A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale(SGS) model based on coherent structures and temporal approximate deconvolution(MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation(LES) of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence(FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation(DNS) results. Compared with the LES results using the temporal approximate deconvolution model(TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.     

Subcritical finite-amplitude solutions for plane Couette flow of viscoelastic fluids

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. The results suggest a scenario for weakly turbulent viscoelastic flow which is similar to the one for Newtonian fluids as a function of Reynolds number.     

Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method

We develop a discrete model for multi-component viscoelastic fluids based on the lattice Boltzmann method. The model newly introduces the kinetics of polymers so that viscoelasticity is included. We perform three-dimensional simulations of a Newtonian drop in shear flow of a viscoelastic fluid in order to investigate the validity of the current model. In the investigation, effects of viscoelasticity on deformation and orientation of drops are evaluated. The simulation results are compared with experimental measurements quantitatively, and they show good agreement with each other.     

Direct numerical simulation of the turbulent flows of power-law fluids in a circular pipe

Fully developed turbulent pipe flows of power-law fluids are studied by means of direct numerical simulation. Two series of calculations at generalised Reynolds numbers of approximately 10000 and 20000 were carried out. Five different power law indexes n from 0.4 to 1 were considered. The distributions of components of Reynolds stress tensor, averaged viscosity, viscosity fluctuations, and measures of turbulent anisotropy are presented. The friction coefficient predicted by the simulations is in a good agreement with the correlation obtained from experiment. Flows of power-law fluids exhibit stronger anisotropy of the Reynolds stress tensor compared with the flow of Newtonian fluid. The turbulence anisotropy becomes more significant with the decreasing flow index n. An increase in apparent viscosity away from the wall leads to the damping of the wall-normal velocity pulsations. The suppression of the turbulent energy redistribution between the Reynolds stress tensor components observed in the simulations leads to a strong domination of the axial velocity pulsations. The damping of wall-normal velocity pulsations leads to a reduction of the fluctuating transport of momentum from the core toward the wall, which explains the effect of drag reduction.     

Viscous heating and the stability of newtonian and viscoelastic taylor-couette flows

The effects of viscous heating on the stability of Taylor-Couette flow were investigated through flow visualization experiments for Newtonian and viscoelastic fluids. For highly viscous Newtonian fluids, viscous heating drives a transition to a new, oscillatory mode of instability at a critical Reynolds number significantly below that at which the inertial transition is observed in isothermal flows. The effects of viscous heating may explain the discrepancies between the observed and predicted critical conditions and the symmetry of the disturbance flow for viscoelastic instabilities.     

Dynamics on the laminar-turbulent boundary and the origin of the maximum drag reduction asymptote

Dynamical trajectories on the boundary in state space between laminar and turbulent plane channel flow-edge states-are computed for Newtonian and viscoelastic fluids. Viscoelasticity has a negligible effect on the properties of these solutions, and, at least at a low Reynolds number, their mean velocity profiles correspond closely to experimental observations for polymer solutions in the maximum drag reduction regime. These results confirm the existence of weak turbulence states that cannot be suppressed by polymer additives, explaining the fact that there is an upper limit for polymer-induced drag reduction.     

On applying the extended intrinsic mean spin tensor to modelling the turbulence in non-inertial frames of reference

Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the “extended intrinsic mean spin tensor” for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to modelling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in physics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-ε models. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also applied to the second-moment closure and the large-eddy simulation of turbulence.     

Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations

Direct numerical simulations(DNS) were performed for the forced homogeneous isotropic turbulence(FHIT) with/without polymer additives in order to elaborate the characteristics of the turbulent energy cascading influenced by drag-reducing effects.The finite elastic non-linear extensibility-Peterlin model(FENE-P) was used as the conformation tensor equation for the viscoelastic polymer solution.Detailed analyses of DNS data were carried out in this paper for the turbulence scaling law and the topological dynamics of FHIT as well as the important turbulent parameters,including turbulent kinetic energy spectra,enstrophy and strain,velocity structure function,small-scale intermittency,etc.A natural and straightforward definition for the drag reduction rate was also proposed for the drag-reducing FHIT based on the decrease degree of the turbulent kinetic energy.It was found that the turbulent energy cascading in the FHIT was greatly modified by the drag-reducing polymer additives.The enstrophy and the strain fields in the FHIT of the polymer solution were remarkably weakened as compared with their Newtonian counterparts.The small-scale vortices and the small-scale intermittency were all inhibited by the viscoelastic effects in the FHIT of the polymer solution.However,the scaling law in a fashion of extended self-similarity for the FHIT of the polymer solution,within the presently simulated range of Weissenberg numbers,had no distinct differences compared with that of the Newtonian fluid case.     

