On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

1973 ◽  
Vol 59 (2) ◽  
pp. 281-335 ◽  
Author(s):  
I. J. Wygnanski ◽  
F. H. Champagne
Keyword(s):  
Energy Balance ◽  
Turbulent Flows ◽  
Turbulent Energy ◽  
Turbulent Pipe Flow ◽  
Entire Cross Section ◽  
Turbulent Fluid ◽  
Dissipation Term ◽  
Onset Of Turbulence ◽  
Order Of Magnitude ◽  
Pressure Transport

Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally atRe> 5 × 104. Transition could be initiated at lowerReby introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for\[ 2000 < Re < 2700 \]when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lowerRe. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

The influence of suction on the structure of turbulence in fully developed pipe flow

1979 ◽  
Vol 90 (1) ◽  
pp. 67-107 ◽  
Author(s):  
M. Schildknecht ◽  
J. A. Miller ◽  
G. E. A. Meier
Keyword(s):  
Energy Balance ◽  
Cross Section ◽  
Pipe Flow ◽  
Friction Velocity ◽  
Turbulent Energy ◽  
Turbulent Pipe Flow ◽  
List Type ◽  
Entire Cross Section ◽  
Uniform Wall ◽  
Critical Layers

The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following.The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that thex-wise components are first affected, then ther-wise and lastly the ϕ-wise components.The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocityUτ.Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

The Fully Developed Wake of a Circular Cylinder

1949 ◽  
Vol 2 (4) ◽  
pp. 451 ◽  
Author(s):  
AA Townsend
Keyword(s):  
Circular Cylinder ◽  
Diffusion Coefficients ◽  
Large Scale ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Small Scale ◽  
Mean Velocity ◽  
Turbulent Fluid ◽  
Air Stream ◽  
Scale Motion

Extending previous work on turbulent diffusion in the wake of a circular-cylinder, a series of measurements have been made of the turbulent transport of mean stream momentum, turbulent energy, and heat in the wake of a cylinder of 0.169 cm. diameter, placed in an air-stream of velocity 1280 cm. sec.-1. It has been possible to extend the measurements to 960 diameters down-stream from the cylinder, and it 1s found that, at distances in excess of 600 diameters, the requirements of dynamical similarity are very nearly satisfied. To account for the observed rates of transport of turbulent energy and heat, it is necessary that only part of this transport be due to bulk convection by the slow large-scale motion of the jets of turbulent fluid emitted by the central, fully turbulent core of the wake, which had been supposed previously to perform most of the transport. The remainder of the transport is carried out by the small-scale diffusive motion of the turbulent eddies within the jets, and may be described by assigning diffusion coefficients to the turbulent fluid. It is found that the diffusion coefficients for momentum and heat are approximately equal, but that for turbulent energy is considerably smaller. On the basis of these hypotheses, it is possible to calculate $he form of the mean velocity distribution in good agreement with experiment, and to give a qualitative explanation of the apparently more rapid diffusion of heat.

scholarly journals Numerical Simulation of Turbulence Flows in Shear Layer

2014 ◽  
Vol 59 (3) ◽  
pp. 1155-1158
Author(s):  
S.V. Fortova
Keyword(s):  
Turbulent Flows ◽  
Shear Layers ◽  
Development Stage ◽  
Inertial Range ◽  
Problem Definition ◽  
Spatial Problem ◽  
Hydrodynamic Instabilities ◽  
Onset Of Turbulence ◽  
Flow Stage ◽  
Vortex Cascade

Abstract For various problems of continuum mechanics described by the equations of hyperbolic type, the comparative analysis of scenarios of development of turbulent flows in shear layers is carried out. It is shown that the development of the hydrodynamic instabilities leads to a vortex cascade that corresponds to the development stage of the vortices in the energy and the inertial range during the transition to the turbulent flow stage. It is proved that for onset of turbulence the spatial problem definition is basic. At the developed stage of turbulence the spectral analysis of kinetic energy is carried out and the Kolmogorov “-5/3” power law is confirmed.

scholarly journals Energy Dissipation During Subglacial Abrasion at Nisqually Glacier, Washington, U.S.A.

1979 ◽  
Vol 23 (89) ◽  
pp. 233-246 ◽  
Author(s):  
Richard C. Metcalf
Keyword(s):  
Energy Balance ◽  
Suspended Sediment ◽  
Water Flux ◽  
Gravitational Energy ◽  
Sediment Flux ◽  
Normal Stresses ◽  
Mount Rainier ◽  
Suspended Sediment Flux ◽  
Basal Sliding ◽  
Order Of Magnitude

AbstractThis study examines the effect of subglacial abrasion on the basal sliding term of the gravitational energy balance of the dynamic, temperate Nisqually Glacier on Mount Rainier, Washington, U.S.A. Subglacial water flux is estimated as 3 × 107 m3 a–1 and suspended sediment flux as 3 × 107 kg a–1. Suspended-sediment flux is assumed to represent, within an order of magnitude, the annual mass eroded by subglacial abrasion.Subglacial abrasion involves both brittle fracture and plastic deformation. Field observations of bas-relief and grooved depression striations appear to have exact counterparts in rock mechanics experiments approximating subglacial velocities and normal stresses. Boulton's ([Cl974]) abrasion model and a new attritivity model proposed herein are shown to predict subglacial abrasion-rates within the limits of natural variability and the error range of measurements. The first crude gravitational energy balance for lower Nisqually Glacier (1.96 km2) is attempted and probably has only order-of-magnitude accuracy. The importance of subglacial abrasion in dissipating basal sliding energy at Nisqually Glacier is confirmed.

Energy balance of averaged and pulsating motion in annular turbulent flows

1970 ◽  
Vol 18 (4) ◽  
pp. 454-458
Author(s):  
B. P. Ustimenko ◽  
V. N. Zmeikov
Keyword(s):  
Energy Balance ◽  
Turbulent Flows

On the role of return to isotropy in wall-bounded turbulent flows with buoyancy

2018 ◽  
Vol 856 ◽  
pp. 61-78 ◽  
Author(s):  
Elie Bou-Zeid ◽  
Xiang Gao ◽  
Cedrick Ansorge ◽  
Gabriel G. Katul
Keyword(s):  
Turbulent Flows ◽  
Complex Dynamics ◽  
Vertical Component ◽  
Turbulent Energy ◽  
Extended Model ◽  
Density Gradients ◽  
Energy Redistribution ◽  
Stable Conditions ◽  
High Reynolds ◽  
Strain Interaction

High Reynolds number wall-bounded turbulent flows subject to buoyancy forces are fraught with complex dynamics originating from the interplay between shear generation of turbulence ($S$) and its production or destruction by density gradients ($B$). For horizontal walls, $S$ augments the energy budget of the streamwise fluctuations, while $B$ influences the energy contained in the vertical fluctuations. Yet, return to isotropy remains a tendency of such flows where pressure–strain interaction redistributes turbulent energy among all three velocity components and thus limits, but cannot fully eliminate, the anisotropy of the velocity fluctuations. A reduced model of this energy redistribution in the inertial (logarithmic) sublayer, with no tuneable constants, is introduced and tested against large eddy and direct numerical simulations under both stable ($B<0$) and unstable ($B>0$) conditions. The model links key transitions in turbulence statistics with flux Richardson number (at $Ri_{f}=-B/S\approx$$-2$, $-1$ and $-0.5$) to shifts in the direction of energy redistribution. Furthermore, when coupled to a linear Rotta-type closure, an extended version of the model can predict individual variance components, as well as the degree of turbulence anisotropy. The extended model indicates a regime transition under stable conditions when $Ri_{f}$ approaches $Ri_{f,max}\approx +0.21$. Buoyant destruction $B$ increases with increasing stabilizing density gradients when $Ri_{f}<Ri_{f,max}$, while at $Ri_{f}\geqslant Ri_{f,max}$ limitations on the redistribution into the vertical component throttle the highest attainable rate of buoyant destruction, explaining the ‘self-preservation’ of turbulence at large positive gradient Richardson numbers. Despite adopting a ‘framework of maximum simplicity’, the model results in novel and insightful findings on how the interacting roles of energy redistribution and buoyancy modulate the variance budgets and the energy exchange among the components.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

Wall Shear Stress in Turbulent Pipe Flow

2009 ◽  
Author(s):  
Roland Gårdhagen ◽  
Jonas Lantz ◽  
Fredrik Carlsson ◽  
Matts Karlsson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flows ◽  
Intima Media Thickness ◽  
Elevated Risk ◽  
Laminar Flows ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
Wall Shear

Low and/or oscillatory Wall Shear Stress (WSS) has been correlated with elevated risk for increased intima media thickness and atherosclerosis in several studies during the last decades [1, 2]. Most of the studies have addressed laminar flows, in which the oscillations mainly are due to the pulsating nature of blood flow. Turbulent flows however show significant spatial and temporal fluctuations although the mean flow is steady.

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