Navier–Stokes analysis methods for turbulent jet flows with application to aircraft exhaust nozzles

This article presents the current status of computational fluid dynamics (CFD) methods as applied to the simulation of turbulent jet flowfields issuing from aircraft engine exhaust nozzles. For many years, Reynolds-averaged Navier–Stokes (RANS) methods have been used routinely to calculate such flows, including very complex nozzle configurations. RANS methods replace all turbulent fluid dynamic effects with a turbulence model. Such turbulence models have limitations for jets with significant three-dimensionality, compressibility, and high temperature streams. In contrast to the RANS approach, direct numerical simulation (DNS) methods calculate the entire turbulent energy spectrum by resolving all turbulent motion down to the Kolmogorov scale. Although this avoids the limitations associated with turbulence modeling, DNS methods will remain computationally impractical in the foreseeable future for all but the simplest configurations. Large-Eddy simulation (LES) methods, which directly calculate the large-scale turbulent structures and reserve modeling only for the smallest scales, have been pursued in recent years and may offer the best prospects for improving the fidelity of turbulent jet flow simulations. A related approach is the group of hybrid RANS/LES methods, where RANS is used to model the small-scale turbulence in wall boundary layers and LES is utilized in regions dominated by the large-scale jet mixing. The advantages, limitations, and applicability of each approach are discussed and recommendations for further research are presented.     

Large-eddy simulation:Past,present and the future

Large-eddy simulation(LES) was originally proposed for simulating atmospheric flows in the 1960 s and has become one of the most promising and successful methodology for simulating turbulent flows with the improvement of computing power. It is now feasible to simulate complex engineering flows using LES. However, apart from the computing power, significant challenges still remain for LES to reach a level of maturity that brings this approach to the mainstream of engineering and industrial computations. This paper will describe briefly LES formalism first, present a quick glance at its history, review its current state focusing mainly on its applications in transitional flows and gas turbine combustor flows, discuss some major modelling and numerical challenges/issues that we are facing now and in the near future, and finish with the concluding remarks.     

基于RANS/LES混合方法的分离流动模拟

飞行器在大迎角、快速俯仰机动时,流场中含有大尺度、非定常的涡结构,传统雷诺平均Navier-Stokes （RANS）模型不能准确模拟流场结构,根据国际上相关研究的发展趋势,需要采用混合RANS/大涡模拟（LES）模型来对复杂分离流动进行准确模拟。本文对基于分区混合与湍流尺度混合的双重RANS/LES混合计算模型进行发展与应用。通过典型简化模型的静、动态湍流大分离流动,测试和验证所采用的脱体涡模拟（DES）类方法,重点研究改进的延迟DES （IDDES）模型在动态问题应用中的正确性和有效性,并对所采用的数值模拟方法和相应的计算软件的可靠性、鲁棒性以及精度进行了考核验证。典型算例包括超声速圆柱底部流动、跨声速方腔流动、NACA0015机翼深失速分离涡模拟等。计算表明：发展的IDDES类混合计算模型可有效解决对数层不匹配的问题;对于定态非定常分离流动,DES、DDES、IDDES等模型计算结果差别不大,随着流动的非定常特性增强,IDDES模型的优势逐渐显现;对于动态非定常分离流动,则需要采用IDDES类模型。     

非均匀网格湍流大涡模拟高精度有限体积解法

为准确预测不可压复杂湍流,提出了一种可用于大涡模拟均匀或非均匀网格上的高精度有限体积法。该方法空间离散采用有限体四阶紧致格式,时间推进采用四阶Runge-Kutta法,压力-速度耦合应用四阶紧致格式的动量插值。通过直接求解顶盖驱动方腔流动证实了该方法具有近四阶的空间精度;并在此基础上,采用动态Smagor-insky亚格子应力模式,成功地实现了充分发展槽道湍流和后台阶湍流流动的大涡模拟计算,所得结果与直接数值模拟结果吻合良好,且采用非均匀网格可在比均匀网格数少的离散系统上得到同样满意的结果。结果表明,该方法是实现高精度湍流大涡数值模拟的一个有效途径。     

复杂湍流流动的混合RANS/LES方法研究

混合RANS/LES方法是近年来复杂湍流模拟的重要方法。简要回顾了混合RANS/LES模拟方法的发展历程,着重总结和分析了分离涡混合模型、类Menter SST混合模型以及湍流能量谱一致混合方法三类混合模型的构造方法和发展历程,对这三种方法的应用以及优缺点进行了简要评述,最后指出了混合RANS/LES方法发展应该兼顾的问题,为下一步的混合RANS/LES模拟提供了参考。     

