Symmetry breaking and instabilities of conical vortex pairs over slender delta wings

2017 ◽  
Vol 832 ◽  
pp. 41-72 ◽  
Author(s):  
Bao-Feng Ma ◽  
Zhijin Wang ◽  
Ismet Gursul
Keyword(s):  
Symmetry Breaking ◽  
Shear Layer ◽  
Dynamic Mode Decomposition ◽  
Stream Velocity ◽  
Dynamic Mode ◽  
Delta Wings ◽  
Similarity Parameter ◽  
Vortex Pairs ◽  
Wide Range ◽  
Layer Mode

An investigation of symmetry breaking and naturally occurring instabilities over thin slender delta wings with sharp leading edges was carried out in a water tunnel using particle image velocimetry (PIV) measurements. Time-averaged location, strength and core radius of conical vortices vary almost linearly with chordwise distance for three delta wings with $75^{\circ }$, $80^{\circ }$ and $85^{\circ }$ sweep angles over a wide range of angles of attack. Properties of the time-averaged vortex pairs depend only on the similarity parameter, which is a function of the angle of attack and the sweep angle. It is shown that time-averaged vortex pairs develop asymmetry gradually with increasing values of the similarity parameter. Vortex asymmetry can develop in the absence of vortex breakdown on the wing. Instantaneous PIV snapshots were analysed using proper orthogonal decomposition and dynamic mode decomposition, revealing the shear layer and vortex instabilities. The shear layer mode is the most periodic and more dominant for lower values of the similarity parameter. The Strouhal number based on the free stream velocity component in the cross-flow plane is a function of only the similarity parameter. The dominant frequency of the shear layer mode decreases with the increasing similarity parameter. The vortex modes reveal the fluctuations of the vorticity magnitude and helical displacement of the cores, but with little periodicity. There is little correlation between the fluctuations in the cores of the vortices.

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.

Reduced-order analysis of buffet flow of space launchers

2017 ◽  
Vol 815 ◽  
pp. 1-25 ◽  
Author(s):  
Vladimir Statnikov ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Shear Layer ◽  
Vortex Shedding ◽  
Separation Bubble ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Main Body ◽  
Reduced Order ◽  
Order Analysis ◽  
Wall Pressure Fluctuations

A reduced-order analysis based on optimized dynamic mode decomposition (DMD) is performed on the turbulent wake of a generic axisymmetric space launcher configuration computed via a zonal large-eddy simulation at the free stream Mach number $Ma_{\infty }=0.8$ and the Reynolds number based on the main body diameter $Re_{D}=6\times 10^{5}$ to investigate the buffet phenomenon. The transonic wake is characterized by an unsteady recirculation region occurring around the nozzle due to the separation of the turbulent boundary layer at the main body shoulder and subsequent dynamic interaction of the unstable free-shear layer with the nozzle surface. This results in strongly periodic and antisymmetric wall pressure fluctuations, for which three distinct frequency ranges are identified using conventional spectral analysis, i.e. $Sr_{D}\approx 0.1$, $Sr_{D}\approx 0.2$ and $Sr_{D}\approx 0.35$. For the spatially integrated side (buffet) loads on the nozzle, the second range is found to be energetically most dominant. To clarify the origin of the detected wake dynamics, the underlying spatio-temporal coherent modes are extracted using DMD. Subsequent analysis of the reduced-order modelled flow field based on the identified DMD modes reveals that at $Sr_{D}\approx 0.1$ a longitudinal cross-pumping motion of the separation bubble takes place, caused by a harmonic antisymmetric oscillation of the main recirculation vortex in the streamwise direction. At $Sr_{D}\approx 0.2$, a cross-flapping motion of the shear layer is determined, triggered by antisymmetric vortex shedding which is in phase with the cross-pumping motion such that it occurs at twice the frequency value. The last range of $Sr_{D}\approx 0.35$ is attributed to a swinging motion of the shear layer caused by a higher harmonic of the vortex shedding mode. Conclusively, the controversial aspect of the true three-dimensional shape of the antisymmetric mode at $Sr_{D}\approx 0.2$ that dominates the buffet phenomenon is scrutinized. Inclined elongated closed-loop vortices are identified that are shed in alternating sequence from azimuthally opposite positions in a longitudinal plane of symmetry that changes its momentary orientation irregularly, maintaining an axisymmetric time-averaged field and spatially isotropic buffet loads.

