On Proper Orthogonal Decomposition or K-L Expansion to Analyze Transient Sound Pressure Fields in Linear Acoustics

2003 ◽  
Author(s):  
Ioannis T. Georgiou ◽  
Christos I. Papadopoulos
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Sound Pressure ◽  
Pressure Field ◽  
Low Frequency ◽  
Temporal Patterns ◽  
Orthogonal Decomposition ◽  
Noise Sources ◽  
Air Cavity ◽  
Spatio Temporal ◽  
Proper Orthogonal

Identification of the most energetic spatio-temporal patterns that govern the low-frequency dynamics of an air cavity excited by noise sources could lead to significant design improvements of enclosures for noise reduction / isolation and / or sound quality. In this work we show how the Proper Orthogonal Decomposition (POD) method can be applied to identify optimum spatio-temporal patterns governing the dynamics of the sound pressure field developed inside an air cavity. The novel feature of this approach resides into the fact that the POD technique is utilized to process databases for acoustic variables produced by state of the art computational methods in acoustics, such as the finite element method. For a cavity with rigid walls and excited by a harmonic point source, the POD technique reveals that the sound pressure field is composed of a very small number of Proper Orthogonal Modes, which are unique since they are optimum by construction. The POD technique identifies the shapes or patterns of these modes.

A Proper Orthogonal Decomposition Analysis to Identify the Dominant Modes of the Steady State Acoustic Pressure Field in a Cavity

2003 ◽  
Author(s):  
Ioannis T. Georgiou ◽  
Christos I. Papadopoulos
Keyword(s):  
Steady State ◽  
Proper Orthogonal Decomposition ◽  
Sound Pressure ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Decomposition Analysis ◽  
Orthogonal Decomposition ◽  
Harmonic Source ◽  
Proper Orthogonal ◽  
Identification Tool

The technique of Proper Orthogonal Decomposition (POD) has been used to develop an identification tool to analyze steady state dynamics in acoustics. The information on the dynamics needed for the POD technique is obtained by solving numerically with the method of finite elements the wave equation inside a cavity. The POD technique identifies optimum spatial patterns it terms of Proper Orthogonal Modes. The steady state sound pressure field in a cavity excited by a single harmonic source responds with a very small number of POD modes. Under certain forcing conditions, the POD modes are identical to the Fourier acoustic modes. The POD technique of Proper Orthogonal Decomposition (POD) proves to be a very effective identification tool.

Study on flow field and aerodynamic noise of electric vehicle rearview mirror

2021 ◽  
pp. 095440702110228
Author(s):  
Xiaowei Hao ◽  
Zhigang Yang ◽  
Qiliang Li
Keyword(s):  
Flow Field ◽  
Proper Orthogonal Decomposition ◽  
Electric Vehicle ◽  
Sound Pressure ◽  
Pressure Level ◽  
Orthogonal Decomposition ◽  
Aerodynamic Noise ◽  
Turbulent Pressure ◽  
Rearview Mirror ◽  
Proper Orthogonal

With the development of new energy and intelligent vehicles, aerodynamic noise problem of pure electric vehicles at high speed has become increasingly prominent. The characteristics of the flow field and aerodynamic noise of the rearview mirror region were investigated by large eddy simulation, acoustic perturbation equations and reduction order analysis. By comparing the pressure coefficients of the coarse, medium and dense grids with wind tunnel test results, the pressure distribution, and numerical accuracy of the medium grid on the body are clarified. It is shown from the flow field proper orthogonal decomposition of the mid-section that the sum of the energy of the first three modes accounts for more than 16%. Based on spectral proper orthogonal decomposition, the peak frequencies of the first-order mode are 19 and 97 Hz. As for the turbulent pressure of side window, the first mode accounts for approximately 11.3% of the total energy, and its peak appears at 39 and 117 Hz. While the first mode of sound pressure accounts for about 41.7%, and the energy peaks occur at 410 and 546 Hz. Compared with traditional vehicle, less total turbulent pressure level and total sound pressure level are found at current electric vehicle because of the limited interaction between the rearview mirror and A-pillar.

