body motion, a dynamic coupling numerical simulation model of the towing system is established. The towing attitude simulation calculation of the dynamic coupling numerical simulation model is used to obtain the static pitch angle and dynamic pitch angle of the towing body under different center of gravity and towing point positions. The center of gravity and towing point positions corresponding to the static pitch angle of the towing body being less than the preset first angle threshold and closest to the first angle threshold, and the dynamic pitch angle of the towing body being less than the second angle threshold, are taken as the optimal design scheme.

2. The underwater towing performance design method according to claim 1, characterized in that, The steps for performing static dynamic analysis on the towed body to obtain the positional relationship between the towed body's center of buoyancy, center of gravity, and towing point are as follows: With the towing point as the origin of the coordinate system, the direction pointing to the head of the towing body is... x Direction, pointing towards the port side of the towing hull. y Direction, vertically upwards. z Direction, establish a fixed coordinate system; The center of gravity and center of buoyancy are set based on a fixed coordinate system, and the distances from the center of gravity to the drag point and from the center of buoyancy to the drag point are obtained based on the center of gravity and center of buoyancy positions. Based on the distance from the center of gravity to the towing point, the distance from the center of buoyancy to the towing point, gravity, buoyancy, and the line connecting the towing point and the center of gravity... z The opposite angle of the direction and the line connecting the drag point and the center of buoyancy. z The opposite angle of the direction is used to obtain the torque balance relationship between the center of buoyancy, center of gravity, and towing point of the towing body; Based on the torque balance relationship, the positional relationship between the center of buoyancy, center of gravity, and towing point of the towed body is determined.

3. The underwater towing performance design method according to claim 2, characterized in that, The angle of head lifting while dragging the body is When torque equilibrium is reached, the torque equilibrium equation is: In the formula, Represents gravity; Indicates buoyancy; Indicates the distance from the center of gravity to the drag point; Indicates the distance from the center of buoyancy to the drag point; The line connecting the drag point and the center of buoyancy is... z The angle between the opposite directions; Indicates the angle at which the body lifts its head; The line connecting the buoyancy fulcrum and the center of gravity is... z The angle between the opposite directions.

4. The underwater towing performance design method according to claim 3, characterized in that, A towed body stationary in the water will lift its head due to an initial disturbance. When the disturbance is eliminated, the static restoring torque generated is: A towed body at rest in the water tilts to the right due to an initial disturbance. When the disturbance is eliminated, the static restoring torque generated is: In the formula, This indicates that a towed body at rest in the water experiences a head-up angle due to an initial disturbance. At that time, the static restoring torque generated after the disturbance is eliminated; This indicates that a towed body at rest in the water tilts to the right due to an initial disturbance. At that time, the static restoring torque generated after the disturbance is eliminated; Represents gravity; Indicates buoyancy; This represents the ordinate value of the center of gravity of the drag body in a fixed coordinate system; This represents the ordinate value of the center of buoyancy of the towed body in a fixed coordinate system.

5. The underwater towing performance design method according to claim 1, characterized in that, The expression for the torque generated by hydrodynamic forces on the towing point in towing dynamics analysis is as follows: In the formula, This represents the torque generated by hydrodynamic forces on the towing point in the towing dynamics analysis; This represents the hydrodynamic resistance generated in the opposite direction to the velocity when the towing body is subjected to hydrodynamic forces. This refers to the yaw force perpendicular to the velocity direction generated when the towed body is subjected to hydrodynamic forces. The x-coordinate value represents the hydrodynamic center; This indicates that the towed body generates a yaw angle after being disturbed; the towing dynamics analysis result is: from the expression of the torque generated by the hydrodynamic force on the towing point in the towing dynamics analysis, it can be seen that when the hydrodynamic center is behind the towing point, the torque generated by the lift and yaw force will reduce the yaw angle caused by the disturbance.

6. The underwater towing performance design method according to claim 1, characterized in that, The steps for determining the basic dimensions and weight of the tow body based on the results of towing dynamics analysis and design specifications, and then determining the structural shape of the tow body based on the load, are as follows: The structural dimensions of the tow body are determined based on the type and size of the load equipment carried by the tow body; Based on the results of the towing dynamics analysis, the towing body structure is designed as a closed streamline.

7. The underwater towing performance design method according to claim 1, characterized in that, The steps for obtaining the drag coefficient and lift coefficient by performing hydrodynamic simulation calculations on the towed body structure model are as follows: The expression for the drag coefficient is: The expression for the lift coefficient is: In the formula, Indicates the drag coefficient; Indicates the lift coefficient; This represents the lift force of the fluid perpendicular to the flow direction; This represents the lift force of the fluid flowing in the opposite direction. Indicates fluid density; Indicates the incoming flow velocity; This indicates the projected area of ​​the drag body.

8. The underwater towing performance design method according to claim 1, characterized in that, The steps for constructing the mathematical models of the towed cable motion and the towed body motion based on the drag coefficient and lift coefficient are as follows: The mathematical model for cable towing motion is expressed as follows: In the formula, Indicates the action in the The inertial force at the node corresponding to the infinitesimal element of the cable segment. Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The effective tension at the node corresponding to the micro-element of the cable segment; Indicates the first The external hydrodynamic force experienced at the node corresponding to the micro-element of the tow cable segment; Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates the first The weight corresponding to the micro-element of the tow cable segment; Indicates the first Weight per unit length of a segment of tow cable element in a fluid; Indicates the first The length of the tow cable element after elongation; In the formula, Indicates the first The additional mass matrix of the node corresponding to the segment drag cable micro-element; Indicates the first The acceleration vector of the node corresponding to the infinitesimal element of the cable segment; Indicates the first The diameter corresponding to the micro-element of the tow cable segment; Indicates the normal inertial force coefficient; Represents a 3×3 identity matrix; where, Indicates the first The unit vector of the tangential direction of the tow cable element divides the tow cable into N tow cable elements, and the mass of each tow cable element is concentrated on a node, so there can be N nodes. The mathematical model for dragging motion is expressed as follows: In the formula, Indicates inertial load; Indicates damping load; Represents the stiffness matrix; Indicates the external load on the system; Represents the moment of inertia matrix in generalized rotating coordinates; Indicates the rotational damping of the system; Indicates the rotational stiffness of the system; This represents the external torque acting on the system; Indicates the rotation angle; Indicates angular velocity; Indicates angular acceleration; Indicates the simulation time.

9. The underwater towing performance design method according to claim 8, characterized in that, The expression for the external hydrodynamic force acting on each node is: In the formula, Indicates the first The external hydrodynamic forces acting on the nodes of the cable segment micro-element; The density of seawater; This represents the tensile strain of the i-th cable element; For the first The normal resistance coefficient corresponding to the micro-element of the tow cable segment; For the first The tangential resistance coefficient corresponding to the micro-element of the tow cable; Indicates the water flow relative to the first The normal velocity vector of the tow cable element. Water flow relative to the first The tangential velocity vector of the infinitesimal element of the tow cable segment. For the first The normal inertial force coefficient corresponding to the micro-element of the tow cable segment; Indicates the first The acceleration vector of water particles at the nodes of the cable segment element.

10. The underwater towing performance design method according to claim 8, characterized in that, The shear force expression at each node is: In the formula, Indicates the first Shear force at the node corresponding to the micro-element of the tow cable segment; Indicates the application of tensile strain The next The length of the cable segment micro-element; This indicates the elastic modulus of the cable material; Indicates the first The moment of inertia of the cross section of the tow cable element; Indicates the application of tensile strain The next The length of the cable segment micro-element; Indicates the first Shear force at the node corresponding to the micro-element of the cable segment.

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