Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

On mean flow universality of turbulent wall flows. II. Asymptotic flow analysis

Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.     

Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data

Tensorial decompositions and projections are used to study the performance of algebraic non-linear models and predict the anisotropy of the Reynolds stresses. Direct numerical simulation (DNS) data for plane channel flows at friction Reynolds number (Re_τ = 180, 395, 590, 1000), and for the boundary layer using both DNS (Re_τ = 359, 830, 1271) and experimental data (Re_τ = 2680, 3891, 4941, 7164) are used to build and evaluate the models. These data are projected into tensorial basis formed from the symmetric part of mean velocity gradient and non-persistence-of-straining tensor. Six models are proposed and their performances are investigated. The scalar coefficients for these six different levels of approximations of the Reynolds stress tensor are derived, and made dimensionless using the classical turbulent scales, the kinetic turbulent energy (κ) and its dissipation rate (ε). The dimensionless coefficients are then coupled with classical wall functions. One model is selected by comparing the predicted Reynolds stress components with experimental and DNS data, presenting a good prediction for the shear and normal Reynolds stresses.     

Large-eddy simulations of temporally accelerating turbulent channel flow

The unsteady turbulent channel flow subject to the temporal acceleration is considered in this study. Large-eddy simulations were performed to study the response of the turbulent flow to the temporal acceleration. The simulations were started with the fully developed turbulent channel flow at an initial Reynolds number of Re₀ = 3500 (based on the channel half-height and the bulk-mean velocity), and then a constant temporal acceleration was applied. During the acceleration, the Reynolds number of the channel flow increased linearly from the initial Reynolds number to the final Reynolds number of Re₁ = 22,600. The effect of grid resolution, domain size, time step size on the simulation results was assessed in a preliminary study using simulations of the accelerating turbulent flow as well as simulations of the steady turbulent channel flow at various Reynolds numbers. Simulation parameters were carefully chosen from the preliminary study to ascertain the accuracy of the simulation. From the accelerating turbulent flow simulations, the delays in the response of various flow properties to the temporal acceleration were measured. The distinctive features of the delays responsible for turbulence production, energy redistribution, and radial propagation were identified. Detailed turbulence statistics including the wall shear stress response during the acceleration were examined. The results reveal the changes in the near-wall structures during the acceleration. A self-sustaining mechanism of turbulence is proposed to explain the response of the turbulent flow to the temporal acceleration. Although the overall flow characteristics are similar between the channel and pipe flows, some differences were observed between the two flows.     

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

Strengthened opposition control for skin-friction reduction in wall-bounded turbulent flows

An opposition control scheme with strengthened control input is proposed and tested in turbulent channel flows at friction Reynolds number Re_τ = 180 by direct numerical simulations. When the detection plane is located at less than 20 wall units, the drag reduction rate can be greatly enhanced by increasing the control amplitude parameter. The maximum drag reduction rate achieved in the present study is around 33%, which is much higher than the best value of 25% reported in literature. The strengthened control can be more efficient to attain a given drag reduction rate. Based on the total shear stress at the virtual wall established between the real wall and the detection plane by the control, a new friction velocity is proposed and the corresponding coordinate transform is made. Scaled by the proposed friction velocity, the wall-normal velocity fluctuation and the Reynolds shear stress of the controlled flows are collapsed well with those of the uncontrolled flow in the new coordinate. Based on the similarity, a relation between drag reduction rate and the effectiveness of the virtual wall is deduced, which disclosed that the elevation and residual Reynolds shear stress at the virtual wall are the key parameters to determine the drag reduction rate. The conclusion are also validated at Re_τ = 395 and 590. The decrease of the drag reduction rate with the increase of the Reynolds number is attributed to the enhanced residual Reynolds shear stress at the virtual wall.     

Intermittency,Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.     

Large-eddy simulation of plane channel flow with Vreman's model

In this paper, large-eddy simulations of Vreman's model (VM) have been carried out to investigate its performances in a temporal transitional channel flow and in high Reynolds number turbulent channel flows. As a preliminary work, it is found that cubic root of the cell volume is the best choice of filter width for both VM and dynamic VM based on Germano identity (DVM), according to comparative studies and a-posteriori analyses at Re_τ = 590. VM and DVM are then used to simulate the temporal laminar–turbulent transitional channel flow, and the results turn out that VM and DVM are capable to simulate this temporal transient flow. In simulating high Reynolds number turbulent channel flows with a relatively coarse grid resolution, DVM itself shares the same weakness as the dynamic Smagorinsky model, while it can successfully predict the mean velocity profile and skin friction coefficient when it is coupled with the constrained large eddy simulation methodology. The coupling highly promotes the capability of Vreman's model, offering a new promising approach to simulate high Reynolds number wall-bounded turbulent flows.     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.     

