Non-modal analysis of coaxial jets

2019 ◽  
Vol 872 ◽  
pp. 665-696 ◽  
Author(s):  
D. Montagnani ◽  
F. Auteri
Keyword(s):  
Reynolds Number ◽  
Nonlinear System ◽  
Harmonic Analysis ◽  
Large Scale ◽  
Velocity Ratio ◽  
Maximum Velocity ◽  
Dynamic Mode Decomposition ◽  
Transition To Turbulence ◽  
Dynamic Mode ◽  
Coaxial Jets

In this work, we investigate the subcritical behaviour of a coaxial jet subject to small-amplitude perturbations at the inflow. We use the results of optimal harmonic analysis and dynamic-mode decomposition (DMD) of the flow fields at a Reynolds number, based on the diameter and maximum velocity of the inner inlet pipe, of $Re=200$, to show that, for a sufficiently low value of the Reynolds number, the coherent structures appearing in the perturbed dynamics of the nonlinear system can be effectively described in terms of the harmonic response of the flow. We also show that, for larger subcritical values of the Reynolds number, $Re=400$, a huge amplification of disturbances quickly makes nonlinear effects relevant. Large-scale, near-field coherent dynamics can be still interpreted as an evidence of the preferred response of the system, using DMD of the flow to describe the noise-driven transition to turbulence downstream. The influence of the axial velocity ratio and the rotational motion of the outer stream are assessed as well. Harmonic analysis successfully predicts the prevalence of rotating helical structures observed in the columnar flow for moderate swirl of the outer jet. Finally, we compare the receptivity of the nonlinear system to the optimal linear perturbations with its response to stochastic forcing. Optimal forcing is still more effective than white noise in driving the system to a turbulent state, where nonlinear dynamics prevails. We still conclude that linear optimal forcing may be relevant in investigating the transition to turbulence in coaxial jets, even if more about the transition process could be learnt from a more expensive nonlinear analysis.

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).

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.

scholarly journals Analysis of V-Gutter Reacting Flow Dynamics Using Proper Orthogonal and Dynamic Mode Decompositions

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4886 ◽  
Author(s):  
Yang Yang ◽  
Xiao Liu ◽  
Zhihao Zhang
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Wake Instability ◽  
Shedding Frequency ◽  
Proper Orthogonal

The current work is focused on investigating the potential of data-driven post-processing techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) for flame dynamics. Large-eddy simulation (LES) of a V-gutter premixed flame was performed with two Reynolds numbers. The flame transfer function (FTF) was calculated. The POD and DMD were used for the analysis of the flame structures, wake shedding frequency, etc. The results acquired by different methods were also compared. The FTF results indicate that the flames have proportional, inertial, and delay components. The POD method could capture the shedding wake motion and shear layer motion. The excited DMD modes corresponded to the shear layer flames’ swing and convect motions in certain directions. Both POD and DMD could help to identify the wake shedding frequency. However, this large-scale flame oscillation is not presented in the FTF results. The negative growth rates of the decomposed mode confirm that the shear layer stabilized flame was more stable than the flame possessing a wake instability. The corresponding combustor design could be guided by the above results.

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.

Analysis of the Unsteady Flow Field Inside a Fan-Shaped Cooling Hole Predicted by Large-Eddy Simulation

2020 ◽  
Author(s):  
Shubham Agarwal ◽  
Laurent Gicquel ◽  
Florent Duchaine ◽  
Nicolas Odier ◽  
Jérôme Dombard
Keyword(s):  
Film Cooling ◽  
Large Scale ◽  
Fourier Transforms ◽  
Thermal Environment ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Film Cooling Effectiveness ◽  
Mode Decomposition ◽  
Large Eddy ◽  
Cooling Hole

Abstract Film cooling is a common technique to manage turbine vane and blade thermal environment. Optimizing its cooling efficiency is furthermore an active research topic which goes in hand with a strong knowledge of the flow associated with a cooling hole. The following paper aims at developing deeper understanding of the flow physics associated with a standard cooling hole and helping guide future cooling optimization strategies. For this purpose, Large Eddy Simulations (LES) of the 7-7-7 fan-shaped cooling hole [1] is performed and the flow inside the cooling hole is studied and discussed. Use of mathematical techniques such as the Fast Fourier Transforms (FFT) and Dynamic Mode Decomposition (DMD) is done to quantitatively access the flow modal structure inside the hole based on the LES unsteady predictions. Using these techniques, distinct vortex features inside the cooling hole are captured. These features mainly coincide with the roll-up of the internal shear layer formed at the interface of the separation region at the hole inlet. The topology of these vortex features is discussed in detail and it is also shown how the expansion of the cross-section in case of shaped holes aids in breaking down these vortices. Indeed upon escaping, these large scale features are known to not be always beneficial to film cooling effectiveness.

