scholarly journals Low-order modelling of the wake dynamics of an Ahmed body

2021 ◽  
Vol 927 ◽  
Author(s):  
Bérengère Podvin ◽  
Stéphanie Pellerin ◽  
Yann Fraigneau ◽  
Guillaume Bonnavion ◽  
Olivier Cadot
Keyword(s):  
Vortex Shedding ◽  
Characteristic Time ◽  
Large Scale ◽  
Turbulent Wake ◽  
Flow Dynamics ◽  
Dimensional Model ◽  
Chaotic Model ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Ahmed Body

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ( $Re$ ) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Study on vortex shedding mode on the wake of horn/ridge ice contamination under high-Reynolds conditions

2019 ◽  
Vol 233 (13) ◽  
pp. 5045-5056
Author(s):  
Shufan Hu ◽  
Chen Zhang ◽  
Hong Liu ◽  
Fuxin Wang
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Vortex Shedding ◽  
Large Scale ◽  
Vortex Motion ◽  
Simulation Method ◽  
Orthogonal Decomposition ◽  
Detached Eddy Simulation ◽  
Dynamic Features ◽  
Large Scale Vortex ◽  
Proper Orthogonal

This paper studied the unsteadiness of vortex motion produced by a three-dimensional wing section with horn/ridge ice contamination. Using improved delayed detached eddy simulation method, multi-scale vortex and their associated flow structures were successfully captured. Results have shown a diversity of unsteadiness scales at different time series, including shear layer instability, vortex pairing, co-rotating and breaking up. Proper orthogonal decomposition was then introduced to extract the characteristic vortex shedding modes with scheduling the eigenvalues λi from large to small. The dominate and secondary proper orthogonal decomposition modes under horn ice condition were displayed, which could be illustrated as fluctuations near recirculation zone, and large-scale vortex shedding/reattaching motion, respectively. The proper orthogonal decomposition modal characteristics for ridge ice showed that vortex scales varied from large to small. The trajectory of large-scale vortex reattaching and co-rotating exist simultaneously with the pressure peak and recover, which also verified the association of proper orthogonal decomposition modes with different scales of vortices. Future works would be presented on demonstration of the complex structures and the dynamic features in such flow.

scholarly journals PIV Visualization of Flow Around Airfoil Controlled by Synthetic Jet Actuators at Shear-Layer and Wake Instability Frequencies

2021 ◽  
Author(s):  
Eric Yang ◽  
Pierre E. Sullivan
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Large Scale ◽  
Turbulent Wake ◽  
Synthetic Jet ◽  
Shear Layer Instability ◽  
Image Velocimetry ◽  
Wake Instability ◽  
Proper Orthogonal ◽  
Instability Frequency

Abstract The response of a separated boundary layer to synthetic jet flow control at the global wake instability (F+ ≈ 𝒪(1)) and the shear-layer instability (F+ ≈ 𝒪(10)) measured by particle image velocimetry are presented. The visualization shows that in each of the control cases, coherent vorticity develops and breaks down into a turbulent wake. When the jets are actuated by burst-modulation at the wake instability frequency, they induce regular formation and detachment of large-scale vorticity to form a wide turbulent wake. Excitation at the shear-layer instability frequency, on the other hand, produces a train of alternating velocity fluctuations in the boundary layer which dissipate to a narrower wake. Proper orthogonal decomposition of the velocity fields show that the physical extent of the jet-induced coherent structures is decreased with increasing addition of momentum for both excitation frequencies.

Response Characteristics of a Low-Dimensional Model Neuron

1996 ◽  
Vol 8 (8) ◽  
pp. 1643-1652 ◽  
Author(s):  
Bo Cartling
Keyword(s):  
Time Constant ◽  
Large Scale ◽  
Complex Dynamics ◽  
Model Neuron ◽  
Fast Response ◽  
Dimensional Model ◽  
Constant Input ◽  
Variable Model ◽  
Response Characteristics ◽  
Low Dimensional

It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidation of neurocomputational mechanisms, and applications to large-scale systems.

scholarly journals Substorm classification with the WINDMI model

2003 ◽  
Vol 10 (4/5) ◽  
pp. 363-371 ◽  
Author(s):  
W. Horton ◽  
R. S. Weigel ◽  
D. Vassiliadis ◽  
I. Doxas
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Arrival Time ◽  
Type I ◽  
Type Ii ◽  
Dimensional Model ◽  
Algorithm Optimization ◽  
Data Set ◽  
Low Dimensional ◽  
The Imf

Abstract. The results of a genetic algorithm optimization of the WINDMI model using the Blanchard-McPherron substorm data set is presented. A key result from the large-scale computations used to search for convergence in the predictions over the database is the finding that there are three distinct types of vx Bs -AL waveforms characterizing substorms. Type I and III substorms are given by the internally-triggered WINDMI model. The analysis reveals an additional type of event, called a type II substorm, that requires an external trigger as in the northward turning of the IMF model of Lyons (1995). We show that incorporating an external trigger, initiated by a fast northward turning of the IMF, into WINDMI, a low-dimensional model of substorms, yields improved predictions of substorm evolution in terms of the AL index. Intrinsic database uncertainties in the timing between the ground-based AL electrojet signal and the arrival time at the magnetopause of the IMF data measured by spacecraft in the solar wind prevent a sharp division between type I and II events. However, within these timing limitations we find that the fraction of events is roughly 40% type I, 40% type II, and 20% type III.

A low-dimensional model for simulating three-dimensional cylinder flow

2002 ◽  
Vol 458 ◽  
pp. 181-190 ◽  
Author(s):  
XIA MA ◽  
GEORGE EM KARNIADAKIS
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Orthogonal Decomposition ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Dimensional Model ◽  
The Stability ◽  
Low Dimensional ◽  
Cylinder Flow ◽  
Proper Orthogonal

We investigate the stability and dynamics of three-dimensional limit-cycle states in flow past a circular cylinder using low-dimensional modelling. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition. We show that the limit cycle is reproduced very accurately with only twenty three-dimensional modes. The addition of two-dimensional modes to the Karhunen–Loeve expansion basis improves the ability of the model to capture the three-dimensional bifurcation, including the discontinuity in the Strouhal number discovered experimentally.

Error Estimates for Reduced Order POD Models of Navier-Stokes Equations

2008 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Error Estimates ◽  
Incompressible Flows ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Dimensional Model ◽  
Reduced Order ◽  
Infinite Dimensional ◽  
Low Dimensional ◽  
Proper Orthogonal

Reduced order modeling for the purpose of constructing a low dimensional model from high dimensional or infinite dimensional model has important applications in science and engineering such as fast model evaluations and optimization/control. A popular method for constructing reduced-order model is based on finding a suitable low dimensional basis by proper orthogonal decomposition (POD) and forming a model by Galerkin projection of the infinite dimensional model onto the basis. In this paper, we will discuss error estimates for Galerkin proper orthogonal decomposition method for an unsteady nonlinear coupled partial differential equations arising in viscous incompressible flows. A specific finite element in space and finite difference in time discretization scheme will be discussed.

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