An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. These observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.     

Recent developments in DNS of turbulent combustion

The simulation of turbulent flames fully resolving the smallest flow scales and the thinnest reaction zones goes along with specific requirements, which are discussed from dimensionless numbers useful to introduce the generic context in which direct numerical simulation (DNS) of turbulent flames is performed. Starting from this basis, the evolution of the DNS landscape over the past five years is reviewed. It is found that the flow geometries, the focus of the studies and the overall motivations for performing DNS have broadened, making DNS a standard tool in numerical turbulent combustion. Along these lines, the emerging DNS of laboratory burners for turbulent flame modeling development is discussed and illustrated from DNS imbedded in Large Eddy Simulation (LES) and flow resolved simulation of bluff-body flames. The literature shows that DNS generated databases constitute a fantastic playground for developing and testing a large spectrum of promising machine learning methods for the control and the optimisation of combustion systems, including novel numerical approaches based on the training of neural networks and which can be evaluated in DNS free from sub-model artefacts. The so-called quasi-DNS is also progressively entering the optimisation loop of combustion systems, with the application of techniques to downsize real combustion devices in order to perform fully resolved simulations of their complex geometries. An example of such study leading to the improvement of an incinerator efficiency is reported. Finally, numbers are given relative to the carbon footprint of the generation of DNS databases, motivating the crucial need for community building around database sharing.     

A Web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES

The output from a direct numerical simulation (DNS) of turbulent channel flow at Re_τ ≈ 1000 is used to construct a publicly and Web services accessible, spatio-temporal database for this flow. The simulated channel has a size of 8πh × 2h × 3πh, where h is the channel half-height. Data are stored at 2048 × 512 × 1536 spatial grid points for a total of 4000 time samples every 5 time steps of the DNS. These cover an entire channel flow-through time, i.e. the time it takes to traverse the entire channel length 8πh at the mean velocity of the bulk flow. Users can access the database through an interface that is based on the Web services model and perform numerical experiments on the slightly over 100 terabytes (TB) DNS data on their remote platforms, such as laptops or local desktops. Additional technical details about the pressure calculation, database interpolation, and differentiation tools are provided in several appendices. As a sample application of the channel flow database, we use it to conduct an a-priori test of a recently introduced integral wall model for large eddy simulation of wall-bounded turbulent flow. The results are compared with those of the equilibrium wall model, showing the strengths of the integral wall model as compared to the equilibrium model.     

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper,we present a direct numerical simulation(DNS) of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number(Re = 1) in a three-dimensional straight channel flow for the first time,using the Giesekus constitutive model for the fluid.In order to generate and maintain the turbulent fluid motion in the straight channel,a sinusoidal force term is added to the momentum equation,and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field.Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS.The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.     

ANN based surrogate model for key Physico-chemical effects of cavitation

Intense and localised physico-chemical effects realised by cavitation such as generation of hydroxyl radicals, high-speed jets, and very high energy dissipation rates are being harnessed for a wide range of applications from emulsions, crystallisation, reactions to water treatment and waste valorisation. Single cavity models are typically used to quantitatively estimate such localised effects of cavity collapse. However, these models demand significant computing resources for resolving fast dynamics and therefore are very difficult, if not impossible, to integrate with CFD based cavitation device or reactor scale models. This severely limits the utility of device/ reactor scale models in simulating key applications of interest. In this work, we present, for the first time, artificial neural network (ANN) based surrogate models which accurately represent complex physico-chemical effects of cavity collapse. Recently developed cavity dynamics model was used for generating training data set encompassing both acoustic and hydrodynamic cavitation. Appropriate methodology for training ANN was developed. A shallow three hidden layer dense ANN was found to be more effective for estimating three main effects of cavity collapse: jet velocity, •OH generation and localised energy dissipation rate. The performance of trained ANN was then evaluated by comparing the predictions with the totally unseen data obtained from the cavity dynamics model. The developed ANN was shown to simulate unseen data very well not just within the range of training data (interpolation) but also beyond (extrapolation). Algebraic equations representing ANN are included to facilitate incorporation in device/ reactor scale CFD models. The presented methodology and results will be useful for developing high-fidelity CFD models of cavitation devices/ reactors based on key physico-chemical effects of cavity collapse.     

