Gilmar Mompean

Evaluation of explicit algebraic stress models using direct numerical simulations

The paper deals with evaluation and improvement of two recent explicit algebraic turbulent stress models (EASMs). The first model was derived by Gatski and Rumsey (2001 Closure Strategies for Turbulent and Transitional Flows ed B E Launder and N D Sandham (Cambridge: Cambridge University Press) pp 9–46) and the second is the one devised by Wallin and Johansson (2000 J. Fluid Mech. 403 89–132). These models are studied for the turbulent flow through a square duct which involves a secondary flow and significant anisotropy between the turbulent Reynolds stress tensor components. An a priori evaluation of these models is made using direct numerical simulation (DNS) results of Navier–Stokes equations. In order to handle wall proximity effects, a damping function is suggested. The material frame-indifference (MFI) of these models is studied using the eigenvectors of the rate-of-deformation tensor and their angular velocities. This procedure allows us to evaluate an objective vorticity tensor. For this flow, it ...

Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data

ABSTRACT Tensorial decompositions and projections are used to study the performance of algebraic non-linear models and predict the anisotropy of the Reynolds stresses. Direct numerical simulation (DNS) data for plane channel flows at friction Reynolds number (Reτ = 180, 395, 590, 1000), and for the boundary layer using both DNS (Reτ = 359, 830, 1271) and experimental data (Reτ = 2680, 3891, 4941, 7164) are used to build and evaluate the models. These data are projected into tensorial basis formed from the symmetric part of mean velocity gradient and non-persistence-of-straining tensor. Six models are proposed and their performances are investigated. The scalar coefficients for these six different levels of approximations of the Reynolds stress tensor are derived, and made dimensionless using the classical turbulent scales, the kinetic turbulent energy (κ) and its dissipation rate (ε). The dimensionless coefficients are then coupled with classical wall functions. One model is selected by comparing the predicted Reynolds stress components with experimental and DNS data, presenting a good prediction for the shear and normal Reynolds stresses.

Modeling turbulent-bounded flow using non-Newtonian viscometric functions

Turbulent flows of Newtonian fluids have already been compared with non-Newtonian laminar flows. In this paper the analogy between these classes of flows is explored, and a new approach to derive a turbulent model based on a nonlinear constitutive equation is shown. In order to reach this aim, direct numerical simulation databases of turbulent channel flows are used and analyzed in the light of the classical parameters of non-Newtonian constitutive equations. The Reynolds stress tensor is expressed in terms of a set of basis tensors based on a projection of a nonlinear framework. The coefficients of the model are given as functions of the intensity of the mean strain tensor. The apparent turbulent viscosity, the first and second normal stress difference, are presented in function of the shear rate. A turbulent Weissenberg number, based on a characteristic turbulent time ratio of the first normal stress difference to the apparent viscosity is also presented. These material functions, exhibiting a shear-thinning behavior, are fitted with the power law (the Carreau-type) model. The range of the Reynolds number investigated was 180⩽Re τ⩽2000. One of the advantages of the new algebraic nonlinear power law constitutive equation derived in the paper is that its dependence is only on the mean velocity gradient and can be integrated up to the wall.

On Objective and Non-objective Kinematic Flow Classification Criteria

Turbulent flows present several compact and spatially coherent regions generically known as coherent structures. The understanding of these structures is closely related to the concept of vortex, whose definition is still a subject of controversy within the scientific community. In particular, the role of objectivity in the definition of vortex remains a largely open question. The three most usual criteria for vortex identification (Q, (varDelta ) and (lambda _2)) are non-objective since they all depend on the fluid’s rate-of-rotation, which is not invariant to the reference frame. In the present work, we propose an objective definition of these criteria by using the concept of relative rate-of-rotation with respect to the principal directions of the strain rate tensor. We also explore two novel naturally objective flow classification criteria. All the criteria are applied to instantaneous velocity fields obtained by DNS of both Newtonian and viscoelastic turbulent channel flows. The analysis is carried out here for four friction Reynolds numbers from 180 to 1000, emphasizing the difference between objective and non-objective and classification criteria, as well as between Newtonian and non-Newtonian flows. Moreover, we try to obtain from the results of flow classification criteria information related to the polymer drag reduction phenomenon.

On the evaluation of linear and non-linear models using DNS data of turbulent channel flows

In this paper, a priori and a posteriori analyses of algebraic linear and non-linear models are carried out in order to compare their ability to predict near wall turbulent flows. Tests were done using data from a direct numerical simulation (DNS) of a plane channel flow for three Reynolds numbers, based on the friction velocity, Reτ = 180, Reτ = 395 and Reτ = 590 . These models include the linear standard k - e model, the linear v2- f (Manceau et al., 2002) and the non-linear model of Shih (Shih et al., 1995). The results obtained are then compared with the DNS data of Moser et al. (1999). The comparisons are shown for the mean velocity profile, components of the Reynolds stress tensor, the turbulent kinetic energy (k), and the dissipation rate (e). The results suggest that the v2 - f is an efficient model to capture the turbulent shear stress component of the Reynolds stress near wall flows. However, it is unable to predict correctly the level of anisotropy between normal components of the Reynolds stress tensor. Furthermore, it is shown that the presence of non-linear terms in a turbulent model improves the ability to predict the anisotropy

Direct and Large Eddy Numerical Simulations of Turbulent Viscoelastic Drag Reduction

This work deals with direct numerical simulations (DNS) and temporal large eddy simulations (TLES) of turbulent drag reduction induced by injection of heavy-weight long-chain polymers in a Newtonian solvent. The phenomenon is modelled for the three-dimensional wall-bounded channel flow of a FENE-P dilute polymer solution. The DNS are undertaken with an optimized hybrid high-order finite difference spectral code running in parallel using domain decomposition (mpi) and threading (openmp) on each mpi process.

Turbulence modeling based on non-Newtonian constitutive laws

This work revisits the analogy between Newtonian turbulence and non-Newtonian laminar flows. Several direct numerical simulations (DNS) data of a plane channel flow, for a large range of Reynolds numbers (180 ≤ Reτ ≤ 2000) were explored. The profiles of mean velocity and second moment quantities were used to extract viscometric functions in the non-Newtonian modeling framework. The Reynolds stress tensor is expressed in terms of a set of basis kinematic tensors based on a projection of a nonlinear framework. The coefficients of the model are given as functions of the intensity of the mean strain tensor. The apparent eddy turbulent viscosity, the first and second normal stress differences are presented as function of the shear rate. One of the advantages of the new algebraic nonlinear power law constitutive equation derived in the paper, is that is only dependent on the mean velocity gradient and can be integrated up to the wall.