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.

scholarly journals Robust Mode Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1057
Author(s):  
Gemunu H. Gunaratne ◽  
Sukesh Roy
Keyword(s):  
Experimental Data ◽  
Bluff Body ◽  
Numerical Solutions ◽  
Dynamic Mode Decomposition ◽  
Mode Analysis ◽  
Jet Flows ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Model Free ◽  
Wide Range

In this paper, we introduce a model-free algorithm, robust mode analysis (RMA), to extract primary constituents in a fluid or reacting flow directly from high-frequency, high-resolution experimental data. It is expected to be particularly useful in studying strongly driven flows, where nonlinearities can induce chaotic and irregular dynamics. The lack of precise governing equations and the absence of symmetries or other simplifying constraints in realistic configurations preclude the derivation of analytical solutions for these systems; the presence of flow structures over a wide range of scales handicaps finding their numerical solutions. Thus, the need for direct analysis of experimental data is reinforced. RMA is predicated on the assumption that primary flow constituents are common in multiple, nominally identical realizations of an experiment. Their search relies on the identification of common dynamic modes in the experiments, the commonality established via proximity of the eigenvalues and eigenfunctions. Robust flow constituents are then constructed by combining common dynamic modes that flow at the same rate. We illustrate RMA using reacting flows behind a symmetric bluff body. Two robust constituents, whose signatures resemble symmetric and von Karman vortex shedding, are identified. It is shown how RMA can be implemented via extended dynamic mode decomposition in flow configurations interrogated with a small number of time-series. This approach may prove useful in analyzing changes in flow patterns in engines and propulsion systems equipped with sturdy arrays of pressure transducers or thermocouples. Finally, an analysis of high Reynolds number jet flows suggests that tests of statistical characterizations in turbulent flows may best be done using non-robust components of the flow.

Global linear stability analysis of jets in cross-flow

2017 ◽  
Vol 828 ◽  
pp. 812-836 ◽  
Author(s):  
Marc A. Regan ◽  
Krishnan Mahesh
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Implicitly Restarted Arnoldi

The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275–307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between $R=2$ to $R=4$ observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129), where $R=\overline{v}_{jet}/u_{\infty }$ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when $R=2$, whereas downstream shear-layer instabilities are shown to dominate when $R=4$.

Mode Transition and Intermittency in an Acoustically Uncoupled Lean Premixed Swirl-Stabilized Combustor

2014 ◽  
Author(s):  
Zachary A. LaBry ◽  
Soufien Taamallah ◽  
Gaurav Kewlani ◽  
Santosh J. Shanbhogue ◽  
Ahmed F. Ghoniem
Keyword(s):  
Shear Layer ◽  
Recirculation Zone ◽  
Dynamic Instability ◽  
Turbulent Flame ◽  
Companion Paper ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Transition Event ◽  
Flame Brush

The prediction of dynamic instability remains an open and important issue in the development of gas turbine systems, particularly those constrained by emissions limitations. The existence and characteristics of dynamic instability are known to be functions of combustor geometry, flow conditions, and combustion parameters, but the form of dependence is not well understood. By modifying the acoustic boundary conditions, changes in flame and flow structure due to inlet parameters can be studied independent of the acoustic modes with which they couple. This paper examines the effect of equivalence ratio on the flame macrostructure — the relationship between the turbulent flame brush and the dominant flow structures — in an acoustically uncoupled environment. The flame brush is measured using CH* chemiluminescence, and the flow is interrogated using two-dimensional particle image velocimetry. We examine a range of equivalence ratios spanning three distinct macrostructures. The first macrostructure (ϕ = 0.550) is characterized by a diffuse flame brush confined to the interior of the inner recirculation zone. We observe a conical flame in the inner shear layer, continuing along the wall shear layer in the second macrostructure (ϕ = 0.600). The third macrostructure exhibits the same flame brush as the second, with an additional flame brush in the outer shear layer (ϕ = 0.650). Between the second and third macrostructures, we observe a regime in which the flame brush transitions intermittently between the two structures. We use dynamic mode decomposition on the PIV data to show that this transition event, which we call flickering, is linked to vorticity generated by the intermittent expansion of the outer recirculation zone as the flame jumps in and out of the outer shear layer. In a companion paper, we show how the macrostructures described in this paper are linked with dynamic instability [1].

