A singularity-free model of the local velocity gradient and acceleration gradient structure of turbulent flow

2005 ◽  
pp. 247-260
Author(s):  
Brian Cantwell
Keyword(s):  
Turbulent Flow ◽  
Velocity Gradient ◽  
Gradient Structure ◽  
Local Velocity ◽  
Free Model

Added stresses because of the presence of FENE-P bead–spring chains in a random velocity field

1997 ◽  
Vol 337 ◽  
pp. 67-101 ◽  
Author(s):  
HESHMAT MASSAH ◽  
THOMAS J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Velocity Gradient ◽  
Gradient Field ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Random Velocity

FENE-P bead–spring chains unravel in the presence of large enough velocity gradients. In a turbulent flow, this can result in intermittent added stresses and exchanges of energy between the chains and the fluid, whose magnitudes depend on the degree of unravelling and on the orientations of the bead–spring chains. These effects are studied by calculating the average behaviour at different times of an ensemble of chains, contained in a fluid particle that is moving around in a random velocity field obtained from direct numerical simulation of turbulent flow of a Newtonian fluid in a channel. The results are used to evaluate theoretical explanations of drag reduction observed in very dilute solutions of polymers.In regions of the flow in which the energy exchange with the fluid is positive, the possibility arises that turbulence can be produced by mechanisms other than the interaction of Reynolds stresses and the mean velocity gradient field. Of particular interest, from the viewpoint of understanding polymer drag reduction, is the finding that the exchange is negative in velocity fields representative of the wall vortices that are large producers of turbulence. One can, therefore, postulate that polymers cause drag reduction by selectively changing the structures of eddies that produce Reynolds stresses. The intermittent appearance of large added shear stresses is consistent with the experimental finding of a stress deficit, whereby the total local shear stress is greater than the sum of the Reynolds stress and the time-averaged shear stress calculated from the time-averaged velocity gradient and the viscosity of the solvent.

scholarly journals Sling Effect in Collisions of Water Droplets in Turbulent Clouds

2007 ◽  
Vol 64 (12) ◽  
pp. 4497-4505 ◽  
Author(s):  
Gregory Falkovich ◽  
Alain Pumir
Keyword(s):  
Velocity Gradient ◽  
Dissipation Rate ◽  
Local Velocity ◽  
Collision Rate ◽  
Water Droplets ◽  
Preferential Concentration ◽  
Turbulent Airflow

Abstract The effect of turbulence on the collision rate between droplets in clouds is investigated. Because of their inertia, water droplets can be shot out of curved streamlines of the turbulent airflow. The contribution of such a “sling effect” in the collision rate of the same-size water droplets is described and evaluated. It is shown that already for turbulence with the dissipation rate 103 cm2 s−3, the sling effect gives a contribution to the collision rate of 15-μm droplets comparable to that due to the local velocity gradient. That may explain why the formulas based on the local velocity gradient consistently underestimate the turbulent collision rate, even with the account of preferential concentration.

Transient Lubricating Films With Inertia—Turbulent Flow

1984 ◽  
Vol 106 (1) ◽  
pp. 134-139 ◽  
Author(s):  
H. G. Elrod ◽  
I. Anwar ◽  
R. Colsher
Keyword(s):  
Steady State ◽  
Turbulent Flow ◽  
Stream Function ◽  
Velocity Gradient ◽  
Eddy Viscosity ◽  
Mean Velocity ◽  
Steady State Operation ◽  
Pressure Development ◽  
Transient And Steady State

This paper presents some new equations for the treatment of turbulent lubricating films when the effects of inertia cannot be neglected. The eddy-viscosity concept is used to represent the turbulent stresses in terms of mean-velocity gradient. Transient and steady-state operation are both considered by means of a generalized stream-function-pressure development.

Turbulent flow chracteristics for pitched blade turbine

1988 ◽  
Vol 53 (5) ◽  
pp. 957-969 ◽  
Author(s):  
Zdzisław Jaworski ◽  
Ivan Fořt ◽  
Fryderyk Stręk
Keyword(s):  
Turbulent Flow ◽  
Radial Distribution ◽  
The Other ◽  
Local Velocity ◽  
Cylindrical Tank ◽  
Local Isotropy ◽  
Tracer Particles ◽  
Pitched Blade Turbine ◽  
Instantaneous Values ◽  
The Mean

Measurements of the velocity of a stirred liquid in turbulent flow were performed for the area surrounding a pitched blade turbine. A cylindrical tank equipped with four standard baffles and the stirrer was used in the study. A number of traces of tracer particles were photographed and used to determine instantaneous values of the radial and axial components of the liquid local velocity. Those values were employed to estimate local values of the radial and axial components of the mean and fluctuating velocities. Analysis of the radial distribution of the fluctuating velocity components revealed the existence of the local isotropy of those components for the entire investigated area upstream and downstream the stirrer. Moreover, the homogeneity of turbulence in the stream entering the stirrer and in the induced stream can be assumed. The discharge stream showed an approximate homogeneous turbulence of intensity over 2 times higher than that for the other streams.

