Numerical modeling of downslope flows of different rheology

Naturally occurring flow along a long homogeneous slope is numerically simulated. It is taken into account that the flow is able to capture the slope material and to entrain it into motion. The flow depth and velocity increase with time at the expense of the capture. The medium in motion is simulated using different rheological models including those of Herschel & Bulkley and Cross, as well as the power-law fluid model. For all the models the time dependences of the total depth and the mean flow velocity are obtained. The slope inclination effect on the dynamic flow parameters is studied. For the Herschel–Bulkley model the yield strength effect is also investigated. On the basis of the numerical calculations some assumptions are made and then used to derive asymptotic formulas for the bottom material entrainment rate at large times from the entrainment onset for all the above-listed rheological models.     

Effect of turbulent viscosity on the formation and motion of bottom waves

The problem of linear perturbations of the sandy bottom in a rectangular channel with a heavy incompressible fluid is formulated. The turbulent viscosity of the flow is defined as a drag coefficient function, and the hydrodynamic equations are written in the long-wave Boussinesq approximation. In the expression for the hydrostatic pressure, a correction is applied to the Boussinesq approximation that changes the sediment discharge. The problem of the development of bottom perturbations is solved taking into account the modified formula of sediment discharge, resulting in analytical expressions for the velocity of bottom perturbations and the wavelength of the fastest-growing bottom perturbations at small Froude numbers.     

Effect of drag force on backward-facing step gas-particle turbulent flows

An improved drag force coefficient of gas-particle interaction based on the traditional Wen’s 1966 model is proposed. In this model, a two-stage continuous function is used to correct the discontinuous switch when porosity less than 0.2. Using this proposed correlation and the Wen’s 1966 model, a gas-particle kinetic energy and particle temperature model is developed to predict the hydrodynamic characteristics in backward-facing step gas-particle two-phase turbulent flows. Numerically results showed that they are in good agreement with experiment measurements and presented model are better due to a improvement of momentum transport between gas and particle phases. Particle dispersions take on the distinctively anisotropic behaviors at every directions and gas phase fluctuation velocity are about twice larger than particle phases. Particle phase has a unique transportation mechanism and completely different from the gas phase due to different density. Furthermore, the correlation values of axial–axial gas-particle are always greater than the radial–radial values at fully flow regions. The gas-particle two-phase interactions will make influence on two-phase turbulent flow behaviors.     

Effect of bottom topography on the flow of a non-Newtonian liquid film down an inclined plane

The problem of flow of a nonlinear viscous liquid film down an inclined surface with local microtopography is considered. Numerical and approximate analytic solutions are obtained for steady flows of power-law liquid films down inclined surfaces with topography. Steps, hills, and periodic structures are considered as local topography. Basic properties of flows are found.     

Effect of variable slip boundary conditions on flows of pressure driven non-Newtonian fluids

In microfluidic devices it has been suggested a scheme for enhancing the mixing of two fluids is to use patterned, slip boundary conditions. This has been shown to induce significant transverse flow for Newtonian fluids [S.C. Hendy, M. Jasperse, J. Burnell, Effect of patterned slip on micro- and nanofluidic flows, Phys. Rev. E 72 (2005) 016303]. Here we study the effect of patterned slip on non-Newtonian fluids. Using a power-law model it is shown for shear-thickening fluids patterned slip can induce significant transverse flows comparable in size to those produced for Newtonian fluids. However, for shear-thinning fluids this transverse flow is suppressed. We predict a convenient way to increase the transverse flow for shear-thinning fluids is to use a patterned slip boundary condition coupled to a sinusoidally time-varying pressure gradient. This system is studied using a simple linearized White–Metzner model which has a power-law viscosity function [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, John Wiley & Sons, New York, 1987]. In this case it is shown the two variations combine to produce transverse flow, which can be increased by increasing the frequency of the sinusoidal time-dependent fluctuation.     

Effect of the turbulent viscosity relaxation time on the modeling of nozzle and jet flows

Certain modifications of three-equation turbulence models are proposed. They are intended for increasing the accuracy of the calculations of turbulent flows in nozzles with boundary layer separation and in supersonic jets with complicated shock wave structures. Basing on the idea of the inclusion of flow prehistory in terms of an additional relaxation equation for nonequilibrium turbulent viscosity we propose three modifications of the k-ω-µ _t model based on the k-ω model and a version of the k- ?-µ _t turbulence model. In these modifications we introduce an additional dependence of the nonequilibrium turbulent viscosity relaxation time on different physical parameters which can be important near the point of boundary layer separation from the nozzle wall, such as viscous effects and effects of large gradients of the mean velocity and the kinetic energy of turbulence (turbulent pressure). The comparison of the results of the calculations with the experimental data shows that all the proposed versions of the three-equation models make it possible to improve the accuracy of the calculations of turbulent flows in nozzles and jets.     

