Turbulent Channel Flow

The goal of this research is the development of a theoretical quantitative understanding of the dynamics of high Reynolds number free-surface flows under large free-surface deformations in the presence of one or multiple surfactants. The longterm goal of this research is to understand the effect of the surfactants on (1) turbulence, (2) waves, (3) slick formation and (4) mass transfer through the free surface.

According to the late A.B. Metzner , the phenomenon of polymer-induced drag reduction was independently discovered by two researchers, K.J. Mysels in May 1945, as reported by the discoverer at an AIChE symposium on drag reduction in 1970, and B.A. Toms in the summer of 1945, as reported by the discoverer at the IUTAM symposium on the structure of turbulence and drag reduction held in Washington, DC in 1976. The original fluids studied in these two first experimental investigations were micellar aluminum disoaps or rubber in gasoline (K.J. Mysels) and polymethyl methacrylate in monochlorobenzene (B.A. Toms). However, due to the war, the first records in an accessible publication were found later [2, 3] with journal contributions even much later . Since that time, the field has literally exploded with 500 papers until the seminal review by Virk [6] and 4900 papers by 1995 [1]. The first attribution of drag reduction to fluid viscoelasticity was by Dodge and Metzner [7], whereas the first description of drag reduction as Toms effect was by Fabula at the Fourth International Congress on Rheology, held in 1996 [8]. The first measurements of viscoelasticity of drag-reducing fluids were performed by Metzner and Park [9] and Hershey and Zakin [10]. The first articulations of a maximum drag reduction asymptote for dilute polymer solutions were reported by Castro and Squire [11], Giles and Pettit [12], and Virk et al. [13]. As far as the first proposed mechanisms of drag reduction due to fluid mechanical effects are concerned, Lumley attributed drag reduction to molecular stretching in the radial flow patterns in turbulent flows [14]. Simultaneously, Seyer and Metzner [15] clarified it even further, as due to high extensional deformation rates in radial flow patterns in turbulent flows and high resistance to stretching of viscoelastic fluids. More recently, Lumley and Blossey [16] elaborated further by arguing that polymer additives, by boosting the extensional viscosity of the fluid, affect especially the structure of the turbulent bursts; see also Ref. [17]. This same mechanism is also suspected to be operative when other additives are employed, such as micellar surfactant solutions

The American Physical Society DNS of Viscoelastic Turbulent Channel Flow at High Drag Reduction ANTONY BERIS, University of Delaware, KOSTAS HOUSIADAS, Aegian University, Greece, LUO WANG, University of Delaware -A new method has been developed to enable Direct Numerical Simulations (DNS) of viscoelastic turbulent channel flow with high accuracy spectral methods at high values of drag reduction (HDR), when the polymer molecules undergo high extensional deformation. To faithfully represent that we have expressed the conformation tensor, c, as the exponential of another tensor a, c=exp(a) and we solve for a instead of c. Thus, by construction, the positive definite property of c is always preserved. In addition, a stabilizing artificial diffusion has been added to the viscoelastic constitutive model and efficiently implemented numerically using a multigrid method. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is then used to represent the effect of polymer molecules in solution. To achieve HDR we used high values of the key model parameters: (a) the maximum extensional viscosity, which for the FENE-P constitutive model is proportional to the quantity (1-β)*Lˆ2, where β is the solvent viscosity ratio and L is the maximum extensibility parameter and (b) the friction Weissenberg number, Weτ .

Direct numerical simulations (DNS) have been performed of turbulent flow in a plane channel with a solid top wall and a permeable bottom wall. The permeable wall is a packed bed, which is characterized by the mean particle diameter and the porosity. The main objective is to study the influence of wall permeability on the structure and dynamics of turbulence. The flow inside the permeable wall is described by means of volume-averaged Navier-Stokes equations. Results from four simulations are shown, for which only the wall porosity ( c ) is changed. The Reynolds number based on the thickness of the boundary layer over the permeable wall and the friction velocity varies from Re p τ = 176 for c = 0 to Re p τ = 498 for c = 0.95. The influence of wall permeability can be characterized by the permeability Reynolds number, Re K , which represents the ratio of the effective pore diameter to the typical thickness of the viscous sublayers over the individual wall elements. For small Re K , the wall behaves like a solid wall. For large Re K , the wall is classified as a highly permeable wall near which viscous effects are of minor importance. It is observed that streaks and the associated quasi-streamwise vortices are absent near a highly permeable wall. This is attributed to turbulent transport across the wall interface and the reduction in mean shear due to a weakening of, respectively, the wall-blocking and the wall-induced viscous effect. The absence of streaks is consistent with a decrease in the peak value of the streamwise root mean square (r.m.s.) velocity normalized by the friction velocity at the permeable wall. Despite the increase in the peak values of the spanwise and wall-normal r.m.s. velocities, the peak value of the turbulent kinetic energy is therefore smaller. Turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate from a Kelvin-Helmholtz type of instability. These structures are responsible for an exchange of momentum between the channel and the permeable wall. This process contributes strongly to the Reynolds-shear stress and thus to a large increase in the skin friction.

