Large Eddy Simulation and Extended Dynamic Mode Decomposition of Flow-Flame Interaction in a Lean Premixed Low Swirl Stabilized Flame

In this paper, numerical studies are reported on the effect of flow-flame interaction at large and medium scales and its impact on flame stabilization in a lean premixed low swirl stabilized methane/air flame. The numerical simulations are based on a large eddy simulation (LES) approach with a three-scalar flamelet model with equations for mixture fraction and fuel mass fraction and the level-set G-equation to account respectively for stratification of the mixture, fuel leakage at the trailing edge of the flame, and tracking of the flame front. Distinct frequencies, associated with the flame stabilization process, are identified from point data of LES in the outer and inner shear layers of the burner induced flow field. To understand the effect of the spatial structures related to the observed flow frequencies, a dynamic mode decomposition (DMD) is performed. Based on the analysis of LES data, frequency specific coherent flow structures are extracted along with associated flame structures through an extended version of DMD. The inner shear layer generated vortices are associated with recurring frequency specific coherent structures of both flow and flame and contribute to the flame stabilization in the outer regions of the flow.     

圆湍射流拟序结构研究进展

圆湍射流拟序结构的实验研究,经历了流场显示定性观测、热线、激光单点测量、数字图像等方法全流场定量测量以及当前三维演变机制的探讨。与此同时,静态激励和主动技术的拟序结构控制研究也获得了大量的成果。应用涡方法、直接数值模拟和大涡模拟等对圆湍射流拟序结构进行的数值模拟,在印证试验现象的同时,还进一步深入研究了拟序结构的输运特性、激发机制等相关内容。本文对上述进展进行了综述,以期为进一步开展湍射流的研究和应用提供依据。      

Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 2 × 104

The flow over a circular cylinder at Reynolds number 2 × 10⁴ was predicted numerically using the technique of large-eddy simulation (LES). Both incompressible and compressible flow formulations were used. The present results obtained at a low-Mach number (M?=?0.2) revealed significant inaccuracies like spurious oscillations of the compressible flow solution. A detailed investigation of such phenomena was carried out. It was found that application of blended central-difference or linear-upwind schemes could damp artificial waves significantly. However, this type of schemes has a too dissipative nature compared to pure central-differences. The incompressible flow results were found to be consistent with the existing numerical studies as well as with the experimental data. Basic flow features and flow mechanics were found to be in good agreement with existing experimental data and consistent with previously obtained LES. Special emphasis was put on the spectral analysis. Here, the classical Fourier transform as well as the continuous wavelet transform were applied. Based on the latter, the separated shear-layer instability was precisely clarified. It was found that the Reynolds number dependency between vortex shedding and shear-layer instabilities had a power law relation with n?=?0.5.     

Turbulence structure in a diabatically heated forest canopy composed of fractal Pythagoras trees

We investigate the turbulent flow through a heterogeneous forest canopy by high-resolution numerical modeling. For this purpose, a novel approach to model individual trees is implemented in our large-eddy simulation (LES). A group of sixteen fractal Pythagoras trees is placed in the computational domain and the tree elements are numerically treated as immersed boundaries. Our objective is to resolve the multiscale flow response starting at the diameter of individual tree elements up to the depth of the atmospheric surface layer. A reference run, conducted for the forest flow under neutral thermal stratification, produces physically meaningful turbulence statistics. Our numerical results agree quantitatively with data obtained from former field-scale LESs and wind tunnel experiments. Furthermore, the numerical simulations resolve vortex shedding behind individual branches and trunks as well as the integral response of the turbulent flow through the heterogeneous forest canopy. A focus is the investigation of the turbulence structure of the flow under stable thermal stratification and in response to the heating of the fractal tree crowns. For the stratified flows, statistical quantities, e.g. turbulent kinetic energy and vorticity, are presented and the turbulent exchange processes of momentum and heat are considered in detail. The onset and formation of coherent structures such as elevated shear layers above the diabatically heated forest canopy are analyzed. For the stably stratified flow, temperature ramps above the forest canopy were simulated in agreement with previous observations. Thermally driven vortices with a typical diameter of the canopy height were simulated when the tree crowns were diabatically heated. The impact of the coherent flow structures on the heat flux is investigated.     

