Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery: Part II—Time-Linearized Methods

2012 ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken ◽  
Christian Weckmüller
Keyword(s):  
Boundary Condition ◽  
Linear System ◽  
Near Field ◽  
Linear Equations ◽  
Time Integration ◽  
Aerodynamic Noise ◽  
Fan Noise ◽  
Rotor Stator Interaction ◽  
Complex Linear ◽  
Preconditioned Gmres

This is the second part of a series of two papers on unsteady CFD methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of linearized RANS methods to turbomachinery noise problems. The convective and viscous fluxes of an existing URANS solver are linearized and the resulting unsteady linear equations are transfered into the frequency domain, thereby simplifying the solution problem from unsteady time-integration to a complex linear system. The linear system is solved using a parallel, preconditioned GMRES method with restarts. In order to prescribe disturbances due to rotor stator interaction a so-called gust boundary condition is implemented. Using this inhomogeneous boundary condition one can compute the generation of the acoustic modes and their near field progagation. The application of the time-linearized methods to a modern high-bypass ratio fan is investigated. The tonal fan noise predicted by the time-linearized solver is compared to numerical results presented in the first part and to measurements.

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part II: Time-Linearized Methods

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken ◽  
Christian Weckmüller
Keyword(s):  
Boundary Condition ◽  
Linear System ◽  
Near Field ◽  
Linear Equations ◽  
Time Integration ◽  
Aerodynamic Noise ◽  
Fan Noise ◽  
Rotor Stator Interaction ◽  
Complex Linear ◽  
Computational Fluid Dynamics Cfd

This is the second part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of linearized RANS methods to turbomachinery noise problems. The convective and viscous fluxes of an existing URANS solver are linearized and the resulting unsteady linear equations are transferred into the frequency domain, thereby simplifying the solution problem from unsteady time-integration to a complex linear system. The linear system is solved using a parallel, preconditioned general minimized residual (GMRES) method with restarts. In order to prescribe disturbances due to rotor stator interaction, a so-called gust boundary condition is implemented. Using this inhomogeneous boundary condition, one can compute the generation of the acoustic modes and their near field propagation. The application of the time-linearized methods to a modern high-bypass ratio fan is investigated. The tonal fan noise predicted by the time-linearized solver is compared to numerical results presented in the first part and to measurements.

A Two-Phase Algorithm for the Chebyshev Solution of Complex Linear Equations

1994 ◽  
Vol 15 (6) ◽  
pp. 1440-1451
Author(s):  
Dirk P. Laurie ◽  
Lucas M. Venter
Keyword(s):  
Linear Equations ◽  
Two Phase ◽  
Complex Linear

scholarly journals FDTD Computation of Space/Time Integrated Electromagnetic Lagrangian: New Insights on Mutually Coupled Wide-band Antenna Design

2021 ◽  
Author(s):  
Debdeep Sarkar ◽  
Yahia Antar
Keyword(s):  
Electromagnetic Interference ◽  
Interference Mitigation ◽  
Near Field ◽  
Time Integration ◽  
Wide Band ◽  
Space Time ◽  
Ultra Wideband ◽  
Mimo Antennas ◽  
Electric And Magnetic Fields ◽  
Spatio Temporal

In this paper, we develop a formalism based on either spatially or temporally integrated electromagnetic (EM) Lagrangian, which provides new insights about the near-field reactive energy around generic antennas for arbitrary spatio-temporal excitation signals. Using electric and magnetic fields calculated via FDTD technique and interpolation routines, we compute and plot the normalized values of space/time integrated EM Lagrangian around antennas. While the time-integration of EM Lagrangian sheds light onto the spatial distribution of inductive/capacitive reactive energy, time-variation of spatially integrated EM Lagrangian can help in design of ultra-wideband (UWB) MIMO antennas with low mutual coupling. The EM Lagrangian approach can assist in design of energy harvesting and wireless power transfer systems, as well as for electromagnetic interference mitigation applications.

