Computation of unsteady turbomachinery flows: Part 2—LES and hybrids

The choice of turbulence model can have a strong impact on results for many turbomachinery zones. Palliative corrections to them and also transition modeling can have a further profound solution impact. The spectral gaps necessary for theoretically valid URANS solutions are also lacking in certain turbomachinery zones. Large Eddy Simulation (LES) alleviates the serious area of turbulence modeling uncertainty but with an extreme increase in computational cost. However, there seems a lack of validation data to explore in depth the performance of LES and thus strategies to refine it. LES best practices are needed. Although LES is, obviously, much less model dependent than RANS, grids currently used for more practical simulations are clearly insufficiently fine for the LES model and numerical schemes not to be playing an excessively strong role. Very few turbomachinery simulations make use of properly constructed, correlated turbulence inflow. Even if this is attempted, most measurement sets are incomplete and lack an adequate basis for modeling this inflow. Gas turbines are highly complex coupled systems and hence inflow and outflow boundary condition specification needs to go beyond just synthesizing turbulent structures and preventing their reflection.Despite the strong limitations of the dissipative Smagorinsky model, it still sees the most wide spread use, generally, in excessively dissipative flow solvers. Monotone Integrated LES (MILES) related approaches, hybrid LES–RANS and more advanced LES models seem to have an equal but subservient frequency of use in turbomachinery applications. Clearly the introduction of a RANS layer can have a substantial accuracy penalty. However, it does allow LES to be rationally used, albeit in a diluted sense for industrial applications. The Reynolds numbers found in turbomachinery are substantial. However, in certain areas evidence suggests they will not be enough to ensure a long inertial subrange and hence the use of standard LES modeling practices.Despite the excessively coarse grids used in much of the LES work reviewed, with essentially RANS based codes, meaningful results are often gained. This can perhaps be attributed to the choice of cases, these being ones for which RANS modeling gives extremely poor performance. It is a concern that for practical turbomachinery LES studies grid densities used tend to have an Reynolds number scaling to a strong negative power.     

一种基于CFD的叶轮机非定常气动力组合建模方法

为了获得一个准确高效的非定常空气动力学模型并将其应用于叶轮机叶片颤振特性分析中去,论文发展了一种基于CFD方法的叶轮机非定常气动力组合建模方法,可以快速计算叶轮机叶片在等相角差振动时的气动阻尼系数。运用小扰动流场的叠加原理,通过不同通道数模型的非定常流场求解(通常需要两次或三次),针对流场的周期性边界条件,组合分析得到一系列更多通道数情况下的非定常气动力低阶模型。基于这种降阶模型计算的气动阻尼系数与直接的CFD方法计算结果吻合很好,计算效率提高10倍以上。     

基于系统辨识技术的叶轮机非定常气动力建模方法

 为了快速获得不同刚度的叶轮机叶片颤振特性,提出了一种基于系统辨识技术的叶片排非定常气动力建模方法,分析了叶片气动阻尼随叶间相角差和固有频率的变化特性.该方法通过对多叶片通道的某一叶片单独施加一个扫频振动信号,求解一次非定常流场,得到叶片排上每个叶片的气动力响应,通过系统辨识,获得每个叶片的气动力频率响应.根据小扰动流的叠加原理,得到扫频范围内各固有频率下的叶片排所有叶片共同激励的气动力模型,由此进一步得到各个不同固有频率的所有叶间相角差下的气动阻尼.针对STCF4(Standard Test Configuration 4)算例,该方法的计算结果与直接采用计算流体力学(CFD)方法和直接采用谐振信号的降阶方法(ROM)得到的气动阻尼系数吻合得很好.该方法只需进行一次非定常CFD计算就能得到扫频范围内不同固有频率下的气动阻尼特性曲线,极大地提高了计算效率,方便了叶轮机设计初期的气动弹性稳定性参数分析.     

