Modeling near wall effects in second moment closures by elliptic relaxation
Abstract
The elliptic relaxation model of Durbin (1993) for modeling nearwall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for nearwallturbulence. The essential nearwall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the loglayer is better reproduced by adding a nonhomogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the loglayer. The elliptic operator was quite easily applied to the nonlinear Craft & Launder pressurestrain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressurestrain term, entirely ignored in the models.
 Publication:

Studying Turbulence Using Numerical Simulation Databases. V: Proceedings of the 1994 Summer Program
 Pub Date:
 December 1994
 Bibcode:
 1994stun.proc..323L
 Keywords:

 Channel Flow;
 Elliptic Differential Equations;
 Mathematical Models;
 Reynolds Stress;
 Turbulence;
 Wall Flow;
 Nonlinearity;
 Reynolds Number;
 Viscous Flow;
 Wakes;
 Fluid Mechanics and Heat Transfer