考虑流固耦合的管路系统振动噪声及特性研究
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摘要
流体管道系统广泛应用于海洋工程、生物工程、电力工业、石油能源工业、核工业、舰船、飞行器动力装置以及日常生活中。因为在管路系统中存在泵和阀门等内部声源以及基础振动和管道破裂等外部激励，所以会诱发流体管道产生振动噪声，并在管道和流体中传播。振动噪声问题在舰船管路系统中，显得十分突出，一方面会造成管路以及精密仪器附件破坏，影响管路系统以及动力系统的正常运行；另一方面管路系统的振动噪声会通过船体以及内外部流体交换而产生声辐射，影响其隐身性，直接对舰船安全构成威胁。
首先忽略流体和管道之间摩擦效应的影响，直管考虑轴向泊松耦合效应，弯管考虑泊松耦合效应以及Bourdon耦合效应，参考Tenteralli的建模思想，建立管路系统中最基本的管路部件单元——直管和弯管的动力学模型。模型包括轴向振动、横向振动以及管道的扭转振动，一共14个参量的一阶时域偏微分方程。然后利用Laplace变换把时域方程变换到频域，对于直管，对频域方程经过复杂的推导，把14个多元一阶偏微分方程转化为14个一元高阶常微分方程，对高阶方程直接求解得到直管的频域解析解；对于弯管，借鉴张立翔教授对直管轴向4方程模型的求解思想，同样得到弯管的频域解析解。管道的最终解还必须结合管路系统的边界条件，在这里，把管路的边界简化为六个自由度方向（线弹性和扭转弹性）的弹性刚度，通过设定不同的弹性刚度，可以得到各种组合的边界形式，比如固定边界、简支边界、自由边界以及弹性边界等。
建立典型管路结构的传递矩阵模型，包括直管和弯管、折管、分支管（一点分支以及多点分支）和锥形管的传递矩阵，传递矩阵中管段连接点（点传递矩阵）处支撑可以为任意形式。一点分支通过分支点处的力平衡和位移平衡得到了任意形状分支管的点传递矩阵，并结合边界条件得到了其求解方程；在此基础上，通过在点传递矩阵等式左右添加零矩阵的方法得到了多点分支的传递矩阵，同样结合边界条件得到了其求解方程。锥形管通过划分单元，把锥形管划分为N段，用直管近似等效锥形管的单元，建立了锥形管的传递矩阵。
在管路系统中，存在大量的法兰、阀门、泵等管路附件，这些附件都会影响管路系统的动力学行为，对于法兰、夹具等简化为一个集中质量元件，利用理论力学、结构力学等理论建立了集中质量的传递矩阵；而阀门、泵等声源附件不仅给管路带来了附加质量，而且是管路系统的激励源，因而，利用四端网络法以及力学理论，建立阀门、泵等声源附件的传递矩阵模型。
在前面研究的基础上，利用典型管路结构以及附件等在任意支撑下的点传递矩阵以及场传递矩阵，推导出任意管路系统的整体传递矩阵，结合边界条件得到了管路系统的求解方程，这里的管路系统的传递矩阵以及求解方程适用于任意形状以及布置的管路系统。
设计、搭建管路试验台架，通过测量直管、Y型分支管以及十字型分支管在激励下的轴向和横向振动噪声响应特性参数，通过与理论预测的对比来验证理论模型以及方法的正确性，同时也说明本文方法的应用，并从试验角度对管路流固耦合振动噪声特性进行分析。
最后，对管路典型部件进行计算，通过调整管道的结构参数以及支撑形式等特性参数，对管路振动噪声响应特性进行分析，并从总声级和总速度级的角度出发，研究管路结构振动噪声特性和规律，为管路振动噪声控制以及低噪声设计提供理论指导。
As we all know, liquid-filled pipeline systems exist in many fields, just like marineengineering, biological engineering, electrical industry, petroleum energy industry, nuclearindustry, warships, aircraft device and daily life. Because of the existence of excitation insideand outside as pumps, valves, vibration of basement and cracking of pipelines and so on,vibration and noise of pipelines is induced, and propagating in pipelines. It becomes veryserious in pipeline system of warships. For one thing, the vibration and noise of pipelinesystems can make the pipeline and precision apparatus destroyed, which will affect the run ofpipeline and power system; for another thing, the vibration and noise of pipeline systems canradiate through hull and the process when exchange of inside and outside fluid happens, and itwill affect the conceal of the warship and bring in menace to security.
