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CN114896911A - Variable-stiffness-based bluff body structure vortex-induced vibration numerical simulation method and system - Google Patents

Variable-stiffness-based bluff body structure vortex-induced vibration numerical simulation method and system Download PDF

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CN114896911A
CN114896911A CN202210590432.7A CN202210590432A CN114896911A CN 114896911 A CN114896911 A CN 114896911A CN 202210590432 A CN202210590432 A CN 202210590432A CN 114896911 A CN114896911 A CN 114896911A
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靖洪淼
于春放
张记涛
刘庆宽
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Abstract

本发明涉及一种基于变刚度的钝体结构涡激振动数值模拟方法及系统，具体涉及桥梁与结构风工程技术领域。所述方法包括根据刚度值、待模拟钝体结构的质量和阻尼比，计算刚度值对应的折减风速和阻尼值；根据刚度值、质量和刚度值对应的阻尼值，确定待模拟钝体结构的钝体结构动力方程；根据待模拟钝体结构的钝体结构动力方程和刚度值对待模拟钝体结构进行模拟，得到待模拟钝体结构在刚度值下的振幅；根据各刚度值对应的折减风速和各刚度值下的振幅确定待模拟钝体结构的涡激振动性能。本发明降低了网格划分工作量，显著提高了数值模拟的效率。

Figure 202210590432

The invention relates to a vortex-induced vibration numerical simulation method and system of a bluff body structure based on variable stiffness, in particular to the technical field of bridge and structural wind engineering. The method includes calculating the reduced wind speed and damping value corresponding to the stiffness value according to the stiffness value, the mass and damping ratio of the bluff body structure to be simulated; and determining the bluff body structure to be simulated according to the stiffness value, the damping value corresponding to the mass and stiffness value The dynamic equation of the bluff body structure to be simulated is simulated according to the dynamic equation of the bluff body structure and the stiffness value of the bluff body structure to be simulated, and the amplitude of the bluff body structure to be simulated under the stiffness value is obtained; The decelerating wind speed and the amplitude at each stiffness value determine the vortex-induced vibration performance of the bluff body structure to be simulated. The invention reduces the grid division workload and significantly improves the efficiency of numerical simulation.

Figure 202210590432

Description

一种基于变刚度的钝体结构涡激振动数值模拟方法及系统A method and system for numerical simulation of vortex-induced vibration of bluff body structures based on variable stiffness

技术领域technical field

本发明涉及桥梁与结构风工程技术领域，特别是涉及一种基于变刚度的钝体结构涡激振动数值模拟方法及系统。The invention relates to the technical field of bridge and structural wind engineering, in particular to a vortex-induced vibration numerical simulation method and system of a bluff body structure based on variable stiffness.

背景技术Background technique

基于CFD(Computational Fluid Dynamics)的钝体结构涡激振动数值模拟是检验桥梁与结构中构件涡振性能的重要手段。根据传统基于风洞试验的钝体结构涡振性能测验方法，钝体结构弹性系统的质量、刚度和阻尼比保持不变，通过改变来流风速实现涡振性能测验。为了满足上述测试要求，在基于CFD的数值模拟中，一般根据来流风速、钝体结构尺寸和气流运动粘度，计算得到一组来流风速对应的雷诺数。针对上述雷诺数，需要将计算域进行网格划分，特别是钝体壁面附近网格必须满足一定的厚度要求。这意味着，不同的雷诺数对应不同的网格，且需要重新划分。Numerical simulation of vortex-induced vibration of bluff body structures based on CFD (Computational Fluid Dynamics) is an important means to test the vortex vibration performance of bridges and structures. According to the traditional vortex vibration performance test method of bluff body structure based on wind tunnel test, the mass, stiffness and damping ratio of the elastic system of the bluff body structure remain unchanged, and the vortex vibration performance test is realized by changing the incoming wind speed. In order to meet the above test requirements, in the numerical simulation based on CFD, a set of Reynolds numbers corresponding to the incoming wind speed are generally calculated according to the incoming wind speed, the structure size of the bluff body and the airflow kinematic viscosity. For the above Reynolds number, the computational domain needs to be meshed, especially the meshes near the wall of the bluff body must meet certain thickness requirements. This means that different Reynolds numbers correspond to different meshes and need to be re-divided.

因此，这样有两个问题：(1)不同雷诺数时需要重新划分计算域网格，而不同的来流风速对应不同雷诺数，需要重新划分计算域网格，工作量巨大；(2)较大的来流风速意味着较高的雷诺数，而较高的雷诺数需要划分细密的计算域网格，网格量的增加必然会带来计算量的增大。基于上述原因，钝体结构涡激振动CFD数值模拟需要消耗大量的人工和计算机，难以满足实际工程需要。Therefore, there are two problems: (1) the computational domain grid needs to be re-divided when the Reynolds number is different, and the computational domain grid needs to be re-divided for different incoming wind speeds corresponding to different Reynolds numbers, which is a huge workload; A large incoming wind speed means a higher Reynolds number, and a higher Reynolds number requires a fine meshing of the computational domain. Based on the above reasons, the CFD numerical simulation of vortex-induced vibration of bluff body structures requires a lot of labor and computers, which is difficult to meet the needs of practical engineering.