Direct numerical simulations (DNS) have been performed of turbulent flow in a plane channel with a solid top wall and a permeable bottom wall. The permeable wall is a packed bed, which is characterized by the mean particle diameter and the porosity. The main objective is to study the influence of wall permeability on the structure and dynamics of turbulence. The flow inside the permeable wall is described by means of volume-averaged Navier-Stokes equations. Results from four simulations are shown, for which only the wall porosity ( c ) is changed. The Reynolds number based on the thickness of the boundary layer over the permeable wall and the friction velocity varies from Re p τ = 176 for c = 0 to Re p τ = 498 for c = 0.95. The influence of wall permeability can be characterized by the permeability Reynolds number, Re K , which represents the ratio of the effective pore diameter to the typical thickness of the viscous sublayers over the individual wall elements. For small Re K , the wall behaves like a solid wall. For large Re K , the wall is classified as a highly permeable wall near which viscous effects are of minor importance. It is observed that streaks and the associated quasi-streamwise vortices are absent near a highly permeable wall. This is attributed to turbulent transport across the wall interface and the reduction in mean shear due to a weakening of, respectively, the wall-blocking and the wall-induced viscous effect. The absence of streaks is consistent with a decrease in the peak value of the streamwise root mean square (r.m.s.) velocity normalized by the friction velocity at the permeable wall. Despite the increase in the peak values of the spanwise and wall-normal r.m.s. velocities, the peak value of the turbulent kinetic energy is therefore smaller. Turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate from a Kelvin-Helmholtz type of instability. These structures are responsible for an exchange of momentum between the channel and the permeable wall. This process contributes strongly to the Reynolds-shear stress and thus to a large increase in the skin friction.

Turbulent flow drag reduction on hybrid riblet superhydrophobic surfaces 1 JULIE CROCKETT, RICHARD PERKINS, DANIEL MAYNES, Brigham Young University -We investigate characteristics of turbulent flow in a mini-scale channel where one of the walls is structured with riblets, superhydrophobic microribs, or a hybrid surface that has both structure types present. Individually, large scale riblets, approximately 80 microns tall with 160 micron spacing, provide drag reduction through damping spanwise turbulent motions, and superhydrophobic surfaces, with nearly an order of magnitude smaller features, provide drag reduction through apparent slip at the wall. It is postulated that the combination of the structures will yield a more significant drag reduction than either alone. Experiments were conducted in a rectangular channel with one wall comprised of superhydrophobic features, riblets, or the combination of the two and for channel Reynolds numbers ranging from 4500 to 20000. The velocity profile, turbulent statistics, and shear stress profile are observed using PIV measurements. In addition friction factor and turbulence production are extracted from the PIV data. Modest drag reductions were observed for both the superhydrophobic and riblet surfaces. The combined surfaces showed the greatest drag reduction and turbulence production was significantly reduced for these surfaces.

Recent developments in two approaches to hydrodynamic flow control are considered. One is concerned with the closed-loop large-scale control of maneuvering of biologically-inspired small underwater vehicles in a disturbed littoral ocean environment. The other is the small-scale closed-and open-loop control of turbulence in a boundary layer developing on the outer surface of an ocean going vehicle. Theoretical and experimental progress made are described. The former type appears to be well amenable to closed-loop active control with the potential payoff of a high degree of precision in maneuvering. In the latter type, an active open-loop control appears to have the best potential for turbulence quieting and drag reduction. The paper is limited to exploratory work carried out by the author.

