Reactive Scalar Fields Research Articles

Stochastic and spectra contents of detonation initiated by compressible turbulent thermodynamic fluctuations

A canonical system that contains the basic elements of detonation initiated by compressible turbulence thermodynamic fluctuations was proposed by Towery et al. [“Detonation initiation by compressible turbulence thermodynamic fluctuations,” Combust. Flame 213, 172–183 (2020)] and successfully tested using direct numerical simulation (DNS). In the present study, the DNS dataset is used to assess the applicability of a few compressible turbulence theories to the problem of detonation and to investigate some statistical aspects of the problem and the spectra of the turbulence kinetic energy (TKE) and reactive scalar fields within the context of detonating and deflagrating compressible flows. It has been found that scaling of the dilatational and solenoidal components of compressible turbulence as reported in the literature does not apply to the case of detonation or deflagration. Also, the detonating cases were found to have significantly lower Karlovitz numbers compared to the nondetonating ones and to conform to the Bray–Moss–Libby premixed combustion (bimodal probability density function) model for intense turbulence and large Damkhöler number. The nondetonating cases show distributed pdfs. The stronger combustion in the detonating cases shows effects on the spectra of the TKE and reactive scalars, particularly when the wavenumber is scaled with the Kolmogorov length and the Schmidt number.

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

Abstract

Assessment of an Evolution Equation for the Displacement Speed of a Constant-Density Reactive Scalar Field

The displacement speed that characterises the self-propagation of isosurfaces of a reaction progress variable is of key importance for turbulent premixed reacting flow. The evolution equation for the displacement speed was derived in a recent work of Yu and Lipatnikov (Phys Rev E 100:013107, 2019a) for the case where the flame is described by a transport equation for single reaction progress variable assuming simple transport and one-step chemistry. This equation represents interaction of a number of complex coupled mechanisms related to straining by the velocity field, surface curvature and the scalar gradient. The aim of the current work is to provide detailed physical explanations of the displacement speed equation and its various terms, and to provide a new perspective to understand the mechanisms responsible for observed variations in the displacement speed. The equation is then used to analyze the propagation of a statistically planar reaction wave in homogeneous isotropic constant-density turbulence using direct numerical simulations. Additional emphasis is put on retracting surface segments that have a negative displacement speed, a phenomenon that commonly occurs at high Karlovitz numbers.

Understanding the diesel-like spray characteristics applying a flamelet-based combustion model and detailed large eddy simulations

This investigation analyses the structure of spray A from engine combustion network (ECN), which is representative of diesel-like sprays, by means of large eddy simulations and an unsteady flamelet progress variable combustion model. A very good agreement between modelled and experimental measurements is obtained for the inert spray that supports further analysis. A parametric variation in oxygen concentration is carried out in order to describe the structure of the flame and how it is modified when mixture reactivity is changed. The most relevant trends for the flame metrics, ignition delay and lift-off length are well-captured by the simulations corroborating the suitability of the model for this type of configuration. Results show that the morphology of the flame is strongly affected by the boundary conditions in terms of the reactive scalar spatial fields and Z–T maps. The filtered instantaneous fields provided by the simulations allow investigation of the structure of the flame at the lift-off length, whose positioning shows low fluctuations, and how it is affected by turbulence. It is evidenced that small ignition kernels appear upstream and detached from the flame that eventually merge with its base in agreement with experimental observations, leading to state that auto-ignition plays a key role as one of the flame stabilization mechanisms of the flame.

