A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damköhler numbers (Da) are considered. The low Da case (Da-) features extinction followed by reignition while extinction in the high Da case (Da+) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da- and Da+ cases. The EMST model captures well the trend for extinction and reignition for the Da- case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da+ case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.     

Coupling of mixing models with manifold based simplified chemistry in PDF modeling of turbulent reacting flows

For general reacting flows the numerical simulation faces two main challenges. One is the high dimensionality and stiffness of the governing conservation equations due to detailed chemistry, which can be solved by using simplified chemical kinetics. The other one is the difficulty of modeling the coupling of turbulence with thermo-chemical source term. The probability density function (PDF) method allows to calculate turbulent reacting flows by solving the thermal-chemical source term in closed form. Usually, the PDF method for turbulent processes such as mixing processes and the reduction method for chemical kinetics are developed separately. However, coupling of both processes plays an important role for the numerical accuracy. To investigate the importance of coupling between turbulence and simplified chemistry, two different coupling strategies for mixing and reduced chemistry are discussed and tested for the well-known Sandia Flames E and F, in which there is a strong interaction between turbulence and chemical kinetics. The EMST mixing model is chosen for turbulent mixing, while the Reaction-Diffusion Manifolds (REDIMs) is used as simplified chemistry. However, the proposed strategies are also valid for other mixing models and manifold based simplified chemistry.     

Propagation speed of combustion and invasion waves in stochastic simulations with competitive mixing

We consider the propagation speeds of steady waves simulated by particles with stochastic motions, properties and mixing (Pope particles). Conventional conservative mixing is replaced by competitive mixing simulating invasion processes or conditions in turbulent premixed flames under the flamelet regime. The effects of finite correlation times for particle velocity are considered and wave propagation speeds are determined for different limiting regimes. The results are validated by stochastic simulations. If the correlation time is short, the model corresponds to the KPP–Fisher equation, which is conventionally used to simulate invasion processes. If the parameters of the simulations are properly selected, the model under consideration is shown to be consistent with existing experimental evidence for propagation speeds of turbulent premixed flames.     

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.     

超高分辨差分吸收光谱技术测量火焰中OH自由基

介绍了超高分辨差分吸收光谱测量火焰中OH自由基的实验方法与结果分析.实验以准直氙灯作为光源;使用基长为20 m,反射次数176次,总光程为3 520m的怀特结构多次反射池扩展光程;使用光谱分辨率为3.3pm的超高分辨中阶梯光栅光谱仪作为光谱采集系统.该系统满足对OH自由基单根吸收谱线测量的需求.实验获得了OH自由基在3...     

Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion

Intrachannel four-wave mixing (IFWM) in highly dispersed differential phase-shift keying (DPSK) transmission systems is studied with a simple analytical model and numerical simulation. It is found that the IFWM effect in DPSK systems is smaller and less dependent on the bit pattern than in on-off-keying systems with the same average power. The reduced pulse energy in DPSK and correlation between the nonlinear phase shifts of two adjacent pulses contribute to the robustness of DPSK versus IFWM.     

Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture

We study flame acceleration and deflagration-to-detonation transition (DDT) in channels with obstacles using 2D and 3D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric H₂–air mixture is modeled by a one-step Arrhenius kinetics. Computations show that at initial stages, the flame and flow acceleration is caused by thermal expansion of hot combustion products. At later stages, shock–flame interactions, Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities, and flame–vortex interactions in obstacle wakes become responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. Computations performed for different channel widths d with the distance between obstacles d and the constant blockage ratio 0.5 reproduce the main regimes observed in experiments: choking flames, quasi-detonations, and detonations. For quasi-detonations, both the initial DDT and succeeding detonation reignitions occur when the Mach stem, created by the reflection of the leading shock from the bottom wall, collides with an obstacle. As the size of the system increases, the time to DDT and the distance to DDT increase linearly with d². We also observe an intermediate regime of fast flame propagation in which local detonations periodically appear behind the leading shock, but do not reach it.     

A comparison of different approaches to integrate flamelet tables with presumed-shape PDF in flamelet models for turbulent flames

Flamelet models for turbulent combustion modelling make use of presumed-shape probability density functions (PDFs) for integrating laminar flamelet solutions to obtain an integrated flamelet table that can readily be used for turbulent flame calculations. The existence of non-unique approaches for such an integration has rarely been investigated before. For the first time, this work studies systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable model is used in the study, although the issue exists generally in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. Three different table integration approaches are examined and compared in detail to provide a thorough understanding of the different approaches. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported PDF method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields a more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.     