Toward computationally efficient combustion DNS with complex fuels via principal component transport

We investigate the potential of accelerating chemistry integration during the direct numerical simulation (DNS) of complex fuels based on the transport equations of representative scalars that span the desired composition space using principal component analysis (PCA). The transport of principal components (PCs) can reduce the number of transported scalars and improve the spatial and temporal resolution requirements. The strategy is demonstrated using DNS of a premixed methane–air flame in a 2D vortical flow and is extended to the 3D geometry to demonstrate the resulting enhancement in the computational efficiency of PC transport. The PCs are derived from a priori PCA of the same composition space using DNS. This analysis is used to construct and tabulate the PCs’ chemical source terms in terms of the PCs using artificial neural networks (ANN). Comparison of DNS based on a full thermo-chemical state and DNS based on PC transport with six PCs shows excellent agreement even for terms that are not included in the PCA reduction. The transported PCs reproduce some of the salient features of strongly curved and strongly strained flames. The results also show a significant reduction of two orders of magnitude in the computational cost of the simulations, which enables an extension of the solution approach to 3D DNS under similar computational requirements.     

Three-dimensional direct simulations and structure of expanding turbulent methane flames

Direct numerical simulations (DNS) are ideally suited to investigate in detail turbulent reacting flows in simple geometries. For an increasing number of applications, detailed models must be employed to describe the chemical processes with sufficient accuracy. Despite the huge cost of such simulations, recent progress has allowed the direct numerical simulation of turbulent premixed flames while employing complete reaction schemes. We briefly describe our own developments in this field and use the resulting DNS code to investigate more extensively the structure of premixed methane flames expanding in a three-dimensional turbulent velocity field, initially homogeneous and isotropic. This situation typifies, for example, the initial flame development after spark ignition in a gas turbine or an internal combustion engine. First investigation steps have been carried out at low turbulence levels on this same configuration in the past Symposium, and we build on top of these former results. Here, a considerably higher Reynolds number is considered, the simulation has been repeated twice in to limit the possibility of spurious, very specific results, and several complementary post-processing steps are carried out. Characteristic features concerning the observed combustion regime are presented. We then investigate in a quantitative manner the evolution of flame surface area, global stretch-rate, flame front curvature, flame thickness, and correlation between thickness and curvature. The possibility of obtaining reliable information on flame front curvature from two-dimensional slices is checked by comparison with the exact procedure.     

聚变堆液态包层准二维磁流体湍流模型研究

为研究聚变堆氚增殖包层中液态金属湍流磁流体动力学(MHD)效应,开发了一种新的准二维单方程 MHD 湍流模型,并进行了相关数值模拟程序的编制及验证。对于矩形管道中的准二维 MHD 湍流流动,三维流 动主要发生在哈德曼层中,中心的主流区呈现出二维流动。为了反映这种特殊的流动特征,新湍流模型在标准 k-ε 模型的基础之上去掉了传统的耗散项,代之以电磁耗散项来模拟湍流 MHD 效应。同时,采用 Bradshaw 假设来对 湍流涡粘系数进行模化。为验证该湍流模型是否合理,编制了相关数值模拟程序,并利用直接数值模拟(DNS)结 果对该程序进行了校正,数值模拟结果与 DNS 结果吻合较好。计算结果表明,该湍流模型可应用于聚变堆液态 包层 MHD 湍流流动的数值模拟。     

SGS Reaction rate modelling for MILD combustion based on machine-learning combustion mode classification: Development and a priori study

A neural network (NN) aided model is proposed for the filtered reaction rate in moderate or intense low-oxygen dilution (MILD) combustion. The framework of the present model is based on the partially stirred reactor (PaSR) approach, and the fraction of the reactive structure appearing in the PaSR is predicted using different NN’s, to consider both premixed and non-premixed conditions while allowing the use of imbalanced training data between premixed and non-premixed combustion direct numerical simulation (DNS) data. The key ingredient in the present model is the use of local combustion mode prediction performed by using another NN, which is developed in a previous study. The trained model was then assessed by using two unknown combustion DNS cases, which yields much higher dilution level (more intense MILD condition) and higher Karlovitz number than the DNS cases used as training data. The model performance assessment has been carried out by means of the Pearson’s correlation coefficient and mean squared error. For both the present model and zeroth-order approximated reaction rate, the correlation coefficient with the target values shows relatively high values, suggesting that the trend of predicted field, by the present model and zeroth-order approximation, is well correlated with the actual reaction rate field. This suggests that the use of PaSR equation is promising if the fraction of the reactive structure is appropriately predicted, which is the objective in the present study. On the other hand, substantially lower mean squared error is observed for a range of filter sizes for the present model than that for the zeroth-order approximation. This suggests that the present filtered reaction rate model can account for the SGS contribution reasonably well.     

