两种TVD格式在跨音透平叶栅流场计算中的应用

两种ＴＶＤ格式在跨音透平叶栅流场计算中的应用黄伟光，刘建军（中国科学院工程热物理研究所北京１０００８０）关键词跨音速透平，Ｅｕｌｅｒ方程，ＴＶＤ格式１引言现代高负荷透平大都工作在跨音范围，研究发展能准确预测跨音速透平叶栅内部流场的激波位置与强度以及叶...     

多级轴流压气机气动特性优化

采用轴对称特性优化程序对四级轴流压气机进行气动特性优化,研究分析叶片几何参数变化对设计工况及(n)=1.0、0.9转速线上性能影响.指出在多级轴流压气机气动设计过程中,设计工况性能优化将对非设计工况性能产生关联,因而在追求设计点性能同时必须兼顾各折合转速线上性能.实施非设计工况下设计参数优化有望带来多级轴流压气机性能整体提升.     

轴流透平通用叶型设计模块开发

1前言在叶轮机械气动热力设计体系中，叶型设计是最基本而关键的一环，叶型的好坏及选用适当与否对机组性能有非常大的影响。本文的工作是我们研制的多级轴流透平通流部分气动热力设计体系中的重要组成部分，其目的是要在满足结构、工艺、强度等约束条件的同时，高效、准确地设计出具有良好气动性能的叶型。本模块采用高档微机网络和中文NT操作系统作为支撑环境，选用商业化的CAD／CAM软件作为主要开发工具，在其基础上进行二次开发[1]。2叶型设计的类型与方法根据不同的已知条件，轴流透平叶型设计工作可分为三种类型：2．1已知初始叶…     

多级轴流压气机全工况特性计算

本文使用三维粘性流动计算软件Fine／Numeca,对某十五级轴流压气机进行了内流流场和全工况特性的数值计算尝试。分析了该压气机在设计工况和非设计工况的性能,同时把整机计算结果和前七级叶片的计算结果进行了比较。计算结果表明,当计算的级数较少时,目前的软件和硬件平台可以比较合理地预测压气机的全工况特性;而当计算的级数较多时,准确的数值模拟仍需要更为准确的多级模型和数值方法。     

开式轴流风扇气动噪声预测

本文采用LES/FW-H的匹配方法,研究了开式轴流风扇内部旋涡流动特征及其与叶片表面干涉引起的气动噪声之间的联系,同时进行了远场噪声预测,探讨了叶轮不同表面辐射噪声时的频谱分布特征.研究结果表明,开式轴流风扇吸力面附近形成的叶尖涡和前缘分离涡在吸力面叶片表面相应位置形成大压力波动,形成主要噪声源;叶片吸力面的辐射噪声可以通过改善吸力面附近的旋涡流动来降低;低速轴流叶轮由叶轮壁面辐射的噪声以宽频成分为主.     

二维叶栅气动特性的数值分析

过去研制一种新叶型需要做大量实验以确定其安装角、ｔ／ｂ（栅距／弦长）及出口几何角的使用范围，在可使用范围内还需要确定叶栅的攻角特性。这些在热力透平机械设计过程中是不可缺少的。随着计算机的发展及叶轮机械计算流体动力学的进步，人们已经可以通过主要是数值计算的方法来获得这些特性。本文给出了分析叶栅内二维流动特性的一种数值计算方祛。作者采用压力修正ＴＶＤ格式解雷诺平均的Ｎ－Ｓ方程组，壁面的湍流效应利用低雷诺数湍流模型模拟。运用本文方法计算了跨音及亚音叶栅内的湍流流动，并获得了某新叶型的使用范围及攻角特性。     

轴流透平与排汽系统间流场相互作用研究

为了研究轴流透平与非轴对称排汽系统流场间的相互作用,对带有单级透平的300/600MW汽轮机排汽系统模型内流场进了模型实验,并用商用软件CFX数值计算了实验工况下带有全周叶栅通道的单级透平与排汽系统内的耦合流场.对比实验与数值模拟结果,二者吻合较好.通过对实验和数值结果分析发现,排汽系统内的非轴对称流场使透平叶栅通道内流动沿周向发生变化,扩压器内出现大的流动分离,排汽系统内总压损失增大,静压恢复系数为负.     

轴流压气机转子尖区三维紊流特性

用三维激光多普勒测速系统测量研究了低速大尺寸单级压气机设计状态转子内尖区三维紊流流场．结果表明,设计状态下叶尖泄漏涡是造成压气机转子尖部素流脉动的主要因素,其造成的高素流区沿流向逐渐扩大,并缓慢向通道中部和低叶高方向移动,紊流强度值随旋涡的增强而增大．在泄漏涡影响区域中,径向脉动水平最高,轴向和切向脉动水平相近,三个剪切应力中,轴向一径向最大,切向一径向次之,轴向一切向最小．在叶片通道后段,泄漏涡发生破裂,导致更强、更大范围的紊流脉动,剪切应力中切向-径向应力较高．在叶尖吸力面角区后半部的角涡,紊流强度大,剪切应力也大,尤其是切向-径向剪切应力．     

多级轴流压气机内的流动机理研究

本文对某多级轴流压气机的两级内部流场进行了CFD数值模拟,通过计算结果和通流计算值对比,分析了多级轴流压气机的级间匹配特性,说明该两级压气机的总体匹配特性是合理的.但是,在两端壁附近也存在一些差异.通过对其内部流场的剖析发现,第11级静叶的吸力面两端和第12级动叶吸力面根部均存在一定程度的分离,文中解释了存在分离原因以及分离对压气机匹配特性的不利影响.     