Numerical investigation of auto-igniting turbulent lifted CH4/air jet diffusion flames in a vitiated co-flow using a RANS based stochastic multiple mapping conditioning approach

Numerical simulations of auto-igniting turbulent lifted jet diffusion flames of CH4/air fuel issued into a vitiated coflow of lean combustion products of H2/air are performed using Reynolds-averaged Navier-Stokes (RANS) based stochastic multiple mapping conditioning (MMC) approach. A two-dimensional axisymmetric formulation is used to model the fluid flow, where the gas-phase turbulence terms are closed using the standard two-equation k-ε turbulence model with a modified set of constants. A reduced chemical mechanism ARM2 is used which consists of 19 species and 15 reactions derived from the GRI 3.0 mechanism. In MMC, the concept of mapping function is used, which approximates the cumulative probability distribution of the major scalar, namely mixture fraction for nonpremixed combustion. The corresponding variance of the major scalar is modelled by choosing a standard implementation of the major mixing time scale τϕ modelled in terms of the turbulent time scale as τϕ=τt/Cϕ. For all simulations reported herein, the same major mixing time constant Cϕ=3.0 is used. Additionally, in MMC, a minor mixing time scale τmin is introduced which controls fluctuations of scalars relative to the major fluctuations via the minor mixing time constant, Cmin. Three different values of Cmin=(τmin/τϕ)=0.25,0.35and0.50 are used and the corresponding ratios of minor to turbulent time scales are τmin/τt=0.083,0.116 and 0.166, respectively. The conditional and unconditional reactive scalar fields are found to be highly dependent on the choice of Cmin and hence the ratio of the minor and major mixing time scales. The numerical results are thoroughly validated against the experimental measurements. The variation in lift-off height is found to be in good agreement with the experimental data for the entire range of coflow temperature for Cmin=0.25. Also, the predicted conditional and unconditional scalar fields from the present RANS-MMC model shows an excellent agreement with the experimental measurements.

Investigation of the turbulent flame structure and topology at different Karlovitz numbers using the tangential stretching rate index

Turbulent premixed flames at high Karlovitz numbers exhibit highly complex structures in different reactive scalar fields to the extent that the definition of the flame front in an unambiguous manner is not straightforward. This poses a significant challenge in characterizing the observable turbulent flame behaviour such as the flame surface density, turbulent burning velocity, and so on. Turbulent premixed flames are reactive flows involving physical and chemical processes interacting over a wide range of time scales. By recognizing the multi-scale nature of reactive flows, we analyze the topology and structure of two direct numerical simulation cases of turbulent H2/air premixed flames, in the thin reaction zone and distributed combustion regimes, using tools derived from the computational singular perturbation (CSP) method and augmented by the tangential stretching rate (TSR) analysis. CSP allows to identify the local time scale decomposition of the multi-scale problem in its slow and fast components, while TSR allows to identify the most energetic time scale during both the explosive and dissipative regime of the reactive flow dynamics together with the identification of the flame front in an unambiguous manner. Before facing the complexity of the turbulent flow regime, we carry out a preliminary analysis of a one-dimensional laminar premixed flame in view of highlighting similarities and differences between laminar and turbulent cases. Subsequently, it is shown that the TSR metric provides a reliable way to identify the turbulent flame topologies.

Multiple mapping conditioning for silica nanoparticle nucleation in turbulent flows

In this paper a study of the sparse-Lagrangian multiple mapping conditioning (MMC) model for the synthesis of silica nanoparticles is presented. This is the first attempt using the model to simulate the formation of kinetically limited solid state species. A simplified differential diffusion model, involving a modified mixing timescale, is used to account for the much lower diffusion of the solid species. The model is validated against DNS of a counterflowing double shear layer of silane and hot combustion products. The reduced reaction mechanism involves silane decomposition and clustering leading to silica. The model is implemented in the context of large eddy simulations (LES). The MMC model allows a sparse distribution of stochastic particles for computing the reactive scalar field, including silica number density, by enforcing the property of localness in mixture fraction space onto the mixing model. Gas phase mixture fraction and fast reactive species are predicted with acceptable accuracy. The prediction of silica number density is qualitatively correct although the magnitude is underpredicted somewhat and the rms is greatly underpredicted. The effects of differential diffusion are clearly visible in the modelling and the simplified model correctly predicts the trend of increasing silica formation when differential diffusion is included.

