The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion

DNS data for channel flow, subjected to spanwise (in-plane) wall oscillations at a friction Reynolds number of 1025, are used to examine the turbulence interactions that cause the observed substantial reduction in drag provoked by the forcing. Following a review of pertinent interactions between the forcing-induced unsteady Stokes strain and the Reynolds stresses, identified in previous work by the present authors, attention is focused on the equations governing the components of the enstrophy, with particular emphasis placed on the wall-normal and the spanwise components. The specific objective is to study the mechanisms by which the Stokes strain modifies the enstrophy field, and thus the turbulent stresses. As such, the present analysis sheds fresh light on the drag-reduction processes, illuminating the interactions from a different perspective than that analysed in previous work. The investigation focuses on the periodic rise and fall in the drag and phase-averaged properties during the actuation cycle at sub-optimal actuation conditions, in which case the drag oscillates by around ±2% around the time-averaged 20% drag-reduction margin. The results bring out the important role played by specific strain-related production terms in the enstrophy-component equations, and also identifies vortex tilting/stretching in regions of high skewness as being responsible for the observed strong increase in the spanwise enstrophy components during the drag-reduction phase. Simultaneously, the wall-normal enstrophy component, closely associated with near-wall streak intensity, diminishes, mainly as a result of a reduction in a production term that involves the correlation between wall-normal vorticity fluctuations and the spanwise derivative of wall-normal-velocity fluctuations, which pre-multiplies the streamwise shear strain.     

The role of elongational viscosity in the mechanism of drag reduction by polymer additives

The role of elongational viscosity in the mechanism of drag reduction by polymer additives is investigated qualitatively by means of direct numerical simulations of a turbulent pipe flow. For the polymer solution, a generalised Newtonian constitutive model is utilised in which the viscosity depends on the second and third invariant of the rate-of-strain tensor via an elongation parameter. This elongation parameter is capable of identifying elongational type of regions within the flow. The simulations show that complementary to stretching of the polymers, also compression must be incorporated to have drag reduction, contrary to many suggestions done in the literature on the mechanism which assume that stretching of the polymers is most important.     

Influence of curvature on drag reduction by opposition control in turbulent flow along a thin cylinder

Opposition controlled fully developed turbulent flow along a thin cylinder is analyzed by means of direct numerical simulations. The influence of cylinder curvature on the skin-friction drag reduction effect by the classical opposition control (i.e., the radial velocity control) is investigated. The curvature of the cylinder affects the uncontrolled flow statistics; for instance, skin-friction coefficient increases while Reynolds shear stress (RSS) and turbulent intensity decrease. However, the control effect in the case of a small curvature is similar to that in channel flow. When the curvature is large, the maximum drag reduction rate decreased. However, the optimal location of the detection plane is the same as that in a flat plate. Further, the drag reduction effect is achieved even on a high detection plane where the drag increases in the flat plate. Although a difference in the drag reduction effect can be observed with a change in the curvature, its mechanism considered in this analysis based on the transport of the Reynolds stress is similar to that of the flat plate.     

Influence of molecular weight upon drag reduction by polymers

Summary Drag reduction measurements have been made with samples of polyethyleneoxide and polyacrylamide with relatively narrow molecular weight distributions obtained by fractionation of commercial polymers. Relationships between the polymer molecular weight and the concentration required to give the same drag reduction have been determined. The influence of polymer degradation upon these relationships has been investigated.Molecular weight distributions of commercial polymers have been determined and their influence upon the drag-reducing properties is noted.The influence of wall shear stress has been investigated over the range 1.0 × 10² - 4.5 × 10³ dyn/cm². The results with unfractionated polymers were found to be consistent with other results in the literature.     

A fluctuating lattice-Boltzmann model for direct numerical simulation of particle Brownian motion

A single-relaxation-time fluctuating lattice-Boltzmann （LB） model for direct numerical simulation （DNS） of particle Brownian motion is established by adding a fluctuating component to the lattice-Boltzmann equations （LBEs）. The fluctuating term is proved to be the random stress tensor in fluctuating hydrodynamics by recovering Navier-Stokes equations from LBEs through a Chapman-Enskog expansion. A three-dimensional implementation of the model is also presented, along with simulations of a single spherical particle and 125 spherical particles at short times. Numerical results including the meansquare displacement, velocity autocorrelation function and self-diffusion coefficient of particles compare favorably with theoretical results and previous numerical results.     