发明内容SUMMARY OF THE INVENTION

本发明的目的是提供一种基于变刚度的钝体结构涡激振动数值模拟方法及系统，降低了网格划分工作量，显著提高了数值模拟的效率。The purpose of the present invention is to provide a vortex-induced vibration numerical simulation method and system of a bluff body structure based on variable stiffness, which reduces the workload of mesh division and significantly improves the efficiency of numerical simulation.

为实现上述目的，本发明提供了如下方案：For achieving the above object, the present invention provides the following scheme:

一种基于变刚度的钝体结构涡激振动数值模拟方法，包括：A vortex-induced vibration numerical simulation method for a bluff body structure based on variable stiffness, comprising:

对待模拟钝体结构设置不同的刚度值；Set different stiffness values for the bluff body structure to be simulated;

对于任意一个刚度值，根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值；For any stiffness value, according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated, calculate the reduced wind speed and damping value corresponding to the stiffness value;

根据刚度值、所述待模拟钝体结构的质量和所述刚度值对应的阻尼值，确定所述待模拟钝体结构的钝体结构动力方程；Determine the bluff body structure dynamic equation of the bluff body structure to be simulated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping value corresponding to the stiffness value;

根据所述待模拟钝体结构的钝体结构动力方程和所述刚度值对所述待模拟钝体结构进行模拟，得到所述待模拟钝体结构在所述刚度值下的振幅；The bluff body structure to be simulated is simulated according to the bluff body structure dynamic equation of the bluff body structure to be simulated and the stiffness value, and the amplitude of the bluff body structure to be simulated under the stiffness value is obtained;

根据各刚度值对应的折减风速和各刚度值下的振幅确定所述待模拟钝体结构的涡激振动性能。The vortex-induced vibration performance of the bluff body structure to be simulated is determined according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value.

可选的，所述根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值，具体包括：Optionally, calculating the reduced wind speed and damping value corresponding to the stiffness value according to the stiffness value, the mass of the to-be-simulated bluff body structure, and the damping ratio of the to-be-simulated bluff body structure, specifically including:

根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率；Calculate the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated;

基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速；Calculate the reduced wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value;

根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值。The damping value corresponding to the stiffness value is calculated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated.

可选的，所述根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率，具体为：Optionally, calculating the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated is specifically:

根据公式

Figure BDA0003664513210000021
计算所述刚度值对应的振动频率，其中，Ki为设置的第i个刚度值，fi为设置的第i个刚度值对应的振动频率，M为待模拟钝体结构的质量。According to the formula
Figure BDA0003664513210000021
Calculate the vibration frequency corresponding to the stiffness value, where K i is the set ith stiffness value, f i is the vibration frequency corresponding to the set ith stiffness value, and M is the mass of the bluff body structure to be simulated.

可选的，所述根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值，具体为：Optionally, calculating the damping value corresponding to the stiffness value according to the stiffness value, the mass of the to-be-simulated bluff body structure, and the damping ratio of the to-be-simulated bluff body structure, specifically:

根据公式

Figure BDA0003664513210000022
计算所述刚度值对应的阻尼值，其中，Ki为设置的第i个刚度值，Ci为设置的第i个刚度值对应的阻尼值，M为待模拟钝体结构的质量，ζ为待模拟钝体结构的阻尼比。According to the formula
Figure BDA0003664513210000022
Calculate the damping value corresponding to the stiffness value, where K i is the set i-th stiffness value, C i is the damping value corresponding to the i-th stiffness value set, M is the mass of the bluff body structure to be simulated, and ζ is The damping ratio of the bluff body structure to be simulated.

可选的，所述基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速，具体为：Optionally, calculating the reduced wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value, specifically:

根据公式

Figure BDA0003664513210000023
计算所述刚度值对应的折减风速，其中，Uri表示第i个刚度值对应的折减风速，U0表示来流风速，fi为设置的第i个刚度值对应的振动频率，B表示待模拟钝体结构的参考尺寸。According to the formula
Figure BDA0003664513210000023
Calculate the reduced wind speed corresponding to the stiffness value, where Ur i represents the reduced wind speed corresponding to the ith stiffness value, U 0 represents the incoming wind speed, f i is the vibration frequency corresponding to the set ith stiffness value, B Indicates the reference dimension of the bluff body structure to be simulated.

