Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.

Hybrid Finite Compact-WENO Schemes for Shock Calculation

Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given.

CARS在超音速燃烧研究中的应用

报道了氮、氧和水的Q支CARS谱以及氢的S(5)和S(6)纯转动CARS的测量结果,并用来确定超音速燃烧火焰中的温度及氧的浓度;用水的Q支CARS谱得到共振与非共振谱积分面积比随浓度的变化曲线.提出并发展的同时测量氢和氧的CARS谱新方法,为同时测量火焰温度和氢、氧浓度提供了一条途径,特别对不含氮的燃烧系统更具重要意义.

Multiplex CARS measurements in supersonic H-2/air combustion

H-2 and O-2 multiplex coherent anti-stokes Raman spectroscopy (CARS) employing a single dye laser has been explored to simultaneously determine the temperature and concentrations of H-2 and O-2 in a hydrogen-fueled supersonic combustor. Systematic calibrations were performed through a well-characterized H-2/air premixed flat-flame burner. In particular, temperature measurement was accomplished using the intensity ratio of the H-2 S(5) and S(6) rotational lines, whereas extraction of the H-2 and O-2 concentrations was obtained from the H-2 S(6) and O-2 Q-branch, respectively. Details of the calibration procedure and data reduction are discussed. Quantification of the supersonic mixing and combustion characteristics applying the present technique has been demonstrated to be feasible. The associated detection limits as well as possible improvements are also identified.

氢／空气预混平面火焰CARS温度测量

介绍了一套用于燃烧研究中对温度和成分浓度测量进行校准的氢／空气预混平面火焰燃烧４系统。采用氮ＣＡＲＳ技术对氢／空气预混平面火焰温度进行了系统的测量，包括不同当量比条件下的温度分布，温度的纵向和横向空间分布。结果表明，氮ＣＡＲＳ测温与氢／空气预混平面火焰的理论计算温度之间的误差为３.４％，而在燃烧炉表面上方１ｍｍ以上的空间属于火焰的温度均匀区，温度的不均匀性约为１.８％。

同时测量氢氧CARS光谱确定火焰温度和氢氧浓度的研究

利用YAG激光器和一台染料激光器同时测量了氢/空气预混平面火焰中氢氧CARS光谱。从氢的S(5)和S(6)支纯转动线的强度比获得火焰温度，并与由氮的CARS光谱得到的温度进行了实验校验。氢和氧的浓度分别由氢的S(6)支和氧的Q支光谱求得，并利用氢/空气预混平面火焰的局部热力学平衡计算对所得浓度进行了校验。温度的校验误差为4%，而氢氧浓度的校验误差分别为14%和12%。

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.

USED CARS测量对撞式扩散火焰的温度分布

介绍了用USED CARS技术测量对撞式甲烷/空气扩散火焰前滞止区和尾流区的温度分布剖面。在滞止区富甲烷观察到甲烷燃烧前的热解过程；尾流区温度高于滞止区温度，表明在滞止区有未完全燃烧的中间产物存在，在尾流区发现C_2及CH的光谱也证明了这一点。

同时测量氢和氧CARS谱的新方法

提出一种仅需一台染料激光器即可同时测量火焰中氢和氧的CARS谱的新方法。取带宽为120cm~(-1)，中心波长位于580.4nm的Stokes光束与532nm的泵浦光束相配合，同时测量氢扩散火焰中的氢和氧的CARS谱，用氢的S(6)和S(5)的积分强度比确定火焰中的温度并与氮的Q支CARS谱测量的温度和经过热损耗修正的热电偶测得的温度取得了相当好的一致结果。一次测出氢和氧的CARS谱，避免多次测量中参数的难以重复性，提高了以温度为参数来确定浓度的准确性。