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 On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers

1996 ◽  
Vol 306 ◽  
pp. 293-323 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Large Reynolds Number ◽  
Kolmogorov Flow ◽  
Turbulence Decay ◽  
High Reynolds

High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.

scholarly journals Experimental Study of the Precessing Vortex Core Impact on the Liquid Fuel Spray in a Gas Turbine Model Combustor

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Antoine Renaud ◽  
Sébastien Ducruix ◽  
Laurent Zimmer
Keyword(s):  
Vortex Core ◽  
Gas Turbines ◽  
High Speed ◽  
Large Scale ◽  
Air Flow ◽  
Dynamic Mode Decomposition ◽  
Pollutant Emissions ◽  
Fuel Spray ◽  
Dynamic Mode ◽  
Precessing Vortex Core

Abstract Despite being good candidates for the reduction of pollutant emissions from gas turbines, burners operating in lean premixed prevaporized regimes often face stability issues and can be sensitive to perturbations. The swirling flow used to aerodynamically stabilize the flame can also lead to the appearance of a large-scale coherent flow structure known as the precessing vortex core (PVC). In this study, a swirl-stabilized combustor fed with liquid dodecane is studied at a globally lean operating condition with the help of high-speed diagnostics and dynamic mode decomposition (DMD) as the main postprocessing method. It is shown that the trace of a PVC originating inside the injector is still present in the fuel spray at the entrance of the chamber even though the aerodynamical structure itself is not detectable anymore. The perturbation of the fuel spray is then transmitted to the flame through local equivalence ratio fluctuations. It is observed that the PVC trace on the spray and thus on the flame can be suppressed by air flow modulations generated by a siren device. The suppression of this trace is shown to come from a decay of the aerodynamical structure itself rather than by a change in fuel mixing or vaporization. Analysis of the characteristic frequency of the PVC shows a frequency spread indicating a loss of coherence of the structure with the high-amplitude air flow rate fluctuations.

scholarly journals Reynolds stress scaling in pipe flow turbulence—first results from CICLoPE

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160187 ◽  
Author(s):  
R. Örlü ◽  
T. Fiorini ◽  
A. Segalini ◽  
G. Bellani ◽  
A. Talamelli ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Large Scale ◽  
Strong Support ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Normal Distance ◽  
First Results ◽  
Variance Profile

This paper reports the first turbulence measurements performed in the Long Pipe Facility at the Center for International Cooperation in Long Pipe Experiments (CICLoPE). In particular, the Reynolds stress components obtained from a number of straight and boundary-layer-type single-wire and X-wire probes up to a friction Reynolds number of 3.8×10 4 are reported. In agreement with turbulent boundary-layer experiments as well as with results from the Superpipe, the present measurements show a clear logarithmic region in the streamwise variance profile, with a Townsend–Perry constant of A 2 ≈1.26. The wall-normal variance profile exhibits a Reynolds-number-independent plateau, while the spanwise component was found to obey a logarithmic scaling over a much wider wall-normal distance than the other two components, with a slope that is nearly half of that of the Townsend–Perry constant, i.e. A 2, w ≈ A 2 /2. The present results therefore provide strong support for the scaling of the Reynolds stress tensor based on the attached-eddy hypothesis. Intriguingly, the wall-normal and spanwise components exhibit higher amplitudes than in previous studies, and therefore call for follow-up studies in CICLoPE, as well as other large-scale facilities. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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 Experimental Study of the Precessing Vortex Core Impact on the Liquid Fuel Spray in a Gas Turbine Model Combustor

2019 ◽  
Author(s):  
Antoine Renaud ◽  
Sébastien Ducruix ◽  
Laurent Zimmer
Keyword(s):  
Vortex Core ◽  
Gas Turbines ◽  
High Speed ◽  
Large Scale ◽  
Air Flow ◽  
Dynamic Mode Decomposition ◽  
Pollutant Emissions ◽  
Fuel Spray ◽  
Dynamic Mode ◽  
Precessing Vortex Core

