scholarly journals Prediction of the Optimal Vortex in Synthetic Jets

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1635 ◽  
Author(s):  
Soledad Le Clainche
Keyword(s):  
Stokes Equations ◽  
Flow Patterns ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Dynamic Mode Decomposition ◽  
Computational Time ◽  
Dynamic Mode ◽  
Short Period ◽  
Speed Up ◽  
Low Order

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.

Design Optimization of Micro Synthetic Jet Actuator for Flow Separation Control

2006 ◽  
Vol 128 (5) ◽  
pp. 1053-1062 ◽  
Author(s):  
Oktay Baysal ◽  
Mehti Köklü ◽  
Nurhak Erbaş
Keyword(s):  
Design Methodology ◽  
Moving Boundary ◽  
Stokes Equations ◽  
Wall Slip ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Recirculation Region ◽  
Flow Separation Control ◽  
Analysis And Design ◽  
Design Variables

A computational analysis and design methodology is presented for effective microflow control using synthetic jets. The membrane is modeled as a moving boundary to accurately compute the flow inside the jet cavity. Compressible Navier-Stokes equations are solved with boundary conditions for the wall slip and the temperature jump conditions encountered for a specific range of Knudsen numbers. For validation, microchannel flow and microfilter flow are successfully computed. Then, flow past a backward-facing step in a microchannel is considered. Analysis is coupled with a design methodology to improve the actuator effectiveness. The objective function is selected to be the square of the vorticity (enstrophy) integrated over a separated region. First, from a design of experiments study, orifice and actuator cavity widths are identified as the most effective design variables. Then, a response surface method is constructed to find the improved control of the flow. This optimization results in more than 83% reduction of the enstrophy of the recirculation region.

Direct numerical simulation of high-speed transition due to an isolated roughness element

2014 ◽  
Vol 748 ◽  
pp. 848-878 ◽  
Author(s):  
Pramod K. Subbareddy ◽  
Matthew D. Bartkowicz ◽  
Graham V. Candler
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Stokes Equations ◽  
Roughness Element ◽  
Dynamic Mode Decomposition ◽  
Large Reynolds Number ◽  
Dynamic Mode ◽  
Low Dissipation

AbstractWe study the transition of a Mach 6 laminar boundary layer due to an isolated cylindrical roughness element using large-scale direct numerical simulations (DNS). Three flow conditions, corresponding to experiments conducted at the Purdue Mach 6 quiet wind tunnel are simulated. Solutions are obtained using a high-order, low-dissipation scheme for the convection terms in the Navier–Stokes equations. The lowest Reynolds number ($Re$) case is steady, whereas the two higher $Re$ cases break down to a quasi-turbulent state. Statistics from the highest $Re$ case show the presence of a wedge of fully developed turbulent flow towards the end of the domain. The simulations do not employ forcing of any kind, apart from the roughness element itself, and the results suggest a self-sustaining mechanism that causes the flow to transition at a sufficiently large Reynolds number. Statistics, including spectra, are compared with available experimental data. Visualizations of the flow explore the dominant and dynamically significant flow structures: the upstream shock system, the horseshoe vortices formed in the upstream separated boundary layer and the shear layer that separates from the top and sides of the cylindrical roughness element. Streamwise and spanwise planes of data were used to perform a dynamic mode decomposition (DMD) (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28).

scholarly journals Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 138
Author(s):  
Anqi Bao ◽  
Eduardo Gildin ◽  
Abhinav Narasingam ◽  
Joseph S. Kwon
Keyword(s):  
Hydraulic Fracturing ◽  
Moving Boundary ◽  
Dynamic Mode Decomposition ◽  
Data Driven ◽  
Flow In Porous Media ◽  
Computational Time ◽  
Dynamic Mode ◽  
Reservoir Models ◽  
Trade Offs ◽  
Fracturing Process

Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

scholarly journals Koopman mode expansions between simple invariant solutions

2019 ◽  
Vol 879 ◽  
pp. 1-27 ◽  
Author(s):  
Jacob Page ◽  
Rich R. Kerswell
Keyword(s):  
State Space ◽  
Stokes Equations ◽  
Time Window ◽  
Landau Equation ◽  
Dynamic Mode Decomposition ◽  
Navier Stokes ◽  
Dynamic Mode ◽  
Invariant Solutions ◽  
Mode Decomposition ◽  
Heteroclinic Connection

