Surface-averaged quantities in turbulent reacting flows and relevant evolution equations

While quantities conditioned to an isosurface of reaction progress variable c, which characterizes fluid state in a turbulent reacting flow, have been attracting rapidly growing interest in the recent literature, a mathematical and physical framework required for research into such quantities has not yet been elaborated properly. This paper aims at filling two fundamental gaps in this area, i.e., (i) ambiguities associated with a definition of a surface-averaged quantity and (ii) the lack of rigorous equations that describe evolutions of such quantities. In the first (theoretical) part of the paper, (a) analytical relations between differently defined (area-weighted and unweighted) surface-averaged quantities are obtained and differences between them (quantities) are discussed, (b) a unified method for deriving an evolution equation for bulk area-weighted surface-averaged value of a local characteristic φ of a turbulent reacting flow is developed, and (c) the method is applied for deriving evolution equations for the bulk area-weighted surface-averaged reaction-surface density |∇c|, local reactionwave thickness 1/|∇c|, and local displacement speed Sd , i.e., the speed of an isosurface of the c(x,t) field with respect to the local flow. In the second (numerical) part of the paper, direct numerical simulation data obtained recently from a highly turbulent reaction wave are analyzed in order to (1) highlight substantial differences between area-weighted and unweighted surface-averaged quantities and (2) show that various terms in the derived evolution equations are amenable to accurate numerical evaluation in spite of appearance of the so-called zero-gradient points [C. H. Gibson, Phys. Fluids 11, 2305 (1968)] in a highly turbulent medium. Finally, the obtained analytical and numerical results are used to shed light on the paradox of local flame thinning and broadening which is widely discussed in the turbulent combustion literature

Thin Reaction Zones in Highly Turbulent Medium

In a highly turbulent medium characterized by a low Damk\"ohler number Da, reactions are commonly considered to occur in distributed zones broadened by small-scale turbulent eddies. In the present communication, an alternative regime of propagation of reaction waves in a highly turbulent medium is introduced and studied theoretically and numerically. More specifically, propagation of an infinitely thin reaction sheet in a turbulent medium is analyzed, with molecular mixing of the reactant and product being allowed in wide layers. In this limiting case, an increase in the consumption velocity by turbulence is solely controlled by an increase in the reaction-sheet area. Based on physical reasoning and estimates, the area is hypothesized to be close to the mean area of an inert iso-scalar surface at the same turbulent Reynolds number. This hypothesis leads to a relation for the turbulent consumption velocity, which is similar to the well-known Damk\"ohler scaling associated commonly with distributed reaction zones at a low Da. The obtained theoretical results are validated by analyzing a big database (23 cases characterized by 0.01<Da<1) created recently in 3D direct numerical simulations of propagation of a statistically planar, one-dimensional, dynamically passive reaction wave in statistically stationary, homogeneous, isotropic turbulence. The DNS data well support the aforementioned relation. They also show that the reaction is localized to thin zones even at Da as low as 0.01, with a ratio of the turbulent and laminar consumption velocities being mainly controlled by the reaction-zone-surface area

Assessment of a flamelet approach to evaluating mean species mass fractions in moderately and highly turbulent premixed flames

Complex-chemistry Direct Numerical Simulation (DNS) data obtained from lean methane-air turbulent flames are analysed to perform a priori assessment of predictive capabilities of the flamelet approach to evaluating mean concentrations of various species in turbulent flames characterized by Karlovitz numbers Ka=6.0, 74.0, and 540. Six definitions of a combustion progress variable c are probed and two types of Probability Density Functions (PDFs) are adapted: (i) actual PDFs extracted directly from the DNS data or (ii) presumed β-function PDFs obtained using the DNS data on the first two moments of the c-field. Results show that the mean density, the mean temperature, and the mean mass fractions of CH4, O2, H2O, CO2, CO, CH2O, CH3, and HCO are very well predicted using the temperature-based combustion progress variable c_ and the actual PDF. For other considered species, the quantitative predictions are worse, but still appear to be encouraging (with the exception of CH3O at Ka=540). The use of the flamelet library obtained from the equidiffusive laminar flame improves results for H2, HO2, and H2O2 at the highest Karlovitz number. Alternative definitions of the combustion progress variable perform worse and the reasons for this are explored. The use of the β-function PDF yields worse results fo r intermediate species such as OH, O, H, CH3, and HCO, with this PDF being significantly different from the actual PDF. Application of the flamelet approach to rates of production/consumption of various species is also addressed and implications of obtained results for modeling are discussed

