Prediction of the Optimal Vortex in Synthetic Jets

Abstract

This article presents three different low-order models to predict the main flow patterns in synthetic jets. The first model provides a simple theoretical approach based on experimental solutions explaining how to artificially generate the optimal vortex, which maximizes the production of thrust and system efficiency. The second model is a data-driven method that uses higher-order dynamic mode decomposition (HODMD). To construct this model, (i) Navier–Stokes equations are solved for a very short period of time providing a transient solution, (ii) a group of spatio-temporal data are collected containing the information of the transitory of the numerical simulations, and finally (iii) HODMD decomposes the solution as a Fourier-like expansion of modes that are extrapolated in time, providing accurate predictions of the large size structures describing the general flow dynamics, with a speed-up factor of 8 . 3 in the numerical solver. The third model is an extension of the second model, which combines HODMD with a low-rank approximation of the spatial domain, which is based on singular value decomposition (SVD). This novel approach reduces the memory requirements by 70% and reduces the computational time to generate the low-order model by 3, maintaining the speed-up factor to 8 . 3 . This technique is suitable to predict the temporal flow patterns in a synthetic jet, showing that the general dynamics is driven by small amplitude variations along the streamwise direction. This new and efficient tool could also be potentially used for data forecasting or flow pattern identification in any type of big database.

Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

“…HODMD is an extension of the well known technique, in the field of fluid dynamics, dynamic mode decomposition (DMD) [34], generally used for the analysis of complex data modeling non-linear dynamical systems, solving different applications (e.g, [42], [43], [44]). Similarly to DMD, HODMD decomposes spatio-temporal data into a number of modes, each mode related to a frequency, growth rate and amplitude, as presented in the following DMD expansion…”

“…( 11), then the method is applied iteratively over this data reconstruction until the number of HOSVD modes is the same between two consecutive iterations. The algorithm has been validated and successfully tested in several applications (see [42], [43], [44]). More details about the algorithm can be found in [41].…”

“…In this work, we explore a new method that, to the authors knowledge has not yet been used in the field of medical imaging before: the Higher Order Dynamic Mode Decomposition (HODMD) technique [40]. As has been demonstrated in ( [41], [42], [43], [44]), the HODMD method is a more robust and accurate version of classical DMD, suitable for the analysis of complex signals and non-linear dynamical systems. The enhanced performance of HODMD, solidly grounded on mathematics and computer science principles, justifies our interest in its application for the analysis of medical images.…”

A data-driven model based on modal decomposition: application to the turbulent channel flow over an anisotropic porous wall

“…During recent years, the community has paid special attention to finding new tools that provide low-rank high-fidelity models describing the main flow dynamics, relate inputs to outputs for flow control (e.g. balanced truncation) and develop models for unexplored physics (Sharma 2011;Lassila et al 2014;Le Clainche 2019;Mendez, Balabane and Buchlin 2019).…”

Machine-Learning Methods for Complex Flows

“…For instance, when it comes to developing reduced-order models (ROMs), deep learning (which is an area within ML focused on the use of neural networks with more than one hidden layer) has been shown to provide accurate representations of the temporal dynamics of the near-wall region of turbulence [8], and has also been introduced as a suitable tool to accelerate numerical simulations in complex flows [9,10]. In this context, other data-driven methods, based on the Koopman operator, also have the potential to provide accurate descriptions of the temporal dynamics in these cases [11][12][13][14][15][16], or even the three-dimensional spatio-temporal reconstruction of spare databases [17]. Deep learning has also been used to obtain non-linear modal decompositions of fluid flows, using convolutional neural networks [18] and autoencoders [19], including applications to complex turbulent flows [20].…”