多级轴流压气机的径向掺混

 随着压气机向着更高的级负荷和更低的展弦比方向发展,径向掺混问题在气动分析和气动设计中越来越重要,当前对决定径向掺混的主要因素众说不一。本文用严格的理论,得到了用统一形式表示含二次流和湍流在内的各个径向掺混因素的多级轴流压气机通流基本方程组,并讨论了二维通流流场湍流掺混与实际流场三维剪切结构的关系。基本方程组的数值结果与试验结果以及其它掺混理论结果比较表呀,该方程组能够满意地模拟多级轴流压气机中的径向掺混特性。     

Simulation of underexpanded supersonic jet flows with chemical reactions

To achieve a detailed understanding of underexpanded supersonic jet structures influenced by afterburning and other flow conditions, the underexpanded turbulent supersonic jet with and without combustions are investigated by computational fluid dynamics(CFD) method.A program based on a total variation diminishing(TVD) methodology capable of predicting complex shocks is created to solve the axisymmetric expanded Navier–Stokes equations containing transport equations of species. The finite-rate ratio model is employed to handle species sources in chemical reactions. CFD solutions indicate that the structure of underexpanded jet is typically influenced by the pressure ratio and afterburning. The shock reflection distance and maximum value of Mach number in the first shock cell increase with pressure ratio. Chemical reactions for the rocket exhaust mostly exist in the mixing layer of supersonic jet flows. This tends to reduce the intensity of shocks existing in the jet, responding to the variation of thermal parameters.     

A new two-scale model for large eddy simulation of wall-bounded flows

A new hybrid approach to model high Reynolds number wall-bounded turbulent flows is developed based on coupling a two-level simulation (TLS) approach (Kemenov and Menon, 2006 [1], 2007 [2] in the inner region with conventional large eddy simulation (LES) away from the wall. This new approach is significantly different from previous near-wall approaches for LES. In this hybrid TLS–LES approach, a very fine small-scale (SS) mesh is embedded inside the coarse LES mesh. The SS equations capture fine-scale temporal and spatial variations in all three Cartesian directions for all three velocity components near the wall. The TLS–LES equations are derived using a new scale separation operator that allows a smooth transition between the two regions, with the equations in the transition region obtained by blending the TLS large-scale and LES equations. New terms in the hybrid region are identified. The TLS–LES approach is used to study the near-wall features in canonical turbulent channel flows for a range of Reynolds number using relatively coarse large-scale (LS) grids. Results show that the TLS–LES approach is able to capture the effect of both the LS and SS features in the wall region consistently for the range of simulated Reynolds number.     

Progress and future prospects of CFD in aerospace—Wind tunnel and beyond

A historical perspective of computational fluid dynamics (CFD) in aerospace in the last 30 years is firstly given. It is shown that there still remain a number of problems that are geometrically simple but difficult to simulate even after many simulations were conducted over complex body configurations. The fact indicates that CFD research is now in the “specific phase” and requires some innovation.The innovation includes “evolutionary effort” and “revolutionary effort”. As an example of evolutionary effort, large eddy simulations/ Reynolds-averaged Navier–Stokes simulations (LES/RANS) hybrid method and its application examples are presented. A shift from RANS to LES/RANS hybrid method occurs not because of the advancement of computers but because of our recognition that separated flows are inherently unsteady and successful simulations require LES-like computations.Comment is given that there may be other types of research necessary to make CFD a real useful tool for a design in addition to simply showing CFD capability for complex body configurations. As one of the examples, construction of a CFD database is presented. Another issue is to make CFD infrastructures so that people outside CFD community may use CFD as a tool to formulate or refine their ideas.To find out revolutionary effort, the message given by Prof. Dean Chapman in 1977 is referred. Observation of current CFD research reveals that evaluation methods of “scale effect” that were believed to be the most important benefit of CFD have not yet been established. Such establishment is the key for the revolution of CFD and researchers need to focus their effort on the development of technologies to evaluate scale effect. Only with such new CFD technologies can “conceptual design with CFD” become feasible.     

