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’.

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).

Turbulent–laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces

2012 ◽  
Vol 704 ◽  
pp. 137-172 ◽  
Author(s):  
G. Brethouwer ◽  
Y. Duguet ◽  
P. Schlatter
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Pure Shear ◽  
Stable Stratification ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Turbulence Structures ◽  
Wall Flows ◽  
Near Wall

AbstractDirect numerical simulations of subcritical rotating, stratified and magneto-hydrodynamic wall-bounded flows are performed in large computational domains, focusing on parameters where laminar and turbulent flow can stably coexist. In most cases, a regime of large-scale oblique laminar-turbulent patterns is identified at the onset of transition, as in the case of pure shear flows. The current study indicates that this oblique regime can be shifted up to large values of the Reynolds number $\mathit{Re}$ by increasing the damping by the Coriolis, buoyancy or Lorentz force. We show evidence for this phenomenon in three distinct flow cases: plane Couette flow with spanwise cyclonic rotation, plane magnetohydrodynamic channel flow with a spanwise or wall-normal magnetic field, and open channel flow under stable stratification. Near-wall turbulence structures inside the turbulent patterns are invariably found to scale in terms of viscous wall units as in the fully turbulent case, while the patterns themselves remain large-scale with a trend towards shorter wavelength for increasing $\mathit{Re}$. Two distinct regimes are identified: at low Reynolds numbers the patterns extend from one wall to the other, while at large Reynolds number they are confined to the near-wall regions and the patterns on both channel sides are uncorrelated, the core of the flow being highly turbulent without any dominant large-scale structure.

A coherent structure model of the turbulent boundary layer and its ability to predict Reynolds number dependence

1991 ◽  
Vol 336 (1641) ◽  
pp. 103-129 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Reynolds Stress ◽  
Coherent Structure ◽  
Large Scale ◽  
Outer Region ◽  
Structure Model ◽  
Hairpin Vortices ◽  
Reynolds Number Dependence

The coherent motions identified in passively marked turbulent boundary-layer experiments are reviewed. Data obtained in our laboratory using simultaneous hot-wire anemometry and flow visualization are analysed to provide measures of the percent contribution of the coherent motions to the total Reynolds stress. A coherent structure model is then developed. In the outer region the model incorporates the large-scale motions, the typical eddies and their interactions. In the wall region the model is characterized by the long streaks, their associated hairpin vortices, and the pockets with their associated pocket and hairpin vortices. The motions in both regions have unique phase relations which play an important role in their evolution and the resulting intensity of their interactions. In addition, the inner-outer region interactions are seen to be strong because typical eddies, microscale motions which can directly initiate the bursting process near a wall, are convected towards the wall by the response of the high speed outer region fluid to the presence of the large-scale motions. This interaction establishes a phasing between the inner and outer regions. The length and velocity scales of the typical eddy are used to remove the Reynolds number dependence of the stream wise fluctuations and the Reynolds stress in the fully turbulent portion of turbulent boundary layers over a wide range of Reynolds numbers

scholarly journals Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

2009 ◽  
Vol 628 ◽  
pp. 311-337 ◽  
Author(s):  
ROMAIN MATHIS ◽  
NICHOLAS HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Supporting Evidence ◽  
Scale Structures ◽  
Small Scale Structures ◽  
Near Wall

In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

scholarly journals Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160080 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley McKeon
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
High Reynolds Number ◽  
Phase Relations ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Small Scale ◽  
Scale Interactions ◽  
High Reynolds

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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’.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

The ‘preferred mode’ of the axisymmetric jet

1981 ◽  
Vol 110 ◽  
pp. 39-71 ◽  
Author(s):  
A. K. M. F. Hussain ◽  
K. B. M. Q. Zaman
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Coherent Structure ◽  
Large Scale ◽  
Near Field ◽  
Saddle Points ◽  
Initial Boundary ◽  
Phase Average ◽  
Background Turbulence ◽  
Time Average

The ‘preferred mode’ of an incompressible axisymmetric free jet has been organized through controlled perturbation, and spatial distributions of time-average as well as phase-average flow properties in the near field are documented. The excitation produces noticeable changes in the time-average measures of the jet, although these changes are less dramatic than those for the excitation producing stable vortex pairing. For different stages in the evolution of the preferred-mode coherent structure, the phase-average vorticity, coherent Reynolds stress, and incoherent turbulence intensities and Reynolds stress have been educed through phase-locked hot-wire measurements, over the spatial extent of the structure and without invoking the Taylor hypothesis. For a particular stage of the evolution (i.e. when the structure is centred at x/D ≃ 3) the distributions of these quantities have been compared for both initially laminar and fully turbulent exit boundary layers, and for four jet Reynolds numbers. The relative merits of the coherent structure streamline and pseudo-stream-function patterns, as compared with phase-average velocity contours, for structure boundary identification have been discussed. The structure shape and size agree closely with those inferred from the average streamline pattern of the natural structure educed by Yule (1978).These data as well as τ-spectra show that even excitation at the preferred mode cannot sustain the initially organized large-scale coherent structure beyond eight diameters from the jet exit. The background turbulence is organized by the coherent motions in such a way that the maximum rate of decrease of the coherent vorticity occurs at the structure centres which are the saddle points of the background-turbulence Reynolds-stress distributions. The structure centres are also the locations of peak phase-average turbulence intensities. The evolving shape of the structure as it travels downstream helps explain the transverse variations of the wavelength and convection velocity across the mixing layer. The coherent structure characteristics are found to be independent of whether the initial boundary layer is laminar or turbulent, but depend somewhat on the jet Reynolds number. With increasing Reynolds number, the structure decreases in the streamwise length and increases in the radial width and becomes relatively more energetic, and more efficient in the production of coherent Reynolds stress.

Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109

2010 ◽  
Vol 662 ◽  
pp. 409-446 ◽  
Author(s):  
G. SILANO ◽  
K. R. SREENIVASAN ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Multiple Solutions ◽  
Large Scale ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

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