Drag-reduced Turbulent Channel Flow Research Articles

Dissimilar turbulent momentum and heat transfer associated with viscoelastic vibration in channel flow

This experimental study on the momentum and heat transfer in drag-reducing turbulent channel flow of surfactant solution, i.e., viscoelastic fluid, has revealed a viscoelastic vibration (VEV) as a novel type of ordered turbulent motion in the wall vicinity where the elastic energy is transformed into turbulent kinetic energy. The VEV is a wave-like motion of low-frequency modes in the streamwise direction and causes zero average Reynolds shear stress. However, thermal diffusion occurs continuously due to the movement of a fluid lump owing to the VEV via the additional action of pressure.

Wall-attached structures in a drag-reduced turbulent channel flow

We explore wall-attached structures in a drag-reduced turbulent channel flow with the Navier slip boundary condition. Three-dimensional coherent structures of the streamwise velocity fluctuations (u) are examined in an effort to assess the influence of wall-attached u structures on drag reduction. We extract the u clusters from the direct numerical simulation (DNS) data; the DNS data for the no-slip condition are included for comparison. The wall-attached structures, which are physically adhered to the wall, in the logarithmic region are self-similar with their height and contribute to the presence of logarithmic behaviour. The influence of the streamwise slip on wall-attached structures is limited up to the lower bound of the logarithmic region. Although wall-attached self-similar structures (WASS) slide at the wall, the formation and hierarchy of WASS are sustained. Weakened mean shear by the streamwise slip results in a diminution in the population density of wall-attached structures within the buffer layer, leading to sparse population of WASS. In contrast, the space occupied by WASS in the fluid domain increases. The streamwise slip induces long tails in the near-wall part of WASS, reminiscent of the footprints of large-scale motions. Both a decrease in the population density of WASS and a reduction in the density of skin friction of WASS are responsible for the overall drag reduction.

Deep Learning for Viscoelastic Fluids and Turbulent Diffusion

This study aims to predict the conformation stress field of viscoelastic, drag-reducing turbulent channel flow and to estimate the passive-scalar diffusion in Newtonian turbulent channel flow. In general, understanding of the nature of wall turbulence and predicting of turbulent phenomena have been based on statistical features, but here we would discuss the possibility of extracting non-trivial features from instantaneous fields with the help of machine learning. If we can extract features unique to the instantaneous field, which are lost when equalized by statistical processing, it could be possible to predict the interior (intrinsic physics) and exterior (initial and/or boundary conditions) from limited spatial, temporal information. Using deep learning of CNN such as U-Net, we demonstrated the reproduction of the conformation stress field from the instantaneous velocity field and the estimation of the diffusion point source location from the downstream concentration distribution based on instantaneous local information. We have successfully demonstrated the usefulness of instantaneous local information, which might be lost in statistics, and confirmed the possibility of using deep learning to construct a viscoelastic-fluid surrogate model and a diffusion-source estimation tool.

Drag reduction and transient growth of a streak in a spanwise wall-oscillatory turbulent channel flow

The drag-reduction mechanism of spanwise wall oscillation in a turbulent channel was investigated as an extension of the work of Yakeno et al. [“Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation,” Phys. Fluids 26, 085109 (2014)] at a low Reynolds number. Flow instability was evaluated by computing the transient energy growth under an oscillating base flow which governed the generation of a near-wall streak structure. Oscillation affected the optimal energy growth of the streak mode, whose characteristics were reasonably consistent with those in a direct numerical simulation. The optimal growth of the tilted-streak mode was enhanced with a thicker Stokes layer under longer oscillation periods, while that of the original streak mode was weakened. The transition of the optimal perturbation under oscillation showed that the spanwise Stokes layer shear contributed considerably more to modification than the spanwise velocity did. A new drag-reduction performance estimation model was suggested using the acceleration of the spanwise velocity shear based on streak formation modification under oscillation, which restrains energy transfer to streamwise vortices via a tilting delay due to oscillation. This simple model worked well even under long oscillation periods and was theoretically consistent with that of Yakeno et al. based on the change in the Reynolds shear stress due to a streamwise vortex at a low Reynolds number.

