CN110598337A - Fluid-solid coupling time domain analysis method for vortex-induced vibration of cylinder - Google Patents
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Abstract
The invention relates to a research method of an ocean deepwater riser, in particular to a fluid-solid coupling time domain analysis method of cylinder vortex-induced vibration. The key points of the invention comprise: calculating the fluid force and the vortex shedding frequency of the non-locking area by using the relative speed of the fluid and the cylinder; under the condition of fluid-solid coupling, the pulsating drag force and the vortex-induced lift force change along with the change of the relative speed of the fluid and the cylinder; the frequency of the fluid force is kept unchanged in the locking region, and the important characteristic of vortex-induced vibration, namely frequency locking, is fully embodied; the locking frequency depends not only on the wet modal frequency of the cylinder, but also on the mass ratio of the cylinder to the fluid. The invention has the following advantages: the influence of the cylinder motion on the magnitude and direction of the pulsating drag force and the vortex-induced lift force is correctly described; the property of the fluid force frequency of the locked zone and the unlocked zone, namely the relationship between the pulsating drag force frequency and the vortex induced lift force frequency is correctly described; the locking phenomenon of vortex shedding frequency is correctly described.
Description
Technical Field
The invention relates to a research method of an ocean deepwater riser, in particular to a fluid-solid coupling time domain analysis method of cylinder vortex-induced vibration.
Background
The time domain analysis method of the vortex-induced vibration of the cylinder mainly comprises a wake flow vibrator model and a force decomposition model, wherein the force decomposition model is used for decomposing fluid force borne by the cylinder which generates the vortex-induced vibration into two components in the flow velocity direction and the vertical flow velocity direction of a flow field and respectively calculating downstream vortex-induced vibration and transverse vortex-induced vibration of the cylinder.
Vortex-induced vibrations are generated when a cylinder is subjected to a fluid in a non-stationary flow field whose flow velocity is not parallel to its axis, the flow causing the vortex-induced vibrations being a component of the flow velocity perpendicular to the axis of the cylinder. Thus, the vortex-induced vibrations of the cylinder are all calculated using a flow velocity perpendicular to the axis of the cylinder, as shown in fig. 2.
For the purpose of describing the vortex-induced vibration of a cylinder, 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. The pulsating drag force is defined as the component of the cylinder surface pressure integral in the direction of flow velocity; the vortex-induced lift is defined as the integral of the cylinder surface pressure in the direction perpendicular to the flow velocity. The above definition holds if the stagnation point of the fluid (see fig. 3 for the definition of the stagnation point) is located on the negative x-axis (see fig. 2) and the separation point is symmetrical to the x-axis (see fig. 3).
The stagnation point position of fig. 3 is the case when the cylinder is streaming (the cylinder is stationary in the flow field), when the cylinder is moving in the flow field non-parallel to the direction of the flow velocity, the direction of the velocity of the fluid relative to the cylinder is no longer the direction of the velocity of the flow field, so that the stagnation point and the separation point will also deviate from the position when the cylinder is streaming, as shown in fig. 4.
Therefore, when the cylinder generates vortex-induced vibration, the pulsating drag force applied to the cylinder is no longer along the x-axis direction, and the vortex-induced lift force is no longer along the y-axis direction. However, the current method defaults that even if the cylinder generates vortex-induced vibration, the pulsating drag force of the cylinder still follows the x-axis direction, and the vortex-induced lift force still follows the y-axis direction. Then, according to the theory of forced vibration, the downstream vortex-induced vibration frequency of the cylinder should be the same as the pulsating drag force frequency, and the transverse vortex-induced vibration frequency should be the same as the vortex-induced lift force frequency. This means that the components of the cylinder vortex-induced vibration in the x-axis and the y-axis respectively have only one frequency peak, and the result of the test is that each component has two frequency peaks, the main peak is the same as the corresponding fluid force frequency, and the secondary peak is the same as the fluid force frequency in the other direction, that is, the main peak of the downstream response frequency is the same as the pulsation drag force frequency, and the secondary peak is the same as the vortex-induced lift force frequency; the main peak of the transverse response frequency is the same as the vortex induced lift frequency and the secondary peak is the same as the pulsating drag frequency, as shown in figure 5.
