Lagrangian statistics of turbulent channel flow at Reτ = 950 calculated with direct numerical simulation and Langevin models

Abstract

We present results of Lagrangian statistical quantities for direct numerical simulation (DNS) of turbulent channel flow at Reynolds number Re τ = 950 based on shear velocity and channel half-height. Attention is focused on time correlations of fluid particle velocity and on the wall-normal diffusivity as a function of the wall-normal distance. Away from the wall region the DNS results compare favorably with the results of recent statistical models based on Kolmogorov theory and Onsager symmetry relations. It is found that a value for the Kolmogorov constant of C 0 = 6 gives optimal agreement between DNS results and results of the statistical models for all quantities considered. C 2013 AIP Publishing LLC. [http://dx

Statistical Models of Large Scale Turbulent Flow

“…This is in line with the many results of measurements and DNS obtained for various cases of turbulence: grid turbulence [23], turbulent pipe and channel flow [24,25,33,34], turbulent boundary layers [26] and turbulence between counter rotating disks [4]. [32], with Lagrangian DNS results of pipe, channel and uniform shear [9,30,32] and with Lagrangian based experimental results of pipe flow using particle tracking velocimetry [32]. 3.…”

“…This includes the Lagrangian version of Kolmogorov K-41 similarity theory which is of particular interest to the present analysis. Studies in the past decade confirm several of the universal statistical properties of Lagrangian Kolmogorov Theory [6][7][8][9].…”

“…This is confirmed by a relatively small anti-symmetric part of the cross-correlation functions of particle velocity found for cases of anisotropic turbulence: viz. pipe and channel flow and nonstationary homogeneous anisotropic shear flow [9,31,35]. Results originated from DNS and particle tracking velocimitry.…”

“…The constant enters into the Langevin equation through the connection with the inertial subrange representation of Lagrangian Kolmogorov theory. Recent results of Lagrangian based DNS and measurements indicate that the value of the universal constant C 0 should be somewhere between 6 and 7: see [8,9,[30][31][32], Ref. [3], p. 504.…”

Turbulence attenuation in particle-laden flow in smooth and rough channels

“…If we include PP-DNS of horizontal or non-gravitational particle-laden plane channel flows in our discussion, one-way coupled simulations of such flows were (for example) performed at Re τ = 150 (Pedinotti, Mariotti & Banerjee 1992;Marchioli & Soldati 2002), Re τ = 300 (Lavezzo et al 2010) and Re τ = 950 (Geurts & Kuerten 2012;Kuerten & Brouwers 2013), two-way coupled simulations up to Re τ = 395 (Kuerten, van der Geld & Geurts 2011;Zhao, Andersson & Gillissen 2013) and two-way coupled simulations with inter-particle collisions at Re τ = 125 (Nasr, Ahmadi & McLaughlin 2009).…”