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}=sqrt1+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.
Thermoacoustic oscillations of a turbulent flame stabilized behind a bluff body in a duct are considered using (1) a kinematic model of the response of the flame to oncoming flow velocity ...oscillations and (2) the
n–
τ model of the influence of a localized heat source on longitudinal acoustic waves in a duct. The kinematic model well known in the literature is extended to allow for flame speed increase with the distance from the bluff body. Such an increase is an important peculiarity of practical premixed turbulent flames developing with the distance from a flameholder. For weak, harmonic, uniform fluctuations of the oncoming flow velocity, perturbations in the flame shape and in the total heat release rate are analytically determined. Calculated results show that the development of turbulent flame speed substantially affects both the gain and the phase of the flame transfer function and, in consequence, the stability of the flame studied.
Hetarylammonium 2-hydroxy-4-oxo-4-(thien-2-yl)but-2-enoates and 2-hydroxy-4-oxo-4-(thien-2-yl)but-2-enoic acid hetarylamides were obtained. Their biological activity was studied. Marginally toxic ...compounds with activities comparable to and exceeding those of reference compounds were discovered. Results of biological tests indicated the expediency of seeking hemostatic and anthelminthic agents in the series of hetarylammonium 2-hydroxy-4-oxo-4-(thien-2-yl)but-2-enoates. 2-Hydroxy-4-oxo-4-(thien-2-yl)but-2-enoic acid hetarylamides are promising candidates for developing new drugs possessing anti-inflammatory activity
Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent ...burning are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach for evaluating mean species concentrations. For this purpose, dependencies of mole fractions and rates of production of various species on a combustion progress variable c, obtained from the laminar flame, are averaged adopting either the actual Probability Density Function (PDF) P(c) extracted from the DNS data or a common presumed β-function PDF. On the one hand, the results quantitatively validate the flamelet approach for the mean mole fractions of all species, including radicals, but only if the actual PDF P(c) is adopted. The use of the β-function PDF yields substantially worse results for the radicals’ concentrations. These findings put modeling the PDF P(c) on the forefront of the research agenda. On the other hand, the mean rate of product creation and turbulent burning velocity are poorly predicted even adopting the actual PDF. These results imply that, in order to evaluate the mean species concentrations, the flamelet approach could be coupled with another model that predicts the mean rate and turbulent burning velocity better. Accordingly, the flamelet approach could be implemented as post-processing of numerical data yielded by that model. Based on the aforementioned findings and implications, a new approach to building a presumed PDF is developed. The key features of the approach consist in (i) adopting a re-normalized flamelet PDF for intermediate values of c and (ii) directly using the mean rate of product creation to calibrate the presumed PDF. Capabilities of the newly developed PDF for predicting mean species concentrations are quantitively validated for all species, including radicals.
•A new flamelet-based presumed Probability Density Function approach is developed.•The flamelet approach quantitatively predicts mean concentrations of radicals.•The flamelet approach is useful at Karlovitz number larger than 10.
Data obtained in recent direct numerical simulations (Lee et al.) of statistically one-dimensional and planar, lean complex-chemistry hydrogen-air flames characterized by three different Karlovitz ...numbers Ka ranging from 3 to 33 are further analyzed in order to explore local characteristics and structure of (i) extreme points characterized by the peak (over the computational domain) Fuel Consumption Rate (FCR) or Heat Release Rate (HRR) and (ii) leading points that are also characterized by a high FCR or HRR, but advance furthest into unburned reactants. Results show that, on the one hand, common characteristics of flame perturbations (curvature, strain and stretch rates, displacement speed) fluctuate significantly in the extreme or leading, FCR or HRR points and are different in different flames. Moreover, other two-point local quantities such as the local gradients of combustion progress variables or species (e.g., the radical H) mass fractions are different in different flames. Therefore, a common simple configuration of a perturbed laminar flame cannot be used as a catchall model of the entire local structure of zones surrounding the discussed points at various Ka. On the other hand, single-point local characteristics (temperature, species mass fractions, rates of their production) of the FCR extreme points are comparable in all three turbulent flames and in the critically strained planar laminar flame. In particular, the FCRs in the extreme points fluctuate weakly and are approximately equal to each other and to the peak FCR in the critically strained laminar flame. The latter finding implies that (i) the maximum FCR evaluated in the critically strained laminar flame could be used to characterize, in a first approximation, the local FCR in the extreme or leading points in turbulent flames, thus, supporting the leading point concept, and (ii) almost the same extreme FCR can be reached in substantially different local burning structures.