Derivation of a spectral pressureless formulation for direct numerical simulation of incompressible channel flows based on a functional formalism

In this article, a new computational spectral algorithm is developed for simulation of general three-dimensional, time-dependent, incompressible channel flow. The development is based on a general functional formalism of non-equilibrium thermodynamics, and, although it is illustrated here for a Newtonian fluid, it is easily adapted to non-Newtonian fluids. The advantage of this algorithm is that the scalar pressure is eliminated from the discrete spectral analog to the equations of motion, which are expressed solely in terms of the spectral coefficients of the velocity vector field. This alleviates the need for the application of boundary conditions on the pressure, the specification of which can be a major source of difficulty in direct numerical simulations. At the same time, the velocity spectrum is quite general, and not subject to any a priori constraints. Thus, it is anticipated that the ideas exposed in the present algorithm can lead to the development of better numerical simulation techniques for complicated three-dimensional and turbulent flows.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

Nonequilibrium stretching dynamics of dilute and entangled linear polymers in extensional flow

We propose an extension of the FENE-CR model for dilute polymer solutions [M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech. 29 (1988) 382–432] and the Rouse-CCR tube model for linear entangled polymers [A.E. Likhtman, R.S. Graham, Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation, J. Non-Newtonian Fluid Mech. 114 (2003) 1–12], to describe the nonequilibrium stretching dynamics of polymer chains in strong extensional flows. The resulting models, designed to capture the progressive changes in the average internal structure (kinked state) of the polymer chain, include an ‘effective’ maximum contour length that depends on local flow dynamics. The rheological behavior of the modified models is compared with various results already published in the literature for entangled polystyrene solutions, and for the Kramers chain model (dilute polymer solutions). It is shown that the FENE-CR model with an ‘effective’ maximum contour length is able to describe correctly the hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation also observed and computed by Doyle et al. [P.S. Doyle, E.S.G. Shaqfeh, G.H. McKinley, S.H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech. 76 (1998) 79–110] and Li and Larson [L. Li, R.G. Larson, Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow, Rheol. Acta 39 (2000) 419–427] using Brownian dynamics simulations of bead–spring model. The Rolie–Poly model with an ‘effective’ maximum contour length exhibits a less pronounced hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation.     

On the effects of dilute polymers on driven cavity turbulent flows

Effects of dilute polymer solutions on a lid-driven cubical cavity turbulent flow are studied via particle image velocimetry (PIV). This canonical flow is a combination of a bounded shear flow, driven at constant velocity and vortices that change their spatial distribution as a function of the lid velocity. From the two-dimensional PIV data we estimate the time averaged spatial fields of key turbulent quantities. We evaluate a component of the vorticity–velocity correlation, namely 〈ω₃v〉, which shows much weaker correlation, along with the reduced correlation of the fluctuating velocity components, u and v. There are two contributions to the reduced turbulent kinetic energy production −〈u v〉S_uv, namely the reduced Reynolds stresses, −〈u v〉, and strongly modified pointwise correlation of the Reynolds stress and the mean rate-of-strain field, S_uv. The Reynolds stresses are shown to be affected because of the derivatives of the Reynolds stresses, ∂〈u v〉/∂y that are strongly reduced in the same regions as the vorticity–velocity correlation. The results, combined with the existing evidence, support the phenomenological model of polymer effects propagating from the polymer scale to the velocity derivatives and through the mixed-type correlations and Reynolds stress derivatives up to the turbulent velocity fields. The effects are shown to be qualitatively similar in different flows regardless of forcing type, homogeneity or presence of liquid–solid boundaries.     

Mechanism of drag reduction by spanwise oscillating Lorentz force in turbulent channel flow

Numerical simulations and experimental research are both carried out to investigate the controlled effect of spanwise oscillating Lorentz force on a turbulent channel flow. The variations of the streaks and the skin friction drag are obtained through the PIV system and the drag measurement system, respectively. The flow field in the near-wall region is shown through direct numerical simulations utilizing spectral method. The experimental results are consistent with the numerical simulation results qualitatively, and both the results indicate that the streaks are tilted into the spanwise direction and the drag reduction utilizing spanwise oscillating Lorentz forces can be realized. The numerical simulation results reveal more detail of the drag reduction mechanism which can be explained, since the spanwise vorticity generated from the interaction between the induced Stokes layer and intrinsic turbulent flow in the near-wall region can make the longitudinal vortices tilt and oscillate, and leads to turbulence suppression and drag reduction.     