PROPER ORTHOGONAL DECOMPOSITION OF RANDOM WIND PRESSURE FIELD

1999 ◽  
Vol 13 (7-8) ◽  
pp. 1069-1095 ◽  
Author(s):  
Y. TAMURA ◽  
S. SUGANUMA ◽  
H. KIKUCHI ◽  
K. HIBI
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Pressure Field ◽  
Orthogonal Decomposition ◽  
Wind Pressure ◽  
Proper Orthogonal

Proper Orthogonal Decomposition and Extended- Proper Orthogonal Decomposition Analysis of Pressure Fluctuations and Vortex Structures Inside a Steam Turbine Control Valve

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Peng Wang ◽  
Hongyu Ma ◽  
Yingzheng Liu
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Steam Turbine ◽  
Pressure Fluctuation ◽  
Pressure Field ◽  
Pressure Fluctuations ◽  
Control Valve ◽  
Vortex Structures ◽  
Orthogonal Decomposition ◽  
Pod Analysis ◽  
Proper Orthogonal

In steam turbine control valves, pressure fluctuations coupled with vortex structures in highly unsteady three-dimensional flows are essential contributors to the aerodynamic forces on the valve components, and are major sources of flow-induced vibrations and acoustic emissions. Advanced turbulence models can capture the detailed flow information of the control valve; however, it is challenging to identify the primary flow structures, due to the massive flow database. In this study, state-of-the-art data-driven analyses, namely, proper orthogonal decomposition (POD) and extended-POD, were used to extract the energetic pressure fluctuations and dominant vortex structures of the control valve. To this end, the typical annular attachment flow inside a steam turbine control valve was investigated by carrying out a detached eddy simulation (DES). Thereafter, the energetic pressure fluctuation modes were determined by conducting POD analysis on the pressure field of the valve. The vortex structures contributing to the energetic pressure fluctuation modes were determined by conducting extended-POD analysis on the pressure–velocity coupling field. Finally, the dominant vortex structures were revealed conducting a direct POD analysis of the velocity field. The results revealed that the flow instabilities inside the control valve were mainly induced by oscillations of the annular wall-attached jet and the derivative flow separations and reattachments. Moreover, the POD analysis of the pressure field revealed that most of the pressure fluctuation intensity comprised the axial, antisymmetric, and asymmetric pressure modes. By conducting extended-POD analysis, the incorporation of the vortex structures with the energetic pressure modes was observed to coincide with the synchronous, alternating, and single-sided oscillation behaviors of the annular attachment flow. However, based on the POD analysis of the unsteady velocity fields, the vortex structures, buried in the dominant modes at St = 0.017, were found to result from the alternating oscillation behaviors of the annular attachment flow.

Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

2005 ◽  
Vol 127 (4) ◽  
pp. 553-562 ◽  
Author(s):  
Korn Saranyasoontorn ◽  
Lance Manuel
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Low Frequency ◽  
Orthogonal Decomposition ◽  
Response Variance ◽  
Spectral Models ◽  
Inflow Turbulence ◽  
Using Data ◽  
Low Dimensional ◽  
Proper Orthogonal

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

scholarly journals Spatio-temporal proper orthogonal decomposition of turbulent channel flow

2019 ◽  
Vol 864 ◽  
pp. 614-639 ◽  
Author(s):  
Srikanth Derebail Muralidhar ◽  
Bérengère Podvin ◽  
Lionel Mathelin ◽  
Yann Fraigneau
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Channel Flow ◽  
Nonlinear Effects ◽  
Turbulent Channel Flow ◽  
Wall Layer ◽  
Orthogonal Decomposition ◽  
Closed Form Expression ◽  
Temporal Decomposition ◽  
Spatio Temporal ◽  
Proper Orthogonal

An extension of proper orthogonal decomposition is applied to the wall layer of a turbulent channel flow ($Re_{\unicode[STIX]{x1D70F}}=590$), so that empirical eigenfunctions are defined in both space and time. Due to the statistical symmetries of the flow, the eigenfunctions are associated with individual wavenumbers and frequencies. Self-similarity of the dominant eigenfunctions, consistent with wall-attached structures transferring energy into the core region, is established. The most energetic modes are characterized by a fundamental time scale in the range 200–300 viscous wall units. The full spatio-temporal decomposition provides a natural measure of the convection velocity of structures, with a characteristic value of 12$u_{\unicode[STIX]{x1D70F}}$ in the wall layer. Finally, we show that the energy budget can be split into specific contributions for each mode, which provides a closed-form expression for nonlinear effects.

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