Large-Eddy Simulation of Dispersion from Line Sources in a Turbulent Channel Flow

Large-eddy simulations of the dispersion from scalar line sources at various locations within a fully developed turbulent channel flow at Re = uh/ν = 10,400 are presented. Both mean and fluctuating scalar quantities are compared with those from the single available set of experimental data (Lavertu and Mydlarski, J Fluid Mech 528:135–172, 2005) and differences are highlighted and discussed. The results are also discussed in the context of scalar dispersion in other kinds of turbulent flows, e.g. homogeneous shear-flow. Initial computations at a much lower Reynolds number are also reported and compared with the two available direct numerical simulation data sets.     

Use of a Modified Langevin Equation to Describe Turbulent Dispersion of Fluid Particles in a Channel Flow

A stochastic method to represent the positions and velocities of fluid particles in a nonhomogeneous turbulence was pursued. Spatially varying Lagrangian time scales obtained from direct numerical simulations of turbulent flow in a channel and spatially varying joint Gaussian forcing functions were incorporated into a Langevin equation. The model was tested by comparing calculations of the dispersions and velocities of particles originating from point sources with experiments carried out in a DNS of fully-developed turbulent flows in a channel at Re_τ = 150 and 300. The model captured the dispersions, mean velocities and moments of the velocity fluctuations very well. The use of jointly Gaussian (rather than uncorrelated Gaussian) forcing functions greatly improved the calculation of dispersions and mean velocities in the stream wise direction, as well as turbulence quantities which include stream wise velocity fluctuations. The condition of well-mixedness for the model was verified by considering the behavior of a uniform distribution of sources. This revised version was published online in July 2006 with corrections to the Cover Date.     

Unsteady Turbulent Spiral Flows in a Circular Channel

Turbulent spiral flows of water, developing in a rapidly rotating toroidal channel after abrupt braking, are investigated experimentally. The spiral flow structure is created by fixed-blade diverters located in the channel. The Reynolds number may be as high as 10⁶. A simple model for describing the evolution of the longitudinal and azimuthal velocity components averaged over the channel section is proposed.     

Unsteady Laminar to Turbulent Flow in a Spacer-Filled Channel

A combined numerical and experimental investigation has been carried out to study the flow behaviour in a spacer-filled channel, representative of those used in spiral-wound membrane modules. Direct numerical simulation and particle image velocimetry were used to investigate the fluid flow characteristics inside a 2 × 2 cell at Reynolds numbers that range between 100 and 1000. It was found that the flow in this geometry moves parallel to and also rotates between the spacer filaments and that the rate of rotation increases with Reynolds number. The flow mechanisms, transition process and onset of turbulence in a spacer-filled channel are investigated including the use of the velocity spectra at different Reynolds numbers. It is found that the flow is steady for Re < 200 and oscillatory at Re ～ 250 and increasingly unsteady with further increases in Re before the onset of turbulent flow at Re ～ 1000.     

Simulation and Modelling of a Skewed Turbulent Channel Flow

A time-dependent three-dimensionally skewed flow is investigated using direct numerical simulations of the incompressible Navier-Stokes equations. The effect on the instantaneous and mean turbulent field is investigated. Instantaneous flowfields reveal that the skewing has the effect of initially reducing the strength and height of quasi-streamwise vortices of both signs of rotation with respect to the skewing. A mechanism for this process is put forward. The mean flowfields show drops in turbulence quantities such as turbulence kinetic energy. In addition to this, two-equation turbulence modelling of the flow is carried out. This highlights a deficiency, in that the standard turbulence models are unable to capture the drop in turbulence intensity due to the skewing. A modification based on the exact dissipation equation is found to significantly improve the model behaviour for this flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Passive Scalar in a Turbulent Channel Flow with Wall Velocity Disturbances

Direct Numerical Simulations (DNS) of a passive scalar in a turbulent channel flow with a normal velocity disturbance on the lower wall are presented for high and low Reynolds numbers. The aim is to reproduce the complex physics of turbulent rough flows without dealing with the geometric complexity. In addition, isothermal walls that cannot be easily assigned in an experiment, are considered. The paper explains the increase of heat transfer through the changes of the velocity and thermal structures. As in real rough flows, the transpiration produces an isotropization of the turbulence near the wall.     

Permeability Effects of Turbulent Flow Through a Porous Insert in a Backward-Facing-Step Channel

In the present work, a k– model, based on the work of Lee and Howell (Proceedings of the ASME-JSME Thermal Engineering Hawaii, 1987), is rigorously derived based on time average of spatially averaged Navier–Stokes equations. The model is then employed to solve for a flow in a backward-facing step channel with a porous insert. The numerical solver is modified from the STREAM code (Lien and Leschziner, Comput. Meth. Appl. Mech. Eng. 114 (1994a) 123–148), and it has been validated against the experimental data of Seegmiller and Driver (AIAA Journal 23 (1985) 163–171). The code is then used to perform simulation for cases with a porous insert. The resistance of the porous insert can be altered by changing its permeability (), Forchheimers constant (F), or thickness (b). The goal is to examine the influence of each parameter on the resulting flow and turbulent kinetic energy (k) distributions. It is discovered that, by increasing the resistance of the insert, flow eventually enters a transitional regime towards relaminarization. This is due to the contribution of Darcys and Forchheimers terms in the governing equations, and modifying these two terms changes the levels of P_k and, hence, k and . Generally speaking, lowering or raising F results in a greater suppression of P_k than , causing the flow to relaminarize. Meanwhile, if the pore size is reasonably large to sustain turbulence within the porous media, increasing b reduces but does not eliminate the turbulent activity in the porous insert.     

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.     

Perturbation Structure and Spectra in Turbulent Channel Flow

The strong mean shear in the vicinity of the boundaries in turbulent boundary layer flows preferentially amplifies a particular class of perturbations resulting in the appearance of coherent structures and in characteristic associated spatial and temporal velocity spectra. This enhanced response to certain perturbations can be traced to the nonnormality of the linearized dynamical operator through which transient growth arising in dynamical systems with asymptotically stable operators is expressed. This dynamical amplification process can be comprehensively probed by forcing the linearized operator associated with the boundary layer flow stochastically to obtain the statistically stationary response. In this work the spatial wave-number/temporal frequency spectra obtained by stochastically forcing the linearized model boundary layer operator associated with wall-bounded shear flow at large Reynolds number are compared with observations of boundary layer turbulence. The verisimilitude of the stochastically excited synthetic turbulence supports the identification of the underlying dynamics maintaining the turbulence with nonnormal perturbation growth. Received 30 January 1997 and accepted 27 March 1998     

Steady Natural Convection Flow of a Particulate Suspension Through a Parallel-Plate Channel

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long channel. The walls of the channel are maintained at constant but different temperatures. The two-phase model accounts for particle-phase viscous effects. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Various closed-form solutions for different special cases are obtained. A parametric study of the physical parameters involved in the problem are performed to illustrate the influence of these parameters on the flow and heat transfer aspects of the problem.     

DNS of the Turbulent Channel Flow of a Dilute Polymer Solution

A direct numerical simulation of the turbulent channel flow of a dilute polymer solution has been performed in order to compare its turbulence statistics with those obtained in a Newtonian channel flow. The viscoelastic flow has been simulated by solving the whole set of continuity, momentum and constitutive equations for the six independent components of the extra-stress tensor induced by polymer addition. The Finitely Extensible Nonlinear Elastic dumbbell model was adopted in order to simulate a non-linear modulus of elasticity and a finite extendibility of the polymer macromolecules. Simulations were carried out under the narrow channel assumption at a Reynolds number of 169 based on the channel half height and on the friction velocity; they showed a significant reduction in drag, dependent on the influence of the elastic properties of the chains. A qualitative comparison with experiments at a higher Reynolds number has shown that the model here adopted is capable of reproducing all the main features of the polymer solution flow. Analysis of the turbulence statistics suggests that a dilute polymer solution can affect the intensity of the streamwise vortices, leading to an increase in the spacing between low speed streaks and eventually to a turbulent shear stress reduction.     

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.     

Pulsatory Turbulent Compressible Fluid Flow and Propagation of Pressure Waves in a Channel

The properties of the damping coefficient and phase velocity of propagation of small-amplitude pressure waves as functions of the oscillation frequency are investigated for the turbulent flow of a weakly compressible fluid in a circular pipe. The wall friction is found by solving numerically the equation of motion and the relaxation equations for the turbulent shear stress and viscosity which provide the basis for a turbulent transfer model developed for unsteady conditions. The properties are explained in terms of an analysis of the calculated data on turbulent transfer. The results obtained are compared with experiments.     

Kinematic Simulation of Fully Developed Turbulent Channel Flow

We detail a new method of generating kinematic simulation fields in a channel. We employ a new decomposition for kinematic simulation which ensures that the boundary conditions are automatically satisfied while preserving incompressibility. We impose statistics up to second order, including the Reynolds shear-stress and one-dimensional spectral densities. We observe streak-like structures kinematically similar to those observed in the laboratory, with a similar scaling with the wall-normal distance. We explain the appearance and scaling of the streak-like structures in terms of the two-dimensional spectra imposed on the fields.     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

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.     

A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas

Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier–Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the \(k-\varepsilon \) model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.     

Spectral-Dynamic Model for Large-Eddy Simulations of Turbulent Rotating Channel Flow

A new subgrid-scale model called the spectral-dynamic model is proposed. It consists of a refinement of spectral eddy-viscosity models taking into account nondeveloped turbulence in the subgrid-scales. The proposed correction, which is derived from eddy-damped quasi-normal Markovian statistical theory, is based on an adjustment of the turbulent eddy-viscosity coefficient to the deviation of the spectral slope (at small scales) with respect to the standard Kolmogorov law. The spectral-dynamic model is applied to large eddy simulation (LES) of rotating and nonrotating turbulent plane channel flows. It is shown that the proposed refinement allows for clear improvement of the statistical predictions due to a correct prediction of the near-wall behavior. Cases of rotating and nonrotating low (DNS) and high Reynolds (LES) numbers are then compared. It is shown that the principal structural features of the rotating turbulent channel flow are reproduced by the LES, such as the presence of the near-zero mean absolute vorticity region, the modification of the anisotropic character of the flow (with respect to the nonrotating case), the enhancement of flow organization, and the inhibition of the high- and low-speed streaks near the anticyclonic wall. Only a moderate Reynolds number dependence is exhibited, resulting in a more unstable character of the longitudinal large-scale roll cells at high Reynolds number, and a slight increase of the laminarization tendency on the cyclonic side of the channel. Received 16 October 1997 and accepted 1 October 1998     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini