| Silencers are the most effective devices to attenuate the intake and exhaust noise of power and fluid machinery,computation and analysis for acoustic performance needs to be carried out to design high-performance silencers.The finite element method is widely used for the calculation and analysis of acoustic performance of silencer due to its strong adaptability,high computational efficiency and accuracy.However,for large mechanical equipment like turbocharged diesel engines,gas turbines,and fans,due to the wide frequency band of intake and exhaust noise,it is necessary to conduct broadband acoustic performance computation for silencers.The variation of acoustic wave length within the computational frequency band can reach hundreds of times,and the traditional standard Galerkin finite element method(FEM)cannot adapt to the significant changes in acoustic wave wavelength,has high requirements for mesh resolution to reduce numerical dispersion,which leads to the low computation efficiency.Therefore,in this paper the efficient finite element approaches are developed to compute broadband acoustic attenuation performance of silencer.When the airflow velocity is low,the background flow has little influence on the acoustic performance of silencer,in order to improve the computation efficiency the convected effects generated by airflow can be ignored,and the sound field governing equation is the Helmholtz equation.The weak form of Helmholtz equation for the reactive,dissipative and hybrid silencers are established,the commonly used acoustic boundaries for silencer are discussed,and the corresponding solving strategies are established based on the Galerkin/least-squares finite element method(GLS-FEM)and adaptive polynomial finite element method(p-FEM),expressions for global coefficient matrices are obtained by discretization and assembling the element integral matrices.Compared to FEM,the GLS-FEM introduces a local stability factor in the element to alleviate the mesh resolution requirement,thereby significantly reduces the solving scale.Due to the requirement of the GLS-FEM that the maximum element size cannot be larger than one sixth of the minimum acoustic wavelength,it still cannot adapt to significant changes in acoustic wavelength in broadband acoustic computation.The p-FEM applies hierarchical elements to discrete acoustic models,combining with the element-driven order allocation approach based on a prior error estimation can adaptively adjust the order of each element for a given frequency on a large sized element,thereby achieves preset calculation accuracy and solves broadband acoustic problems efficiently.When the airflow velocity is high,convected effects on the acoustic performance of silencer cannot be ignored.Firstly the governing equation for convected sound field is derived,and the weak form of the equation for the reactive,dissipative and hybrid silencers are established,the boundary conditions involved in the silencers are discussed in detail,then the corresponding solving strategies are established based on the FEM and anisotropic adaptive polynomial finite element method(ap-FEM).FEM can reduce numerical dispersion by reducing element size and raising the element shape function order,hence the relationship between mean flow velocity,frequency and element size and order is established to provide guidance for the discretization of acoustic model.However,the element shape functions used in FEM are constructed based on Lagrange polynomials,the element order is coupled with each other,and elements in the acoustic domain must have the same order.The non-uniformity of flow field makes it difficult to obtain the optimal meshes by discretization,which makes FEM over solve in many regions,and the computational efficiency is low.The ap-FEM retaining the advantages of the p-FEM uses anisotropic hierarchical elements to discrete acoustic models,combining with the edge-driven order computation and allocation approach based on a prior error estimation may consider the influence of mean flow velocity direction on the element order,avoids over solving on the acoustic domain,and greatly improves the efficiency of solving broadband acoustic problems of convected sound field.For the broadband acoustic performance prediction of large silencers,a coupling approach combining finite element formulas and duct mode expansion is proposed to consider threedimensional wave effects(high order modes)in inlet and outlet ducts on acoustic performance.The acoustic variables in boundary integrals of finite element formulas on the inlet and outlet surfaces are expressed analytically in terms of mode expansion.Since the introduced modal amplitude coefficients add unknown variables,the intrinsic functions are used as weighted functions to construct integral equations on the inlet and outlet surfaces to form a closed set of equations.For the given incident modes,calculate the unknown quantities on all nodes and modal amplitude coefficients on outlet,and then calculate the sound power of each mode in the inlet and outlet ducts,thereby obtain the transmission loss of silencer.For the broadband acoustic performance prediction of large silencing devices,in order to avoid the problem of too large solving scale in direct computation,the impedance-scattering matrix substructure method based on mode matching is proposed by combining p-FEM or apFEM.The silencing device is divided into several substructures,the impedance matrix of each substructure is captured by using p-FEM or ap-FEM.Then based on the mode matching method,the scattering matrix denoting the relationship between mode amplitude coefficients on inlet and outlet of the substructure is extracted from the impedance matrix.Finally,the scattering matrix of the whole silencing device is obtained through matrix operations,the transmission loss is captured for the given incident modes.In order to apply the above methods to acoustic computation and engineering analysis,a high-performance program architecture is constructed to implement the aforementioned algorithms,a computation program called Sound Lab is developed,which includes FEM/GLSFEM module,p-FEM module and ap-FEM module,the calculation process of each module is introduced in detail.The program is applied to predict the transmission loss of some typical silencers,the correctness of the aforementioned methods and program is verified by comparing the predictions with the data from published literatures or analytical solutions,and the computational performance of these modules are also compared and analyzed.For the stabilized finite element method,the computation accuracy of Sound Lab is equivalent to that of commercial software,its calculation speed and solving scale are better than that of commercial software,and it is able to perform calculations on the acoustic model with 100 million elements.In absence of flow,the p-FEM improves the computation speed by about an order of magnitude compared to the GLS-FEM.In the presence of flow,the calculation speed of the ap-FEM is improved by two orders of magnitude compared to FEM,and the memory occupation is reduced by up to 80%,the maximum calculation speed of the ap-FEM is about 4.1 times that of the pFEM in these cases,and the memory occupation is decreased by up to 60%.Sound Lab is the first acoustic finite element program with independent intellectual property rights based on pFEM and ap-FEM in China,realizes efficient and high-precision computation of broadband acoustic performance for large silencers,combing preprocessing,CFD,and post-processing tools forms a complete solution for acoustic performance prediction of silencers.Based on the two-load method,the acoustic properties of glass fiber and the transmission loss of typical silencers are measured,the correctness of the aforementioned methods and program are further verified by comparing the measurements and predictions from the present program.As applications of Sound Lab,acoustic performance of several typical silencers is calculated and analyzed. |
PDF Full Text Request