Shear-stress transport model

The (isotropic) eddy viscosity concept and the use of a k i model are known to be inappropriate in rotating and/or strongly 3-D flows (see, e.g., Wilcox, 1993). This issue will be addressed in more detail in Section IV. Some researchers prefer different models for the eddy viscosity, such as the k o> model (where o> denotes vorticity) that performs better in regions closer to walls. For this latter reason, the k-e model and the k-co model are often blended into the so-called Shear-Stress-Transport (SST) model (Menter, 1994) with the view of using these two models in those regions of the flow domain where they perform best. In spite of these objections, however, RANS simulations mostly exploit the eddy viscosity concept rather than the more delicate and time-consuming RSM turbulence model. They deliver simulation results of in many cases reasonable or sufficient accuracy in a cost-effective way. 

It is noted that in recent papers several extended turbulence models, i.e., the standard k-e [50], RNG k-e [97, 98, 99, 82, 66], realizable k-e [81], Chen-Kim k-e [11], optimized Chen-Kim k-e [44], standard k-uj [96], k-uj shear-stress transport (SST) [56, 57, 58] and the standard Reynolds stress models, have been proposed and validated. However, little or no significant improvements have been achieved considering the predictivity of the turbulence models, although each of them may have minor advantages and disadvantages. A few... 

The commercial software ANSYS FLUENT was used for CFD analysis. Unsteady flow was modeled to obtain the variation of granule temperature with time. The k-to with shear-stress transport turbulence model was used. The modeled flue gases included four gas species, referring to CO2, H2O, N2, and O2. The boundary condition was velocity-inlet at the inlet, pressure outlet at the outlet, and symmetry for the four sides. Second-order upwind scheme was used for the momentum, species, and energy equations. 

For turbulent expiratory conditions, avoiding the intensive computational efforts involved with a three-dimensional Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), a Reynolds-Averaged Navier Stokes (RANS) equations coupled to a Shear Stress Transport (SST) fc- y turbulent model is used to model the fluid. The governing equations are essentially similar to (1) and (2) above, but with the inclusion of Reynolds stress... 

The two-fluid method using the volume of fluid (VOF) approach, coupled with the k-co SST (shear stress transport) turbulence model, is employed to simulate the formation and fragmentation of a swirling conical liquid sheet firom a typical swirl nozzle. In the VOF approach, the volume firaction of liquid (/) is defined in each computational cell. If the cell is completely filled with liquid then/= 1 and if it is filled with gas then its value is 0. At the gas-liquid interface, the value of / is between 0 and 1. In the OpenFOAM VOF formulation, the interface motion is governed by the convective transport equation of the volume fraction... 

Lampart, P. Swirydczuk, J. Gardzilewicz, A. Yershov, S. and Rusanov, A. The comparison of performance of the menter shear stress transport and baldwin-lomax models with respect to CFD prediction of losses in HP axial turbine stages. Technol. Fluid/ ThermaVStruct/Chem. Sys. Indust. Appl. ASME. 2001,1(424), 1-12. 

Handbook of membrane reactors Shear-stress transport (SST) model... 

For dynamical studies of diffusion, conformational and transport behavior under shear stress, or kinetics of relaxation, one resorts to dynamic models [54,58,65] in which the topological connectivity of the chains is maintained during the simulation. 

A three dimensional turbulent flow field in unbaffled tank with turbine stirrer or 6-paddle stirrer was numerically simulated by the method of finite volume elements [80], whereas in the case of free surface the vortex profile was also determined using iterative techniques. The prediction of the velocity and turbulence fields in the whole tank and the stirrer power was compared with literature data and their own results. Of the two simulation techniques used, turbulent eddy-viscosity/zc-e turbulence model and the DS model (differential 2. order shear stress), only the latter produced satisfactory results. In particular it proved that fluctuating Coriolis forces have to be taken into account by source terms in the transport equation for the Reynolds shear stress. 

The modeling procedure can be sketched as follows. First an approximate description of the velocity distribution in the turbulent boundary layer is required. The universal velocity profile called the Law of the wall is normally used. The local shear stress in the boundary layer is expressed in terms of the shear stress at the wall. From this relation a dimensionless velocity profile is derived. Secondly, a similar strategy can be used for heat and species mass relating the local boundary layer fluxes to the corresponding wall fluxes. From these relations dimensionless profiles for temperature and species concentration are derived. At this point the concentration and temperature distributions are not known. Therefore, based on the similarity hypothesis we assume that the functional form of the dimensionless fluxes are similar, so the heat and species concentration fluxes can be expressed in terms of the momentum transport coefficients and velocity scales. Finally, a comparison of the resulting boundary layer fluxes with the definitions of the heat and mass transfer coefficients, indiates that parameterizations for the engineering transfer coefficients can be put up in terms of the appropriate dimensionless groups. 