圆形射流中心线上小尺度湍流的统计特性及其受高频噪声的影响

本文采用热线风速仪测量了出口雷诺数为Re (≡ U_jd/ν) = 20100的圆形射流的中心线轴向速度,其中U_j为动量平均出口速度,d为喷嘴出口直径,ν为运动黏性系数.在有效去除热线测量数据中的高频噪声后,作者对射流中心线上小尺度湍流统计量的变化规律进行了系统的分析.研究发现,射流在经过一定距离的发展后,其小尺度统计量逐渐进入自相似状态,湍动能平均耗散率ε随下游距离的增加以指数形 关键词： 恒温热线 圆形湍射流 耗散率 小尺度     

Three measuring techniques for assessing the mean wall skin friction in wall-bounded flows

The present paper aims at evaluating the mean wall skin friction data in laminar and turbulent boundary layer flows obtained from two optical and one thermal measuring techniques, namely, laser-Doppler anemometry (LDA), oil-film interferometry (OFI), and surface hot-film anemometry (SHFA), respectively. A comparison among the three techniques is presented, indicating close agreement in the mean wall skin friction data obtained, directly, from both the OFI and the LDA near-wall mean velocity profiles. On the other hand, the SHFA, markedly, over estimates the mean wall skin friction by 3.5–11.7% when compared with both the LDA and the OFI data, depending on the thermal conductivity of the substrate and glue material, probe calibration, probe contamination, temperature drift and Reynolds number. Satisfactory agreement, however, is observed among all three measuring techniques at higher Reynolds numbers, Re _x >10⁶, and within ±5% with empirical relations extracted from the literature. In addition, accurate velocity data within the inertial sublayer obtained using the LDA supports the applicability of the Clauser method to evaluate the wall skin friction when appropriate values for the constants of the logarithmic line are utilized.     

雷诺数对圆形渐缩喷嘴湍流射流的影响

本文研究雷诺数(Re)对圆形渐缩喷嘴湍流射流的影响.实验在射流出口雷诺数为 Re = 4050—20100 的范围内进行,分别测量了射流出口、中心线的平均及湍流流场以及部分径向剖面速度分布.所有测量均采用单热线恒温热线风速仪进行高频采样,所测流场范围在轴向上为 0—30d(这里d为射流出口直径).虽然出口速度分布均为"平顶帽"形,但测量结果依然反映出Re对射流出口以及下游流场有强烈的影响.当Re小于临界值(～10000)时 关键词： 雷诺数 圆形射流 热线风速仪     

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine the spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analysed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation and velocity gradient invariants Q and R and their joint spatial distributions, using data from a direct numerical simulation of isotropic turbulence at Re_λ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus, a geometric characterisation in terms of these sets’ correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behaviour. Nevertheless, the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow.     

Large-scale forcing with less communication in finite-difference simulations of stationary isotropic turbulence

This study proposes a new forcing scheme suitable for massively-parallel finite-difference simulations of stationary isotropic turbulence. The proposed forcing scheme, named reduced-communication forcing (RCF), is based on the same idea as the conventional large-scale forcing scheme, but requires much less data communication, leading to a high parallel efficiency. It has been confirmed that the RCF scheme works intrinsically in the same manner as the conventional large-scale forcing scheme. Comparisons have revealed that a fourth-order finite-difference model run in combination with the RCF scheme (FDM-RCF) is as good as a spectral model, while requiring less computational costs. For the range 80 < Re_λ < 540, where Re_λ is the Taylor microscale-based Reynolds number, large computations using the FDM-RCF scheme show that the Reynolds dependences of skewness and flatness factors have similar power-laws as found in previous studies.     