In summary, the prior art has the following disadvantages:
1. the effect of the lateral motion of the cylinder on the fluid-solid coupling is not considered.
2. The effect of stagnation point and separation point shifts on fluid forces due to cylinder motion is not considered.
3. There is no reaction frequency locking phenomenon-in the locking area, the load frequency remains unchanged. Only the locked and unlocked regions are considered, the difference in the pulsating drag frequency and the vortex induced lift frequency.
4. The effect of the quality ratio on the locking frequency is not taken into account.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a fluid-solid coupling time domain analysis method for vortex-induced vibration of a cylinder.
The technical scheme of the invention is as follows:
the invention provides a fluid-solid coupling time domain analysis method for vortex-induced vibration of a cylinder, which comprises the following steps:
1) establishing vortex-induced vibration equation of cylinder
Wherein:
locking zone (4)
Non-locking zone (5)
In the formula: f. ofD-a pulsating drag force;
fL-vortex induced lift;
ρ -fluid density;
d-cylinder diameter;
-vortex shedding frequency;
t is time;
St-Strouhal number;
m is cylinder mass;
ma-a fluid additional mass;
c-structural damping of the cylinder;
ca-additional damping of the fluid;
k-cylinder stiffness;
x,-displacement, velocity and acceleration of the cylinder in the forward direction;
y,-cylinder lateral displacement, velocity and acceleration;
C′D-a pulsating drag force coefficient;
C′L-vortex induced lift coefficient;
u-velocity vector of the flow field;
v-the velocity vector of the cylinder, the coordinate components of which are eachAndnamely:i and j are unit vectors of the x axis and the y axis respectively;
mu is the frequency coefficient of the pulsating drag force, the non-locking area mu is 1, and the locking area mu is 2;
beta is the included angle between the relative velocity vector U-v and the flow velocity vector U;
fn-the wet modal frequency of the cylinder;
m-mass ratio.
2) Establishing an incremental finite element equation of the formula (1), wherein the formula (1) is an implicit equation, and therefore, an iterative method is adopted for calculation:
in the formula: [ M ] -cylinder mass matrix;
[C] -a cylinder damping matrix;
[K] -a cylinder stiffness matrix;
-node increment additionThe speed of the motor is controlled by the speed of the motor,
-the node incremental speed is calculated,
{ Δ a } -node incremental displacement, { Δ a } - [ Δ x ═1,Δy1,…,Δxn,Δyn]T；
{ Δ F } -node incremental load, { Δ F } - [ Δ F } - ]x1,ΔFy1,…,ΔFxn,ΔFyn]T，
ΔFx＝ΔfDcosβ-ΔfLsinβ,ΔFy＝ΔfDsinβ+ΔfLcosβ；
n is the total number of nodes.
3) Let t be 0 and k be 0, and convert the initial values toAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAnd
4) will be provided withAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndin this case, t is Δ t, and k is 1. And repeating the iteration until the convergence condition is:
and the precision condition that epsilon is set by a calculator is met. At this time, t ═ Δ t, k ═ s, and s is the number of iterations in the time step.
5) Let t be t +. DELTA.t and k be 0, and start the calculation of the next time step. I.e. the result of the previous time stepAnd(s is the number of iterations of the last time step) are sequentially substituted into the formulas (6), (4)/(5), (2) and (3) for calculationThen substituted into formula (7) and calculated by time course analysis methodAnd
6) will be provided withAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndwhen t is t +. DELTA.t, k is 1; and repeating the iteration until the convergence condition is:
is satisfied; at this time, t ═ t +. DELTA.t, k ═ s, s is the number of iterations of the time step, and the two steps 5 and 6 are repeated until the time t reaches the calculation time length preset by the calculator.
The invention achieves the following beneficial effects:
(1) the invention correctly describes the influence of cylinder motion on the magnitude and direction of the pulsating drag force and the vortex induced lift force.
