The effects of turbulence on the mean flow past square rods

1983 ◽  
Vol 137 ◽  
pp. 331-345 ◽  
Author(s):  
Y. Nakamura ◽  
Y. Ohya
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Cross Section ◽  
Large Scale ◽  
Small Scale ◽  
Mean Flow ◽  
Flow Past ◽  
The Mean ◽  
Scale Turbulence ◽  
Main Effects

There are two main effects of turbulence on the mean flow past rods of square cross-section aligned with the approaching flow. Small-scale turbulence increases the growth rate of the shear layer, while large-scale turbulence enhances the roll-up of the shear layer. The consequences of these depend on the length of a square rod. The mean base pressure of a square rod varies considerably with turbulence intensity and scale as well as with its length.

scholarly journals Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

2015 ◽  
Vol 787 ◽  
pp. 396-439 ◽  
Author(s):  
Xuesong Wu ◽  
Xiuling Zhuang
Keyword(s):  
Nonlinear Dynamics ◽  
Coherent Structures ◽  
Large Scale ◽  
Shear Layers ◽  
Small Scale ◽  
Evolution System ◽  
Mean Flow ◽  
Free Shear Layers ◽  
The Mean ◽  
Scale Turbulence

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

Vortex shedding from square prisms in smooth and turbulent flows

1986 ◽  
Vol 164 ◽  
pp. 77-89 ◽  
Author(s):  
Yasuharu Nakamura ◽  
Yuji Ohya
Keyword(s):  
Flow Visualization ◽  
Turbulent Flows ◽  
Cross Section ◽  
Vortex Shedding ◽  
Large Scale ◽  
Resonant Interaction ◽  
The Other ◽  
Flow Past ◽  
Scale Turbulence ◽  
Main Effects

Visualization and measurements of velocity and pressure were made for the flow past prisms of variable length with square cross-section, placed normal to smooth and turbulent approaching flows. Square prisms shed vortices in one of the two fixed wake planes. The plane of shedding is switched irregularly from one to the other. Flow visualization confirms the two main effects of small– and large-scale turbulence on the flow past square prisms that had previously been suggested. In particular, large-scale turbulence intensifies vortex shedding from square prisms through resonant interaction, thereby reducing the base pressure considerably.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Aerodynamic sound generation in a pipe

1968 ◽  
Vol 32 (4) ◽  
pp. 765-778 ◽  
Author(s):  
H. G. Davies ◽  
J. E. Ffowcs Williams
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Sound Field ◽  
Convective Motion ◽  
Energy Output ◽  
Small Scale ◽  
Mean Flow ◽  
Limited Region ◽  
Aerodynamic Sound ◽  
Scale Turbulence

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

Flow Past a Permeable Manipulator Ring Placed in a Turbulent Pipe Flow

2011 ◽  
Author(s):  
Koji Utsunomiya ◽  
Suketsugu Nakanishi ◽  
Hideo Osaka
Keyword(s):  
Turbulent Flow ◽  
Shear Layer ◽  
Pipe Flow ◽  
Area Ratio ◽  
Turbulent Pipe Flow ◽  
Wall Region ◽  
Open Area ◽  
Mean Flow ◽  
Flow Past ◽  
The Mean

Turbulent pipe flow past a ring-type permeable manipulator was investigated by measuring the mean flow and turbulent flow fields. The permeable manipulator ring had a rectangular cross section and a height 0.14 times the pipe radius. The experiments were performed under four conditions of the open area ratio β of the permeable ring (β = 0.1, 0.2, 0.3 and 0.4) for Reynolds number of 6.2×104. The results indicate that as the open-area ratio increased, the separated shear layer arising from the permeable ring top became weaker and the pressure loss was reduced by increasing fluid flow through the permeable ring. When β was less than 0.2, the velocity gradient was steeper over the permeable ring and in the shear layer near the reattachment region. When β was greater than 0.3, the width of the shear layer showed a relatively large augmentation and the back pressure in the separating region increases. Further, the response of the turbulent flow field to the permeable ring was delayed compared with that of the mean velocity field, and these differences increased with β. The turbulence intensities and Reynolds shear stress profiles near the reattachment point increased near the wall region as β increased, while those peak values that were taken at the locus of the manipulator ring height decreased as β increased.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

scholarly journals Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

2016 ◽  
Vol 73 (5) ◽  
pp. 2229-2253 ◽  
Author(s):  
Navid C. Constantinou ◽  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Large Scale ◽  
Cooperative Interaction ◽  
Small Scale ◽  
Mean Flow ◽  
Theoretical Understanding ◽  
Laminar Jet ◽  
Planetary Scale ◽  
Statistical State ◽  
Beta Plane ◽  
Scale Turbulence

Abstract Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

Relaxation of Spatially Advancing Coherent Structures in a Turbulent Curved Channel Flow

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Koji Matsubara ◽  
Tomoya Ohishi ◽  
Keisuke Shida ◽  
Takahiro Miura
Keyword(s):  
Small Scale ◽  
Computational Domain ◽  
Mean Flow ◽  
Curved Channel ◽  
Concave Wall ◽  
Convex Wall ◽  
Mean Pressure ◽  
Coherent Vortex ◽  
The Mean ◽  
Scale Turbulence

A direct numerical simulation is made for the incompressible turbulent flow in the 180 deg curved channel with a long straight portion connected to its exit port. An examination is made for how the organized coherent vortex grows and decays in the curved channel: the radius ratio of 0.92, the aspect ratio of 7.2, and the succeeding straight section length of 75 times the channel half width. The 1552 × 91 × 128 ( = 18,427,136) grids are allocated to the computational domain. The frictional-velocity-based Reynolds number is kept at 150 to resolve the long domain including curved and straight regions. In contrast to that the coherent vortex grows along the concave wall, the vortex remains strong in the convex-wall side after the curvature accompanying a tail of the small-scale turbulence near the convex wall. The dissimilarity between the onset and disappearing of the coherent vortex essentially comes from the mean pressure gradient, which aids or averts the near-wall fluid oppositely between the curvature inlet and the exit. The mean flow is decelerated near the inlet of the convex wall to destabilize the flow and to trigger the onset of the coherent vortex. Contrary, the mean flow is accelerated near the exit of the convex wall to weaken the coherent vortex, and is decelerated near the exit of the concave wall to enhance the turbulence. Therefore, the turbulence enhancement and attenuation occurs oppositely between the inlet and exit of the curvature, and the coherent vortex draws a wake in the convex-side rather than the concave-side where it starts.

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