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.     

湍流大涡数值模拟进展

本文简要陈述湍流大涡数值模拟的原理、优点,着重讨论湍流大涡数值模拟方法的关键问题及其可能解决的途径,包括脉动的过滤、亚格子模型、近壁模型和标量湍流的大涡数值模拟中的特殊问题.文章强调大涡数值模拟中亚格子应力的本质是可解尺度湍流和不可解尺度湍流动量间的输运,并以作者最近提出的新型亚格子模型说明发展亚格子模型的正确途径.文章最后提出湍流大涡数值模拟近期需要迫切解决的问题和其他具有挑战性的方向.     

On near wall measurements of wall bounded flows—The necessity of an accurate determination of the wall position

The present review paper is an account on the experimental determination of the wall position relative to the probe in wall-bounded turbulent flow studies. A thorough review on common measurement techniques as well as correction methods reveals, that there are a number of pitfalls, that—when not accounted for—can lead to wrong conclusions about the wall position and thereby also on the near-wall behaviour of mean and turbulence quantities. Employing the state-of-the-art databases from direct numerical simulations of wall-bounded turbulent flows various indirect methods have been tested and assessed in terms of their robustness and accuracy. It is also demonstrated that accurate measurements reaching the viscous sublayer are necessary in order to ensure a correctly deduced wall position, and dependent quantities as for instance the near-wall scaling of mean (e.g. Reynolds number dependence of the buffer region or the log law constants) and turbulence (e.g. the near-wall peak location of Reynolds stresses) quantities.In experiments using hot-wires near the wall it is well known that heat conduction between the hot-wire and the wall gives errors and mean velocity data from the viscous sublayer can usually not be used to determine the wall position. In this paper we introduce a new method which takes advantage of the similarity of the probability density distributions (pdf) in the near wall region. By using the high velocity data of the pdf, which is shown not to be affected by heat conduction, the heat conduction problem can be circumvented.Extensive appendices are included, describing the history and present knowledge about the scaling of the mean velocity in the near wall and overlap regions in wall bounded turbulent flows.     

高雷诺数槽道湍流的壁面模化大涡模拟研究

选取基准壁湍流的槽道流动,研究了多种模型的壁面模化大涡模拟.模型包括经典的大涡模拟、Spalart-Allmaras、分离涡模拟和一种动态混合模型.基于摩擦速度的雷诺数范围为395~12000,采用3组粗糙网格,流向和展向维数分别同取37,49和65,法向维数保证y+(1)~1.主要研究平均速度、雷诺切应力分布、详细分析了各模型的特性差异并展示了相应的湍流结构.研究表明:在高雷诺数粗糙网格下,大涡模拟失去求解精度,分离涡模拟出现对数律不匹配,动态混合模型的计算接近直接数值模拟,其对数率区可解应力约占雷诺切应力的93%,边界层外层可解应力约占99%.这说明合适的混合模型可以在经济成本下保证计算精度,具有解决实际问题的潜力.      

GAO-YONG湍流模型对湍流传热的数值模拟

将GAO-YONG湍流模型应用于湍流传热的研究,分别计算了平板剪切湍流和二维平面冲击射流的湍流传热问题.边界层剪切湍流流动与换热的计算表明:与传统的湍流模型不同,GAO-YONG湍流模型不需要对近壁区域做任何特殊处理(比如壁面函数、低Reynolds数修正等)即可模拟出从壁面到主流区的全部流动与传热情况;另外,对于冲击射流Nusselt数的模拟也得到了与实验符合较好的计算结果,准确地捕捉到了2种冲击高度下流场换热的不同特征,表明了GAO-YONG湍流模型能够较高精度地计算湍流换热.      

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.     

Numerical simulations of shock/boundary layer interactions using time-dependent modeling techniques: A survey of recent results

Supersonic or hypersonic flows within and around flight vehicles inevitably involve interactions of strong shock waves with boundary layers. Flows within inlet/isolator configurations, and flows induced by control surface deflections are some examples. Such interactions are time dependent in nature and are often subject to low-frequency, large-scale motion that induces local pressure and heating loads. With recent increases in available computer power, it has now become possible to simulate such interactions at experimentally relevant Reynolds numbers using time-dependent techniques, such as direct numerical simulation (DNS), large-eddy simulation (LES), and hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes (LES–RANS) methods. This paper will survey some recent work in this area and will describe insights in shock/boundary layer interaction physics gained by using these high-fidelity methods. Attention will be focused on studies that compare directly with experimental data at the same (or nearly the same) Reynolds number. Challenges in the application of these techniques to even more complicated high-speed flow fields are also outlined.     

一种改进的类DES湍流模拟方法

构造了一种基于一方程S-A(Spalart-Allmaras)模型和一方程Yoshizawa亚格子模型的混合RANS/LES(Reynolds-averaged Navier-Stokes/large eddy simulation)湍流模拟方法.在涡黏假设的基础上,将Yoshizawa亚格子湍动能方程转化为等效的亚格子湍流涡黏性输运方程,并采用混合函数将其与S-A模型方程进行混合,从而改进了DES(detached eddy simulation)模型的亚格子行为,同时克服了其依靠网格控制模型转换的缺点.模拟了超声速的带斜坡凹腔流动,并与相同网格下的LES及DES结果进行了比较,结果表明该混合RANS/LES方法在远离壁面的自由剪切流区域与LES行为一致,而在附着边界层区域表现优于LES和DES方法.      

壁面湍流模型对湍流分离流动数值模拟的影响

本文用三种近壁湍流模型计算了二个二维的湍流分离流动：单包流动和多包流动。结果表明：二层模型和低Reynolds数模型具有类似的特性。它们基本上给出合理的分离流动结构。壁函数的方法由于对数律的假定基本上不适合于计算湍流的分离流动。     

环形燃烧室两相喷雾燃烧的大涡模拟

在三维任意曲线坐标系下采用欧拉-拉格朗日两相大涡模拟方法对环形燃烧室火焰筒气液两相紊流瞬态反应流进行数值模拟.采用椭圆偏微分方程生成三维贴体网格,计算中所采用的数学度模型有:k方程亚网格尺度模型估算亚网格紊流粘性;亚网格EBU燃烧模型估算化学反应速率;热通量辐射模型估算辐射换热.并在非交错网格体系下气相采用SIMPLE算法和混合差分格式求解,液相采用随机离散模型(Stachasttc Separated Flow,简称SSF),在拉格朗日坐标系下追踪各油珠群沿各自轨道运动、质量损失及能量变化.通过计算结果与实验数据相比较,表明在三维贴体坐标系下对燃烧室火焰筒两相紊流油雾燃烧流场进行大涡模拟,采用欧拉-拉格朗日两相大涡模拟方法能反映两相紊流化学反应流流动及实际燃烧过程.     

超声速湍流边界层中横向声速喷流的混合LES/RANS模拟

通过对超声速湍流边界层中横向声速喷流的计算,对一种混合大涡/雷诺平均Navier-Stokes(LES/RANS)模拟方法进行了测试,该方法采用一个依赖于到壁面的距离及当地湍流参数的混合函数结合两方程k-ω SST(shear stress transport)湍流模型和混合尺度亚格子模型来封闭湍流项.计算结果表明:混合模拟方法能够捕捉到喷流/湍流边界层相互干扰的非定常大尺度结构,且对分离区长度、壁面静压峰值和膨胀区静压分布的计算精度要高于RANS(Reynolds-averaged Navier-Stokes)方法.      

旋转盘腔紊流流动的数值研究

为了比较近壁紊流模型对旋转盘腔内流动特征模拟精度的影响，采用在核心区选用标准k-ε模型、在近壁区选用单方程和Launder-Sharma两方程两种低雷诺数模型的区域紊流模化方法，对具有径向出流的转-静盘腔和具有径向出流的共旋盘腔结构的流动进行了数值计算研究，计算结果表明：在计算的两个算例中，前者采用近壁单方程模型要稍优于两方程模型，后者采用近壁两方程模型要明显优于单方程模型，因此近壁区紊流特性的处理对旋转盘腔内的流场模拟精度具有重要的影响。     

壁面函数在激波诱导分离流动中的应用

以数值模拟激波-附面层干扰引起的流动分离问题为研究背景,发展了基于有限体积方法的雷诺平均Navier—Stokes（RANS）方程的流场数值模拟方法。利用壁面函数模型得到壁面剪切应力,通过修正壁面粘性通量,构造了一种新的湍流边界处理方法,并将其耦合到RANS方程和SSTk-ω湍流模型的数值求解中;同时,针对激波诱导引起的附面层流动分离问题,提出一种附面层网格加密技术,能够自适应加密分离区内附面层网格,使得在流动分离区域也能够使用壁面函数模型。数值算例表明,壁面函数模型能够降低数值模拟结果对网格的依赖性;同时也验证了壁面函数耦合附面层网格自适应方法,在处理激波诱导引起的附面层流动分离问题时的有效性和准确性。     

展向不同间距壁面粗糙元对近壁湍流拟序结构的影响

采用氢气泡流动显示技术,研究了壁面不同展向间距粗糙元对近壁湍流拟序结构的影响。实验中粗糙元布置在氢泡丝前,其间距按如下两种排列设置：粗糙元直径的0、1和3倍,等间距1、2和4cm;每种情况粗糙元直径均为2.3、4和6mm。基于平均流速和水力直径的流动雷诺数从14000到48000变化。实验观测了光滑壁面和粗糙元壁面的近壁湍流拟序结构条带特征。发现：对于两种不同排列,相同雷诺数和相同粗糙元间距条件下条带有量纲间距均随着粗糙元直径增大而减小,条带有量纲高度均随粗糙元直径的增大而增大;相同雷诺数和相同直径粗糙元条件下条带有量纲间距均随着展向间距增大而增大,条带有量纲高度均随展向间距的增大而减小。粗糙元壁面湍流条带有量纲间距均比光滑壁面小,条带有量纲高度均比光滑壁面大。研究结果对近壁湍流的流动控制具有重要指导意义。     