应用高分辨率迎风格式精确分析透平叶栅三维湍流流场

应用高收敛率、高精度和高分辨率的数值计算方法,通过求解全三维可压缩雷诺平均的Navier－Stokes方程和q－ω低雷诺数双方程湍流模型,数值模拟了VKI跨音速叶栅内的三维流场,对叶棚内的三维流动结构进行了细致的分析。计算表明,本文采用的计算方法可以精确模拟叶轮机械内部的复杂流动。     

用代数多重网格法求解一维分裂格式的Euler方程

提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gaus-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展了它的应用范围,数值结果表明了它的有效性和强壮性。     

RKDG有限元法求解一维拉格朗日形式的Euler方程

描述一种新的求解Euler方程的拉格朗日格式,该格式用Runge-Kutta Discontinuous Galerkin(RKDG)方法在拉格朗日坐标系求解Euler方程,剖分网格随流体运动.新格式不仅保证流体的质量、动量和能量守恒,而且能够在时间和空间上同时达到二阶精度.数值算例表明在一维情况,随着拉氏网格的移动和改变,格式在时间和空间上仍保持二阶精度,并且没有数值震荡.     

On the Dynamics of Navier-Stokes and Euler Equations

This is a detailed study on certain dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a) zero viscosity limit of the spectra of linear Navier-Stokes operator, (b) heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Due to the difficulty of the problem for the full Navier-Stokes and Euler equations, we also propose and study two simpler models of them.     

Error Analysis of a PFEM Based on the Euler Semi-Implicit Scheme for the Unsteady MHD Equations

In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “∇·u=0”, which allows us to transform the saddle point problem into two smaller problems to solve. The Euler semi-implicit scheme is based on a first order backward difference formula for time discretization and semi-implicit treatments for nonlinear terms. It is worth mentioning that the error estimates of the fully discrete PFEM are rigorously derived, which depend on the penalty parameter ϵ, the time-step size τ, and the mesh size h. Finally, two numerical tests show that our scheme is effective.     

后掠风力机叶片气动性能数值模拟

采用商用软件FINE~(TM)/Turbo,以2.5MW风力机DF90风轮叶片为原型,在确认数值方法的基础上,将中叶展以上做后掠变型,进行三维定常数值模拟研究,讨论了后掠叶型对叶片气动特性的影响,并提出了一种定义后掠叶片静压系数的方法。     

A third-order finite-volume residual-based scheme for the 2D Euler equations on unstructured grids

A residual-based (RB) scheme relies on the vanishing of residual at the steady-state to design a transient first-order dissipation, which becomes high-order at steady-state. Initially designed within a finite-difference framework for computations of compressible flows on structured grids, the RB schemes displayed good convergence, accuracy and shock-capturing properties which motivated their extension to unstructured grids using a finite volume (FV) method. A second-order formulation of the FV–RB scheme for compressible flows on general unstructured grids was presented in a previous paper. The present paper describes the derivation of a third-order FV–RB scheme and its application to hyperbolic model problems as well as subsonic, transonic and supersonic internal and external inviscid flows.     

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson–Kruskal direct approach is employed to investigate the exact solutions of the2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2)and sech(kt/2) due to the rotational parameter k = 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.     

A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids

A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook (BGK) formulation is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The idea behind this approach is to combine the robustness of the BGK scheme with the accuracy of the DG methods in an effort to develop a more accurate, efficient, and robust method for numerical simulations of viscous flows in a wide range of flow regimes. Unlike the traditional discontinuous Galerkin methods, where a Local Discontinuous Galerkin (LDG) formulation is usually used to discretize the viscous fluxes in the Navier-Stokes equations, this DG method uses a BGK scheme to compute the fluxes which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at a cell interface through a simple hybrid gas distribution function. The developed method is used to compute a variety of viscous flow problems on arbitrary grids. The numerical results obtained by this BGKDG method are extremely promising and encouraging in terms of both accuracy and robustness, indicating its ability and potential to become not just a competitive but simply a superior approach than the current available numerical methods.     

The effect of shocks on second order sensitivities for the quasi-one-dimensional Euler equations

The effect of discontinuity in the state variables on optimization problems is investigated on the quasi-one-dimensional Euler equations in the discrete level. A pressure minimization problem and a pressure matching problem are considered. We find that the objective functional can be smooth in the continuous level and yet be non-smooth in the discrete level as a result of the shock crossing grid points. Higher resolution can exacerbate that effect making grid refinement counter productive for the purpose of computing the discrete sensitivities. First and second order sensitivities, as well as the adjoint solution, are computed exactly at the shock and its vicinity and are compared to the continuous solution. It is shown that in the discrete level the first order sensitivities contain a spike at the shock location that converges to a delta function with grid refinement, consistent with the continuous analysis. The numerical Hessian is computed and its consistency with the analytical Hessian is discussed for different flow conditions. It is demonstrated that consistency is not guaranteed for shocked flows. We also study the different terms composing the Hessian and propose some stable approximation to the continuous Hessian.