Numerical models for the study of the nonlinear frequency mixing in two and three-dimensional resonant cavities filled with a bubbly liquid

The objective of this work is to develop versatile numerical models to study the nonlinear distortion of ultrasounds and the generation of low-ultrasonic frequency signals by nonlinear frequency mixing in two and three-dimensional resonators filled with bubbly liquids. The interaction of the acoustic field and the bubble vibrations is modeled through a coupled differential system formed by the multi-dimensional wave equation and a Rayleigh-Plesset equation. The numerical models we develop are based on multi-dimensional finite-volume techniques and a time discretization carried out by finite differences. Numerical experiments are performed for complex modes in many different cavities considering different kinds of boundary conditions and taking advantage of the dispersive character of the bubbly fluid to match specific resonances of the cavities. Results show the distribution of fundamental and harmonics for single frequency excitation and difference-frequency component for two-frequency excitation that are promoted by the strong nonlinearity of the bubbly medium. The numerous simulations analyzed suggest that the new numerical models developed and proposed in this paper are useful to understand the behavior of ultrasounds in bubbly liquids for sonochemical processes and applications of nonlinear frequency mixing.     

An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative

Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.     

An energy sum constraint of event mixing for Bose-Einstein correlations in reactions with ππX final states around 1 GeV

We present a new event mixing technique for measuring two-pion Bose-Einstein correlations(BEC)in reactions with only two identical bosons among three final state particles.This new mixing method contains a missing mass consistency(MMC)cut and an energy sum order(ESO)cut.Unlike the previous proposed pion energy cut,which abandons nearly half the original events,the ESO cut does not eliminate any original events and hence improves the statistics of both original events and mixed events.Numerical tests using theγp→π~0π~0p events around1 Ge V are carried out to verify the validity of the ESO cut.This cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects.In addition,its ability to observe BEC effects is tested by an event sample in the presence of BEC effects.Simulation results show the BEC effects can be observed clearly as an enhancement in the correlation function,and the BEC parameters extracted by this event mixing cut are consistent with the input BEC parameters.     

An analytical algorithm for the evaluation of two-electron integrals in diatomics: A test calculation with an elliptical basis set

A purely analytical method designed to compute the two-electron integrals that appear in anab-initio calculation of the electronic structures of diatomic molecules using elliptical basis set is presented. Test calculations are successfully carried out on LiH molecule.     

Renormalization group running of lepton mixing parameters in see-saw models with <Emphasis Type="Italic">S</Emphasis><Subscript>4</Subscript> flavor symmetry

We study the renormalization group running of the tri-bimaximal mixing predicted by the two typical S ₄ flavor models at leading order. Although the textures of the mass matrices are completely different, the evolution of neutrino mass and mixing parameters is found to display approximately the same pattern. For both normal hierarchy and inverted hierarchy spectrum, the quantum corrections to both atmospheric and reactor neutrino mixing angles are so small that they can be neglected. The evolution of the solar mixing angle θ ₁₂ depends on tanb\tan\beta and neutrino mass spectrum, the deviation from its tri-bimaximal value could be large. Taking into account the renormalization group running effect, the neutrino spectrum is constrained by experimental data on θ ₁₂ in addition to the self-consistency conditions of the models, and the inverted hierarchy spectrum is disfavored for large tanb\tan\beta. The evolution of light-neutrino masses is approximately described by a common scaling factor.     

An evaluation of the reproducibility of 1H-MRS GABA and GSH levels acquired in healthy volunteers with J-difference editing sequences at varying echo times

Recent advances in J-difference-edited proton magnetic resonance spectroscopy (¹H MRS) data acquisition and processing have led to the development of Hadamard Encoding and Reconstruction of MEGA-Edited Spectroscopy (HERMES) techniques, which enable the simultaneous measurement of ɣ-aminobutyric acid (GABA), the primary inhibitory amino acid neurotransmitter in the central nervous system, and of glutathione (GSH), the most abundant antioxidant in living tissue, at the commonly available magnetic field strength of 3 T. However, the reproducibility of brain levels of GABA and GSH measured across multiple scans in human subjects using HERMES remains to be established. In the present study, twelve healthy volunteers completed two consecutive HERMES scans of the dorsal anterior cingulate cortex (dACC) to assess the test-retest reproducibility of the technique for GABA and GSH measurements at TE = 80 ms. Eleven of the twelve participants additionally completed two consecutive MEGA-PRESS scans at TE = 120 ms, with editing pulses configured for GSH acquisition, to compare the reliability of GSH in the same voxel measured using the standard MEGA-PRESS at TE = 120 ms. The primary findings of study were that, 1) the coefficient of variation (CV) of measuring GABA with HERMES was 16.7%, which is in agreement with the reliability we previously reported for measuring GABA using MEGA-PRESS; and 2) the reliability of measuring GSH with MEGA-PRESS at TE = 120 ms was more than twice as high as that for measuring the antioxidant with HERMES at TE = 80 ms (CV = 7.3% vs. 19.0% respectively). These findings suggest that HERMES and MEGA-PRESS offer similar reliabilities for measuring GABA, while MEGA-PRESS at TE = 120 ms is more reliable for measuring GSH relative to HERMES at TE = 80 ms.