CN113204821B - Method for establishing tandem double-cylinder wake flow oscillation unsteady aerodynamic force mathematical model - Google Patents
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Abstract
The invention provides a method for establishing a tandem double-cylinder wake flow galloping unsteady aerodynamic mathematical model, which comprises the following specific steps of: simulating the wake flow galloping of the tandem double cylinders with the upstream cylinder fixed and the downstream cylinder transversely vibrated by adopting computational fluid dynamics software to obtain a wake flow galloping geometric model of the tandem double cylinders and carrying out grid division on the geometric model; establishing a working condition according to a geometric model, and analyzing a frequency spectrum rule of wake flow galloping aerodynamic force of the tandem double cylinders; establishing a wake flow galloping aerodynamic mathematical model of the tandem bicylinder containing unknown parameters according to the wake flow galloping of the tandem bicylinder with the upstream cylinder fixed and the downstream cylinder transversely vibrated; and fitting a pneumatic damping force parameter and a vortex force parameter in the self-excitation force by adopting a least square parameter identification method based on energy equivalence, and solving a wake flow galloping pneumatic force mathematical model of the tandem double cylinders. And a tandem double-cylinder wake flow galloping model is established, so that the existing engineering construction is facilitated, and the stability and reliability of the engineering construction are improved.
Description
Technical Field
The invention relates to the technical field of double-cylinder building simulation, in particular to a method for establishing a tandem double-cylinder wake flow galloping unsteady aerodynamic mathematical model.
Background
In actual engineering, the buildings are usually pillar structures, such as offshore structures, submarine pipelines, large group chimneys, heat exchange tubes, piers, guys, masts, chemical reaction towers, neighboring skyscrapers and power transmission lines. Fluid force is an important factor for designing the engineering structures, so that understanding of the influence of adjacent column group structures on flow-induced vibration has important engineering practical significance. The double cylinder is an ideal model for researching the flow-induced vibration of the cylinder array due to the simple form. When the two cylinders are brought into close proximity, vortex shedding by the upstream cylinder induces a second cylinder vibration.
The arrangement form of the double cylinders and the distance between the double cylinders are important factors influencing the wake flow galloping. The following designs and experiments exist in the prior art:
the wind tunnel experimental research shows that the amplitude characteristic of the wake flow galloping development stage is approximately linearly increased along with the increase of the converted wind speed. In the study on wake flow interference of double cylinders with equal diameters, the distance between the two cylinders has a great determining effect on the induction of wake flow galloping, a wake flow area flowing through an upstream cylinder forms three areas, namely a short-distance unstabilized area, a stable area and a long-distance unstabilized area, for a downstream conductor, and the wake flow galloping can only occur in a specific interval.
Based on the difference of the fluid form and the relative position between the double cylinders with equal diameters, the influence of the wake flow on the downstream cylinder is divided into two types of wake flow interference and short-distance interference, and L/D =3.5 and T/D =2 are used as two key distances, wherein L is the vertical distance of the two cylinders in the flowing direction, T is the vertical distance of the two cylinders in the transverse flowing direction, and D is the diameter of the cylinders.
The wake flow area of the parallel wires with equal diameters is divided in detail through wind tunnel experiment results, the wire spacing ratio corresponding to a close-distance interference area is 1-1.1, the wire spacing ratio of wake flow galloping phenomenon is 1.1-3.8, and the wire spacing ratio exceeding 3.8 is a long-distance interference area.
Experiments were performed on the elastically supported downstream cylinder (allowing only transverse oscillations) behind the fixed cylinder, and wake galloping phenomena with increasing amplitude with reduced wind speed were observed at tandem distances L/D = 3-5.6. Full-scale experiments are carried out by researchers on the double cylinders with the same diameter and the same serial arrangement interval of L/D =4.3-8.7 by using wind tunnels, and the wake flow galloping phenomenon of the downstream cylinder is observed when the L/D =4.3 and disappears when the L/D = 6.5. Meanwhile, researchers perform wind tunnel tests on double cylinders with different spacing ratios, and 7 flow-induced vibration response modes are divided according to whether the upstream cylinder and the downstream cylinder generate relaxation vibration and vortex-induced resonance or not.
Wake vibrations, a complex vibration form common in engineering, have been studied and analyzed by many researchers for other factors affecting its aerodynamic properties and vibration response, in addition to the effects of pitch.
For example, the disturbance galloping of the elastically supported cylindrical slings under the wake was studied experimentally, and it was found that the critical wind speed of the wake galloping increases with the increase of the Sc number.
The influence of the structural damping and the aerodynamic damping of the transmission line on the wake vibration response is systematically studied, for example.
For example, the wake flow galloping of the downstream guy cable is researched through a wind tunnel test, and the result shows that the vibration response of the downstream guy cable under the effect of the wake flow can be influenced by the Reynolds number and the wind speed. These research results have some promotion effect on revealing the characteristics of wake flow galloping, but the mechanism and the reason for the wake flow galloping are not deeply revealed.
The traditional wake flow test focuses on characteristics such as structural response, surface pressure distribution and flow field form, and researches on non-constant relaxation force nonlinear characteristics are less. In the prior art, the earliest design is based on a quasi-stationary constant hypothesis, and a linear analysis method is used for judging the possibility of the wake flow galloping instability of the power transmission line.
Secondly, based on the wave transfer theory, a transfer matrix method is adopted to carry out research on the vibration characteristics of wake flow galloping of the split conductor, and the wake flow galloping vibration response is predicted.
Based on the two research results, researchers perfect a quasi-stationary normal mechanical model of wake flow galloping and establish a nonlinear vibration equation of the wake flow galloping. The spatial distribution rule of the average aerodynamic coefficient of the wake flow transmission line is measured by adopting a wind tunnel test method, and the amplitude of the wake flow galloping is obtained by adopting a Runge-Kutta method for solving. Although the wake flow galloping model has certain rationality, the wake flow galloping model is established on the basis of a calibration and constancy theory, and the aerodynamic model is still constant and has certain limitations. Therefore, it is necessary to establish a non-linear mathematical model of unsteady aerodynamic force based on unsteady aerodynamic force time-course data.
Disclosure of Invention
In view of the above, the invention provides a method for establishing a tandem double-cylinder wake flow galloping unsteady aerodynamic mathematical model, which is used for establishing a tandem double-cylinder wake flow galloping model, and is beneficial to the existing engineering construction and improving the stability and reliability of the engineering construction.
