Navier-Stokes方程的局部投影稳定化方法

将Matthies,Skrzypacz和Tubiska的思想从线性的Oseen方程拓展到了非线性的Navier-Stokes方程,针对不可压缩的定常Navier-Stokes方程,提出了一种局部投影稳定化有限元方法.该方法既克服了对流占优,又绕开了inf-sup条件的限制.给出的局部投影空间既可以定义在两种不同网格上,又可以定义在相同网格上.与其他两级方法相比,定义在同一网格空间上的局部投影稳定化格式更紧凑.在同一网格上,除了给出需要bubble函数来增强的逼近空间外,还特别考虑了两种不需要用bubble函数来增强的新的空间.基于一种特殊的插值技巧,给出了稳定性分析和误差估计.最后,还列举了两个数值算例,进一步验证了理论结果的正确性.

瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方法

基于压力投影和梯形外推公式,对速度/压力空间采用等阶多项式逼近,针对高Reynolds数下的瞬态Navier-Stokes方程提出了一种新的全离散粘性稳定化方法.该方法不仅绕开了inf-sup条件的限制,克服了高Reynolds数下对流占优造成的不稳定性,而且在每一时间步上,只需要进行线性计算,从而减少了计算量.给出了稳定性证明,并得出了与粘性系数一致的误差估计.理论和数值结果表明该方法具有二阶精度.

Navier-Stokes方程自由面数值模拟（英文）

本文建立了不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法,数值模拟二维水槽的自由面波高.数值模拟研究了在不同的激励加速度和雷诺数下自由面波高,目前的数值方法很好地吻合了之前出版的结果.数值解结果表明自由面波高随时间在逐步地衰减,拍的周期数随雷诺数的增加也在减少.最后,自由面的波高随雷诺数的减少自由面的波高保持一个相对的稳定的波高.

An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.

Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Local projection stabilized finite element method for Navier-Stokes equations

This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier- Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.

A new full discrete stabilized viscosity method for transient Navier-Stokes equations

A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number （small viscosity coefficient） is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pres- sure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.

A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

Study of Tunnel Thruster Performance and Flow by Quasi-Steady Reynolds-Averaged Navier-Stokes Simulation

A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance and flow of tunnel thrusters.The flow passages between adjacent blades are discretized with prismatic cells so that the boundary layer flow is resolved down to the viscous sub-layer.The hydrodynamic performances predicted by the quasi-steady approach agree well with the experimental data for three impellers covering a range of blade area and pitch.Through analysis of the flow field,the reason why the hub of impeller also contributes to thrust which can amount to 40%—60% of the impeller thrust,and the mechanism of the impeller inducing an axial force on the hull are elucidated.

Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations

This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.

水陆两栖飞机全机模型静水滑行水动性能预报

水面起飞性能是水面飞行器的基本性能,也是总体技术的核心,涉及多个学科领域。水陆两栖飞机水面高速滑行水动力性能与排水型船不同,具有速度高、运动复杂等特点,高速滑行时一方面受到较大的水动升力,另一方面受到机翼的升力。结合水陆两栖飞机水面高速滑行特点,利用雷诺平均法(Reynolds average navier-stokes, RANS)数值方法和重叠网格技术对水陆两栖飞机全机模型开展数值仿真模拟,分析了自由液面水气分布、机身底部压力分布特征,并将阻力、姿态和升沉与水池模型试验结果进行对比,验证了数值方法的准确性,为水陆两栖飞机静水滑行水动性能数值预报提供技术基础。