轴对称弯道流动的N—S方程数值解

利用涡量—流函数方法求解离心压气机进气弯道中的轴对称粘性流场。本文推导出了q—τ湍流模型方程在正交曲线坐标系下的表达式,并用以预测湍流流场。文中在涡量方程及q—τ方程中引进非定常项,采用时间推进法求解。通过对二维直通道及复杂边界的轴对称弯道内的层流、湍流流动的计算,获得了令人满意的结果。      

A Nonlinear Sub-grid Scale Model for Compressible Turbulent Flow

本文采用直接过滤的Navier-Stokes方程组作为可压缩湍流大涡模拟控制方程组。方程组中因过滤产生的高阶相关项用Taylor级数展开近似,但仅保留级数的一阶导数项。这样产生的误差相当于丢失了模型的部分耗散作用,本文用一种动力学非线性亚格子模型来补偿丢失的耗散影响。本文根据Caylay-Hamilton定理导出了一个非线性亚格子模型,模型中包含的系数由动力学模式确定。与传统的动力学Smagorinsky模式相比,这种动力学非线性模型(DNM)稳定性更好,且不需要在统计均匀方向进行统计平均来计算模型系数,因此减少了计算开销。本文用这种非线性亚格子模型对绕双椭球高超声速湍流进行了模拟,并将所得结果与实验值、计算值及理论值进行了对比。结果表明,本文模型可以有效地模拟可压缩湍流流场。     

模型燃烧室紊流燃烧的大涡模拟

采用了两种不同的亚网格尺度燃烧模型对带 V型稳定器的模型燃烧室紊流化学反应流动进行了大涡模拟 ,用 k-ε方程亚网格尺度模型确定亚网格紊流粘性 ,为了考虑热辐射对燃烧室壁温和气流温度的影响 ,运用热流法辐射模型估算热辐射通量 ,用 SIMPLE算法和混合差分求解大涡模拟各守恒方程 ,通过对两种不同亚网格尺度燃烧模型数值模拟结果与实验值的比较表明 ,两种燃烧模型都与实验值较吻合 ,但 G方程小火焰模型要比亚网格 EBU燃烧模型符合得更好些      

Numerical simulation of compression corner flows at Mach number 9

A hypersonic vehicle encounters a wide range of conditions during its complete flight regime. These flight conditions may vary from low to high Mach numbers with varying angles of attack. The near-wall viscous dissipation associated with flows at combined high Mach and Reynolds numbers leads to significant wall heat transfer rates and shear stresses. The shock wave/boundary-layer interaction results in a flow separation region, which commonly augments total pressure losses in the flow and lowers the efficiency of aerodynamic control surfaces such as fins installed on a vehicle. The standard turbulence models, when used to resolve such flows, result in incorrect separation bubble size for large separated flows. Therefore, it results in an inaccurate aerodynamic load, such as the wall pressures, skin friction distribution, and heat transfer rate. In previous studies, the application of the shock-unsteadiness correction to the standard two-equation k-ω turbulence model improved the separation bubble size leading to an accurate pressure prediction and shock definition with the assumption of constant Prandtl number. In the present work, the new shock-unsteadiness modification to the k-ω turbulence model is applied to the hypersonic compression corner flows. This new model with variable Prandtl number is based on the model parameter, which depends upon the local density ratio. The computed wall pressures, heat flux and flow field are compared to the experimental data. A parametric study is carried out by varying compression deflection angles, free stream Reynolds number and wall temperatures to compute the flow field and wall data accurately, particularly in the shock boundary layer interaction region. The new shock-unsteadiness modified k-ω model with variable Prandtl number shows an accurate prediction of initial pressure rise location, pressure distribution in the plateau region and heat flux in comparison to the standard k-ω model.     

基于RANS/LES方法的超声速底部流场数值模拟

分别采用基于两方程k-ω剪切应力输运(SST)湍流模型的延迟DES(DDES)、更改的DDES(MDDES)和改进的DDES(IDDES)方法,并引入可压缩修正,结合三阶MUSCL-Roe和五阶WENO-Roe两种空间离散格式,针对超声速底部的复杂流动现象,开展了数值模拟研究。计算结果表明本文方法能够捕捉到超声速底部流动中丰富的湍流结构,通过分析计算结果对超声速底部的流动机理有了进一步的认识,为下一步的超声速底部流动减阻改进和雷诺平均NavierStokes/大涡模拟(RANS/LES)方法在非定常高可压缩性流动中的应用提供了参考。通过对比分析不同空间离散格式的计算结果研究了数值耗散对计算的影响,五阶WENO-Roe格式的计算结果与实验结果吻合良好;对不同RANS/LES混合方法的计算结果进行了对比分析,结果表明IDDES方法在近壁区的表现优于DDES和MDDES方法。     

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.