Numerical Modelling of Boundary Layers and Far Field Acoustic Propagation in Thermoviscous Fluid

2019 ◽  
Vol 105 (6) ◽  
pp. 1137-1148
Author(s):  
Nicolas Joly ◽  
Petr Honzík
Keyword(s):  
Finite Element ◽  
Integral Representation ◽  
Acoustic Radiation ◽  
Element Formulation ◽  
Open Domain ◽  
Uniqueness Of Solutions ◽  
Resonant Frequencies ◽  
Time Harmonic ◽  
Finite Element Node ◽  
Thermoviscous Fluid

To model linear acoustics in a thermoviscous fluid in open domain and time-harmonic regime, a Finite Element formulation in a bounded meshed domain is combined with the integral representation of the field for the propagative solution. The integrals are non-singular and involve the only Finite Element node values for temperature variation and particle velocity variables. To overcome the non-uniqueness of solutions at fictitious resonant frequencies, a Burton-Miller combination of integral representation is used. This formulation is suitable to compute acoustic radiation, scattering and diffraction by objects or mutual interaction between transducers. Two-dimensional computational experiments are presented in an infinite, open domain (exterior), showing that the model can be achieved in meshing only a thin domain surrounding the physical boundaries of a device.

Quench Process Modeling and Optimization

2000 ◽  
Author(s):  
Ravi S. Bellur-Ramaswamy ◽  
Nahil A. Sobh ◽  
Robert B. Haber ◽  
Daniel A. Tortorelli
Keyword(s):  
Particle Size ◽  
Finite Element ◽  
Process Parameters ◽  
Degrees Of Freedom ◽  
Programming Algorithm ◽  
Precipitate Size ◽  
Rate Theory ◽  
Element Formulation ◽  
Balancing Energy ◽  
Finite Element Node

Abstract We optimize continuous quench process parameters to produce a desired precipitate distribution in aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include a cost function, constraint functions and their sensitivities with respect to the process parameters. These functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine a discrete precipitate particle size distribution. Both the temperature and the precipitate models are solved via the finite element method. Since we use a discrete particle size model, there are as many as 105 degrees-of-freedom per finite element node. After we compute the temperature and precipitate size distributions, we must also compute their sensitivities. This seemingly intractable computational task is resolved by using an element-by-element discontinuous Galerkin finite element formulation and a direct differentiation sensitivity analysis which allows us to perform all of the computations on a PC.

FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART II: TURBOFAN ACOUSTIC RADIATION

2004 ◽  
Vol 12 (03) ◽  
pp. 431-446 ◽  
Author(s):  
EIVIND LISTERUD ◽  
WALTER EVERSMAN
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Acoustic Pressure ◽  
Acoustic Radiation ◽  
Near Field ◽  
Element Formulation ◽  
Computational Accuracy ◽  
Element Modeling ◽  
Quadratic Performance ◽  
Serendipity Elements

A study is made of computational accuracy and efficiency for finite element modeling of acoustic radiation in a nonuniform moving medium. For a given level of accuracy for acoustic pressure, cubic serendipity elements are shown to require a less dense mesh than quadratic elements. These elements have been applied to the near field of inlet and aft acoustic radiation models for a turbofan engine and they yield considerable reduction in the dimensionality of the problem without sacrificing accuracy. The results show that for computation of acoustic pressure the cubic element formulation model is superior to the quadratic. Performance gains in computation of acoustic potential are not as significant. In the external radiated field, improved convergence using cubic serendipity elements is shown by comparison of contours of constant pressure magnitude.

Application of the Boundary Element Method and Modal Analysis to Tire Acoustics Problems

1993 ◽  
Vol 21 (2) ◽  
pp. 66-90 ◽  
Author(s):  
Y. Nakajima ◽  
Y. Inoue ◽  
H. Ogawa
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Traffic Noise ◽  
Noise Prediction ◽  
Prediction System ◽  
Tire Noise ◽  
Acoustic Contribution ◽  
Element Method

Abstract Road traffic noise needs to be reduced, because traffic volume is increasing every year. The noise generated from a tire is becoming one of the dominant sources in the total traffic noise because the engine noise is constantly being reduced by the vehicle manufacturers. Although the acoustic intensity measurement technology has been enhanced by the recent developments in digital measurement techniques, repetitive measurements are necessary to find effective ways for noise control. Hence, a simulation method to predict generated noise is required to replace the time-consuming experiments. The boundary element method (BEM) is applied to predict the acoustic radiation caused by the vibration of a tire sidewall and a tire noise prediction system is developed. The BEM requires the geometry and the modal characteristics of a tire which are provided by an experiment or the finite element method (FEM). Since the finite element procedure is applied to the prediction of modal characteristics in a tire noise prediction system, the acoustic pressure can be predicted without any measurements. Furthermore, the acoustic contribution analysis obtained from the post-processing of the predicted results is very helpful to know where and how the design change affects the acoustic radiation. The predictability of this system is verified by measurements and the acoustic contribution analysis is applied to tire noise control.

Calculating the response of waveguides to base excitation using the wave and finite element method

2021 ◽  
pp. 107754632098131
Author(s):  
Jamil Renno ◽  
Sadok Sassi ◽  
Wael I Alnahhal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Functions ◽  
Travelling Waves ◽  
Model Free ◽  
Time Harmonic ◽  
Element Approach ◽  
Response Transfer ◽  
Free Wave Propagation ◽  
Element Method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

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