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The structure of premixed turbulent flames and governing physical mechanisms of the influence of turbulence on premixed burning are often discussed by invoking combustion regime diagrams. In the majority of such diagrams, boundaries of three combustion regimes associated with (i) flame preheat zones broadened locally by turbulent eddies, (ii) reaction zones broadened locally by turbulent eddies, and (iii) local extinction are based on a Karlovitz number Ka, with differently defined Ka being used to demarcate different combustion regimes. The present paper aims to overview different definitions of Ka, comparing them, and suggesting the most appropriate choice of Ka for each combustion regime boundary. Moreover, since certain Karlovitz numbers involve a laminar flame thickness, the influence of complex combustion chemistry on the thickness and, hence, on various Ka and relations between them is explored based on results of complex-chemistry simulations of unperturbed (stationary, planar, and one-dimensional) laminar premixed flames, obtained for various fuels, equivalence ratios, pressures, and unburned gas temperatures.

The influence of statistically stationary, homogeneous isotropic turbulence (i) on the mean area of a passive front propagating in a constant-density fluid and, hence, (ii) on the mean fluid consumption velocity u¯T is explored, particularly in the case of an asymptotically high turbulent Reynolds number, and an asymptotically high ratio of the Kolmogorov velocity to a constant speed u0 of the front. First, a short early transient stage is analyzed by assuming that the front remains close to a material surface that coincides with the front at the initial instant. Therefore, similarly to a material surface, the front area grows exponentially with time. This stage, whose duration is much less than an integral time scale of the turbulent flow, is argued to come to an end once the volume of fluid consumed by the front is equal to the volume embraced due to the turbulent dispersion of the front. The mean fluid consumption velocity averaged over this stage is shown to be proportional to the rms turbulent velocity u′. Second, a late statistically stationary regime of the front evolution is studied. A new length scale characterizing the smallest wrinkles of the front surface is introduced. Since this length scale is smaller than the Kolmogorov length scale ηK under conditions of the present study, the front is hypothesized to be a bifractal with two different fractal dimensions for wrinkles larger and smaller than ηK. Finally, a simple scaling of u¯T∝u′ is obtained for this late stage as well.

The paper deals with the self-ignition and combustion of hydrogen jets in a high-speed transverse flow of hot vitiated air in a duct. The Improved Delayed Detached Eddy Simulation (IDDES) approach based on the Shear Stress Transport (SST) model is used, which in this paper is applied to a turbulent reacting flow with finite rate chemical reactions. An original Adaptive Implicit Scheme for unsteady simulations of turbulent flows with combustion, which was successfully used in IDDES simulation, is described. The simulation results are compared with the experimental database obtained at the LAERTE experimental workbench of the ONERA—The French Aerospace Laboratory. Comparison of IDDES with experimental results shows a strong sensitivity of the simulation results to the surface roughness and temperature of the duct walls. The results of IDDES modeling are in good agreement with experimental pressure distributions along the wall and with the results of videoregistration of the excited radical chemiluminescence.

In the article, a differential Reynolds stress model is recalibrated using turbulent channel flow direct numerical simulation data in the range of friction Reynolds numbers 550–5200. The calibration aims to produce a RANS sublayer model for use within the hybrid RANS/LES framework. The model is designed to capture the average field of a thin near-wall part of a boundary layer as accurately as possible. An a posteriori procedure is employed in which one-dimensional channel flow calculations are performed for all variations of the model coefficients at each stage of the optimization procedure. The coefficients are initialized with their original values and then optimized by minimizing the appropriately chosen norm. An improved representation of the mean velocity profile and peak Reynolds stress values is demonstrated. Both models—baseline and recalibrated—are implemented in an in-house CFD code, and several simulations, including a channel flow, a flat plate boundary layer and a boundary layer separation from a rounded step, are performed. The latter benchmark flow is also simulated in hybrid RANS/LES mode. The updated model is compared to the original one, demonstrating improvements over the baseline model in the cases it was designed for.

