CN113962165A - Underwater vehicle motion trajectory prediction method under action of internal solitary wave - Google Patents

Underwater vehicle motion trajectory prediction method under action of internal solitary wave Download PDF

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CN113962165A
CN113962165A CN202111201438.2A CN202111201438A CN113962165A CN 113962165 A CN113962165 A CN 113962165A CN 202111201438 A CN202111201438 A CN 202111201438A CN 113962165 A CN113962165 A CN 113962165A
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underwater vehicle
resistance
solitary wave
underwater
motion
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王红萍
张志伟
余义德
李智生
蔡强
张厚强
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Unite 91550 Of Pla
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Abstract

The invention belongs to the field of analysis and research on motion response of an underwater vehicle, and particularly relates to a method for predicting motion trail of the underwater vehicle under the action of internal solitary waves. The method adopts a time domain finite displacement motion equation, establishes a relative motion response theoretical model under the strong nonlinear action of the internal solitary wave for the motion process of the underwater vehicle in the water middle section, predicts the motion track of the underwater vehicle under the action of the internal solitary wave, quantitatively evaluates the motion response of the underwater vehicle under different conditions of different positions of the underwater vehicle from the trough of the internal solitary wave, different initial depths of emission, different waves of the internal solitary wave and the like, and is used for analyzing the motion response of the underwater vehicle under the action of the internal solitary wave.

Description

Underwater vehicle motion trajectory prediction method under action of internal solitary wave
Technical Field
The invention belongs to the field of analysis and research on motion response of an underwater vehicle, and particularly relates to a method for predicting motion trail of the underwater vehicle under the action of internal solitary waves.
Background
The density stratification phenomenon of seawater in some sea areas is obvious, the change of submarine topography is severe, and the flow pattern is variable, which all provide natural marine environmental conditions for the generation of waves in the sea areas. For a vertically launched underwater high-speed moving navigation body, if launching is carried out at a large depth underwater, the underwater navigation body needs to pass through a variable density layer and encounter internal waves in the horizontal direction, even shearing of solitary waves in a large scale. Compared with the uniform density fluid, the density stratification effect can generate larger shearing action on the moving body in the transverse direction and the vertical direction, the instability of the moving posture of the underwater vehicle is increased, and the water outlet posture of the underwater vehicle is influenced. At present, a great deal of engineering software and related theoretical calculation methods for analyzing the motion response characteristics of an underwater vehicle under the action of flow before water outlet are successfully applied to engineering practice, however, the knowledge of the motion response performance of the underwater vehicle under the action of the internal solitary wave is not clear, so that the research on the motion response analysis of the underwater vehicle under the action of the internal solitary wave is necessary.
Disclosure of Invention
In order to solve the problems, the invention provides a method for predicting the motion trail of an underwater vehicle under the action of internal solitary waves. The method adopts a time domain finite displacement motion equation, establishes a relative motion response theoretical model under the strong nonlinear action of the internal solitary wave for the motion process of the underwater vehicle in the water middle section, predicts the motion track of the underwater vehicle under the action of the internal solitary wave, quantitatively evaluates the motion response of the underwater vehicle under different conditions of different positions of the underwater vehicle from the trough of the internal solitary wave, different initial depths of emission, different waves of the internal solitary wave and the like, and is used for analyzing the motion response of the underwater vehicle under the action of the internal solitary wave.
The technical scheme of the invention is as follows:
a method for predicting a motion trail of an underwater vehicle under the action of internal solitary waves comprises the following specific steps:
1. establishing a coordinate system
Let the depth and density of the upper layer fluid be h1And ρ1The depth and density of the lower layer fluid are respectively h2And ρ2The total depth of water is h, and subscripts 1 and 2 correspond to the upper and lower layers, respectively. And establishing a two-dimensional rectangular coordinate system XOY, wherein an XOY surface is superposed with an undisturbed inner interface, an OY axis is right above a wave trough, an OX axis points to the propagation direction of the inner solitary wave, and the OY axis is vertically upward and is positive. Let ζ be the internal solitary wave interface displacement, propagating in the positive direction along the OX axis at wave velocity V, as shown in fig. 1. And a following coordinate system XOY and a fixed coordinate system XOY are established by taking the fully submerged floating center of the underwater vehicle as an origin, as shown in FIG. 2.
