CFD predictions of LBO limits for aero-engine combustors using fuel iterative approximation

Lean blow-out （LBO） is critical to operational performance of combustion systems in propulsion and power generation. Current predictive tools for LBO limits are based on decadesold empirical correlations that have limited applicability for modern combustor designs. According to the Lefebvre＇s model for LBO and classical perfect stirred reactor （PSR） concept, a load parameter （LP） is proposed for LBO analysis of aero-engine combustors in this paper. The parameters contained in load parameter are all estimated from the non-reacting flow field of a combustor that is obtained by numerical simulation. Additionally, based on the load parameter, a method of fuel iterative approximation （FIA） is proposed to predict the LBO limit of the combustor. Compared with experimental data for 19 combustors, it is found that load parameter can represent the actual combustion load of the combustor near LBO and have good relativity with LBO fuel/air ratio （FAR）. The LBO FAR obtained by FIA shows good agreement with experimental data, the maximum prediction uncertainty of FIA is about ±17.5%. Because only the non-reacting flow is simulated, the time cost of the LBO limit prediction using FIA is relatively low （about 6 h for one combustor with computer equipment of CPU 2.66 GHz · 4 and 4 GB memory）, showing that FIA is reliable and efficient to be used for practical applications.

ON REICH'S OPEN QUESTION

Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann.

UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION

The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇ s open question is given. The results presented extend and improve Zhang Shisheng＇ s recent ones in the following aspects ： （i） Zhang＇ s stronger condition that the sequence of iterative parameters converges to zero is removed; （ii） Zhang＇ s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （iii） Zhang＇ s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.

Solving two-dimensional Volterra-Fredholm integral equations of the second kind by using Bernstein polynomials

In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind（2DV-FK2）. Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model

In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition（POD）. Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.

Randomized Primal–Dual Proximal Block Coordinate Updates

In this paper,we propose a randomized primal–dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints.Assuming mere convexity,we establish its O(1/t)convergence rate in terms of the objective value and feasibility measure.The framework includes several existing algorithms as special cases such as a primal–dual method for bilinear saddle-point problems(PD-S),the proximal Jacobian alternating direction method of multipliers(Prox-JADMM)and a randomized variant of the ADMM for multi-block convex optimization.Our analysis recovers and/or strengthens the convergence properties of several existing algorithms.For example,for PD-S our result leads to the same order of convergence rate without the previously assumed boundedness condition on the constraint sets,and for Prox-JADMM the new result provides convergence rate in terms of the objective value and the feasibility violation.It is well known that the original ADMM may fail to converge when the number of blocks exceeds two.Our result shows that if an appropriate randomization procedure is invoked to select the updating blocks,then a sublinear rate of convergence in expectation can be guaranteed for multi-block ADMM,without assuming any strong convexity.The new approach is also extended to solve problems where only a stochastic approximation of the subgradient of the objective is available,and we establish an O(1/√t)convergence rate of the extended approach for solving stochastic programming.

Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation（PS） model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.

Asymptotic Variability Analysis for Multi-Server Generalized Jackson Network in Overloaded

The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded （OL） case, the asymptotic variability is studied for five performance measures： queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with （reflected） Brownian motions. We conduct numerical examples to provide insights on these LIL results.

Accidental Degeneracies in N dimensions for Potential Class αr^(2d-2)-βr^(d-2) via Asymptotic Iteration Method(AIM)

In mathematical physics the main goal of quantum mechanics is to obtain the energy spectrum of an atomic system.In many practices,Schrodinger equation which is a second order and linear differential equation is solved to do this analysis.There are many theoretic mathematical methods serving this purpose.We use Asymptotic Iteration Method(AIM) to obtain the energy eigenvalues of Schrodinger equation in N-dimensional euclidean space for a potential class given as αr^(2d-2)-βr^(d-2).We also obtain a restriction on the eigenvalues that gives degeneracies.Besides,we crosscheck the eigenvalues and degeneracies using the perturbation theory in the view of the AIM.