A direct comparison of turbulence in drag-reduced flows of polymers and surfactants

Abstract

Energy balance in lubricated drag-reduced turbulent channel flow

Abstract

Geometric decomposition of the conformation tensor in viscoelastic turbulence

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Effects of polymer stresses on analogy between momentum and heat transfer in drag-reduced turbulent channel flow

The effects of polymer stresses on the analogy between momentum and heat transfer are examined by using a direct numerical simulation (DNS) of viscoelastic turbulent channel flows using a constant heat flux boundary condition. The Reynolds number based on the friction velocity and channel half height is 125, and the Prandtl number is 5. The polymer stress is modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (DR) (52%) cases are examined. The Colburn analogy is found to be inapplicable for viscoelastic turbulent flows, suggesting dissimilarity between the momentum and heat transfer at the macroscopic coefficient level. The mean temperature profile also shows behaviour different from the mean velocity profile in drag-reduced flows. In contrast to the dissimilarity in the mean profiles, the turbulent Prandtl number Prt predicted by the DNS is near unity. This implies that turbulent heat transfer is still analogous t...

Numerical simulation of drag-reducing channel flow by using bead-spring chain model

Numerical simulations of the drag-reducing turbulent channel flow caused by polymer addition are performed. A bead-spring chain model is employed as a model of polymer aggregation. The model consists of beads and springs to represent the polymer dynamics. Three drag-reduction cases are studied with different spring constants that correspond to the relaxation time of the polymer. The energy budget is mainly focused upon to discuss the drag-reduction mechanism. Our results show that a decreasing pressure-strain correlation mainly contributes to strengthening the anisotropy of the turbulence. Furthermore, energy transport by the polymer models attenuates the turbulence. These viscoelastic effects on the drag-reducing flow are intensified with decreasing spring constant. By visualizing the flow field, it is found that this polymer energy transport is related to the orientation of the polymer.

On the pressure-strain correlation in fibrous drag-reduced turbulent channel flow

The pressure-strain correlation is studied in detail using the direct numerical simulation data obtained by a direct Monte-Carlo simulation of turbulent drag reduction in a channel flow caused by rigid fiber additives. This is used to analyze the energy redistribution process and to explain the pronounced anisotropy of the drag-reduced flow as compared to its Newtonian counterpart. Moreover, the change in pressure fluctuations and strain-rate fluctuations are studied to explain the modifications in the pressure-strain term. It is found that the reduction in strain-rate fluctuations is mainly responsible for the change in the pressure-strain term and the effect of pressure fluctuations is modest.

On the structure of vorticity and near-wall partial enstrophy in fibrous drag-reduced turbulent channel flow

The structure of the vorticity field and the near-wall partial enstrophy in a fibrous drag-reduced channel flow at Reτ=180 with about 16% percentage drag reduction are studied and compared to the Newtonian flow by means of direct numerical simulation. The vorticity fluctuations as well as the distribution of the vorticity tilting angle is analyzed in detail. Moreover, the budget of near-wall partial enstrophy is investigated. It is found that in the drag-reduced flow, the tilting angle of vorticity reaches to the 45° more away from the wall than the Newtonian counterpart. Also, the decrease in the production term of vorticity fluctuations in the fibrous flow up to the wall distance z+=140 is attributed to the decrease in the streamwise vorticity fluctuations and the decrease in the correlation coefficient between the streamwise and wall-normal vorticity fluctuations.

Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation

The conditional averaging technique is applied to quasi-streamwise vortices in order to clarify the impact of their structural modification on the resultant drag reduction effect in a turbulent channel flow subjected to spanwise harmonic wall oscillation. The quantitative contributions of quadrant Reynolds shear stresses induced by the quasi-streamwise vortices are calculated on the basis of the Fukagata-Iwamoto-Kasagi identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. It is found that the Q2 event characterized by upwelling of low-speed fluid away from the wall governs the skin friction drag reduction at relatively small oscillation periods, whereas the Q4 event characterized by downwelling of high speed fluid toward the wall slightly contributes to drag reduction at small oscillation periods, and then to drag increase significantly with increasing the oscillation period. Detailed investigation of the conditionally averaged velocity field around the detected vortices reveals that the suppression of Q2 occurs at a certain phase when the wall motion is applied so as to oppose the rotation of near-wall streamwise vortices, whereas the enhancement of Q4 at a large oscillation period is caused by spanwise tilting of coherent structures due to the alternating spanwise shear induced by spanwise wall oscillation. Based on these findings, we develop a new predictive correlation for drag reduction effect applicable to a wide range of oscillation periods and amplitudes.