The coordinate conversion relation between the random coordinate system XOY and the fixed coordinate system XOY is as follows:
x＝X+xd，z＝Z-hd
wherein x isdIs the horizontal distance h from the trough to the central axis of the underwater vehicledThe vertical distance from the center of the underwater vehicle to the interface of two layers of fluid.
2. Stress analysis of underwater vehicle under action of internal solitary wave
The external forces applied to the underwater vehicle are the gravity of the underwater vehicle, the buoyancy applied to the submerged part, the thrust acting on the underwater vehicle, the hydrodynamic force and the moment thereof. The concrete formula calculation methods of various forces are given below.
(1) Drag and lateral drag
When the underwater vehicle moves in the internal solitary wave, the hydrodynamic force applied to the head of the underwater vehicle is defined as the incident flow resistance, and the hydrodynamic force applied to the side of the underwater vehicle is defined as the side resistance. The underwater vehicle is mainly divided into an incident flow resistance and a side resistance by the fluid resistance in the launching process, and the dimensionless resistance coefficient corresponding to the incident flow resistance and the side resistance is defined asCxAndCythe formula of the incident flow resistance and the side resistance is as follows:
resistance to flow
Figure BDA0003305088510000021
Side resistance
Figure BDA0003305088510000022
Wherein S1＝πDL+πD,S2D is the diameter of the underwater vehicle, and L is the length of the underwater vehicle.
sign(v1) Is v is1Direction of (v), sign (v)1) Is defined as follows:
Figure BDA0003305088510000031
wherein v is1The speed of the underwater vehicle in the x direction.
Coefficient of resistance to incident flow CxAnd coefficient of lateral resistance CyThe specific calculation method is as follows:
coefficient of resistance to incident flow CxFrom coefficient of friction resistance CxfAnd differential pressure drag coefficient CxpComposition, i.e. Cx＝Cxf+Cxp。
The friction resistance coefficient directly utilizes a flat friction resistance coefficient formula to calculate the friction resistance coefficient of the underwater vehicle:
Figure BDA0003305088510000032
coefficient of differential pressure resistance CxpA rotating body pressure difference resistance coefficient calculation formula given by a Barpamel is adopted:
Figure BDA0003305088510000033
wherein R iseIs Reynolds number; s is the maximum cross-sectional area of the underwater vehicle; omega is the soaking area of the underwater vehicle; e is the length of the tapered part at the rear section of the underwater vehicle;
coefficient of lateral resistance CyIn the small deflection angle range, the following can be expressed:
Figure BDA0003305088510000034
f is the slenderness ratio of the underwater vehicle, wherein f is L/d, L is the calculated length of the underwater vehicle, and d is the turning radius of the section of the underwater vehicle; sMIs the maximum longitudinal sectional area of the underwater vehicle.
(2) Gravity force
Gravity G is
G＝mg
Wherein m is the mass of the underwater vehicle and g is the acceleration of the free-fall.
(3) Buoyancy force
Buoyancy force FBIs composed of
FB＝ρV
Wherein rho is the density of the seawater, and V is the volume of the underwater vehicle. The net buoyancy Δ B may be recorded as
ΔB＝FB-G
(4) Thrust force
When the power is not transmitted
FT＝0
Wherein FTIs the launching thrust of the underwater vehicle.
(5) Internal soliton wave loading
The acting force of the inner solitary wave received along the axial direction of the underwater vehicle can be calculated by adopting a method of pressure difference between the upper surface and the lower surface, namely Froude-Krylov force, as shown in the following formula:
dFp＝pnds
wherein P is dynamic pressure in the flow field, S is the upper and lower surface area of the underwater vehicle, and n is the unit normal vector of the upper and lower surfaces.