Public reporting for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports,

In recent years, the increased use of off-the-shelf components and the large-scale adoption of parallel computing have led to a dramatic reduction in the costs associated with high-performance computing. This has enabled increased usage of compute-intensive methods, such as Direct Numerical Simulation (DNS), for the simulation of turbulent flows. We introduce a sophisticated DNS code that incorporates a number of advanced features: high-order central differencing; a shock-preserving advection scheme from the total variation diminishing (TVD) family; entropy splitting of the Euler terms and the associated stable boundary treatment. A series of test cases was devised in order to test the scalability of the code and the scalability of the parallel platforms that were available. The benchmark case considered is based on the flow between two infinite parallel plates with isothermal walls driven by a constant pressure gradient. Turbulent flow is triggered by constructing disturbances with a combination of different wavelengths and with periodic boundary conditions forced in the streamwise and spanwise directions. Performance measurements are presented for a range of parallel systems, including the Cray T3E, the SGI Origin 3000 and clusters based on commodity processors and off-the-shelf networking components, and show excellent scalability across the range of platforms.

Numerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number Re and Deborah number De. The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high Re and De, calls for some care. In this paper we present a study of drag reduction by rodlike polymers in a turbulent channel flow using direct numerical simulation and illustrate how these numerical results should be related to the recently developed theory.

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number De ≫ 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydro-elastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to to the cross-stream component of the elastic stress tensor. This component is smaller than the stream-wise component by a factor proportional to De 2 . Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.

In this paper, we present new experimental measurements of the turbulent transport of salt across an interface between two layers of fluid of equal depth but different salinities. The fluid is confined to a cylindrical annulus with a vertical axis. The outer cylinder is stationary and the inner cylinder rotates to produce a turbulent flow field consisting of an approximately irrotational mean azimuthal flow, with narrow boundary layers on the inner and outer cylinders. We focus on the limit of high-Richardson-number flow, defined as Ri = g ρH/(ρ 0 u 2 rms ), where ρ 0 is a reference density, ρ is the time-dependent difference of the layers' mean densities, u rms is the root mean square of the turbulent velocity fluctuations and H is the layer depth. The mean flow has Reynolds number of the order of 10 4 -10 5 , and the turbulent fluctuations in the azimuthal and radial directions have root-mean-square speed of order 10 % of the mean azimuthal flow. Measurements based on our experimental system show that when the Richardson number is in the range 7 < Ri < 200, the interface between the two layers remains sharp, each layer remains well mixed, and the vertical flux of salt between the layers, F s ∼ (1.15 ± 0.15)Ri -1 A(H/∆ R )u rms S, where S is the spatially-averaged time-dependent salinity difference between the layers and in general A(H/∆ R ) is a dimensionless function of the tank aspect ratio, here taken to be unity, with ∆ R being the gap width of the annulus. The salt transport appears to be caused by turbulent eddies scouring and sharpening the interface and implies a constant rate of conversion of the turbulent kinetic energy to potential energy, independent of the density contrast between the layers. For smaller values of Ri, the flow regime changes qualitatively, with eddies penetrating the interface, causing fluid in the two layers to co-mingle and rapidly homogenize.

Superhydrophobic surfaces (SHSs) can reduce the friction drag in turbulent flows. In the laminar regime, it has been shown that trace amounts of surfactant can negate this drag reduction, at times rendering these surfaces no better than solid walls (Peaudecerf et al., Proc. Natl. Acad. Sci. USA 114(28), 7254-9, 2017). However, surfactant effects on the drag-reducing properties of SHSs have not yet been studied under turbulent flow conditions, where predicting the effects of surfactant in direct numerical simulations remains expensive by today's standards. We present a model for turbulent flow inclusive of surfactant, in either a channel or boundary-layer configuration, over long but finite-length streamwise ridges that are periodic in the spanwise direction, with period P and gas fraction φ. We adopt a technique based on a shifted log law to acquire an expression for the drag reduction. The average streamwise and spanwise slip lengths are derived by introducing a local laminar model within the viscous sublayer, whereby the effect of surfactant is modelled by modifying the average streamwise and spanwise slip lengths. Our model agrees with available laboratory experimental data from the literature when conditions are clean (surfactant-free), or when there are low surfactant levels. However, we find an appreciable drag increase for larger background surfactant concentrations that are characteristic of turbulent flows over SHSs for marine applications.

In this paper, we present new experimental measurements of the turbulent transport of salt across an interface between two layers of fluid of equal depth but different salinities. The fluid is confined to a cylindrical annulus with a vertical axis. The outer cylinder is stationary and the inner cylinder rotates to produce a turbulent flow field consisting of an approximately irrotational mean azimuthal flow, with narrow boundary layers on the inner and outer cylinders. We focus on the limit of high-Richardson-number flow, defined as Ri = gΔρH/(ρ0u2rms), where ρ0 is a reference density, Δρ is the time-dependent difference of the layers&#39; mean densities, urms is the root mean square of the turbulent velocity fluctuations and H is the layer depth. The mean flow has Reynolds number of the order of 104−105, and the turbulent fluctuations in the azimuthal and radial directions have root-mean-square speed of order 10% of the mean azimuthal flow. Measurements based on our experimental sy...