一种基于变刚度的钝体结构涡激振动数值模拟系统，包括：A vortex-induced vibration numerical simulation system for a bluff body structure based on variable stiffness, comprising:

刚度设置模块，用于对待模拟钝体结构设置不同的刚度值；The stiffness setting module is used to set different stiffness values for the bluff body structure to be simulated;

折减风速和阻尼值计算模块，用于对于任意一个刚度值，根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值；The reduced wind speed and damping value calculation module is used for any stiffness value, according to the stiffness value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated, calculate the corresponding stiffness value The reduced wind speed and damping value of ;

钝体结构动力方程确定模块，用于根据刚度值、所述待模拟钝体结构的质量和所述刚度值对应的阻尼值，确定所述待模拟钝体结构的钝体结构动力方程；a bluff body structure dynamic equation determination module, configured to determine the bluff body structure dynamic equation of the bluff body structure to be simulated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping value corresponding to the stiffness value;

振幅确定模块，用于根据所述待模拟钝体结构的钝体结构动力方程和所述刚度值对所述待模拟钝体结构进行模拟，得到所述待模拟钝体结构在所述刚度值下的振幅；an amplitude determination module, configured to simulate the bluff body structure to be simulated according to the bluff body structure dynamic equation of the bluff body structure to be simulated and the stiffness value, so as to obtain the bluff body structure to be simulated under the stiffness value amplitude;

涡激振动性能模拟模块，用于根据各刚度值对应的折减风速和各刚度值下的振幅确定所述待模拟钝体结构的涡激振动性能。The vortex-induced vibration performance simulation module is used to determine the vortex-induced vibration performance of the bluff body structure to be simulated according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value.

可选的，所述折减风速和阻尼值计算模块包括：Optionally, the reduced wind speed and damping value calculation module includes:

振动频率计算单元，用于根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率；a vibration frequency calculation unit, configured to calculate the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated;

折减风速计算单元，用于基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速；a reduced wind speed calculation unit, configured to calculate the reduced wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value;

阻尼值计算单元，用于根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值。A damping value calculation unit, configured to calculate a damping value corresponding to the stiffness value according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated.

可选的，所述振动频率计算单元包括：Optionally, the vibration frequency calculation unit includes:

振动频率计算子单元，用于根据公式

Figure BDA0003664513210000031
计算所述刚度值对应的振动频率，其中，Ki为设置的第i个刚度值，fi为设置的第i个刚度值对应的振动频率，M为待模拟钝体结构的质量。Vibration frequency calculation subunit, used to calculate according to the formula
Figure BDA0003664513210000031
Calculate the vibration frequency corresponding to the stiffness value, where K i is the set ith stiffness value, f i is the vibration frequency corresponding to the set ith stiffness value, and M is the mass of the bluff body structure to be simulated.

可选的，所述阻尼值计算单元包括：Optionally, the damping value calculation unit includes:

阻尼值计算子单元，用于根据公式

Figure BDA0003664513210000032
计算所述刚度值对应的阻尼值，其中，Ki为设置的第i个刚度值，Ci为设置的第i个刚度值对应的阻尼值，M为待模拟钝体结构的质量，ζ为待模拟钝体结构的阻尼比。Damping value calculation subelement for
Figure BDA0003664513210000032
Calculate the damping value corresponding to the stiffness value, where K i is the set i-th stiffness value, C i is the damping value corresponding to the i-th stiffness value set, M is the mass of the bluff body structure to be simulated, and ζ is The damping ratio of the bluff body structure to be simulated.

可选的，所述折减风速计算单元包括：Optionally, the reduced wind speed calculation unit includes:

折减风速计算子单元，用于根据公式

Figure BDA0003664513210000041
计算所述刚度值对应的折减风速，其中，Uri表示第i个刚度值对应的折减风速，U0表示来流风速，fi为设置的第i个刚度值对应的振动频率，B表示待模拟钝体结构的参考尺寸。Reduced wind speed calculation subunit, used to calculate according to the formula
Figure BDA0003664513210000041
Calculate the reduced wind speed corresponding to the stiffness value, where Ur i represents the reduced wind speed corresponding to the ith stiffness value, U 0 represents the incoming wind speed, f i is the vibration frequency corresponding to the set ith stiffness value, B Indicates the reference dimension of the bluff body structure to be simulated.

根据本发明提供的具体实施例，本发明公开了以下技术效果：本发明根据刚度值、待模拟钝体结构的质量和阻尼比，计算刚度值对应的折减风速和阻尼值；根据刚度值、质量和刚度值对应的阻尼值，确定待模拟钝体结构的钝体结构动力方程；根据待模拟钝体结构的钝体结构动力方程和刚度值对应的折减风速对待模拟钝体结构进行模拟，得到待模拟钝体结构在刚度值下的振幅；根据各刚度值对应的折减风速和各刚度值下的振幅确定待模拟钝体结构的涡激振动性能，降低了网格划分工作量，显著提高了数值模拟的效率。According to the specific embodiment provided by the present invention, the present invention discloses the following technical effects: the present invention calculates the reduced wind speed and damping value corresponding to the stiffness value according to the stiffness value, the mass and damping ratio of the bluff body structure to be simulated; The damping value corresponding to the mass and stiffness values is used to determine the dynamic equation of the bluff body structure to be simulated; The amplitude of the bluff body structure to be simulated under the stiffness value is obtained; the vortex-induced vibration performance of the bluff body structure to be simulated is determined according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value, which reduces the workload of meshing, significantly Improve the efficiency of numerical simulation.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative labor.