Wooden windows: Sound insulation evaluation by means of artificial neural networks

Windows are the weakest part of a façade in terms of acoustic performance: the weighted sound insulation index (R_w), measured according to ISO 140-3, is the fundamental parameter to evaluate the façade acoustic insulation.The paper aims at developing an artificial neural network (ANN) model to estimate the R_w value of wooden windows based on a limited number of windows parameters; this is a new approach because acoustic phenomena are non-linear and affected by a plurality of factors and, therefore, usually investigated through experimentation.Data set is taken from experimental campaigns carried out at the Laboratory of Acoustics, University of Perugia. A multilayer feed-forward approach was chosen and the model was implemented in MATLAB. On the basis of the results obtained by means of a preliminary training and test campaign of several ANN architectures, five main parameters were selected as network inputs: window typology, frame and shutters thickness, number of gaskets, R_w of glazing; R_w value of the window is the network output. Different ANN configurations were trained and a root mean-square error less than 3% was obtained, comparable to measurement uncertainty.This approach allows to develop a model which, with input parameters varying within appropriate ranges, can easily estimate the acoustic performance of wooden windows without experimental campaign on prototypes, saving both money and time. If the training data set is large enough, the presented approach could be very useful for design and optimization of acoustic performance of new products.     

Machine learning for detailed chemistry reduction in DNS of a syngas turbulent oxy-flame with side-wall effects

A novel chemistry reduction strategy based on convolutional neural networks (CNNs) is developed and applied to direct numerical simulation (DNS) of a turbulent non-premixed flame interacting with a cooled wall. The fuel syngas mixture is burning in pure oxygen. The training and the subsequent application of the CNN rely on the processing of two-dimensional (2D) images built from species mass fractions and temperature (CNN input), to predict the corresponding chemical sources at the center of the image (CNN output). This image-type treatment of chemistry is found to efficiently capture intermediate radicals species highly sensitive to the local flame topology. To reduce the CPU cost, a simplified 2D DNS database with detailed chemistry serves as reference and is used for training and testing the neural network. Comparisons are also made a posteriori against the same 2D DNS with a reduced chemical scheme specialized for syngas. Then, three-dimensional (3D) DNS are conducted either with CNN or the reduced chemistry for more a posteriori tests. The CNN reduced chemistry outperforms the reduced Arrhenius based mechanism in the prediction of radical species, such as monoatomic hydrogen, and also in terms of CPU cost.     

An improved dynamic subgrid-scale model and its application to large eddy simulation of rotating channel flows

Rotating turbulence occurs extensively in nature and engineering circumstances. Meanwhile, understanding physical mechanisms of the rotating turbulence is important to the fundamental research of turbulence. The turbulent flow in rotating frames undergoes two kinds of Coriolis force effects. First, a secondary flow is induced in the case that there is a mean vorticity component perpendicular to the rotating axis. Second, there are augmenting or suppressing effects on the turbulence if there i…     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

An efficient approach to optimize the vibration mode of bar-type ultrasonic motors

The electromechanical coupled dynamic model of the stator of the bar-type ultrasonic motor is derived based on the finite element method. The dynamical behavior of the stator is analyzed via this model and the theoretical result agrees with the experimental result of the stator of the prototype motor very well. Both the structural design principles and the approaches to meet the requirements for the mode of the stator are discussed. Based on the pattern search algorithm, an optimal model to meet the design requirements is established. The numerical simulation results show that this optimal model is effective for the structural design of the stator.     

Periodic Filtering as a subgrid-scale model for LES of laminar separation bubble flows

Laminar separation bubbles develop over many blades and airfoils at moderate angles of attack and Reynolds numbers ranging from 10⁴ to 10⁵. More accurate simulation tools are necessary to enable higher fidelity design optimisation for these airfoils and blades as well as to test flow control schemes. Following previous investigators, an equivalent problem is formulated by imposing suitable boundary conditions for flow over a flat plate which allows to use a high accuracy spectral solver. Large eddy simulation (LES) of such a flow were performed at drastically reduced resolution to assess the accuracy of several LES modelling approaches: the explicit dynamic Smagorinsky model, implicit LES, and the truncated Navier–Stokes approach (TNS). To mimic dissipation that occurs in implicit LES, the solution on a coarse mesh is filtered at every time step and two different filter strengths are used. In the TNS approach, the solution is filtered periodically, every few hundred time steps. The performance of each approach is evaluated against benchmark direct numerical simulation (DNS) data focusing on pressure and skin friction distributions, which are critical to airfoil designers. TNS results confirm that periodic filtering can act as an apt substitute for explicit subgrid-scale models, whereas filtering at every time step demonstrates the dependence of implicit LES on details of numerics.     