The side surface of the incident flow part of the underwater vehicle is subjected to drag force and inertia force, and is calculated by adopting a Morison formula, wherein the formula is as follows:
Figure BDA0003305088510000041
wherein S is the cross-sectional area of the underwater vehicle, D is the equivalent diameter of the underwater vehicle,
Figure BDA0003305088510000042
and V are the instantaneous acceleration and instantaneous horizontal velocity of the water particle perpendicular to the underwater vehicle, respectively.
Wherein drag coefficient CdAnd coefficient of inertia force CmThe test result is obtained by fitting the experimental result of solitary wave load in the underwater navigation body, and the fitting formula is as follows:
Cd＝173.3×exp(-9.171×10-3×Re)+0.6265
Cm＝[95.02-21.97(h1/h2)2]KC-1.108
wherein Re is Reynolds number and KC is KC number.
The moment generated by the load of the inner solitary wave on the underwater vehicle is as follows:
dMW＝rB×dFc＝(z-zc)(dFd+dFm)
3. equation of motion of underwater vehicle under action of internal solitary wave
The motion equation of the underwater vehicle with 3 degrees of freedom under the action of the internal solitary wave is as follows:
Figure BDA0003305088510000051
wherein m is the mass of the underwater vehicle, J is the moment of inertia of the underwater vehicle, and lambda11And λ22For additional mass in the longitudinal and vertical directions, λ66For additional moment of inertia, F1Horizontal external loads for underwater vehicles, F2Is a vertical external load of the underwater vehicle, F3The external load moment of the underwater vehicle, the point above the variable representing the derivative with respect to time.
The external load of the underwater navigation body comprises an internal solitary wave dynamic load FWAnd its moment MWResistance force FfAnd its moment MfBuoyancy FBAnd its moment MBAnd anThe underwater vehicle self-gravity. After the above loads and moments are obtained in sequence, the external load vector F applied to the underwater vehicle can be expressed as
F＝F1i+F2K＝FW+FB+Ff-mgk
M＝F3e3＝MW+MB+Mf
Where i, j, k are unit vectors of a fixed coordinate system XOY, e1，e2，e3Is a unit vector of the coordinate system xoy along with the body, and g is the gravity acceleration.
The selection of the additional mass is given in detail below.
When the object moves in the fluid without constraint, the object can move in 3 directions and can rotate, so that all the additional masses form a (6 x 6) additional mass matrix lambda.
First, for a non-swirling flow characterized by a velocity potential φ, in the fluid region V, the kinetic energy T is given by:
Figure BDA0003305088510000061
and i takes 1, 2, 3.
Figure BDA0003305088510000062
S is the boundary of the fluid region, and the translation speed of the underwater vehicle is now set to have a component U at the origin1，U2，U3And the angular velocity of rotation of the underwater vehicle has a component U4，U5，U6. For each component a of the motion of the object, the fluid has a corresponding velocity potential. Unit UαThe corresponding velocity potential is represented by phiαAnd (4) showing. At this time, the laplace equation and the boundary conditions (absence of separation and cavitation that generate free surfaces) are linear, so the solutions of the equations can be superimposed. So, regardless of the movement of the underwater vehicle, for the general case:
φ＝Uαφα，α＝1,2，...，6
the results obtained were:
Figure BDA0003305088510000063
wherein the subscripts alpha and beta take the values of integers of 1-6, and:
Figure BDA0003305088510000064
from the formula, it can be shown thatαβIs a component of the additional mass tensor, andαβis symmetrical.
Kinematic boundary conditions of the object surface:
Figure BDA0003305088510000065
wherein is
Figure BDA0003305088510000066
The vector of the velocity is such that,
Figure BDA0003305088510000067
is a vector of the rotation of the rotating body,
Figure BDA0003305088510000068
is a position vector (from the origin to a point on the surface of the object), and
Figure BDA0003305088510000069
is the unit vector of the external normal of the underwater navigation body. Let n4，n5，n6Is defined as
Figure BDA00033050885100000610
The equation can be simplified to:
Figure BDA00033050885100000611
and the value of alpha is from 1 to 6. Due to all UαThe values are true, so:
Figure BDA0003305088510000071
thereby can obtain
Figure BDA0003305088510000072
Because of phiαIs UαThe stated additional mass depends only on the shape and orientation of the object, and the way the object moves, and is independent of the linear velocity, or angular velocity, or acceleration of the object, for a velocity potential of 1.