Sparse-Lagrangian MMC simulations of an n-dodecane jet at engine-relevant conditions

Simulations are presented for the engine combustion network (ECN) n-dodecane spray A using the sparse-Lagrangian multiple mapping conditioning model for the reactive scalar field coupled with a large eddy simulation for the flow (MMC-LES). This is the first application of the MMC-LES to both transient and engine conditions and, in line with earlier simulations of the ECN flames, the fuel injection is modelled as a gas-jet. The model is evaluated initially for a baseline non-reacting case with ambient temperature of 900 K. Results for vapour penetration lengths and the radial profiles of mixture fraction show good agreement with experiments. The model is then applied to reacting cases, featuring transient ignition and combustion with a lifted flame base. A 106-species chemistry mechanism is employed. Simulations are performed at various ambient temperatures (800–1100 K) and various volume fractions of ambient oxygen (13–21%) that correspond to conditions in both conventional and advanced diesel engines. The trend towards decreasing ignition delay time and lift-off length with increasing ambient temperature and oxygen is predicted well. The quantitative agreement between the computed and experimental ignition delay times is satisfactory. The accuracy of lift-off length predictions is less accurate but comparable to the existing literature. Better results are obtained at the conditions with lower ambient temperatures and oxygen concentrations. This outcome is explored with a detailed analysis of heat release and scalar dissipation rates under various ambient temperature conditions. It is revealed that at high ambient temperatures, flame stabilisation occurs in a region with significant turbulence–chemistry interactions and close to the nozzle exit where the liquid phase would be expected to influence the flame.

Reactive scalar field near the turbulent/non-turbulent interface in a planar jet with a second-order chemical reaction

The reactive scalar field near the turbulent/non-turbulent (T/NT) interface is analyzed using a direct numerical simulation (DNS) of a planar jet with an isothermal second-order chemical reaction A + B → P. Reactants A and B are supplied from the jet and ambient flows, respectively. The DNS of the reactive jet is performed for Damköhler numbers Da = 0.1, 1, and 10. A visualization of the T/NT interface shows that most of the product P is contained in the turbulent region. The conditional mean concentrations of the reactive species change sharply near the T/NT interface. The width of the jump in the conditional mean concentration is almost independent of the chemical species and the Damköhler number. For the slow reaction (Da = 0.1), the conditional average of the chemical production rate gradually increases from the non-turbulent region toward the turbulent region. In contrast, the conditional average of the production rate for Da = 1 and 10 has a large peak value slightly inside the T/NT interface. The chemical reaction near the T/NT interface strongly depends on the interface orientation. The reactant A is deficient near the T/NT interface. The production rate is large near the interface toward which the deficient reactant A is frequently transported by the velocity fields. The transport due to the velocity relative to the interface movement strongly depends on the relationship between the interface geometry and the mean flow field. The dependence of the chemical reaction on the interface orientation becomes strong as Da increases. When the interface propagates toward the non-turbulent region, the reactant A and product P are contained in the turbulent region although the molecular diffusion and reaction contribute to the increase in the concentrations of A (non-reactive case) and P in the non-turbulent region. In contrast, the interface propagation toward the turbulent region leaves the fluids containing A and P in the non-turbulent region.

Numerical Simulation of Reactive Turbulent Scalar Mixing Layer by the Random Fourier Modes Method and Lagrangian Molecular Mixing Model

A new computational scheme using Lagrangian model of the velocity and molecular mixing for the fluid particle is developed to calculate the reactive scalar field in grid generated turbulence. The model is composed of three parts. The Lagrangian velocity of fluid particle which carries the reacting species is generated by the Random Fourier Modes method. The molecular mixing model(the modified Curl's model)is used to calculate the mixing and diffusion of reactive concentration field, and the chemical reaction model is a second-order and irreversible reaction in the scalar mixing layer. It is shown that the simulated results of the first and second moments of reactive and productive species show the good agreements with of the experimental data.

