A transition prediction method for flow over airfoils based on high-order dynamic mode decomposition

This article presents a novel approach for predicting transition locations over airfoils, which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver. This approach combines Dynamic Mode Decomposition (DMD) with e^N criterion. The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory (LST) analysis to quantify the spatial growth of Tollmien–Schlichting (TS) waves. Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter. To improve robustness, the high-order version of DMD technique (known as HODMD) is employed. A theoretical derivation is conducted to interpret how a spatial high-order DMD analysis can extract the growth rate of the unsteady perturbations. The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow (NLF) airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613. The transition locations predicted by our HODMD/e^N method agree well with experimental data and compare favorably to those obtained by some existing methods (LST/e^N or $\gamma -\stackrel{￣}{R{e}_{\theta \text{t}}}$). It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations.     

高超声速边界层的转捩及预测

首先描述了边界层转捩的基本过程及研究内容。在此基础上,指出了高超声速边界层不同于不可压缩边界层的流动不稳定性特性,并介绍了边界层的转捩机理与感受性特征;给出了高超声速三维边界层中预测转捩的常用方法,并着重介绍了多用于工程实际的e N方法以及对e N方法的理性改进,同时列举了在高超声速三维边界层中应用e N方法实现转捩预测的多个实例。最后,分析并总结了高超声速边界层转捩预测所存在的困难及需要解决的问题。     

Quantification of parametric uncertainty in γ-Reθ model for typical flat plate and airfoil transitional flows

Owing to the lack of physical knowledge of boundary layer transition, the γ-Re_θ transition model introduces closure parameters, which increase the uncertainty of transition prediction. The objective of this work is to quantify the uncertainties of closure parameters in the quantities of interests and identify the key parameters. The six closure parameters in the uncertainty intervals are used as input variables, and the uncertainties of the output results are propagated by a stochastic expansion based on the point-collocation nonintrusive polynomial chaos method. The relative contribution of each parameter to uncertainty is evaluated by the Sobol index. The computational cases include natural and bypass transitional flows on zero-pressure-gradient flat plates, and subsonic and transonic flows around airfoils. For most cases, c_e2, c_a2, and c_a1 dominate the uncertainty, and the influence of σ_θt is also significant when the history effects of flow are evident. The contribution of parameters in airfoils is more complex than that in flat plates. The transonic airfoil case shows that flow separation dramatically changes the distribution of Sobol indices, which poses a challenge to the accurate prediction of transition. Generally, c_e2 and c_a2 are the key parameters of the γ-Re_θ model.     

HyTRV流场特征与边界层稳定性特征分析

高超声速转捩研究飞行器（HyTRV）是为研究三维复杂外形的边界层转捩问题而设计的一款具备真实飞行器典型特征的升力体标模。为支撑更加全面系统的理论分析、数值模拟、风洞试验和飞行试验研究,采用高精度数值模拟方法、线性稳定性理论（LST）和e^N方法对HyTRV标模的典型流动特征和边界层失稳特征进行了分析。研究表明,HyTRV展现出多个相对独立的横流区域和多个流向涡结构;HyTRV的边界层存在横流失稳模态、第二模态、附着线失稳模态等常见模态。横流失稳模态出现在周向高低压区之间的横流区域,能够主导转捩发生;横流区域同时也存在第二模态,其N值普遍比横流失稳模态小;附着线失稳模态呈现出第二模态特性,且频率非常高。还研究了攻角和单位雷诺数的影响。结果表明,随着攻角增加,标模下表面中心线的流向涡结构逐渐消失,横流雷诺数逐渐减小;上表面流向涡结构逐渐从腰部移向顶端,并出现新的流向涡结构。增加攻角,所有失稳模态的N值总体上逐渐减小;增加单位雷诺数,N值显著增加。基于研究结果,针对流向涡失稳、横流失稳、第二模态和附着线失稳等给出了研究建议。     

Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties

It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions. In order to seek a more robust natural laminar flow control effect, it is necessary to develop an effective optimization design method. Meanwhile, attention must be given to the impact of crossflow(CF) instability brought on by the sweep angle. This paper constructs a robust optimization design framework based on discrete adjoint methods ...     

小攻角高超声速钝锥边界层失稳特性

利用高阶紧致格式,采用直接数值模拟(DNS)和线性稳定性(LST)分析方法,对高超声速边界层的失稳机制和转捩特点进行了研究.通过对马赫数为6的2?攻角高超声速钝锥边界层的稳定性分析发现:小攻角高超声速钝锥边界层存在多枝不稳定模态;周向速度使钝锥的稳定性特征与不考虑周向速度时有本质的差别;转捩线在接近背风面处出现拐折现象是由失稳模态发生转换引起的.      