scholarly journals Development of an Improved LMD Method for the Low-Frequency Elements Extraction from Turbine Noise Background

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 805
Author(s):  
Lida Liao ◽  
Bin Huang ◽  
Qi Tan ◽  
Kan Huang ◽  
Mei Ma ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Wind Turbine ◽  
Condition Monitoring ◽  
Renewable Energy Sources ◽  
Near Field ◽  
Low Frequency ◽  
Aerodynamic Noise ◽  
Frequency Noise ◽  
Human Society ◽  
Noise Background

Given the prejudicial environmental effects of fossil-fuel based energy production, renewable energy sources can contribute significantly to the sustainability of human society. As a clean, cost effective and inexhaustible renewable energy source, wind energy harvesting has found a wide application to replace conventional energy productions. However, concerns have been raised over the noise generated by turbine operating, which is helpful in fault diagnose but primarily identified for its adverse effects on the local ecosystems. Therefore, noise monitoring and separation is essential in wind turbine deployment. Recent developments in condition monitoring provide a solution for turbine noise and vibration analysis. However, the major component, aerodynamic noise is often distorted in modulation, which consequently affects the condition monitoring. This study is conducted to explore a novel approach to extract low-frequency elements from the aerodynamic noise background, and to improve the efficiency of online monitoring. A framework built on the spline envelope method and improved local mean decomposition has been developed for low-frequency noise extraction, and a case study with real near-field noises generated by a mountain-located wind turbine was employed to validate the proposed approach. Results indicate successful extractions with high resolution and efficiency. Findings of this research are also expected to further support the fault diagnosis and the improvement in condition monitoring of turbine systems.

A Numerical Study of the Blade Passing Frequency Noise of a Centrifugal Fan

2012 ◽  
Author(s):  
Jian-Cheng Cai ◽  
Da-Tong Qi ◽  
Yong-Hai Zhang
Keyword(s):  
Pressure Fluctuation ◽  
Sound Radiation ◽  
Aerodynamic Noise ◽  
Sound Power ◽  
Centrifugal Fan ◽  
Structural Noise ◽  
Tonal Noise ◽  
Fan Noise ◽  
Blade Passing Frequency ◽  
Dipole Sources

Tonal noise constitutes the major part of the overall fan noise, especially the blade passing frequency (BPF) noise which is generally the most dominant component. This paper studies the BPF tonal noise of a centrifugal fan, including the blade noise, casing aerodynamic noise, and casing structural noise caused by the flow-induced casing vibration. Firstly, generation mechanism and propagation process of fan noise were discussed and the measured spectra of fan noise and casing vibration were presented. Secondly, a fully 3-D transient simulation of the internal flow field of the centrifugal fan was carried out by the computational fluid dynamics (CFD) approach. The results revealed that the flow interactions between the impeller and the volute casing caused periodic pressure fluctuations on the solid walls of the impeller and casing. This pressure fluctuation induces aerodynamic noise radiation as dipole sources, as well as structural vibration as force excitations. Thirdly, using the acoustic analogy theory, the aeroacoustic dipole sources on the casing and blade surface were extracted. The BPF casing and blade aerodynamic sound radiation were solved by the boundary element method (BEM) taking into account the scattering effect of the casing structure. Finally, the casing structural noise was studied. The casing forced vibration and sound radiation under the excitation of BPF pressure fluctuation were calculated by finite element method (FEM) and BEM, respectively. The result indicates that at the studied flow rate, the sound power levels of the casing aerodynamic noise, blade aerodynamic noise and casing structural noise are 103 dB, 91 dB and 79 dB with the reference sound power of 1×10−12 W, respectively.