Dynamics of robust structures in turbulent swirling reacting flows

2017 ◽  
Vol 816 ◽  
pp. 554-585 ◽  
Author(s):  
S. Roy ◽  
T. Yi ◽  
N. Jiang ◽  
G. H. Gunaratne ◽  
I. Chterev ◽  
...  
Keyword(s):  
Shear Layer ◽  
High Speed ◽  
Large Scale ◽  
Swirling Flow ◽  
Dynamic Mode Decomposition ◽  
Flow Structures ◽  
Dynamic Mode ◽  
Complete Suppression ◽  
Tangential Flow ◽  
The Mean

High-speed synchronized stereo particle-imaging velocimetry and OH planar laser-induced fluorescence (PIV/OH-PLIF) measurements are performed on multiple $R{-}\unicode[STIX]{x1D703}$ planes downstream of a high-Reynolds-number swirling jet. Dynamic-mode decomposition (DMD) – a frequency-resolved data-reduction technique – is used to identify and characterize recurrent flow structures. Illustrative results are presented in a swirling flow field for two cases – the nominal flow dynamics and where self-excited combustion driven oscillations provide strong axisymmetric narrowband forcing of the flow. The robust constituent of the nominal reacting swirl flow corresponds to a helical shear-layer disturbance at a Strouhal number ($St$) of ${\sim}0.30$, $St=fD/U_{0}$, where $f$, $D$ and $U_{0}$ denote the precessing vortex core (PVC) frequency (${\sim}800~\text{Hz}$), the swirler exit diameter (19 mm) and the bulk velocity at the swirler exit ($50~\text{m}~\text{s}^{-1}$) respectively. Planar projections of the PVC reveal a pair of oscillating skew-symmetric regions of velocity, vorticity and OH-PLIF intensity that rotate in the same direction as the mean tangential flow. During combustion instabilities, the large-amplitude acoustics-induced axisymmetric forcing of the flow results in a fundamentally different flow response dominated by a nearly axisymmetric disturbance and almost complete suppression of the large-scale helical shear-layer disturbances dominating the nominal flow. In addition, reverse axial flows around the centreline are significantly reduced. Time traces of the robust constituent show reverse axial flows around the centreline and negative axial vorticity along the inner swirling shear layer when the planar velocity is in the same direction as the mean tangential flow. For both stable and unstable combustion, recurrent flow structures decay rapidly downstream of the air swirler, as revealed by the decreasing amplitude of the velocity, axial vorticity and OH-PLIF intensity.

scholarly journals Challenges in dynamic mode decomposition

2021 ◽  
Vol 18 (185) ◽  
Author(s):  
Ziyou Wu ◽  
Steven L. Brunton ◽  
Shai Revzen
Keyword(s):  
Time Series ◽  
Numerical Models ◽  
Predictive Ability ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
System Matrix ◽  
Spatial And Temporal Patterns ◽  
Oscillatory Systems ◽  
Mode Decomposition ◽  
Wide Range

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modelling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables. Our numerical models include system and measurement noise. We explore the influences of dataset metrics, the spectrum of the latent dynamics, the normality of the system matrix and the geometry of the dynamics. Our results show that even for these very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability. Our work is motivated by our experience modelling multilegged robot data, where we have encountered great difficulty in reconstructing time series for oscillatory systems with intermediate transients, which decay only slightly faster than a period.

Predicted Effects of Tangential Slot Injection on Turbulent Boundary Layer Flow over a Wide Speed Range

1979 ◽  
Vol 101 (4) ◽  
pp. 699-704 ◽  
Author(s):  
A. M. Cary ◽  
D. M. Bushnell ◽  
J. N. Hefner
Keyword(s):  
Shear Layer ◽  
High Speed ◽  
Turbulence Modeling ◽  
Near Field ◽  
Velocity Ratio ◽  
Anomalous Behavior ◽  
Numerical Code ◽  
Stream Velocity ◽  
Wall Region ◽  
Wide Range

Paper describes a numerical calculation method using eddy viscosity/mixing length concepts for tangential slot injection (wall-wake) flows; application of the method over a wide range of flow conditions indicates increased accuracy compared to previous work. Predictions from the numerical code were in good agreement with experiment (velocity profile, skin friction, and effectiveness data) for low and high speed flows. To achieve improved accuracy, improvements in the turbulence modeling, compared to previous research, were necessary for the imbedded shear layer region in the near field and for the wall region near shear layer impingement. Anomalous behavior was noted for far field experimental velocity profiles in low speed flow when the slot-to-free stream velocity ratio was near one.

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