CN115859748A - Flexible cable vortex-induced vibration analysis method for dragging type thermohaline depth measuring instrument - Google Patents

Flexible cable vortex-induced vibration analysis method for dragging type thermohaline depth measuring instrument Download PDF

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CN115859748A
CN115859748A CN202310113176.7A CN202310113176A CN115859748A CN 115859748 A CN115859748 A CN 115859748A CN 202310113176 A CN202310113176 A CN 202310113176A CN 115859748 A CN115859748 A CN 115859748A
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vortex
cable
equation
induced vibration
analysis method
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CN115859748B (en
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杜立彬
刘晨
刘杰
高鼎
刘云梁
董瑞春
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Shandong University of Science and Technology
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Shandong University of Science and Technology
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Abstract

The invention discloses a flexible cable vortex-induced vibration analysis method of a dragging type thermohaline depth measuring instrument, belongs to the technical field of shipboard auxiliary equipment, and is used for flexible cable vortex-induced vibration analysis. The invention adopts the relative speed of the fluid and the cable to calculate the fluid force and the vortex discharge frequency of the non-locking area, and describes the influence of the cable movement on the magnitude and the direction of the pulsating drag force and the vortex induced lift force and the property of the fluid force frequency of the locking area and the non-locking area, namely the relation between the pulsating drag force frequency and the vortex induced lift force frequency. The coupling vibration response of the UCTD cable is researched, a complete coupling vibration model is established for analyzing the nonlinear vortex excitation vibration response prediction problem of the UCTD cable, and the locking of the structure and the displacement mutation phenomenon are well simulated.

Description

Flexible cable vortex-induced vibration analysis method for dragging type thermohaline depth measuring instrument
Technical Field
The invention discloses a flexible cable vortex-induced vibration analysis method for a dragging type thermohaline depth measuring instrument, and belongs to the technical field of auxiliary equipment on ships.
Background
The towed Temperature-salinity-Depth measuring instrument (UCTD) is characterized in that a measuring probe can be towed at the stern during the sailing process to carry out towed measurement. The system mainly comprises a mother ship, a measuring probe towed under water and a cable for connection. In the UCTD measurement system, the cable is used as a main connecting component and plays an important role, on one hand, the cable is a power for the underwater probe to advance along with the mother ship, and on the other hand, the stability and safety of the cable also affect the acquisition of the measurement signal. With the need of ocean exploration, the application of the thermohaline deep profile measuring system is more and more extensive, and especially when the thermohaline deep profile measuring system is applied to the military field, higher requirements are put forward on the equipment, and higher safety and stability are ensured. The water flow through the cable alternately generates vortices, thus generating periodic pressure variations around the cable, and since the cable is of a flexible construction, the alternating water pressure causes the construction to vibrate periodically, i.e. vortex induced vibration. Vortex-induced vibration (VIV) research relates to structural and fluid bidirectional coupling analysis, so that the research method and the phenomenon are complex. The vortex-induced vibration phenomenon is widely concerned on deep sea risers, but the natural frequency of the flexible cable is low, the flexibility is high, and the probability of fatigue damage is low, so that the research on the vortex-induced vibration of the underwater cable hardly causes necessary attention, and the vortex-induced vibration force with small amplitude is often ignored in the mooring and streamer dynamics analysis of a general large-scale floating structure. However, considering the small scale characteristic of the towed thermohaline depth measuring instrument and the requirement of signal anti-interference, the VIV response prediction of the underwater large flexible cable is very important.
The response research is mainly realized by a method for measuring through a specific experimental device, the method has the advantages that the obtained data are more reliable, the obtained phenomenon is more intuitive, but the method for researching the vibration characteristic of the cable rope through the experiment has certain defects, such as high experiment research cost, limitation of experiment structure size by the space size of an experiment field, difficulty in simulation of complex flow profile and the like. In recent years, along with the rapid development of computer computing speed, the CFD method is widely applied to predicting cable vortex-induced vibration responses, most of the CFD research is limited to developing numerical simulation of vortex-induced vibration responses of rigid cables at present, and CFD numerical simulation of vortex-induced vibration responses of long and thin flexible cables is very difficult.