A ratio of turbulent burning velocity to laminar flame speed is well known to be abnormally high in lean hydrogen-air mixtures, with this phenomenon being commonly attributed to differential ...diffusion effects. Magnitude of such effects is known to be increased by pressure, but a few recent studies have indicated that the effects are mitigated when reactants are preheated. It is not yet known, however, which of these two counteracting trends is of more importance under elevated pressures and temperatures associated with combustion in engines. Accordingly, it is not yet clear whether or not models of differential diffusion effects are required for research and development of future ultra-clean and highly efficient engines that burn hydrogen (the emphasized effects are typically ignored in engineering computations). To clarify the issue, numerical simulations of lean complex-chemistry hydrogen-air strained laminar flames are performed by varying strain rate, pressure 1≤P≤50 bar, temperature 300≤Tu≤900 K, and equivalence ratio (Φ=0.4, 0.55, and 0.7). This simple problem is selected because maximal consumption speeds reached in critically strained (close to extinction) lean hydrogen-air laminar flames are considered to characterize the influence of differential diffusion on turbulent burning rates within the framework of Zel'dovich's leading point concept, which was well supported in recent studies. Computed results show that, even at Tu=900 K, the aforementioned consumption speeds are significantly larger than the unperturbed laminar flame speeds if the mixture is sufficiently lean (the equivalence ratio Φ=0.55 or lower) and pressure is sufficiently high (P≥30 bar). Therefore, differential diffusion effects are expected to be of importance when burning so lean hydrogen-air mixtures in engines and should be properly modeled.
•Magnitude of differential diffusion effects is increased by pressure.•Magnitude of such effects is decreased with increasing temperature.•These trends are controlled by variations in Zel'dovich number.•Differential diffusion effects are of importance under engine conditions.
A Direct Numerical Simulation (DNS) study of statistically one-dimensional and planar, lean complex-chemistry hydrogen-air flames characterized by a low Lewis number Le and three different Karlovitz ...numbersKa ranging from 3 to 33 is performed, with the same complex-chemistry flames being also simulated by setting molecular diffusivities of all species equal to the heat diffusivity of the mixture. The simulations predict a significant increase in a ratio of turbulent burning velocity to the laminar flame speed in the former (Le<1) flames when compared to the latter (equidiffusive) flames. Extreme points characterized by the peak (over the computational domain) Fuel Consumption Rate (FCR) or Heat Release Rate (HRR) are found at each instant. In the equidiffusive flames, such extreme FCR and HRR are close to their peak values in the unperturbed laminar flame. If Le is low, the former rates are significantly higher than the latter ones due to an increase in the local temperature, equivalence ratio, and radical mass fractions, caused by diffusive-thermal effects. While the studied extreme points may appear sufficiently far from the leading edge of the instantaneous flame brush, leading points characterized by a lower, but still high (Le<1) FCR or HRR are observed close to the leading edge at each instant. Various local characteristics (temperature, equivalence ratio, species mass fractions and their gradients, reaction rates, etc.) of the extreme and leading points are explored and significant differences between zones characterized by high FCR or HRR are revealed. For instance, in the latter zones, major chemical pathways are changed. Moreover, while the extreme HRRs strongly fluctuate in time, with their mean and rms values being significantly increased by Ka, the extreme FCRs fluctuate weakly and are close at different Ka, thus, implying that almost the same extreme FCR can be reached in substantially different local burning structures.
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