Embedding quasi laminar 1D flame profiles to model turbulent premixed combustion with a joint PDF method

A new model for turbulent premixed combustion is presented which is based on a joint velocity composition probability density function (JPDF) method. The key idea is a scale separation approach. The method combines the model by Bray, Moss and Libby [1] (BML) for premixed combustion with the flamelet approach for nonpremixed combustion. Here, a Lagrangian formulation of the BML model is considered. The progress variable used by the BML model becomes a computational particle property and its value is triggered by the arrival of the flame front at the particle's position. Similar as in the flamelet approach we assume that the smallest eddies are not small enough to disturb the reactive diffusive flame structure. To resolve the (embedded) quasi laminar flame structure, a flame residence time is introduced. With that residence time, the evolution of the particle composition, including enthalpy, can be determined from precomputed laminar 1D flames. The main challenge with this approach is to model the probability that an embedded flamefront arrives at the particle location, which is necessary to close the chemical source term. Numerical experiments of a turbulent premixed flame show good agreement with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameterized Scalar Profile Mixing Model for Turbulent Combustion Simulations

The composition fields in turbulent reacting flows are affected by turbulent transport (macromixing), molecular diffusion (micromixing), and chemical reactions. In the joint velocity-composition probability density function transport equation the highly non-linear macromixing and chemical reaction terms appear in closed form. This is a considerable advantage over moment closure methods. Micromixing on the other hand requires modeling and especially for turbulent combustion accurate mixing models are crucial. Our approach to model the mixing of scalars, e.g. species mass fractions or temperature, is based on considering one-dimensional parameterized scalar profiles (PSP). Here, an extension of the PSP mixing model to inhomogeneous flows is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Examination of errors of table integration in flamelet/progress variable modeling of a turbulent non-premixed jet flame

A flamelet model implementation consists of two steps: the generation of a set of laminar flamelet solutions and the integration of the laminar flamelet solutions with presumed shape probability density functions (PDFs) to produce a flamelet table for turbulent flame simulations. Many studies have been done in the past to examine the effect of different flamelet modeling strategies including the effect of employing different laminar flamelet solutions for the modeling. However, little work has been done to examine the effect of different presumed PDF table integration approaches on different flamelet model predictions. This work aims at investigating the source of errors arising from the flamelet table integration. The flamelet/progress variable model is chosen as a representative flamelet model, and three different presumed PDF table integration approaches are compared to examine the effect of table integration on flamelet model predictions. A laboratory-scale turbulent non-premixed jet flame (Sandia flame D) is chosen as a test case for the examination. In general, some evident sensitivity of the modeling results to the different flamelet table integration approaches is observed. The underlying reasons for the performance difference of different approaches are explored, and it is found that a model that preserves the one-dimensional laminar flamelet structure during the presumed-PDF table integration can improve the model prediction accuracy. Different sources of errors involved in flamelet model implementation are investigated, including numerical integration errors, flamelet table errors, and the errors in the predictions of the flamelet independent variables.     

内变量和伪弹性的热力学模型

在固体相变中经常出现滞后,需要内变量以描述滞后现象。对记忆合金单晶拉伸实验,所需内变量是奥氏体和马氏体区域的界面数。本文首先讨论有关的实验结果,然后给出以此内变量为基础的热力学模型。     

PARALLEL STABILIZATION

1.IntroductionLetusconsideranevolutionsystemwhosestateisgivenbythesolutionofaPartialDifferentialEquation(PDE)whichiswritten(formallyforthetimebeing)asIn(1.1),(1.2),whichmaybealinearoranonlinearPDE,ydenotesthestate,andvdenotesthecontrol.TheoperatorA,w...     

