scholarly journals Three-dimensional instability of a flow past a sphere: Mach evolution of the regular and Hopf bifurcations

2018 ◽  
Vol 855 ◽  
pp. 1088-1115 ◽  
Author(s):  
A. Sansica ◽  
J.-Ch. Robinet ◽  
F. Alizard ◽  
E. Goncalves
Keyword(s):  
Reynolds Number ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Base Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Weakly Nonlinear ◽  
Mode Decomposition ◽  
Mach Numbers ◽  
Noise Amplifier

A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.

Unravelling the large-scale circulation modes in turbulent Rayleigh–Bénard convection

2021 ◽  
Author(s):  
Susanne Horn ◽  
Peter J. Schmid ◽  
Jonathan M. Aurnou
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mean Flow ◽  
Large Scale Circulation ◽  
Convective Systems ◽  
Aspect Ratios ◽  
Mode Decomposition ◽  
Coherent Flow Structure

Abstract The large-scale circulation (LSC) is the most fundamental turbulent coherent flow structure in Rayleigh-B\'enard convection. Further, LSCs provide the foundation upon which superstructures, the largest observable features in convective systems, are formed. In confined cylindrical geometries with diameter-to-height aspect ratios of Γ ≅ 1, LSC dynamics are known to be governed by a quasi-two-dimensional, coupled horizontal sloshing and torsional (ST) oscillatory mode. In contrast, in Γ ≥ √2 cylinders, a three-dimensional jump rope vortex (JRV) motion dominates the LSC dynamics. Here, we use dynamic mode decomposition (DMD) on direct numerical simulation data of liquid metal to show that both types of modes co-exist in Γ = 1 and Γ = 2 cylinders but with opposite dynamical importance. Furthermore, with this analysis, we demonstrate that ST oscillations originate from a tilted elliptical mean flow superposed with a symmetric higher order mode, which is connected to the four rolls in the plane perpendicular to the LSC in Γ = 1 tanks.

Numerical Investigation of the Flow Around a Generic Car Using Dynamic Mode Decomposition

2014 ◽  
Author(s):  
Martin Peichl ◽  
Steffen Mack ◽  
Thomas Indinger ◽  
Friedhelm Decker
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Wake Flow ◽  
Dynamic Mode Decomposition ◽  
Wind Tunnels ◽  
Dynamic Mode ◽  
Dynamic Information ◽  
Cfd Simulations ◽  
Mode Decomposition ◽  
Vortex Systems

The drag of a car is highly dependent on the topology of its complex wake system. Small changes in the shape of the car, that do not have a big effect when considered separately, can lead to significant changes in the total drag when the vortex systems of the changed part of the car body interact with the wake vortices. To understand these interferences, a method is necessary that decomposes the flow based on dynamic information. In this paper, the feasibility of using the Dynamic Mode Decomposition (DMD) to analyze the dynamic behavior of the wake flow of a car is investigated. The DMD is found to extract useful information from the flow when applied to three dimensional velocity vector fields. The CFD simulations are validated by yet unpublished experimental results from experiments in two different wind tunnels.

scholarly journals Flow Structures on a Planar Food and Drug Administration (FDA) Nozzle at Low and Intermediate Reynolds Number

Fluids ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Adrián Corrochano ◽  
Donnatella Xavier ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Reynolds Number ◽  
Drug Administration ◽  
Food And Drug Administration ◽  
Vortex Street ◽  
Dynamic Mode Decomposition ◽  
Numerical Code ◽  
Flow Structures ◽  
Dynamic Mode ◽  
General Description ◽  
Mode Decomposition

In this paper, we present a general description of the flow structures inside a two-dimensional Food and Drug Administration (FDA) nozzle. To this aim, we have performed numerical simulations using the numerical code Nek5000. The topology patters of the solution obtained, identify four different flow regimes when the flow is steady, where the symmetry of the flow breaks down. An additional case has been studied at higher Reynolds number, when the flow is unsteady, finding a vortex street distributed along the expansion pipe of the geometry. Linear stability analysis identifies the evolution of two steady and two unsteady modes. The results obtained have been connected with the changes in the topology of the flow. Finally, higher-order dynamic mode decomposition has been applied to identify the main flow structures in the unsteady flow inside the FDA nozzle. The highest-amplitude dynamic mode decomposition (DMD) modes identified by the method model the vortex street in the expansion of the geometry.

