A reduced-order model for compressible flows with buffeting condition using higher order dynamic mode decomposition with a mode selection criterion

Abstract The Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) are used to analyze the coherent structures of turbulent flow around vibrating isolated and piggyback cylinders configurations subjected to a uniform flow at a laminar Reynolds number (Re=200) and a upper transition Reynolds number (Re=3.6×106). Numerical simulations using two-dimensional URANS (Unsteady Reynolds Averaged Navier-Stokes) approach with the k-omega SST turbulence model are used to obtain the flow fields snapshots for the analysis. The wake flows behind the cylinders are decomposed into energy optimal modes (POD modes) and dynamical relevant modes (DMD modes). A reduced-order model for the flow is built based on the modal analysis. A comparison of POD and DMD is performed to characterize their special features. The present study provides new insights into the flow physics of fluid-structure interaction problem of two coupled cylinders. The characteristic vortex shedding frequencies and their harmonics are identified by DMD modes in all the investigated configurations. It is observed that for single cylinder configurations the most energetic and the most dynamically important mode is associated with the fundamental shedding frequency. For the stationary piggyback configuration, the gap flow between the cylinders appears to be a dominant flow feature as evidenced by leading DMD modes. The cylinder vibration increases significantly number of modes necessary to obtain a reduced order model (ROM) at given level of accuracy compared to respective stationary configurations.

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Data-driven construction of a reduced-order model for supersonic boundary layer transition

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.470 ◽

2019 ◽

Vol 874 ◽

pp. 1096-1114 ◽

Cited By ~ 5

Author(s):

Ming Yu ◽

Wei-Xi Huang ◽

Chun-Xiao Xu

Keyword(s):

Compressible Flows ◽

Incompressible Flows ◽

Temporal Evolution ◽

Reduced Order Model ◽

Boundary Layer Transition ◽

Galerkin Projection ◽

Data Driven ◽

Dynamic Mode ◽

Order Model ◽

Reduced Order

In this study, a data-driven method for the construction of a reduced-order model (ROM) for complex flows is proposed. The method uses the proper orthogonal decomposition (POD) modes as the orthogonal basis and the dynamic mode decomposition method to obtain linear equations for the temporal evolution coefficients of the modes. This method eliminates the need for the governing equations of the flows involved, and therefore saves the effort of deriving the projected equations and proving their consistency, convergence and stability, as required by the conventional Galerkin projection method, which has been successfully applied to incompressible flows but is hard to extend to compressible flows. Using a sparsity-promoting algorithm, the dimensionality of the ROM is further reduced to a minimum. The ROMs of the natural and bypass transitions of supersonic boundary layers at $Ma=2.25$ are constructed by the proposed data-driven method. The temporal evolution of the POD modes shows good agreement with that obtained by direct numerical simulations in both cases.

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Data Driven Modal Decomposition of the Wake behind an NREL-5MW Wind Turbine

International Journal of Turbomachinery Propulsion and Power ◽

10.3390/ijtpp6040044 ◽

2021 ◽

Vol 6 (4) ◽

pp. 44

Author(s):

Stefania Cherubini ◽

Giovanni De Cillis ◽

Onofrio Semeraro ◽

Stefano Leonardi ◽

Pietro De Palma

Keyword(s):

Flow Field ◽

Wind Turbine ◽

Large Scale ◽

Reduced Order Model ◽

Dynamic Mode Decomposition ◽

Speed Ratio ◽

Dynamic Mode ◽

Order Model ◽

Modal Decomposition ◽

Reduced Order

The wake produced by a utility-scale wind turbine invested by a laminar, uniform inflow is analyzed by means of two different modal decompositions, the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), in its sparsity-promoting variant. The turbine considered is the NREL-5MW at tip-speed ratio λ=7 and a diameter-based Reynolds number of the order 108. The flow is simulated through large eddy simulation, where the forces exerted by the blades are modeled using the actuator line method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by both modal decompositions are compared and some differences emerge that can be of great importance for the formulation of a reduced-order model. In particular, a high-frequency mode directly related to the tip vortices is found using both methods, but it is ranked differently. The other dominant modes are composed by large-scale low-frequency structures, but with different frequency content and spatial structure. The most energetic 200 POD modes account for ≈20% only of the flow kinetic energy. While using the same number of DMD modes, it is possible to reconstruct the flow field to within 80% accuracy. Despite the similarities between the set of modes, the comparison between these modal-decomposition techniques points out that an energy-based criterion such as that used in the POD may not be suitable for formulating a reduced-order model of wind turbine wakes, while the sparsity-promoting DMD appears able to perform well in reconstructing the flow field with only a few modes.

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Reduced-order Model Predictions of Wind Turbines via Mode Decomposition and Sparse Sampling

AIAA Scitech 2021 Forum ◽

10.2514/6.2021-1602 ◽

2021 ◽

Author(s):

Ala' E. Qatramez ◽

Daniel Foti

Keyword(s):

Wind Turbines ◽

Sparse Sampling ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Mode Decomposition ◽

Model Predictions

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Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

Logic Journal of IGPL ◽

10.1093/jigpal/jzaa060 ◽

2020 ◽

Author(s):

Christian Amor ◽

José M Pérez ◽

Philipp Schlatter ◽

Ricardo Vinuesa ◽

Soledad Le Clainche

Keyword(s):

Proper Orthogonal Decomposition ◽

Turbulent Wake ◽

Orthogonal Decomposition ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

Square Cylinder ◽

Complex Flow ◽

Reduced Order ◽

Mode Decomposition ◽

Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

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