In the selection of the empirical model, for the convenience of describing the vortex-induced vibration phenomenon, it is generally decomposed into two components parallel to the flow velocity and perpendicular to the flow velocity, which are called downstream vibration and transverse vibration, respectively, and the corresponding two fluid force components are called pulsating drag force and vortex-induced lift force, respectively. At present, the research on the vortex-induced vibration of the cable is mainly focused on the influence of longitudinal fluid-solid coupling, while the cable of the UCTD has more complex mechanical properties compared with the rigid cable mentioned in the general research, and the influence of longitudinal and transverse motion on the fluid-solid coupling and the influence of stagnation point and separation point deviation caused by the motion of the cable on the fluid force are considered for the underwater motion attitude. The vortex induced vibration response of the UCTD cable has yet to be further investigated.
Disclosure of Invention
The invention aims to provide a flexible cable vortex-induced vibration analysis method for a dragging type thermohaline depth measuring instrument, and aims to solve the problem that in the prior art, the precision of a flexible cable vortex-induced vibration analysis result is low.
A flexible cable vortex-induced vibration analysis method for a towed thermohaline depth measuring instrument comprises the following steps:
s1, establishing a vortex-induced vibration implicit equation of the cable;
s2, establishing an increment finite element equation of a vortex-induced vibration equation of the cable;
s3, performing loop iterative computation;
and S4, performing analog simulation by using hydrodynamic simulation software FLUENT.
The implicit equation of the vortex-induced vibration of the cable is as follows:
Figure SMS_1
；
wherein ,
Figure SMS_24
adding mass to a fluid>
Figure SMS_25
，/>
Figure SMS_27
For adding a quality factor, is selected>
Figure SMS_29
The fluid is subjected to additional damping in order to,
Figure SMS_30
wherein F is the vortex shedding frequency->
Figure SMS_31
，/>
Figure SMS_32
The pulsating drag force is applied to the surface of the pipe,
Figure SMS_33
，/>
Figure SMS_34
is an average resistance factor>
Figure SMS_35
In order to generate the vortex-induced lift force,
Figure SMS_36
， />
Figure SMS_37
fluid density, D is cable diameter->
Figure SMS_38
Is the vortex shedding frequency, t is the time>
Figure SMS_39
Is the strouhal number, m is the mass of the mooring rope, c is the structural damping, and is ignored during calculation; />
Figure SMS_40
Is the structural rigidity of the cable, N is the axial tension of the cable, x, & gt>
Figure SMS_2
、/>
Figure SMS_3
Respectively, displacement, speed and acceleration, y, in the downstream direction of the cable>
Figure SMS_5
、/>
Figure SMS_8
Respectively, a displacement, a speed and an acceleration in the transverse direction of the cable, are present>
Figure SMS_10
Pulse drag force coefficient, <' > based on the measured value>
Figure SMS_11
The vortex-induced lift coefficient, U, represents the velocity vector of the flow field, U represents the pressure or the velocity vector of the flow field>
Figure SMS_12
Representing the incoming flow velocity, the velocity vector of the v-rope, whose coordinates are ≥ respectively>
Figure SMS_13
and />
Figure SMS_14
I.e. is->
Figure SMS_15
I and j are unit vectors on the x-axis and y-axis, respectively>
Figure SMS_17
Frequency coefficient of the pulsating drag force, non-locking zone>
Figure SMS_19
In the locking zone>
Figure SMS_21
；/>
Figure SMS_23
Is the angle between the relative velocity vector U-v and the velocity vector U>
Figure SMS_26
Is the frequency of the wet mode of the cable, < > is>
Figure SMS_28
In the lock zone, as a mass ratio>
Figure SMS_4
In the non-locking zone>
Figure SMS_6
，/>
Figure SMS_7
，/>
Figure SMS_9
, wherein />
Figure SMS_16
、/>
Figure SMS_18
、/>
Figure SMS_20
、/>
Figure SMS_22
The calculation formula (2) is collectively called as a node incremental load calculation formula.