Assessment of an evolution equation for the averaged displacement speed of a reactive scalar field

For turbulent premixed reacting flow modeled by a simplified transport equation for a reaction progress scalar field, an evolution equation for the displacement speed conditionally averaged on the reaction progress was derived in a recent work. In the current paper this equation isused to analyze the basic problem of propagation of a planar reaction wave in homogeneous isotropic constant-density turbulence using a DNS approach. We examine both the transient process of the initial planar wave being disturbed by turbulence as well as the fully developedwave after all statistics has evolved to a stationary state. The numerical results support the derived equation by showing good match between the left hand side term and the sum of all right hand side terms. The derived equation reveals three effects that cause temporal variation in averaged displacement speed: (i) T1, the isosurface-following rate of change in reaction surface density, (ii) T2, the isosurface-following rate of change due to diffusion, and (iii) T3, a stretch-rate-induced difference between averaged isosurface-following derivative and time derivative of the isosurface averaged value. For a fully developed wave the equation reduces to a constraint of zero sum of the three terms; this is realized by (i) the terms T1 andT3 averaged over all reaction scalar zones stay positive and negative, respectively, and (ii) T2 stays largely positive except in the preheat zone for a highly disturbed reaction wave where it becomes slightly negative. Among the three terms, the diffusion contribution term T3 is found to be largely responsible for early transient variation in averaged displacement speed. For the transient evolution of highly turbulent reaction waves, it is also found that all three terms tend to flip their signs when moving from the preheat zone to the reaction zone

The Relationship between Gene Polymorphism of miRNAs Regulating FGA and Schizophrenia

AIM: To investigate the relationship between the polymorphism of related gene loci of miRNAs regulated fibrinopeptide A and schizophrenia. Lay the foundation for the aetiology of schizophrenia. METHODS: Adapt to the phase match of sex and age case-control study, a total of 513 Chinese Han patients with schizophrenia were selected as the case group, 513 normal healthy persons as a control group. Obtaining SNPs information of the FGA gene by querying the dbSNP database, and reference HapMap database included SNPs site frequency information for screening. The frequency distributions of SNPs were genotyped by iMLDR® SNP detection technology. Two SNPs (pre-hsa-miR-605rs2043556 T&gt;C, pre-hsa-miR-499a/pre-hsa-miR-499brs4909237 T &lt; C) were analyzed to demonstrate their association with susceptibility to schizophrenia. RESULTS: There were no significant differences between patients and controls in genotype and allele distribution of SNPs（rs2043556 and rs4909237）in the precursor region of hsa-miR-605 and pre-hsa-miR-499a/pre-hsa-miR-499b. Their gene-gene interaction, which suggests that the polymorphisms of miRNA genes might not contribute to schizophrenia susceptibility in the Han Chinese population. CONCLUSION: No significant difference existed between schizophrenic patients and controls in SNP (rs2043556 and rs4909237) in the precursor region of hsa-miR-605 and pre-hsa-miR-499a/pre-hsa-miR-499b. There may not regulate FGA gene expression. Thus, hsa-miR-605 and pre-hsa-miR-499a/pre-hsa-miR-499b may not influence the risks of schizophrenia

Deep learning of nonlinear flame fronts development due to Darrieus–Landau instability

