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In this study, using the results of a DNS of drag-reduced turbulent channel flow, vortical flow structures especially in the near-wall region are investigated. For this purpose, a Lagrangian Monte-Carlo method has been used to simulate the spatial orientation of fibers. Namely, the flow field is treated in an Eulerian manner whereas the fiber dynamics is described by a Lagrangian point of view. This method yields the exact solution of the governing equations. Vorticity fluctuations in the channel are studied and it turns out that the level of these fluctuations decreases in the drag-reduced flow. The reason for this reduction is explained using the reduction in velocity gradient fluctuations. Also, the distribution of the angle between the vorticity axis and the wall is studied and it turns out that horseshoe vortices exist in both flows. However, in the drag-reduced flow, they are formed farther away from the wall which indicates a weakening of sweep and ejection mechanism in the vicinity of the wall. This weakening leads to drag reduction. Also, the orientation of vortices in the drag-reduced flow is well ordered.

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In this paper, a new algebraic closure model for the DNS of turbulent drag reduction in a channel flow using microfiber additives is presented. This model is an extension of an existing model and cures some the shortcomings of the old model. In the proposed model, using the velocity correlation tensor in the modeling process, more physical conditions of the flow field are taken into account. With this, some of the shortcomings of other models are cured. The proposed model is used to directly simulate turbulent drag reduction in a horizontal channel flow under the action of a constant pressure gradient. For this purpose, time-dependent, three-dimensional Navier-Stokes equations for the incompressible flow of a non-Newtonian fluid are numerically solved. Statistical quantities of obtained by the new model are compared with the results of previous simulations. The good agreement between the results demonstrates the proper accuracy of the new model. Especially, the root-mean-square of velocity fluctuations in the streamwise direction is predicted with high accuracy as compared to previous models. Other statistical quantities are also computed with appropriate accuracy. This model is capable of prediction all properties of a microfiber-induced drag-reduced flow.

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Accurate modeling of the sub-grid scales (SGS) is crucial in determining the accuracy of the large eddy simulations (LES) in turbulent flow analysis. In recent years, new branches of the sub-grid scales models called gradient-based models were developed in computing the sub-grid scales stresses and heat fluxes and used in large eddy simulations. In this work, the modulated gradient model (MGM) equations were implemented in the OpenFOAM package, and pimpleFoam solver was modified to improve the solution accuracy. The modulated gradient model is based on the Taylor-series expansion of the sub-grid scales stress and employs the local equilibrium hypothesis to evaluate the sub-grid scales kinetic energy. To assess the accuracy of the modulated gradient model as well as the improved pimpleFoam solver, turbulent channel flow at a frictional Reynolds number of 395 was simulated via the OpenFOAM package and results were compared with the direct numerical simulation (DNS) data as well as the numerical solution of the Smagorinsky, Dynamic Smagorinsky, Deardorff models. The results show that modulated gradient model evaluates first and second order turbulence parameters with a high-level of accuracy.

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“Minimum-dissipation sub-grid models” are simple alternatives to the Smagorinsky-type approaches to imposing sub-grid scales (SGS)' effects in the large-eddy simulation (LES) approach. Recently, a new model in this family called “anisotropic minimum-dissipation (AMD)” model is represented. AMD is classified as a static type eddy-viscosity sub-grid scale model. The model is more cost effective than the dynamic Smagorinsky model, furthermore; it is not only able to consider the effect of various directions in computing sub-grid stress but also capable of operating for transitional flows from laminar to turbulent. In this study, this sub-grid model has been implemented in the open source package OpenFOAM and its performance is evaluated in the prediction of the flow field inside a channel with a pressure driven air flow. The accuracy of the model has been investigated at different Reynolds numbers including transient and fully turbulent flows and compared with the dynamic Smagorinsky model as well as direct numerical simulation (DNS) solutions. Results reveal that this sub-grid model is quite accurate over a broad range of Reynolds numbers once calculating velocity profiles as well as first and second-order turbulent quantities.