If the underwater vehicle is simplified into a simple cylinder with the diameter D and the length l, the additional mass of the underwater vehicle can be simply obtained. Under the full-wet and void-free state, the elongated cylinder is a shaft-symmetric body. Taking symmetry into account, only λ of the additional quality matrix λ11、λ22、λ33、λ55、λ66、λ26And λ35Is a non-zero term, and the motion equation of the underwater vehicle with 3 degrees of freedom under the action of the internal solitary wave is a two-dimensional simplified model, so lambda33、λ55、λ35Are not considered in the movement. With the elongated body theory, i.e. assuming no interference between the sections of the column, the added mass of the column is the integral of the added mass of the sections along the longitudinal axis of the column. The additional mass λ of the cross section is calculated belowij(x) The following were used:
Figure BDA0003305088510000073
and its total additional mass is
Figure BDA0003305088510000074
It is possible to obtain:
Figure BDA0003305088510000075
λ11which is a small quantity compared to the mass of the object, the approximate formula is as follows:
Figure BDA0003305088510000076
4. prediction of motion trajectory of underwater vehicle under action of internal solitary wave
The angular velocity of the underwater navigation body and the velocity at the floating center are respectively set as omega in the satellite coordinate systemx，vx，vy(ii) a The mass of the underwater vehicle is m, and the rotational inertia of the oz axis of the underwater vehicle is JZZ。
Through the analysis in the step 1-3, a kinematic equation set of the underwater vehicle under the satellite coordinate system can be obtained as follows:
Figure BDA0003305088510000081
combined angular velocity omegazAnd rate of change of attitude angle
Figure BDA0003305088510000082
The relation between the two components is shown in the specification,
Figure BDA0003305088510000083
the simplified equation of motion is
Figure BDA0003305088510000084
Wherein the content of the first and second substances,
A＝[(mxc+λ26)(G·LoGcosθ+FyLorsinθ-MW-mxcvxωx)-(Jzt+λ66)(ΔBcosθ+Fy sinθ-mvxωz)]
B＝[(mxc+λ26)(ΔBcosθ+Fysinθ-Fc-mvxωz)-(m+λ22)(G·LoGcosθ+Fy·Lorsinθ-mxcvxωz)]
the motion trail of the underwater vehicle under the action of the internal solitary wave can be predicted through the simplified motion equation shown in the formula.
The invention has the following beneficial effects: the method adopts a time domain finite displacement motion equation, aims at the stress analysis of the underwater vehicle under the action of the internal solitary wave, respectively obtains various stressed loads and moments, establishes a 3-degree-of-freedom motion equation under the strong nonlinear action of the internal solitary wave, predicts the motion trail of the underwater vehicle under the action of the internal solitary wave, and can be used for the motion response analysis of the underwater vehicle under the action of the internal solitary wave.
Drawings
FIG. 1 is a schematic diagram of soliton waves in two layers of fluid and their coordinate systems;
FIG. 2 is a force analysis diagram of the underwater vehicle;
fig. 3 is a schematic diagram of the motion trajectory of the underwater vehicle at different launching positions.
Detailed Description
The following further describes a specific embodiment of the present invention with reference to the drawings and technical solutions.
In this embodiment, the motion trajectory of the underwater vehicle is predicted by using the method of the present invention at different positions from the troughs of the internal solitary wave, the initial depth is 30m, the height of the internal wave is 50m, and the displacement and the deflection angle of the underwater vehicle at the initial position of X0-0 m, X1-100 m, X2-200 m, X3-300 m, X4-400 m, and X5-500 m are shown in table 1.
The initial position in the table is the initial coordinates of the center of the underwater vehicle in the coordinate system XOY. As can be seen from the table, when the initial position is X0 ═ 0, that is, the launch position of the underwater vehicle is directly above the trough of the internal solitary wave, the offset and deflection of the underwater vehicle relative to other positions are maximum, because the fluid velocity near this position is maximum, the internal solitary wave has a large effect, so that the movement locus of the underwater vehicle deviates from the original trajectory, and the same result can be observed in fig. 3, and at the position (X5 ═ 500m) far from the internal solitary wave, the underwater vehicle moves approximately vertically upward; the closer to the inner solitary wave, the more obvious the deviation of the motion track of the underwater vehicle is.