On the generation of sound by turbulent boundary layer flow over a rough wall

1984 ◽  
Vol 395 (1809) ◽  
pp. 247-263 ◽  
Keyword(s):  
Boundary Layer ◽  
Near Field ◽  
Spectral Characteristics ◽  
Rigid Wall ◽  
Control Surface ◽  
Aerodynamic Noise ◽  
Stream Velocity ◽  
Main Stream ◽  
Wall Roughness ◽  
Boundary Layer Turbulence

The production of sound by scattering of the near field of low Mach number boundary-layer turbulence by a rough, rigid wall is examined on the basis of Lighthill’s theory ( Proc. R. Soc. Lond . A 211, 564 (1952)) of aerodynamic noise. The radiation is expressed in terms of the turbulence pressure spectrum on a control surface that is parallel to the mean plane of the wall and at a stand-off distance equal to the height of the wall roughness elements, the surface irregularities being modelled by a distribution of hemispherical bosses on an otherwise plane wall. The intensity of the sound produced by unit area of the wall varies as the sixth power of the main stream velocity and, for given wall roughness, increases as the boundary-layer thickness decreases. These conclusions are in accord with experimental observations reported by Hersh { AIAA paper no. 83-0786) of the generation of high frequency sound by turbulent flow from sand-roughened pipes, and it is shown how, for moderately rough pipes, the theory reproduces the spectral characteristics of Hersh’s data.

LES of the Flow and Acoustics Generated by an Aircraft Fan Running in the Vicinity of the Ground

2005 ◽  
Author(s):  
Dragos¸ Moroianu ◽  
Arne Karlsson ◽  
Laszlo Fuchs
Keyword(s):  
Sound Pressure ◽  
Near Field ◽  
Pressure Level ◽  
Velocity Variation ◽  
Noise Generation ◽  
Fan Noise ◽  
Blade Passage ◽  
Homogeneous Wave ◽  
Sound Spectrum ◽  
Homogeneous Wave Equation

An important component of the aircraft generated noise, especially ahead of it, is the fan noise created by the high velocity variation near the blades and the interaction of the rotating fan with the fluid. In order to predict the sound, the method used involves the acoustical analogy developed by Ffowcs Williams and Hawkings. Computation of the flow field is performed in the incompressible LES framework, while the noise is evaluated using a non-homogeneous wave equation. In this work the influence of the angle between the fan and ground, on the total sound spectrum, the noise generation and the noise propagation is investigated. It is found that the near field is dominated by the blade passage frequency and an upward inclination of the fan will produce a slightly different sound pressure level than a horizontal or downward inclination.

Finite Elements in Time and Space

1969 ◽  
Vol 73 (708) ◽  
pp. 1041-1044 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Linear Equations ◽  
Time Integration ◽  
Fixed Time ◽  
Time Interval ◽  
Structural Elements ◽  
Dynamic Problems ◽  
System Of Linear Equations ◽  
Interpolation Procedure ◽  
Variational Statement

The present paper seeks to apply the ideas of discretisation to time dependent phenomena. As a suitable variational statement we may use Hamilton's principle. In practise this means that the time is discretised into a set of finite elements which are taken to be the same for all structural elements. A finite element in time consists simply of a fixed time interval. In our present discussion we detail in particular the case when at the beginning and end of the time interval the generalised displacements and velocities are given. For dynamic problems this is the minimum of information required, but the technique may easily be extended to account for additional “timewise degrees of freedoms”. Introducing an appropriate interpolation procedure we may obtain the displacement and velocity at any instant of time. It is then possible to carry out in the variational statement the time integration explicitly and to obtain hence a system of linear equations. The method is extremely simple, since the time interpolation of all structural freedoms of an element in space is the same. We also demonstrate that the general case of a multi-degree of freedoms system can be made to depend on the matrices which describe the unidimensional motion of a mass point.

scholarly journals A Novel Technique to Solve the Fuzzy System of Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 850
Author(s):  
Nasser Mikaeilvand ◽  
Zahra Noeiaghdam ◽  
Samad Noeiaghdam ◽  
Juan J. Nieto
Keyword(s):  
Linear System ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Linear Equations ◽  
Second Step ◽  
Negative Solution ◽  
System Of Linear Equations ◽  
Vector Solution ◽  
Novel Technique ◽  
Fuzzy Linear System

The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

Sign in / Sign up

Export Citation Format

Share Document