Interaction of a Particle‐Laden Gaseous Jet with a Confined Annular Turbulent Flow

A numerical analysis of polydispersed glass particles interacting with a confined turbulent bluff‐body flow was performed by combining the finite‐volume method for the gaseous flow with a mesh‐free Lagrangian approach for the particulate flow. Three turbulence‐closure models, namely the Reynolds‐stress, the standard k‐ϵ, and the nonlinear k‐ϵ models, were first comparatively studied for the single‐phase flow. The second‐moment Reynolds‐stress model was then selected for the prediction of the turbulent gaseous flow in a gas‐particle system, where an improved eddy‐interaction model was used to predict turbulence‐induced particle dispersion. The interaction between the two phases was accounted for through coupling source terms. Numerical predictions of two‐phase mean and fluctuating velocities for particle sizes ranging from 15 to 115 μm were compared with corresponding experimental data. Reasonably good agreement was achieved for the mean properties of both the gaseous and particulate flows.     

Lagrangian dynamics and statistical geometric structure of turbulence

The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.     

Validity of Taylor's dissipation-viscosity independence postulate in variable-viscosity turbulent fluid mixtures

G. I. Taylor's postulate [Proc. R. Soc. A 151, 421 (1935)] that dissipation is independent of viscosity at high Reynolds numbers is the foundation of many single-fluid turbulence theories and closure models. The validity of this key postulate in an important class of flows, turbulent mixtures, is not yet clearly established. We devise a simple numerical experiment of decaying turbulence in a mixture of two fluids of vastly different viscosities to examine dissipation scaling. Initially, the two fluids are segregated, and dissipation is directly proportional to viscosity. As turbulence evolves and fluids mix, the velocity gradients rapidly adapt to the viscosity field, and within one-half eddy turnover time, dissipation-viscosity independence is established. Viscosity-weighted velocity-gradient skewness is shown to be constant, leading to the validity of Taylor's postulate in turbulent mixtures.     

Large-eddy simulations of a forced homogeneous isotropic turbulence with polymer additives

Large-eddy simulations （LES） based on the temporal approximate deconvolution model were performed for a forced homogeneous isotropic turbulence （FHIT） with polymer additives at moderate Taylor Reynolds number. Finitely extensible nonlinear elastic in the Peterlin approximation model was adopted as the constitutive equation for the filtered conformation tensor of the polymer molecules. The LES results were verified through comparisons with the direct numerical simulation results. Using the LES database of the FHIT in the Newtonian fluid and the polymer solution flows, the polymer effects on some important parameters such as strain, vorticity, drag reduction, and so forth were studied. By extracting the vortex structures and exploring the flatness factor through a high-order correlation function of velocity derivative and wavelet analysis, it can be found that the small-scale vortex structures and small-scale intermittency in the FHIT are all inhibited due to the existence of the polymers. The extended self-similarity scaling law in the polymer solution flow shows no apparent difference from that in the Newtonian fluid flow at the currently simulated ranges of Reynolds and Weissenberg numbers.     

圆截面直流道中微粒黏弹性聚焦机理研究

微粒黏弹性聚焦技术近年来受到了广泛的研究重视, 但影响粒子聚焦特性的关键参数调控机理仍不清楚. 基于此目的, 本文量化研究了圆截面直流道中非牛顿流体诱导微粒黏弹性聚焦的行为, 给出了流速和流道长度对粒子聚焦特性的调控机理. 具体而言: 首先, 对比分析不同黏度牛顿流体(水和22 wt%甘油水溶液)和非牛顿流体(8 wt%聚乙烯吡咯烷酮水溶液)中粒子横向迁移行为, 发现非牛顿流体中粒子将在弹性力主导下聚焦至流道中心区域, 而牛顿流体中粒子则在惯性升力主导下迁移形成Segré-Silberberg圆环. 其次, 量化分析粒子尺寸和驱动流速对黏弹性聚焦效果的影响, 发现随着流速的增加, 粒子聚焦效果逐渐变好并最终趋于稳定, 且大粒子较小粒子具有更好的聚焦效果. 最后, 研究粒子沿流道长度的动态聚焦过程, 推导并验证了粒子聚焦所需安全流道长度的数学模型, 发现大粒子聚焦所需安全流道长度显著短于小粒子. 上述研究结果对于提升粒子黏弹性聚焦机理和过程的理解, 实现微粒聚焦特性的灵活控制具有非常重要的意义.     

