Mixing of a passive scalar across a thin shearless layer: concentration of intermittency on the sides of the turbulent interface

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylor’s microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (?5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations.     

Conserved scalar mixing in a confined-opposed-jets flow

The focus of this paper is on the mixing of a conserved passive scalar for Sc = 1 (Sc is the Schmidt number) in axisymmetric turbulence for which the initial injections of turbulent kinetic energy and scalar variance are similar. Two confined-opposed-jets (COJ) are experimentally studied through simultaneous PIV (particle image velocimetry) and PLIF (planar laser induced fluorescence) measurements, for different flow regimes. One-point transport equation for the scalar variance is assessed through experimental data, along the common axis of the two opposed jets, and different physical phenomena are revealed (production, diffusion, dissipation). The production of scalar variance is equilibrated by the diffusion term (～75%) and the mean dissipation of the scalar variance (～25%). To further assess the scalar behaviour at each scale in this anisotropic, but axisymmetric, flow, a scale-by-scale scalar variance budget equation is derived for axisymmetric turbulence. This equation reduces to Yaglom's 4/3 law, under additional restrictions. The equation is assessed through experimental data, in the impingement region between the two COJ. In particular, the anisotropic energy transfer along different directions is quantified. It is shown that for scales smaller than the size of the central region, Δ, the cascade of the scalar variance is completely inhibited, independently of the particular direction. For scales larger than Δ, the apparent aspect of the energy transfer is that of an inverse cascade, with positive values of the scalar variance transfer. Nonetheless, inhomogeneity of the flow and mixing at those scales is directly responsible for these positive values.     

Experimental study of velocity-scalar filtered joint density function for LES of turbulent combustion

The velocity-scalar filtered joint density function (FJDF) used in large eddy simulation (LES) of turbulent combustion is experimentally studied. Measurements are made in the fully developed region of an axisymmetric turbulent jet using an array consisting of three X-wires and resistance-wire temperature sensors. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor’s hypothesis, respectively. The means of the FJDF conditional on the subgrid-scale (SGS) turbulent kinetic energy and the SGS scalar variance at a given location range from close to joint normal to bimodal with the peaks separated in both velocity and scalar spaces, which correspond to qualitatively different mixing regimes. For close to joint normal FJDFs, the SGS fields are well mixed. For bimodal FJDFs, the conditionally filtered scalar diffusion and dissipation strongly depend on the SGS velocity and scalar, consistent with a combination of diffusion layers and plane strain in the SGS fields, which is similar to the counter-flow model for laminar flamelets. The results suggest that in LES, both mixing regimes could potentially be modeled accurately. The velocity field affects the SGS variance and the filtered scalar dissipation rate primarily by changing the degree of nonequilibrium of the SGS scalar and the SGS time scale, respectively. This study further demonstrates the importance of including velocity in mixing models.     

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.     

A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.     

Scalar dissipation rates in isothermal and reactive turbulent opposed-jets: 1-D-Raman/Rayleigh experiments supported by LES

Isothermal and reactive turbulent opposed flows are presented, which are appropriate to test the applicability and performance of models for turbulence, mixing, chemical reaction, and turbulence-chemistry interaction. Transient flow and scalar fields are measured using laser Doppler velocimetry and one-dimensionally resolved Raman/Rayleigh spectroscopy. Aside of statistical moments of temperature, mean species, and velocity components, scalar dissipation rate across the mixing and reaction layer is determined on a single-shot base. Using large eddy simulation in connection with a steady flamelet model, it is shown how numerical data can serve to estimate the influence of experimental noise upon a measured quantity, such as scalar dissipation. As a key result, it is shown that an increase in scalar rate of dissipation by chemical reactions is caused by a significant increase in the mixture fraction diffusivity, which outweighs the decrease in mixture fraction gradients. In mixture fraction space, local maxima of scalar dissipation rate are found on the rich side, which cannot be correctly reproduced by the steady flamelet model assuming equal species diffusivity. Furthermore, the impact of experimental noise on conditional probability density functions of scalar dissipation rate is shown (exemplary) to lead to erroneous conclusions from experimental data.     

Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity(the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for singleparticle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time". Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.     

Decaying turbulence: What happens when the correlation length varies spatially in two adjacent zones

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where the turbulent kinetic energy is initially uniform and leave them to interact and evolve in time. The different length scales produce different decay rates in the two regions. Since the smaller-scale region decays faster, a transient turbulent energy gradient is generated at the interface between the two regions. The transient is characterized by three phases in which the kinetic energy gradient across the interface grows, peaks and then slowly decays. The transient lifetime is almost proportional to the initial ratio of the correlation lengths. The direct numerical simulations also show that the interface width grows in time. The velocity moments inside this interaction zone are seen to depart from their initial isotropic values and, with a certain lag, the anisotropy is seen to spread to small scales. The longitudinal derivative moments also become anisotropic after a few eddy turnover times. This anisotropic behaviour is different from that observed in sheared homogeneous turbulent flows, where high transverse derivative moments are generated, but longitudinal moments almost maintain the isotropic turbulence values. Apart from the behaviour of the energy gradient transients, the results also show the timescaling of the interface diffusion width, and data on the anisotropy of the large and small scales, observed through one-point statistics determined inside the intermittency sublayer, which is associated with the interaction zone.     

3维Mortar谱元法模拟Kelvin-Helmhtz不稳定性混合层

采用Mortar谱元法和多处理器并行计算技术模拟了Kelvin-Helmhtz界面不稳定性湍流的混合发展过程,通过对混合层动量厚度、能谱和总动能的计算,评估了Kelvin-Helmhtz混合层的演化机理。计算结果表明:3维Mortar谱元法具有高计算精度和光滑区域的指数收敛特性,可以有效模拟混合层流动的湍流混合和演化,能够捕捉到涡的合并现象和大涡到小涡的级联过程;初期的混合层层流运动发展成具有连续谱结构的湍流运动过程,实现了Kelvin-Helmhtz界面不稳定性混合层流动从2维发展到3维的转捩特征,总湍流统计动能的变化反映了粘性耗散过程的作用。通过对Kelvin-Helmhtz 3维界面不稳定性混合层流动和3维层流向湍流转捩过程的数值模拟,程序的有效性得到了验算,表明谱元法应用于湍流混合模拟是可行的。     

Turbulence characteristics from minisodar data

Vertical profiles of atmospheric turbulence characteristics, including spatial and temporal longitudinal and transverse velocity structure functions, velocity structure characteristics, and turbulent kinetic energy dissipation rates retrieved from time series of vertical profiles of the wind velocity vector measured with a minisodar operating at a frequency of 4900 Hz are presented. It is established that the structure functions first increase with the separation distance between the observation points and then are saturated; moreover, the longitudinal structure function is much greater than the transverse one, which is in agreement with the data available from the literature. The velocity structure characteristic is well described by the z^−2/3 altitude dependence predicted theoretically. Calculated values of the turbulent energy dissipation rate are in agreement with the data available from the literature.     

Conditional analysis of temperature and strain rate effects on dissipation structure in turbulent non-premixed jet flames