TABLE 1 Displacement and deflection Angle of Underwater vehicle, launched at different distances from trough
Figure BDA0003305088510000091

Claims (1)

1. A method for predicting the motion trail of an underwater vehicle under the action of internal solitary waves is characterized by comprising the following specific steps:
step 1, establishing a coordinate system
Let the depth and density of the upper layer fluid be h1And ρ1The depth and density of the lower layer fluid are respectively h2And ρ2The total water depth is h, and subscripts 1 and 2 respectively correspond to an upper layer and a lower layer; establishing a two-dimensional rectangular coordinate system XOY, wherein an XOY surface is superposed with an undisturbed inner interface, an OY axis is right above a wave trough, an OX axis points to the propagation direction of an inner solitary wave, and the OY axis is vertically upward and is positive; setting zeta as inner solitary wave interface displacement and propagating along positive direction of OX axis with wave speed V; establishing a following coordinate system XOY and a fixed coordinate system XOY by taking the fully submerged floating center of the underwater vehicle as an origin;
the coordinate conversion relation between the random coordinate system XOY and the fixed coordinate system XOY is as follows:
x＝X+xd，z＝Z-hd
wherein x isdIs the horizontal distance h from the trough to the central axis of the underwater vehicledThe vertical distance from the center of the underwater vehicle to the interface of two layers of fluid;
step 2, stress analysis of underwater vehicle under action of internal solitary wave
(1) Drag and lateral drag
When the underwater vehicle moves in the internal solitary wave, the hydrodynamic force applied to the head of the underwater vehicle is defined as the incident flow resistance, and the hydrodynamic force applied to the side surface of the underwater vehicle is defined as the side resistance; the underwater vehicle is mainly divided into an incident flow resistance and a side resistance by the fluid resistance in the launching process, and a dimensionless resistance coefficient corresponding to the incident flow resistance and the side resistance is defined as CxAnd CyThe formula of the incident flow resistance and the side resistance is as follows:
resistance to flow
Figure FDA0003305088500000011
Side resistance
Figure FDA0003305088500000012
Wherein S1＝πDL+πD,S2D is the diameter of the underwater vehicle, and L is the length of the underwater vehicle;
sign(v1) Is v is1Direction of (v), sign (v)1) Is defined as follows:
Figure FDA0003305088500000021
wherein v is1The speed of the underwater vehicle in the x direction;
coefficient of resistance to incident flow CxAnd coefficient of lateral resistance CyThe specific calculation method is as follows:
coefficient of resistance to incident flow CxFrom coefficient of friction resistance CxfAnd differential pressure drag coefficient CxpComposition, i.e. Cx＝Cxf+Cxp；
The friction resistance coefficient directly utilizes a flat friction resistance coefficient formula to calculate the friction resistance coefficient of the underwater vehicle:
Figure FDA0003305088500000022
coefficient of differential pressure resistance CxpA rotating body pressure difference resistance coefficient calculation formula given by a Barpamel is adopted:
Figure FDA0003305088500000023
wherein R iseIs Reynolds number; s is the maximum cross-sectional area of the underwater vehicle; omega is the soaking area of the underwater vehicle; e is the length of the tapered part at the rear section of the underwater vehicle;
coefficient of lateral resistance CyIn the range of small declination angles, the following are expressed:
Figure FDA0003305088500000024
f is the slenderness ratio of the underwater vehicle, wherein f is L/d, L is the calculated length of the underwater vehicle, and d is the turning radius of the section of the underwater vehicle; sMThe maximum longitudinal cross-sectional area of the underwater vehicle;
(2) gravity force
Gravity G is
G＝mg
Wherein m is the mass of the underwater vehicle, and g is the acceleration of the free-fall;
(3) buoyancy force
Buoyancy force FBIs composed of
FB＝ρV
Wherein rho is the density of seawater, and V is the volume of the underwater vehicle; the net buoyancy Δ B is then recorded as
