Turbulent burning velocity and thermodiffusive instability of premixed flames

Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermodiffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λ_{n} that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained, and (ii) simulations of turbulent flames are performed by varying the width from Λ<Λ_{n} (in this case, the instability is suppressed) to Λ>Λ_{n} (in this case, the instability may grow). Moreover, simulations are performed either using mixture-averaged transport properties (low Lewis number flames) or setting diffusivities of all species equal to heat diffusivity of the mixture (equidiffusive flames), with all other things being equal. Obtained results show a significant increase in turbulent burning velocity U_{T} when the boundary Λ=Λ_{n} is crossed in weak turbulence, but almost equal values of U_{T} are computed at Λ<Λ_{n} and Λ>Λ_{n} in moderately turbulent flames characterized by a Karlovitz number equal to 3.4 or larger. These results imply that thermodiffusive instability of laminar premixed flames substantially affects burning velocity in weak turbulence only, in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev. E 107, 015102, (2023)10.1103/PhysRevE.107.015102).

Simple criterion of importance of laminar flame instabilities in premixed turbulent combustion of mixtures characterized by low Lewis numbers

By (i) highlighting the mitigation effect of strain rates on laminar flame instabilities and (ii) comparing peak growth rates of laminar flame instabilities with strain rates generated by small-scale turbulent eddies, a simple criterion of importance of the influence of the instabilities on an increase in premixed flame surface area in turbulent flows is suggested. The criterion implies that, even in lean hydrogen-air mixtures, laminar flame instabilities can significantly affect the flame area only in weak or moderate turbulence (the Karlovitz number defined using laminar flame speed, thermal flame thickness, and Kolmogorov time scale is on the order of 10 or less under room conditions).

Smallest scale of wrinkles of a Huygens front in extremely strong turbulence

By analyzing the statistically stationary stage of propagation of a Huygens front in homogeneous, isotropic, constant-density turbulence, a length scale l_{0} is introduced to characterize the smallest wrinkles on the front surface in the case of a low constant speed u_{0} of the front when compared to the Kolmogorov velocity u_{K}. The length scale is derived following a hypothesis of dynamical similarity that highlights a balance between (i) creation of a front area due to advection and (ii) destruction of the front area due to propagation. Consequently, the front speed is compared with the magnitude of the fluid velocity difference in two points separated by a distance smaller than the Kolmogorov length scale. Appropriateness of the smallest wrinkle scale is demonstrated by applying a fractal approach to evaluating the mean area of the instantaneous front surface. Since the scales of the smallest and larger wrinkles belong to different subranges (dissipation and inertial, respectively) of the Kolmogorov turbulence spectrum, the front is hypothesized to be a bifractal characterized by two different fractal dimensions in the two subranges. Both fractal dimensions are evaluated adapting the aforementioned hypothesis of dynamical similarity. Such a bifractal model yields a linear relation between the mean fluid consumption velocity, which is equal to the front speed u_{0} multiplied with a ratio of the mean area of the instantaneous front surface to the transverse projected area, and the rms turbulent velocity u^{'} even if a ratio of u_{0}/u^{'} tends to zero.

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 reaction-wave thickness 1/|∇c|, and local displacement speed S_{d}, 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)PFLDAS0031-917110.1063/1.1691820] 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.

LC/MS at the whole protein level: Studies of biomolecular structure and interactions using native LC/MS and cross-path reactive chromatography (XP-RC) MS

Interfacing liquid chromatography (LC) with electrospray ionization (ESI) to enable on-line MS detection had been initially implemented using reversed phase LC, which in the past three decades remained the default type of chromatography used for LC/MS and LC/MS/MS studies of protein structure. In contrast, the advantages of other types of LC as front-ends for ESI MS, particularly those that allow biopolymer higher order structure to be preserved throughout the separation process, enjoyed relatively little appreciation until recently. However, the past few years witnessed a dramatic surge of interest in the so-called "native" (with "non-denaturing" being perhaps a more appropriate adjective) LC/MS and LC/MS/MS analyses within the bioanalytical and biophysical communities. This review focuses on recent advances in this field, with an emphasis on size exclusion and ion exchange chromatography as front-end platforms for protein characterization by LC/MS. Also discussed are the benefits provided by the integration of chemical reactions in the native LC/MS analyses, including both ion chemistry in the gas phase (e.g., limited charge reduction for characterization of highly heterogeneous biopolymers) and solution-phase reactions (using the recently introduced technique cross-path reactive chromatography).

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

Analytical and numerical study of travelling waves using the Maxwell-Cattaneo relaxation model extended to reaction-advection-diffusion systems

Within the framework of the Maxwell-Cattaneo relaxation model extended to reaction-diffusion systems with nonlinear advection, travelling wave (TW) solutions are analytically investigated by studying a normalized reaction-telegraph equation in the case of the reaction and advection terms described by quadratic functions. The problem involves two governing parameters: (i) a ratio φ^{2} of the relaxation time in the Maxwell-Cattaneo model to the characteristic time scale of the reaction term, and (ii) the normalized magnitude N of the advection term. By linearizing the equation at the leading edge of the TW, (i) necessary conditions for the existence of TW solutions that are smooth in the entire interval of -∞<ζ<∞ are obtained, (ii) the smooth TW speed is shown to be less than the maximal speed φ^{-1} of the propagation of a substance, (iii) the lowest TW speed as a function of φ and N is determined. If the necessary condition of N>φ-φ^{-1} does not hold, e.g., if the magnitude N of the nonlinear advection is insufficiently high in the case of φ^{2}>1, then, the studied equation admits piecewise smooth TW solutions with sharp leading fronts that propagate at the maximal speed φ^{-1}, with the substance concentration or its spatial derivative jumping at the front. An increase in N can make the solution smooth in the entire spatial domain. Moreover, an explicit TW solution to the considered equation is found provided that N>φ. Subsequently, by invoking a principle of the maximal decay rate of TW solution at its leading edge, relevant TW solutions are selected in a domain of (φ,N) that admits the smooth TWs. Application of this principle to the studied problem yields transition from pulled (propagation speed is controlled by the TW leading edge) to pushed (propagation speed is controlled by the entire TW structure) TW solutions at N=N_{cr}=sqrt[1+φ^{2}], with the pulled (pushed) TW being relevant at smaller (larger) N. An increase in the normalized relaxation time φ^{2} results in increasing N_{cr}, thus promoting the pulled TW solutions. The domains of (φ,N) that admit either the smooth or piecewise smooth TWs are not overlapped and, therefore, the selection problem does not arise for these two types of solutions. All the aforementioned results and, in particular, the maximal-decay-rate principle or appearance of the piecewise smooth TW solutions, are validated by numerically solving the initial boundary value problem for the reaction-telegraph equation with natural initial conditions localized to a bounded spatial region.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.