Flame propagation speed and Markstein length of spherically expanding flames: Assessment of extrapolation and measurement techniques

Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar.     

Extrapolation for Aeroengine Gas Path Faults with SVM Bases on Genetic Algorithm

Mining aeroengine operational data and developing fault diagnosis models for aeroengines are to avoid running aeroengines under undesired conditions. Because of the complexity of working environment and faults of aeroengines, it is unavoidable that the monitored parameters vary widely and possess larger noise levels. This paper reports the extrapolation of a diagnosis model for 20 gas path faults of a double-spool turbofan civil aeroengine. By applying support vector machine (SVM) algorithm together with genetic algorithm (GA), the fault diagnosis model is obtained from the training set that was based on the deviations of the monitored parameters superimposed with the noise level of 10%. The SVM model (C = 24.7034; γ = 179.835) was extrapolated for the samples whose noise levels were larger than 10%. The accuracies of extrapolation for samples with the noise levels of 20% and 30% are 97% and 94%, respectively. Compared with the models reported on the same faults, the extrapolation results of the GASVM model are accurate.     

L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

Richardson-extrapolated sequential splitting and its application

During numerical time integration, the accuracy of the numerical solution obtained with a given step size often proves unsatisfactory. In this case one usually reduces the step size and repeats the computation, while the results obtained for the coarser grid are not used. However, we can also combine the two solutions and obtain a better result. This idea is based on the Richardson extrapolation, a general technique for increasing the order of an approximation method. This technique also allows us to estimate the absolute error of the underlying method. In this paper we apply Richardson extrapolation to the sequential splitting, and investigate the performance of the resulting scheme on several test examples.     

三维矩形域上泊松方程四面体线元的超逼近与外推

改进三角元的积分恒等式,使之适用于拟一致四面体元,借此证明了泊松方程四面体线元梯度有超逼近现象,函数值Richardson外推可以提高精度.     

椭圆型方程四面体线元的超逼近与外推

重新讨论了三角线元的积分恒等式,使之适用于三维区域的拟一致四面体元,借此证明了椭圆型方程有限元解梯度有超逼近现象,函数值Richardson外推可以提高精度.     

The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi's periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers $h_{i}^{3}(i=1,...,d)$, which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.     

Lattice calculation of the κ meson

We study the κ meson in 2+1 flavor QCD with sufficiently light u/d quarks. Using numerical simulations, we measure the point-to-point κ correlators in the "Asqtad" improved staggered fermion formulation. We then analyze these correlators using rooted staggered chiral perturbation theory (rSχPT), with particular attention paid to bubble contribution. After chiral extrapolation, we obtain the physical κ mass with 828±97 MeV, which is within the recent experimental value of 800-900 MeV. These numerical simulations are carried out with MILC 2+1 flavor gauge configurations at a lattice spacing of a ≈ 0.12 fm.     

垂直于界面V型缺口尖端的应力奇异性及其应用

基于双材料垂直于界面V型缺口理论,给出了单一材料和双材料裂纹问题、V型缺口问题应力强度因子的统一定义,得到了应力外推法计算双材料K_I的公式,数值算例验证了本文方法的有效性.以双材料单向拉伸和三点弯曲模型为对象,深入研究了双材料中弹性模量、泊松比、缺口深度、缺口张角对缺口尖端奇异应力场的影响,获得了一定范围内各种参数变化对缺口尖端奇异应力场的影响规律,为异体材料形成的V型缺口在应力断料中的应用提供了必要的参考依据.