Study on Turbulent Plane Jet with Chemical Reaction in Liquid

A turbulent plane jet with a chemical reaction (A + B → R) in a liquid is investigated experimentally. The instantaneous concentrations of all species (A, B, and R) are measured simultaneously by using the light absorption spectrometric method and the mass conservation law. Statistics of the reactive scalar field are compared with those of the nonreactive scalar (frozen limit) and instantaneous reaction (equilibrium limit) fields. It is ascertained that, in comparison with the frozen limit, the mean concentrations of reactants A and B decrease while the mean concentration of product R increases in the downstream direction because of the chemical reaction. With regard to scalar fluctuations, it is also observed that in the region near the exit of the jet, the r.m.s. values of species A become larger than those in the frozen limit, whereas the r.m.s. values of species B become smaller than those in the frozen limit; the reverse situation is observed in the downstream and outer regions. Furthermore, the concentration correlations between species A and B have negative values. The segregation coefficients have values between 0 and -0.3 on the jet centerline and have minimum values at the location separated from the centerline in the cross-stream direction. The data obtained in the present study provide very useful and important information for modeling concentration correlation and the chemical source term in a turbulent reactive flow.

Direct and indirect thermal expansion effects in turbulent premixed flames

AbstractThe thermal expansion induced by the exothermic chemical reactions taking place in a turbulent reactive flow affects the velocity field so strongly that the large-scale velocity fluctuations as well as the small-scale velocity gradients can be governed by chemistry rather than by turbulence. Moreover, thermal expansion is well known to be responsible for counter-gradient turbulent diffusion and flame-generated turbulence phenomena. In the present study, by making use of an original splitting procedure applied to the velocity field, we establish the occurrence of two distinct thermal expansion effects in the flamelet regime of turbulent premixed combustion. The first is referred to as the direct thermal expansion effect. It is associated with a local flamelet crossing contribution as previously considered in early analyses of turbulent transport in premixed flames. The second, denoted herein as the indirect thermal expansion effect, is an outcome of the turbulent wrinkling processes that increases the flame surface area. Based on a splitting procedure applied to the velocity field, the respective influences of the two effects are identified and analysed. Furthermore, the theoretical analysis shows that the thermal expansion induced through the local flames can be treated separately in the usual continuity and momentum equations. This description of the turbulent reactive velocity field, leads also to relate all of the usual turbulent quantities to the reactive scalar field. Finally, algebraic closures for the turbulent transport terms of mass and momentum are proposed and successfully validated through comparison with direct numerical simulation data.

Direct and indirect thermal expansion effects in turbulent premixed flames

The thermal expansion induced by the exothermic chemical reactions taking place in a turbulent reactive flow affects the velocity field so strongly that the large-scale velocity fluctuations as well as the small-scale velocity gradients can be governed by chemistry rather than by turbulence. Moreover, thermal expansion is well known to be responsible for counter-gradient turbulent diffusion and flame-generated turbulence phenomena. In the present study, by making use of an original splitting procedure applied to the velocity field, we establish the occurrence of two distinct thermal expansion effects in the flamelet regime of turbulent premixed combustion. The first is referred to as the direct thermal expansion effect. It is associated with a local flamelet crossing contribution as previously considered in early analyses of turbulent transport in premixed flames. The second, denoted herein as the indirect thermal expansion effect, is an outcome of the turbulent wrinkling processes that increases the flame surface area. Based on a splitting procedure applied to the velocity field, the respective influences of the two effects are identified and analysed. Furthermore, the theoretical analysis shows that the thermal expansion induced through the local flames can be treated separately in the usual continuity and momentum equations. This description of the turbulent reactive velocity field, leads also to relate all of the usual turbulent quantities to the reactive scalar field. Finally, algebraic closures for the turbulent transport terms of mass and momentum are proposed and successfully validated through comparison with direct numerical simulation data.

On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid

The shallow water equations coupled to the set of reaction–advection–diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.