A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time dependence. Attempting a Koopman decomposition is simple in practice due to a connection with dynamic mode decomposition (DMD). However, there are non-trivial requirements for the Koopman decomposition and DMD to overlap, which mean it is often difficult to establish whether the latter is truly approximating the former. Here, we focus on nonlinear systems containing multiple simple invariant solutions where it is unclear how to construct a consistent Koopman decomposition, or how DMD might be applied to locate these solutions. First, we derive a Koopman decomposition for a heteroclinic connection in a Stuart–Landau equation revealing two possible expansions. The expansions are centred about the two fixed points of the equation and extend beyond their linear subspaces before breaking down at a cross-over point in state space. Well-designed DMD can extract the two expansions provided that the time window does not contain this cross-over point. We then apply DMD to the Navier–Stokes equations near to a heteroclinic connection in low Reynolds number ($Re=O(100)$) plane Couette flow where there are multiple simple invariant solutions beyond the constant shear basic state. This reveals as many different Koopman decompositions as simple invariant solutions present and once more indicates the existence of cross-over points between the expansions in state space. Again, DMD can extract these expansions only if it does not include a cross-over point. Our results suggest that in a dynamical system possessing multiple simple invariant solutions, there are generically places in phase space – plausibly hypersurfaces delineating the boundary of a local Koopman expansion – across which the dynamics cannot be represented by a convergent Koopman expansion.

Numerical Simulation of a Synthetic Jet Actuator Using a Simplified Periodic Boundary Condition

2010 ◽  
Author(s):  
Antonio Pascau ◽  
Nelson Garci´a
Keyword(s):  
Stokes Equations ◽  
Synthetic Jet ◽  
Navier Stokes ◽  
Computational Time ◽  
Test Case ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Synthetic Jet Actuator ◽  
Collocated Grid ◽  
Face Velocity

When using a collocated grid for the discretization of the unsteady Navier-Stokes equations special care has to be taken in the evaluation of the cell face velocity as if it is not properly calculated the resulting flow field may be dependent on the time step. This dependency increases as the time step is reduced so this problem can be of paramount importance in rapidly varying flows. As an illustration of the problem in a flow of industrial interest a synthetic jet has been chosen. Although the primary goal of the paper is not to compare computational and experimental results, the assessment with experimental data will highlight the discrepancies in the computational results with different time steps. For comparison purposes a well documented case was chosen: the first test case of the synthetic jet workshop organized by NASA in 2004, but with the new 2006 data. This flow is produced by a moving diaphragm at one of the sides of a cavity connected to an otherwise stagnant air through a slot. Near the slot exit the flow is almost bidimensional so in order to reduce computational time it has been modelled in a 2D domain with a transpiration velocity at the bottom boundary of a simplified cavity. This velocity tries to reproduce the waveform of the measurements at the slot exit with an appropriate combination of Fourier modes.

scholarly journals Dynamic reconstruction and data reconstruction for subsampled or irregularly sampled data

2017 ◽  
Vol 825 ◽  
pp. 133-166
Author(s):  
Jakub Krol ◽  
Andrew Wynn
Keyword(s):  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Decomposition Algorithms ◽  
Cylinder Wake ◽  
Sampled Data ◽  
Mode Decomposition ◽  
Image Velocimetry ◽  
Flow Evolution ◽  
Irregularly Sampled Data ◽  
Low Order

The Nyquist–Shannon criterion indicates the sample rate necessary to identify information with particular frequency content from a dynamical system. However, in experimental applications such as the interrogation of a flow field using particle image velocimetry (PIV), it may be impracticable or expensive to obtain data at the desired temporal resolution. To address this problem, we propose a new approach to identify temporal information from undersampled data, using ideas from modal decomposition algorithms such as dynamic mode decomposition (DMD) and optimal mode decomposition (OMD). The novel method takes a vector-valued signal, such as an ensemble of PIV snapshots, sampled at random time instances (but at sub-Nyquist rate) and projects onto a low-order subspace. Subsequently, dynamical characteristics, such as frequencies and growth rates, are approximated by iteratively approximating the flow evolution by a low-order model and solving a certain convex optimisation problem. The methodology is demonstrated on three dynamical systems, a synthetic sinusoid, the cylinder wake at Reynolds number $Re=60$ and turbulent flow past the axisymmetric bullet-shaped body. In all cases the algorithm correctly identifies the characteristic frequencies and oscillatory structures present in the flow.