The increment finite element equation of the vortex-induced vibration equation of the cable is calculated by adopting an iteration method:
Figure SMS_42
, in the formula ,/>
Figure SMS_44
Is a cable quality matrix, is based on>
Figure SMS_46
Is a cable damping matrix, is>
Figure SMS_48
Is a cable stiffness matrix, based on the measured value of the measured value>
Figure SMS_50
Is a node incremental acceleration, based on>
Figure SMS_52
，/>
Figure SMS_54
For node incremental speed, <' > in>
Figure SMS_41
，/>
Figure SMS_43
For the incremental displacement of the node(s),
Figure SMS_45
，/>
Figure SMS_47
in order to incrementally load the load on the node,
Figure SMS_49
；/>
Figure SMS_51
，/>
Figure SMS_53
and n is the total number of nodes.
S3 comprises the following steps: s3.1. Order
Figure SMS_55
Will pick the initial value up and hold>
Figure SMS_56
and />
Figure SMS_57
Sequentially substituting into the node increment load calculation formula to calculate ^ greater than or equal to>
Figure SMS_58
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_59
and />
Figure SMS_60
；
S3.2. Will
Figure SMS_65
and />
Figure SMS_66
Successively substituting in node incremental load computational calculations &>
Figure SMS_67
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_68
and />
Figure SMS_69
When it is->
Figure SMS_70
，/>
Figure SMS_71
And repeating the iteration until the convergence condition is reached:
Figure SMS_61
is satisfied with>
Figure SMS_62
For calculating a precision condition set by a person, in which case->
Figure SMS_63
，/>
Figure SMS_64
S is the number of iterations of the time step;
s3.3. Order
Figure SMS_72
and />
Figure SMS_73
Starting the calculation of the next time step, and calculating the result of the previous time step
Figure SMS_74
and />
Figure SMS_75
Substituting node increment load calculation formula in turn>
Figure SMS_76
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_77
and />
Figure SMS_78
；
S3.4. Will
Figure SMS_80
and />
Figure SMS_81
Substituting node increment load calculation formula in turn>
Figure SMS_83
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_85
and />
Figure SMS_86
When it is->
Figure SMS_87
，/>
Figure SMS_88
And repeating the iteration until the convergence condition is reached: />
Figure SMS_79
When is->
Figure SMS_82
，/>
Figure SMS_84
And S is the iteration number of the time step, and the steps S5 and S6 are repeated until the time reaches the preset calculation duration.
S4, adopting a k-epsilon model suitable for high Reynolds number simulation, wherein the basic control equation of the k-epsilon model is as follows:
continuity equation:
Figure SMS_89
，
momentum vector equation:
Figure SMS_90
；
in the formula
Figure SMS_92
Is a significant viscosity coefficient, and->
Figure SMS_93
μ is a kinetic viscosity coefficient,. Mu.>
Figure SMS_94
Is a turbulent viscosity coefficient, wherein>
Figure SMS_95
，/>
Figure SMS_96
Is constant, generally taken>
Figure SMS_97
，/>
Figure SMS_98
For correcting pressure>
Figure SMS_91
The k and epsilon values can be derived by both processes;
turbulent kinetic energy k equation:
Figure SMS_99
；
turbulent kinetic energy dissipation ratio
Figure SMS_100
The equation: />
Figure SMS_101
；
wherein
Figure SMS_103
、/>
Figure SMS_104
、/>
Figure SMS_105
、/>
Figure SMS_106
Is constant and is->
Figure SMS_107
、/>
Figure SMS_108
、/>
Figure SMS_109
、/>
Figure SMS_102
The value of the shearing generating item G is obtained according to the following formula:
Figure SMS_110
selecting a k-epsilon turbulence module in a mixture multinomial flow model in Fluent software to carry out steady calculation, setting the calculation iteration step length to be 1000 steps, adopting a second-order windward difference format to carry out calculation processing on momentum and turbulence energy, and adopting a SIMPLE algorithm for pressure-velocity coupling to improve the calculation precision.