Separated turbulent diffuser flows have long been an object of experimental and computational investigations due to their wide use in engineering applications and fundamental importance for understanding turbulent effects. The accuracy of simulating such flows depends mainly on turbulence modeling subtleties, numerical method, and the correspondence between the boundary conditions and the experimental set-up. The current review of selected articles focuses on revealing some of the computational challenges that may occur while modeling asymmetric subsonic diffuser flows. These challenges include the influence of sidewalls on the separation, issues with grid convergence, and the definition of boundary conditions. Several known experimental test cases and attempts at simulating them are studied. The novelty of this paper is in the fact that it is focused on a specific type of diffusers (asymmetric and subsonic) and based on relatively recent data. It is concluded that for all the test cases considered, Reynolds stress models and hybrid eddy-resolving methods are the most appropriate tools for obtaining reasonable results.

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation.

The improved delayed detached Eddy simulation (IDDES) approach used in the part I of this investigation to study the self-ignition and combustion of hydrogen jets in a high-speed transverse flow of hot vitiated air in a duct is extended in the following directions: (i) the wall boundary conditions are modified to take into account the optical windows employed in the experiments; (ii) the detailed chemical kinetic model with 19 reactions is used; (iii) a nonlinear turbulence model is implemented in the code to capture the secondary flows in the duct corners; (iv) the wall roughness model is adapted; (v) the synthetic turbulence generator is imposed upstream of the fuel injection. As a result of improving the mathematical and physical problem statements, a good agreement between the simulation and the experimental database obtained at the LAERTE workbench (ONERA) is achieved.

The second-order structure functions (SFs) of the velocity field, which characterize the velocity difference at two points, are widely used in research into non-reacting turbulent flows. In the present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states at two different points (reactant–reactant, reactant–product, product–product, etc.) are introduced in the paper and a relevant exact transport equation is derived in the appendix. Subsequently, in order to demonstrate the capabilities of the newly developed approach for advancing the understanding of turbulent reacting flows, the conditioned SFs are extracted from three-dimensional (3-D) direct numerical simulation data obtained from two statistically 1-D planar, fully developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants and even (iii) allow us to detect a new phenomenon such as the appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat-release zones indicate a highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent flow in the case of a low Damköhler number. In the cited paper, the theory is also supported by Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent premixed combustion is argued. The present work aims at complementing the theory with a new mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c ( x , t ) is considered to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c ( x , t ) < 1 , where molecular transport plays an important role, and (ii) equilibrium products, c ( x , t ) = 1 . The two zones are separated by an infinitely thin reaction sheet, where c ( x , t ) = 1 and | ∇ c | is fixed in order for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable, its second moment, and instantaneous characteristic functions. Averaging of these equations yields exact, unclosed transport equations for the conditioned reaction-progress-variable moments and Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet. The closure problem for the derived equations is beyond the scope of the paper.

We present a new subgrid stress model for the large eddy simulation of turbulent flows based on the solution of transport equations for stress tensor components. The model was a priori term-by-term calibrated against an open DNS database on forced isotropic turbulence (Johns Hopkins University database). After that, it was applied in a large eddy simulation of non-premixed turbulent combustion. To demonstrate the impact of the new subgrid stress model on scalar fields, we excluded the backward effect of heat release on the subgrid stresses, considering an isothermal reaction (i.e., diluted mixture; the density variations associated with chemical heat release can be neglected) and a Burke–Schumann reaction sheet approximation. A periodic box filled with a homogeneous turbulent velocity field and a three-layer top-hat mixture fraction field was studied. Four simulations were performed in which a fixed model for mixture fraction and its variance was combined with either the proposed subgrid stress model or one of the standard models, including Smagorinsky, dynamic Smagorinsky and WALE. Qualitatively correct backscatter was observed in a simulation with the new model. The differences in the statistics of the mixture fraction and reactive component fields caused by the new subgrid stress model were analyzed and discussed. The importance of using an advanced subgrid stress model was highlighted.