scholarly journals Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions

2017 ◽  
Vol 832 ◽  
pp. 483-513 ◽  
Author(s):  
Matteo de Giovanetti ◽  
Hyung Jin Sung ◽  
Yongyun Hwang
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Vortical Structure ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Hairpin Vortices ◽  
Large Scale Motion ◽  
Scale Motion

It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an ‘amplified’ streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$ where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of $\unicode[STIX]{x1D706}_{x}/h\simeq 1{-}5$ ($h$ is the half-height of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuous-mode instability of the streak, a subprocess of the self-sustaining mechanism of the large-scale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the large-scale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of very-large-scale motion.

A numerical study of shear layer characteristics of low-speed transverse jets

2016 ◽  
Vol 790 ◽  
pp. 275-307 ◽  
Author(s):  
Prahladh S. Iyer ◽  
Krishnan Mahesh
Keyword(s):  
Velocity Profile ◽  
Shear Layer ◽  
Convective Instability ◽  
Numerical Study ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Dominant Frequencies

Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129) at velocity ratios ($R=\overline{v}_{j}/u_{\infty }$) of 2 and 4 and Reynolds number ($Re=\overline{v}_{j}D/{\it\nu}$) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ($St=0.65$) is dominant along the length of the shear layer for $R=2$, whereas the dominant frequencies change along the shear layer for $R=4$. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

Quantitative Analysis of Forced and Unforced Turbulent Multiphase Coaxial Jets

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
D. J. Forliti ◽  
J. Wegener ◽  
C. Min ◽  
I. A. Leyva
Keyword(s):  
Acoustic Waves ◽  
Acoustic Resonance ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Confined Space ◽  
Coaxial Jets ◽  
Mode Decomposition ◽  
Global Signal ◽  
Background Turbulence ◽  
Signal Processing Methods

Abstract This study explores the structure of liquid/gas coaxial jets under forced and unforced conditions. The forcing is in the form of a transverse acoustic resonance within the confined space where the mixing occurs. The studied flows are relevant to combustion instabilities which involve an interaction between acoustic waves and reactant mixing. A variety of local and global signal processing methods were applied to digital flow visualization data to identify spatial and temporal features. The unforced case is in particular chaotic and influenced by a broad range of spatial and temporal phenomena. Proper orthogonal decomposition (POD) was able to extract flapping and convecting features, and spectral content of these behaviors is presented. The forced case results in organized structures that emerge above the background turbulence, including harmonics of the forcing frequency and nonlinear interactions between specific frequencies. The dynamic mode decomposition (DMD) performs the best in the forced case, clearly isolating all of these features. Wavelet analysis showed that forcing tended to reorganize energy from longer to shorter time scales. Bicoherence analysis of the data showed that the forcing causes a much different energy exchange in the outer and inner shear layers. The outer-to-inner jet coupling during forced conditions appears to be limited to an axial extent of about one to three inner jet diameters downstream of the jet exit. The recirculation zone between the inner and outer jet, extending about one inner jet diameter downstream, appears to disrupt the influence of forcing on the inner jet.

scholarly journals Wavy Walls, a Passive Way to Control the Transition to Turbulence. Detailed Simulation and Physical Explanation

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3937
Author(s):  
Andrés Mateo-Gabín ◽  
Miguel Chávez ◽  
Jesús Garicano-Mena ◽  
Eusebio Valero
Keyword(s):  
Control Strategies ◽  
Reynolds Numbers ◽  
Dynamic Mode Decomposition ◽  
Transition To Turbulence ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Detailed Simulation ◽  
Walled Channel ◽  
Laminar And Turbulent Regimes ◽  
Careful Design

Inducing spanwise motions in the vicinity of solid boundaries alters the energy, mass and/or momentum transfer. Under some conditions, these motions are such that drag is reduced and/or transition to turbulence is delayed. There are several possibilities to induce those spanwise motions, be it through active imposition a predefined velocity distribution at the walls or by careful design of the wall shape, which corresponds to passive control.In this contribution, we investigate the effect that wavy walls might have on delaying transition to turbulence. Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes are conducted. A pseudo laminar regime that remains stable until a Reynolds number 20% higher that the critical is found for the wavy-walled simulations. Dynamic Mode Decomposition applied to the simulation data reveals that in these configurations, modes with wavelength and frequency compatible with the surface undulation pattern appear. We explain and visualize the appearance of these modes. At higher Reynolds numbers we show that these modes remain present but are not dominant anymore. This work is an initial demonstration that flow control strategies that trigger underlying stable modes can keep or conduct the flow to new configurations more stable than the original one.

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