ΔB＝FB-G
(4) Thrust force
When the power is not transmitted
FT＝0
Wherein FTThe launching thrust of the underwater vehicle;
(5) internal soliton wave loading
The force of the inner solitary wave applied along the axial direction of the underwater vehicle is calculated by adopting a method of pressure difference between the upper surface and the lower surface, namely Froude-Krylov force, which is shown as the following formula:
dFp＝pnds
wherein P is dynamic pressure in a flow field, S is the upper and lower surface areas of the underwater vehicle, and n is the unit normal vector of the upper and lower surfaces;
the side surface of the incident flow part of the underwater vehicle is subjected to drag force and inertia force, and is calculated by adopting a Morison formula, wherein the formula is as follows:
Figure FDA0003305088500000031
wherein S is the cross-sectional area of the underwater vehicle, D is the equivalent diameter of the underwater vehicle,
Figure FDA0003305088500000032
and V is the instantaneous acceleration and the instantaneous horizontal velocity of the water particle vertical to the underwater vehicle respectively;
wherein drag coefficient CdAnd coefficient of inertia force CmThe test result is obtained by fitting the experimental result of solitary wave load in the underwater navigation body, and the fitting formula is as follows:
Cd＝173.3×exp(-9.171×10-3×Re)+0.6265
Cm＝[95.02-21.97(h1/h2)2]KC-1.108
wherein Re is Reynolds number, and KC is KC number;
the moment generated by the load of the inner solitary wave on the underwater vehicle is as follows:
dMW＝rB×dFc＝(z-zc)(dFd+dFm)
step 3. equation of motion of underwater vehicle under action of internal solitary wave
The motion equation of the underwater vehicle with 3 degrees of freedom under the action of the internal solitary wave is as follows:
Figure FDA0003305088500000041
wherein m is the mass of the underwater vehicle, J is the moment of inertia of the underwater vehicle, and lambda11And λ22For additional mass in the longitudinal and vertical directions, λ66For additional moment of inertia, F1Horizontal external loads for underwater vehicles, F2Is a vertical external load of the underwater vehicle, F3The external load moment of the underwater vehicle, the point above the variable representing the derivative with respect to time;
the external load of the underwater navigation body comprises an internal solitary wave dynamic load FWAnd its moment MWResistance force FfAnd its moment MfBuoyancy FBAnd its moment MBAnd the self gravity of the underwater vehicle; after the above loads and moments are obtained in sequence, the external load vector F received by the underwater vehicle is expressed as:
F＝F1i+F2K＝FW+FB+Ff-mgk
M＝F3e3＝MW+MB+Mf
where i, j, k are unit vectors of a fixed coordinate system XOY, e1，e2，e3Is a unit vector of the satellite coordinate system xoy, and g is the gravity acceleration;
the selection method of the additional mass is as follows:
the object can not only move in 3 directions but also rotate when moving unconstrained in the fluid, so all additional masses constitute a (6 × 6) additional mass matrix λ;
first, for a non-swirling flow characterized by a velocity potential φ, in the fluid region V, the kinetic energy T is given by:
Figure FDA0003305088500000042
and i takes 1, 2, 3;
Figure FDA0003305088500000051
s is the boundary of the fluid region, and the translation speed of the underwater vehicle is now set to have a component U at the origin1，U2，U3And the angular velocity of rotation of the underwater vehicle has a component U4，U5，U6(ii) a For each component α of the motion of the object, the fluid has a corresponding velocity potential; unit UαThe corresponding velocity potential is represented by phiαRepresents; at this time, the laplace equation and the boundary condition are linear, so the solutions of the equations can be superimposed; so, regardless of the movement of the underwater vehicle, for the general case:
φ＝Uαφα，α＝1,2，...，6
the results obtained were:
Figure FDA0003305088500000052
wherein the subscripts alpha and beta take the values of integers of 1-6, and:
Figure FDA0003305088500000053
from the formula, it can be shown thatαβIs a component of the additional mass tensor, andαβis symmetrical;
