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.     

DNS and Modelling of Passive Scalar Transport in Turbulent Channel Flow with a Focus on Scalar Dissipation Rate Modelling

A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation. The Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half width is 265. Budgets are presented for the passive scalar variance and its dissipation rate, as well as for the individual scalar flux components. These form a basis for a discussion of modelling issues related to explicit algebraic scalar flux modelling. This revised version was published online in July 2006 with corrections to the Cover Date.     

DNS and LES of Passively Controlled Turbulent Backward-Facing Step Flow

A passive control approach (no external energy input) for an unsteady separated flow case was investigated numerically. A surface-mounted control fence was positioned upstream of a backward-facing step, and as an oncoming flow a thin and fully developed turbulent boundary layer with a thickness of δ/h = 0.8 was used. The objective of the passive control was to enhance the entrainment rate of the shear layer bounding the separation zone behind the step, thereby reducing the mean reattachment length,〈 X _r0 〉. Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) at Re _h = 3000 (based on the step height, h, and the free stream velocity, U _∞) were carried out for the uncontrolled and the controlled flow case. The LES results were in good agreement with the DNS reference solutions. Adaptively controlled feedback simulations showed that a certain minimum distance between the step edge and the upstream position of the control fence is required to achieve a maximum reduction of the reattachment length.     

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.     

Structures of Density Fluctuations at a Low-Mach-Number Turbulent Boundary Layer by DNS

We performed a direct numerical simulation of a low-Mach-number turbulent boundary layer using fundamental equations of compressible flow to investigate the relation between vortex structures and the density distribution. A fully developed turbulent boundary layer of compressible flow was reproduced in the simulation. From the turbulence statistics and instantaneous structures of the density fluctuation, we identified different features in the three regions of a near-wall field, far field and flow field outside the turbulent boundary layer. Structures of the density fluctuation could correspond to sound sources in a turbulent boundary layer. We then observed fine-scale structures of the density fluctuation that were strongly related to turbulent vortices in the vicinity of the wall. In addition, there were large-scale density structures in the upper boundary layer. The large-scale structures seem to correlate with the fine-scale structures close to the wall, with there being a non-steady larger-scale density fluctuation profile in the outer region of the boundary layer.     

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     

DNS of a Laminar Separation Bubble in the Presence of Oscillating External Flow

A three-dimensional Direct Numerical Simulation (DNS) of a laminar separation bubble in the presence of oscillating flow is performed. The oscillating flow induces a streamwise pressure gradient varying in time. The special shape of the upper boundary of the computational domain, together with the oscillating pressure gradient causes the boundary layer flow to alternately separate and re-attach. When the inflow decelerates, the shear layer starts to separate and rolls up. Simultaneously the flow becomes 3D. After a transient period, the phase-averaged reverse flow inside the separation bubble reaches speeds ranging from 20 up to 150% of the free-stream velocity. During these phases, the flow is absolutely unstable and self-sustained turbulence can exist. When the inflow starts to accelerate, a spanwise roll of turbulent flow is shed from the shear layer. Shortly after this, the remainder of the separation bubble moves downstream and rejoins with the shed turbulent roll. During the flow-acceleration phase, a patch of laminar boundary layer flow is obtained. Along the flat plate, a series of turbulent patches of flow travelling downstream, separated by laminar flow can be observed, reminiscent of boundary layer flow in a turbine cascade with periodically appearing free-stream disturbances.     

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.     

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.     

Reconstruction of Scalar Source Intensity Based on Sensor Signal in Turbulent Channel Flow

We consider a turbulent channel flow, where a scalar point source with a time-harmonic intensity releases a substance that can be modeled as a passive scalar. With the source location known, our objective is to estimate the time history of the source intensity based on sensor measurements at different locations downstream of the source by adopting an adjoint approach. It is shown that the proposed algorithm reproduces the original coherent sinusoidal wave of the scalar source accurately from the chaotic scalar signals measured by our sensors. By systematically changing the source-sensor distance and the pulsation frequency of the source, we clarify how these two factors affect the estimation accuracy. The proposed scheme is also applicable to estimation with multiple sensors. We demonstrate that increasing the number of sensors improves the estimation greatly when the scalar is released from a source away from the wall, where large-scale eddies dominate the scalar dispersion. In contrast, the estimation performance remains poor even with multiple sensors when the scalar source is located near the wall, where the source information is quickly lost due to the strong turbulence activity and the scalar diffusion in the near-wall region.     

Temporal Evolution of Vortical Structures in the Wall Region of Turbulent Channel Flow

Hairpin-like vortical structures that form in the wall region of turbulent channel flow are investigated. The analysis is performed by following a procedure in which the Navier-Stokes equations are first integrated by means of a computational code based on a mixed spectral-finite difference technique in the case of the flow in a plane channel. A DNS turbulent-flow database, representing the turbulent statistically steady state of the velocity field through 10 viscous time units, is computed and the vortex-detection method of the imaginary part of the complex eigenvalue pair of the velocity-gradient tensor is applied to the velocity field. As a result, hairpin-like vortical structures are educed. Flow visualizations are provided of the processes of evolution that characterize hairpin vortices in the wall region of turbulent channel flow. The relationship is investigated between vortex dynamics and 2nd- and 4th- quadrant events, showing that ejections and sweeps play a fundamental role in the way the morphological evolution of a hairpin vortex develops with time.     

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     

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     

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.     

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.     

DNS of Turbulent Flows in Ducts with Complex Shape

We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type \(\eta R \sin (N_{w}\theta )\). Simulations by varying N _w at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing N _w and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.     

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.     

Large-Scale Streamwise Vortices in Turbulent Channel Flow Induced by Active Wall Actuations

Direct numerical simulations of turbulent flow in a plane channel using spanwise alternatively distributed strips (SADS) are performed to investigate the characteristics of large-scale streamwise vortices (LSSVs) induced by small-scale active wall actuations, and their role in suppressing flow separation. SADS control is obtained by alternatively applying out-of-phase control (OPC) and in-phase control (IPC) to the wall-normal velocity component of the lower channel wall, in the spanwise direction. Besides the non-controlled channel flow simulated as a reference, four controlled cases with 1, 2, 3 and 4 pairs of OPC/IPC strips are studied at M =?0.2 and R e =?6,000, based on the bulk velocity and the channel half height. The case with 2 pairs of strips, whose width is Δz ⁺ =?264 based on the friction velocity of the non-controlled case, is the most effective in terms of generating large-scale motions. It is also found that the OPC (resp. IPC) strips suppress (resp. enhance) the coherent structures and that leads to the creation of a vertical shear layer, which is responsible for the LSSVs presence. They are in a statistically steady state and their cores are located between two neighbouring OPC and IPC strips. These motions contribute significantly to the momentum transport in the wall-normal and spanwise directions showing potential for flow separation suppression.