A quantitative method for a priori evaluation of combustion reaction models

In recent years, direct numerical simulations have been used increasingly to evaluate the validity and performance of combustion reaction models. This study presents a new, quantitative method to determine the ideal model performance attainable by a given parameterization of the state variables. Data from direct numerical simulation (DNS) of unsteady CO/H₂–air jet flames is analysed to determine how well various parameterizations represent the data, and how well specific models based on those parameterizations perform. Results show that the equilibrium model performs poorly relative to an ideal model parameterized by the mixture fraction. The steady laminar flamelet model performs quite well relative to an ideal model parameterized by mixture fraction and dissipation rate in some cases. However, at low dissipation rates or at dissipation rates exceeding the steady extinction limit, the steady flamelet model performs poorly. Interestingly, even in many cases where the steady flamelet model fails (particularly at low dissipation rate), the DNS data suggests that the state may be parameterized well by the mixture fraction and dissipation rate. A progress variable based on the CO₂ mass fraction is proposed, together with a new model based on the CO₂ progress variable. This model performs nearly ideally, and demonstrates the ability to capture extinction with remarkable accuracy for the CO/H₂ flames considered.     

The application of chemical reduction methods to a combustion system exhibiting complex dynamics

A number of chemical model reduction techniques have been developed over recent years with a growing range of applications in combustion. The following work demonstrates the application of such reduction techniques for a combustion system describing the oxidation of carbon monoxide + hydrogen in a continuously stirred tank reactor (CSTR) at very low pressure. The system exhibits complex dynamics including oscillatory glow, oscillatory ignition and mixed mode oscillations. It is demonstrated that a range of local reduction methods can be applied to such complex systems, as long as sufficient coverage of the accessed regions of phase space are included in the reduction analysis. The methods include sensitivity analysis, the quasi-steady state approximation (QSSA) and repro-modelling based on the concept of an intrinsic low dimensional manifold (ILDM). The system is qualitatively different from some previous applications of ILDM methods where trajectories tend towards a fixed equilibrium. The underlying dimension of the system is seen to vary throughout selected trajectories with rapid increases occurring over very short time-scales during oscillatory ignition. Nevertheless, a final reduced model of only four variables is developed using fitted orthonormal polynomials describing the system dynamics on a slow manifold. The application serves to demonstrate that the relationship between local reduced model error and global errors can be complex for systems exhibiting complex dynamics, with regions of seemingly small local mapping gradients requiring tighter error control in order to control global errors. This feature may be common in cases where nearby trajectories are seen to diverge within the slow manifold over time.     

Probability distribution for the number of cycles between successive regime transitions for the Lorenz model

The Lorenz model has been widely used for exploring many real world problems. In this paper we obtain, with the help of an invariant manifold technique, the return map for the maximum value of the variable x of the model and use this return map to derive the simple, empirically obtained, regime transition rules for forecasting regime changes and length in the new regime for the model. The probability distribution for number of cycles between successive regime transitions of the Lorenz model may be of interest in many disciplines. We apply the Perron-Frobenius algorithm over the return map to estimate the probability distribution for the number of cycles between successive regime transitions. These probabilities are also estimated for the forced Lorenz model, which is a conceptual model to explore the effects of sea surface temperature on seasonal rainfall.     

Oxidation enthalpies for reduction of ceria surfaces

The thermodynamic properties of surface ceria were investigated through equilibrium isotherms determined by flow titration and coulometric titration measurements on high-surface-area ceria and ceria supported on La-modified alumina (LA). While the surface area of pure ceria was found to be unstable under redox conditions, the extent of reduction at 873 K and a P(O₂) of 1.6 × 10⁻²⁶ atm increased with surface area. Because ceria/LA samples were stable, equilibrium isotherms were determined between 873 and 973 K on a 30-wt% ceria sample. Oxidation enthalpies on ceria/LA were found to vary with the extent of reduction, ranging from −500 kJ/mol O₂ at low extents of reduction to near the bulk value of −760 kJ/mol O₂ at higher extents. To determine whether +3 dopants could affect the oxidation enthalpies for ceria, isotherms were measured for Sm⁺³-doped ceria (SDC) and Y⁺³-doped ceria. These dopants were found to remove the phase transition observed in pure ceria below 973 K but appeared to have minimal effect on the oxidation enthalpies. Implications of these results for catalytic applications of ceria are discussed.     

Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows

We study the transport and mixing properties of flows in a variety of settings, connecting the classical geometrical approach via invariant manifolds with a probabilistic approach via transfer operators. For non-divergent fluid-like flows, we demonstrate that eigenvectors of numerical transfer operators efficiently decompose the domain into invariant regions. For dissipative chaotic flows such a decomposition into invariant regions does not exist; instead, the transfer operator approach detects almost-invariant sets. We demonstrate numerically that the boundaries of these almost-invariant regions are predominantly comprised of segments of co-dimension 1 invariant manifolds. For a mixing periodically driven fluid-like flow we show that while sets bounded by stable and unstable manifolds are almost-invariant, the transfer operator approach can identify almost-invariant sets with smaller mass leakage. Thus the transport mechanism of lobe dynamics need not correspond to minimal transport.The transfer operator approach is purely probabilistic; it directly determines those regions that minimally mix with their surroundings. The almost-invariant regions are identified via eigenvectors of a transfer operator and are ranked by the corresponding eigenvalues in the order of the sets’ invariance or “leakiness”. While we demonstrate that the almost-invariant sets are often bounded by segments of invariant manifolds, without such a ranking it is not at all clear which intersections of invariant manifolds form the major barriers to mixing. Furthermore, in some cases invariant manifolds do not bound sets of minimal leakage.Our transfer operator constructions are very simple and fast to implement; they require a sample of short trajectories, followed by eigenvector calculations of a sparse matrix.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport

A new dimension-reduction method, the Invariant Constrained-equilibrium Edge Pre-Image Curve (ICE-PIC) method, to simplify chemical kinetics has recently been developed by Ren et al. [Z. Ren, S.B. Pope, A. Vladimirsky, J.M. Guckenheimer, J. Chem. Phys. 124 (2006) 114111]. In the present work, the ICE-PIC method is first applied to the homogeneous autoignition of stoichiometric methane/air and its accuracy is shown to compare favorably to those of other methods (QSSA and RCCE). For inhomogeneous systems such as flames, spatial transport by molecular diffusion causes a small perturbation of the composition away from the attracting, low-dimensional, invariant manifold identified by the ICE-PIC method. A “close-parallel” assumption is introduced which allows this perturbation to be determined, and leads to an additional “transport coupling” term in the evolution equation for the reduced variables. For the test case of a steady, one-dimensional, laminar, methane/air flame, it is shown that the inclusion of transport coupling can reduce the dimension-reduction errors by a factor of 100. The ICE-PIC method with eight degrees of freedom (including transport coupling) exhibits comparable accuracy to a quasi-steady state assumption (QSSA) reduced mechanism with 12 degrees of freedom.     

Development of metal borohydrides for hydrogen storage

A metal borohydride M(BH₄)_n is a potential candidate for hydrogen storage materials because of its high gravimetric hydrogen density. The important research issues for M(BH₄)_n are to control the thermodynamic stability and to achieve the faster reaction kinetics. To clarify the thermodynamic stability, M(BH₄)_n (M=Mg, Ca∼Mn, Zn, Al, Y, Zr and Hf; n=2-4) were synthesized by mechanical milling and its thermal desorption properties were investigated. The hydrogen desorption temperature T_d of M(BH₄)_n decreases with increasing Pauling's electronegativities χ_P of M. Because Mn, Zn, and Al borohydrides (χ_P?1.5) desorb borane, they are too unstable for hydrogen storage applications. The enthalpy changes of desorption reaction ΔH_des can be estimated by using our predicted heat of formation of M(BH₄)_n ΔH_boro and reported data for decomposed products ΔH_prod, which are useful indicators for searching M(BH₄)_n with appropriate stability for hydrogen storage material. In the latter case, microwave processing was adopted for achieving fast reaction kinetics. Among metal borohydrides, LiBH₄ was rapidly heated above 380 K by microwave irradiation, 13.7 mass% of hydrogen was desorbed by microwave irradiation. The composites of LiBH₄ with B or C desorbed hydrogen within 3 min. Microwave heating aids in realizing faster kinetics of the hydrogen desorption reaction.     

Dimension reduction method for ODE fluid models

We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution.     

The application of the QSSA via reaction lumping for the reduction of complex hydrocarbon oxidation mechanisms

The quasi-steady-state approximation (QSSA) has been widely applied for the purposes of chemical kinetic model reduction. Although it is essentially a low-order approximation, it can be shown to lead to significant reductions in the number of fast variables within a mechanism without significant loss of accuracy for model predictions. Due to the couplings between QSSA expressions, the species are commonly solved for using numerical inner iteration techniques. Therefore, although the stiffness of the model system can be reduced, there is a computational overhead in solving the often nonlinear QSSA equations. Greater computational savings can be made where QSS species can be removed from the chemical model via explicit analytical expressions. In many cases these expressions are equivalent to reaction lumping. Where such reaction lumping can be achieved, a reduced mechanism in standard kinetic form can be developed, which contains new lumped reaction rate coefficients, but leads to the removal of QSS species. This paper describes such an approach for mechanisms describing the oxidation of the hydrocarbon fuels n-heptane and cyclohexane, and shows that significant reductions in both species and reactions can be achieved, leading to substantial computational speed-ups. The resulting schemes clearly demonstrate the main atomic flux patterns within the oxidation process. Patterns related to the time-scales of hydrocarbon radical species within alkane oxidation mechanisms are discussed, as well as the potential significance of non-QSS radicals in determining ignition behaviour.     

Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of “minimal relaxation” of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.     

A physical model for dimensional reduction and its effects on the observable parameters of the universe

We construct a physical model to study the effects of dimensional reduction that might have taken place during the inflationary phase of the universe. The model we propose is a (1 + D)-dimensional (D > 3), nonsingular, spatially homogeneous and isotropic Friedmann model. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. Independent of the details of the process of dimensional reduction, we impose suitable boundary conditions across the transitions and trace the effects of dimensional reduction to the currently observable parameters of the universe. In order to exhibit the cosmological features of the proposed model, we construct a (1 + 4)-dimensional toy model for both closed and open cases of Friedmann geometries. It is shown that in these models the universe makes transition into the lower dimension when the critical length parameter l _4,3, which signals dimensional reduction, reaches the Planck length in D = 3. The numerical models we present in this paper have the capability of making definite predictions about the cosmological parameters of the universe such as the Hubble parameter, age and density.     

FPGA-based architecture for real-time data reduction of ultrasound signals

This paper describes a novel method for on-line real-time data reduction of radiofrequency (RF) ultrasound signals. The approach is based on a field programmable gate array (FPGA) system intended mainly for steel thickness measurements. Ultrasound data reduction is desirable when: (1) direct measurements performed by an operator are not accessible; (2) it is required to store a considerable amount of data; (3) the application requires measuring at very high speeds; and (4) the physical space for the embedded hardware is limited. All the aforementioned scenarios can be present in applications such as pipeline inspection where data reduction is traditionally performed on-line using pipeline inspection gauges (PIG). The method proposed in this work consists of identifying and storing in real-time only the time of occurrence (TOO) and the maximum amplitude of each echo present in a given RF ultrasound signal. The method is tested with a dedicated immersion system where a significant data reduction with an average of 96.5% is achieved.     

工质热物理性质的计算方法及程序设计

文中就工质物性计算程序中常用的公式法和数据库法进行了讨论 ,并着重介绍了公式法的应用原理和编程方法。以低温工质为例 ,介绍了程序计算模块和界面模块各自的特点和相互关系 ,并分别采用 Fortran和 VC+ +两种语言混合编程的方法 ,实现了程序模块间的连接。此方法为DOS和 Windows不同平台间程序的移植提供了借鉴思路     

Numerical and experimental studies on housing optimization for noise reduction of an axial piston pump

This paper presents a methodology to reduce the noise of an axial piston pump through modification of the housing structure, combined with both numerical and experimental methods. The finite element models of the housing and cover are established, and are assembled together. The finite element models are validated and updated using experimental modal analysis. The frequency response function of the assembly is calculated, and the shell element in the inner surfaces of the housing is added. The effects of the thickness of the shell element on the frequency response function are identified. A topology optimization is conducted for the purpose of reducing the frequency response function and the increase of mass. The prototype pump is manufactured and assembled. Different experimental measurements are carried out, including the measurement of the vibration and the distributions of the sound pressure levels around the pump. Results show that the vibration and noise are reduced by using the optimized housing. In particular, the average sound pressure level is reduced by about 2 dB(A) at the discharge pressure of 250 bar, and the sound pressure level at the second harmonic is reduced significantly. The method proposed here can also be used for other kinds of displacement pumps.     

Optimization of global kinetics parameters for heterogeneous propellant combustion using a genetic algorithm

We examine the combustion of heterogeneous propellants for which, necessarily, the chemical kinetics is modelled using simple global schemes. Choosing the parameters for such schemes is a significant challenge, one that, in the past, has usually been met using hand-fitting of experimental data (target data) for global burning properties such as steady burning rates, burn-rate temperature sensitivity, and the like. This is an unsatisfactory strategy in many ways. It is not optimal; and if the target set is large and includes such things as stability criteria, or bounds, difficult to implement. Here we discuss the use of a general optimization strategy which can handle large data sets of a general nature. The key numerical tool is a genetic algorithm that uses MPI on a parallel platform. We use this strategy to determine parameters for HMX/HTPB propellants and AP/HTPB propellants. Only one-dimensional target data are used, corresponding to the burning of pure HMX (AP) or a homogenized blend of fine HMX (AP) and HTPB. The goal is to generate kinetics models that can be used in the numerical simulation of three-dimensional heterogeneous propellant combustion. The results of such simulations will be reported in a sequel.     

Effects of turbulence-chemistry interactions on auto-ignition and flame structure for n-dodecane spray combustion

The Engine Combustion Network (ECN) spray A under diesel engine conditions is investigated with a non-adiabatic 5D Flamelet Generated Manifolds (FGM) model with the consideration of detailed chemical kinetic mechanisms. The enthalpy deficit due to droplet vapourisation is considered by employing an additional controlling parameter in the FGM library. In this FGM model, β-PDF is used for the PDF integration over the control variable space. Validation results in non-reacting conditions indicate relatively good agreement between the predicted and experimental data in terms of liquid and vapour penetrations and mixture fraction spatial distribution. In reacting conditions, the effects of variance of mixture fraction and progress variable were examined. The ignition delay time and the quasi-steady flame structure are both affected by the variances. The variance of mixture fraction delays the ignition process and the variance of progress variable accelerates it. For mixture fraction, the ignition process is quicker at any stage in the case of neglecting variance. While things are more complex for progress variable, the ignition process is advanced in the case of neglecting variance at early times, but surpassed by the case of β-PDF later and until auto-ignition. When variance of mixture fraction is considered, the OH mass fraction shows a wide spatial distribution. While if not, a very thin flame is observed with a higher peak in OH, and a very large lift-off length. The variance of progress variable has little impact on the global flame structure, but makes the flame lift-off length much shorter. This study confirms the general observation, that the variance of mixture fraction is of higher importance in high temperature non-premixed combustion, however, we found that the variance of progress variable is far from negligible.     

The fluorescence interference in Raman spectrum of raw coals and its application for evaluating coal property and combustion characteristics

Fluorescence interference in Raman spectrum is a big barrier for rapid and precise analysis of coal structures by Raman spectroscopy. Dealing with fluorescence interference suitably is one of the key tasks before efficient application of Raman spectroscopy in coal assessment. In this study, Raman spectra and coal combustion characteristics of 32 kinds of Chinese coals were respectively obtained in a micro-Raman spectrometer and Thermal Gravimetric Analyzer. The degree of fluorescence interference in Raman spectrum was firstly defined and quantified as the drift coefficient α using a simple method without curve-fitting the spectrum. The correlations between the degree of fluorescence interference and coal property, coal combustion characteristics were set up and multivariable analysis was done. The results indicate that the degree of fluorescence interference is well related to the coal structures, and it is synthetically determined by volatile, moisture and ash content in coal. With the increase of volatile, moisture content in coal, the fluorescence interference increases continuously, and it can be reduced but not eliminated by drying the moisture in coals. Significant mathematical relations between the drift coefficient α and volatile, moisture content, coal combustion characteristic temperatures have been found. Coal with more evident fluorescence interference in Raman spectrum usually has lower degree of coalification, more polar functional groups, and burns at a lower temperature. The drift coefficient α can act as an efficient probe for coal property and coal combustion characteristics. This study provided a new and simple approach for evaluating coal property and coal combustion characteristics by fluorescence interference in Raman spectrum.     

Combustion of alane and aluminum with water for hydrogen and thermal energy generation

The combustion of alane and aluminum with water in its frozen state has been studied experimentally and theoretically. Both nano and micron-sized particles are considered over a broad range of pressure. The linear burning rate and chemical efficiency are obtained using a constant-pressure strand burner and constant-volume cell, respectively. The effect of replacing nano-Al particles by micron-sized Al and alane particles are examined systematically with the additive mass fraction up to 25%. The equivalence ratio is fixed at 0.943. The pressure dependence of the burning rate follows the power law, r_b = aPⁿ, with n ranging from 0.41 to 0.51 for all the materials considered. The burning rate decreases with increasing alane concentration, whereas it remains approximately constant with cases containing only Al particles. The chemical efficiency ranged from 32% to 83%, depending on the mixture composition and pressure. Thermo-chemical analyses are conducted to provide insight into underlying causes of the decreased burning rate of the alanized compositions. A theoretical model is also developed to explore the detailed flame structure and burning properties. Reasonably good agreement is achieved with experimental observations.