Some recent subgrid-scale models are evaluated in turbulent channel flow at Re τ = 395. The models considered were chosen among those performing best in decaying isotropic turbulence, following the study by Winckelmans & Jeanmart (2001): the dynamic Smagorinsky model (used as a baseline); a dynamic and regularized version of the variational multiscale model of Hughes, Mazzei, Oberai & Wray (2001); a dynamic "Smagorinsky + hyperviscosity" model (here with two dynamic coefficients); and a dynamic Smagorinsky model acting on an artificially-enhanced velocity field. The last three models put more emphasis than the Smagorinsky model on the subgrid-scale (SGS) dissipation at small scales, leading to significant improvement of the results in isotropic turbulence. The last two models combine viscosity and hyperviscosity effects. The dynamic procedure was implemented for each model, with and without adding a test projection in the wall-normal direction. The projection uses a combined "sampling + interpolation" procedure, applied in physical space. The models are assessed and compared to the direct numerical simulation (DNS) data of Moser, on the basis of mean profiles of velocity, rms velocities and reduced (deviatoric) turbulence intensities. A main outcome is the good behavior of the multiscale model of Hughes et al. as compared to the Smagorinsky model. Good results are also obtained when using the Smagorinsky model acting on an artificiallyenhanced velocity field. In all cases, the dynamic procedure without test "sampling + interpolation" in the wall-normal direction leads to better agreement with the DNS data. The poor performance of "sampling + interpolation" is most probably due to the interpolation part, and a possible solution to the problem is proposed.

Validation experiments of the two-dimensional inverse algorithm are performed in a pulsed Poiseuille flow exposing shear reversal phases. The method is applied to the three-segment electrodiffusion (ED) probe for which a specific nondimensionalization process is suggested, allowing to better link measurements from a real ED probe to the modeled one in the inverse problem. This approach provided a two-component wall shear rate in good agreement with the one obtained from laser Doppler anemometry (LDA) measurements, thus validating the ability of ED probes to deal with high-amplitude unsteady flows. The classic linear velocity approximation ($u=sy$) in the probe vicinity is also investigated in such a flow.

Bubbly flow shows complicated behavior due to a strong dynamic interaction between bubble and vortex motions. A technique for generating a strong surface flow by using a bubble curtain has been proposed by the authors. In the future, bubble curtain is expected to be a new type of oil fence because it can generate a strong and wide surface flow over the bubble generation system . The present paper is concerned with the mechanism of generating the surface flow. Furthermore , the internal two-phase flow structure of the surface fl ow generation induced by the bubble curtain is discussed using PIV (particle imaging velocimetry) measurement data after separating bubbles and particles from the original images .

Probability density functions (PDFs) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the PDF of each of these quantities (except for u,y), is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the PDFs are also independent of Reynolds number. Similar behavior is observed for the PDFs of the second derivatives. The pseudodissipation rate of kinetic energy exhibits lognormal behavior.

Lattice Boltzmann method (LBM) has become an alternative method of computing a variety of fluid flows, ranging from low Reynolds number laminar flows to highly turbulent flows. For turbulent flows, non-uniform grids are preferred. Taylor series expansion-and least-squares-based LBM (TLLBM) is an effective and convenient way to extend standard LBM to be used on arbitrary meshes. In order to show its ability to solve turbulent flows, we combine it with k-ω and S-A turbulence models. To validate these combinations, the benchmark problems of the turbulent channel flow and the turbulent flow over a backward facing step at Re = 44 000 are simulated. Our results compare well with the analytical solution and the experimental results of Kim et al. [22]. This shows that the combination of TLLBM with turbulence model can solve turbulent flows effectively.

The incentive for this research is to gain insight into fundamental aspects of turbulent fluid-particle flows. The project investigates the influence of inter-particle collisions on the particle and fluid phase variables in the context of particle agglomeration, dispersion and deposition for turbulent bounded flows laden with low particle numbers. The mathematical modelling technique used is large eddy simulation (LES), with flow solutions provided by this method coupled to a discrete element method (DEM) to predict particle motion and interaction. The results have been compared with single-phase bounded flows in order to investigate the effect of the particles on turbulence statistics. The four-way coupled simulations are also contrasted with one-way coupled (flow affects the particles only) results in which the inelastic collisions between particles are neglected. The influence of different particle surface energies, particle size, particle density, particle concentration and flow...