Effect of Near Wall Turbulence on the Particle Removal From Bed Deposits in Horizontal Wells

2016 ◽  
Author(s):  
Majid Bizhani ◽  
Ergun Kuru ◽  
Sina Ghaemi
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Reynolds Stress ◽  
Turbulence Intensity ◽  
Experimental Program ◽  
Local Velocity ◽  
Cutting Bed ◽  
Cuttings Bed ◽  
The Impact ◽  
Near Wall

Although solids entrainment and deposition mechanisms have been studied extensively over the years, our understanding of fluids-particle interactions near bed interface is still limited. Progress toward such understanding has been relatively slow because of the difficulties inherent simultaneous measurement of local solids transport and adjacent near-bed fluid flow. With the introduction of non-intrusive measurement techniques such as Particle Image Velocimetry (PIV), it is now possible to determine the instantaneous velocity field and observe particle deposition/resuspension simultaneously under non-uniform flow conditions. An experimental program was conducted to investigate different aspects of turbulent flow of water over the cuttings bed deposited in horizontal annuli. A large-scale horizontal flow loop consisting of 9 m long high quality optic glass pipes (95 mm ID of outer pipe and 38 mm OD of inner pipe) equipped with state of the art PIV system has been used for the experiments. Turbulent flow over cuttings bed experiments were conducted at superficial Reynolds numbers of 9300 and 10800. Natural irregular shaped quartz sands with 3 different mean sieve sizes of 260, 350 and 600 micron were used as solid particles. The proposed work was accomplished through several tasks: i-) conduct experiments to measure the instantaneous local velocity profile during turbulent flow in the horizontal concentric annuli and examine the effect of stationary cutting bed on the local velocity profile, Reynolds stress and turbulence intensity; ii-) investigate the impact of particle size on the near-wall turbulent activities. Results have indicated that existence of a cuttings bed on the lower side of the wellbore dramatically alters the near wall velocity profile comparing to the case with no cuttings bed. Presence of cuttings bed causes the maximum velocity to shift toward the inner pipe. Presence of stationary cutting bed causes a reduction in Reynolds stress, axial and radial turbulence intensity, which in turn, would adversely affect the hole cleaning. Larger cuttings slightly enhanced turbulent stress and radial intensities. However, the increase in these entities as a result of increasing cutting size was far less than the decrease in them as a consequence of presence of stationary cutting bed. Axial turbulence intensity was the same in the core flow away from the cuttings bed for flow with and without a cuttings bed. However, the peak of axial intensities is shown to be less for flow near the cuttings bed.

Stochastic analysis of the local velocity gradient in a trickle-bed reactor

1994 ◽  
Vol 49 (24) ◽  
pp. 5281-5289 ◽  
Author(s):  
M.A. Latifi ◽  
A. Naderifar ◽  
N. Midoux
Keyword(s):  
Velocity Gradient ◽  
Stochastic Analysis ◽  
Local Velocity ◽  
Trickle Bed Reactor ◽  
Trickle Bed

On the Reynolds number dependence of velocity-gradient structure and dynamics

2018 ◽  
Vol 861 ◽  
pp. 163-179 ◽  
Author(s):  
Rishita Das ◽  
Sharath S. Girimaji
Keyword(s):  
Reynolds Number ◽  
Velocity Gradient ◽  
Probability Distributions ◽  
Small Scale ◽  
Gradient Structure ◽  
Local Pressure ◽  
Non Local ◽  
Normalized Gradient ◽  
Scalar Invariants ◽  
Reynolds Number Dependence

We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ($Re_{\unicode[STIX]{x1D706}}$). The analysis factorizes the velocity gradient ($\unicode[STIX]{x1D608}_{ij}$) into the magnitude ($A^{2}$) and normalized-gradient tensor ($\unicode[STIX]{x1D623}_{ij}\equiv \unicode[STIX]{x1D608}_{ij}/\sqrt{A^{2}}$). The focus is on bounded $\unicode[STIX]{x1D623}_{ij}$ as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of $\unicode[STIX]{x1D623}_{ij}$ and its scalar invariants are shown to attain $Re_{\unicode[STIX]{x1D706}}$ independence. The critical values beyond which each feature attains $Re_{\unicode[STIX]{x1D706}}$ independence are established. We proceed to characterize the $Re_{\unicode[STIX]{x1D706}}$ dependence of $\unicode[STIX]{x1D623}_{ij}$-conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.

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