基于RANS/LES混合方法的三维L型弯管流场特性数值模拟

L型弯管是船用典型部件,可实现流体质量输运和热量交换等功能。由于弯曲段曲率的影响,其内部流动十分复杂。传统的雷诺平均方法(RANS)无法模拟弯曲段的复杂流动,而大涡模拟方法(LES)则计算量太大。为此,采用RANS/LES混合方法对经典L型弯管进行数值模拟研究,该方法在近壁面区域采用RANS方法,在湍流核心区采用LES方法,不仅可保持模拟精度,而且网格需求量较低更适用于工程应用。针对商软中的2类RANS/LES方法——脱体涡方法(IDDES)及应力混合涡模拟(SBES)方法,比较分析其在L型弯管内部流场仿真方面的优劣,并同时考虑流向曲率修正的影响。结果表明:SBES方法对弯管内二次流(迪恩涡)的预测能力优于IDDES方法,且曲率修正模型可进一步改善SBES方法的仿真结果。

一种半潜式商用6 MW级风力机载荷数值模拟研究

针对海上漂浮式风力机在其运行状态下的叶轮气动载荷与平台运动状态难以预测的问题,本文以一种商用6 MW级漂浮式风力机为研究对象,基于非稳态的雷诺平均湍流模型,进行了全耦合数值模拟和水池模型试验研究。结果显示:浮式风力机自由衰减周期的模拟值在纵摇、横揺和垂荡上与实验值吻合度较高,而在纵荡、横荡和艏摇上,衰减周期的模拟值与实验值存在一定误差,这主要是由数值模型中对系泊系统进行悬链线简化时造成的。在静水工况下,风力机气动载荷的波动主要受塔影效应影响,机舱加速度的波动与叶轮推力系数变化呈正相关,浮式风力机纵荡和纵摇运动主要受叶轮气动载荷波动的影响;在规则波和非规则波工况下,叶轮推力的波动受浮式基础纵荡和纵摇的影响较大,叶轮推力系数变化和机舱速度呈负相关。浮式风力机的运动主要受波浪载荷的影响,气动载荷对其影响相对较小。

不同叶高水平的透平叶片气动特性分析

为了能够通过CFD手段优化透平叶片气动性能,本文使用雷诺平均方法针对工程上应用的66、44以及22 mm共3种典型叶高水平的透平模型进行了数值模拟,并将计算结果同实验测量结果进行了对比。同时,使用大涡模拟数值方法对22 mm叶高的模型进行非定常计算,得到了与实验结果吻合更好的等熵效率、质量流量等流场宏观参数,在三维流场上透平叶片的叶根与叶顶处的流动更为复杂。研究结果表明:雷诺平均方法可以对66和44 mm叶高的透平模型进行较准确的评估,对于22 mm叶高的透平,只有大涡模拟方法才能够清晰地捕捉到端壁区域紊乱的流动细节。叶片端部区域损失较大,雷诺平均方法处理得到的短叶片端壁区域丢失了流动的脉动细节,导致无法进行准确计算其端壁区域的流动。

基于雷诺平均法的四圆柱桩绕流数值模拟研究

为研究河海深水中水流对桥梁桩基础的动力学作用。文章基于ANSYS/FLUENT数值仿真软件,采用雷诺平均法研究四圆柱桩的绕流特征,分析7种不同迎流角及3种典型间距比下的四圆柱桩流场特征、各桩阻力系数及桩周床面所受切应力的分布。结果表明:迎流角与间距比均对四圆柱桩绕流特性有较强的影响;随迎流角从0°增大到45°,下游桩周床面切应力分布模式由屏蔽状态逐渐转变为分离流冲击状态;当间距比为1.0时,临界屏蔽角为5°;当间距比为1.5或2.0时,迎流角处在20°~30°之间,各桩阻力系数值均处于1.0±0.2范围,此时屏蔽效应最小。

Investigating the Effects of Injection Pipe Orientation on Mixing and Heat Transfer for Fluid Flow Downstream a T-Junction