图1为本发明实施例提供的一种基于变刚度的钝体结构涡激振动数值模拟方法的流程图；1 is a flowchart of a method for numerical simulation of vortex-induced vibration of a bluff body structure based on variable stiffness provided by an embodiment of the present invention;

图2是采用本发明实施例提供的基于变刚度的钝体结构涡激振动数值模拟方法计算得到的宽高比为4:1的柱体，在雷诺数为1000，阻尼比为1.9％时的“振幅-折减风速”结果图。Fig. 2 is a cylinder with an aspect ratio of 4:1 calculated by using the numerical simulation method for vortex-induced vibration of a bluff body structure based on variable stiffness provided by an embodiment of the present invention, when the Reynolds number is 1000 and the damping ratio is 1.9% "Amplitude-Reduced Wind Speed" result graph.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

本发明实施例提供的基于变刚度的钝体结构涡激振动数值模拟方法，通过改变建立的钝体结构动力方程中的刚度值，而质量保持不变，从而使钝体结构具有不同的振动频率，首先建立钝体结构的动力方程，通过改变动力方程中的刚度值，其质量保持不变，进而使钝体结构具有不同的振动频率；同时根据设置的刚度值和质量，以及钝体结构要保持的阻尼比，确定动力方程中的阻尼值；数值模拟过程中，来流风速和钝体结构尺寸始终保持不变，通过改变钝体结构振动频率，实现折减风速的变化；最终通过流固耦合数值模拟得到不同折减风速时的振幅，获得该钝体结构的涡激振动性能。本发明改变钝体结构流固耦合数值模拟中变风速而不变振动频率的传统模式，仅需使用一套网格就可以完成模拟，降低了网格划分工作量，显著提高了数值模拟的效率，具有很好的应用价值，如图1所示，所述方法具体包括：The vortex-induced vibration numerical simulation method of the bluff body structure based on the variable stiffness provided by the embodiment of the present invention, by changing the stiffness value in the established dynamic equation of the bluff body structure, while the mass remains unchanged, so that the bluff body structure has different vibration frequencies , first establish the dynamic equation of the bluff body structure, by changing the stiffness value in the dynamic equation, its mass remains unchanged, so that the bluff body structure has different vibration frequencies; The damping ratio in the dynamic equation is determined by maintaining the damping ratio. During the numerical simulation, the incoming wind speed and the size of the bluff body structure remain unchanged. By changing the vibration frequency of the bluff body structure, the change of the wind speed can be reduced; Coupled numerical simulations are used to obtain the amplitudes at different reduced wind speeds, and the vortex-induced vibration performance of the bluff body structure is obtained. The invention changes the traditional mode of variable wind speed and constant vibration frequency in the fluid-structure coupling numerical simulation of bluff body structure, and only needs one set of grids to complete the simulation, reduces the workload of grid division, and significantly improves the efficiency of numerical simulation , has good application value, as shown in Figure 1, the method specifically includes:

对待模拟钝体结构设置不同的刚度值。Set different stiffness values for the bluff body structure to be simulated.

对于任意一个刚度值，根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值。For any stiffness value, the reduced wind speed and damping value corresponding to the stiffness value are calculated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated.

根据刚度值、所述待模拟钝体结构的质量和所述刚度值对应的阻尼值，确定所述待模拟钝体结构的钝体结构动力方程。The bluff body structure dynamic equation of the bluff body structure to be simulated is determined according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping value corresponding to the stiffness value.

根据所述待模拟钝体结构的钝体结构动力方程和所述刚度值对所述待模拟钝体结构进行模拟，得到所述待模拟钝体结构在所述刚度值下的振幅。具体的，将所述刚度值和阻尼值代入钝体结构动力方程，通过CFD数值模拟，计算得到对应的振幅，更具体为：根据刚度值，设置模拟工况，进行CFD流固耦合数值模拟；最后得到弹性系统在折减风速Uri时的最大振幅yi，并根据公式

Figure BDA0003664513210000051
做无量纲化处理，继而得到折减风速Uri时的无量纲最大振幅Ai。The bluff body structure to be simulated is simulated according to the bluff body structure dynamic equation of the bluff body structure to be simulated and the stiffness value, and the amplitude of the bluff body structure to be simulated under the stiffness value is obtained. Specifically, the stiffness value and the damping value are substituted into the dynamic equation of the bluff body structure, and the corresponding amplitude is calculated through CFD numerical simulation. Finally, the maximum amplitude y i of the elastic system when reducing the wind speed Ur i is obtained, and according to the formula
Figure BDA0003664513210000051
Do dimensionless processing, and then obtain the dimensionless maximum amplitude A i when the wind speed Ur i is reduced.