Large eddy simulation of turbulent diffusion flame combustion using a conserved scalar methodology

The present paper describes an LES prediction of turbulent diffusion flame combustion in a simplified axi-symmetric combustor geometry.The calculations are carried out using a well-tested finite volume incompressible LES code which has been modified to handle variable density and reacting flows.The basic mixture fraction conserved scalar method is used with the chemical state relationships described by fast chemistry.The turbulence-chemistry interaction is modelled by a sub-grid PDF method and the PDF is assumed to follow a Beta-function shape.The LES predictions have been time-averaged over 3.5 flow-through times to generate the mean radial profiles of mixture fraction,product mass fraction,temperature,axial velocity and axial rms.The agreement of the LES predictions with the experimental data is good for all the above quantities at four different axial positions with largest differences at the first measurement plane.The LES method also provides information on the unsteady nature of turbulent diffusion combustion. For turbulent reacting flows with large density ratio,it was found necessary to use a relaxation method in order to remove unphysical high-frequency fluctuations and to maintain numerical stability.      

模型加力室大涡模拟的并行计算

采用基于MPI(消息传递库)的并行算法,在贴体网格下对带V形槽稳定器模型加力燃烧室紊流化学反应流场进行数值模拟,湍流模型采用k方程亚网格尺度模型,燃烧模型采用亚网格EBU模型,采用热通量辐射模型估算辐射通量。在程序设计中,采用动态内存分配、分区算法和多点重合交错网格系统,并行计算的结果与单机运行结果的对比表明计算结果是正确的,可以明显的提高运算效率,是解决复杂燃烧流动大规模数值模拟的有效手段。      

三维方柱不可压缩绕流的大涡模拟计算

用非定常不可压缩流动求解方法对三维方柱绕流问题作了大涡模拟计算研究.求解程序采用虚拟压缩方法和双时间步的时间推进方案,对流项的差分采用高阶精度的数值差分格式.通过与实验和文献结果比较分析,验证了基于虚拟压缩方法的湍流大涡模拟计算方案对于复杂的三维钝体绕流计算是可行的.     

A high-order compact finite-difference scheme for large-eddy simulation of active flow control

The purpose of this article is to summarize a computational approach, which developed and matured over an extended period of time, and has been shown to be useful for performing large-eddy simulation (LES) of flows with active control. Because of the nature of active flow control, simulation of this class of problems typically cannot be carried out accurately by methods less sophisticated than LES. Active control flowfields are highly unsteady, and can be characterized by small-scale fluid structures which are produced by the control process, but may also be inherent in the original uncontrolled situation. The numerical scheme is predicated upon an implicit time-marching algorithm, and utilizes a high-order compact finite-difference approximation to represent spatial derivatives. Robustness of the scheme is maintained by employing a low-pass Pade-type nondispersive spatial filter, which also accounts for the fine-scale turbulent dissipation that otherwise is traditionally provided by an explicitly added subgrid-scale (SGS) stress model. Geometrically complex applications are accommodated by an overset grid technique, where spatial accuracy is preserved through use of high-order interpolation. Utility of the method is illustrated by specific computational examples, including suppression of acoustic resonance in supersonic cavity flow, leading-edge vortex control of a delta wing, efficiency enhancement of a transitional highly loaded low-pressure turbine blade, and separation control of a wall-mounted hump model. Control techniques represented in these examples are comprised of both steady and pulsed mass injection or removal, as well as plasma-based actuation. For each case, features of the flowfield are elucidated and the solutions are compared to the baseline situation where no control was enforced. Where available, comparisons are also made with experimental data.     

超声速喷流混合流场大涡模拟

以光学窗口外冷喷流为研究背景，采用大涡模拟方法对后台阶外形切向喷流混合流场进行了研究。数值方法基于隐式亚格子模型，采用高精度WENO格式进行空间离散，并通过超声速平面混合层流动对数值方法进行了考核验证。喷流混合流场计算模型与试验一致，来流和喷流马赫数分别为3.4和2.5。数值模拟清晰地捕捉到了流场波系以及混合剪切层、壁面边界层等典型流场结构，并精细预测了混合层发生失稳、转捩及发展为充分发展湍流的时空发展过程。数值模拟得到的湍流大尺度结构的位置和形态与实验图像一致。通过对瞬时流场、统计平均流场和脉动参数的分析，揭示了流场结构特征及其时空演化规律，并获得了流场密度脉动特性。      

