Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number of Re_τ = 950 and centreline-based Reynolds number of Re₀ = 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales.     

A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers

Direct Numerical Simulation (DNS) data on high pressure H₂/O₂ and H₂/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.     

混合层流场中涡结构对流速度的特性

基于大涡模拟和光线追踪方法, 对光线穿越流场后的光程分布与混合层流场中涡结构之间的关系进行了分析, 提出了一种基于涡核位置提取的涡结构瞬时对流速度定量计算方法, 并使用直接几何测量数据进行了验证. 通过对不同尺寸的涡结构、涡-涡配对及融合过程中的涡结构和强压缩性流场中涡结构瞬时对流速度的定量数值计算, 揭示了混合层流场中涡结构对流速度的特性: 对单个涡结构而言, 其瞬时对流速度具有脉动特性, 且脉动幅度随涡结构尺寸和流场压缩性而变化; 在涡-涡配对及融合过程中, 涡对中各个涡结构的瞬时对流速度都表现出类似正弦波动的特点. 针对混合层流场中涡结构对流速度的特性, 给出了其背后的物理原因.     

新型大涡数值模拟亚格子模型及应用

基于湍流大小尺度间动量输运的结构函数方程,提出了一种新的湍流大涡模型(LES)亚格子涡粘模式．新亚格子涡粘系数正比于纵向速度增量的扭率,它表征大小尺度湍流间的能量输运和耗散之比．新模式通过各向同性湍流直接数值模拟数据库的检验,并用于槽道湍流的大涡模拟计算,将所得结果与DNS结果进行了比较．     

Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

脉冲激励下超音速混合层涡结构的演化机理

采用大涡模拟方法对脉冲激励作用下的超音速混合层流场进行数值模拟,所得结果清晰展示了流场中涡结构的独特生长机理.基于涡核位置提取方法,对超音速混合层流场中涡结构的空间尺寸和瞬时对流速度等动态特性进行了定量计算.通过分析流场中涡结构的动态特性在不同频率脉冲激励下的变化,揭示出受脉冲激励超音速混合层流场中涡结构的演化机理:涡结构的生长不再是依靠相邻涡-涡结构之间的配对与融合,而是通过涡核外围的一串小涡旋结构被依次吸进涡核来实现,且受激励流场中各个涡结构的空间尺寸变化较小;流场中的涡结构数量与脉冲频率成正比例关系,而涡结构的空间尺寸与脉冲频率成反比例关系;涡结构的平均对流速度随脉冲频率的增大而减小.针对受脉冲激励超音速混合层,给出了能够表征涡结构特性与脉冲激励参数之间关系的方程式,即受激励流场中涡结构的平均对流速度与脉冲周期的乘积近似等于流场中涡结构的空间尺寸(涡结构平均直径).     

壁面在展向作周期运动的槽道湍流的大涡模拟

分别采用3种亚格子模式:传统的Smagorinsky模式、动力Smagorinsky模式和Cui(2004)基于Kolmogorov方程所提出的新模式,对壁面在展向作周期运动的槽道湍流进行了大涡模拟,以考察这3种模式对平均运动为三维、非定常的湍流流动的模拟能力.通过对湍流基本统计量的分析,发现动力模式和新模式都可以较好地预测这种三维非定常的湍流流动;对相位平均的湍流统计量,动力模式的结果略优于新模式;传统的Smagorinsky模式对这种流动的预测结果是最差的.     

Interaction between strain and vorticity in compressible turbulent boundary layer

The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions.It is found that large enstrophy production is associated with high dissipation and high enstrophy,while large enstrophy destruction with moderate ones.The enstrophy production and destruction are also correlated with the dissipation production and destruction.Moreover,the enstrophy producing region has a distinct tendency to be‘sheet-like’structures and the enstrophy destroying region tends to be‘tube-like’in the inner layer.Correspondingly,the tendency to be‘sheet-like’or‘tube-like’structures is no longer obvious in the outer layer.Further,the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies.It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer,and the enstrophy production(destruction)mainly on the alignment between the vorticity vector and the extensive(compressive)eigenvector in the outer layer.     

Experimental evidence for non-linear growth in compressible mixing layer

An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected for two flow conditions at convective Mach numbers Mc=0.11 and 0.47.The coherent vortices,braids and eruptions in the mixing zone were observed,interpreted as evidence of multi-scale,three-dimensional structures at a high Reynolds number.The mixing layers with a large visualized range present two stages along the streamwise direction,corresponding to the initial mixing and the well-developed stage.A new method,the gray level ensemble average method(GLEAM),by virtue of the similarity of the mixing layer,was applied to measure the growth rate of the CML thickness.New evidence for a nonlinear growth of CML is reported,providing an interpretation of previous observations of the scattering of the growth rate.     