Stability Properties of POD–Galerkin Approximations for the Compressible Navier–Stokes Equations

Fluid flows are very often governed by the dynamics of a mall number of coherent structures, i.e., fluid features which keep their individuality during the evolution of the flow. The purpose of this paper is to study a low order simulation of the Navier–Stokes equations on the basis of the evolution of such coherent structures. One way to extract some basis functions which can be interpreted as coherent structures from flow simulations is by Proper Orthogonal Decomposition (POD). Then, by means of a Galerkin projection, it is possible to find the system of ODEs which approximates the problem in the finite-dimensional space spanned by the POD basis functions. It is found that low order modeling of relatively complex flow simulations, such as laminar vortex shedding from an airfoil at incidence and turbulent vortex shedding from a square cylinder, provides good qualitative results compared with reference computations. In this respect, it is shown that the accuracy of numerical schemes based on simple Galerkin projection is insufficient and numerical stabilization is needed. To conclude, we approach the issue of the optimal selection of the norm, namely the H ¹ norm, used in POD for the compressible Navier–Stokes equations by several numerical tests. Received 21 April 1999 and accepted 18 November 1999     

Detached Eddy Simulation of Flow around A-Airfoil

In this study the flow around the Aérospatiale A-airfoil at maximum lift (α = 13.3°) and Re = 2 × 10⁶ is investigated by RANS and DES to quantify the influence of transient flow patterns on the quality of the flow prediction. This flow features a highly unsteady pressure-induced trailing-edge separation. The fairly high Reynolds number makes LES rather unattractive from a practical point of view as the numerical costs scale with ≈ Re^1.95 [9] and lead to an unreasonable effort to carry out these simulations. Like LES, DES is designed to capture the unsteady flow features and consequently is supposed to give results superior to RANS. The RANS solution captures the separation, but is notable to predict transient vortex shedding. The application of DES to a 2D domain leads to results comparable to those obtained by 2D-RANS. Only the 3D-DES is capable of predicting both the unsteady flow features and the development of the boundary layer on the airfoil. As expected, the spanwise resolution has a strong impact on the vortex shedding and on the size of the separation bubble. Attention must be paid to both accommodating the full extent of the flow structures and providing the adequate spatial resolution in order to accomplish satisfactory results – that compare favourably with LES – at only a fraction of computational cost.     

Direct Numerical Simulation of a Recirculating, Swirling Flow

A direct numerical simulation (DNS) of a recirculating, swirling flow is performed at a Reynolds number of 5000. Detailed one and two point statistics are presented in this paper. Flow visualization and frequency analysis are used to identify a precessing vortex core and to characterize its position, extent and influence on the flow field. The results are compared with laser Doppler velocimetry (LDV) measurements as well as large eddy simulation (LES) data reported in the literature. The present work constitutes a first step in setting up a DNS data base for complex flows.     

Large eddy simulation of high-Reynolds-number atmospheric boundary layer flow with improved near-wall correction

It is highly attractive to develop an efficient and flexible large eddy simulation(LES) technique for high-Reynolds-number atmospheric boundary layer(ABL) simulation using the low-order numerical scheme on a relatively coarse grid, that could reproduce the logarithmic profile of the mean velocity and some key features of large-scale coherent structures in the outer layer. In this study, an improved near-wall correction scheme for the vertical gradient of the resolved streamwise velocity in the s...     

Numerical prediction of turbulent flow structure generated by a synthetic cross‐jet into a turbulent boundary layer

A detailed numerical study using large‐eddy simulation (LES) and unsteady Reynolds‐averaged Navier–Stokes (URANS) was undertaken to investigate physical processes that are engendered in the injection of a circular synthetic (zero‐net mass flux) jet in a zero pressure gradient turbulent boundary layer. A complementary study was carried out and was verified by comparisons with the available experimental data that were obtained at corresponding conditions with the aim of achieving an improved understanding of fluid dynamics of the studied processes. The computations were conducted by OpenFOAM C++, and the physical realism of the incoming turbulent boundary layer was secured by employing random field generation algorithm. The cavity was computed with a sinusoidal transpiration boundary condition on its floor. The results from URANS computation and LES were compared and described qualitatively and quantitatively. There is a particular interest for acquiring the turbulent structures from the present numerical data. The numerical methods can capture vortical structures including a hairpin (primary) vortex and secondary structures. However, the present computations confirmed that URANS and LES are capable of predicting current flow field with a more detailed structure presented by LES data as expected. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of the flow around a simplified vehicle model with active flow control

Large-eddy simulation (LES) was used to study the influence and the resulting flow mechanisms of active flow control applied to a two-dimensional vehicle geometry. The LES results were validated against existing Particle Image Velocimetry (PIV) and force measurement data. This was followed by an exploration of the influence of flow actuation on the near-wake flow and resulting aerodynamic forces. Not only was good agreement found with the previous experimental study, but new knowledge was gained in the form of a complex interaction of the actuation with the coherent flow structures. The resulting time-averaged flow shows a strong influence of the extension of the actuation slots and the lateral solid walls on the near-wake flow structures and thereby on the resulting drag.     

Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder

A coupled experimental/numerical analysis of turbulent flow past a square cylinder is performed at the ERCOFTAC Reynolds number Re = U_∞D/ν = 21,400, where U_∞ is the inflow velocity and D the cylinder height. Complementary Laser Doppler Velocimetry (LDV) and high-order large-eddy simulations (LES) approaches, based on a spectral vanishing technique (SVV-LES), provide a comprehensive data base including both instantaneous data and post-processed statistics. Beyond these results, an achievement of the paper is to investigate the coherent structures developing on the sides and in the wake of the cylinder with a special focus on the flow features in the near-wall region. The flow is found to separate at the leading edge of the cylinder with the occurence of three-dimensional Kelvin-Helmholtz (KH) pairings localized in the separating shear layer. The interaction between these KH vortical structures and Von Kármán vortex shedding (VK) in the near wake is discussed based on both visualisations and frequency analysis. In particular, signatures of VK and KH vortical structures are found on velocity time samples.     

Vortex mechanism of heat transfer enhancement in a channel with spherical and oval dimples

Vortex mechanism of heat transfer enhancement in a narrow channel with dimples has been investigated numerically using LES and URANS methods. The flow separation results in a formation of vortex structures which significantly enhance heat transfer on dimpled surfaces leading to a small increase in pressure loss. The heat transfer can be significantly increased by rounding the dimple edge and use of oval dimples. To get a deep insight into flow physics LES is performed for single phase flow in a channel with a spherical dimple. The instantaneous vortex formation and separation are investigated in and around the dimple area. Considered are Reynolds numbers (based on dimple print diameter) Re_D = 20,000 and Re_D = 40,000 the depth to print diameter ratio of Δ = 0.26. Frequency analysis of LES data revealed the presence of dominating frequencies in unsteady flow oscillations. Direct analysis of the flow field revealed the presence of coherent vortex structure inclined to the mean flow. The structure changes its orientation in time causing the long period oscillations with opposite-of-phase motion. Three dimensional proper orthogonal decomposition (POD) analysis is carried out on LES pressure and velocity fields to identify spatio-temporal structures hidden in the random fluctuations. Tornado-like spatial POD structures have been determined inside dimples.     

Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration

The turbulent flows around four cylinders in an in-line square configuration with different spacing ratios of 1.5, 2.5, 3.5 and 5.0 have been investigated experimentally at subcritical Reynolds numbers from 11,000 to 20,000. The mean and fluctuating velocity distributions were obtained using the laser Doppler anemometry (LDA) measurement. The digital particle image velocimetry (DPIV) was employed to characterize the full field vorticity and velocity distributions as well as other turbulent quantities. The experimental study indicated that several distinct flow patterns exist depending on the spacing ratio and subcritical Reynolds number for turbulent flow. The three-dimensional numerical simulations were also carried out using the large eddy simulation (LES) at Reynolds number of 15,000 with the spacing ratio of 1.5 and 3.5. The results show that the LES numerical predictions are in good agreement with the experimental measurements. Therefore, the three-dimensional vortex structures and the full field instantaneous and mean quantities of the flow field such as velocity field, vorticity field, etc., which are very difficult to obtain experimentally, can be extracted from the simulation results for the deepening of our understanding on the complex flow phenomena around four cylinders in in-line configuration.     

Investigation of the Dynamic Response of Swirling Flows Based on LES and Experiments

The dynamic response of a swirling flow undergoing vortex breakdown is investigated via Large Eddy Simulation (LES) and experiments in a water flow facility. The investigation is carried out following previous work on the link between thermoacoustic combustion instabilities and coherent structures in lean premixed gas turbine combustors. The velocity field transfer function is obtained in LES from the Unit Impulse Response determined via application of a low intensity broadband noise perturbation of the inflow mass flow rate and the Wiener-Hopf filtering method. In the experiments, harmonic fluctuations in the water flow rate through the swirler are generated via a piston mounted on the side wall of the test facility and activated with a low frequency linear motor. The velocity field transfer function is then obtained via phase averaging applied to Particle Image Velocimetry snapshots which are collected at prescribed values of the harmonic phase. The analysis, which is carried out in terms of coherent structures identified via Proper Orthogonal Decomposition, gives numerical transfer functions with amplitude and phase consistent with the experimental ones.     

高亚声速湍流喷流气动噪声数值分析

为适应航空噪声管制规定要求,发动机喷流噪声控制成为目前气动声学研究中的重要课题,预测分析喷流噪声辐射并揭示其产生机理将为噪声控制奠定基础.采用高精度并行LES（large eddy simulation）方法计算分析马赫数0.9高亚声速喷流的湍流演化和气动噪声现象.首先,仔细验证喷流LES湍流场计算保真性,并分析流场中不同尺度涡结构的演化形态.其次,利用可穿透面FW-H（Ffowcs Williams and Hawkings）方法外推喷流近场声源数据获得精确声辐射远场,进而分析声场主导声模态特性.最后,通过分析声源机制、分离声模态等方法研究势流核末端大尺度拟序涡运动演化形成的低波数波包在噪声主导声模态产生中的重要作用.数值结果表明LES结合可穿透面FW-H方法可精确预测高亚声速喷流的流场及声场特征,且数值分析揭示涡环对并形成的大尺度拟序结构在喷流中心线上沿径向融合,产生了在远场低方位角占优的主导声模态,并构成强指向性声场,噪声峰值方位角约为30°.      