Terascale direct numerical simulations of turbulent combustion using S3D

Computational science is paramount to the understanding of underlying processes in internal combustion engines of the future that will utilize non-petroleum-based alternative fuels, including carbon-neutral biofuels, and burn in new combustion regimes that will attain high efficiency while minimizing emissions of particulates and nitrogen oxides. Next-generation engines will likely operate at higher pressures, with greater amounts of dilution and utilize alternative fuels that exhibit a wide range of chemical and physical properties. Therefore, there is a significant role for high-fidelity simulations, direct numerical simulations (DNS), specifically designed to capture key turbulence-chemistry interactions in these relatively uncharted combustion regimes, and in particular, that can discriminate the effects of differences in fuel properties. In DNS, all of the relevant turbulence and flame scales are resolved numerically using high-order accurate numerical algorithms. As a consequence terascale DNS are computationally intensive, require massive amounts of computing power and generate tens of terabytes of data. Recent results from terascale DNS of turbulent flames are presented here, illustrating its role in elucidating flame stabilization mechanisms in a lifted turbulent hydrogen/air jet flame in a hot air coflow, and the flame structure of a fuel-lean turbulent premixed jet flame. Computing at this scale requires close collaborations between computer and combustion scientists to provide optimized scaleable algorithms and software for terascale simulations, efficient collective parallel I/O, tools for volume visualization of multiscale, multivariate data and automating the combustion workflow. The enabling computer science, applied to combustion science, is also required in many other terascale physics and engineering simulations. In particular, performance monitoring is used to identify the performance of key kernels in the DNS code, S3D and especially memory intensive loops in the code. Through the careful application of loop transformations, data reuse in cache is exploited thereby reducing memory bandwidth needs, and hence, improving S3D's nodal performance. To enhance collective parallel I/O in S3D, an MPI-I/O caching design is used to construct a two-stage write-behind method for improving the performance of write-only operations. The simulations generate tens of terabytes of data requiring analysis. Interactive exploration of the simulation data is enabled by multivariate time-varying volume visualization. The visualization highlights spatial and temporal correlations between multiple reactive scalar fields using an intuitive user interface based on parallel coordinates and time histogram. Finally, an automated combustion workflow is designed using Kepler to manage large-scale data movement, data morphing, and archival and to provide a graphical display of run-time diagnostics.

液相格子乱流における反応性スカラー拡散の研究 : 第1報,単一反応の場合(流体工学,流体機械)

A diffusion field with a one-step reaction (R+B→S) in a liquid grid-turbulence has been experimentally investigated. The instantaneous concentrations of two species R and S are measured simultaneously by the light absorption spectrometric method, while the concentration of species B is determined by the conservation law. The statistics of reactive scalar fields are compared with the nonreactive scalar ones. It is ascertained that the mean concentrations of reactants R and B decrease while that of product S increases in the downstream direction because of the chemical reaction. With regard to the scalar fluctuations, it is also observed that the r.m.s. values for species R become smaller than those in the nonreactive case under the present experimental conditions, whereas the r.m.s. values for species B become larger. Furthermore, the correlation coefficient between species R and B is negative and varies from -0.9 to -0.95 in the present measurement region. The present data give very important information for the modeling of the concentration correlation and chemical source term in a turbulent reactive flow.

液相格子乱流における反応性スカラー拡散の研究 : 第2報,連続競争反応の場合(流体工学,流体機械)

A diffusion field with a competitive-consecutive reaction (A+B→R, R+B→S) in a liquid grid-turbulence has been experimentally investigated. The instantaneous concentrations of two reactive species (R and S) and a nonreactive dye (C) are measured simultaneously by the light absorption spectrometric method. The concentration of species A and B are determined by the conservation law. The statistics of reactive scalar fields are compared with the nonreactive scalar ones. It is found that the mean concentrations of reactants A and B decrease while those of product R and S increase in the downstream direction by a chemical reaction. With regard to the scalar fluctuations, it is also observed that the r.m.s. values for species A become larger than those in the nonreactive case under the present experimental conditions, whereas the r.m.s. values for species B become smaller. Furthermore, the correlation coefficients between species A and B are negative and those between B and R are positive in the present measurement region. The present data give very important information for the modeling of the concentration correlation and chemical source term in a turbulent reactive flow.