In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An important property of this 1D model is that one can construct from its solutions a family of exact solutions of the 3D Navier-Stokes equations. The nonlinear structure of the 1D model has some very interesting properties. On one hand, it can lead to tremendous dynamic growth of the solution within a short time. On the other hand, it has a surprising dynamic depletion mechanism that prevents the solution from blowing up in finite time. By exploiting this special nonlinear structure, we prove the global regularity of the 3D Navier-Stokes equations for a family of initial data, whose solutions can lead to large dynamic growth, but yet have global smooth solutions.

To study extreme hydrodynamic wave impact in offshore and coastal engineering, the VOF-based CFD simulation tool ComFLOW is being developed. In this paper we will present its turbulence modeling. In particular, a blend of a QR-model and a regularization model has been designed. The QR-model belongs to a class of modern eddy-viscosity models, where the amount of turbulent eddy viscosity is kept minimal. Also, to enhance efficieny, local grid refinement has been added. For validation, experiments have been carried out at MARIN.

A large eddy simulation (LES) with an extended Smagorinsky model has been carried to investigate numerically the fully developed turbulent flow of a shear thinning fluid (n=0.75) in a stationary pipe at a simulation&#39;s Reynolds number equals to 4000 with a grid resolution of 65 3 gridpoints in axial, radial and circumferential directions and a domain length of 20R. The present study set out to critically evaluate the influence of the Non-Newtonian rheological and hydrodynamic behaviour on the turbulence main features, as well as to ascertain the accuracy and reliability of the laboratory code predicted results. The turbulent flow statistics obtained compared reasonably well with the experimental data and DNS results. A reasonably good agreement has been obtained between the predicted results and available results of literature. The main findings suggest that the mean axial velocity fluctuations were generated in the wall vicinity and transferred to the radial and spanwise compone...

Large Eddy Simulations (LES) have been increasing popularity due to the decrease of computational power cost. Indeed, engineering applications which have previously involved mainly RANS, are now shifting to LES. Many eddy-viscosity models have been developed during the last decades. They all share a general structure, which derive from a dimensional analysis: ν SGS = (C m ∆) 2 D(Ū), where in order appear the model constant, the length scale and the differential operator underlying the model. The aim of this paper is to investigate the influence of length scale ∆ definition on highly anisotropic grids, because most of the research has focused mainly on the model constant and differential operator roles. The main length scale definitions that will be compared are: i) the most popular is ∆ vol = V 1 3 ii) ∆ ω iii) ∆ lsq. In order to do so, we first calibrate the model constant, then we carry out a set of simulations in Open-FOAM to assess the ∆ definition influence. In order to assess the resilience of the models for highly anisotropic meshes, these simulations will be carried out also on meshes having control volumes with high aspect ratios. Results for standard test cases such as a decaying Homogeneous Isotropic Turbulence (HIT) and a turbulent periodic plane channel will be presented and compared to reference cases.

Smagorinsky‐based models are assessed in a turbulent channel flow simulation at Reb=2800 and Reb=12500. The Navier–Stokes equations are solved with three different grid resolutions by using a co‐located finite‐volume method. Computations are repeated with Smagorinsky‐based subgrid‐scale models. A traditional Smagorinsky model is implemented with a van Driest damping function. A dynamic model assumes a similarity of the subgrid and the subtest Reynolds stresses and an explicit filtering operation is required. A top‐hat test filter is implemented with a trapezoidal and a Simpson rule. At the low Reynolds number computation none of the tested models improves the results at any grid level compared to the calculations with no model. The effect of the subgrid‐scale model is reduced as the grid is refined. The numerical implementation of the test filter influences on the result. At the higher Reynolds number the subgrid‐scale models stabilize the computation. An analysis of an accurately r...

A fast algorithm for the estimation of statistical error in DNS (or experimental) time averages PAOLO LUCHINI, University of Salerno -DIIN, SERENA RUSSO, University of Naples Federico II -A standard final step in the DNS (but the same can be said of experimental measurements) of turbulence, is the time-and space-averaging of the instantaneous results in order to give their means or correlations or other statistical properties. These averages are necessarily performed over a finite time and space window, and are therefore more correctly just estimates of the "true" statistical averages. The choice of the appropriate window size is most often subjectively based on individual experience, but as subtler statistics enter the focus of investigation, an objective criterion becomes desirable. Classical estimators of the averaging error of finite time series fall in two categories: "batch means" algorithms, fast but not very accurate, and ARMA methods, slower because they estimate the complete correlation function to start with. Here a modification of the batch means algorithm will be presented, which retains its speed while removing its biasing error. As a side benefit, an automatic determination of batch size is also included. Examples will be given involving both an artificial time series of known statistics and an actual DNS of turbulence.