化学氧碘激光器内流场亚跨超音速混合的大涡模拟研究

 利用大涡模拟对化学氧碘激光器内的亚跨超音速混合过程进行模拟分析,其结果表明了大涡模拟对这种低压、低密度、亚跨超音速及夹杂多种介质的化学流场的可执行性。与传统的雷诺平均仿真结果相比较,大涡模拟能掌握更多的流场细节数据,能够对混合过程进行精准地判断和分析。在此基础上,提出了碘流反向45°入流的设计方案以增强混合程度,计算表明采用此种方案在相应出光面上平均小信号增益系数提高了5%。     

化学氧碘激光器内流场亚跨超音速混合的大涡模拟研究

利用大涡模拟对化学氧碘激光器内的亚跨超音速混合过程进行模拟分析,其结果表明了大涡模拟对这种低压、低密度、亚跨超音速及夹杂多种介质的化学流场的可执行性。与传统的雷诺平均仿真结果相比较,大涡模拟能掌握更多的流场细节数据,能够对混合过程进行精准地判断和分析。在此基础上,提出了碘流反向45°入流的设计方案以增强混合程度,计算表明采用此种方案在相应出光面上平均小信号增益系数提高了5%。     

激波作用不同椭圆氦气柱过程中流动混合研究

在激波与气柱相互作用问题中,压力与密度间断不平行产生的斜压涡量会引起流动的不稳定性,从而促进物质间的混合.本文基于双通量模型,结合五阶加权基本无振荡(WENO)格式,求解多组分二维Navier-Stokes方程,分析激波作用面积相同结构不同的椭圆气柱所致的流动和混合.数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性引起的气柱界面变形和波系演化.同时定量地从界面运动、界面结构参数变化(长度和高度)、气柱体积压缩率、环量及混合率等角度分析激波诱导的流动混合机制,研究椭圆几何构型对氦气混合过程的影响.结果表明,界面及相关参数的演化与气柱初始形状密切相关.当激波沿椭圆长轴作用于气柱时,气柱前端出现空气射流结构,且射流不断增长并渗透到下游界面,致使气柱分离成两个独立涡团,离心率越大,射流发展越快;同时激波作用气柱后在界面处产生不规则反射现象.圆形气柱界面演化与这种作用情形类似.当激波沿椭圆短轴作用于气柱时,界面上游出现类平面结构,随后平面上下缘处产生涡旋,主导流动发展,激波在界面作用产生规则反射,离心率越大,这些现象越明显.界面高度、长度、体积压缩率也因此有所差异.对界面演化、环量和混合率的综合分析表明,激波沿长轴作用于气柱且离心率较大时,流动发展较快,不稳定性导致的流动越复杂,越有利于氦气与环境介质的混合.     

Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer

The thin interface separating the inner turbulent region from the outer irrotational fluid is analysed in a direct numerical simulation of a spatially developing turbulent mixing layer. A vorticity threshold is defined to detect the interface separating the turbulent from the non-turbulent regions of the flow, and to calculate statistics conditioned on the distance from this interface. The conditional statistics for velocity are in remarkable agreement with the results for other free shear flows available in the literature, such as turbulent jets and wakes. In addition, an analysis of the passive scalar field in the vicinity of the interface is presented. It is shown that the scalar has a jump at the interface, even stronger than that observed for velocity. The strong jump for the scalar has been observed before in the case of high Schmidt number (Sc). In the present study, such a strong jump is observed for a scalar with Sc ≈ 1. Conditional statistics of kinetic energy and scalar dissipation are presented. While the kinetic energy dissipation has its maximum far from the interface, the scalar dissipation is characterised by a strong peak very close to the interface. Finally, it is shown that the geometric features of the interfaces correlate with relatively large scale structures as visualised by low-pressure isosurfaces.     

平板混合层流动中两相脉动关联矩的大涡模拟

在气粒两相平板混合层流动中,对气相流动采用大涡模拟,对颗粒相流动采用轨道模拟,研究了两相脉动关联矩。由两相各自瞬时速度出发可以直接获得两相脉动关联矩的统计结果。模拟获得的颗粒相一阶矩、二阶矩以及两相脉动关联矩与实验结果定量符合,表明基于细观模拟是不通过模型获得和研究两相脉动关联矩的可行途径。     

Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10^?4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.     

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Experimental and numerical study on instability structure of the supersonic mixing layer (Mc = 0.5)

The parameters of instability wave of supersonic mixing layer(Mc=0.5,M1=3.5/M2=1.4) are measured by flow visualization and calculated by means of two-dimensional direct numerical simulaitons of the compressible Navier-Stokes equations.In both cases of the mixing layer with harmonic disturbance or not,the comparative results indicate that the wavelength of the two-dimensional wave is equal to the vortex spacing in the streamwise direction because the difference between them is less than 1%.However,the measur...     

Interaction of inner and outer layers in plane and radial wall jets

Large eddy simulations of turbulent radial and plane wall jets were performed at different Reynolds numbers using the Lagrangian dynamic eddy viscosity subgrid-scale model. The results were validated with experimental data available in the literature. Compared to the plane ones, the radial wall jets have an extra direction for expansion, which causes faster decay rates. Thus, the resulting pressure gradient distributions are different. However, the comparison of the results with the turbulent boundary layers under adverse and favourable pressure gradients reveals that these pressure gradients are not strong enough to cause any fundamental physical difference between plane and radial wall jets. In both cases, the local Reynolds number is an important determining factor in characterisation of the flow. The joint probability density function analysis shows that the local Reynolds number determines the level of intrusion of the outer layer into the inner layer: the lower the local Reynolds number, the stronger is the interaction of the inner and outer layers. These results can be used to clarify the scatter of the reported log-law constants in the literature.