kinematic boundary conditions of the object surface:
Figure FDA0003305088500000054
wherein is
Figure FDA0003305088500000055
The vector of the velocity is such that,
Figure FDA0003305088500000056
is a vector of the rotation of the rotating body,
Figure FDA0003305088500000057
is a position vector, and
Figure FDA0003305088500000058
is a unit vector of the external normal of the underwater navigation body; let n4，n5，n6Is defined as
Figure FDA0003305088500000059
The equation reduces to:
Figure FDA00033050885000000510
the value of alpha is from 1 to 6; due to all UαThe values are true, so:
Figure FDA00033050885000000511
thereby obtaining:
Figure FDA0003305088500000061
because of phiαIs Uα1, so the additional mass depends only on the shape and orientation of the object, and the way the object moves, and is independent of the linear velocity, or angular velocity, or acceleration of the object;
if the underwater vehicle is simplified into a simple cylinder with the diameter D and the length l, the additional mass of the underwater vehicle can be simply obtained; in a fully wet, non-vacuolated state, slenderThe cylinder is a shaft symmetry body; taking symmetry into account, only λ of the additional quality matrix λ11、λ22、λ33、λ55、λ66、λ26And λ35Is a non-zero term, and the motion equation of the underwater vehicle with 3 degrees of freedom under the action of the internal solitary wave is a two-dimensional simplified model, so lambda33、λ55、λ35Are not considered in the movement; adopting the theory of the elongated body, namely assuming that no interference exists among all sections of the cylinder, and the additional mass of the cylinder is the integral of the additional mass of the sections along the longitudinal axis direction of the cylinder; calculating the additional mass λ of the cross sectionij(x) The following were used:
Figure FDA0003305088500000062
and its total additional mass is
Figure FDA0003305088500000063
Obtaining:
Figure FDA0003305088500000064
λ11which is a small quantity compared to the mass of the object, the approximate formula is as follows:
Figure FDA0003305088500000065
step 4, predicting the motion track of the underwater vehicle under the action of the internal solitary wave
The angular velocity of the underwater navigation body and the velocity at the floating center are respectively set as omega in the satellite coordinate systemx，vx，vy(ii) a The mass of the underwater vehicle is m, and the rotational inertia of the oz axis of the underwater vehicle is JZZ；
The kinematic equation set of the underwater vehicle under the satellite coordinate system is obtained by the analysis of the step 1-3 and is as follows:
Figure FDA0003305088500000071
combined angular velocity omegazAnd rate of change of attitude angle
Figure FDA0003305088500000072
The relation between the two components is shown in the specification,
Figure FDA0003305088500000073
the simplified equation of motion is:
Figure FDA0003305088500000074
wherein the content of the first and second substances,
A＝[(mxc+λ26)(G·LoGcosθ+FyLorsinθ-MW-mxcvxωx)-(Jzt+λ66)(ΔBcosθ+Fysinθ-mvxωz)]
B＝[(mxc+λ26)(ΔBcosθ+Fysinθ-Fc-mvxωz)-(m+λ22)(G·LoGcosθ+Fy·Lorsinθ-mxcvxωz)]
and predicting the motion trail of the underwater vehicle under the action of the internal solitary wave by simplifying a motion equation.
CN202111201438.2A 2021-10-15 2021-10-15 Underwater vehicle motion trajectory prediction method under action of internal solitary wave Pending CN113962165A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
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CN114818539A (en) * 2022-04-29 2022-07-29 山东大学 Underwater structure viscous drag resistance prediction method and system based on exponential function
CN116834939A (en) * 2023-06-19 2023-10-03 山东大学 Energy-saving method of underwater internal wave boosting carrier

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114818539A (en) * 2022-04-29 2022-07-29 山东大学 Underwater structure viscous drag resistance prediction method and system based on exponential function
CN116834939A (en) * 2023-06-19 2023-10-03 山东大学 Energy-saving method of underwater internal wave boosting carrier
CN116834939B (en) * 2023-06-19 2024-03-12 山东大学 Energy-saving method of underwater internal wave boosting carrier

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