根据各刚度值对应的折减风速和各刚度值下的振幅确定所述待模拟钝体结构的涡激振动性能Ai＝g(Uri)。具体的，通过CFD数值模拟得到钝体结构在不同刚度值时的振幅，以各刚度值对应的折减风速为横坐标，以各刚度值下的振幅为纵坐标绘制曲线图，进而根据曲线图获得该钝体结构的涡激振动性能。The vortex-induced vibration performance A i =g(Uri ) of the bluff body structure to be simulated is determined according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value. Specifically, the amplitude of the bluff body structure at different stiffness values is obtained through CFD numerical simulation, the reduced wind speed corresponding to each stiffness value is taken as the abscissa, and the amplitude under each stiffness value is taken as the ordinate to draw a graph, and then according to the graph The vortex-induced vibration performance of the bluff body structure is obtained.

在实际应用中，钝体结构的动力方程为Mx″(t)+Cx′(t)+Kx′(t)＝F(t)，其中，M为质量值、C为阻尼值、K为刚度值，x″(t)、x′(t)、x(t)依次表示钝体结构运动时的加速度、速度和位移；F(t)表示钝体结构在气流中受到的气动力。气动力F通过CFD数值模拟得到。当气动力系统的质量M，某一刚度K和阻尼C确定后，就可以通过数值方法求解该动力方程(二阶微分方程)，例如Newmark-β法和龙格库塔法，通过求解这个动力方程可以得到振幅时程，而yi为该振幅时程的最大振幅。In practical applications, the dynamic equation of the bluff body structure is Mx″(t)+Cx′(t)+Kx′(t)=F(t), where M is the mass value, C is the damping value, and K is the stiffness value, x″(t), x′(t), x(t) represent the acceleration, velocity and displacement of the bluff body structure in sequence; F(t) represents the aerodynamic force of the bluff body structure in the airflow. The aerodynamic force F was obtained by CFD numerical simulation. When the mass M of the aerodynamic system, a certain stiffness K and damping C are determined, the dynamic equation (second-order differential equation) can be solved numerically, such as Newmark-β method and Runge-Kutta method, by solving the dynamic equation The equation can get the amplitude time history, and yi is the maximum amplitude of the amplitude time history.

在实际应用中，所述根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值，具体包括：In practical applications, calculating the reduced wind speed and damping value corresponding to the stiffness value according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated, specifically including :

根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率。The vibration frequency corresponding to the stiffness value is calculated according to the stiffness value and the mass of the bluff body structure to be simulated.

基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速。The reduced wind speed corresponding to the stiffness value is calculated based on the vibration frequency corresponding to the stiffness value.

根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值。The damping value corresponding to the stiffness value is calculated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated.

在实际应用中，所述根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率，具体为：In practical applications, the calculation of the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated is as follows:

根据公式

Figure BDA0003664513210000061
计算所述刚度值对应的振动频率，其中，Ki为设置的第i个刚度值，fi为设置的第i个刚度值对应的振动频率，M为待模拟钝体结构的质量。According to the formula
Figure BDA0003664513210000061
Calculate the vibration frequency corresponding to the stiffness value, where K i is the set ith stiffness value, f i is the vibration frequency corresponding to the set ith stiffness value, and M is the mass of the bluff body structure to be simulated.

在实际应用中，所述根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值，具体为：In practical application, the damping value corresponding to the stiffness value is calculated according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated, specifically:

根据公式

Figure BDA0003664513210000062
计算所述刚度值对应的阻尼值，其中，Ki为设置的第i个刚度值，Ci为设置的第i个刚度值对应的阻尼值，M为待模拟钝体结构的质量，ζ为待模拟钝体结构的阻尼比。According to the formula
Figure BDA0003664513210000062
Calculate the damping value corresponding to the stiffness value, where K i is the set i-th stiffness value, C i is the damping value corresponding to the i-th stiffness value set, M is the mass of the bluff body structure to be simulated, and ζ is The damping ratio of the bluff body structure to be simulated.

在实际应用中，所述基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速，具体为：In practical applications, the calculation of the reduced wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value is specifically:

根据公式

Figure BDA0003664513210000071
计算所述刚度值对应的折减风速，其中，Uri表示第i个刚度值对应的折减风速，U0表示来流风速，fi为设置的第i个刚度值对应的振动频率，B表示待模拟钝体结构的参考尺寸。According to the formula
Figure BDA0003664513210000071
Calculate the reduced wind speed corresponding to the stiffness value, where Ur i represents the reduced wind speed corresponding to the ith stiffness value, U 0 represents the incoming wind speed, f i is the vibration frequency corresponding to the set ith stiffness value, B Indicates the reference dimension of the bluff body structure to be simulated.