Rotation effect on near-wall turbulence statistics and flow structures

Turbulent flow in an axially rotating pipe, involving complicated physical mecha- nism of turbulence, is a typical problem for the study of rotating turbulent flow. The pipe rotation induces two effects on the flow. One is the stabilizing effect due to the centrifu- gal and Coriolis forces, which accounts for the relaminarization of the turbulence[1—3] and the reduction of the friction coefficient at the pipe wall. The behavior is also related to the wall streaks inclining to the azimuthal di…     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

Non-Steady Wall-Bounded Flows of Viscoelastic Fluids Under Periodic Forcing

The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy’s law is obtained in the frequency domain and an explicit expression for the dependence of the dynamic permeability on the fluid parameters and forcing frequency is derived. Previous results in both viscoelastic and Newtonian fluids are here shown to be particular cases of our results. On the basis of our calculations, a possible explanation for the observed damping of local dynamic response as the forcing frequency increases is given. Good fitting with recent experimental studies of wave propagation in viscoelastic media is here exhibited. Sound wave propagation in viscoelastic media flowing inside straight pipes is investigated. In particular, we obtain the local dynamic response for weakly compressible flows.     

Direct numerical simulations of second-order Stokes wave driven smooth-walled oscillatory channel: investigation of net current formation

In wall-bounded time-periodic flows, nonlinearity, associated with higher harmonic term(s) in velocity and/or acceleration outside the boundary layer, can significantly change the wall turbulence compared with that in the linear Stokes Boundary Layer. A significant feature of a nonlinear wall-bounded turbulent time-periodic flow is the formation of a net current which has not yet been mechanistically explained. This study investigates the effects of asymmetric velocity outside the boundary layer on wall turbulence and net current formation through Direct Numerical Simulations of a smooth-walled planar channel driven by the Second-order Stokes Wave. Simulation results suggest that net current characteristics depend on whether developed turbulence is present. When turbulence is developed, asymmetric viscous length scale is found to be the primary reason of the net current whereby a vertical offset between negative and positive Reynolds shear stress profiles, associated with forward and reverse flows, respectively, is created in a cycle. After averaging over a cycle, residual Reynolds shear stress, which drives the net current, is observed to be within the offset layer.     

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper,we present a direct numerical simulation(DNS) of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number(Re = 1) in a three-dimensional straight channel flow for the first time,using the Giesekus constitutive model for the fluid.In order to generate and maintain the turbulent fluid motion in the straight channel,a sinusoidal force term is added to the momentum equation,and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field.Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS.The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.     

Effect of viscoelasticity on dynamics and stability in roll coatings

Flow behaviors and coating windows of Newtonian and viscoelastic liquids in forward and reverse roll coating processes have been examined. Viscoelastic liquids considered in this study, as a Boger fluid, have different elastic or extensional properties but almost same shear viscosity as Newtonian case. Coating thickness in both flows strongly depends on the viscoelasticity in polymer solutions as well as operating conditions such as capillary number and gap size between two rolls. Also, uniform coating windows are drastically reduced for the viscoelastic liquids. These results evidently support that a small amount of polymer in coating liquids play an indispensable role in altering dynamics and stability of coating processes.     

A theoretical model of turbulent fiber suspension and its application to the channel flow

A theoretical model of turbulent fiber suspension is developed by deriving the equations of Reynolds averaged Navier-Stokes,turbulence kinetic energy and turbulence dissipation rate with the additional term of fibers.In order to close the above equations,the equation of probability distribution function for mean fiber orientation is also derived.The theoretical model is applied to the turbulent channel flow and the corresponding equations are solved numerically.The numerical results are verified by comparisons with the experimental ones.The effects of Reynolds number,fiber concentration and fiber aspect-ratio on the velocity profile,turbulent kinetic energy and turbulent dissipation rate are analyzed.Based on the numerical data,the expression for the velocity profile in the turbulent fiber suspension channel flow,which includes the effect of Reynolds number,fiber concentration and aspect-ratio,is proposed.