Compared with the prior art, the invention has the following beneficial effects: the method is researched aiming at the coupling vibration response of the UCTD cable, and a complete coupling vibration model is established for analyzing the nonlinear vortex excitation vibration response prediction problem of the UCTD cable, so that the locking of the structure and the displacement mutation phenomenon are well simulated; the effect of UCTD cable motion on the magnitude and direction of the pulsating drag force and the vortex induced lift force and the properties of the latching and unlatching region fluid force frequencies, i.e. the pulsating drag force frequency versus the force frequency, are described.
Drawings
FIG. 1 is a technical flow diagram of the present invention.
FIG. 2 is a graph of simulated vortex induced vibration transverse response spectra.
Fig. 3 is a lateral displacement time course of the cable.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention are described clearly and completely below, and it is obvious that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A method for analyzing vortex-induced vibration of a flexible cable of a towed thermohaline depth measuring instrument, as shown in fig. 1, includes:
s1, establishing a vortex-induced vibration implicit equation of the mooring rope;
s2, establishing an increment finite element equation of a vortex-induced vibration equation of the mooring rope;
s3, performing loop iterative computation;
and S4, adopting hydrodynamic simulation software FLUENT to perform analog simulation.
The implicit equation of the vortex-induced vibration of the cable is as follows:
Figure SMS_111
；
wherein ,
Figure SMS_129
adding a mass to the fluid>
Figure SMS_131
，/>
Figure SMS_133
For adding a quality factor, is selected>
Figure SMS_136
The fluid is subjected to additional damping in order to,
Figure SMS_138
wherein F is the vortex shedding frequency->
Figure SMS_141
，/>
Figure SMS_142
Pulsating mopThe drag force is generated by the drag force,
Figure SMS_143
，/>
Figure SMS_144
is an average resistance factor>
Figure SMS_145
In order to generate the vortex-induced lift force,
Figure SMS_146
， />
Figure SMS_147
fluid density, D is cable diameter->
Figure SMS_148
For the vortex shedding frequency, t is time->
Figure SMS_149
Is the strouhal number, m is the mass of the mooring rope, c is the structural damping, and is ignored during calculation; />
Figure SMS_150
Is the structural rigidity of the cable, N is the axial tension of the cable, x, & gt>
Figure SMS_112
、/>
Figure SMS_114
Respectively, displacement, speed and acceleration, y, in the downstream direction of the cable>
Figure SMS_117
、/>
Figure SMS_119
Respectively, a displacement, a speed and an acceleration in the transverse direction of the cable, are present>
Figure SMS_121
Pulse drag force coefficient, <' > based on>
Figure SMS_123
The vortex-induced lift coefficient, U, represents the velocity vector of the flow field, U represents the pressure or the velocity vector of the flow field>
Figure SMS_124
Representing the incoming flow velocity, the velocity vector of the v-rope, whose coordinates are ≥ respectively>
Figure SMS_126
and />
Figure SMS_128
I.e. is->
Figure SMS_130
I and j are unit vectors on the x-axis and y-axis, respectively>
Figure SMS_132
Frequency factor of the pulsating drag force, non-locking zone>
Figure SMS_134
Locking zone->
Figure SMS_135
；/>
Figure SMS_137
Is the angle between the relative velocity vector U-v and the velocity vector U>
Figure SMS_139
Is the frequency of the wet mode of the cable, < > is>
Figure SMS_140
In the lock-in zone, in mass ratio>
Figure SMS_113
In the non-locking zone>
Figure SMS_115
，/>
Figure SMS_116
，/>
Figure SMS_118
, wherein />
Figure SMS_120
、/>
Figure SMS_122
、/>
Figure SMS_125
、/>
Figure SMS_127
The calculation formula (2) is collectively called as a node incremental load calculation formula. The simulated vortex-induced vibration transverse response spectrum is shown in fig. 2.
