scholarly journals Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition

2006 ◽  
Vol 35 (2) ◽  
pp. 208-226 ◽  
Author(s):  
K. Willcox
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Flow Sensing ◽  
Proper Orthogonal

Analysis of Unsteady Flow Structures in a Radial Turbomachine by Using Proper Orthogonal Decomposition

2018 ◽  
Author(s):  
Matthias Witte ◽  
Benjamin Torner ◽  
Frank-Hendrik Wurm
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Flow Structures ◽  
Periodic Flow ◽  
Noise Emission ◽  
Turbulent Flow Field ◽  
Proper Orthogonal

Tonalities in hydro and airborne noise emission are a known problem of turbomachines, wherein the tonalities in the noise spectrum are associated with the different orders of the blade passing frequency (BPF). The proper orthogonal decomposition (POD) method was utilized to find the relationship between the fluctuations in the pressure field at the BPF orders which are the origin of the noise emission and the correlated fluctuations in the turbulent velocity field in terms of coherent, periodic flow structures. In order the provide the input data for the POD analysis, a URANS k-ω-SST scale adaptive simulation (SAS) of the turbulent flow field in a single stage radial pump under part load conditions was performed. Compared to traditional two equation turbulence models this approach is less dissipative and allows the development of small scale turbulence structures and is therefore an appropriate method for this study. In order to compute the POD correlation matrix Sirovich’s “Methods of Snapshots” was applied to the unsteady pressure and velocity fields from the CFD simulation. The discrimination of coherent, periodic flow structures and the incoherent, chaotic turbulence was carried out by analyzing the POD eigenvalue distributions, the POD mode shapes and the spectral properties of the POD time coefficients. Five coupled POD mode pairs were identified in total, which were strictly correlated with the 1st, 2nd, 3rd, 4th and 5th order of the BPF and therefore responsible for the noise emission at these discrete frequencies. The coherent structures were explored on the basis of the spatial POD velocity und pressure mode shapes and in terms of vortical structures after an additional phase averaging. The scope of this study is to introduce an enhanced collection of post processing techniques which are capable of analyzing highly unsteady flow fields from numerical simulations in a better way than is possible by just using traditional techniques like the evaluation of integral or time averaged quantities. The identified coherent flow structures and their associated pressure fluctuations are key elements for a proper comprehension of the internal dynamics of the turbulent flow field in a turbomachine and therefore essential for the understanding of the noise generation processes and the optimization of such machines.

Model order reduction using sparse coding exemplified for the lid-driven cavity

2016 ◽  
Vol 808 ◽  
pp. 189-223 ◽  
Author(s):  
Rohit Deshmukh ◽  
Jack J. McNamara ◽  
Zongxian Liang ◽  
J. Zico Kolter ◽  
Abhijit Gogulapati
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Sparse Coding ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Driven Cavity ◽  
Reduced Order ◽  
Multi Scale ◽  
Small Set ◽  
Proper Orthogonal

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

Application of the Proper Orthogonal Decomposition Method in Analyzing Active Separation Control With Periodic Vibration Wall

2019 ◽  
Vol 36 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Jin-Chun Wang ◽  
Xin Fu ◽  
Guo-Ping Huang ◽  
Shu-Li Hong ◽  
Yuan-Chi Zou
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Excitation Frequency ◽  
Orthogonal Decomposition ◽  
Maximum Lyapunov Exponent ◽  
Periodic Excitation ◽  
Control Effect ◽  
Higher Modes ◽  
Proper Orthogonal

AbstractThe proper orthogonal decomposition (POD) method is employed to analyze the unsteady flow control mechanism because it is a good approach to decouple the spatial and temporal structures of unsteady flow fields. The results showed that the main effect of the periodic excitation is reallocating the energy of each mode, and selectively strengthening or weakening certain modes. Under proper amplitude and frequency of periodic excitation, the energy in higher modes will be transferred to the first mode and the translation of the modal energy is coming from the reconstructing of spatial flow structures and the ordering of modal evolution characteristics. The best control effect will be achieved when the total energy ratio of the first mode is the highest and the excitation frequency reaches the separation vortex frequency at the same time. In order to quantitatively analyze the order degree of the unsteady flow field, the maximum Lyapunov exponent was introduced. The results showed that with the energy in higher modes transferred to the lower modes, the flow field transfers from a disordered pattern to an ordered one.