本发明实施例针对上述方法提供了一种基于变刚度的钝体结构涡激振动数值模拟系统，包括：An embodiment of the present invention provides a vortex-induced vibration numerical simulation system for a bluff body structure based on variable stiffness for the above method, including:

刚度设置模块，用于对待模拟钝体结构设置不同的刚度值。The stiffness setting module is used to set different stiffness values for the bluff body to be simulated.

折减风速和阻尼值计算模块，用于对于任意一个刚度值，根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比，计算所述刚度值对应的折减风速和阻尼值。The reduced wind speed and damping value calculation module is used for any stiffness value, according to the stiffness value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated, calculate the corresponding stiffness value The reduced wind speed and damping values.

钝体结构动力方程确定模块，用于根据刚度值、所述待模拟钝体结构的质量和所述刚度值对应的阻尼值，确定所述待模拟钝体结构的钝体结构动力方程。The bluff body structure dynamic equation determination module is used for determining the bluff body structure dynamic equation of the bluff body structure to be simulated according to the stiffness value, the mass of the bluff body structure to be simulated and the damping value corresponding to the stiffness value.

振幅确定模块，用于根据所述待模拟钝体结构的钝体结构动力方程和所述刚度值对所述待模拟钝体结构进行模拟，得到所述待模拟钝体结构在所述刚度值下的振幅。an amplitude determination module, configured to simulate the bluff body structure to be simulated according to the bluff body structure dynamic equation of the bluff body structure to be simulated and the stiffness value, so as to obtain the bluff body structure to be simulated under the stiffness value amplitude.

涡激振动性能模拟模块，用于根据各刚度值对应的折减风速和各刚度值下的振幅确定所述待模拟钝体结构的涡激振动性能。The vortex-induced vibration performance simulation module is used to determine the vortex-induced vibration performance of the bluff body structure to be simulated according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value.

作为一种可选的实施方式，所述折减风速和阻尼值计算模块包括：As an optional implementation manner, the reduced wind speed and damping value calculation module includes:

振动频率计算单元，用于根据所述刚度值和所述待模拟钝体结构的质量计算所述刚度值对应的振动频率。A vibration frequency calculation unit, configured to calculate the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated.

折减风速计算单元，用于基于所述刚度值对应的振动频率计算所述刚度值对应的折减风速。A reduced wind speed calculation unit, configured to calculate the reduced wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value.

阻尼值计算单元，用于根据所述刚度值、所述待模拟钝体结构的质量和所述待模拟钝体结构的阻尼比计算所述刚度值对应的阻尼值。A damping value calculation unit, configured to calculate a damping value corresponding to the stiffness value according to the stiffness value, the mass of the bluff body structure to be simulated, and the damping ratio of the bluff body structure to be simulated.

作为一种可选的实施方式，所述振动频率计算单元包括：As an optional embodiment, the vibration frequency calculation unit includes:

振动频率计算子单元，用于根据公式

Figure BDA0003664513210000072
计算所述刚度值对应的振动频率，其中，Ki为设置的第i个刚度值，fi为设置的第i个刚度值对应的振动频率，M为待模拟钝体结构的质量。Vibration frequency calculation subunit, used to calculate according to the formula
Figure BDA0003664513210000072
Calculate the vibration frequency corresponding to the stiffness value, where K i is the set ith stiffness value, f i is the vibration frequency corresponding to the set ith stiffness value, and M is the mass of the bluff body structure to be simulated.

作为一种可选的实施方式，所述阻尼值计算单元包括：As an optional implementation manner, the damping value calculation unit includes:

阻尼值计算子单元，用于根据公式

Figure BDA0003664513210000081
计算所述刚度值对应的阻尼值，其中，Ki为设置的第i个刚度值，Ci为设置的第i个刚度值对应的阻尼值，M为待模拟钝体结构的质量，ζ为待模拟钝体结构的阻尼比。Damping value calculation subelement for
Figure BDA0003664513210000081
Calculate the damping value corresponding to the stiffness value, where K i is the set i-th stiffness value, C i is the damping value corresponding to the i-th stiffness value set, M is the mass of the bluff body structure to be simulated, and ζ is The damping ratio of the bluff body structure to be simulated.

