Turbulent Channel Flow with an Artificial Two-Dimensional Wall Layer

Turbulent flow of an incompressible fluid in a plane channel with parallel walls is considered. The three-dimensional time-dependent Navier-Stokes equations are solved numerically using the spectral finite-difference method. An artificial force which completely suppresses lateral oscillations of the velocity is introduced in the near-wall zone (10 % of the channel half-width in the neighborhood of each wall). Thus, the three-dimensional flow zone, in which turbulent oscillations can develop, is separated from the wall by a fluid layer. It is found that the elimination of three-dimensionality in the neighborhood of the walls leads to a significant reduction in the drag. However, complete laminarization does not occur. The flow in the stream core remains turbulent and can be interpreted as a turbulent flow in a channel with walls located on the boundary of the two-dimensional layer and traveling at the local mean-flow velocity. The oscillations developing inside the two-dimensional layer, which have significant amplitude, distort the flow only in the adjacent zone. Beyond this zone the distributions of the mean characteristics and the structure of instantaneous fields completely correspond to ordinary turbulent flow in a channel with rigid walls. The results obtained confirm the hypothesis of the unimportance of the no-slip boundary conditions for the fluctuating velocity component in the mechanism of onset and self-maintenance of turbulence in wall flows.     

Direct Numerical Simulation of Flow in a Ribbed Channel

The issue of turbine lifetime is an important one, particularly for modern turbines operating at high temperature regimes. A cooling design such as ribs may achieve an improved lifetime and complex mechanisms of heat transfer need to be well studied. In this paper, a Direct Numerical Simulation (DNS) is presented for a 3-D channel flow with two square ribs on the lower wall. The full unsteady compressible Navier-Stokes equations are solved with an original hybrid finite difference/finite element scheme. The Reynolds number of the simulation is 7 000 based on the bulk velocity at the inlet and the channel height. The present study is mainly devoted to understand the mechanism of heat transfer at the wall through the topological analysis of the flow and the temperature flux. Results show that the large-scale structures generated by obstacles splash onto the lower surface and induce longitudinal vortices which enhance heat transfer at the wall. A comprehensive data base including 56 correlations was set up for testing and improving turbulence models for this complex, separated flow.     

Numerical Simulation of a Turbulent Flow in a Channel with Surface Mounted Cubes

In this paper we report on a fourth-order, spectro-consistent simulation of a complex turbulent flow. A spatial discretization of a convection-diffusion equation is termed spectro-consistent if the spectral properties of the convective and diffusive operators are preserved, i.e. convection skew-symmetric; diffusion symmetric positive definite. We consider a fully developed flow in a channel, where a matrix of cubes is placed at a wall of the channel. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13,000. The three-dimensional flow around the surface mounted cubes has served at a test case at the 6th ERCOFTAC/IAHR/COST workshop on refined flow modeling (Delft, June 1997). Here, mean velocity profiles as well as Reynolds stresses at various locations in the channel have been computed without using any turbulence models. The results agree well with the available experimental data.     

Bifurcation of a Main Steady-State Viscous Fluid Flow in a Plane Divergent Channel

The evolution of steady-state viscous incompressible fluid flows in a plane divergent channel is investigated. For the classical formulation of the Jeffery-Hamel problem a complete solution is given as a function of the determining parameters. For a fixed angle of divergence the behavior of the main unimodal flow is determined as a function of the Reynolds number. Critical values at which the flow pattern bifurcates and the steady-state unimodal flow ceases to exist are found. The mechanism of bifurcation is established and its diagram is constructed. This mechanism and the diagram were not previously known in the scientific literature in connection with the investigation of the Jeffery-Hamel problem. The critical Reynolds number at which bifurcation occurs is given as a function of the channel divergence angle. The results may be of interest for hydromechanical, technological, and geophysical applications.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 25–36.Original Russian Text Copyright © 2005 by Akulenko and Kumakshev.     