The technical scheme is as follows:
a method for establishing a tandem double-cylinder wake flow oscillation unsteady aerodynamic force mathematical model is characterized by comprising the following specific steps:
s1: adopting computational fluid dynamics software to simulate the wake flow galloping of the tandem bicylinder with the upstream cylinder fixed and the downstream cylinder transversely vibrating under the condition that the flow direction interval L/D =4 to obtain a wake flow galloping geometric model of the tandem bicylinder and perform mesh division on the geometric model;
wherein, L is the vertical distance of the two cylinders in the flow direction, and D is the diameter of the cylinder;
s2: establishing at least one working condition according to the wake flow galloping geometric model of the tandem bicylinder, and analyzing the frequency spectrum law of the wake flow galloping aerodynamic force of the tandem bicylinder;
s3: according to the wake flow galloping of the tandem double cylinders with the upstream cylinder fixed and the downstream cylinder transversely vibrated in the step S1, establishing a wake flow galloping aerodynamic mathematical model of the tandem double cylinders with unknown parameters; the aerodynamic force is expressed in two forms of self-excitation force and vortex-induced force;
s4: fitting a pneumatic damping force parameter and a vortex force parameter in self-excitation force by adopting a least square parameter identification method based on energy equivalence to obtain a final wake flow relaxation vibration pneumatic force mathematical model of a tandem double cylinder;
s5: and (4) comparing the wake flow galloping force mathematical model of the tandem double cylinders obtained in the step (S4).
Through the construction of the steps, under the condition that wake flow galloping is most likely to occur when L/D =4, double cylinders are simulated by adopting Computational Fluid Dynamics (CFD), and the wake flow galloping of the double cylinders with fixed front columns and transversely vibrating tandem rear columns is simulated when the flow direction of double-cylinder wind is upward. And (3) providing a mathematical parameter expression of the aerodynamic force model, and obtaining the final tandem bicylinder wake flow galloping aerodynamic force mathematical model after solving unknown parameters. After verification and comparison, the model has good rationality and high accuracy, and is beneficial to more stable construction projects in the later construction process.
In a further technical scheme, in step S1, in the wake flow relaxation vibration of the tandem bicylinder, the lateral vibration of the downstream cylinder is solved by using a wake flow cylinder lateral vibration equation, where the downstream cylinder lateral vibration equation is:
wherein m is the downstream cylinder mass; y, y,
And
respectively displacement, velocity and acceleration perpendicular to the flow direction; c and k are divided into structural damping and rigidity constants; f y Is the vertical force to which the cylinder is subjected.
In the invention, when the simulation working condition is set, the unsteady incompressible RANS equation of the two-dimensional cylindrical streaming is as follows:
wherein u i And p represents the average velocity and average pressure, respectively; ρ is the fluid density; mu is molecular viscosity; s ij Is the mean stress tensor;
is the reynolds stress tensor.
A shear stress transfer model, namely an SST-k omega model, is used during the setting of the simulation working condition. The model involves two transport equations, turbulence energy and dissipation ratio equations, in which an Unsteady Separation Algorithm (USA) is employed. For a model, see the article: two-equation two-dimensional interference modules for engineering applications [ J ] Aiaa journal.1994,32.
The velocity expression is processed by a SIMPLE algorithm when being coupled, and a second-order implicit scheme is adopted for the unstable condition. A second order implicit scheme is used for the convection terms in the k- ω transfer equation and the momentum equation.
Further, in step S1, in the wake flow galloping geometric model of the tandem double cylinders, a rectangular calculation domain is 60D × 40d, and D is a cylinder diameter;
in the rectangular calculation domain, the distance between the center of the upstream cylinder and the inlet boundary is 25D, and the distance between the center of the downstream cylinder and the outlet boundary is 31D;
in the rectangular calculation domain, setting an entrance boundary as a speed entrance boundary condition;
in the rectangular calculation domain, setting a basin outlet boundary as a pressure outlet boundary condition;
in the rectangular calculation domain, the upper and lower boundaries are defined as symmetric boundary conditions;
in the rectangular calculation domain, the upstream cylinder and the downstream cylinder are both cylinders, and the surfaces of the cylinders are non-slip walls.
Further, in step S1, a non-uniform quadrilateral structured grid is used when the geometric model is subjected to grid division, and surface grids of the upstream and downstream cylindrical surfaces are O-shaped grids;
because the flow field near the wall surface changes violently, the grid near the wall surface of the cylinder is encrypted and the height of the first layer of grid on the wall surface is controlled when the geometric model is subjected to grid division, so that the height y of the first layer of grid on the wall surface of the upstream cylinder and the downstream cylinder is enabled to be high + Is less than 1; to reduce the influence of the grid on the numerical calculation.
To simulate cylindrical unsteady vibrations, the interfaces 27D and 34D downstream of the inlet in the rectangular computational domain employ a sliding mesh technique, with the mesh being updated using dynamic tiling at the lateral boundaries.
Still further, in step S3, the vortex vibration and the relaxation vibration force are mainly self-excited force, and the vortex-excited force acts only in the vibration development stage. The vortex-induced forces of two frequencies in the wake relaxation vibration force exist all the time in each stage of vibration, and the component ratio is large, so that the consideration is needed. And (3) according to the upstream cylinder fixed and downstream cylinder transverse vibration wake flow relaxation vibration equation in the upstream cylinder fixed and downstream cylinder transverse vibration wake flow relaxation vibration of the tandem double cylinders mentioned in the step (S1), obtaining the wake flow relaxation vibration aerodynamic force mathematical model of the tandem double cylinders with unknown self-excitation force parameters and unknown vortex excitation force parameters.
The mathematical model of the tandem bicylinder wake flow galloping aerodynamic force containing the unknown self-excitation force parameters and the unknown vortex-excitation force parameters is as follows:
wherein, F y Is the total aerodynamic force of the structure;
is an expression for self-excited force, wherein self-excited force is caused by self-excited vibration as a result of mutual feedback of force and motion state of the system, so that such self-excited vibration force can be generally described as a function of structure speed and displacement;
wherein, F v (f v ) Is an expression of vortex-induced force; the vortex-induced forces are caused by vortex shedding by the upstream cylinder or by the downstream cylinder itself, and the vortex shedding frequency is indicative of vortex shedding, and thus the surface pressure caused by vortex shedding can be generally described as a function of the vortex shedding frequency.
in the formula g ij Are pneumatic parameters. g 00 This term is associated with y and describing the response state
All have no relation, and this term can be considered as a static term, which has no effect on the wake galloping dynamic response, so that it is ignored. From the previous aerodynamic spectra, it can be seen that the contribution to the entire frequency component is large, substantially within the 5 th order frequency multiplication, so that the excess y in the Taylor expansion can be set 5 And
the term (1) is truncated.
Based on the principle of energy equivalence,
the medicine consists of three parts: the aerodynamic damping force term (changing the damping of the structure), the aerodynamic stiffness force term (changing the stiffness of the structure) and the pure force term (neither changing the damping of the structure nor the stiffness of the cylinder).
Then, the self-excitation force can be written as
Neglecting pure force terms, the dimensionless self-exciting force expression is as follows
For lateral vibrations, the aerodynamic stiffness term only slightly changes the structural frequency, and may not be considered, and the above formula can be reduced to:
ρ is the fluid density, U is the incoming flow velocity, D is the cylinder diameter, y is the displacement perpendicular to the flow direction,
velocity perpendicular to the flow direction; alpha (alpha) ("alpha") 01 Is a first-order dimensionless aerodynamic damping parameter, alpha 03 For three-order dimensionless aerodynamic damping parameters, alpha 05 Five-order dimensionless pneumatic damping parameters which are unknown parameters;
first, there are two maximum vortex shedding frequencies f v1 And f v2 And since the vortex-induced force is always closely related to the vortex shedding frequency, it can be first expressed as a function of the vortex shedding frequency, and the expression for the vortex-induced force can be changed as follows:
due to the phase angle in the above formula
And
are all in need ofThe parameters to be fitted and solved can be rewritten after dimensionless as follows:
in the formula: delta 11 ,δ 12 ,δ 21 ,δ 22 The parameter is a dimensionless vortex-induced force parameter;
S t1 is the upstream cylindrical Steyr number; s t2 Is the downstream cylindrical Steyr number; ρ is the fluid density; u shape r To convert wind speed, f s Is the natural frequency; v. of 11 v 12 v 21 v 22 Respectively representing the parameters of the vortex-induced force before dimensionless;
therefore, a simplified model of wake relaxation forces considering only stable amplitudes can be expressed as follows:
still further, the specific content of step S5 is:
s51: according to the obtained wake flow galloping aerodynamic mathematical model of the tandem double cylinders, the displacement and the speed are inversely calculated by adopting a Runge-Kutta method;
s52: parameter name defining downstream cylinder energy:
ω s is the natural circular frequency of the downstream cylinder;
W s (t) isThe accumulated work of the downstream cylinder structure damping at the current time consumes negative energy;
W a,v (t) the accumulated work of the downstream cylinder aerodynamic damping force and vortex-induced force at the current time is back-calculated by using the fitted parameters, the supplied energy is positive,
E e (t) the mechanical energy of the downstream cylinder at the current time, wherein the mechanical energy comprises kinetic energy and potential energy;
s53: substituting the displacement and the speed obtained in the step S51 into formulas (1) - (3), and reconstructing to obtain the accumulated work of the pneumatic damping force and the vortex-induced force;
s54: and comparing the accumulated work of the pneumatic damping force and the vortex-induced force with the simulation value of the wake flow galloping geometric model of the tandem bicylinder.
Compared with the prior art, the invention has the beneficial effects that:
the tandem bicylinder wake flow galloping mathematical model of unsteady aerodynamic force is established, is suitable for bicylinder building wake flow galloping, has wide application range, provides favorable data support for the building mechanics analysis containing bicylinders later, and can be reversely deduced and exercised after analysis and comparison and mutually support with other approved prior art. The correctness and reliability thereof are determined.
Drawings
FIG. 1 is a schematic diagram of computational domains and boundary conditions;
FIG. 2 is a diagram illustrating the result of the division of the computational domain mesh and the cylindrical wall mesh;
FIG. 3 is a schematic of a grid dependency study;
FIG. 4 is a schematic diagram of the results of dimensionless amplitude variation with reduced wind speed for three simulated conditions;
FIG. 5 shows the wake galloping development phase U r =9.179 corresponding to the schematic diagram of the variation of the lift force spectrum in the whole time course;
FIG. 6 shows the wake flow galloping development phase U r Schematic diagram of lift spectrum variation corresponding to full time course of 14.49;
FIG. 7 is a schematic diagram of lift spectra for different reduced wind speeds under a single operating condition;
FIG. 8 shows S of the upstream and downstream cylinders t Number following U r Schematic diagram of variation rule of (1);
FIG. 9 is a view showing a state in U r Schematic diagrams of lift force work and mechanical energy time courses reconstructed by the pneumatic parameters of = 13.889;
FIG. 10 is a view showing a structure in U r Schematic diagram of displacement time-course effect of pneumatic parameter reconstruction of = 13.889;
FIG. 11 is a view showing a structure in U r The parameters of the =12.08 vortex-induced force and the aerodynamic damping force are reconstructed to respectively obtain a working curve and a reconstructed force curve schematic diagram;
FIG. 12 is a view showing a structure in U r Schematic diagram of effect of each aerodynamic force on displacement =12.08
FIG. 13 is a view showing a structure in U r Schematic diagrams of self-excitation force and vortex-induced force time courses reconstructed by the parameters of = 12.08;
FIG. 14 is a view showing a position at U r =12.08 parametric reconstructed lift versus simulated value schematic;
FIG. 15 is a schematic diagram of a dimensionless vortex-induced magnitude parameter for a first operating condition based on lift time course fitting;
FIG. 16 is a schematic diagram of the result of aerodynamic parameter identification;
FIG. 17 is a schematic diagram of aerodynamic model predicted amplitude versus simulated value;
FIG. 18 is a flow chart of the series bi-cylinder wake flow galloping unsteady aerodynamic mathematical model building steps;
FIG. 19 is a flow chart of the comparative steps of a wake flow galloping mathematical model of tandem bicylinders.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
Referring to fig. 1-12, a method for establishing a tandem bicylinder wake flow galloping unsteady aerodynamic mathematical model is provided, which comprises the following specific steps:
s1: adopting computational fluid dynamics software to simulate the wake flow galloping of the tandem bicylinder with the upstream cylinder fixed and the downstream cylinder transversely vibrating under the condition that the flow direction interval L/D =4 to obtain a wake flow galloping geometric model of the tandem bicylinder and perform mesh division on the geometric model;
wherein, L is the vertical distance of the two cylinders in the flow direction, and D is the diameter of the cylinder;
when L/D =4, wake flow galloping is easy to occur;
in this embodiment, the unsteady incompressible RANS equation for two-dimensional cylindrical streaming is as follows:
wherein u is i And p represents the average velocity and average pressure, respectively, ρ is the fluid density, μ is the molecular viscosity, S ij In order to be the mean stress tensor,
is the reynolds stress tensor.
The present invention uses a shear stress transfer model, i.e., the SST-k ω model. The model involves two transport equations, namely the turbulence energy and dissipation ratio equations. In which a non-steady state separation algorithm (USA) is used. For a model, see the article: "two-evaluation-theory modules for engineering applications [ J ]. Aiaa journal.1994,32.
The velocity expression is processed by a SIMPLE algorithm when being coupled, and a second-order implicit scheme is adopted for the unstable condition. A second order implicit scheme is used for the convection terms in the k- ω transfer equation and the momentum equation.
In step S1, in the wake relaxation oscillation of the tandem bicylinder, the lateral vibration of the downstream cylinder is solved by using a wake cylinder lateral vibration equation, where the downstream cylinder lateral vibration equation is:
wherein m is the downstream cylinder mass; y, y,
And
respectively displacement, velocity and acceleration perpendicular to the flow direction; c and k are divided into structural damping and rigidity constants; f y Is the vertical force to which the cylinder is subjected.
In this embodiment, in step S1, in the wake flow galloping geometric model of the tandem bicylinder, as can be seen from fig. 1, the adopted rectangular calculation domain is 60D × 40d, and D is the diameter of the cylinder; the maximum blockage rate is 5%, in the rectangular calculation domain, the distance from the center of the upstream cylinder to the inlet boundary is 25D, and the distance from the center of the downstream cylinder to the outlet boundary is 31D; in the rectangular calculation domain, setting an entrance boundary as a speed entrance boundary condition; in the rectangular calculation domain, setting the boundary of a basin outlet as a pressure outlet boundary condition; in the rectangular calculation domain, the upper and lower boundaries are defined as symmetric boundary conditions; in the rectangular calculation domain, the upstream cylinder and the downstream cylinder are both cylinders, and the surfaces of the cylinders are non-slip walls.
As can be seen from fig. 2, in this embodiment, the non-uniform quadrilateral structured mesh is used for meshing the geometric model, and the surface meshes of the upstream and downstream cylindrical surfaces are O-shaped meshes;
when the geometric model is subjected to meshing division, the meshes of the near wall surface of the cylinder are encrypted and the height of the first layer of meshes of the wall surface is controlled, so that the height y of the first layer of meshes of the upstream and downstream cylinder wall surfaces + Less than 1; the influence of the grid on numerical calculation is reduced. In the rectangular computational domain, to simulate cylindrical unsteady vibrations, the interfaces 27D and 34D downstream of the entrance employ a sliding mesh technique, with dynamic tiling to update the mesh at the lateral boundaries. For the simulation of the cylindrical streaming with periodicity, the time step is at least 100 time steps in a unit period.
In order to verify the feasibility of the numerical simulation method and the accuracy of the meshing strategy, the aerodynamic characteristics of two fixed cylinders are simulated, and the simulated cylinder distance is selected to be L/D =6,T/D =0-4. Reynolds number Re =3.48 × 10 4 Re = ρ UD/μ, ρ being the fluid density,mu is the viscosity coefficient of the fluid, U is the incoming flow velocity, and is in the subcritical range, and the turbulence is 1%. By ensuring y + Less than 1, and the height of the first layer of the grid on the wall surface is 0.013mm. The method comprises the steps of encrypting grids around a cylinder, selecting 4 grids with different numbers for simulation, and comparing the obtained average resistance coefficient with the existing experimental result, wherein the details are shown in documents Wu W, huang S, barltrop N].Applied Ocean Research.2002,24(5):287-297.
The number of grids is from 1.3X 10 5 Increased to 3.7 × 10 5 As can be seen from fig. 3 (a), the average drag coefficient is close to the current experimental result. As can be seen in fig. 3 (b), the resistance coefficient time course curve appears to converge. When the number of grids is from 3.7 x 10 5 Increase to 4.5X 10 5 And in the process, the average resistance coefficients corresponding to the two grids are very close, the resistance coefficient time-course curves are almost overlapped in a stable section, and the grids have no great influence on the result. Therefore, the subsequent dynamic cylinder simulation is selected and used as 3.7 multiplied by 10 5 The grid division strategy with the same grid number is that the height y of the first layer of grid of the cylindrical wall surface + The growth rate of o-block near the wall surface is 1.05, and the growth rate of grids in other areas is 1.08. The aspect ratio of the grid is controlled to be within 5, and the sizes of the adjacent grids are close.
S2: establishing at least one working condition according to the wake flow galloping geometric model of the tandem bicylinder, and analyzing the frequency spectrum law of the wake flow galloping aerodynamic force of the tandem bicylinder;
as shown in Table 1, three working conditions are included, and based on the three working conditions, wake flow galloping simulation of the working conditions with small Sc number of three downstream cylinders is carried out.
TABLE 1 data sheet of characteristic parameters and Sc number of wake flow cylinders under three simulation conditions
| Mass ratio m * | Damping ratio ζ | Natural frequency f s | Sc | |
| Working condition one | 84.35 | 0.24％ | 6.9Hz | 3.39 |
| Working condition two | 113.24 | 0.28％ | 6.78Hz | 4 |
| Three working conditions | 142.12 | 0.26％ | 7.12Hz | 4.64 |
In Table 1, mass ratio m * ＝m/ρD 2 ， m Is the mass per unit length of the downstream cylinder. Sc =2m * (2 pi ζ), ξ is the structural damping ratio of the downstream cylinder itself. Converted wind speed U r ＝U/f s D。
The scattergram of dimensionless amplitude A/D with the converted wind speed for three simulated conditions is shown in detail in FIG. 4.
U of working condition one r =9.179 and U r The displacement time course curve and the displacement time course frequency spectrum of the corresponding full time course of the =14.49 are shown in detail in the figure5 and 6.
Wherein, as can be seen from fig. 5, U r =9.179, the corresponding displacement time-course spectrum behaves very roughly, and the motion behaves like quasi-periodic motion.
As can be seen from fig. 6, when U is r In the time range of =14.49, the corresponding displacement time course spectrum shows smoother, and the motion shows similar periodic motion.
The division point of the two displacement phenomena is converted into wind speed U r =13.5, and the wind speed in the simulation results happens to be the wind speed at which the amplitude increase rate is in accordance with the quasi-stationary theorem, which is illustrated in U r In the case of =9.179, the wind speed range is affected more by the unsteady effect, and is in the case of U r The unsteady effect of =14.49 is gradually decreasing. The main frequency of the displacement time-range frequency spectrum corresponding to each wind speed is the natural vibration frequency, but the main frequency also contains other weak frequencies.
Wake flow galloping development stage U r =9.179 and U r The lift spectrum corresponding to 14.49 can be seen in fig. 7:
the aerodynamic lift spectral content based on all wind speeds comprises mainly 7 main frequencies;
the self-oscillation frequency of 1-5 orders is kept unchanged along with the increase of the converted wind speed, and aerodynamic force corresponding to the self-oscillation frequency of 1-5 orders is defined as self-oscillation force;
the 6-7 order frequency increases linearly with the reduced wind speed, and the aerodynamic force corresponding to the 6-7 order frequency is defined as the vortex-induced force.
S3: according to the wake flow galloping of the tandem double cylinders with the upstream cylinder fixed and the downstream cylinder transversely vibrated in the step S1, establishing a wake flow galloping aerodynamic mathematical model of the tandem double cylinders with unknown parameters; the aerodynamic force is expressed in two forms of self-excitation force and vortex-excitation force;
in step S3, the mathematical model of the wake flow galloping aerodynamic force of the tandem bicylinder with unknown parameters is:
the unknown parameters include: unknown self-excitation force parameters and unknown vortex-induced force parameters;
F y is the total aerodynamic force of the structure;
for expression of self-excitation force, F v (f v ) Is an expression of vortex-induced force;
in the formula g ij Are pneumatic parameters. g 00 This term is associated with the sum of y describing the response state
All have no relation, and this term can be considered as a static term, which has no effect on the wake galloping dynamic response, so that it is ignored. From the previous aerodynamic spectra, it can be seen that the contribution to the entire frequency component is large, substantially within the 5 th order frequency multiplication, so that the excess y in the Taylor expansion can be set 5 And
the term (1) is truncated.
Based on the principle of energy equivalence,
the medicine consists of three parts: the aerodynamic damping force term (changing the damping of the structure), the aerodynamic stiffness force term (changing the stiffness of the structure) and the pure force term (neither changing the damping of the structure nor the stiffness of the cylinder)。
Then, the self-excitation force can be written as
Neglecting pure force terms, the dimensionless self-excited force expression is as follows
For lateral vibrations, the aerodynamic stiffness term only slightly changes the structural frequency, and may not be considered, and the above formula can be reduced to:
ρ is the fluid density, U is the incoming flow velocity, D is the cylinder diameter, y is the displacement perpendicular to the flow direction,
velocity perpendicular to the flow direction; alpha is alpha 01 For a first-order dimensionless aerodynamic damping parameter, alpha 03 For three-order dimensionless aerodynamic damping parameters, alpha 05 Five-order dimensionless pneumatic damping parameters which are unknown parameters;
due to the maximum of two vortex shedding frequencies f v1 And f v2 Since the vortex-induced force is always closely related to the vortex shedding frequency, it can first be expressed as a function of the vortex shedding frequency, and the expression for the vortex-induced force can be written as:
two cylindrical stethods Ha Er number S t Referring to fig. 8 in detail, it can be seen that the stohar number of the upstream and downstream cylinders is not a constant value. The upstream cylinder is a stationary static cylinder having a Stockholr number of0.209 is slowly reduced to 0.184 in a nearly linear way, and the wind speed is increased continuously, so that the wind speed tends to be stable; the downstream cylinder is a dynamic cylinder, the Strouhal value of which is slowly increased from 0.302 and finally levels to 0.315, which is consistent with the trend of the amplitude changing along with the wind speed. The Stockhol number of the upstream static cylinder and the downstream dynamic cylinder is slowly changed along with the converted wind speed, but is not a constant value so as to ensure that the formula
The calculation of the eddy-induced force has higher prediction accuracy, and the change of the Stockholr number must be accurately considered.
And because in the expression of the vortex-induced force, the phase angle
And
all are parameters to be fitted and solved, and can be rewritten as follows after dimensionless:
in the formula: delta 11 ,δ 12 ,δ 21 ,δ 22 The parameter is a dimensionless vortex-induced force parameter;
S t1 is the upstream cylindrical Steyr number; s t2 Is the downstream cylindrical Stockholr number; ρ is the fluid density; u shape r To convert wind speed, f s Is the natural frequency; v. of 11 v 12 v 21 v 22 Respectively representing the parameters of the vortex-induced force before dimensionless;
then it is possible to obtain:
the downstream cylinder provides energy input or consumption for the downstream cylinder in the vibration process, and the downstream cylinder has pneumatic damping force, structure self-damping and vortex-induced force.
S4: fitting a pneumatic damping force parameter and a vortex force parameter in self-excitation force by adopting a least square parameter identification method based on energy equivalence to obtain a final wake flow relaxation vibration pneumatic force mathematical model of a tandem double cylinder;
among them, the least square parameter identification method based on energy equivalence is described in detail in Gao G Z, zhu L. Nonlinear chemical model of unsettling university force on a rectangle 2.
S5: and (5) comparing the wake flow galloping force mathematical models of the tandem bicylinders obtained in the step (S4).
The specific content of the step S5 is as follows:
s51: according to the obtained wake flow galloping aerodynamic mathematical model of the tandem double cylinders, the displacement and the speed are inversely calculated by adopting a Runge-Kutta method;
s52: parameter names defining downstream cylinder energy:
ω s is the natural circular frequency of the downstream cylinder;
W s (t) is the accumulated work of the structure damping of the downstream cylinder at the current time, and the consumed energy is a negative value;
W a,v (t) the accumulated work of the aerodynamic damping force and the vortex-induced force of the downstream cylinder at the current time is inversely calculated by utilizing the fitted parameters, and the energy is provided to be a positive value;
E e (t) is a downstream cylinderMechanical energy of previous time, including kinetic energy and potential energy;
s53: substituting the displacement and the speed obtained in the step S51 into formulas (1) - (3), and reconstructing to obtain the accumulated work of the pneumatic damping force and the vortex-induced force;
s54: and comparing the accumulated work of the pneumatic damping force and the vortex-induced force with the simulation value of the wake flow galloping geometric model of the tandem bicylinder.
By U r For example, =13.889, see fig. 9, for a comparison relationship between each work and mechanical energy, details of a comparison between a displacement time course reconstructed from parameters obtained by fitting and a displacement time course calculated by Fluent are shown in fig. 10.
The actually calculated lift accumulation working time course curve is well matched with the reconstruction of the fitting parameters, the maximum relative error of the two is only 3 percent, and E e (t) the time course curve is also related to W a,v (t)-W s (t) are very close, the maximum relative error between the two is only 6%, and the error of the "jitter" of these work curves comes from the high-frequency oscillation components neglected by the relaxation force model, and the contribution of these components is almost negligible.
For the displacement time course curve of fig. 10, although there is an obvious phase difference between the two curves, which is neglected the pneumatic stiffness term, the fit degree between the amplitude and the development process of the parametric reconstruction relaxation-oscillation displacement curve and the Fluent calculation is better, and the maximum relative error between the two curves is only 1%.
