Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Abstract

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.

Proper orthogonal decomposition of the flow in geometries containing a narrow gap

“…Interestingly, a recent numerical work suggests that, in the presence of oscillations, turbulence presents strong anisotropy and a 2D behaviour in the narrow gap [14], thus supporting the validity of the hypothesis made.…”

“…An in-house code has been used, where the Navier-Stokes Eqs. (5) and (6) are solved in boundary-fitted coordinates [14,18]. The Sub-Grid-Scale (SGS) stresses (7) are modelled through a dynamic model [19] where the C s in (8) is determined locally.…”

“…The convective fluxes have been discretized through a second-order central scheme suitable for boundary-fitted coordinates while time advancement has been carried out through an Adams-Bashforth scheme. Details of the numerical practices and details of the results are available in Merzari and Ninokata [14].…”

“…Extensive results on the calculations carried out are reported in Merzari and Ninokata [14]. Figure 11 however shows a brief comparison for the case with Re = 3,200 and available DNS data for channel flow [20].…”

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry

“…It has to be noted that the oscillations observed by Guellouz and Tavoularis 4 and Hopper and Rehme 5 have not been observed experimentally for eccentric channels. A recent numerical work 6 supports the assumption that the oscillations are indeed present for the flow in eccentric annuli for certain combinations of the geometric parameters and the Reynolds number.…”