Analysis on low-frequency fluctuation of aerodynamic force acting on an automobile and flow using proper orthogonal decomposition

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.

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

Noise Control and Acoustics ◽

10.1115/imece2003-41922 ◽

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.

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Advanced Identification of Coherent Structures in Swirl-Stabilized Combustors

Volume 4A: Combustion, Fuels and Emissions ◽

10.1115/gt2016-56591 ◽

2016 ◽

Author(s):

Moritz Sieber ◽

Christian Oliver Paschereit ◽

Kilian Oberleithner

Keyword(s):

Heat Release ◽

Proper Orthogonal Decomposition ◽

Coherent Structures ◽

High Speed ◽

Low Frequency ◽

Orthogonal Decomposition ◽

Time Resolved ◽

Operation Conditions ◽

Natural Dynamics ◽

Proper Orthogonal

We present an application of a newly introduced method to analyze the time-resolved experimental data from the flow field of a swirl-stabilized combustor. This method is based on classic proper orthogonal decomposition (POD) extended by a temporal constraint. The filter operation embedded in this method allows for continuous fading from the classic POD to the Fourier mode decomposition. This new method — called spectral proper orthogonal decomposition (SPOD) — allows for a clearer separation of the dominant mechanisms due to a clean spectral separation of phenomena. In this paper, the fundamentals of SPOD are shortly introduced. The actual focus is put on the application to a combustor flow. We analyze high-speed PIV measurements from flow fields in a combustor at different operation conditions. In these measurements, we consider externally actuated, as well as natural dynamics and reveal how the natural and actuated modes interact with each other. As shown in the paper, SPOD provides detailed insight into coherent structures in swirl flames. Two distinct PVC structures are found that are very differently affected by acoustic actuation. The coherent structures are related to heat release fluctuations, which are derived from simultaneously acquired OH* chemiluminescence measurements. Besides the actuated modes, a low frequency mode was found that significantly contribute to the global heat release fluctuations.

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Application of Proper Orthogonal Decomposition to High Speed Imaging for the Study of Combustion Oscillations

Volume 4B: Combustion, Fuels and Emissions ◽

10.1115/gt2017-64602 ◽

2017 ◽

Cited By ~ 2

Author(s):

Siddhartha Gadiraju ◽

Suhyeon Park ◽

David Gomez-Ramirez ◽

Srinath V. Ekkad ◽

K. Todd Lowe ◽

...

Keyword(s):

Proper Orthogonal Decomposition ◽

High Speed ◽

Equivalence Ratio ◽

Flame Structure ◽

Low Frequency ◽

Orthogonal Decomposition ◽

Pressure Measurements ◽

High Speed Imaging ◽

Flame Structures ◽

Proper Orthogonal

The flame structure and characteristics generated by an industrial low emission, lean premixed, fuel swirl nozzle were analyzed for understanding combustion oscillations. The experimental facility is located at the Advanced Propulsion and Power Laboratory (APPL) at Virginia Tech. The experiments were carried out in a model optical can combustor operating at atmospheric pressures. Low-frequency oscillations (<100 Hz) were observed during the reaction as opposed to no reaction, cold flow test cases. The objective of this paper is to understand the frequency and magnitude of oscillations due to combustion using high-speed imaging and associate them with corresponding structure or feature of the flame. Flame images were obtained using a Photron Fastcam SA4 high-speed camera at 500 frames per second. The experiments were conducted at equivalence ratios of 0.65, 0.75; different Reynolds numbers of 50K, 75K; and three pilot fuel to main fuel ratios of 0%, 3%, 6%. In this study, Reynolds number was based on the throat diameter of the fuel nozzle. Since the time averaged flame images are not adequate representation of the flame structures, proper orthogonal decomposition (POD) was applied to the flame images to extract the dominant features. The spatiotemporal dynamics of the images can be decomposed into their constituent modes of maximum spatial variance using POD so that the dominant features of the flame can be observed. The frequency of the dominant flame structures, as captured by the POD modes of the flame acquisitions, were consistent with pressure measurements taken at the exit of the combustor. Thus, the oscillations due to combustion can be visualized using POD. POD was further applied to high-speed images taken during instabilities. Specifically, the instabilities discussed in this paper are those encountered when the equivalence ratio is reduced to the levels approaching lean blowout (LBO). As the equivalence ratio is reduced to near blowout regime, it triggers low-frequency high amplitude instabilities. These low-frequency instabilities are visible as the flapping of the flame. The frequencies of the dominant POD modes are consistent with pressure measurements recorded during these studies.

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Advanced Identification of Coherent Structures in Swirl-Stabilized Combustors

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4034261 ◽

2016 ◽

Vol 139 (2) ◽

Cited By ~ 16

Author(s):

Moritz Sieber ◽

Christian Oliver Paschereit ◽

Kilian Oberleithner

Keyword(s):

Heat Release ◽

Proper Orthogonal Decomposition ◽

Coherent Structures ◽

High Speed ◽

Low Frequency ◽

Orthogonal Decomposition ◽

Time Resolved ◽

Operation Conditions ◽

Natural Dynamics ◽

Proper Orthogonal

We present an application of a newly introduced method to analyze the time-resolved experimental data from the flow field of a swirl-stabilized combustor. This method is based on the classic proper orthogonal decomposition (POD) extended by a temporal constraint. The filter operation embedded in this method allows for continuous fading from the classic POD to the Fourier mode decomposition. This new method—called spectral proper orthogonal decomposition (SPOD)—allows for a clearer separation of the dominant mechanisms due to a clean spectral separation of phenomena. In this paper, the fundamentals of SPOD are shortly introduced. The actual focus is put on the application to a combustor flow. We analyze high-speed particle image velocimetry (PIV) measurements from flow fields in a combustor at different operation conditions. In these measurements, we consider externally actuated, as well as natural dynamics and reveal how the natural and actuated modes interact with each other. As shown in the paper, SPOD provides detailed insight into coherent structures in the swirl flames. Two distinct PVC structures are found that are very differently affected by acoustic actuation. The coherent structures are related to the heat release fluctuations, which are derived from simultaneously acquired OH* chemiluminescence measurements. Besides the actuated modes, a low frequency mode was found that significantly contribute to the global heat release fluctuations.

Download Full-text