The Darrieus–Landau instability is studied using a data-driven, deep neural network approach. The task is set up to learn a time-advancement operator mapping any given flame front to a future time. A recurrent application of such an operator rolls out a long sequence of predicted flame fronts, and a learned operator is required to not only make accurate short-term predictions but also reproduce characteristic nonlinear behavior, such as fractal front structures and detached flame pockets. Using two datasets of flame front solutions obtained from a heavy-duty direct numerical simulation and a light-duty modeling equation, we compare the performance of three state-of-art operator-regression network methods: convolutional neural networks, Fourier neural operator (FNO), and deep operator network. We show that, for learning complicated front evolution, FNO gives the best recurrent predictions in both the short and long term. A consistent extension allowing the operator-regression networks to handle complicated flame front shape is achieved by representing the latter as an implicit curve

Large Eddy Simulation of Turbulent Flow and Combustion in HCCI Engines

This thesis deals with numerical simulations of the turbulent combustion process in Homogeneous Charge Compression Ignition (HCCI) engines. An accurate and computationally efficient Large Eddy Simulation (LES) model was developed and used throughout this thesis to investigate the development of in-cylinder turbulence, temperature stratification, onset of auto-ignition, and development of the reaction fronts. Compared with the conventional Reynolds averaged Navier-Stokes (RANS) approaches, LES has the potential of capturing the fine spatial and temporal structures in engine combustion chambers. Yet, there are several difficulties when applying LES to engine flows. It is often not possible to have the fine resolution needed for some of the flow scales in the cylinder, for example in the near-wall regions. In addition to the difficulty of resolving the flow scales there is a lack of a numerically accurate and affordable method for coupling the detailed auto-ignition chemical kinetic to the flow field simulations. An efficient auto-ignition model is developed based on parameterization of auto-ignition history obtained from detailed chemical kinetics calculations. The model is implemented to the LES solver and used to improve the understanding of the fundamental physical and chemical process in HCCI engines. First, an experimental engine with a rectangular shaped combustion chamber operating at low speed was chosen as a test case for validation of the LES model. Fairly good agreement between the LES results and the PIV (particle image velocimetry) experiments are found with respect to the cycle averaged mean flow field and turbulence fluctuations. Several spatial and temporal average methodologies were examined based on one single cycle LES data to characterize the mean flow and turbulence. The LES model is then used to study several HCCI experimental engines that have realistic cylinder geometry and engine speed. With very high spatial and temporal resolution the LES model successfully simulated the development of flow structures during the different strokes of the engine cycle. The effect of intake gas, residual gas, wall temperature, and piston geometry on the turbulent flow and temperature stratification was quantified. The LES revealed fundamental aspects of HCCI combustion, and its dependence on engine cylinder geometry, cooling, and operational conditions such as intake gas preheating. The LES results indicated that the effect of the geometry is not to alter the production of in-cylinder turbulence, but instead, to affect the heat transfer between the in-cylinder gas and the bowl wall. Compared with flat piston engines, the bowl-in-piston engine generates a high level of temperature stratification in the cylinder which leads to an earlier auto-ignition. By controlling the intake gas temperature to obtain the same auto-ignition timing, it was found that the combustion duration was increased with the bowl-in-piston as compared to a flat piston. This phenomenon was first observed in HCCI engine experiments. With the present LES study a clearer understanding of the flow-heat transfer-reaction coupling was obtained. Systematic LES studies carried out in this thesis showed that the effect of turbulence can be important for the formation and destruction of the temperature stratification in the engine cylinders. Turbulence can decrease the temperature inhomogeneity in the bulk flow far away from the walls. Therefore residual gas/intake gas induced temperature stratification is suppressed by strong turbulence eddy motion. On the other hand, turbulence eddy motion in the wall boundary layers is responsible for the generation of temperature stratification in the cylinder. Turbulence was found to be able to affect the reaction front propagation directly in HCCI engines under conditions that the large eddies and the hot reaction zones are comparable in size

Evolution equations for the decomposed components of displacement speed in a reactive scalar field