Experimental investigation of flow field in a laboratory-scale compressor

The inner flow environment of turbomachinery presents strong three-dimensional, rota-tional, and unsteady characteristics. Consequently, a deep understanding of these flow phenomena will be the prerequisite to establish a state-of-the-art design system of turbomachinery. Currently the development of more accurate turbulence models and CFD tools is in urgent need for a high-quality database for validation, especially the advanced CFD tools, such as large eddy simu-lation (LES). Under this circumstance, this paper presents a detailed experimental investigation on the 3D unsteady flow field inside a laboratory-scale isolated-rotor with multiple advanced measure-ment techniques, including traditional aerodynamic probes, hotwire probes, unsteady endwall static pressure measurement, and stereo particle image velocimetry (SPIV). The inlet boundary layer pro-file is measured with both hotwire probe and aerodynamic probe. The steady and unsteady flow fields at the outlet of the rotor are measured with a mini five-hole probe and a single-slanted hotwire probe. The instantaneous flow field in the rotor tip region inside the passage is captured with SPIV, and then a statistical analysis of the spatial distribution of the instantaneous tip leakage vortex/flow is performed to understand its dynamic characteristics. Besides these, the uncertainty analysis of each measurement technique is described. This database is quite sufficient to validate the advanced numerical simulation with LES. The identification process of the tip leakage vortex core in the instantaneous frames obtained from SPIV is performed deliberately. It is concluded that the ensemble-averaged flow field could not represent the tip leakage vortex strength and the trajectory trace. The development of the tip leakage vortex could be clearly cataloged into three phases according to their statistical spatial distribution. The streamwise velocity loss induced by the tipleakage flow increases until the splitting process is weak and the turbulent mixing phase is dominant.     

轴向三级旋流燃烧室流场结构大涡模拟

为深入了解真实航空发动机燃烧室内部复杂流场结构，在自有CFD平台上采用动态亚网格模型对一种轴向3级旋流燃烧室的单个头部矩形试验模型0.5MPa下冷态流场结构进行了LES(大涡模拟).为避免试验模型简化误差，对包括火焰筒上约2000个气膜孔在内的燃烧室所有精细结构进行了完全仿真.计算模拟了燃烧室内复杂流场从静止启动到统计定常状态的完整非定常发展过程，成功捕捉到主旋流与横向对冲射流相互影响作用及涡旋破碎等细观结构，获得的测点湍动能谱与湍流经典理论中惯性子区-5/3规律一致，LES时间平均流场结构与已有PIV（particle image velocimetry）试验结果吻合，表明所建立的高仿真网格与LES方法可进一步用于真实航空发动机环形燃烧室流场数值模拟.      

Coupled simulation of flow-structure interaction in turbomachinery

The aeroelastic behaviour of vibrating blade assemblies is usually investigated in the frequency domain where the determination of aeroelastic stability boundaries is separated from the computation of linearized unsteady aerodynamic forces. However, nonlinear fluid-structure interaction caused by oscillating shocks or strong flow separation may significantly influence the aerodynamic damping and hence effect a shift of stability boundaries. In order to investigate such aeroelastic phenomena, the governing equations of structural and fluid motion have to be simultaneously integrated in time.In this paper a technique is presented which analyses the flutter behaviour of turbomachinery bladings in the time domain. The structural part of the governing aeroelastic equations is time-integrated according to the algorithm of Newmark, while the unsteady airloads are computed at every time step by a Navier–Stokes code. The link between the two time integrations is an automatic grid generation in which the used mesh is dynamically deformed so that it conforms with the deflected blades at every time step.The computed time series of the aeroelastic simulation of an assembly of highly loaded compressor blades vibrating freely in transonic flow are presented. The energy transfer between fluid and structure is here dominated by vibrating shocks and shock-boundary layer interaction. It is investigated if the predicted aeroelastic stability boundaries differ from those of a linearised method.     

黏性彻体力建模方法及其应用

研究了将Navier-Stokes方程中黏性项简化为黏性彻体力的建模方法,并将该模型加入已有的计算流体力学(CFD)程序中,实现了用三维欧拉方程加黏性彻体力模型快速模拟叶轮机三维非定常流动的方法.使用该方法对进气周向总压畸变条件下的某双级压气机非定常流场进行了模拟,并与雷诺平均的Navier-Stokes(RANS)程...     

Investigation of flow unsteadiness in a highly-loaded compressor cascade using a dynamic mode decomposition method

Unsteady flow in the hub endwall region has long been a hot topic in the turbomachinery community. However important it is to the performance of the whole engine, the coherent unsteady flow phenomena are still not well understood. In this paper, the complex flow field in the hub endwall of a cantilevered compressor cascade has been investigated through numerical approach. The predicted results were validated by experimental data. To highlight the dominant flow structures among irregular and chao...     