This work presents results from simultaneous high-resolution temperature and velocity measurements in a series of turbulent non-premixed jet flames. The filtered Rayleigh scattering (FRS)-based temperature measurements demonstrate sufficient signal-to-noise (SNR) and spatial resolution to estimate the smallest scalar length scales and accurately determine dissipation rate fields. A comprehensive set of conditional statistics are used to characterize the small-scale structure, including the dependence of dissipation layer widths on Reynolds number, temperature, and dissipation magnitude. In general, the dissipation layer thickness decrease with increasing Reynolds number and increase with increasing temperature. However, dissipation layer widths show two distinct behaviors with respect to dissipation magnitude. For small dissipation values, increases in magnitude results in broadening of the dissipation layer, while for larger magnitude values of dissipation, the layer widths are thinned, highlighting the complexity of small-scale turbulent mixing. Additionally, measured ratios of the dissipation layer width to the Batchelor length scale are consistent across all Reynolds numbers and agree with previous studies in non-reacting flows. The unique aspect about the current set of measurements is the ability to examine the interaction of dissipation structure with turbulent flow parameters for the first time in turbulent non-premixed flames. Particularly, the strain rate/dissipation relationship is examined and compared to previous studies in non-reacting flows. It is found that the dissipation layers tend to align normal to the principal compressive strain axis and this tendency increases with increasing Reynolds number. For the lowest Reynolds number case, no dependence of the dissipation layer width nor dissipation rate magnitude on strain rate is found. However, for higher Reynolds numbers, a strong dependence of the dissipation layer width and dissipation rate magnitude on the principal compressive strain rate is observed. These results indicate the direct role of the compressive strain rate field on small-scale mixing structure in reacting flows.     

Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES

This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97 × 10⁶ nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.     

3维Mortar谱元法模拟Kelvin-Helmhtz不稳定性混合层

采用Mortar谱元法和多处理器并行计算技术模拟了Kelvin-Helmhtz界面不稳定性湍流的混合发展过程,通过对混合层动量厚度、能谱和总动能的计算,评估了Kelvin-Helmhtz混合层的演化机理。计算结果表明：3维Mortar谱元法具有高计算精度和光滑区域的指数收敛特性,可以有效模拟混合层流动的湍流混合和演化,能够捕捉到涡的合并现象和大涡到小涡的级联过程;初期的混合层层流运动发展成具有连续谱结构的湍流运动过程,实现了Kelvin-Helmhtz界面不稳定性混合层流动从2维发展到3维的转捩特征,总湍流统计动能的变化反映了粘性耗散过程的作用。通过对Kelvin-Helmhtz 3维界面不稳定性混合层流动和3维层流向湍流转捩过程的数值模拟,程序的有效性得到了验算,表明谱元法应用于湍流混合模拟是可行的。     

槽道流POD重构及湍流动能耗散率分析

采用二维粒子图像测速仪（2DPIV）对槽道内涡波流场进行实验研究,用POD技术对2DPIV瞬态速度矢量场进行主导模态重构,得到槽道内的平均流速和湍流动能分布;采用大涡PIV方法对湍流动能耗散率分布进行计算.结果表明：重构流场表征了原始流场的主导结构,剔除了噪声等干扰信息;大涡PIV方法能有效地估算动能耗散率的分布;湍流动能在壁面附近较小,在接近槽道中心区域湍流动能越来越大,呈现出射流的特征;动能耗散率的峰值出现在壁面附近和槽道中心区域,动能耗散率随着远离壁面程度的增加先降低后逐渐增加直至达到峰值.     

Turbulent scalar flux transport in head-on quenching of turbulent premixed flames: a direct numerical simulations approach to assess models for Reynolds averaged Navier Stokes simulations

The statistical behaviour and the modelling of turbulent scalar flux transport have been analysed using a direct numerical simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by an isothermal wall. A range of different values of Damköhler, Karlovitz numbers and Lewis numbers has been considered for this analysis. The magnitudes of the turbulent transport and mean velocity gradient terms in the turbulent scalar flux transport equation remain small in comparison to the pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation when the flame is away from the wall but the magnitudes of all these terms diminish and assume comparable values during flame quenching before vanishing altogether. It has been found that the existing models for the turbulent transport, pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation do not adequately address the respective behaviours extracted from DNS data in the near-wall region during flame quenching. Existing models for transport equation-based closures of turbulent scalar flux have been modified in such a manner that these models provide satisfactory prediction both near to and away from the wall.     