作为一种可选的实施方式，所述折减风速计算单元包括：As an optional implementation manner, the reduced wind speed calculation unit includes:

折减风速计算子单元，用于根据公式

Figure BDA0003664513210000082
计算所述刚度值对应的折减风速，其中，Uri表示第i个刚度值对应的折减风速，U0表示来流风速，fi为设置的第i个刚度值对应的振动频率，B表示待模拟钝体结构的参考尺寸。Reduced wind speed calculation subunit, used to calculate according to the formula
Figure BDA0003664513210000082
Calculate the reduced wind speed corresponding to the stiffness value, where Ur i represents the reduced wind speed corresponding to the ith stiffness value, U 0 represents the incoming wind speed, f i is the vibration frequency corresponding to the set ith stiffness value, B Indicates the reference dimension of the bluff body structure to be simulated.

本发明实施例提供了将上述方法应用到宽高比＝4:1，质量M＝100，阻尼比ζ＝1.9％，来流风速U0＝1，参考尺寸B＝1，运动粘度ν＝0.001，雷诺数1000的柱体结构，进行横流向涡激振动CFD数值模拟，其中动力方程采用Newmark-β法求解。计算工况和柱体结构弹性系统的参数按表1取值，最终由CFD流固耦合数值模拟得到的该宽高比4:1柱体的涡振结果如图2所示，图中A表示振幅，Ur表示折减风速。The embodiment of the present invention provides that the above method is applied to aspect ratio=4:1, mass M=100, damping ratio ζ=1.9%, incoming wind speed U 0 =1, reference dimension B=1, kinematic viscosity ν=0.001 , a cylindrical structure with a Reynolds number of 1000, and a CFD numerical simulation of transverse vortex-induced vibration was carried out, in which the dynamic equation was solved by the Newmark-β method. The calculation conditions and the parameters of the elastic system of the cylinder structure are set according to Table 1. Finally, the vortex vibration results of the 4:1 cylinder with an aspect ratio of 4:1 obtained by the CFD fluid-structure interaction numerical simulation are shown in Figure 2. In the figure, A represents the amplitude, Ur represents the reduced wind speed.

表1图2数值模拟中的宽高比4:1柱体结构弹性系统相关参数Table 1 Figure 2 Relevant parameters of the elastic system of the 4:1 column structure in the numerical simulation

Figure BDA0003664513210000083
Figure BDA0003664513210000083

本发明有以下技术效果：The present invention has the following technical effects:

1、本发明改变钝体结构流固耦合数值模拟中改变风速U0而不改变振动频率f的传统模式，将传统钝体CFD流固耦合数值模拟中改变来流速度U0的模式，转变为弹性系统刚度K的变化，可使不同折减风速Ur时的雷诺数不变，进而整个数值模拟过程仅需一套计算域网格，无需重新划分，降低了网格划分工作量并且节省了网格划分所需的人工，显著提高了数值模拟效率。1. The present invention changes the traditional mode of changing the wind speed U 0 without changing the vibration frequency f in the fluid-structure interaction numerical simulation of the bluff body structure, and transforms the mode of changing the incoming flow velocity U 0 in the traditional bluff body CFD fluid-structure interaction numerical simulation into The change of the stiffness K of the elastic system can make the Reynolds number unchanged at different reduced wind speeds Ur, so that the entire numerical simulation process only needs one set of computational domain grids, and does not need to be re-divided, which reduces the workload of grid division and saves the network. The labor required for grid division significantly improves the efficiency of numerical simulation.

2、本发明涡激振动数值模拟方法可以有效模拟钝体结构的涡激振动，在现有的CFD数值模拟技术条件下，实现无需重新划分计算域网格，使其满足检测涡激振动性能的需要，方便实际应用。2. The vortex-induced vibration numerical simulation method of the present invention can effectively simulate the vortex-induced vibration of the bluff body structure. Under the existing CFD numerical simulation technology conditions, it is not necessary to re-divide the computational domain grid, so that it meets the requirements for detecting the vortex-induced vibration performance. needed for practical application.

本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的系统而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant part can be referred to the description of the method.

本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (10)

