基于高阶方法的工业大涡模拟进展（英文）

众所周知,在达到相同精度的情况下,用高阶方法进行大涡模拟,速度可以比二阶方法快几个数量级。由于具有这种潜力,将这些高阶方法"工业化"并在实际中应用已经取得了很大的进展。在过去的十年中,在工业界,特别是在涡轮机械中,大涡模拟的使用已显著增加,这可能是因为燃气轮机中的雷诺数不是特别高,并且此类模拟对理解关键流动机理具有很大影响。在本文中,我们回顾过去十年应用高阶方法在大涡模拟方面取得的最新进展,并展望在不久的将来将大涡模拟推入设计过程最有前景的研究领域。     

基于隐式大涡模拟的高超声速热流计算研究

传统的大涡模拟方法面临着很多的困难,新提出的隐式大涡模拟可以作为解决这些挑战的一个方法。目前,隐式大涡模拟方法主要是在有限体积法中应用,也可将隐式大涡模拟应用于有限差分方法,使方程的截断误差更容易被控制,提高了隐式大涡模拟方法的精度。首先推导了有限差分方法中隐式大涡模拟的方程以及证明了其有效性,并提出了有限差分方法应用隐式大涡模拟方法数值计算的要求,隐式大涡模拟方法具有应用简单、普适性强、计算效率高的特点。最后编写了隐式大涡模拟方法的程序进行了数值试验,应用于高超声速湍流流场的热流计算,验证了方法的正确性。     

特征无反射边界条件应用于二维圆柱绕流模拟

采用特征无反射边界条件和吸收层技术相结合的边界处理方法,研究了二维圆柱绕流模拟的边界反射问题。近年来在计算气动声学中提出了将大涡模拟和声学传播方程结合的混合方法求解声场,基于计算量的考虑,须在较小的计算区域内进行大涡模拟,这就需要在计算区域较小时,边界的反射尽可能小。作为大涡模拟研究的技术储备,将该方法应用于二维圆柱绕流的模拟中。数值结果表明这种方法在计算区域较小时,能起到很好的无反射效果,计算结果与前人在计算区域取得很大时的结果比较吻合。     

分区LES/DES混合方法及缝翼三维流场模拟

提出一种分区大涡/脱体涡模拟混合方法,采用高阶空间有限差分方法和二阶隐式LU-SGS时间推进方法,对有限展长缝翼的三维流场进行了数值计算。该混合方法吸收了脱体涡模拟方法和大涡模拟方法各自的优点,在非核心区域使用脱体涡方法进行计算,相对于大涡模拟方法具有较高的计算效率;相对于分区脱体涡模拟中采用的雷诺平均方法,在计算量没有明显增加的条件下提高了对流场各尺度流动的模拟能力。计算结果与风洞实验数据吻合良好,同时缝翼流场主要观测点的压力脉动数据为后续缝翼噪声分析和低噪声优化提供了基础。     

ENO-AUSMPW格式对激波涡干扰的数值模拟

高阶ENO格式在复杂流场计算中具有重要的地位,它理论上可以达到任何阶的精度。本文采用二维高阶ENO插值方法,构造了高阶AUSMPW格式,并对包含复杂激波结构的激波涡干扰流场进行了数值模拟。计算结果表明了高阶ENO插值下的AUSMPW格式具有较高的激波分辨率和较低的数值耗散。     

洁净室流场大涡模拟

应用湍流大涡模拟方法对矢流洁净室和全顶棚送风下部两侧回风式洁净室进行了数值模拟。计算中使用了隐含流线抑风耗散作用的具有三阶部分展开的Taylor-Galerkin离散格式，导出了经Gauss滤波后的基本方程组的有限元列式，应用涡粘性亚格子模式的湍流大涡模拟方法进行数值模拟。数值计算结果与实验结果符合较好，表明湍流大涡模拟能够较准确地捕捉到洁净室流场中旋涡的位置和尺度，在洁净室的数值仿真方面，与标准的K－ε湍流模式相比，湍流大涡模拟结果具有较高的可靠性。     

用于可压缩壁面湍流DNS及LES入口湍流边界条件的回收-调节方法综述

很多湍流流动问题的大涡模拟和直接数值模拟的入口湍流脉动边界条件对于计算结果的影响很大,本文叙述了用于可压缩壁面湍流入口脉动生成的一种方法——“回收－调节”方法（recycling-rescaling method）,叙述了这种方法的理论基础及简要推导过程,介绍了几种常用的“回收－调节”方法并指出了实现中的几个关键问题,分析了这种方法中存在的不足并对其应用进行了总结评述。本文可为超声速流动、燃烧问题的大涡模拟和直接数值模拟方法的发展提供参考。     

一种混合格式的构建及其在多尺度流动中的应用

面向非定常湍流数值模拟方法精度提升问题,构建了实用的矢通量分裂(FVS)形式高阶精度混合格式。该格式平滑区具有五阶精度线性紧致格式的高分辨率特证,而强间断和强梯度区呈二阶耗散型格式特征,进而保证全流场计算的稳定性。基于所建立的混合格式开展有限体积大涡模拟(LES)计算,将其应用于三维高Reynolds数非定常湍流预测中。结果显示,所建立的数值格式能够可靠预测湍流多尺度涡结构特征,且计算量小,具有较高分辨率和鲁棒性。     

可压缩湍流边界层近壁区马蹄涡的演化

采用大涡模拟方法对可压缩槽道湍流进行了数值模拟.通过给定扰动波方法确定进口边界条件,很快得到了完全发展的湍流.利用动态亚格子模型、预处理技术以及高阶格式和方法,得到了精确的数值结果.计算得到的速度剖面和脉动分量与直接数值模拟的解进行了对比,验证了计算结果的可靠性.结果清楚地展示了湍流场中马蹄涡的生成和演化过程,包括对称涡腿、单侧涡腿的马蹄涡结构,以及流场中存在由亚谐波引起的拟序结构的交错现象.分析了湍流边界层近壁区可能出现的复杂的马蹄涡结构,及其涡结构形状也不严格对称的现象.     

用确定性涡方法模拟二维钝体绕流

以离散涡方法为基础,采用粒子强度交换法模拟涡量扩散方程,对粒子场分布产生扭曲变形时采用粒子强度重分配,数值模拟了突然起动圆柱、风攻角为的方形截面和大海带东桥的流场,计算结果与解析解及其他数值方法计算的结果均吻合的很好,数值结果显示确定性涡方法的高精度的特性使其在模拟钝体扰流问题方面具有很大的优势.     

基于高阶耗散紧致格式的GMRES方法收敛特性研究

计算效率较低是当前限制高阶精度计算方法应用的重要因素。为了提高高阶精度混合型耗散紧致格式（HDCS）的计算效率,发展了适合多块对接网格的广义最小残值（GMRES）方法,并利用GMRES方法开展了HDCS格式的加速收敛研究。首先研究了GMRES的预处理方法、CFL数和内层迭代步数对HDCS数值模拟收敛特性的影响,计算结果显示：点松弛方法是一种高效的预处理方法;CFL数对计算收敛速度影响较大;GMRES方法存在最优的内层迭代步数。利用GMRES方法完成了NACA 0012翼型绕流、NLR 7301翼型绕流和DLR-F4翼身组合体绕流的数值模拟,并与其他隐式时间推进方法进行了对比,GMRES方法计算更加稳定,并且计算效率相对LU-SGS（Lower-Upper Symmetric Gauss-Seidel）方法可以提高5倍以上。研究结果表明,本文发展的GMRES方法在多块对接网格中具有良好的计算稳定性,计算结果的残差可以收敛到更低的量级,并且可以较大幅度地提高高阶精度数值模拟的计算效率。     

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.     

高阶气体动理学格式在湍流数值模拟中的应用

本文回顾了高阶气体动理学格式在湍流数值模拟中的应用。与传统的Riemann求解器相比,气体动理学格式可以提供时空耦合的演化过程,这对发展高精度格式十分重要。因此,基于两步四阶时间离散和高精度WENO重构,发展了具有四阶时间精度的气体动理学格式。该格式有更高的数值精度和稳定性,并且具有更好的处理复杂流动问题的能力。目前,两步四阶格式已经成功地应用到低雷诺数湍流直接数值模拟和高雷诺数工程湍流RANS模拟中,包括低速槽道湍流、超声速均匀各向同性衰减湍流、二维亚声速翼型湍流和三维跨声速翼身湍流等。数值结果表明该格式对湍流直接数值模拟和湍流RANS模拟具有高数值精度和高数值稳定性。下一步将利用高阶气体动理学格式研究更具有挑战性的可压缩湍流问题,例如超声速湍流边界层和激波边界相互作用等。     

后向台阶超声速流动的动力混合RANS／LES模拟

针对可压缩湍流流动,构建了1种动力混合RANS/LES模式。运用该模式模拟了超声速后向台阶流动,结果再现了二维后向台阶剪切层的拟序结构,计算得到了统计平均的压力分布,回流区长度与实验结果符合较好。与定系数的一般混合RNAS/LES模拟结果的对比表明,动力混合RANS/LES模式在对流场拟序结构的捕捉、流动时均压力分布方面表现较优。     

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.     

三阶HWCNS的构造及其在高超声速流动中的应用

对网格质量要求高、计算稳定性差和计算效率低是制约高阶精度格式应用于高超声速复杂流动模拟的重要因素。针对这些问题,发展了三阶精度的混合节点半节点加权紧致非线性格式(HWCNS3),改进其光滑测试因子和非线性权得到了HWCNS3-OP,并给出了它们的频谱特性。利用Lax和Osher-Shu算例测试了格式对间断和高频波的捕捉能力;通过钝锥和航天飞机的高超声速绕流算例,考察了HWCNS3-OP在真实流动模拟中热流和气动力的预测精度及其计算效率。研究结果表明:HWCNS3-OP具有较高的分辨率和良好的间断捕捉能力,高频波捕捉能力相对HWCNS3提高了约3倍,相对守恒律的单调迎风中心格式(MUSCL)提高了约4倍;HWCNS3-OP计算稳定性较好,计算效率相对五阶HWCNS提高了2~3倍,HWCNS3-OP是一种较适合高超声速复杂流动模拟的高阶精度格式。     

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.     

高阶精度有限差分方法几何守恒律研究进展

针对高阶精度有限差分格式的几何守恒律问题,系统梳理了国内外离散几何守恒律问题方面的研究工作,以有限差分格式离散后的自由流保持问题为切入点,综述了近年来课题组在有限差分离散几何守恒律方面的研究工作,包括守恒网格导数算法(CMM)、对称守恒网格导数算法(SCMM)等,并通过若干典型算例验证了几何守恒律的满足对高阶精度有限差分方法数值模拟能力的提升。通过对有限差分离散几何守恒律问题研究工作的系统梳理,总结相关认识如下:1)直接基于网格变换导数的传统计算形式采用有限差分离散不能满足几何守恒律,需采用网格变换导数的守恒计算形式同时还需满足CMM条件;2)SCMM条件是满足几何守恒律的充分条件,且网格变换导数和雅克比均需采用其对称守恒计算形式,具有唯一性;3)自由流保持只是满足几何守恒律的一种表现形式;4)几何守恒律的满足能够有效提升高阶精度有限差分格式的数值模拟能力。     

厚覆冰导线升力突变机理及数值模拟研究

针对新月形厚覆冰导线的升力系数在风攻角15°附近存在突变的问题,分别采用基于k-ωSST湍流模型的雷诺时均法和大涡模拟(LES)的数值方法对新月形厚覆冰导线在风攻角10°~20°范围进行了模拟。通过对比两种数值方法计算得到的覆冰导线气动力系数、流场结构和表面风压,发现LES方法能够更好地捕捉新月形覆冰导线表面的小尺度涡结构,得到的覆冰导线气动力参数计算结果与风洞试验数据高度吻合;而k-ωSST湍流模型难以模拟壁面上小尺度涡,捕捉不到升力系数的突变。根据覆冰导线不同壁面区域的压力分布,发现上侧壁面处的涡结构影响整体流场,并在下侧壁面曲率、来流夹角和壁面切线方向共同作用下导致升力系数突变。LES的气动力参数模拟结果可为覆冰导线防舞提供参考。     

High-order implicit discontinuous Galerkin schemes for unsteady compressible Navier–Stokes equations

Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin(DG) discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta(IRK) scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.