Physics-based model for boundary layer transition prediction in a wide speed range

A new physics-based model employing three transport equations is developed for the simulation of boundary layer transitions in a wide speed range. The laminar kinetic energy is used to represent pretransitional streamwise velocity fluctuations, taking account of different instability modes. The fluctuation velocity components normal to the streamwise direction are modeled by another transport equation. Transition is triggered automatically with the development of the pretransitional velocity fluctuations. In the fully turbulent region, the model reverts to the k-ω turbulence model. Different test cases, including subsonic, supersonic and hypersonic flows around flat plates, airfoils and straight cones, are numerically simulated to validate the performance of the model. The results demonstrate the excellent predictive capabilities of the model in different paths of transition. The model can serve as a basis for the extension of additional transition mechanisms, such as rotation and curvature effects, roughness-induced transition and crossflow-induced transition.     

A numerical and experimental study of a transitional separation bubble

A combined numerical and experimental study of a two-dimensional transitional separation bubble due to an adverse pressure gradient is reported. The experiments have been performed in the MTL wind tunnel with a contoured wall imposing an adverse pressure gradient on the flow over a flat plate. The separated shear-layer is highly unstable and transition to turbulence occurs in the flow. The experimental separation bubble flow is modelled numerically using two-dimensional direct numerical simulations (DNS). Prescribing free stream boundary conditions in the wall normal velocity the experimental bubble is reproduced. The development of artificially forced two-dimensional instability waves is investigated and good agreement is found between experiments, simulations and linear stability theory (LST). The performance of several engineering transition prediction methods applied on the present separation bubble is presented and compared. Methods based on simplifications of the eⁿ-method yield predictions in accordance with experiments and DNS.     

旋翼三维非定常跨音速绕流的数值模拟

 利用小扰动位势方程，用有限差分方法求解了旋翼跨音速流场。导出了严格的三维非定常位势方程远场无反射边界条件，并成功地用于数值计算中，缩小了物理求解域的空间尺度。采用了贴体坐标和网格加密技术，以得到合理的非均匀网格分布。应用较少的网格点数成功地计算了无升力情况下旋翼的三维非定常亚、跨音速绕流流场，得到了与实验结果符合良好的数值解     

Assessment and improvement of k-ω-γ model for separation-induced transition prediction

The purpose of this work is to improve the k-ω-γ transition model for separationinduced transition prediction. The fundamental cause of the excessively small separation bubble predicted by k-ω-γ model is scrutinized from the perspective of model construction. On the basis,three rectifications are conducted to improve the k-ω-γ model for separation-induced transition.Firstly, a damping function is established via comparing the molecular diffusion timescale with the rapid pressure-strain timescale...     

高压压气机叶栅的高速模型和低速模型的相似变换准则

本文以相似理论为基础,从线性小扰动方程、跨音小扰动方程和全扰动势方程出发,推导出一组在进口马赫数不同时,保持两组叶栅气动力相似的变换准则。变换涉及跨音与亚音,跨音和不可压,亚音与不可压及其全扰动的情形。应用二维和准三维无粘数值计算方法进行数值验证,证明了变换关系在无粘下的正确性。文中使用了局部线化概念和一些假设,其合理性一并由数值试验得到证实。本文在理论和数值试验上为压气机叶栅的高速模型和低速模型之间的相似变换提供了必要的基础。      

γ-Re_(θt)-CF转捩模型在Spalart-Allmaras湍流模型中的推广及验证

横流(CF)不稳定性是三维流动中诱发转捩的一项非常重要的因素,考虑到γ-Reθt-CF转捩模型对流向Tollmien-Schlichting波和横流波不稳定性引起转捩的判定均是完全基于当地变量,且Spalart-Allmaras(SA)湍流模型计算效率高,因而将γ-Reθt-CF转捩模型与SA湍流模型相结合,并将其引入开源Standford University Unstructured(SU2)计算流体力学分析平台。为了考察和验证模型的预测精度,分别使用原始γ-Reθt模型和γ-Reθt-CF-SA模型,对NLF(2)-0415后掠翼型和标准6∶1椭球模型进行了转捩预测数值模拟。算例结果表明,γ-Reθt-CF-SA模型的计算结果与试验数据吻合程度远远优于原始γ-Reθt模型,γ-Reθt-CF-SA模型能正确地预测出三维流动中的横流不稳定性引起转捩的现象。     