Experimental Study on the Turbulent Reactive Plane Jet in Liquid

A turbulent plane jet with a one-step reaction (R + B → S) in a liquid is investigated experimentally. The instantaneous concentrations of species R and S are measured simultaneously by using the light absorption spectrometric method, while the concentration of species B is determined by the conservation law. Statistics of reactive scalar field are compared with those of nonreactive scalar field. It is ascertained that, in comparison with the nonreactive case (frozen limit), the mean concentrations of reactants R and B decrease while the mean concentration of product S increases in the downstream direction because of the chemical reaction. With regard to scalar fluctuations, it is also observed that the change in the r.m.s. values of species R is small but these values become slightly small in comparison with those in the frozen limit, whereas the r.m.s. values of species B become apparently larger than those in the frozen limit. Furthermore, the segregation coefficients of species R and B in the frozen limit increase in the downstream direction because of the progress in mixing. In contrast, the segregation coefficients in the reactive case become slightly smaller than those in the frozen limit and lie between -0.14 and -0.02 in the measurement region. The present data show that the scalar covariance can not be neglected for modeling reactive flow, and provide very useful and important information for modeling concentration correlation and the chemical source term in a turbulent reactive flow.

Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data

The interaction between turbulence and reactive scalar fields is discussed for the wrinkled flamelets regime of turbulent premixed combustion. Emphasis is placed on the effects associated with the turbulent straining term. In the regime of turbulent combustion under consideration, which corresponds to Karlovitz and Damköhler numbers such that Ka < 1 and Da > 1, a clear and simple formulation is proposed to explain and to model the influence of the correlation between velocity and reactive scalar gradients. This formulation is based on the conservative variables budget across one-dimensional premixed laminar flamelets. The analysis firmly confirms the dependence on both the Damköhler number and the expansion factor, a feature already foreseen in recent studies. Nevertheless, in contrast with previous work, (i) the scaling arguments used in the present contribution are different from those used in other recent proposals, and (ii) the proposed closures are not only deduced from dimensional arguments but also from the consideration of conservative variable budgets across laminar flamelets. The resulting functional dependence on the expansion factor is found to be influenced by the underlying one-dimensional flamelet representation and two possible closures are put forward to take this dependence into account. (iii) The two closures do not exhibit a proportionality to the mean scalar dissipation rate as suggested in previous studies but to the square of this quantity. This results in the presence of a second contribution proportional to in the modelled transport equation for the mean scalar dissipation rate, in addition to the modelled molecular dissipation term. (iv) Since previous Direct Numerical Simulation (DNS) studies have been essentially devoted to the influence of the Damköhler number, the present DNS validation step is focused on the effects of the expansion rate. To this purpose, the proposed models are validated against three available DNS databases obtained for turbulent premixed flames with different values of the density ratio between unburned and fully burned gases.

Iso-scalar surfaces, mixing and reaction in turbulent flows

Turbulent scalar mixing with chemical reaction is investigated in terms of the local geometrical features of the iso-scalar surfaces—‘scalar field topologies’—, using Direct Numerical Simulation data. Two scalars with identical initial distribution, one inert and the other obeying a prescribed Arrhenius-like chemical reaction, evolve in homogeneous isotropic turbulence with a mesh size 256 3. The two local principal curvatures, k 1 and k 2 , of the iso-scalar surface at each point are straightforwardly obtained from the curvature tensor, n i , j , whose elements are the spatial derivatives of the unit vector normal to the iso-surface. The scalar diffusive flux is decomposed into a ‘flat-front’ contribution plus a curvature induced molecular transport. Expressions for the normal propagating velocity relative to the fluid of iso-surfaces, of both the inert and the reactive scalar fields, are provided making use of the previous decomposition. The ‘flat-front’ and the curvature induced contributions to the diffusive fluxes, beside to the chemical reaction rate, are correlated with the principal curvatures. Results, including the joint statistics of the principal curvatures and their correlations with the scalar dissipation, are also presented. To cite this article: C. Dopazo et al., C. R. Mecanique 334 (2006).