The effect of turbulence on mixing in prototype reaction‐diffusion systems

The effect of turbulence on mixing in prototype reaction‐diffusion systems is analyzed here in the special situation where the turbulence is modeled ideally with two separated scales consisting of a large‐scale mean flow plus a small‐scale spatiotemporal periodic flow. In the limit of fast reaction and slow diffusion, it is rigorously proved that the turbulence does not contribute to the location of the mixing zone in the limit and that this mixing zone location is determined solely by advection of the large‐scale velocity field. This surprising result contrasts strongly with earlier work of the authors that always yields a large‐scale propagation speed enhanced by small‐scale turbulence for propagating fronts. The mathematical reasons for these differences are pointed out. This main theorem rigorously justifies the limit equilibrium approximations utilized in non‐premixed turbulent diffusion flames and condensation‐evaporation modeling in cloud physics in the fast reaction limit. The subtle nature of this result is emphasized by explicit examples presented in the fast reaction and zero‐diffusion limit with a nontrivial effect of turbulence on mixing in the limit. The situation with slow reaction and slow diffusion is also studied in the present work. Here the strong stirring by turbulence before significant reaction occurs necessarily leads to a homogenized limit with the strong mixing effects of turbulence expressed by a rigorous turbulent diffusivity modifying the reaction‐diffusion equations. Physical examples from non‐premixed turbulent combustion and cloud microphysics modeling are utilized throughout the paper to motivate and interpret the mathematical results. © 2000 John Wiley & Sons, Inc.     

An Approach to Model Partially Premixed Turbulent Combustion withProbability Density Function (PDF) Methods

In turbulent combustion one distinguishes between premixed, non-premixed and partially premixed combustion. While laminar flamelet models proved to be extremely valuable for a wide range of non-premixed flame simulations, similar approaches are more problematic in the partially premixed regime. Here the laminar flamelet concept for non-premixed turbulent combustion simulations is generalized for the partially premixed regime. Similar as in the unsteady flamelet approach, the joint statistics of a progress variable, mixture fraction and scalar dissipation rate is used to obtain the joint statistics of the compositions from pre-computed flame tables. The required distribution is computed with a joint PDF method and the main differences between the new approach and previous ones, are the pre-computed tables and the way the evolution of the progress variable is calculated. Instead of evolving 1D flamelets, steady 2D solutions of burning flamelets propagating into unburned mixtures with varying mixture fraction are considered. The location of a fluid particle in this 2D laminar flame is defined by its mixture fraction and a burning time, which are modeled for each computational particle used in the PDF method. Numerical experiments of a turbulent lifted diffusion flame and a premixed Bunsen flame demonstrate that this approach can be employed for a wide range of applications. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inversion-Based Feedforward Control for the Transient Shaping of a Piezo-Actuated Cantilevered Kirchhoff Plate

Nowadays piezoelectric actuators are successfully applied for vibration suppression in structural mechanics. The progress in material and actuator development allows to put focus also on novel applications. In this contribution, a systematic approach for inversion–based feedforward control and motion planning is presented for the realization of a transient deflection profile of a cantilevered piezo–actuated plate modeling an adaptive wing. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust variable selection for finite mixture regression models

Finite mixture regression (FMR) models are frequently used in statistical modeling, often with many covariates with low significance. Variable selection techniques can be employed to identify the covariates with little influence on the response. The problem of variable selection in FMR models is studied here. Penalized likelihood-based approaches are sensitive to data contamination, and their efficiency may be significantly reduced when the model is slightly misspecified. We propose a new robust variable selection procedure for FMR models. The proposed method is based on minimum-distance techniques, which seem to have some automatic robustness to model misspecification. We show that the proposed estimator has the variable selection consistency and oracle property. The finite-sample breakdown point of the estimator is established to demonstrate its robustness. We examine small-sample and robustness properties of the estimator using a Monte Carlo study. We also analyze a real data set.     

明渠中变密度变粘度牛顿流体紊动基本方程式

本文利用Navier－Stokes方程及雷诺时均法则,导出了变密度变粘度牛顿流体的紊动微分方程式,并进一步导出了变密度变粘度牛顿流体在明渠中紊流流动时的运动微分方程式.文中首次提出了密度紊动应力与粘度紊动应力的概念.     