Wall Versus Centerline Polymer Injection in Turbulent Channel Flows

This experimental study compares the mean and turbulence characteristics of turbulent channel flows with polymer injection at the wall and at the centerline to assess the impact of the injection location on drag reduction. It also contrasts the drag reduction performance of a hydrolyzed polymer versus a non-ionic polymer under the same conditions. Wall injection of non-ionic and hydrolized polymers resulted in 23% and 9% larger drag reduction than corresponding centerline injection, respectively. In all cases, the polymer was structured and the presence of macromolecular polymer structures, even when concentrated mostly away from the wall, seemed to be able to affect the turbulence structure in the flow.     

The Use of DNS to Define Stress Producing Events for Turbulent Flow over a Smooth Wall

Over the past 15 years direct numerical simulations (DNS) of turbulent flow and particle image velocimetry (PIV) have provided the opportunity to obtain information about a turbulent velocity field simultaneously at a large number of locations. This paper gives a personal viewpoint of how these techniques are providing new insights about the Reynolds stress producing structures in turbulence generated by flow over a smooth boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

Forced Convection with Laminar Pulsating Flow in a Saturated Porous Channel or Tube

A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube occupied by a saturated porous medium modeled by the Brinkman equation, produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of this Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak decreases as the modified Prandtl number increases. The phase (relative to that of the steady component) decreases from π/2 to − π/2. The height of the peak at first increases, goes through a maximum, and then decreases as the Darcy number decreases.     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.     

Unsteady Self-Similar Flow of a Viscous Incompressible Fluid in a Plane Divergent Channel

The problem of two-dimensional unsteady flow of a viscous incompressible fluid in a sector-like domain is considered. Initially a strictly radial flow is imposed, which makes it possible to seek solutions within the class of self-similar flows. A numerical method based on mixed finite-difference and spectral spatial discretization is developed, making it possible to find the self-similar solution efficiently. The process of development and establishment of the steady Hamel-Jeffery and Moffatt flows is modeled mathematically.     

Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium

Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number.     

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

槽道纤维悬浮流稳定性的实验研究

对槽道纤维悬浮流进行染色线流动显示和流场PIV实验测量,实验中选用的是直径为20μm、长径比为20～100的尼龙纤维。PIV2100处理器被用来加工处理采集的实验数据。槽道长度1.5m,横截面为矩形,尺寸为105×19mm。实验结果说明在Reynolds数相同的情况下,纤维悬浮流比对应的牛顿流更不容易失稳,悬浮流中的纤维起着抑制流场失稳的作用,而且随着纤维体积分数和长径比的增大,抑制失稳的程度也提高。扰动衰减率的最小值随纤维体积分数和长径比的增加而增大,这一效果在大Re数时更明显。     

低速二维流动的粒子仿真研究

本文运用信息保存法对低速二维的流动现象进行模拟，考察了低速条件下的有限平板绕流以及微槽道气体流动问题。研究表明：在对低速流动的模拟过程中，运用IP法在能够获得较好的结果的同时，具有比DSMC方法更高的计算效率。     

Numerical and Physical Modeling of the Circulation Flow in a Vortex Cell in the Wall of a Rectilinear Channel

The results of physical and numerical modeling of the three-dimensional vortex flow in a circular cell forming a recess in the wall of a rectangular constant-area channel are presented.     

Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow

The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Principles of Integrated Flow Modeling

Integrated flow modeling is the combination of a traditional flow simulator with a petrophysical model. By combining a petrophysical model with a traditional flow model, it is possible to perform calculations that improve our ability to monitor fluid movement in porous media. This paper outlines the formulation of an integrated flow model IFLO and its multi-variable, Newton–Raphson IMPES solution procedure. The benefits of integrated flow modeling and the underlying principles involved in the integration of a flow model with a petrophysical model are presented. Results from the IFLO model are used to illustrate the principles.     

DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure

We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇² φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered and validated with help of our simulation results. This revised version was published online in July 2006 with corrections to the Cover Date.