The mixture stress of non-uniform suspensions is expressed by the symmetric part and the antisymmetric parts with the pseudo and the real vectors. The closure relations for the three components of the stress are derived from the basic criteria such as Galilean invariance and parity. By the numerical simulations of many particles under the Stokes approximation with the non-uniform ensemble averaging technique and the systematic parameterizations, the closure coefficients including the effective viscosity are determined in the large system limit. The resultant closure relations are valid not only for the specific problem but for force, torque, and shear problems, and, as a result, for arbitrary flows generated by the linear combination of the three problems, because of the linearity of the Stokes approximation.

We address the phenomenon of drag reduction by a dilute polymeric additive to turbulent flows, using direct numerical simulations (DNS) of the FENE-P model of viscoelastic flows. It had been amply demonstrated that these model equations reproduce the phenomenon, but the results of DNS were not analyzed so far with the goal of interpreting the phenomenon. In order to construct a useful framework for the understanding of drag reduction we initiate in this paper an investigation of the most important modes that are sustained in the viscoelastic and Newtonian turbulent flows, respectively. The modes are obtained empirically using the Karhunen-Loéve decomposition, allowing us to compare the most energetic modes in the viscoelastic and Newtonian flows. The main finding of the present study is that the spatial profile of the most energetic modes is hardly changed between the two flows. What changes is the energy associated with these modes, and their relative ordering in the decreasing ord...

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

A new mixed model which uses the Leonard expansion (truncated to one term) supplemented by a purely dissipative term (dynamic Smagorinsky) has been devel- oped and tested in actual Large Eddy Simulations (LES) of decaying homogeneous turbulence and of channel flow. This model assumes that the LES lter is smooth in wave space, which is the case of most lters dened in physical space (e.g. ,t op hat, Gaussian, discrete lters). The dynamic procedure has been extended for the mixed model. It is used to determine the model coecient, C, for the added Smagorinsky term. The one-term Leonard model provides signicant local backscatter while re- maining globally dissipative. In ap rioritesting, its correlation with DNS is greater than 0:9. However, when used on its own in actual LES, this model is found to provide too little dissipation. Hence the need for added dissipation, here provided by the dynamic Smagorinsky term. In 643 LES of decaying homogeneous turbu- lence started from Gaussian lter...

The spreading of a tracer in a bubbly two-phase grid-generated turbulent flow system is studied. In this work both particle image velocimetry (PIV) and planer laser-induced fluorescence (PLIF) are used to study the effect of the dispersed phase flow rate on the mixing characteristics of the tracer. The turbulent intensity of the continuous phase in the bubbly two-phase grid-generated turbulent flow is close to isotropic, and increasing the gas void fraction reduces the degree of non-isotropicity. The self-similarity of mean and RMS values of the cross-stream concentration distribution is observed. A new mathematical model is suggested to describe the self-similarity of the cross-stream profiles of the mean concentration based on two separate Gaussian curves into the central and outer region of the flow. The turbulent diffusivity is calculated using the Taylor hypothesis, which is based on the growth of the variance of the cross-stream profiles of the mean concentration, with a posit...

Direct numerical simulations of the turbulent dispersion of a buoyant line of hot fluid released at the inlet of a plane channel flow are reported (Re s = 180, Gr = 10 7 and Pr = 0.7). Results of turbulent dispersion of a neutrally buoyant scalar and mixed convection flow are also included. The buoyancy force induces a vertical movement that, although small in mean, exhibits a significant fluctuation in the vertical velocity component and deflects the plume with the consequent loss of symmetry found in the neutrally buoyant results. The modification of the budgets for the time averaged momentum and heat transport equations reflects the rearranging of the different contributions induced by the buoyancy force.

We discuss a dynamic Lagrangian averaging approach applied in conjunction with the standard dynamic model for large-eddy simulation. Unlike the conventional Lagrangian dynamic model where the Lagrangian time scale contains an adjustable parameter $\theta$, we propose ...