Experimental investigation of polymer diffusion in the drag-reduced turbulent channel flow of inhomogeneous solution

Spatial polymer diffusion in the drag-reduced turbulent channel flow of an inhomogeneous polymer solution was investigated by simultaneously measuring velocity and concentration fields using particle imaging velocimetry and planar laser-induced fluorescence techniques. The polymer solution was dosed into the turbulent channel flow from the surface of one-side of the channel wall. The Reynolds number (based on channel height, bulk velocity and solvent viscosity) was set as 4.0×104 and the weight concentrations of dosed polymer solution were set to 25, 50 and 100ppm. The measurements were obtained in the streamwise wall-normal (x–y) plane at three streamwise positions along the dosing wall. The detailed statistical analyses consisting of concentration distribution, turbulence modification, turbulent mass flux, and eddy diffusivities of momentum and of mass are presented. The results show that the polymer diffusion, which has a close relationship with the local polymer concentration and drag reduction in the drag-reduced turbulent channel flow, is suppressed due to the inhibited turbulence other than the diffusion of passive scalar in ordinary turbulence. Two characteristic regions exist in the near-wall region according to the diffusion characteristics and altered motions in the wall-normal direction. The wall-normal turbulent fluxes that control the transport of mass are reduced significantly in the near-wall region for the drag-reduced flow when compared with the case of dosing water. With the increase of local polymer concentration in the “effective position”, the corresponding drag reduction rate (DR) increases. The turbulent Schmidt number (ScT), which represents the relative intensities of the eddy diffusivities of momentum and of mass, is also found to increase with increasing DR. The mean value of ScT for the drag-reduced flow can rise to 2.9, while it is 1.2 for the case of dosing water in the present measurements.

0319 粘弾性流体乱流おける低レイノルズ数型k-ε モデルの改良(OS3-4 流れの抵抗低減,OS3 流れの抵抗低減)

We propose a modified low-Reynolds-number k-ε turbulence model, in which anisotropy of the Reynolds normal stresses is considered, for viscoelastic fluids and have tested it to predict the drag-reduced turbulent channel flow. In order to obtain the constitutive stresses more accurately, we solved numerically the averaged constitutive equation based on the Giesekus model. This equation includes several terms that pertain to the correlation between velocity and constitutive-stress fluctuations and require to be modeled. We employ a model, in which the Reynolds stress and the viscoelastic stress were used to estimate the correlation terms, and hence it is important to predict the Reynolds normal stress precisely. In this study, we propose an algebraic equation to model the anisotropic Reynolds normal stresses using a damping function of the eddy viscosity. The present proposal allows the constitutive stresses to be predicted well.

0321 スパン方向進行波状壁を有する抵抗低減チャネル乱流のLES(OS3-4 流れの抵抗低減,OS3 流れの抵抗低減)

0321 スパン方向進行波状壁を有する抵抗低減チャネル乱流のLES(OS3-4 流れの抵抗低減,OS3 流れの抵抗低減)

Comparison of heat-transfer reduction in drag-reduced turbulent channel flows with different fluid and thermal boundary conditions

Direct numerical simulations of drag-reduced viscoelastic turbulent channel flow with heat transfer were carried out for four kinds of rheologically different fluids, that is, with different values of Weissenberg number and viscosity ratio. Two different thermal boundary conditions were considered. We present the budget of temperature variance and the relationship between the Heat-Transfer Reduction (HTR) and the Drag Reduction (DR) for each rheologically-different fluid. A case with a low viscosity ratio was found to give rise to high DR, with relatively low HTR compared with that obtained with a high Weissenberg number, suggesting dissimilarity between the heat and momentum transports.