The increment finite element equation of the vortex-induced vibration equation of the cable is calculated by adopting an iteration method:
Figure SMS_152
, in the formula ,/>
Figure SMS_154
Is a cable quality matrix, is based on>
Figure SMS_156
Is a cable damping matrix, is>
Figure SMS_157
Is a cable stiffness matrix, based on the measured value of the measured value>
Figure SMS_159
Is a node incremental acceleration, based on>
Figure SMS_161
，/>
Figure SMS_163
For node incremental speed, <' > in>
Figure SMS_151
，/>
Figure SMS_153
In order to displace the node in increments,
Figure SMS_155
，/>
Figure SMS_158
is node incremental load, greater or lesser>
Figure SMS_160
；
Figure SMS_162
，/>
Figure SMS_164
And n is the total number of nodes.
S3 comprises the following steps: s3.1. Order
Figure SMS_165
Will pick the initial value up and hold>
Figure SMS_166
and />
Figure SMS_167
Successively substituting into node increment load calculation formula, calculating->
Figure SMS_168
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_169
and />
Figure SMS_170
；
S3.2. Will
Figure SMS_172
and />
Figure SMS_173
Substituting node increment load calculation formula in turn>
Figure SMS_175
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_178
and />
Figure SMS_179
When it is->
Figure SMS_180
，/>
Figure SMS_181
And repeating the iteration until the convergence condition is reached:
Figure SMS_171
is satisfied with>
Figure SMS_174
For calculating a precision condition set by a person, in which case->
Figure SMS_176
，/>
Figure SMS_177
S is the number of iterations of the time step;
s3.3. Order
Figure SMS_182
and />
Figure SMS_183
Starting the calculation of the next time step, and calculating the result of the previous time step
Figure SMS_184
and />
Figure SMS_185
Substituting node increment load calculation formula in turn>
Figure SMS_186
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_187
and />
Figure SMS_188
；
S3.4. Will
Figure SMS_189
and />
Figure SMS_191
Substituting node increment load calculation formula in turn>
Figure SMS_194
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure SMS_195
and />
Figure SMS_196
When it is->
Figure SMS_197
，/>
Figure SMS_198
And repeating the iteration until the convergence condition is reached: />
Figure SMS_190
When it is->
Figure SMS_192
，/>
Figure SMS_193
And S is the iteration number of the time step, and the steps S5 and S6 are repeated until the time reaches the preset calculation duration.
S4, adopting a k-epsilon model suitable for high Reynolds number simulation, wherein the basic control equation of the k-epsilon model is as follows:
continuity equation:
Figure SMS_199
，
momentum vector equation:
Figure SMS_200
；
in the formula
Figure SMS_202
Is a significant viscosity coefficient, and->
Figure SMS_203
μ is a kinetic viscosity coefficient,. Mu.>
Figure SMS_204
Is a turbulent viscosity coefficient, wherein>
Figure SMS_205
，/>
Figure SMS_206
Is constant, generally taken>
Figure SMS_207
，/>
Figure SMS_208
For correcting pressure>
Figure SMS_201
The k and epsilon values can be derived by both processes;
turbulent kinetic energy k equation:
Figure SMS_209
；
turbulent kinetic energy dissipation ratio
Figure SMS_210
The equation: />
Figure SMS_211
；
wherein
Figure SMS_213
、/>
Figure SMS_214
、/>
Figure SMS_215
、/>
Figure SMS_216
Is constant and is->
Figure SMS_217
、/>
Figure SMS_218
、/>
Figure SMS_219
、/>
Figure SMS_212
And the value of the shearing generating item G is obtained according to the following formula:
Figure SMS_220
selecting a k-epsilon turbulence module in a mixture multinomial flow model in Fluent software to carry out steady calculation, setting the calculation iteration step length to be 1000 steps, adopting a second-order windward difference format to carry out calculation processing on momentum and turbulence energy, and adopting a SIMPLE algorithm to improve the calculation precision in pressure-velocity coupling, wherein the transverse displacement time course of the cable is shown in figure 3.
The method is researched aiming at the coupling vibration response of the UCTD cable, and a complete coupling vibration model is established for analyzing the nonlinear vortex excitation vibration response prediction problem of the UCTD cable, so that the locking of the structure and the displacement mutation phenomenon are well simulated; the effect of UCTD cable motion on the magnitude and direction of the pulsating drag and vortex induced lift and the nature of the lock-in and unlock-in zone fluid force frequencies, i.e. the relationship of the pulsating drag frequency to the force frequency, are described.