Effect of insoluble surfactant on turbulent bubbly flows in vertical channels

The effect of an insoluble surfactant on the structure of turbulent bubbly upflow in a vertical channel is examined by direct numerical simulations (DNS). For nearly spherical bubbles the presence of a surfactant reduces the lateral lift on the bubbles and changes the structure of the flow in major ways. Clean bubbles are driven to the walls by the lift force and the void fraction distribution has a well defined peak near the walls, resulting in significant reduction in flow rate. Bubbles with strong enough surfactants do not experience significant lateral lift and remain in the bulk flow. Indeed, when surfactant is present the addition of bubbles to a turbulent flow has relatively little effect on the flow, once the pressure gradient is adjusted to account for the reduced weight of the mixture.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

The numerical simulation of turbulent flows of Newtonian and a sort of non-Newtonian fluid in 180-degree square sectioned bend

Using k-εmodel of turbulence and measured wall functions.turbulent flows ofNewtonian(pure water)and a sort of non-Newtonian fluid(dilute,drag-reduction solutionof polymer in a180-degree curved bend were simulated numerically.The calculated resultsagreed well with the measured velocity profiles.On the basis of calculation andmeasurement,appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.     

The effect of the expansion ratio on a turbulent non-Newtonian recirculating flow

 Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. Received: 31 July 2000 / Accepted: 27 August 2001     

A conditional sampling method based on fuzzy clustering for the analysis of large-scale dynamics in turbulent flows

A conditional sampling technique, based on fuzzy clustering, is used to educe the organization of the secondary flow motions observed in the large-eddy simulation of a turbulent square channel flow. The data analysed are the multi-valued time series obtained from sampling the secondary velocity components at a fixed cross-section of the channel, over consecutive time steps. The mean values of the secondary flow motion velocities are one order of magnitude lower than their r.m.s values. The purpose of the conditional sampling scheme used is to replace the picture of the secondary flow motions provided by the unconditional time mean with several ensemble averages. In this way the whole variability of the instantaneous data can be split in two parts: one for the difference between the observed ensemble averages, and the other for the variability within each ensemble. Unlike other conditional sampling schemes which sort only part of the data into one or more families depending on an externally fixed condition, the fuzzy clustering approach used here first determines the optimum number of families or clusters and then classifies all the recorded time steps. The results show that the local turbulence intensities of the ensemble averages obtained from fuzzy clustering can be reduced by one order of magnitude. In addition, the classification of all the time steps into several clusters or families enables the large scale dynamics of the educed structures to be analysed.     

A note on unsteady unidirectional flows of a non-Newtonian fluid

Exact solutions are established for a class of unsteady unidirectional flows of an in compressible second grade fluid wherein inertial effects are not ignored. Amongst the several interesting flows which belong to this class are the flow due to a rigid plate oscillating in its own direction, the flow between two rigid boundaries one of which is suddenly started and the time-periodic Poiseuille flow due to an oscillating pressure gradient.     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Consistent formulation of the power-law rheology and its application to the spreading of non-Newtonian droplets

In this work, we introduce a general form of the Navier-Stokes equations for Generalized Newtonian fluids with an Ostwald power-law. The derivation, based on the covariant formalism, is frame-independent and gives rise to a source term in the Navier-Stokes equations referred to as the Ostwald vector which is characterized by the power-law exponent. The governing equations are then simplified in the long-wave approximation framework and applied to the spreading of an axisymmetric gravity current in the creeping flow regime. Well-known spreading laws are recovered through similarity solutions and a new derivation based on scaling arguments is proposed. Experimental results related to the spreading of gravity current are then presented and the potential to infer unknown rheological parameters from spreading rates is critically discussed in the context of a thorough error analysis.     

Lagrangian model on the turbulent motion of small solid particle in turbulent boundary layer flows

.Intr0ductionSurfaceerosionofmaterialbysolid-particleimpactisanimportantprobleminmultiphaseflowindustriaIdevicesandthecharacteristicsoftheparticIe'smotioninaturbulentboundarylayerflowisthebaseofthestudyofthematerialsurfaceerosion.Manycalculationmodelshave…     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。