This study addresses the dynamics of kinetic-energy backscatter in the context of large-eddy simulations (LES) of turbulent chemically-reacting compressible flows. As a case study, a-priori analyses of direct numerical simulations (DNS) of reacting and inert supersonic, time-developing, hydrogen-air turbulent mixing layers with complex chemistry and multi-component diffusion are conducted herein to examine the effects of compressibility and combustion on subgrid-scale (SGS) backscatter of kinetic energy. General formulations of SGS backscatter with dilatation are provided, including an LESbased energy-transfer diagram that illustrates the conversion dynamics. Lastly, influences of SGS backscatter on the Boussinesq eddy viscosity are analyzed.

Fully developed turbulent channel flow has been simulated americally at . Reynolds number 19800, based on centerline velocity and channel half width. The large-scale flow field has been obtained by directly integrating the filtered, three-dimensional, tine-dependent, Davies-Stokes equations. The smallscale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time-dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall. I. Introduction Large-eddy simulation (LBS) is a relatively new approach to the calculation of turbulent flows. The basic idea stems from two experimental observations. First, the large-scale structure of turbulent flows varies greatly from flow to flow (e.g., jets vs. boundary layers) and consequently is difficult, if not impossible, to model in a general way. Second, the small-scale turbulence structures are nearly isotropic, very universal in character (Chapman, 1979) and hence such sore amenable to general modeling. In LBS, one actually calculates the large-scale notions in a time-dependent, three-*Portions of this work were carried out while the authors held NRC Research Associateships at Ames Research Center. a locally isotropic: part and an iahomc.-Qeneous part, he employed a separate partial differential equation for SGS turbulent kinetic energy. However, the added differential equation did not improve the results over the calculations in which only an eddy viscosity model was used ( Schumann, 1975). Gr8tzbach and Schumann ( 1977) extended their channel flow calculations to account for temperature fluctuations and heat transfer. Later extensions by GrBtzbach include calculations of secondary flows in partly roughened chanr nels, inclusion of buoyancy effects, and liquid metal flows in plane channels and annuli. A recent -4view of this group's work in LES was given by Schumann et al. (1979). In all of the above computations, the dynamics of the inner region of the boundary layer (viscous sublayer and butter layer) was essentially ignored. It is in this region that virtually all of the production of turbulence kinetic energy takes place (Townsend, 1956;. Artificial boundary conditions in the logarithmic region were used to simulate the inner layers. Aside from the fact that these boundary conditions are designed to be consistent iu the mean with the law of thx wall, there is little justification or experimental evidence to warrant their use for the detailed flow field. however, the computations of and especially those of the Karlsruhe group have produced successful comparisons with experimental data in the regions away from the walls. With a relatively modest number of grid points, they have been able to extract considerable information of practical interest from their computations. The first numerical simulation of turbulent channel flow that computed ^rather than modeled the flow in the immediate neighborhood of the wall was that of . In this calculation only 16 uniformly spaced grid points were used in each of the streamwise, x, and spanwise, z, directions

Drag is a mechanical force generated by a solid object moving through a fluid. For drag to be generated, the solid body must be in contact with the fluid. Drag is generated by the difference in velocity between the solid object and the fluid. Drag acts in the direction opposite to the direction of motion of the body. Microbubbles is a drag reduction device that reduces skin friction of a solid body moving in water by injecting small bubbles into the turbulent boundary layer developing on the solid body. Its application is confined to the ships, especially large ships. Ships such as tankers play a major role in marine transportation. They are very large and move very slowly. They are especially suited to microbubbles application. With the development of the Microbubbles technology almost 20-80% drag reduction is possible. In this paper we study about different drag reduction mechanisms and factor affecting net power saving in large ship.

To date, the most successful turbulence control technique is the dissolution of certain rheology-modifying additives in liquid flows, which results in a universal maximum drag reduction (MDR) asymptote. The MDR asymptote is a well-known phenomenon in the turbulent flow of complex fluids; yet recent direct numerical simulations of Newtonian fluid flow have identified time intervals showing key features of MDR. These intervals have been termed "hibernating turbulence" and are a weak turbulence state which is characterised by low wall-shear stress and weak vortical flow structures. Here, in this experimental investigation, we monitor the instantaneous wall-shear stress in a fully-developed turbulent channel flow of a Newtonian fluid with a hot-film probe whilst simultaneously measuring the streamwise velocity at various distances above the wall with laser Doppler velocimetry. We show, by conditionally sampling the streamwise velocity during low wall-shear stress events, that the MDR velocity profile is approached in an additive-free, Newtonian fluid flow. This result corroborates recent numerical investigations, which suggest that the MDR asymptote in polymer solutions is closely connected to weak, transient Newtonian flow structures.

