Improved DRW Model for Prediction of Deposition and Dispersion of Nano- and Micro-Particles in Turbulent Flows

In this study, the accuracy of the discrete random walk (DRW) stochastic model in generating the instantaneous velocity fluctuations as seen by micro- and nano-particles in inhomogeneous turbulent flows were examined. Particular attention was given to the effects of the non-uniform normal RMS velocity fluctuations and turbulence time scale on the DRW model predictions. The trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm in a duct were evaluated using an in-house Matlab particle tracking code. The particle equation of motion included the drag and Brownian forces. The fully developed mean velocity and RMS fluctuation velocity profiles were exported from the RANS (v2f) simulations and were used for the particle dispersion and transport analysis. It was assumed that the particle-laden flow is sufficiently dilute so that the particle-particle collisions and the two-way coupling effects of particles on the flow could be ignored. To incorporate the instantaneous turbulence velocity fluctuations effects on particle dispersion, the Conventional-DRW model (in the absence of drift corrections), which was originally developed for homogenous turbulent flows, was first used. It was shown that the Conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The Modified-DRW model with an appropriate velocity gradient drift correction term was also tested. It was found that the predicted concentration profiles of tracer particles still are not uniform. It was hypothesized that the reason for this erroneous prediction is due to the inhomogeneous turbulence time macroscale in the channel flow. A new drift correction term as a function of gradients of both RMS fluctuation velocity and the turbulence time macroscale was proposed. It was shown that the new Improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size particles. It was shown that the predicted deposition velocities of different size particles by the proposed Improved-DRW model are in good agreement with the available experimental data as well as the predictions of the empirical models and earlier DNS results.

Beyond Normality: Estimation of Near-Bed Sediment Concentrations Accounting for Asymmetric Distribution and Spatial Influence of Turbulence Coherent Structures

<p>Abstract</p><p>Recent experiments have established that the sediment particle motion, especially for particles near the bed, may not follow the normal (Fickian) diffusion behavior. To modify the diffusion equation where the fluctuation velocity is based on the normal distribution, this investigation hypothesizes that the fluctuation velocity based on bivariate probability distributions and particle-bed collision in open channel can provide some physical insight into the particle diffusion behavior. The distribution of fluctuation velocity is obtained using the Gram-Charlier expansion which considers the first four statistical moments of turbulent fluctuation velocity. The correlation between two-dimensional fluctuation velocities is modeled by performing Monte Carlo simulations. Besides, the uniform momentum zones (UMZ) are further identified and consequently the spatial locations of the edges that demarcate UMZs can be estimated. Once UMZs in the turbulent boundary layers can be characterized, the streamwise momentum deficit, and occurrences of ejection events and sweep events in the vicinity of UMZ edges under different Reynolds numbers can be simulated. The spatial influence of turbulent coherent structures on sediment particle trajectory can be demonstrated.</p>

On the Reynolds-Averaged Navier-Stokes Equations

This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

On closure problem of incompressible turbulent flow

This paper attempts to clarify an issue regarding the lasting unsolved problem of turbulence, namely the closure problem. This study shows that all perspectives regarding the numbers of un- known quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor. The current literatures have a consensus that the Reynolds stress tensor has six unknowns; however, this study shows that the Reynolds stress tensor actually has only three ones, namely the three components of fluctuation velocity. With this new understanding, the closed turbulence equations for incompressible flows are proposed.

Closed integral-differential equations of incompressible Navier-Stokes turbulent flow

This paper showed that turbulence closure problem is not an issue at all. All mistakes in theliterature regarding the numbers of unknown quantities in the Reynolds turbulence equations stemfrom the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has statedthat the symmetric Reynolds stress tensor has six unknowns; however, it actually has only threeunknowns, i.e., the three components of fluctuation velocity. We showed the integral-differentialequations of the Reynolds mean and fluctuation equations have exactly eight equations, which equalto the numbers of quantities in total, namely, three components of mean velocity, three componentsof fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding,the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated.This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

New boundary conditions for fluid interaction with hydrophobic surface

Solution of both laminar and turbulent flow with consideration of hydrophobic surface is based on the original Navier assumption that the shear stress on the hydrophobic surface is directly proportional to the slipping velocity. In the previous work a laminar flow analysis with different boundary conditions was performed. The shear stress value on the tube walls directly depends on the pressure gradient. In the solution of the turbulent flow by the k-ε model, the occurrence of the fluctuation components of velocity on the hydrophobic surface is considered. The fluctuation components of the velocity affect the size of the adhesive forces. We assume that the boundary condition for ε depending on the velocity gradients will not need to be changed. When the liquid slips over the surface, non-zero fluctuation velocity components occur in the turbulent flow. These determine the non-zero value of the turbulent kinetic energy K. In addition, the fluctuation velocity components also influence the value of the adhesive forces, so it is necessary to include these in the formulation of new boundary conditions for turbulent flow on the hydrophobic surface.