At T-junctions, where hot and cold streams flowing in pipes join and mix, significant temperature fluctuations can be created in very close neighborhood of the pipe walls. The wall temperature fluctuations cause cyclical thermal stresses which may induce fatigue cracking. Temperature fluctuation is of crucial importance in many engineering applications and especially in nuclear power plants. This is because the phenomenon leads to thermal fatigue and might subsequently result in failure of structural material. Therefore, the effects of temperature fluctuation in piping structure at mixing junctions in nuclear power systems cannot be neglected. In nuclear power plant, piping structure is exposed to unavoidable temperature differences in a bid to maintain plant operational capacity. Tightly coupled to temperature fluctuation is flow turbulence, which has attracted extensive attention and has been investigated worldwide since several decades. The focus of this study is to investigate the effects of injection pipe orientation on flow mixing and temperature fluctuation for fluid flow downstream a T-junction. Computational fluid dynamics (CFD) approach was applied using STAR CCM+ code. Four inclination angles including 0 (90), 15, 30 and 45 degrees were studied and the mixing intensity and effective mixing zone were investigated. K-omega SST turbulence model was adopted for the simulations. Results of the analysis suggest that, effective mixing of cold and hot fluid which leads to reduced and uniform temperature field at the pipe wall boundary, is achieved at 0 (90) degree inclination of the branch pipe and hence may lower thermal stress levels in the structural material of the pipe. Turbulence mixing, pressure drop and velocity distribution were also found to be more appreciable at 0 (90) degree inclination angle of the branch pipe relative to the other orientations studied.

不同SST模型在圆柱绕流仿真中的应用比较

分别运用SST、SST-SAS湍流模型对Re=3 900的圆柱绕流进行了数值研究,重点从湍流结构捕捉、气动力计算等方面比较了雷诺平均RANS方法与RANS/LES混合方法的计算能力。数值结果表明:SST模型可以捕捉到流场主要特征,求解效率较高;SAS方法可以捕捉到流场小涡结构,并能较好地反映出尾迹非定常特性,但SAS求解占用更多的资源;使用SAS方法可释放更多的流场信息,求解的阻力系数、分离角等关键气动特征参数与试验值更接近;一般工程计算中推荐使用SST模型,高精度计算可使用SAS方法。

Development of SOM combustion model for Reynolds-averaged and large-eddy simulation of turbulent combustion and its validation by DNS

The derivation and closure methods of the second-order moment (SOM) combus- tion model are proposed. The application of this model to Reynolds averaged (RANS) and large-eddy simulation (LES) of turbulent swirling diffusion combustion, jet diffusion combustion, and bluff-body stabilized premixed combustion is sum- marized. It is indicated that the SOM model is much better than the eddy-beak-up (EBU) and presumed PDF models widely used in commercial software and engi- neering. The SOM modeling results are close to those obtained using the most accurate but much more complex PDF equation model. Moreover, it can save much more computation time than the PDF equation model. Finally, the SOM model is validated by the direct numerical simulation (DNS) of turbulent reacting channel flows.

Phase-averaged waveforms of Reynolds stress in wall turbulence during the burst events of coherent structures

The time sequence signals of instantaneous longitudinal and normal velocity components at different vertical locations in the turbulent boundary layer over a smooth flat plate have been finely measured by constant temperature anemometry of model IFA-300 and X-shaped hot-wire sensor probe in a wind tunnel. The longitudinal and normal velocity components have been decomposed into multi-scales by wavelet transform. The upward eject and downward sweep motions in a burst process of coherent structure have been detected by the maximum energy criterion of identifying burst event in wall turbulence through wavelet analysis. The relationships of phase-averaged waveforms among longitudinal velocity component, normal velocity component and Reynolds stress component have been studied through a correlation function method. The dynamics course of coherent structures and their effects on statistical characteristics of turbulent flows are analyzed.

大Reynolds数Navier-Stokes方程带回溯技巧的两水平方法

本文考虑了一种求解大Reynolds数定常Navier-Stokes方程带回溯(backtracking)技巧的两水平有限元方法.其基本思想是,首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上求解一个亚格子模型稳定化的线性Newton问题,最后又回到粗网格上求解线性化的校正问题.通过适当的稳定化参数和粗细网格尺寸的选取,本文的算法能取得最优渐近收敛阶.数值实验检验了理论分析的正确性和算法的有效性.