At first, neglecting friction between pipeline and fluid, the model of two most commonpipeline section elements is established, namely, straight and curved pipeline, and the axismotion, flexural motion and torsion motion are included. For straight pipeline, Poissoncoupling is considered, and for curved pipeline, Poisson coupling as well as Bourdoncoupling is considered. Then, the time-domain equations describing vibration of pipelinesconsidering fluid-structure interaction are transformed into frequency domain by Laplacetransformation, and for straight pipeline, twelve fourth order ordinary differential equationsand two second order ordinary differential equations are deduced from the frequency-domainequations; for curved pipeline, using the reference of the method of professor Zhang solvingfour-equation model of axis motion, the analytical solution of curved pipeline is also obtained.In order to get the final solution of pipelines, boundary conditions of pipeline is required.Here, the boundary conditions are simplified to springs along six freedoms. Using the method,all the pipelines with classical constraints can be easily calculated by simply setting thestiffness of the restraining springs from zero to infinite, for example fixed supported, simplysupported, freely supported and elastically supported pipelines.
The transfer matrix models of pipeline components, as straight and curved pipeline,L-shaped pipeline, branch pipeline (one branch point and multi-branch point inclueded) andtaper pipeline are established. Here, the joint condition between pipeline sections can bearbitrary. Through balance of displacement and force of branch point, the transfer matrixmodel for branch pipeline with one branch point is also obtained. Combined with boundaryconditions, the solution equation for it is got. Base on these, through complex matrixtransformation, the transfer matrix model for branch pipeline with more branch points isobtained. The solution equation is also gained with boundary condition. For taper pipeline, by divided into N sections, and any section equivalent with straight pipeline, the transfer matrixmodel of taper pipeline is set up.
There exist many flanges, clamps, valves and pumps in pipeline systems, which canaffect the dynamic behavior of pipeline systems. Flanges and clamps, can be simplified intoconvergence mass component, and with theory of mechanics, the transfer matrix of them aregained. But valves and pumps, not only they can increase an added mass on pipelines, butalso they are the excitation of the pipelines. So, using four-channel method and theory ofmechanics, the transfer matrix model of valves and pumps are set up.
Based on the results above, with the point transfer matrix and field transfer matrix ofpipeline components and accessories with arbitrary support, the transfer matrix for arbitrarypipeline systems is set up. The solution equation is also obtained combined with boundarycondition, which can be used for any pipeline systems.
A testing bed for measuring pipelines is designed and built. By the measurement ofcharacteristic parameters of the response of straight pipeline, Y-shaped pipeline andcross-shaped pipeline under excitation, the correctness of the model and method is validated.And the characteristic of the vibration and noise of pipeline considering fluid-structureinteraction is also analyzed through the measurement data.
In the end, the classic pipeline components are calculated and analyzed with differentstructural parameters and types of support. And the characteristic and law of vibration ofpipelines considering fluid-structure interaction is analyzed, which can be used to guide thecontrol of vibration and noise of pipeline and design of low-noise pipeline components.
首先忽略流体和管道之间摩擦效应的影响，直管考虑轴向泊松耦合效应，弯管考虑泊松耦合效应以及Bourdon耦合效应，参考Tenteralli的建模思想，建立管路系统中最基本的管路部件单元——直管和弯管的动力学模型。模型包括轴向振动、横向振动以及管道的扭转振动，一共14个参量的一阶时域偏微分方程。然后利用Laplace变换把时域方程变换到频域，对于直管，对频域方程经过复杂的推导，把14个多元一阶偏微分方程转化为14个一元高阶常微分方程，对高阶方程直接求解得到直管的频域解析解；对于弯管，借鉴张立翔教授对直管轴向4方程模型的求解思想，同样得到弯管的频域解析解。管道的最终解还必须结合管路系统的边界条件，在这里，把管路的边界简化为六个自由度方向（线弹性和扭转弹性）的弹性刚度，通过设定不同的弹性刚度，可以得到各种组合的边界形式，比如固定边界、简支边界、自由边界以及弹性边界等。
建立典型管路结构的传递矩阵模型，包括直管和弯管、折管、分支管（一点分支以及多点分支）和锥形管的传递矩阵，传递矩阵中管段连接点（点传递矩阵）处支撑可以为任意形式。一点分支通过分支点处的力平衡和位移平衡得到了任意形状分支管的点传递矩阵，并结合边界条件得到了其求解方程；在此基础上，通过在点传递矩阵等式左右添加零矩阵的方法得到了多点分支的传递矩阵，同样结合边界条件得到了其求解方程。锥形管通过划分单元，把锥形管划分为N段，用直管近似等效锥形管的单元，建立了锥形管的传递矩阵。
在管路系统中，存在大量的法兰、阀门、泵等管路附件，这些附件都会影响管路系统的动力学行为，对于法兰、夹具等简化为一个集中质量元件，利用理论力学、结构力学等理论建立了集中质量的传递矩阵；而阀门、泵等声源附件不仅给管路带来了附加质量，而且是管路系统的激励源，因而，利用四端网络法以及力学理论，建立阀门、泵等声源附件的传递矩阵模型。
在前面研究的基础上，利用典型管路结构以及附件等在任意支撑下的点传递矩阵以及场传递矩阵，推导出任意管路系统的整体传递矩阵，结合边界条件得到了管路系统的求解方程，这里的管路系统的传递矩阵以及求解方程适用于任意形状以及布置的管路系统。
设计、搭建管路试验台架，通过测量直管、Y型分支管以及十字型分支管在激励下的轴向和横向振动噪声响应特性参数，通过与理论预测的对比来验证理论模型以及方法的正确性，同时也说明本文方法的应用，并从试验角度对管路流固耦合振动噪声特性进行分析。