1. A bluff body structure vortex-induced vibration numerical simulation method based on variable stiffness is characterized by comprising the following steps:
setting different rigidity values for the bluff body structure to be simulated;
for any one rigidity value, calculating a reduction wind speed and a damping value corresponding to the rigidity value according to the rigidity value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated;
determining a passive body structure dynamic equation of the passive body structure to be simulated according to the rigidity value, the mass of the passive body structure to be simulated and the damping value corresponding to the rigidity value;
simulating the bluff body structure to be simulated according to a bluff body structure power equation and the rigidity value of the bluff body structure to be simulated to obtain the amplitude of the bluff body structure to be simulated under the rigidity value;
and determining the vortex-induced vibration performance of the bluff body structure to be simulated according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value.
2. The method according to claim 1, wherein the calculating of the wind reduction speed and the damping value corresponding to the stiffness value according to the stiffness value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated specifically comprises:
calculating the vibration frequency corresponding to the rigidity value according to the rigidity value and the mass of the bluff body structure to be simulated;
calculating a reduced wind speed corresponding to the rigidity value based on the vibration frequency corresponding to the rigidity value;
and calculating a damping value corresponding to the rigidity value according to the rigidity value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated.
3. The method according to claim 2, wherein the calculating of the vibration frequency corresponding to the stiffness value according to the stiffness value and the mass of the bluff body structure to be simulated is specifically:
according to the formula
Figure FDA0003664513200000011
Calculating the vibration frequency corresponding to the rigidity value, wherein K i To set i-th stiffness value, f i And M is the mass of the bluff body structure to be simulated, wherein M is the vibration frequency corresponding to the set ith stiffness value.
4. The variable-stiffness-based bluff body structure vortex-induced vibration numerical simulation method according to claim 2, wherein the calculating of the damping value corresponding to the stiffness value according to the stiffness value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated specifically comprises:
according to the formula
Figure FDA0003664513200000012
Calculating a damping value corresponding to the rigidity value, wherein K i To a set i-th stiffness value, C i And M is the mass of the bluff body structure to be simulated, and zeta is the damping ratio of the bluff body structure to be simulated.
5. The variable-stiffness-based numerical simulation method for vortex-induced vibration of a bluff body structure according to claim 2, wherein the calculating of the depreciation wind speed corresponding to the stiffness value based on the vibration frequency corresponding to the stiffness value specifically comprises:
according to the formula
Figure FDA0003664513200000021
Calculating the reduction wind speed corresponding to the rigidity value, wherein Ur i Representing the depreciation wind speed, U, corresponding to the ith stiffness value 0 Representing the incoming wind speed, f i For the vibration frequency corresponding to the set i-th stiffness value, B represents the reference dimension of the bluff body structure to be simulated.
6. A bluff body structure vortex-induced vibration numerical simulation system based on variable rigidity is characterized by comprising:
the rigidity setting module is used for setting different rigidity values for the bluff body structure to be simulated;
the calculation module of the reduced wind speed and the damping value is used for calculating the reduced wind speed and the damping value corresponding to the rigidity value according to the rigidity value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated for any rigidity value;
the passive body structure dynamic equation determining module is used for determining a passive body structure dynamic equation of the passive body structure to be simulated according to the rigidity value, the mass of the passive body structure to be simulated and the damping value corresponding to the rigidity value;
the amplitude determining module is used for simulating the bluff body structure to be simulated according to a bluff body structure power equation of the bluff body structure to be simulated and the rigidity value to obtain the amplitude of the bluff body structure to be simulated under the rigidity value;
and the vortex-induced vibration performance simulation module is used for determining the vortex-induced vibration performance of the bluff body structure to be simulated according to the reduced wind speed corresponding to each stiffness value and the amplitude under each stiffness value.
7. The system of claim 6, wherein the module for calculating the reduced wind speed and damping value comprises:
the vibration frequency calculation unit is used for calculating the vibration frequency corresponding to the rigidity value according to the rigidity value and the mass of the bluff body structure to be simulated;
the wind speed reduction calculation unit is used for calculating the wind speed reduction corresponding to the rigidity value based on the vibration frequency corresponding to the rigidity value;
and the damping value calculating unit is used for calculating a damping value corresponding to the rigidity value according to the rigidity value, the mass of the bluff body structure to be simulated and the damping ratio of the bluff body structure to be simulated.
8. The variable-stiffness-based numerical simulation system for vortex-induced vibration of a bluff body structure according to claim 7, wherein the vibration frequency calculation unit comprises:
a vibration frequency calculating subunit for calculating the frequency of vibration according to the formula
Figure FDA0003664513200000031
Calculating the vibration frequency corresponding to the rigidity value, wherein K i To set i-th stiffness value, f i And M is the mass of the bluff body structure to be simulated, wherein M is the vibration frequency corresponding to the set ith stiffness value.
9. The variable-stiffness-based numerical simulation system for vortex-induced vibration of a bluff body structure according to claim 7, wherein the damping value calculation unit comprises:
a damping value calculating operator unit for calculating a damping value according to a formula
Figure FDA0003664513200000032
Calculating a damping value corresponding to the rigidity value, wherein K i To a set i-th stiffness value, C i And M is the mass of the bluff body structure to be simulated, and zeta is the damping ratio of the bluff body structure to be simulated.
10. The system for simulating vortex-induced vibration of a bluff body structure based on variable stiffness according to claim 7, wherein the wind speed reduction calculation unit comprises:
wind speed reduction calculatorUnit for generating a formula
Figure FDA0003664513200000033
Calculating the reduction wind speed corresponding to the rigidity value, wherein Ur i Representing the depreciation wind speed, U, corresponding to the ith stiffness value 0 Representing the incoming wind speed, f i For the vibration frequency corresponding to the set i-th stiffness value, B represents the reference dimension of the bluff body structure to be simulated.
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