Our ambition in the paragraphs to follow is to illustrate an approximate heuristic model which shows how the presence of an applied shear stress can result in mass transport mediated deformation. We begin with the notion that the crystal of interest is subjected to a shear stress. From a two-dimensional perspective, for example, we then make use of the fact that the shear stress... 

Abstract A united mathematical model for the rheological and transport properties of saturated clays is proposed. The foundation of the model is the unification of filtration s consolidation theory and the theory of the stability of lyophobic colloids, which is based on the conception of disjoining pressure as a surplus in relation to hydraulic pressure. This pressure is caused by surface capacities and exists in water films between clay particles. In this work it is shown that the problem of the shrinkage of a clay layer can be reduced to the well known problem. We obtained the approximate solution for pressing the water out of a clay layer. The solution that we obtained requires introduction of a concept for the limit shear stress for clays. We investigated the model, and explained some characteristic features of transfer processes in clays (the existence of anomalous high pressures in clays, the flocculation at diffusion in clays, etc.). It is shown that solutions which we received are in harmony with results of experiments. 

As mentioned previously, even when the flow becomes turbulent in the boundary layer, there exists a thin sub-layer close to the surface in which the flow is laminar. This layer and the fully turbulent regions are separated by a buffer layer, as shown schematically in Figure 7.1. In the simplified treatments of flow within the turbulent boundary layer, however, the existence of the buffer layer is neglected. In the laminar sub-layer, momentum transfer occurs by molecular means, whereas in the turbulent region eddy transport dominates. In principle, the methods of calculating the local values of the boundary layer thickness and shear stress acting on an immersed surface are similar to those used above for laminar flow. However, the main difficulty stems from the fact that the viscosity models, such as equations (7.13) or (7.27),... 

The liver is a vital organ in the body that plays a primary role in the digestive system in detoxification, protein synthesis, and filtering of blood [56]. Liver-on-a-chip platforms have been developed to understand liver function better and to study drug hepatotoxicity and metabolism [29, 57, 58]. A microfluidic-based device fabricated to mimic the permeable sinusoid endothelial barrier between hepa-tocytes and liver [29] includes three main sections—a central channel to pack the hepatocytes, a microfluidic sinusoid barrier consisting of a set of narrow (2 mm wide) microchannels to model the endothelial barrier, and a convection microfluidic channel surrounding the barrier (Fig. 5A). The flow of nutrients through the convection microfluidic channel feeds the hepatocytes. This system mimics the transportation between blood flow and hepatocytes, and the shear stress over hepatocytes with a patterned set of microchannels. 

The combined wave and current model for obliquely incident waves by Kobayashi et al is improved by including the finite-depth effect on the relationship between the oscillatory horizontal velocity and free surface elevation as well as the wind stresses for future field applications. The numeric integrations involved in the bottom shear stresses and energy dissipation rate are replaced by sufficiently accurate analytic expressions. These modifications improve the computational efficiency and numeric stability of the wave and current model. The sediment transport model developed by Kobayashi et for normally incident waves is extended... 

Rheological properties of foams (elasticity, plasticity, and viscosity) play an important role in foam production, transportation, and applications. In the absence of external stress, the bubbles in foams are symmetrical and the tensions of the formed foam films are balanced inside the foam and close to the walls of the vessel [929], At low external shear stresses, the bubbles deform and the deformations of the thin liquid films between them create elastic shear stresses. At a sufficiently large applied shear stress, the foam begins to flow. This stress is called the yield stress, Tq- Then, Equation 4.326 has to be replaced with the Bingham plastic model [930] ... 

To predict the transport properties and performance of fiber sweeps under downhole conditions, the rheological properties of the base fluid and suspension must be understood. The proposed formulations for such fiber sweeps will be most effective when the rheology has been accurately modeled and fine-tuned for specific wellbore conditions. To begin to grasp how the fluid behaves, the relationship between shear stress and shear rate must be known. This is denoted as the shear viscosity profile, which is an aspect of the rheology of a fluid that is thought to control the hydrodynamics of flow. The most common shear viscosity models used in the oil and gas industry to characterize non-Newtonian drilling fluids include ... 

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