基于Cholesky分解的增量式RELM及其在时间序列预测中的应用

针对应用于混沌时间序列预测的正则极端学习机(RELM)网络结构设计问题,提出一种基于Cholesky分解的增量式RELM训练算法.该算法通过逐次增加隐层神经元的方式自动确定最佳的RELM网络结构,并以Cholesky分解方式计算其输出权值,有效减小了隐层神经元递增过程的计算代价.混沌时间序列预测实例表明,该算法可有效实现最佳RELM网络结构的自动确定,且计算效率高.利用该算法训练后的RELM预测模型具有预测精度高的优点,适用于混沌时间序列预测. 关键词： 神经网络 极端学习机 混沌时间序列 时间序列预测     

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.     

Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data

Tensorial decompositions and projections are used to study the performance of algebraic non-linear models and predict the anisotropy of the Reynolds stresses. Direct numerical simulation (DNS) data for plane channel flows at friction Reynolds number (Re_τ = 180, 395, 590, 1000), and for the boundary layer using both DNS (Re_τ = 359, 830, 1271) and experimental data (Re_τ = 2680, 3891, 4941, 7164) are used to build and evaluate the models. These data are projected into tensorial basis formed from the symmetric part of mean velocity gradient and non-persistence-of-straining tensor. Six models are proposed and their performances are investigated. The scalar coefficients for these six different levels of approximations of the Reynolds stress tensor are derived, and made dimensionless using the classical turbulent scales, the kinetic turbulent energy (κ) and its dissipation rate (ε). The dimensionless coefficients are then coupled with classical wall functions. One model is selected by comparing the predicted Reynolds stress components with experimental and DNS data, presenting a good prediction for the shear and normal Reynolds stresses.     

The application of artificial neural networks to the inversion of the positron lifetime spectrum

A new method of processing positron annihilation lifetime spectra is proposed.It is based on an artificial neural network(ANN)-back propagation network(BPN).By using data from simulated positron lifetime spectra which are generated by a simulation program and tested by other analysis programs,the BPN can be trained to extract lifetime and intensity from a positron annihilation lifetime spectrum as an input.In principle,the method has the potential to unfold an unknown number of lifetimes and their intensities from a measured spectrum.So far,only a proof-of-principle type preliminary investigation was made by unfolding three or four discrete lifetimes.The present study aims to design the network.Besides,the performance of this method requires both the accurate design of the BPN structure and a long training time.In addition,the performance of the method in practical applications is dependent on the quality of the simulation model.However,the chances of satisfying the above criteria appear to be high.When appropriately developed,a trained network could be a very efficient alternative to the existing methods,with a very short identification time.We have used the artificial neural network codes to analyze data such as the positron lifetime spectra for single crystal materials and monocrystalline silicon.Some meaningful results are obtained.     

Large Eddy Simulation composition equations for single-phase and two-phase fully multicomponent flows

The Large Eddy Simulation (LES) equations for multicomponent (MC) fuel single-phase (SP) flow and two-phase (TP) flow with phase change are derived from the Direct Numerical Simulation (DNS) equations by filtering the DNS equations using a top-hat filter. Additional to the equations solved for single-component (SC) fuels, composition equations enter the formulation. The species composition is represented through a Probability Distribution Function (PDF), and DNS equations for the PDF moments are solved to find the composition. The TP filtered equations contain three categories of subgrid-scale (SGS) terms: (1) SGS–flux terms, (2) filtered source terms (FSTs) and (3) terms representing the ‘LES assumptions’. For SP flows no FSTs exist. The SGS terms in the LES equations must be either shown negligible or modeled. It is shown that for the composition equations, two equivalent forms of the DNS equations lead to two non-equivalent forms of the LES equations. Criteria are proposed to select the form best suited for LES. These criteria are used in conjunction with evaluations based on a DNS database portraying mixing and phase change, and lead to choosing one of the LES forms which satisfies all criteria. It is shown that the LES assumptions lead to additional SGS terms which require modeling. Further considerations are made for reactive flows.