However, referring to FIG. 11, at U r In the case of 12.08, the vortex-induced force reconstructed based on the parameters of the energy-equivalent least-squares fitting is only 1.1 times of the aerodynamic damping force, which is contrary to the FFT-transformed spectrum (vortex shedding frequency is very high). Since the cumulative work of the vortex-induced force in the whole galloping vibration process is almost 0, the contribution of the downstream cylindrical motion energy is mainly derived from the pneumatic damping force term. When the method is based on energy fitting, the vortex-induced force is insensitive to the energy, so that the parameter error of the fitted vortex-induced force term is large. In conclusion, the pneumatic damping force term plays an absolute control role in energy input of the downstream cylinder, the vortex-induced force term parameter is insensitive to energy change, and fitting of the vortex-induced force term parameter in the model needs to be started from the force, namelyAnd fitting the force with the aerodynamic damping force term subtracted in the lift force by directly utilizing a least square method, and then carrying out rule analysis on vortex-induced force parameters.
The aerodynamic damping parameters are obtained by energy fitting, and the other aerodynamic parameters are obtained by fitting from the force itself. In order to more clearly illustrate the effect of the vortex-induced force term and the aerodynamic stiffness term on the displacement, the displacement reconstructed by using the parameter of the formula (4) is compared with the displacement reconstructed by only not including the parameter of the vortex-induced force term and the parameter of the aerodynamic stiffness term. As shown in fig. 12, in the wake flow relaxation development time period 14s-14.6s, the maximum relative error of the displacement amplitude of the parameter reconstruction of the equation (4) and the model parameter reconstruction which only does not include the aerodynamic stiffness force term is 1%, but a large phase difference exists between the two, while the displacement amplitude of the parameter reconstruction of the equation (4) is higher than that of the parameter reconstruction which only does not include the vortex-induced force term, but a small phase difference exists between the two. In the wake flow galloping stable time period of 41s-41.6s, the phase difference relationship of the three is consistent with the wake flow galloping development time period, the difference is that the displacement amplitudes of the three are close to each other, and the maximum relative error is 1%. This shows that in the whole stage of wake flow galloping, the pneumatic stiffness force term does not change the displacement amplitude, and only plays a role of changing the phase difference, which is consistent with the calculation result of the equivalent linear system; the vortex-shedding forced vibration of the vortex-induced force term only provides a large perturbation effect in the early stage of the galloping, so that the galloping is rapidly developed, but the final steady-state displacement amplitude is not influenced, and the assumption that the work of the vortex-induced force in the whole vibration process is close to 0 is also verified.
The time-course curve of the parameter reconstruction force is shown in fig. 13, the peak value of the vortex-induced force is 0.151N, the peak value of the self-excitation force (aerodynamic damping force + aerodynamic stiffness force + pure force) is only 0.032N, the value of the self-excitation force is only 20% of the vortex-induced force, the vortex-induced force is consistent with the phenomenon that the vortex-induced frequency is very high, and the vortex-induced force parameter obtained by directly fitting the force per se can better reflect the actual vibration state of the downstream cylinder. As can be seen from fig. 14, the force reconstructed only from the aerodynamic damping force parameter and the vortex force parameter is matched with the lift force of the Fluent simulation result very well in both phase and amplitude, and the error is about 4% at most, which indicates that the proportion of the aerodynamic stiffness force component to the pure force component in the self-excitation force is very small and can be ignored. In conclusion, the simplified model of the component equation (5) of the vortex-induced force term and the aerodynamic damping force term has sufficient accuracy regardless of the prediction of the steady-state displacement or the aerodynamic force.
See FIG. 15. Vortex shedding of the upstream cylinder causes a dimensionless vortex-induced force parameter amplitude A of the downstream cylinder surface v1 The amplitude A of the dimensionless vortex-induced force parameter of the surface is caused by vortex shedding of the downstream cylinder per se along with the nearly linear decrease of the increase of the reduced wind speed v2 The small fluctuation state with the value of 0.195-0.205 is always kept, which shows that in the wake flow galloping interval range, the influence of the vortex shedding effect of the upstream cylinder on the surface pressure generated by the downstream cylinder along with the increase of the converted wind speed begins to weaken, the excitation effect of the vortex shedding of the downstream cylinder per se along with the change of the converted wind speed shows better regularity, and the prominence of the laws has great promotion effect on the establishment of a vortex-induced force parameter model.
The verification of the model is as follows:
the pneumatic parameters of the working condition I have obvious regularity, and the force and displacement reconstructed through the parameters are close to the analog value. If the wake flow galloping aerodynamic model is applied to engineering prediction, the wake flow galloping aerodynamic model does not only have applicability to the working condition one, the values of the aerodynamic parameters are only related to the structural appearance and the converted wind speed at fixed intervals, and the values of the aerodynamic parameters have similar aerodynamic rules to the working condition two and the working condition three, so that dimensionless aerodynamic parameters are identified for the cylindrical wake flow galloping of the working condition two and the working condition three, and the distribution rules of the dimensionless aerodynamic parameters are observed so as to obtain a commonly-adapted mathematical prediction formula.
The identification result of the dimensionless parameters of the vortex-induced force and the dimensionless parameters of the aerodynamic damping force is shown in fig. 16. As can be seen from fig. 16, the dimensionless aerodynamic damping parameters and the dimensionless eddy-induced force parameters of the three operating conditions have a certain discreteness, because a certain approximation is adopted for the wake relaxation force when the aerodynamic model is established, and the contributions of higher-order nonlinear frequency and some random eddy-induced frequency components to the aerodynamic force are ignored. However, the parameters in the graph generally fall into one area, and the objective regularity is more definite and similar. The pneumatic parameters of the three working conditions present relatively similar rules,the aerodynamic force model established based on the first working condition is applicable to the first working condition only, and the universality and the applicability of the wake flow galloping aerodynamic force model are proved to be certain. Alpha is alpha 01 、α 03 、α 05 、A v1 And A v2 Corresponding polynomials can be selected according to the scattered point rule for fitting, the pneumatic parameters of the three working conditions can be averaged in the fitting process, and then the average values are utilized for carrying out least square fitting. As shown in fig. 16, the fitted curve is smooth, and the aerodynamic rules of the dimensionless parameters with the converted wind speed can be embodied to a greater extent. First order dimensionless pneumatic damping parameter alpha 01 Third order dimensionless pneumatic damping parameter alpha 03 And a five-order dimensionless aerodynamic damping parameter α 05 At U r The wind speed is understood to be a divided wind speed affected by the unsteady effect, and the wind speed has a leap characteristic when the value of = 13.5. Therefore, the dimensionless aerodynamic damping parameters for these two phases will be analyzed separately next.