(2) The present invention correctly describes the property of the fluid force frequency of the lock zone and the unlock zone, namely the relationship between the pulsating drag force frequency and the vortex induced lift force frequency.
(3) The present invention correctly describes the locking phenomenon of vortex shedding frequency.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic of a cylinder and flow rate.
Fig. 3 is a schematic view of stagnation and separation points formed by the streaming.
FIG. 4 is a schematic diagram of the stagnation point and the separation point of the cylinder moving along the y-axis.
Fig. 5 is a graph of measured vortex excitation motion response spectra.
Where U is the flow rate and o is the cylinder axis.
Detailed Description
To facilitate an understanding of the present invention by those skilled in the art, specific embodiments thereof are described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a fluid-solid coupling time domain analysis method for vortex-induced vibration of a cylinder, including:
1) s1 establishing vortex-induced vibration equation of cylinder
Wherein:
locking zone (4)
Non-locking zone (5)
In the formula: f. ofD-a pulsating drag force;
fL-vortex induced lift;
ρ -fluid density;
d-cylinder diameter;
-vortex shedding frequency;
t is time;
St-Strouhal number;
m is cylinder mass;
ma-a fluid additional mass;
c-structural damping of the cylinder;
ca-additional damping of the fluid;
k-cylinder stiffness;
x,-displacement, velocity and acceleration of the cylinder in the forward direction;
y,-cylinder lateral displacement, velocity and acceleration;
C′D-a pulsating drag force coefficient;
C′L-vortex induced lift coefficient;
u-velocity vector of the flow field;
v-the velocity vector of the cylinder, the coordinate components of which are eachAndnamely:i and j are unit vectors of the x axis and the y axis respectively;
mu is the frequency coefficient of the pulsating drag force, the non-locking area mu is 1, and the locking area mu is 2;
beta is the included angle between the relative velocity vector U-v and the flow velocity vector U;
fn-the wet modal frequency of the cylinder;
m-mass ratio.
2) S2, establishing an incremental finite element equation of formula (1), and since formula (1) is an implicit equation, calculating by using an iterative method:
in the formula: [ M ] -cylinder mass matrix;
[C] -a cylinder damping matrix;
[K] -a cylinder stiffness matrix;
-the incremental acceleration of the node(s),
-the node incremental speed is calculated,
{ Δ a } -node incremental displacement, { Δ a } - [ Δ x ═1,Δy1,…,Δxn,Δyn]T；
{ Δ F } -node incremental load, { Δ F } - [ Δ F } - ]x1,ΔFy1,…,ΔFxn,ΔFyn]T，
ΔFx＝ΔfDcosβ-ΔfLsinβ,ΔFy＝ΔfDsinβ+ΔfLcosβ；
n is the total number of nodes.
3) S3 compares t with 0 and k with 0, and calculates the initial valueAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAnd
4) s4 is toAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndin this case, t is Δ t, and k is 1. S5 iterates so many times until a convergence condition:
and the precision condition that epsilon is set by a calculator is met. At this time, t ═ Δ t, k ═ s, and s is the number of iterations in the time step.