最后，对管路典型部件进行计算，通过调整管道的结构参数以及支撑形式等特性参数，对管路振动噪声响应特性进行分析，并从总声级和总速度级的角度出发，研究管路结构振动噪声特性和规律，为管路振动噪声控制以及低噪声设计提供理论指导。
As we all know, liquid-filled pipeline systems exist in many fields, just like marineengineering, biological engineering, electrical industry, petroleum energy industry, nuclearindustry, warships, aircraft device and daily life. Because of the existence of excitation insideand outside as pumps, valves, vibration of basement and cracking of pipelines and so on,vibration and noise of pipelines is induced, and propagating in pipelines. It becomes veryserious in pipeline system of warships. For one thing, the vibration and noise of pipelinesystems can make the pipeline and precision apparatus destroyed, which will affect the run ofpipeline and power system; for another thing, the vibration and noise of pipeline systems canradiate through hull and the process when exchange of inside and outside fluid happens, and itwill affect the conceal of the warship and bring in menace to security.
At first, neglecting friction between pipeline and fluid, the model of two most commonpipeline section elements is established, namely, straight and curved pipeline, and the axismotion, flexural motion and torsion motion are included. For straight pipeline, Poissoncoupling is considered, and for curved pipeline, Poisson coupling as well as Bourdoncoupling is considered. Then, the time-domain equations describing vibration of pipelinesconsidering fluid-structure interaction are transformed into frequency domain by Laplacetransformation, and for straight pipeline, twelve fourth order ordinary differential equationsand two second order ordinary differential equations are deduced from the frequency-domainequations; for curved pipeline, using the reference of the method of professor Zhang solvingfour-equation model of axis motion, the analytical solution of curved pipeline is also obtained.In order to get the final solution of pipelines, boundary conditions of pipeline is required.Here, the boundary conditions are simplified to springs along six freedoms. Using the method,all the pipelines with classical constraints can be easily calculated by simply setting thestiffness of the restraining springs from zero to infinite, for example fixed supported, simplysupported, freely supported and elastically supported pipelines.
The transfer matrix models of pipeline components, as straight and curved pipeline,L-shaped pipeline, branch pipeline (one branch point and multi-branch point inclueded) andtaper pipeline are established. Here, the joint condition between pipeline sections can bearbitrary. Through balance of displacement and force of branch point, the transfer matrixmodel for branch pipeline with one branch point is also obtained. Combined with boundaryconditions, the solution equation for it is got. Base on these, through complex matrixtransformation, the transfer matrix model for branch pipeline with more branch points isobtained. The solution equation is also gained with boundary condition. For taper pipeline, by divided into N sections, and any section equivalent with straight pipeline, the transfer matrixmodel of taper pipeline is set up.
There exist many flanges, clamps, valves and pumps in pipeline systems, which canaffect the dynamic behavior of pipeline systems. Flanges and clamps, can be simplified intoconvergence mass component, and with theory of mechanics, the transfer matrix of them aregained. But valves and pumps, not only they can increase an added mass on pipelines, butalso they are the excitation of the pipelines. So, using four-channel method and theory ofmechanics, the transfer matrix model of valves and pumps are set up.
Based on the results above, with the point transfer matrix and field transfer matrix ofpipeline components and accessories with arbitrary support, the transfer matrix for arbitrarypipeline systems is set up. The solution equation is also obtained combined with boundarycondition, which can be used for any pipeline systems.
A testing bed for measuring pipelines is designed and built. By the measurement ofcharacteristic parameters of the response of straight pipeline, Y-shaped pipeline andcross-shaped pipeline under excitation, the correctness of the model and method is validated.And the characteristic of the vibration and noise of pipeline considering fluid-structureinteraction is also analyzed through the measurement data.
In the end, the classic pipeline components are calculated and analyzed with differentstructural parameters and types of support. And the characteristic and law of vibration ofpipelines considering fluid-structure interaction is analyzed, which can be used to guide thecontrol of vibration and noise of pipeline and design of low-noise pipeline components.
引文
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