U r ＜13.5：α 01 And alpha 05 Decreases with increasing reduced wind speed, and alpha 03 Is increased with increasing reduced wind speed. Alpha is alpha 01 Constant positive value in wind speed range, which shows the aerodynamic damping force
Always negative damping, and three-order dimensionless aerodynamic damping parameter alpha 03 And a five-order dimensionless aerodynamic damping parameter α 05 The wind speed range has positive or negative values,
is to change from negative damping to positive damping,
it changes from positive damping to negative damping, but a 03 And alpha 05 Almost any reduced wind speed always maintains a positive-negative opposite state. At a specific reduced wind speed, the nonlinear total damping of the downstream cylinder is negative in the oscillation starting stage,
and
or
And
and the downstream cylinder continuously transmits the energy required by the development of the galloping vibration amplitude, so that the downstream cylinder wake flow galloping amplitude is continuously increased. As the amplitude of the wave is continuously increased,
or
And the positive damping provided by the structure is gradually increased until the positive damping is equal to the negative damping, the nonlinear total damping of the downstream cylinder is 0, the energy absorbed by the downstream cylinder from the air is the same as the dissipated energy, the downstream cylinder is in a dynamic balance state and performs limit ring oscillation with stable amplitude, and alpha is 03 And alpha 05 The mutual restriction of the wind speed generator is a key factor for ensuring that the wake flow galloping has amplitude self-limitation at each wind speed. From the whole galloping development wind speed range, the unsteady effect of the coupling of the vortex vibration and the galloping is not only reflected on a displacement time course curve, but also obviously reflected on the strong change of dimensionless pneumatic parameters along with the converted wind speed.
U r ＞13.5：α 01 、α 03 And alpha 05 Is much smaller than U r A dimensionless aerodynamic damping parameter value of < 13.5, alpha as a whole 01 、α 03 And alpha 05 Finally, the wind speed increases to a constant value, and alpha 03 The steady value is a positive damping value close to 0, and alpha 05 The steady value is a negative damping value close to 0, both still maintaining opposite signs. Although all dimensionless aerodynamic damping parameters are still varying with reduced wind speed within a small range, this is trueThe amplitude of the time variation is already very small, which marks the weakening of the unsteady effect, and as the reduced wind speed continues to increase, all parameters approach a constant, so that the amplitude curve can be explained to show a linear increase in the following.
After the dimensionless pneumatic parameters of the working condition I, the working condition II and the working condition III are scattered and integrated into a unified usable mathematical formula, an unsteady mechanical equation can be brought in to directly predict the unsteady wake flow oscillation amplitude of the working condition I, the working condition II and the working condition III. As can be seen from fig. 17, the maximum relative error between the predicted amplitudes for the first, second, and third conditions and the amplitude calculated by Fluent simulation is mainly concentrated in a small amplitude region in a small range, because the amplitudes are very sensitive to small difference changes. Working condition one maximum amplitude difference in the whole prediction interval is 0.06D in U r The maximum relative error is only 7% when the error is more than 9, the maximum amplitude difference of the working condition II in the whole prediction interval is 0.06D r The maximum relative error of > 9.45 is only 10%. Although the relative error fluctuation of the working condition III in the whole prediction interval is large, the maximum amplitude difference is only 0.07D, and the result shows that the influence of the self characteristics of the cylinder on the dimensionless pneumatic parameters of the pneumatic model cannot be completely eliminated through the average method fitting, but the amplitude prediction results of most of the converted wind speed ranges of the three working conditions are ideal and meet the engineering precision requirement. And the prediction result can restore the objective law that the amplitude changes along with the reduced wind speed to a greater extent, such as the slope change of the amplitude increase under the low reduced wind speed, the platform for transitioning from the unsteady vibration to the steady vibration, the near-linear increase of the amplitude under the high reduced wind speed and the like. In conclusion, the wake flow galloping aerodynamic model has high applicability to the second working condition and the third working condition, and meanwhile, the reliability and the accuracy of the prediction result of the aerodynamic model are further verified.
In summary, by the above method, the following can be obtained:
(1) Establishing a new unsteady aerodynamic force nonlinear model aiming at the low Sc number wake flow relaxation vibration. Aerodynamic forces are expressed in the form of a sum of self-excited and vortex-excited forces. Based on the energy equivalence principle, the self-excitation force is divided into a pneumatic damping force, a pneumatic rigidity force and a pure force item, wherein the pneumatic damping item plays a main role in steady-state amplitude of wake flow galloping. Vortex-induced forces are expressed as a function of the vortex shedding frequency of the structure. In combination with the aerodynamic force spectrum of the stationary upstream and downstream cylinders, the vortex-induced forces contain mainly the vortex shedding frequencies of the two cylinders.
(2) The pneumatic parameters of the pneumatic force model are identified, and the reliability of the identification method and the accuracy of the pneumatic parameters are verified. The vortex-induced force provides a disturbance only in the early stages of vibration, and contributes almost 0 energy throughout the vibration process. The least square method based on energy equivalence is selected for fitting of the pneumatic damping parameters, and the least square method fitting is performed on the time course of the slave force for fitting of the vortex-excited force parameters. The results of the fitting parameters, namely the force acting reconstruction, the displacement reconstruction and the force reconstruction, show that the parameter identification of the pneumatic damping item and the parameter identification of the vortex-induced item have high identification precision, and the reliability and the accuracy of the fitting method adopted for the pneumatic parameters are verified.
(3) And summarizing the common rule of the dimensionless pneumatic parameters of the working condition I, the working condition II and the working condition III. The pneumatic parameters identified by the working condition I, the working condition II and the working condition III generally fall into one area, and show clear and similar objective laws, and the laws can be expressed into a unified practical formula by using specific mathematical expressions. The amplitude results of the three working conditions are predicted by a formula to be ideal, the engineering precision requirement is met, and the objective rule that the amplitude changes along with the reduced wind speed can be restored to a large extent, such as the slope change of the amplitude increase under the low reduced wind speed, the platform for transferring from the unsteady vibration to the steady vibration, the near-linear increase of the amplitude under the high reduced wind speed and the like. The wake flow galloping unsteady aerodynamic nonlinear model has higher applicability to the second working condition and the third working condition, and the reliability and the accuracy of the model prediction result are further verified.
Finally, it should be noted that the above-mentioned description is only a preferred embodiment of the present invention, and those skilled in the art can make various similar representations without departing from the spirit and scope of the present invention.