The study of a turbulent premixed flame often involves analysing quantities conditioned to different iso-surfaces of a reactive scalar field. Under the influence of turbulence, such a surface is deformed and translated. To track the surface motion, the displacement speed (Sd) of the scalar field respective to the local flow velocity is widely used and this quantity is currently receiving growing attention. Inspired by the apparent benefits from asimple decomposition of Sd into contributions due to (i) curvature, (ii) normal diffusion and (iii) chemical reaction, this work aims at deriving and exploring new evolution equations for these three contributions averaged over the reaction surface. Together with a previously obtained Sd-evolution equation, the three new equations are presented in a form that emphasizes the decomposition of Sd into three terms. This set of equations is also supplemented with a curvature-evolution equation, hence providing a new perspective to link the flame topology and its propagation characteristics. Using two direct numerical simulation databases obtained from constant-density and variable-density reaction waves, all the derived equations and the term-wise decomposition relations are demonstrated to hold numerically. Comparison of the simulated results indicates that the thermal expansion weakly affects the key terms in the considered evolution equations. Thermal expansion can cause variations in the averaged Sd and its decomposed parts through multiple routes more than introducing a dilatation term. The flow plays a major role to influence the key terms in all equations except the curvature one, due to a cancellation between negatively and positively curved surface elements

DNS study of the bending effect due to smoothing mechanism

Propagation of either an infinitely thin interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is simulated by solving unsteady 3D Navier-Stokes equations and either a level set (G) or a reaction-diffusion equation, respectively, with all other things being equal. In the case of the interface, the fully developed bulk consumption velocity normalized using the laminar-wave speed S L depends linearly on the normalized rms velocity u 0 /S L . In the case of the reaction wave of a nonzero thickness, dependencies of the normalized bulk consumption velocity on u 0 /S L show bending, with the effect being increased by a ratio of the laminar-wave thickness to the turbulence length scale. The obtained bending effect is controlled by a decrease in the rate of an increase δA F in the reaction-zone-surface area with increasing u 0 /S L . In its turn, the bending of the δA F (u 0 /S L )-curves stems from inefficiency of small-scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles characterized by a high local curvature are smoothed out by molecular transport within the reaction wave

DNS STUDY OF ROLE PLAYED BY MOLECULAR TRANSPORT IN BENDING EFFECT

A DNS study of propagation of either an infinitely thin passive interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence was performed by solving Navier-Stokes equations and either level set or reaction-diffusion equation, respectively, with all other things being equal. The simulations covered a wide range of conditions, i.e. five different (from 0.5 to 10.0) ratios of the rms turbulent velocity u' to the laminar wave speed S_L^0, three different (2.1, 3.7, and 6.7) ratios of the integral length scale L_11 of the turbulence to the laminar wave thickness δ_F, three different turbulent Reynolds numbers, and two different Zeldovich numbers Ze = 6.0 and 17.1. Accordingly, the Damköhler Da and Karlovitz Ka numbers were varied from 0.2 to 13.5 and 0.55 to 36.2, respectively, thus, covering both flamelet and thin-reaction-zone regimes of premixed turbulent combustion. The computed fully-developed bulk consumption velocity is significantly reduced when L_11⁄δ_F is decreased, with the effect being most pronounced at the highest u'⁄(S_L^0 )=10. Moreover, the consumption velocity normalized using S_L^0 and obtained by simulating the self-propagation of an infinitely thin interface by solving the level set equation depends linearly on u'⁄(S_L^0 ). On the contrary, dependencies of the normalized consumption velocity on u'⁄(S_L^0 ), computed by solving the reaction-diffusion equation (which describes a reaction wave of a nonzero thickness), show bending, with the effect being increased by δ_F⁄L_11 . Under conditions of the present study, the bending effect is controlled by a decrease in the rate of a relative increase δA_F in the reaction-zone-surface area with increasing u'⁄(S_L^0 ). In its turn, the bending of the δA_F (u'⁄(S_L^0 ))-curves stems from inefficiency of small-scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles characterized by a high local curvature are smoothed out by molecular transport within the reaction wave