叶轮机非定常气动设计的缘线匹配(II)数值研究

缘线匹配通过考虑多叶排叶轮机相邻叶排间前排叶片尾缘线与后排叶片前缘线空间相对位置匹配关系来进一步提升叶轮机性能,有潜力使叶轮机非定常设计走向工程实际。以一单级跨声轴流压气机和一单级轴流透平为例,尝试用基元流动展向积分方法和全优化方法改善其性能,从而示例应用缘线匹配的具体方法及前景。结果表明,缘线匹配为叶轮机非定常设计提供了可操作的自由度。     

高性能叶轮机全3维叶片技术趋势展望

高性能叶轮机是驱动先进航空发动机/地面燃气轮机发展的核心技术,为明晰叶轮机技术发展问题与趋势,在相关文献调研基础上,从基元叶栅、展向积叠、端区处理、精细化设计以及全局观念等方面出发,概要分析阐述了中国叶轮机全3维叶片技术继续发展的要点与突破口,指出全面综合最大折转亚声速叶栅、允许分离超声速叶栅、弱化激波叶栅、掠弯参数化积叠、叶身/端壁融合等基础研究成果并结合伴随方法进行精细化设计的负荷最大化技术,再辅以3维空间、非定常流动、细节关联等全局观念下派生的技术是全3维叶片技术的重要发展方向.未来全3维叶片将注重全3维空间流线曲率的良好控制.     

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.     

叶轮机非定常气动设计的缘线匹配技术

本文提出一种新的叶轮机气动设计自由度——缘线匹配技术。缘线匹配是指相邻两叶排中前排叶片后缘线与后排叶片前缘线的空间关系,更准确地说是其相位角关系。叶片尾缘线表征了叶片出口气流的分布型,它囊括了尾迹、激波、二次流等所有影响,另一方面,叶片前缘线代表了其对上游流场的势干扰。定常气动设计体系只能部分考虑叶片缘线的相互影响,大部分则被忽略了,然而在非定常框架下,相邻叶排缘线所代表的相互影响是显著的。本文首次提出了叶轮机非定常设计的缘线匹配技术,并通过理论分析及直列涡轮叶栅的非定常数值模拟结果展示了缘线匹配技术在未来提高叶轮机气动性能、气弹性能、气动噪声和热传导性能上的潜在能力。作者认为,缘线匹配技术将使叶轮机的非定常气动设计具有真实而可操作的内容,是叶轮机非定常气动设计的核心技术之一。      

The LES model's role in jet noise

Problem definition, near wall modeling and other factors, including grid structure along with its implications on filter definition, are suggested to be of potentially greater importance for practical jet simulations than the LES (large eddy simulation) model. This latter element in itself can be theoretically questionable. When moving to realistic engine conditions, it is noted that disentangling numerical influences from the LES model's appear difficult and negates the model value with its omission potentially being beneficial. Evidence cited suggests that if using an LES model for jets, choosing the numerically best conditioned or the one the code has or, for a dissipative solver, even LES model omission seems sensible. This view point precludes combustion modeling. Tensors of additional derivatives, used in non-linear LES models, when expanded, can yield potentially several hundred interesting derivatives. It is suggested that the MILES (monotone-integrated LES) and LES communities should move towards seeing where modified equation derivatives connect with derivatives that appear in more state of the art non-linear LES models. Then the best features could be combined to form mixed MILES–LES models or even mixed MILES–LES–RANS models. Combustion modeling also presents hybridization potential but in a different context. Most MILES-modified equation analysis focus on the spatial discretization and not the temporal. However, with some codes the spatial discretization terms are deliberately constructed to cancel temporal truncation error terms. Hence, the two things work in harmony and the temporal discretization can make a strong impact on resolved scales.     

高超声速滚转阻尼导数数值模拟

采用非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程描述物体简谐振动流场,并在Ｅｔｋｉｎ理论下给出绕定轴转动时滚转阻尼导数的计算公式,定常流场的计算采用空间二阶精度的交替方向隐式分解的ＮＮＤ格式,非定常流场的计算采用时、空二阶精度的Ｒｕｎｇｅ－Ｋｕｔｔａ多步格式,采用代数和方法生成物体静、动网格。最后给出高超声速下钝体外形滚转阻尼导数的计算结果,以及滚转力矩系数随瞬时振幅的变化曲线。     

三角翼过失速非定常洞壁干扰修正

分别以固壁条件和洞壁附近实测的压力分布,模拟各类实壁和透气壁试验段的洞壁边界条件,利用N-S方程数值求解模型在风洞中的绕流场,得出洞壁干扰对跨音速模型绕流的影响和气动力修正结果。初步研究结果表明,该方法能较有效地模拟模型在跨音速风洞中的绕流场,GBM04A模型在0.6m风洞中的试验结果经洞壁干扰修正后与无干扰参考结果吻合较好     