5) S6 starting the next time step by making t equal to t +. DELTA.t and k equal to 0And (4) calculating. I.e. the result of the previous time stepAnd(s is the number of iterations of the last time step) are sequentially substituted into the formulas (6), (4)/(5), (2) and (3) for calculationThen substituted into formula (7) and calculated by time course analysis methodAnd
6) s7 is toAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndin this case, t + Δ t and k are 1. S8 iterates so many times until a convergence condition:
is satisfied; at this time, t + Δ t, k is s, and s is the number of iterations in the time step. And S9, repeating the steps 5 and 6 until the time t reaches the calculation time preset by the calculator.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (1)
1. A fluid-solid coupling time domain analysis method for cylinder vortex-induced vibration is characterized by comprising the following steps:
1) establishing vortex-induced vibration equation of cylinder
Wherein:
in the formula: f. ofD-a pulsating drag force;
fL-vortex induced lift;
ρ -fluid density;
d-cylinder diameter;
-vortex shedding frequency;
t is time;
St-Strouhal number;
m is cylinder mass;
ma-a fluid additional mass;
c-structural damping of the cylinder;
ca-additional damping of the fluid;
k-cylinder stiffness;
x,-displacement, velocity and acceleration of the cylinder in the forward direction;
y,-cylinder lateral displacement, velocity and acceleration;
C′D-a pulsating drag force coefficient;
C′L-vortex induced lift coefficient;
u-velocity vector of the flow field;
v-the velocity vector of the cylinder, the coordinate components of which are eachAndnamely:
i and j are unit vectors of the x axis and the y axis respectively;
mu is the frequency coefficient of the pulsating drag force, the non-locking area mu is 1, and the locking area mu is 2;
beta is the included angle between the relative velocity vector U-v and the flow velocity vector U;
fn-the wet modal frequency of the cylinder;
m-mass ratio;
2) establishing an incremental finite element equation of the formula (1), wherein the formula (1) is an implicit equation, and therefore, an iterative method is adopted for calculation:
in the formula: [ M ] -cylinder mass matrix;
[C] -a cylinder damping matrix;
[K] -a cylinder stiffness matrix;
-the incremental acceleration of the node(s),
-the node incremental speed is calculated,
{ Δ a } -node incremental displacement, { Δ a } - [ Δ x ═1,Δy1,…,Δxn,Δyn]T；
{ Δ F } -node incremental load, { Δ F } - [ Δ F } - ]x1,ΔFy1,…,ΔFxn,ΔFyn]T，
ΔFx＝ΔfDcosβ-ΔfLsinβ,ΔFy＝ΔfDsinβ+ΔfLcosβ；
n is the total number of nodes;
3) let t be 0 and k be 0, and convert the initial values toAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAnd
4) will be provided withAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndwhen t ═ Δ t, k ═ 1; and repeating the iteration until the convergence condition is:
the accuracy condition that epsilon is set by a calculator is met; at the moment, t is delta t, k is s, and s is the iteration number of the time step;
5) let t be t +. DELTA.t and k be 0, start the calculation of the next time step; i.e. the result of the previous time stepAnd(s is the number of iterations of the last time step) are sequentially substituted into the formulas (6), (4)/(5), (2) and (3) for calculationThen substituted into formula (7) and calculated by time course analysis methodAnd
6) will be provided withAndcalculating by sequentially substituting the formulas (6), (4)/(5), (2) and (3)Then substituted into formula (7) and calculated by time course analysis methodAndwhen t is t +. DELTA.t, k is 1; repeating the above stepsIterating until a convergence condition is met:
is satisfied; at this time, t ═ t +. DELTA.t, k ═ s, s is the number of iterations of the time step, and the two steps 5 and 6 are repeated until the time t reaches the calculation time length preset by the calculator.
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Cited By (3)
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| CN111985138A (en) * | 2020-08-21 | 2020-11-24 | 哈尔滨工业大学（威海） | Flexible structure transverse flow and downstream direction vortex-induced vibration coupling response prediction method |
| CN113758666A (en) * | 2021-08-25 | 2021-12-07 | 浙江大学 | Experiment table and method for testing flow-induced vibration of valve rod of valve |
| CN115859748A (en) * | 2023-02-15 | 2023-03-28 | 山东科技大学 | Flexible cable vortex-induced vibration analysis method for dragging type thermohaline depth measuring instrument |
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| CN111985138A (en) * | 2020-08-21 | 2020-11-24 | 哈尔滨工业大学（威海） | Flexible structure transverse flow and downstream direction vortex-induced vibration coupling response prediction method |
| CN111985138B (en) * | 2020-08-21 | 2023-12-19 | 哈尔滨工业大学（威海） | Flexible structure cross flow and forward flow direction vortex-induced vibration coupling response prediction method |
| CN113758666A (en) * | 2021-08-25 | 2021-12-07 | 浙江大学 | Experiment table and method for testing flow-induced vibration of valve rod of valve |
| CN115859748A (en) * | 2023-02-15 | 2023-03-28 | 山东科技大学 | Flexible cable vortex-induced vibration analysis method for dragging type thermohaline depth measuring instrument |
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