On the dynamics of grafted branched polymers—a Monte Carlo simulation study

A simplified model of grafted branched polymers was designed and investigated. The model consisted of star-branched chains constructed on a simple cubic lattice. The star polymers were built of three arms of equal lengths. The chains were attached to an impenetrable flat surface with one arm’s end. The arm attached to the surface (a stem) was built of segments different from those in two remaining arms (branches). During the Monte Carlo simulation of the system, the conformation of each chain was modified according to the metropolis sampling algorithm with local changes of chain conformations. The simulations were performed for different chain lengths and the temperature of the system (solvent conditions). The structure of a polymer film formed on the grafting surfaces depended strongly on the temperature and the low temperature films consisted of two separate layers with the insoluble layer located near the grafting surface. The short-time relaxation of the branches and stems of chains was also investigated. The analysis of the dynamics of the model system shows the influence of the structure of the system on relaxation times of various parameters. Paper presented at the AERC 2005 held on April 21–23, 2005 in Grenoble, France.     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

Multiphase drag reduction: Effect of eliminating slugs

Two-phase pressure drop measurements were taken for air/water mixtures in a 0.052-m diameter horizontal pipe with special focus on the superficial liquid velocity range of 0.03–1.2 m/s at superficial gas velocities of 3.8, 5.2, and 6.6 m/s. It was found that the addition of 400 ppm of sodium dodecyl sulfate (SDS) to the water reduced the pressure drop by 25–40% when compared to equal flow rates without SDS. The pressure drop reduction occurred where the SDS eliminated the occurrence of the intermittent flow present with water. It was also found that the same concentration of SDS had virtually no effect on single phase liquid pressure drop. The pressure drop reduction appears to be due solely to the suppression of intermittent flow patterns.     

On the friction drag reduction mechanism of streamwise wall fluctuations

Understanding how to decrease the friction drag exerted by a fluid on a solid surface is becoming increasingly important to address key societal challenges, such as decreasing the carbon footprint of transport. Well-established techniques are not yet available for friction drag reduction. Direct numerical simulation results obtained by Józsa et al. (2019) previously indicated that a passive compliant wall can decrease friction drag by sustaining the drag reduction mechanism of an active control strategy. The proposed compliant wall is driven by wall shear stress fluctuations and responds with streamwise wall velocity fluctuations. The present study aims to clarify the underlying physical mechanism enabling the drag reduction of these active and passive control techniques. Analysis of turbulence statistics and flow fields reveals that both compliant wall and active control amplify streamwise velocity streaks in the viscous sublayer. By doing so, these control methods counteract dominant spanwise vorticity fluctuations in the near-wall region. The lowered vorticity fluctuations lead to an overall weakening of vortical structures which then mitigates momentum transfer and results in lower friction drag. These results might underpin the further development and practical implementation of these control strategies.     

The influence of the injection system on drag reduction

The influence of the injection system for centerline injected polymer solutions (threads) on drag reduction in a turbulent pipe flow was studied using injectors of different length and grids. Compared with a short injector, the long injector showed a different behavior: the drag reduction was lower and its onset point was shifted to higher Reynolds numbers.The velocity profiles for the polymer-phase and the water-phase were measured simultaneously with a combination of laser-Doppler-velocimetry LDV and laser-induced fluorescence LIE It was found that the analysis of the LDV measurements with respect to the difference in velocity between the polymer-phase and the water-phase can give information about the mixing between both phases. For a Reynolds number of 30000 the difference between the phases is comparatively large for low drag reduction and very small for high drag reduction. The results indicate that the drag reduction achieved by injecting a concentrated polymer solution is mainly caused by a mixing process between polymer and water.     

Direct numerical simulation of a turbulent plane Couette-Poiseuille flow with zero-mean shear

Direct numerical simulations of a turbulent Couette-Poiseuille flow with zero-mean-shear at the moving wall (SL-flow) is performed to examine flow features compared to those for a turbulent pure Poiseuille flow (P-flow). Profiles of the streamwise mean velocity, indicator function and ratio of production to dissipation show that the logarithmic region is significantly elongated for the SL-flow compared to that for the P-flow at a similar Reynolds number. In addition, the magnitudes of the Reynolds stresses are found to be larger in both inner and outer layers for the SL-flow than those for the P-flow. The spanwise spectra of the production term in the turbulent kinetic energy equation are examined to provide a structural basis for explaining the statistical behaviors. In addition, because the growth of the energy-containing motions extends to the outer layer further for the SL-flow due to the presence of a positive mean shear throughout the entire wall layer, the self-similar behavior of the energy balance between the production and transport terms with respect to the self-similar wavenumber is found far from the wall. We also find the increase in the number of uniform momentum zones in the SL-flow, revealing the hierarchical distribution of the energy-containing eddies which are composed of multiple uniform momentum zones. These coherent motions lead to the elongation of the logarithmic region for the SL-flow. Finally, investigation of the turbulent energy transfer process in a spectral domain for the SL-flow demonstrates importance of outer layer very-long structures, and these structures attribute to the energy transport process in an entire flow field.