Unsteady flow characteristics in centrifugal pump based on proper orthogonal decomposition method

2021 ◽  
Vol 33 (7) ◽  
pp. 075122
Author(s):  
Zhengchuan Zhang ◽  
Hongxun Chen ◽  
Junlian Yin ◽  
Zheng Ma ◽  
Qi Gu ◽  
...  
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Centrifugal Pump ◽  
Decomposition Method ◽  
Flow Characteristics ◽  
Orthogonal Decomposition ◽  
Proper Orthogonal

Unsteady Flow Interactions Between a High- and Low-Pressure Turbine: Part 2 — Rotor-Synchronic Averaging and Proper Orthogonal Decomposition of the Unsteady Flow Fields

2019 ◽  
Author(s):  
M. Dellacasagrande ◽  
P. Z. Sterzinger ◽  
S. Zerobin ◽  
F. Merli ◽  
L. Wiesinger ◽  
...  
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Low Pressure ◽  
Fast Response ◽  
Orthogonal Decomposition ◽  
Pressure Probe ◽  
Low Pressure Turbine ◽  
Aerodynamic Pressure ◽  
Proper Orthogonal

Abstract This paper, the second of two parts, presents an experimental investigation of the unsteady flow field evolving in a two-stage two-spool test turbine facility. The experimental setup, which was designed to reproduce the operating condition of modern commercial aero-engines, consists of a high-pressure turbine (HPT) stage followed by a turbine center frame (TCF) with non-turning struts, and a co-rotating low-pressure turbine (LPT) stage. Measurements carried out with a fast-response aerodynamic pressure probe (FRAPP) were post-processed to describe the unsteady evolution of the flow downstream of the HPT rotor, through the TCF duct, and at the exit of the LPT stage. The time-resolved results presented in the first part of this paper show that deterministic fluctuations due to both rotors characterize the flow field downstream of the LPT. In order to characterize the deterministic unsteadiness induced by all the components constituting the turbine facility (HPT, TCF and LPT) and their interactions, measurements were carried out in three different planes located downstream of the HPT, at the exit of the TCF and downstream of the LPT stage. The unsteady results obtained in the plane located at the exit of the LPT are discussed in more details in this second part of this paper, providing information about the interactions between the two rotors. A proper phase-average procedure, known as rotor synchronic averaging (RSA), which takes into account the rotorrotor interaction, was adopted to capture the unsteadiness due to both rotors. Proper Orthogonal Decomposition (POD) was also applied to provide a characterization of the major contributors in terms of energy to the deterministic unsteadiness occurring in the test turbine facility. At the exit of the LPT rotor, the perturbations induced by the HPT stage and the interactions between the two rotors were found to dominate over the unsteadiness due to the LPT only.

Unsteady Behaviors of Steam Flow in a Control Valve With T-Junction Discharge Under the Choked Condition: Detached Eddy Simulation and Proper Orthogonal Decomposition

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Peng Wang ◽  
Hongyu Ma ◽  
Yingzheng Liu
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Control Valve ◽  
Orthogonal Decomposition ◽  
Detached Eddy Simulation ◽  
Flow Passage ◽  
Eddy Simulation ◽  
Periodic Fluctuations ◽  
Proper Orthogonal

Due to the practical space limitation, the control valve in industrial utilities is usually immediately followed by a short flow passage, which would introduce considerable complexity into highly unsteady flow behaviors, along with the flow noise and structure vibration. In the present study, the unsteady behaviors of the steam flow inside a control valve with a T-junction discharge, when the valve operates under the choked condition, are numerically simulated. Toward this end, the detached eddy simulation (DES) is used to capture the spatiotemporally varying flow field in the serpentine flow passage. The results show periodic fluctuations of the aerodynamic forces on the valve spindle and periodic fluctuations of the pressure and flow rate at the two discharge outlets. Subsequently, proper orthogonal decomposition (POD) analysis is conducted using the velocity field and pressure field, identifying, respectively, the dominant coherent structures and energetic pressure fluctuation modes. Finally, the extended-POD method is used to delineate the coupling between the pressure fluctuations with the dominant flow structures superimposed in the highly unsteady flow field. The fourth velocity mode at St = 0.1, which corresponds to the alternating oscillations of the annular wall-attached jet, is determined to cause the periodic flow imbalance at the two discharge outlets, whereas signatures of the first three modes are found to be dissipated in the spherical chamber. Such findings could serve as facts for vibration prediction and optimization design. Particularly, the POD and extended-POD techniques were demonstrated to be effective methodologies for analyzing the highly turbulent flows in engineering fluid mechanics.

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