An improved modeling approach for circular flexure hinges with application to geometry optimization

Within this paper, a modeling approach for flexure hinges based on the Euler-Bernoulli beam theory for beams of variable cross section is investigated in a static analysis. The proposed approach is implemented in a finite beam element routine, for which two different discretizations are discussed. The results are compared to a full scale three dimensional model. It is shown that a circular flexure hinge cannot be modeled accurately with one element. An improved model with three elements across the flexure hinge length is presented which shows excellent accordance with the reference model. A geometry optimization is realized based on the improved, low-DOF model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scaling laws for turbulent boundary layer flows in favorable and adverse pressure gradient

An analytical theory is proposed to describe incompressible plane and axisymmetric turbulent boundary layer flows in favorable and adverse pressure gradients for near-equilibrium conditions. Scaling laws for the mean velocity, the Reynolds stress components, and the skin friction have been established. A universal friction law makes it possible to represent the skin friction distributions corresponding to different Reynolds numbers and pressure gradients in terms of a function of one variable. The theory is based on general physical assumptions and does not involve any special hypotheses on the nature of the turbulent motion. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A wavelet filtering based estimation of output gap

Accurate estimation of output gap is an important and challenging problem for any economy. We consider here the problem of estimating the output gap for the Indian economy. The estimation of output gap involves a hypothetical variable, the potential output of the economy. In this paper, we propose a wavelet filtering based technique for estimation of output gap using monthly the Index of Industrial Production (IIP) series. We compare the results obtained using the proposed wavelet based technique with the widely used Hodrick-Prescott filtering and Seasonal ARIMA modeling based techniques. In order to compare the output gap estimated using the proposed technique with the other techniques, we explore the causal relationship between the estimates of output gap and the growth rate of an equity market indicator. It is observed that the wavelet filtering technique gives better results than the more popular econometric and standard time-series modeling techniques.     

基于Fuzzy推理的时变系统建模

提出一种基于Fuzzy推理的时变系统建模方法,其基本思想是:对时间维度进行分割,在每个较短的时间间隔内用时不变模型代替时变模型,将这些时不变模型组合在一起,最终获得一个整体非线性时变的微分方程模型.分别研究了输入输出型时变系统和状态空间型时变系统的模型建立方法,除了从理论上保证了所获得的模型对系统的逼近性,还从仿真实验验证了用该方法建立的模型对非线性时变系统有很好的逼近效果.     

Extended flamelet model and improved interaction of chemistry and turbulence for modeling partially premixed combustion with a joint PDF method

Turbulent combustion is commonly categorized into premixed, non-premixed and partially premixed combustion. For nonpremixed combustion simulations the laminar flamelet concept proved to be very valuable while for the more complex case of partially premixed combustion this model shows considerable deficiencies. Here, the classical laminar flamelet approach is extended to the partially premixed combustion regime. For that, the joint statistics of mixture fraction, scalar dissipation rate and a progress variable, calculated with a joint probability density function (PDF) method, is used to get the statistics of the compositions and of the chemical energy source term from pre-processed flame tables. This approach can be compared with the unsteady flamelet concept; the main differences consists of the way the progress variable evolution is computed and in the pre-computed flame tables. The progress variable describes the point of time a fluid parcel is consumed by a flame front. The fluid parcels are represented by computational particles, which are used for PDF methods. The pre-computed flame tables are computed from steady solutions 2D stabilized flames propagating into an unburnt mixture with varying mixture fraction. The corresponding position of a fluid particle in such a 2D laminar flame is determined by its mixture fraction and a burning time; both to be modeled for each computational particle in the PDF simulation. Numerical experiments of turbulent diffusion jet flames demonstrate that this approach can be employed for challenging test cases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.     

An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. III. Evaporation and condensation problems

An analytical version of the discrete-ordinates method, the ADO method, is used here to solve two problems in the rarefied gas dynamics field, that describe evaporation/condensation between two parallel interfaces and the case of a semi-infinite medium. The modeling of the problems is based on a general expression which may represent four different kinetic models, derived from the linearized Boltzmann equation. This work is an extension of two other previous works, devoted to rarefied gas flow and heat transfer problems, where the complete development of the ADO solution, which is analytical in terms of the spatial variable, is presented in a way, such that, the four kinetic models are considered, in an unified approach. A series of numerical results are showed in order to establish a general comparative analysis between this consistent set of results provided by the same methodology, based on kinetic models, and results obtained from the linearized Boltzmann equation. In particular, the temperature and density jumps are evaluated.     

A dynamic subgrid-scale model for the large eddy simulation of stratified flow

A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa’s eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis