叶栅激波流场的数值模拟与高分辨率差分格式

一、前言 近年来,激波流场数值模拟技术的一个重要进展,是各种高分辨率总变差减小(TVD)格式的建立和发展。这类格式与常用的中心差分方法相比,其突出的优点在于,不需要人为地在差分方程中附加耗散项就能给出激波上、下游无波动的数值解,保证了数值流场具有很高的空间分辨率。目前这种方法已引起人们的高度重视,并逐渐发展成为应用计算中的流行格式。本文的目的,是探讨TVD格式在叶栅激波流场数值分析     

涡流数值模拟中的计算格式粘性分辨率探讨

采用理论分析和三角翼数值模拟实验相结合的方法,研究了目前常用的CFD计算格式——Jameson中心格式、RoeFDS格式、VanLeerFVS格式、迎风TVD格式等的粘性分辨率,论述了Jameson中心格式和RoeFDS格式在粘性分辨率上具有的优势,以及VanLeerFVS格式和迎风TVD格式在此方面的不足     

用高分辨差分格式解SNS方程

本文从Sweby的显式TVD格式^[2,3]出发,构造发一个推进方向一阶精度、侧向二阶精度的隐式TVD差分格式,并用于解可压缩流定常简化Naviev-Stokes(SNS)方程。对不出现流向分离的平板边界层和激波—边界层相互干扰两个问题的数值计算表明,方法可以有效捕捉流场中的间断。     

一种具有较小数值耗散的对称TVD格式

为了减小TVD格式的数值粘性,提高TVD格式的分辨度,提出了一种具有较小数值耗散的Harten型TVD格式.数值模拟结果表明,这种Harten型TVD格式比原来的Harten格式^[1]及其改进形式Harten-Yee^[2]的TVD格式能更好地模拟出边界层及涡流.     

多级风扇/压气机三维粘性流场的数值分析

采用叶排间掺混面模型,研究了多级跨音速风扇及压气机三维粘性流动数值模拟问题,利用ＬＵ－ＳＧＳ隐式算法使计算过程快速收敛,通过高分辨率格式改善跨音速流场中激波的分辨率。对某双级跨音速风扇及五级压气机流场进行了计算,双级风扇各状态的计算结果与实验数据吻合较好。     

非平衡化学反应流场NS方程计算研究

介绍一种新的与化学问题相耦合的NS方程数值方法,用来计算有限速率化学反应再入流场.采用迎风TVD差分格式的激波捕捉法,求解控制方程。本项研究针对轴对称流动。然而,可以直接推广到三维流动和其它的化学反应系统。所采用的整个泰氟隆-空气化学反应模型是由23个化学组元和35个化学反应所组成。对钝头球锥体全流场(包括前体和近尾迹)进行了数值模拟,获得了充分收敛的数值解。对清洁空气流场计算的峰值电子数密度与实验结果符合很好。     

跨音速轴流压气机级三维粘性流场全工况数值模拟

采用一种快速求解三维粘性流场的计算方法求解跨音速轴流压气机级内部流场及全工况特性。该方法以LU-SGS-GE隐式格式和MUSCL TVD迎风格式为基础,结合壁面函数方法和简单的混合长度湍流模型,对三维可压缩雷诺平均Navie-Stokes方程进行求解。叶列间参数的传递采用混合平面方法并应用了微机网络并行计算技术。计算得到了NASA 37号低展弦比、跨音速轴流压气机级70％设计转速下的全工况性能曲线,并重点分析了其中一些典型工况下的内部流场。计算与实验结果的对比表明此方法能快速得到三维粘性流场的流动特性且计算精度较高,可用来模拟跨音速轴流压气机级内的全工况三维粘性流动。     

