Linear Viscosity Models Research Articles

Airborne flow dynamics near free-falling bulk materials: CFD analysis from analytical pressure field

The dust generated and spread by free fall of bulk materials is analyzed through CFD simulations that allow visualization of the velocity vector field and the air masses close to the main material stream (core) that generate preferential paths for the formation and escape of dust. The air velocity field near a free-falling bulk material is obtained through a CFD solution from the analytical pressure field; the model was fed with properties described in empirical studies allowing comparison and validation. CFD results allow visualization of the boundary layer formed close to the bulk material stream. The results indicate the existence of a critical height that, when reached, transforms the pressure field inducing the emergence of a toroidal vortex around the mainstream. This causes the expansion of the boundary layer leading to an increase in particle absorption and formation of dust dispersion zones. A relationship between the critical height and the material stream diameter is proposed. The results indicate that the fluid viscosity inside the boundary layer is constant - before its complete expansion - and after increases linearly. A linear viscosity model, adapted from Einstein's proposal, is applied in the CFD model to establish the relationship to the induced airflow as a function only of the fall height and core diameter.

Enhanced stability of free viscous films due to surface viscosity

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that Γi(nl)>3D/M provides a simple criterion for enhanced stability, where Γi(nl), D, and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

Modeling Surface Riblets Skin Friction Reduction Effect with the Use of Computational Fluid Dynamics

Towards the minimization of fuel consumption and aicraft emissions reduction, many disruptive technologies have been proposed in aviation industry regarding the improvement of aircraft aerodynamic performance. Among others, these technologies involve innovative passive and active flow control methodologies and techniques. A passive flow control methodology which is studied in the current work is the implementation of riblets, which are inspired by shark skin morphology, on a NACA 0012 airfoil. The main purpose of riblets is to alter the boundary layer characteristics near the wall region in such a way that the total skin friction decreases, resulting in an overall drag reduction of the aircraft with a straightforward impact on fuel consumption and thus emissions. The riblets are implemented in the Reynolds Averaged Navier Stokes equations with appropriate source terms in the turbulent dissipation transport equation. Two turbulence models are used, the k-? SST linear eddy viscosity model and the Baseline Reynolds Stress model which also uses the transport equation of the specific rate of turbulence dissipation (?). The computational results are compared with available experimental data of NACA 0012 with surface riblets attached. Drag and skin friction coefficients are presented for various angles of attack and the maximum potential benefit from riblet use is evaluated regarding aerodynamic performance and consequently reduction of emissions and fuel consumption.

The effect of nonlinear material viscosity on the energy harvesting performance of dielectric elastomer generators

Dielectric elastomer generators are capable of converting mechanical energy from a variety of sources into electrical energy. The energy harvesting performance depends on the interplay between electromechanical coupling, material viscosity, and multiple failure modes. Experiments also suggest that the material viscosity of dielectric elastomers is deformation-dependent, which makes the prediction of the performance of dielectric elastomer generators more challenging. By adopting the coupled field theory, finite-deformation viscoelasticity theory, and the theory for polymer dynamics, this work investigates the harvested energy and conversion efficiency of dielectric elastomer generators from theoretical perspective. By comparing the simulation results from the nonlinear viscosity model to the experimental data and the simulation results from the linear viscosity model, we further examine the possible factors that may strongly influence the performance of dielectric elastomer generators. It is found that dielectric elastomer generators exhibit higher harvested energy when nonlinear material viscosity is considered. Moreover, by selecting a higher voltage of the power supply for the generator, the conversion efficiency of dielectric elastomer generators can be greatly improved. The theoretical framework in this study is expected to offer some new insights into optimizing the design of dielectric elastomer generators and thus improving their performance.

Nonlinear subscale turbulent models for very large eddy simulation of turbulent flows

A brief introduction of the time-filtered Navier–Stokes (TFNS) equations for very large eddy simulation (VLES) and its distinct features is presented. A set of nonlinear subscale models and their advantages over the linear subscale eddy viscosity models are described. A guideline for conducting a TFNS/VLES simulation is also provided. In this paper, we present simulations for three turbulent flows. The first one is the turbulent pipe flow at both low and high Reynolds numbers to illustrate the basic features of TFNS/VLES; the second one is the swirling turbulent flow in an LM6000 single injector to further demonstrate the differences between the results from nonlinear models versus linear viscosity models; the third one is a more complex turbulent flow generated in a single-element lean direct injection combustor, which demonstrates that the current TFNS/VLES approach is capable of predicting dynamically important, unsteady turbulent structures even with a relatively coarse mesh grid.

LES analysis of the flow in a simplified PWR assembly with mixing grid

The flow in fuel assemblies of Pressurized Water Reactors (PWR) with mixing grids has been analysed with Computational Fluid Dynamics (CFD) by numerous authors. The comparisons between calculation and experiment are mostly focused on the flow in the near wake of the mixing grid, i.e. on the flow in the first 5 to 10 hydraulic diameters (dh) downstream of the grid. In the study presented here, the comparison between the measurements in the AGATE facility (5 × 5 tube bundle) and Trio_U calculations is done for the whole distance between two successive mixing grids that is up to about 50 dh downstream of the grid.The AGATE experiments have originally not been designed for CFD validation but to characterize different types of mixing grids. Nevertheless, the quality of the experimental data allows the quantitative comparison between measurement and calculation. The conclusions of the comparison are summarized below:•Linear turbulent viscosity models seem to work rather well as long as the cross flow velocity in the rod gaps is advection controlled, that is directly downstream of the mixing grid,•Further downstream, when the cross flow velocity is reduced and anisotropic turbulence becomes a more and more important mixing phenomena, linear viscosity models can fail,•The mixing grid affects the cross flow velocity up to the successive grid. The flow in fuel assemblies is never similar to that in undisturbed rod bundles.The test section of the AGATE facility has been discretized on 300 million control volumes by using a staggered grid approach on tetrahedral meshes. 20 days of CPU on 4600 cores of the High Performance Computer (HPC) cluster CURIE of the Centre de Calcul, Recherche et Technologie (CCRT) were necessary to converge the statistics of the turbulent fluctuations, completely converge the mean velocity and incompletely converge the RMS of the turbulent fluctuations.

Drag reduction by linear viscosity model in turbulent channel flow of polymer solution

A further numerical study of the theory that the drag reduction in the turbulence is related to the viscosity profile growing linearly with the distance from the wall was performed. The constant viscosity in the Navier-Stokes equations was replaced using this viscosity model. Some drag reduction characteristics were shown comparing with Virk’s phenomenology. The mean velocity and Reynolds stress profiles are consistent with the experimental and direct numerical simulation results. A drag reduction level of 45% was obtained. It is reasonable for this linear viscosity model to explain the mechanism of turbulence drag reduction in some aspects.

Particle distribution for dilute suspension in flow.

Analytic expressions for the velocity profile and particle distribution of a dilute suspension in flow were obtained as functions of radial distance. Einstein's linear viscosity model and the hypothesis of “minimum energy dissipation” were used. The methods of variational calculus were applied during the mathematical development. A parabolic velocity profile, which is a modified form of that for Hagen-Poiseuille flow, and a uniform particle distribution were obtained. An attempt is made to explain the results in light of some of the widely held theories on suspension flow and the rather severe limitations of Einstein's viscosity model. A suggestion of future work is made for improving the results of the present.