Claims (6)
1. A method for establishing a tandem double-cylinder wake flow oscillation unsteady aerodynamic force mathematical model is characterized by comprising the following specific steps:
s1: adopting computational fluid dynamics software to simulate the wake flow galloping of the tandem bicylinder with the upstream cylinder fixed and the downstream cylinder transversely vibrating under the condition that the flow direction interval L/D =4 to obtain a wake flow galloping geometric model of the tandem bicylinder and perform mesh division on the geometric model;
wherein, L is the vertical distance of the two cylinders in the flow direction, and D is the diameter of the cylinder;
s2: establishing at least one working condition according to the wake flow galloping geometric model of the tandem bicylinder, and analyzing the frequency spectrum law of the wake flow galloping aerodynamic force of the tandem bicylinder;
s3: according to the wake flow galloping of the tandem double cylinders with the upstream cylinder fixed and the downstream cylinder transversely vibrated in the step S1, establishing a wake flow galloping aerodynamic mathematical model of the tandem double cylinders with unknown parameters; the aerodynamic force is expressed in two forms of self-excitation force and vortex-induced force;
s4: fitting a pneumatic damping force parameter and a vortex force parameter in self-excitation force by adopting a least square parameter identification method based on energy equivalence to obtain a final wake flow relaxation vibration pneumatic force mathematical model of a tandem double cylinder;
s5: according to the wake flow galloping aerodynamic force mathematical model of the tandem double cylinders obtained in the step S4, the displacement and the speed are inversely calculated by adopting a Runge-Kutta method, the accumulated work of the pneumatic damping force and the vortex-induced force is reconstructed and calculated, and the accumulated work of the pneumatic damping force and the vortex-induced force is compared with the wake flow galloping aerodynamic force mathematical model of the tandem double cylinders;
in a step S3, the process is carried out,
the mathematical model of the wake flow galloping aerodynamic force of the tandem bicylinder containing unknown parameters is as follows:
the unknown parameters include: unknown self-excitation force parameters and unknown vortex-induced force parameters;
F y total aerodynamic force for the structure;
for expression of self-excitation force, F v (f v ) Is an expression of vortex-induced force;
wherein the content of the first and second substances,
ρ is the fluid density, U is the incoming flow velocity, D is the cylinder diameter, y is the displacement perpendicular to the flow direction,
velocity perpendicular to the flow direction; alpha is alpha 01 For a first-order dimensionless aerodynamic damping parameter, alpha 03 For three-order dimensionless aerodynamic damping parameters, alpha 05 Five-order dimensionless pneumatic damping parameters which are unknown parameters;
in the formula:
δ 11 ,δ 12 ,δ 21 ,δ 22 the parameter is a dimensionless vortex-induced force parameter;
S t1 is the upstream cylindrical Steyr number; s t2 Is the downstream cylindrical Stockholr number; ρ is the fluid density; u shape r To convert wind speed, f s Is the natural frequency; v. of 11 v 12 v 21 v 22 Respectively representing the parameters of the vortex-induced force before dimensionless;
namely:
2. the method for establishing the tandem bicylinder wake flow relaxation oscillation unsteady aerodynamic mathematical model as claimed in claim 1, wherein: in step S1, in the wake relaxation oscillation of the tandem bicylinder, the lateral vibration of the downstream cylinder is solved by using a wake cylinder lateral vibration equation, where the downstream cylinder lateral vibration equation is:
wherein m is the downstream cylinder mass; y, y,
And
respectively displacement, velocity and acceleration perpendicular to the flow direction; c and k are respectively a structural damping constant and a rigidity constant; f y Is the vertical force to which the cylinder is subjected.
3. The method for establishing the tandem bicylinder wake flow relaxation oscillation unsteady aerodynamic mathematical model as claimed in claim 1, wherein: in the step S1, in the wake flow galloping geometric model of the tandem double cylinders, the adopted rectangular calculation domain is 60D multiplied by 40D, and D is the diameter of the cylinder;
in the rectangular calculation domain, the distance between the center of the upstream cylinder and the inlet boundary is 25D, and the distance between the center of the downstream cylinder and the outlet boundary is 31D;
in the rectangular calculation domain, setting an entrance boundary as a speed entrance boundary condition;
in the rectangular calculation domain, setting a basin outlet boundary as a pressure outlet boundary condition;
in the rectangular calculation domain, the upper and lower boundaries are defined as symmetric boundary conditions;
in the rectangular calculation domain, the upstream cylinder and the downstream cylinder are both cylinders, and the surfaces of the cylinders are non-slip walls.
4. The method for establishing the tandem bicylinder wake flow relaxation oscillation unsteady aerodynamic mathematical model as claimed in claim 1, wherein: in the step S1, non-uniform quadrilateral structured grids are adopted when the geometric model is subjected to grid division, and O-shaped grids are adopted as surface grids on the surfaces of an upstream cylinder and a downstream cylinder;
when the geometric model is subjected to meshing division, the meshes of the near wall surface of the cylinder are encrypted and the height of the first layer of meshes of the wall surface is controlled, so that the height y of the first layer of meshes of the upstream and downstream cylinder wall surfaces + ＜1；
In the rectangular computational domain, the interfaces 27D and 34D downstream of the entry employ a sliding mesh technique, with dynamic tiling being used to update the mesh at the lateral boundaries.
5. The method for establishing the tandem bicylinder wake flow relaxation oscillation unsteady aerodynamic mathematical model as claimed in claim 1, wherein: in step S2, the spectral law of the wake flow galloping aerodynamic force of the tandem bicylinder obtained by analysis is as follows:
the aerodynamic lift spectral component based on all wind speeds consists mainly of 7 dominant frequencies;
the self-oscillation frequency of 1-5 orders is kept unchanged along with the increase of the converted wind speed, and aerodynamic force corresponding to the self-oscillation frequency of 1-5 orders is defined as self-excitation force;
the 6-7 order frequency increases linearly with the reduced wind speed, and the aerodynamic force corresponding to the 6-7 order frequency is defined as the vortex-induced force.
6. The method for establishing the tandem bicylinder wake flow relaxation oscillation unsteady aerodynamic mathematical model as claimed in claim 1, wherein: the specific content of the step S5 is as follows:
s51: according to the obtained wake flow galloping aerodynamic mathematical model of the tandem double cylinders, the displacement and the speed are inversely calculated by adopting a Runge-Kutta method;
s52: parameter names defining downstream cylinder energy:
ω n is the natural circular frequency of the downstream cylinder;
ξ n the damping ratio of the structure of the downstream cylinder is adopted;
W s (t) is the accumulated work of the structure damping of the downstream cylinder at the current time, and the consumed energy is a negative value;
W a,v (t) the accumulated work of the downstream cylinder aerodynamic damping force and vortex-induced force at the current time is back-calculated by using the fitted parameters, the supplied energy is positive,
E e (t) the mechanical energy of the downstream cylinder at the current time, wherein the mechanical energy comprises kinetic energy and potential energy;
s53: substituting the displacement and the speed obtained in the step S51 into formulas (1) - (3), and reconstructing to obtain the accumulated work of the pneumatic damping force and the vortex-induced force;
s54: and comparing the accumulated work of the pneumatic damping force and the vortex-induced force with the simulation value of the wake flow galloping geometric model of the tandem bicylinder.
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