The energy and dissipation of turbulent fluctuations of wind velocity and temperature in the boundary layer of the atmosphere

The relationships between the energy of small-scale turbulence and its dissipation rate are studied based on the data of long-term high-frequency measurements of temperature and wind velocity fluctuations in urban area. It is shown that the energy of wind velocity turbulent fluctuations is linearly related to the dissipation rate ɛ. The proportionality coefficient between turbulent kinetic energy (TKE) and ɛ is dimensional and does not depend on the stratification of the atmosphere, the Richardson number, or the Monin-Obukhov scale. Measurements in different seasons show that this coefficient can be related to the mean velocity of adiabatic motions (sound speed or air temperature), which enables one to select a more universal constant, γ. A linear relationship between the temperature fluctuations variance (the characteristic of the inner energy of turbulence) and their dissipation rate is also shown. The revealed proportionality is confirmed by measurements in urban and forest conditions, as well as in the surface layer over a flat desert terrain.     

标量湍流的能量传输特性

应用直接数值模拟数据,从标量湍流传输的三波关系出发,进行湍流及标量湍流传输谱的多尺度分析,研究不同尺度间的能量传输性质,证实标量能量的传输与湍动能传输具有不同性质,大尺度速度脉动对标量传输有较大贡献,尤其是与标量小尺度脉动的相互作用,使标量模拟需要有比速度场更高的网格分辨率;并发现标量湍流的能量传输具有明显的非局部性;另外,定义了能量传输系数,发现在相同的Re数和Pe数条件下,标量湍流的对流惯性较速度脉动的惯性子区宽.     

Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics

The partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics as an effort to develop a prediction model for the turbulent flame lift off. The essence of the flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of the quenching holes initially created by the local quenching events. The numerical simulation for the flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for a constant-density fuel–air channel mixing layer to obtain the background turbulent flow and mixing fields, from which a time series of two-dimensional scalar-dissipation-rate array is extracted. Subsequently, a Lagrangian simulation of the flame hole random walk mapping, projected to the scalar dissipation rate array, yields a temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. In particular, the probability of encountering the reacting state, while conditioned with the instantaneous scalar dissipation rate, is examined to reveal that the conditional probability has a sharp transition across the crossover scalar dissipation rate, at which the flame edge changes its direction of propagation. This statistical characteristic implies that the flame edge propagation instead of the local quenching event is the main mechanism controlling the partial quenching events in turbulent flames. In addition, the conditional probability can be approximated by a heavyside function across the crossover scalar dissipation rate.     

A-priori evaluations of subgrid-scale terms for large-eddy simulation of compressible turbulent flows

The subgrid-scale terms for different formulations of the energy equation are evaluated from a-priori tests using the direct numerical simulation (DNS) data of a compressible mixing layer at a moderate Mach number of M = 0.65. To extend the generality of the results, the simulations were performed with three different initial conditions for the velocity fields. To examine the impact of strong temperature variations on the subgrid scales, a non-isothermal mixing layer with lower to upper free-stream temperature ratio of 3 is also considered. For cold simulations, with equal free-stream temperatures, the total energy equation is shown to be the best choice in view of the accuracy and the subgrid-scale modelling requirements. For hot simulations, with the free-stream temperature ratio equal to 3, the total enthalpy equation is found to be the best formulation for the energy equation. Furthermore, it is shown that the subgrid-scale pressure dilatation term, which has been largely neglected so far, is of the same order of the subgrid-scale heat flux. Based on the present results, the contribution of the subgrid-scale pressure dilatation can be up to 46% of the total sugbrid-scale activity. Moreover, the time evolutions of the volume-average mean kinetic energy, turbulent kinetic energy, production, dissipation, and pressure dilatation terms are considered. Unlike the subgrid-scale pressure dilatation term, the volume-average pressure dilatation terms are negligible, and compressibility does not affect the large-scale evolutions of the mean and turbulent kinetic energies.