LES of film cooling for different jet fluids

The present paper investigates the impact of the velocity and density ratio on the turbulent mixing process in gas turbine blade film cooling.A cooling fluid is injected from an inclined pipe at α=30° into a turbulent boundary layer profile at a freestream Reynolds number of Re∞=400000.This jet-in-a-crossflow(JICF) problem is investigated using large-eddy simulations(LES).The governing equations comprise the Navier-Stokes equations plus additional transport equations for several species to simulate a non-reacting gas mixture.A variation of the density ratio is simulated by the heat-mass transfer analogy,i.e.,gases of different density are effused into an an air crossflow at a constant temperature.An efficient large-eddy simulation method for low subsonic flows based on an implicit dual time-stepping scheme combined with low Mach number preconditioning is applied.The numerical results and experimental velocity data measured using two-component particle-image velocimetry (PIV) are in excellent agreement.The results show the dynamics of the flow field in the vicinity of the jet hole,i.e.,the recirculation region and the inclination of the shear layers,to be mainly determined by the velocity ratio.However,evaluating the cooling efficiency downstream of the jet hole the mass flux ratio proves to be the dominant similarity parameter,i.e.,the density ratio between the fluids and the velocity ratio have to be considered.      

DNS/LES方法在剪切湍流模拟中的应用

提出采用DNS/LES混合方法进行自由剪切类混合流动湍流研究,该方法兼顾了直接数值模拟(DNS)方法在转捩线性范围内的高精确度模拟和大涡模拟(LES)方法在转捩非线性及全湍流区的高效模拟两方面优点,通过对低对流Mach数流场计算表明该方法可以较好地模拟流场的转捩过程.同时,文中还对比实验分析了湍流场对光学传输效应的影响,给出了与实验一致的结论.     

Wall-layer models for large-eddy simulations

The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.     

Large eddy simulation of turbulent combustion processes in propulsion and power systems

Progress toward application of the large eddy simulation (LES) technique to turbulent multiphase combustion processes is presented with emphasis placed on propulsion and power systems. The primary objective is to provide a systematic analysis of the current state-of-the-art and assist in the development of technical performance metrics for model development and validation. Research is currently required to provide both improved multiphase combustion models and improved datasets for validation. Requirements for further model development must be established through detailed analyses of the space–time characteristics of small-scale flame structures and turbulence–chemistry interactions. Concurrently, a refined set of implementation requirements must be established. Steps taken towards these goals are described by first providing a generalized formulation of the filtered conservation equations using an arbitrary filter function that operates on both spatial and temporal scales, with no a priori assumptions made regarding the character of the multiphase fluid elements present in the system. The distinct requirements for LES are listed with a discussion that highlights current progress and unresolved issues. Two case studies are then presented that demonstrate the predictive capabilities of LES when implemented with the appropriate numerics and grid resolution, under highly controlled conditions, and with well-defined boundary conditions. The paper is concluded by highlighting recent findings associated with the International Workshop on Measurement and Computation of Turbulent Nonpremixed Flames.     

基于火焰面模型的超声速燃烧混合LES/RANS模拟

为了明晰超燃冲压发动机燃烧室内部燃烧过程的细节,建立了超声速湍流燃烧稳态火焰面亚格子模型,并采用混合LES/RANS方法对氢燃料超燃冲压发动机进行算例验证.控制方程对流项用五阶精度WENO格式离散,时间方向采用二阶Runge-Kutta方法.研究表明:(1)冷流流场中燃料分布与大尺度结构分布相似,说明混合过程受大涡控制;(2)燃烧流场中涡的尺寸明显变大,且仅存在于火焰面上,另外温度分布和主要生成物分布与涡量云图基本相同,说明燃烧过程也由大涡控制;(3)时均计算结果与实验阴影基本符合,速度剖面和温度剖面与实验测量值定性一致,说明本文的数值模拟方法和燃烧模型可以较好地描述和预测超声速流动燃烧过程.     

Towards the use of large eddy simulation in engineering

This paper reviews some important aspects of Large Eddy Simulation (LES) as applied to engineering flows. We first summarize the present status of modeling in incompressible, compressible and reacting multi-phase flows, with a view towards the overall formalism instead of the intrinsic details of different subgrid models. On the basis of the assumed requirements on future LES, expected to handle full-scale flows and reacting flows with detailed chemistry, we discuss some potentially interesting LES methods for the future. These methods are exclusively based on multi-scale modeling, in which simplified equations are solved within each LES cell, instead of semi-empirical modeling based on the resolved flow scales only. After that we outline a few flows studied by LES at the Swedish Defense Research Agency—FOI, which form the basis for the subsequent discussion of validation and verification, and quality management, being of increasing importance for practical engineering flows. Next we summarize some practical aspects of LES of engineering applications, many of which being crucial to the successful use of LES, and being of increasing importance for engineering flows. Finally, a view of the future use of LES in engineering is presented, which is based primarily on the evolutionary use of LES during the last decade in the fields of hydrodynamics and combustion.