The effect of subgrid-scale models on the entrainment of a passive scalar in a turbulent planar jet

Classical large-eddy simulation (LES) modelling assumes that the passive subgrid-scale (SGS) models do not influence large-scale quantities, even though there is now ample evidence of this in many flows. In this work, direct numerical simulation (DNS) and large-eddy simulations of turbulent planar jets at Reynolds number Re_H = 6000 including a passive scalar with Schmidt number Sc = 0.7 are used to study the effect of several SGS models on the flow integral quantities e.g. velocity and scalar jet spreading rates. The models analysed are theSmagorinsky, dynamic Smagorinsky, shear-improved Smagorinsky and the Vreman. Detailed analysis of the thin layer bounding the turbulent and non-turbulent regions – the so-called turbulent/non-turbulent interface (TNTI) – shows that this region raises new challenges for classical SGS models. The small scales are far from equilibrium and contain a high fraction of the total kinetic energy and scalar variance, but the situation is worse for the scalar than for the velocity field. Both a-priori and a-posteriori (LES) tests show that the dynamic Smagorinsky and shear-improved models give the best results because they are able to accurately capture the correct statistics of the velocity and passive scalar fluctuations near the TNTI. The results also suggest the existence of a critical resolution Δ_x, of the order of the Taylor scale λ, which is needed for the scalar field. Coarser passive scalar LES i.e. Δ_x ≥ λ results in dramatic changes in the integral quantities. This fact is explained by the dynamics of the small scales near the jet interface.     

On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

ABSTRACT

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry.     

Simulations of turbulent asymptotic suction boundary layers

A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) of Re = 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective of Re and domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasing Re, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective of Re. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically high Re. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasing Re. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which – in accordance with the results from the temporal simulation – indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times.     

Reynolds number and scale dependence of turbulent eddy decorrelation

The temporal decay of the Lagrangian velocity correlation function of isotropic, homogeneous turbulence is calculated by following particle trajectories and via continued fraction representation. We report on the eddy size as well as on the Reynolds number dependence. Most remarkably, the exponential relaxation approximation for the correlation function turns out to be insufficient. Memory effects result in a considerable enhancement: the decay is more than an order of magnitude faster. The very high Reynolds number turbulent flow fields are generated by a reduced wave vector set approximation of the Navier-Stokes dynamics, but for smaller Re the conclusions are confirmed by direct numerical simulations. Two orders of magnitude of the Taylor-Reynolds number are covered, up to Re _λ ? 10⁴.     

High-order incompressible large-eddy simulation of fully inhomogeneous turbulent flows

The subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the turbulent flow in an Re = 12,000 lid-driven cubical cavity by comparison to the direct numerical simulation (DNS) data of Leriche and Gavrilakis [Phys. Fluids 12 (2000) 1363]. This appears to be the first test of this class of model to flows without any homogeneous flow directions, which is typical of flows in complex geometries. Additional LES predictions at Re = 18,000 and Re = 22,000 are compared to the DNS data of Leriche [J. Sci. Comp. 27 (2006)]. The new LES framework yielded excellent agreement for both the mean velocity and Reynolds stress profiles and matches DNS data better than the more traditional Smagorinsky-based SGS models.     

POD-based wall boundary conditions for the numerical simulation of turbulent channel flows

Simulation of turbulent wall-bounded flows requires a high spatial resolution in the wall region, which limits the range of Reynolds numbers which can be effectively reached. In previous work, we proposed proper orthogonal decomposition (POD) based wall boundary conditions to bypass the simulation of the inner wall region. Tests were carried out for direct numerical simulation at a low Reynolds number Re_τ = 180. The boundary condition is based on the POD spatial eigenfunctions which are determined a priori in the full channel. It consists of a three-component velocity field on the plane y⁺ = 50 which is reconstructed at each instant from a combination of selected eigenfunctions. The coefficients of the combination are estimated from the simulation in the reduced domain using the threshold-based reconstruction method described in Podvin et al. The study is now extended to large-eddy simulation at higher Reynolds numbers Re_τ = 295 and Re_τ = 590. Two versions of the reconstruction method are considered. In the first version, both the phases and the moduli of the coefficients are allowed to vary. In the second version, only the phases are adjusted. We find that the latter method is associated with improved statistics and is relatively robust with respect to the reconstruction threshold. However, it is sensitive to the details of the numerical simulation, unlike the former method, which is associated with less accurate statistics and is more dependent on the reconstruction threshold.