Although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or some or all of the technical features may be equivalently replaced, and the modifications or the replacements may not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (5)

1. A method for analyzing vortex-induced vibration of a flexible cable of a towed thermohaline depth measuring instrument is characterized by comprising the following steps:
s1, establishing a vortex-induced vibration implicit equation of the mooring rope;
s2, establishing an increment finite element equation of a vortex-induced vibration equation of the mooring rope;
s3, performing loop iteration calculation;
and S4, adopting hydrodynamic simulation software FLUENT to perform analog simulation.
2. The method for analyzing the vortex-induced vibration of the flexible cable of the towed thermohaline depth measuring instrument according to claim 1, wherein the implicit equation of the vortex-induced vibration of the cable is as follows:
Figure QLYQS_1
；
wherein ,
Figure QLYQS_20
adding a mass to the fluid>
Figure QLYQS_22
，/>
Figure QLYQS_24
For adding a quality factor, is selected>
Figure QLYQS_26
The fluid is subjected to additional damping in order to,
Figure QLYQS_28
wherein F is the vortex shedding frequency->
Figure QLYQS_31
，/>
Figure QLYQS_32
The pulsating drag force is applied to the surface of the pipe,
Figure QLYQS_33
，/>
Figure QLYQS_34
is an average resistance factor>
Figure QLYQS_35
In order to generate the vortex-induced lift force,
Figure QLYQS_36
， />
Figure QLYQS_37
fluid density, D is cable diameter, and>
Figure QLYQS_38
is the vortex shedding frequency, t is the time>
Figure QLYQS_39
Is the strouhal number, m is the mass of the mooring rope, c is the structural damping, and is ignored during calculation; />
Figure QLYQS_40
Is the structural rigidity of the cable, N is the axial tension of the cable, x, & gt>
Figure QLYQS_2
、/>
Figure QLYQS_4
Respectively, displacement, speed and acceleration, y, in the downstream direction of the cable>
Figure QLYQS_6
、/>
Figure QLYQS_8
Respectively, a displacement, a speed and an acceleration in the transverse direction of the cable, are present>
Figure QLYQS_10
Pulse drag force coefficient, <' > based on the measured value>
Figure QLYQS_12
The vortex-induced lift coefficient, U, represents the velocity vector of the flow field, U represents the pressure or the velocity vector of the flow field>
Figure QLYQS_14
Representing the incoming flow velocity, the velocity vector of the v-rope, whose coordinates are ≥ respectively>
Figure QLYQS_15
and />
Figure QLYQS_16
I.e. is->
Figure QLYQS_19
I and j are unit vectors on the x-axis and y-axis, respectively>
Figure QLYQS_21
Frequency coefficient of the pulsating drag force, non-locking zone>
Figure QLYQS_23
In the locking zone>
Figure QLYQS_25
；/>
Figure QLYQS_27
Is the angle between the relative speed vector U-v and the speed vector U>
Figure QLYQS_29
Is the frequency of the wet mode of the cable, < > is>
Figure QLYQS_30
In the lock-in zone, in mass ratio>
Figure QLYQS_3
In the non-locking zone>
Figure QLYQS_5
，/>
Figure QLYQS_7
，/>
Figure QLYQS_9
, wherein />
Figure QLYQS_11
、/>
Figure QLYQS_13
、/>
Figure QLYQS_17
、/>
Figure QLYQS_18
The calculation formula (2) is collectively called as a node incremental load calculation formula.
3. The towed thermohaline depth gauge flexible cable vortex-induced vibration analysis method according to claim 2, characterized in that the incremental finite element equation of the cable vortex-induced vibration equation is calculated by an iterative method:
Figure QLYQS_42
, in the formula ,/>
Figure QLYQS_44
For the cable quality matrix, in>
Figure QLYQS_46
Is a cable damping matrix, is>
Figure QLYQS_48
In the cable stiffness matrix>
Figure QLYQS_52
In the form of node incremental acceleration>
Figure QLYQS_53
，
Figure QLYQS_54
For node incremental speed, <' > in>
Figure QLYQS_41
，/>
Figure QLYQS_43
In order to displace the node in increments,
Figure QLYQS_45
，/>
Figure QLYQS_47
is node incremental load, greater or lesser>
Figure QLYQS_49
；
Figure QLYQS_50
，/>
Figure QLYQS_51
And n is the total number of nodes.