利用O型环抑制圆柱绕法流涡脱落的数值研究

圆柱绕流涡脱落诱发较大的振动和声,如何有效地抑制值得关注.利用大涡模拟技术求解了Navier-Stokes方程,得到了涡脱落频率,升力脉动幅值及平均阻力系数.计算表明二维模拟不能体现流动基本特征,三维计算与实验吻合较好.为了抑制涡脱落,在直径为D的圆柱表面装入间距为1D,直径为0.0167D的O型环.通过升力、速度谱分析以及柱向横截面流场分析可知,在光滑圆柱外表面加入O型环能诱发流体边界层分离,有效地抑制涡脱落现象,升力脉动和观测点速度脉动幅值几乎完全消失,阻力系数也略微降低,适合在实际工程中采用.     

细颗粒泥沙净冲刷和输移的大涡模拟研究

在传统水沙输移数值模拟研究中一般采用雷诺时均模拟技术(Reynolds-averaged simulation,RANS).与RANS相比,大涡模拟技术(large eddy simulation,LES)能够更加精确反映细部流动结构,计算机的发展使得采用LES探讨水流和泥沙运动规律成为可能.本文尝试给出净冲刷条件下悬沙计算的边界条件,采用动态亚格子模式对循环槽道和长槽道中的水流运动和泥沙输移进行了三维大涡模拟研究.利用直接数值模拟(direct numerical simulation,DNS)结果对LES模型进行了率定,计算结果符合良好,在此基础上初步探讨了泥沙浓度、湍动强度和湍动通量等的分布特征.结果表明,净冲刷条件下输沙平衡时泥沙浓度符合Rouse公式分布,单向流动中泥沙浓度沿着流向逐渐增大.泥沙浓度湍动强度和湍动通量都在近底部达到最大值,沿着垂向迅速减小.湍动黏性系数和扩散系数基本上在水深中间处达到最大.湍动Schmidt数沿着水深方向不是常数,在近底部和自由水面附近较大,在水深中间处较小.     

DNS and LES of some engineering flows

In this paper, direct numerical simulations (DNS) and large eddy simulations (LES) of three engineering flows carried out in the author's research group are presented. The first example, simulated both with DNS and LES, is the flow in a low-pressure turbine cascade with wakes passing periodically through the cascade channel. In this situation, the laminar–turbulent transition of the boundary layers on the blade surfaces, which is strongly influenced by the passing wakes, is of special interest. Next, LES of the flow past the Ahmed body is presented, which is a car model with slant back. In spite of the fairly simple geometry, the flow around the model has many features of the complex, fully 3D flow around real cars. The third example, for which LES is presented, is the flow past a surface mounted circular cylinder of height-to-diameter ratio of 2.5. In this case also complex 3D flow develops with interaction of various vortices behind the cylinder. By means of these examples, the paper shows that complex turbulent flows of engineering relevance can be predicted realistically by DNS and LES, albeit at large cost. The methods are particularly suited and superior to RANS methods for situations where unsteadiness like shedding and large-scale structures dominate the flow, and DNS has evolved into an important tool for studying transition mechanisms.     

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.     

Dynamic Mode Decomposition of a Wing-Body Junction Flow

Junction flows are subject to an intense adverse pressure gradient and three-dimensional separation when encountering a wall-mounted obstacle. A dynamically rich horseshoe vortex system is formed in this region. In this study the junction flow at the interaction of a wing and a flat plate is investigated. The numerical modelling is carried out using the three-dimensional large eddy simulation (LES) approach at the Reynolds number Re = 1.15×10⁵ based on the wing’s maximum thickness T and the free stream velocity U_ref. The comparison with the experimental results shows that the numerical simulations fairly accurately reproduce the phenomenon under study. The dynamic mode decomposition (DMD) of the resolved flow field is employed to obtain the coherent dynamics of the flow. To clearly demonstrate the oscillation characteristics and the horseshoe vortex structures of junction flow the velocity field in the plane of symmetry is decomposed with eduction of two dominant DMDmodes. These two DMDmodes are reconstituted and developed, together with the mean flow mode to explain the latent dynamics. Mode 1 reveals the merging of the horseshoe vortices and mode 2 is responsible for the process of fission and stretching.