Transition prediction and sensitivity analysis for a natural laminar flow wing glove flight experiment

Natural laminar flow technology can significantly reduce aircraft aerodynamic drag and has excellent technical appeal for transport aircraft development with high aerodynamic efficiency. Accurately and efficiently predicting the laminar-to-turbulent transition and revealing the maintenance mechanism of laminar flow in a transport aircraft’s flight environment are significant for developing natural laminar flow wings. In this research, we carry out natural laminar flow flight experiments with different Reynolds numbers and angles of attack. The critical N-factor is calibrated as 9.0 using flight experimental data and linear stability theory from a statistical perspective, which makes sure that the relative error of transition location is within 5%. We then implement a simplified e^N transition prediction method with a similar accuracy compared with linear stability theory. We compute the sensitivity information for the simplified e^N method with an adjoint-based method, using the automatic differentiation technique (ADjoint). The impact of Reynolds numbers and pressure distributions on TS waves is analyzed using the sensitivity information. Through the sensitivity analysis, we find that: favorable pressure gradients not only suppress the development of TS waves but also decrease their sensitivity to Reynolds numbers; there exist three special regions which are very sensitive to the pressure distribution, and the sensitivity decreases as the local favorable pressure gradient increases. The proposed sensitivity analysis method enables robust natural laminar flow wings design.     

纵向大扰动方程的变参数型变分裂法

 本文用变参数型变分裂法,解定常跨音速纵向大扰动方程。计算翼型气动力。对变参数型变分裂法以及它的参数选取方法作了必要的介绍。对NACA0012翼型,M_∞=0.8,α_A=0°;M_∞=0.95,α_A=0°;M_∞=0.75,α_A=1°,进行了计算。所得结果与其它结果进行了比较,表明本方法是快速收敛的、可靠的。     

嵌边法出流条件在可压缩流直接数值模拟中的应用

以嵌边法为出口边界条件试算了亚、超声速平板边界层扰动波的演化、超声速流中涡的传播、亚声速平板边界层尾缘扰动的演化等,以验证嵌边法作为出流条件在可压缩流中的有效性。然后,探讨了嵌边法有关参数的选取问题。     

边界层横流驻定扰动稳定性问题

采用直接对稳定性方程进行数值积分的方法,计算和研究三维可压（可带边界层控制）边界层横流驻定扰动（ｓｔａｔｉｏｎａｒｙｄｉｓｔｕｒｂａｎｃｅ）稳定性问题。导出积分初始边界处用于数值计算的矩阵表达式。通过改进的正则正交化并与误差判断相结合的方法,有效地控制正交化进程,克服了稳定性方程是刚性方程在积分求解中的困难。算例分析研究了跨音速后掠翼前部横流驻定扰动稳定性变化的关键因子和主要影响因素,结果是满意的     

计算三维粘性／无粘性干扰流动的准联立分区算法

 应用摄动理论导出了粘性／无粘性流动的匹配条件，与边界层方程联立形成能计及粘性／无粘性干扰效应的模型方程。同时引用等效吮吸理论对该模型方程与全位势方程进行交替迭代求解，建立了计算高雷诺数流动的一种快速收敛的粘性／无粘性分区算法。计算结果表明该算法适用于包括小尺度分离的流动；与传统的半逆解法相比，计算效率明显提高     

飞船返回舱跨声速全局稳定性研究

根据国内外在飞船返咽舱这类短钝飞行器的亚、跨声速风洞试验中都发现了极限环振动形态这一问题,利用全局稳定性分析和数字仿真方法,研究了返回舱在跨声速和高亚声带飞行时的动稳定性,得到与风洞试验类似的结果,即返回舱处于极限环振动形态。因此,在返回舱再入亚、跨声这飞行段,为保证飞行安全,采用有效和可靠的姿态控制系统来控制和减缓动不稳定影响是必需的。     

二维可压湍流边界层改进的积分方法

采用含高阶项的边界层动量积分方程,同时对常规边界层卷吸方程及延迟方程进行相应的高阶影响修正,得到改进的边界层积分方程组。应用此方程组对多种高亚音速及跨音速翼型边界层流动作了计算,并与一阶Ｇｒｅｅｎ方法计算结果及实验结果作了比较。结果表明,在边界层积分方程中保留法向压力梯度项及雷诺法向应力项,明显改进了翼面边界层接近分离区域处参数的计算精度。