A Study on the Coanda Effect and the Thrust Characteristics of Synthetic Jets

2014 ◽  
Author(s):  
Takahiro Iwasaki ◽  
Koichi Nishibe ◽  
Kotaro Sato ◽  
Kazuhiko Yokota ◽  
Donghyuk Kang
Keyword(s):  
Vortex Pair ◽  
Numerical Data ◽  
Rigid Wall ◽  
Flow Patterns ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Coanda Effect ◽  
Rigid Boundary ◽  
Thrust Characteristics ◽  
Coandǎ Effect

Although there have recently been various studies on synthetic jets, many issues remain to be clarified, including details of the structure, Coanda effect and thrust characteristics. The present study clarifies some fundamental flow characteristics of synthetic jets near a rigid boundary by experiments and numerical simulations. In addition, a thruster model using the Coanda effect of synthetic jets is proposed and thrust characteristics are evaluated. As the main results, the flow of a synthetic jet near a rigid boundary is visualized and the trajectory of a vortex pair is demonstrated. It is confirmed that the flow patterns of the synthetic jets near a rigid boundary depend on H/b0 (offset ratio, normalized step height). The behavior of the asymmetric synthetic jets caused by the presence of the rigid wall was observed experimentally and the results were compared with numerical data. Furthermore, typical flow patterns around the proposed synthetic jet thruster and its thrust characteristics curves are shown.

Convective Heat Transfer in an Impinging Synthetic Jet: A Numerical Investigation of a Canonical Geometry

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Luis A. Silva ◽  
Alfonso Ortega
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Stokes Equations ◽  
Heated Surface ◽  
Vortex Pair ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Navier Stokes ◽  
Scaling Analysis ◽  
Dependent Flow

Synthetic jets are generated by an equivalent inflow and outflow of fluid into a system. Even though such a jet creates no net mass flux, net positive momentum can be produced because the outflow momentum during the first half of the cycle is contained primarily in a vigorous vortex pair created at the orifice edges; whereas in the backstroke, the backflow momentum is weaker, despite the fact that mass is conserved. As a consequence of this, the approach can be potentially utilized for the impingement of a cooling fluid onto a heated surface. In previous studies, little attention has been given to the influence of the jet's origins; hence it has been difficult to find reproducible results that are independent of the jet apparatus or actuators utilized to create the jet. Furthermore, because of restrictions of the resonators used in typical actuators, previous investigations have not been able to independently isolate effects of jet frequency, amplitude, and Reynolds number. In the present study, a canonical geometry is presented, in order to study the flow and heat transfer of a purely oscillatory jet that is not influenced by the manner in which it is produced. The unsteady Navier–Stokes equations and the convection–diffusion equation were solved using a fully unsteady, two-dimensional finite volume approach in order to capture the complex time dependent flow field. A detailed analysis was performed on the correlation between the complex velocity field and the observed wall heat transfer. Scaling analysis of the governing equations was utilized to identify nondimensional groups and propose a correlation for the space-averaged and time-averaged Nusselt number. A fundamental frequency, in addition to the jet forcing frequency, was found, and was attributed to the coalescence of consecutive vortex pairs. In terms of time-averaged data, the merging of vortices led to lower heat transfer. Point to point correlations showed that the instantaneous local Nusselt number strongly correlates with the vertical velocity v although the spatial-temporal dependencies are not yet fully understood.

Application of Dynamic Mode Decomposition to Study Temporal Flow Behavior in a Saccular Aneurysm

2021 ◽  
Author(s):  
Paulo Yu ◽  
Vibhav Durgesh
Keyword(s):  
Flow Behavior ◽  
Frame Rate ◽  
Dynamic Mode Decomposition ◽  
Mode Shapes ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
The Impact ◽  
Temporal Flow ◽  
Inflow Conditions ◽  
Low Order

Abstract Aneurysms are abnormal expansion of weakened blood vessels which can cause mortality or long-term disability upon rupture. Several studies have shown that inflow conditions spatially and temporally influence aneurysm flow behavior. The objective of this investigation is to identify impact of inflow conditions on spatio-temporal flow behavior in an aneurysm using Dynamic Mode Decomposition (DMD). For this purpose, low-frame rate velocity field measurements are performed in an idealized aneurysm model using Particle Image Velocimetry (PIV). The inflow conditions are precisely controlled using a ViVitro SuperPump system where non-dimensional fluid parameters such as peak Reynolds number (Rep) and Womersely number (α) are varied from 50-270 and 2-5, respectively. The results show the ability of DMD to identify the spatial flow structures and their frequency content. Furthermore, DMD captured the impact of inflow conditions, and change in mode shapes, amplitudes, frequency, and growth rate information is observed. The DMD low-order flow reconstruction also showed the complex interplay of flow features for each inflow scenario. Furthermore, the low-order reconstruction results provided a mathematical description of the flow behavior in the aneurysm which captured the vortex formation, evolution, and convection in detail. These results indicated that the vortical structure behavior varied with the change in α while its strength and presence of secondary structures is influenced by the change in Rep.

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