| In order to improve the comfort of construction machinery products,it is necessary to design a muffler with good performance matching with the intake and exhaust noise spectrum to control the noise.Muffler product development is generally divided into concept stage,design stage,manufacturing stage,testing stage and batch production stage.In order to improve the research and development efficiency and reduce the cost of manufacturing and testing,numerical methods have been widely used in the research and development process.In the concept stage,the selection of muffler product appearance and internal structure would be limited by the installation space and product cost,so it needs numerical method to effectively screen different design schemes.Compared with other numerical methods,the finite element method has the advantages of considering three-dimensional complex structure,not limited by the cut-off frequency of plane wave and high calculation efficiency.However,the traditional finite element method used in commercial software can not consider the influence of gas flow in muffler.The deviation between the predicted results and the experimental results will still lead to the increase of development cost and cycle.Considering the research and development demand of muffler products,this paper developed a kind of calculation method of muffler acoustic behavior based on the research of finite element method.Considering the relationship between the acoustic behavior of muffler with and without flow,the finite element method based on Helmholtz equation is proposed to select the muffler products in the concept stage.By calculating the acoustic behavior of double expansion and the three-pass perforated tube muffler,it was found that the inlet/outlet pipes position and internal structure of the muffler can be adjusted to meet the different requirements of the intake and exhaust noise control.At the same time,the calculation results under the condition of no flow will provide basic data for the sensitivity analysis of acoustic behavior of muffler to gas flow.In the product design stage,the calculation of acoustic behavior of muffler needs to consider the influence of non-uniform flow.If the Mach number in the muffler is less than 0.3,the coupling effect of the flow field and the sound field can be considered as one-way.By neglecting the influence of the sound field on the flow field,a one-way flow-acoustics coupling method of the acoustic behavior of the muffler has been established based on the convected wave control equation.The first step is to calculate the steady-state distribution of gas flow velocity inside the muffler on the flow mesh by computational fluid dynamics method and the second step is to use linear interpolation method to ensure that the flow field information is effectively transmitted to the acoustic grid for acoustic calculation.By calculating the acoustic behavior of different types of perforated pipe mufflers,it was found that the effect of gas flow on the resonance frequency is significant.In order to reduce the sensitivity of gas flow to acoustic behavior,a conical tube was introduced to reduce the air velocity at the holes under the condition of grazing flow.Through the detailed study of acoustic behavior of three-pass perforated tube muffler,the principle of selecting the boundary type of perforated area in the mixed flow type is clarified.In order to further consider the two-way coupling between the flow field and the sound field,a finite element method in frequency domain is established by linearizing the compressible Navier-Stokes equation.Compared with Helmholtz equation and convected wave control equation,diffusion term,convection term and reaction term in linearized Navier-Stokes equation can provide more accurate acoustic model.The results presented that the acoustic energy conversion and vortical dissipation under the action of two-way flow-acoustics coupling will change the acoustic behavior and affect the extraction accuracy of the incident and transmitted sound pressure of muffler.Considering the computational efficiency of linearized Navier-Stokes equations due to the increase of variables,three kinds of ways were proposed to reduce the computational freedom.On this basis,the acoustic behavior of Helmholtz resonators,double expansion mufflers and perforated tube mufflers were analyzed in detail,and the solutions to reduce the sensitivity of acoustic behavior of mufflers to gas flow were given.According to the phenomenon that the transmitted sound pressure is greater than the incident sound pressure at a specific gas velocity in the testing stage of muffler products,a linear stability determination method under the flow-acoustics coupling effect was proposed to predict the flow induced noise.The method does not consider the vibration of the muffler wall,and considers that the amplified sound energy comes from the flow-acoustics coupling oscillation between the unstable vortex structure(hydraulic mode)and the acoustic mode of the side branch structure.Based on the assumption that the oscillation problem of the acoustic system develops from a linear state to a nonlinear state,the generalized Nyquist stability criterion and the acoustic energy stability criterion based on the control theory were used to determine whether the system is stable,and the evaluation intensity of the system instability was given.Compared with the experimental results of Helmholtz resonator and straight-through perforated tube muffler,it was found that this method can effectively predict the frequency of the flow induced noise and the sequence of the corresponding frequency of the sound pressure.On this basis,the influence of the adjustment of scattering matrix and reflection matrix on the instability of acoustic system was studied in detail. |
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