4. The towed thermohaline depth gauge flexible cable vortex-induced vibration analysis method according to claim 3, wherein S3 comprises: s3.1. Order
Figure QLYQS_55
Will pick the initial value up and hold>
Figure QLYQS_56
and />
Figure QLYQS_57
Sequentially substituting into the node increment load calculation formula to calculate ^ greater than or equal to>
Figure QLYQS_58
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure QLYQS_59
and />
Figure QLYQS_60
；
S3.2. Will
Figure QLYQS_62
and />
Figure QLYQS_64
Substituting node increment load calculation formula in turn>
Figure QLYQS_67
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure QLYQS_68
and />
Figure QLYQS_69
When is->
Figure QLYQS_70
，/>
Figure QLYQS_71
And iterating repeatedly in such a way until the convergence condition is met: />
Figure QLYQS_61
Is satisfied with>
Figure QLYQS_63
For calculating a precision condition set by a person, in which case->
Figure QLYQS_65
，/>
Figure QLYQS_66
S is the number of iterations of the time step;
s3.3. Order
Figure QLYQS_72
and />
Figure QLYQS_73
Starting the calculation of the next time step, and calculating the result of the previous time step
Figure QLYQS_74
and />
Figure QLYQS_75
Substituting node increment load calculation formula in turn>
Figure QLYQS_76
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure QLYQS_77
and />
Figure QLYQS_78
；
S3.4. Will
Figure QLYQS_80
and />
Figure QLYQS_81
Substituting node increment load calculation formula in turn>
Figure QLYQS_83
Then substituting the calculated value into an increment finite element equation and calculating by a time course analysis method>
Figure QLYQS_85
and />
Figure QLYQS_86
When it is->
Figure QLYQS_87
，/>
Figure QLYQS_88
And repeating the iteration until the convergence condition is reached:
Figure QLYQS_79
when it is->
Figure QLYQS_82
，/>
Figure QLYQS_84
And S is the iteration number of the time step, and the steps S5 and S6 are repeated until the time reaches the preset calculation duration.
5. The towed thermohaline depth gauge flexible cable vortex-induced vibration analysis method according to claim 4, characterized in that S4 employs a k-epsilon model suitable for high reynolds number simulation, the basic control equation of the k-epsilon model being as follows:
continuity equation:
Figure QLYQS_89
，
momentum vector equation:
Figure QLYQS_90
；
in the formula
Figure QLYQS_92
Is a significant viscosity coefficient, and->
Figure QLYQS_93
μ is a kinetic viscosity coefficient, and>
Figure QLYQS_94
is a turbulent viscosity coefficient, wherein
Figure QLYQS_95
，/>
Figure QLYQS_96
Is constant, typically taken>
Figure QLYQS_97
，/>
Figure QLYQS_98
For correcting pressure>
Figure QLYQS_91
The k and epsilon values can be derived by both processes;
turbulent kinetic energy k equation:
Figure QLYQS_99
；
turbulent kinetic energy dissipation ratio
Figure QLYQS_100
The equation: />
Figure QLYQS_101
；
wherein
Figure QLYQS_103
、/>
Figure QLYQS_104
、/>
Figure QLYQS_105
、/>
Figure QLYQS_106
Is constant and is->
Figure QLYQS_107
、/>
Figure QLYQS_108
、/>
Figure QLYQS_109
、/>
Figure QLYQS_102
The value of the shearing generating item G is obtained according to the following formula:
Figure QLYQS_110
selecting a k-epsilon turbulence module in a mixture multinomial flow model in Fluent software to carry out steady calculation, setting the calculation iteration step length to be 1000 steps, adopting a second-order windward difference format to carry out calculation processing on momentum and turbulence energy, and adopting a SIMPLE algorithm for pressure-velocity coupling to improve the calculation precision. />
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