Abstract Despite being good candidates for the reduction of pollutant emissions from gas turbines, burners operating in Lean Premixed Prevaporized regimes often face stability issues and can be sensitive to perturbations. The swirling flow used to aero-dynamically stabilize the flame can also lead to the appearance of a large-scale coherent flow structure known as the Precessing Vortex Core (PVC). In the present study, a swirl-stabilized combustor fed with liquid dodecane is studied at a globally lean operating condition with the help of high-speed diagnostics and Dynamic Mode Decomposition (DMD) as the main post-processing method. It is shown that the trace of a PVC originating inside the injector is still present in the fuel spray at the entrance of the chamber even though the aerodynamical structure itself is not detectable anymore. The perturbation of the fuel spray is then transmitted to the flame through local equivalence ratio fluctuations. It is observed that the PVC trace on the spray and thus on the flame can be suppressed by air flow modulations generated by a siren device. The suppression of this trace is shown to come from a decay of the aerodynamical structure itself rather than by a change in fuel mixing or vaporization. Analysis of the characteristic frequency of the PVC shows a frequency spread indicating a loss of coherence of the structure with the high amplitude air flow rate fluctuations.

Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer

2014 ◽  
Vol 763 ◽  
pp. 136-165 ◽  
Author(s):  
Nicola De Tullio ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
High Speed ◽  
Stokes Equations ◽  
Roughness Element ◽  
Transition To Turbulence ◽  
Local Boundary ◽  
Wake Modes

AbstractThe excitation of instability modes in the wake generated behind a discrete roughness element in a boundary layer at Mach 6 is analysed through numerical simulations of the compressible Navier–Stokes equations. Recent experimental observations show that transition to turbulence in high-speed boundary layers during re-entry flight is dominated by wall roughness effects. Therefore, understanding the roughness-induced transition to turbulence in this flow regime is of primary importance. Our results show that a discrete roughness element with a height of about half the local boundary-layer thickness generates an unstable wake able to sustain the growth of a number of modes. The most unstable of these modes are a sinuous mode (mode SL) and two varicose modes (modes VL and VC). The varicose modes grow approximately 17 % faster than the most unstable Mack mode and their growth persists over a longer streamwise distance, thereby leading to a notable acceleration of the laminar–turbulent transition process. Two main mechanisms are identified for the excitation of wake modes: the first is based on the interaction between the external disturbances and the reverse flow regions induced by the roughness element and the second is due to the interaction between the boundary-layer modes (first modes and Mack modes) and the non-parallel roughness wake. An important finding of the present study is that, while being less unstable, mode SL is the preferred instability for the first of the above excitation mechanisms, which drives the wake modes excitation in the absence of boundary-layer modes. Modes VL and VC are excited through the second mechanism and, hence, become important when first modes and Mack modes come into interaction with the roughness wake. The new mode VC presents similarities with the Mack mode instability, including the tuning between its most unstable wavelength and the local boundary-layer thickness, and it is believed to play a fundamental role in the roughness-induced transition of high-speed boundary layers. In contrast to the smooth-wall case, wall cooling is stabilising for all the roughness-wake modes.

scholarly journals The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160078 ◽  
Author(s):  
K. Deguchi ◽  
P. Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Equilibrium Solutions ◽  
New Family

The present work is based on our recent discovery of a new class of exact coherent structures generated near the edge of quite general boundary layer flows. The structures are referred to as free-stream coherent structures and were found using a large Reynolds number asymptotic approach to describe equilibrium solutions of the Navier–Stokes equations. In this paper, first we present results for a new family of free-stream coherent structures existing at relatively large wavenumbers. The new results are consistent with our earlier theoretical result that such structures can generate larger amplitude wall streaks if and only if the local spanwise wavenumber is sufficiently small. In a Blasius boundary layer, the local wavenumber increases in the streamwise direction so the wall streaks can typically exist only over a finite interval. However, here it is shown that they can interact with wall curvature to produce exponentially growing Görtler vortices through the receptivity process by a novel nonparallel mechanism. The theoretical predictions found are confirmed by a hybrid numerical approach. In contrast with previous receptivity investigations, it is shown that the amplitude of the induced vortex is larger than the structures in the free-stream which generate it. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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.

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