Modal Analysis of Wake behind Stationary and Vibrating Cylinders

2020 ◽  
pp. 1-24
Author(s):  
Marek Janocha ◽  
Guang Yin ◽  
Muk Chen Ong
Keyword(s):  
Reynolds Number ◽  
Modal Analysis ◽  
Reduced Order Model ◽  
Dynamic Mode Decomposition ◽  
Navier Stokes ◽  
Dynamic Mode ◽  
Order Model ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Sst Turbulence Model

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.

Temporal and spatial evolution of cavitating bubbles and coherent structures in a confined submerged jet shear layer

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Runqiang Zhang ◽  
Guoyong Sun ◽  
Yuchuan Wang ◽  
Sebastián Leguizamón
Keyword(s):  
Shear Layer ◽  
Coherent Structures ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Content Type ◽  
Cavitation Inception ◽  
Mode Decomposition ◽  
The Relationship

PurposeThe study aims to display the bubbles' evolution in the shear layer and their relationship with the pressure fluctuations. Furthermore, the coherent structures of the first six modes are extracted, in order to provide insight into their temporal and spatial evolution and determine the relationship between cavitating bubbles and coherent structures.Design/methodology/approachIn the present study, numerical simulations of submerged jet cavitating flow were carried out at a cavitation inception condition inside an axisymmetric cavity using the large eddy simulation (LES) turbulence model and the Schnerr–Sauer (S–S) cavitation model. Based on snapshots produced by the numerical simulation, dynamic mode decomposition (DMD) was performed to extract the three-dimensional coherent structures of the first six modes in the shear layer.FindingsThe cavitating bubbles in the shear layer are deformed to elongated ellipsoid shapes by shear forces. The significant pressure fluctuations are induced by the collapse of the biggest bubble in the group. The first mode illustrates the mean characteristics of the flow field. The flow in the peripheral region of the shear layer is mainly dominated by large-scale coherent structures revealed by the second and third modes, while different small-scale coherent structures are contained in the central region. The cavitating bubbles are associated with small size coherent structures as the sixth or higher modes.Practical implicationsThis work demonstrates the feasibility of LES for high Reynolds number shear layer flow. The dynamic mode decomposition method is a novel method to extract coherent structures and obtain their dynamic information that will help us to optimize and control the flow.Originality/value(1) This paper first displays the three-dimensional coherent structures and their characteristics in the shear layer of confined jet flow. (2) The relationship of bubbles shape and pressure fluctuations is illustrated. (3) The visualization of coherent structures benefits the understanding of the mixing process and cavitation inception in jet shear layers.

Recovery of the inherent dynamics of noise-driven amplifier flows

2016 ◽  
Vol 797 ◽  
pp. 130-145 ◽  
Author(s):  
Juan Guzmán Iñigo ◽  
Denis Sipp ◽  
Peter J. Schmid
Keyword(s):  
Frequency Response ◽  
State Space Model ◽  
Dynamic Mode Decomposition ◽  
Order System ◽  
Dynamic Mode ◽  
Identification Algorithm ◽  
Mode Decomposition ◽  
Dimensional Boundary ◽  
Tollmien Schlichting ◽  
Noise Amplifier

Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. The spectrum of the identified model compares well with the results reported in literature for the full-order system. Yet the comparison appears to be only qualitative, due to the poor robustness properties of eigenvalue spectra in noise-amplifier flows. We therefore advocate the use of the frequency response between the upstream sensor and the flow dynamics, which is revealed to be a robust quantity. The frequency response is validated against full-order computations and compares well with a local spatial stability analysis.

Dynamic Mode Decomposition Analysis of Separated Boundary Layers Under Variable Reynolds Number and Free-Stream Turbulence

2020 ◽  
Author(s):  
M. Dellacasagrande ◽  
J. Verdoya ◽  
D. Barsi ◽  
D. Lengani ◽  
D. Simoni
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Reynolds Number ◽  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Data Set ◽  
Separated Shear Layer ◽  
Mode Decomposition

Abstract A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (70000 < Re < 150000) and turbulence intensity level (1.5% < Tu < 2.5%). The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer. The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of Re and Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects due to the main flow parameters on the amplification of the dominant streamwise wavelengths within the separated shear layer (Kelvin-Helmholtz modes). The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. In order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level. The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control.

Sign in / Sign up

Export Citation Format

Share Document