局域能量注入对高超声速进气道流动影响研究

研究了局域能量脉冲注入条件下高超声速进气道流场的扰动情况。数值模拟采用三维雷诺平均N-S方程,分别利用ROE格式和二阶中心格式对对流通量和粘性通量进行离散处理;用高斯-赛德尔隐式格式对方程进行时间推进求解,采用k-ε两方程模型用于湍流的数值模拟。开展了高超风洞平板流场能量注入实验,获取了高速纹影图像,并对实验结果与计算结果进行比较。研究表明,能量注入产生的冲击波能与高超流动产生的斜激波发生强烈干扰,脉冲能量的引入可能引起高超声速进气道流量俘获率产生剧烈震荡,从而导致进气道流场的性能急剧下降。     

可燃悬浮寺燃烧诱导激波可其加速过程研究

以铝粉为例，基于双流体模型，分别采用ＴＶＤ格式和ＭａｃＣｏｍａｃｋ格式计算气相和颗粒相流场，基于Ａｒｒｉｈｅｎｉｕｓ定律及管道壁面湍流ｋ－ε模型计算流场反应速度，对水平燃烧管内可燃悬浮粉尘在弱点火条件下激波的产生及加强过程进行了理论分析与数值模拟。研究发现，壁面湍流在火焰加速及燃烧诱导激波过程中起着关键作用，数值计算结果揭示了可燃悬浮粉尘云中压缩波到激波的转捩机制及气固两相流场参数的变化规律。计算     

用TVD及MmB方法模拟理想非线性色谱过程

用高精度、高分辨率的激波捕捉法TVD(全变差衰减)及MmB(局部保最大、最小、有界)差分格式,对理想非线性色谱过程进行了数值模拟,以较高的分辨率确定了非线性色谱过程和激波效应,并计算了流出过程的保留时间,所得结果与理论分析及实验结果作了比较.     

2阶精度时间后差隐式格式TVD充分条件

非定常流动问题计算中常用到含三个时间层的二阶精度时间后差隐式格式,并且希望构成TVD格式,然而理论上的问题多年一直没有解决。本文找到了解决办法,构造了这种类型的隐式TVD格式,证明了其为TVD的充分条件。理论结果为计算所验证,并表明通常未采取本文对时间差分处理方法的格式尚不具备TVD性质。     

On large time step TVD scheme for hyperbolic conservation laws and its efficiency evaluation

A large time step (LTS) TVD scheme originally proposed by Harten is modified and further developed in the present paper and applied to Euler equations in multidimensional problems. By firstly revealing the drawbacks of Harten’s original LTS TVD scheme, and reasoning the occurrence of the spurious oscillations, a modified formulation of its characteristic transformation is proposed and a high resolution, strongly robust LTS TVD scheme is formulated. The modified scheme is proven to be capable of taking larger number of time steps than the original one. Following the modified strategy, the LTS TVD schemes for Yee’s upwind TVD scheme and Yee–Roe–Davis’s symmetric TVD scheme are constructed. The family of the LTS schemes is then extended to multidimensional by time splitting procedure, and the associated boundary condition treatment suitable for the LTS scheme is also imposed. The numerical experiments on Sod’s shock tube problem, inviscid flows over NACA0012 airfoil and ONERA M6 wing are performed to validate the developed schemes. Computational efficiencies for the respective schemes under different CFL numbers are also evaluated and compared. The results reveal that the improvement is sizable as compared to the respective single time step schemes, especially for the CFL number ranging from 1.0 to 4.0.     

Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry

The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the atmosphere in perfect gas. In this study, the simplified velocity distribution function equation for various flow regimes is presented on the basis of the kinetic Boltzmann–Shakhov model. The discrete velocity ordinate technique and numerical quadrature methods, such as the Gauss quadrature formulas with the weight function 2/π^1/2exp(?V²) and the Gauss–Legendre numerical quadrature rule, are studied to resolve the barrier in simulating complex flows from low Mach numbers to hypersonic problems. Specially, the gas-kinetic finite-difference scheme is constructed for the computation of three-dimensional flow problems, which directly captures the time evolution of the molecular velocity distribution function. The gas-kinetic boundary conditions and numerical procedures are studied and implemented by directly acting on the velocity distribution function. The HPF (high performance fortran) parallel implementation technique for the gas-kinetic numerical method is developed and applied to study the hypersonic flows around three-dimensional complex bodies. The main purpose of the current research is to provide a way to extend the gas-kinetic numerical algorithm to the flow computation of three-dimensional complex hypersonic problems with high Mach numbers. To verify the current method and simulate gas transport phenomena covering various flow regimes, the three-dimensional hypersonic flows around sphere and spacecraft shape with different Knudsen numbers and Mach numbers are studied by HPF parallel computing. Excellent results have been obtained for all examples computed.     

Implicit preconditioned WENO scheme for steady viscous flow computation

A class of lower–upper symmetric Gauss–Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier–Stokes equations of primitive variables with Spalart–Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.     

用多块多网格方法数值模拟三维粘性流动

本文给出了一个模拟三维粘性流动的数值方法．该方法来用高分辨率 ＴＶＤ Ｌａｘ－Ｗｅｎｄｒｏｆｆ格式求解三维雷诺平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，使用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ模型估计湍流粘性系数，用多重网格技术加速收敛，采用多块结构化网格处理复杂的物理域．文中给出了叶轮机械多个叶片排和透平排汽缸内的全三维粘性流动的数值结果．     

An improved wavelength selection scheme for Monte Carlo solvers applied to hypersonic plasmas

A new databasing scheme is developed for Monte Carlo Ray Tracing methods applied to hypersonic planetary entry. In this scheme, the complex relationships for the emission wavelength selection of atomic and molecular species in nonequilibrium flows are simplified by developing random number relationships for individual transitions, as opposed to using relationships for the spectral emission coefficient of a given species. These new techniques speed up wavelength selection by about 2 orders of magnitude, and offer flexibility for use in weighted or part-spectrum Monte Carlo solvers.     

高分辨率激波捕捉格式及其CFD应用

在曲线坐标下将高分辨率AUSMPW激波捕捉格式扩展到三维问题。为了提高计算精度,采用三阶MUSCL格式,将AUSMPW格式与隐械时间推进法LU－SGS方法结合,应用于可压缩无粘和有粘流动的数散模拟,计算结果与文献中计算结果和实验数据相符,并将该格式与CD、TVD、FVS和FD格式进行了比较。     

Multi-dimensional limiting for high-order schemes including turbulence and combustion

In the present paper a fourth/fifth order upwind biased limiting strategy is presented for the simulation of turbulent flows and combustion. Because high order numerical schemes usually suffer from stability problems and TVD approaches often prevent convergence to machine accuracy the multi-dimensional limiting process (MLP) [1] is employed. MLP uses information from diagonal volumes of a discretization stencil. It interacts with the TVD limiter in such a way, that local extrema at the corner points of the volume are avoided. This stabilizes the numerical scheme and enables convergence in cases, where standard limiters fail to converge. Up to now MLP has been used for inviscid and laminar flows only. In the present paper this technique is applied to fully turbulent sub- and supersonic flows simulated with a low Reynolds-number turbulence closure. Additionally, combustion based on finite-rate chemistry is investigated. An improved MLP version (MLP^ld, low diffusion) as well as an analysis of its capabilities and limitations are given. It is demonstrated, that the scheme offers high accuracy and robustness while keeping the computational cost low. Both steady and unsteady test cases are investigated.     

湿蒸汽两相流动问题的耦合求解

控制湿蒸汽两相流动(汽相和液相)的方程个数多,其数值模拟通常采用将两相分开、两相间用参数传递的方法来处理。本文首次尝试将湿蒸汽两相流动汽相和液相的8个控制方程统一求解,推导了这一方程组的特征值及对应的特征向量,结合控制体积方法,采用TVD格式和时间推进法数值求解这一耦合方程组,研发了相应计算软件。对二维喷管中的自发凝结和非均质凝结算例进行的数值模拟和分析,表明了本文方法和计算软件的有效性和可靠性。