基于多小波的Volterra级数非定常气动力建模方法

非定常气动力建模除了要准确描述气动力的非定常特性,还要反映其非线性特性。Volterra级数因为对系统非线性具有很强的描述能力正日益受到重视。一阶Volterra核只能表达线性特性,要建立反映非线性特性的非定常气动力模型,需要引入二阶核甚至更高阶核的影响。高阶Volterra核辨识的主要困难在于待辨识参数的数量随着核阶次的增加而呈指数增加导致计算难度急剧加大,即出现所谓维数灾难问题。以一种分段二次多小波为基函数将Volterra核展开,求解一个高维病态方程组来计算展开系数,利用小波的多分辨分析在时间和频率两个维度的分解特性将方程降维,最终将问题转化为求解一个低维方程组得到稳定解。通过NACA0012翼型在马赫数0.8下作沉浮运动时,升力系数、阻力系数和俯仰力矩系数的二阶核和三阶核的辨识构建非定常气动力模型,然后由此计算不同减缩频率下的气动力并与CFD结果进行比较,验证了Volterra级数对非线性非定常气动力的描述能力和多小波处理方法的有效性。     

上游尾迹与涡轮叶栅通道涡相互作用研究

采用三维粘性非定常数值模拟方法研究了上游尾迹与涡轮叶栅通道涡的相互作用,对定常、非定常时均以及瞬时时刻流动机理进行了分析.结果表明:上游尾迹的非定常作用一方面增强了叶栅通道涡的径向涡,使得流动损失增大;另一方面能够一定程度上抑制通道涡中流向涡的发展,对控制损失起到正面作用,端区的综合非定常效应取决于两者之间的平衡.在本文计算条件下,上述两方面综合影响使得通道涡的非定常损失增大.      

Fourier methods for turbomachinery applications

Rapid increase in computing power has made a huge difference in scales and complexities of the problems in turbomachinery that we can tackle by use of computational fluid dynamics (CFD). It is recognised, however, that there is always a need for developing efficient methods for applications to blade designs. In a design cycle, a large number of flow solutions are sought to interact iteratively or concurrently with various options, opportunities and constraints from other disciplines. This basic requirement for fast prediction methods in a multi-disciplinary design environment remains unchanged, regardless of computer speed. And it must be recognised that the multi-disciplinary nature of blading design increasingly influences outcomes of advanced gas turbine and aeroengine developments. Recently there has been considerable progress in the Fourier harmonic modelling method development for turbomachinery applications. The main driver is to develop efficient and accurate computational methodologies and working methods for prediction and analysis of unsteady effects on aerothermal performance (loading and efficiency) and aeroelasticity (blade vibration due to flutter and forced response) in turbomachinery. In this article, the developments and applications of this type of methods in the past 20 years or so are reviewed. The basic modelling assumptions and various forms of implementations for the temporal Fourier modelling approach are presented and discussed. Computational examples for realistic turbomachinery configurations/flow conditions are given to illustrate the validity and effectiveness of the approach. Although the major development has been in the temporal Fourier harmonic modelling, some recent progress in use of the spatial Fourier modelling is also described with demonstration examples.     

上游尾迹与涡轮转子泄漏流相互作用数值模拟

叶轮机内部流动本质上是周期性非定常的,研究涡轮转子叶尖区域的非定常相互作用机理,对提高小展弦比高负荷涡轮性能具有重要意义.利用数值模拟方法研究了上游静子尾迹与涡轮转子叶尖泄漏流的非定常相互作用,分析了定常结果、时间平均结果以及瞬时时刻结果的流动图画.结果表明:上游静子尾迹与涡轮转子尖区二次流的相互作用能明显影响泄漏涡和机匣通道涡的时空演化规律,从而改变转子尖区的损失分布.上游尾迹在转子通道中传播时,诱导泄漏涡和通道涡区域出现周期性的扰动涡对,扰动涡对沿着泄漏涡和通道涡的轨迹向下游运动,使得转子尖区二次流结构呈现周期性变化.      

旋转弹气动力建模与飞行轨迹仿真

运用一种自回归滑动平均(ARMA)的时域气动力建模方法,以计算流体力学与刚体动力学(CFD/RBD)耦合仿真的输出结果为样本,对旋转弹的非定常气动力进行建模。利用建立的气动力模型与刚体动力学方程求解模块耦合,实现了旋转弹轨迹的快速仿真,并讨论了不同的建模方式对仿真精度的影响。算例结果表明:采用气动力模型与刚体动力学方程耦合仿真技术可以在不同初始发射条件下进行旋转弹飞行姿态与运动轨迹预测,且与CFD/RBD仿真结果吻合较好,证明ARMA气动力建模方法可以在保证旋转弹轨迹预测精度的同时大幅缩短仿真时间,节省计算资源。