The Influence of Spanwise Rotation on the Redistribution of Turbulent Kinetic Energy in Fully-Developed Channel Flows CHARLES PETTY, KARUNA KOPPULA, ANDRE BENARD, Michigan State University -A recently developed universal, realizable, anisotropic prestress (URAPS-) closure for the normalized Reynolds (NR-) stress is used to predict the influence of spanwise rotation on the components of the NR-stress in fully-developed channel flows. Direct numerical simulation (DNS-) results are used to determine the relative time scales needed to solve the non-linear URAPS-equation. The new closure, which predicts the existence of a region of zero intrinsic vorticity on the high pressure side of the channel, provides an explanation of how rotation redistributes turbulent kinetic energy among the three components of the fluctuating velocity. The non-linear algebraic URAPS-equation is formulated as a mapping of the NR-stress into itself; therefore, fixed points of the URAPS-equation are realizable for all turbulent flows, regardless of the benchmark flows used to calibrate the model parameters. The URAPS-closure together with closed transport equations for the turbulent kinetic energy and the turbulent dissipation provide a low-order closure for the RANS-equation.

Measurements have been made using Laser Doppler Anemometry (LDA) in a fully developed turbulent channel flow with the aim of determining second-order and third-order temporal and spatial structure functions of the longitudinal velocity fluctuation. A reliable determination of these moments requires the data to be corrected for the effect of noise. Correction procedures are outlined, based on the behaviour of temporal or spatial correlation functions in the limit of small time intervals or small separations. No a priori assumptions about the nature of the noise are made so that the procedure should be quite general. The corrected LDA data indicate that, especially for spatial separations, the effect of noise can be felt even within the inertial range. The corrected structure functions should allow an unambiguous assessment to be made of Taylor's hypothesis and of the extended self-similarity (ESS) method; examples are given in each case. Temporal structure functions obtained by hot wire anemometry (HWA) are much less affected by noise than the LDA data.

Two-point measurements of the streamwise velocity L~ in a turbulent channel flow are performed using laser-Doppler LE anemometry. High spatial and temporal resolutions (about ND 1 Kolmogorov microscale in space and time) are achieved, r Data are obtained at several distances from the wall for R% in RA, B(Z) the range 1500-5000. Results from correlation functions are Ra~(r) compared with the hypotheses of Taylor and Tennekes: they reproduce the experimental data even at low Reynolds num

A turbulent channel flow apparatus was used to determine the adhesion strength of the three perimetamorphic stages of the asteroid Asterina gibbosa, i.e. the brachiolaria larvae, the metamorphic individuals and the juveniles. The mean critical wall shear stresses (wall shear stress required to dislodge 50% of the attached individuals) necessary to detach larvae attached by the brachiolar arms (1.2 Pa) and juveniles attached by the tube feet (7.1 Pa) were one order of magnitude lower than the stress required to dislodge metamorphic individuals attached by the adhesive disc (41 Pa). This variability in adhesion strength reflects differences in the functioning of the adhesive organs for these different life stages of sea stars. Brachiolar arms and tube feet function as temporary adhesion organs, allowing repetitive cycles of attachment to and detachment from the substratum, whereas the adhesive disc is used only once, at the onset of metamorphosis, and is responsible for the strong attachment of the metamorphic individual, which can be described as permanent adhesion. The results confirm that the turbulent water channel apparatus is a powerful tool to investigate the adhesion mechanisms of minute organisms.

In the present study, we investigated flow structures and properties of elastic turbulence in straight 2D channel viscoelastic fluid flow and tested earlier observations. We discovered self-organized cycling process of weakly unstable coherent structures (CSs) of co-existing streaks and stream-wise vortices, with the former being destroyed by Kelvin-Helmholtz-like instability resulting in chaotic structures. The sequence periodically repeats itself leading to stochastically steady state. This selfsustained process (SSP) remarkably resembles one investigated theoretically and experimentally for Newtonian turbulence in straight channel flow. The unexpected new ingredient is the observation of elastic waves, which finds to be critical for existence of CSs and SSP generation due to energy pumping from large to smaller scales preceding sharp power-law decay in elastic turbulence energy spectrum. The reported finding suggests the universality of CSs in transition to turbulence via self-organized cycling (SSP) in linearly stable plane shear flows of both elastic and Newtonian fluids.

We discuss a dynamic Lagrangian averaging approach applied in conjunction with the standard dynamic model for large-eddy simulation. Unlike the conventional Lagrangian dynamic model where the Lagrangian time scale contains an adjustable parameter $\theta$, we propose ...