DNS study on viscoelastic effect in drag-reduced turbulent channel flow

The effect of viscoelastic contribution on wall-bounded turbulent flow of drag-reducing surfactant solution is investigated through direct numerical simulations (DNS). A series of DNS on turbulent channel flow is performed for different rheological properties at two different Reynolds numbers. It is found that high drag reduction is achieved by suppressing the turbulent contribution for the high Weissenberg number, and/or by decreasing the viscosity ratio and the effective viscosity. A highly drag-reduced turbulent flow at a high Reynolds number is mainly caused by the viscoelastic effect in the elastic layer, whereas the outer layer flow hardly affects the drag reduction. Moreover, we focus on the viscoelastic contribution term in the budget of Reynolds stress and its relation to the local flow pattern. It is shown that in the near-wall region of the highly drag-reduced flow a positive work done by viscoelastic stress is closely associated with vortex stretching that produces turbulent kinetic energy from stored elastic energy, whereas a negative one causes vortex compression.

Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

Direct numerical simulation of the drag-reducing turbulent boundary layer of viscoelastic fluid

Direct numerical simulation of a zero-pressure gradient drag-reducing turbulent boundary layer of homogeneous viscoelastic fluids was performed using constitutive equation models such as the Oldroyd-B and Giesekus models. Mean velocity profiles and turbulence statistics at the different streamwise locations were discussed using both inner and outer scaling. The maximum drag reduction ratio for the Oldroyd-B model, which has the higher elongational viscosity, is larger than for the Giesekus model. The distinct difference in turbulence statistics near the wall between the Oldroyd-B model and Newtonian fluid is observed, as reported in the drag-reducing turbulent channel flow, while in the outer region, distributions of turbulence statistics for the Oldroyd-B model with a drag reduction ratio of about 40% are similar to those for Newtonian fluid. The production term for the turbulent boundary layer does not correspond to the amount of drag reduction, which is consistent with the fact that the streamwise turbulence intensity profile is not a direct indication of the drag reduction. The contribution of the advection term to the budget of streamwise Reynolds normal stress, which does not appear for the turbulent channel flow, is not negligible near the wall for the Oldroyd-B model. For the Oldroyd-B model with a maximum drag reduction ratio of 42%, we can see that quasi-streamwise vortices are weakened and become larger in the streamwise direction, compared to Newtonian fluid. On the other hand, quasi-streamwise vortices for the Giesekus model with a maximum drag reduction ratio of 16% are slightly larger than those for Newtonian fluid. These modifications of near-wall coherent structures are explained by the profile of the trace of mean viscoelastic stress and the elastic energy theory presented by Min et al. [J. Fluid Mech. 486, 213 (2003)] for the drag-reducing turbulent channel flow.

Investigation of turbulence structures in a drag-reduced turbulent channel flow with surfactant additive by stereoscopic particle image velocimetry

In the present study, we employed stereoscopic particle image velocimetry (PIV) to investigate the characteristics of turbulence structures in a drag-reduced turbulent channel flow with addition of surfactant. The tested drag-reducing fluid was a CTAC/NaSal/Water (CTAC: cetyltrimethyl ammonium chloride; NaSal: sodium salicylate) system at 25°C. The weight concentration of CTAC was 30 ppm. Stereoscopic PIV measurement was performed for a water flow (Re=1.1×104) and a CTAC solution flow (Re=1.5×104 with 54% drag reduction) in both the streamwise–spanwise and wall-normal-spanwise planes, respectively. The three-dimensionality of hairpin vortex structures in the near-wall region for wall-bounded turbulent flow was reproduced by conditionally averaging the stereoscopic two-dimensional-three-component velocity fields. A series of wall-normal vortex cores were found to align with the near-wall low-speed streaks with opposite vorticity signals at both sides of the streaks and with the vorticity decreased on average by about one order of magnitude in CTAC solution flow compared with water flow; the spanwise spacing between the near-wall low-speed streaks in the solution flow is increased by about 46%. The streamwise vorticity of the vortex cores appearing in the wall-normal-spanwise plane was also decreased by the use of drag-reducing surfactant additives.