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Chemical explosive mode analysis for a turbulent lifted ethylene jet flame in highly-heated coflow
Abstract
The recently developed method of chemical explosive mode (CEM) analysis (CEMA) was extended and employed to identify the detailed structure and stabilization mechanism of a turbulent lifted ethylene jet flame in heated coflowing air, obtained by a 3-D direct numerical simulation (DNS). It is shown that CEM is a critical feature in ignition as well as extinction phenomena, and as such the presence of a CEM can be utilized in general as a marker of explosive, or pre-ignition, mixtures. CEMA was first demonstrated in 0-D reactors including auto-ignition and perfectly stirred reactors, which are typical homogeneous ignition and extinction applications, respectively, and in 1-D premixed laminar flames of ethylene–air. It is then employed to analyze a 2-D spanwise slice extracted from the 3-D DNS data. The flame structure was clearly visualized with CEMA, while it is more difficult to discern from conventional computational diagnostic methods using individual species concentrations or temperature. Auto-ignition is identified as the dominant stabilization mechanism for the present turbulent lifted ethylene jet flame, and the contribution of dominant chemical species and reactions to the local CEM in different flame zones is quantified. A 22-species reduced mechanism with high accuracy for ethylene–air was developed from the detailed University of Southern California (USC) mechanism for the present simulation and analysis.
... Improved identifications on the premixed and diffusion flames are desired. 16,[28][29][30] Based on our recent experience with the mixed modes of supersonic and subsonic combustion, 31 flame index conditioning on the local Heat Release Rate (HRR) is expected to properly identify different combustion modes. In this study, some quantified flame dynamics and statistics in the mixed modes of premixed and diffusion combustion are targeted. ...
... 16,21,[31][32][33][34][35][36] The measurement conducted by Waidmann et al. 20 is chosen as the base case, upon which parametrical numerical simulations are performed with different fuel injector numbers and injection pressures and temperatures. Compared with the conventional TFIbased methods 15,[17][18][19][22][23][24][25][26] and some new development, 16,[28][29][30] this study is not limited to solely identifying different flame modes. Analyses on the temporal and statistical distributions of different flame modes are further performed. ...
... However, it has been found that flame index may also peak in non-reactive flows. 16,28 Considering premixed or diffusion opposed jets at room temperature, rY F Á rY O may be pronounced solely due to the high flow strain rate or mixing rate. Therefore, flame may not actually exist although n SFI is nonzero. ...
Combustion in scramjets generally proceeds in diffusion mode due to the independent injection of fuel and air streams. However, premixed combustion is also important especially in the recirculation zones for overall flame stabilization. Flame dynamics and statistics of mixed modes of premixed and diffusion combustion under varied fuel injector number, injection pressure, and temperature (denoted as N j, p H 2, and T H 2, respectively) in a strut–based, hydrogen-fueled model supersonic combustor are numerically investigated. The overall heat release rate, combustion efficiency, and premixed flame liftoff distance are calculated. Three spanwise-averaged fractions for the premixed flow region, premixed combustion region, and heat release rate from the premixed combustion, respectively, are compared to identify the mixed combustion modes. The spatial probability distributions of premixed and diffusion combustion modes are analyzed based on multiple instantaneous numerical snapshots. The supersonic combustion cases with changed N j and p H 2 exhibit typical characteristics of triplet lifted jet flames. An upstream premixed flame reservoir beneficial to downstream flame propagation is essential for the overall flame stabilization in these cases. With increased T H 2, the combustion field shows a propensity of lifted autoignition flames after the upstream forced ignition. The flame base monotonically moves toward the strut base with increased N j, p H 2, and T H 2. However, the premixed flame liftoff distance indicates different oscillation modes when increasing the above qualities. They include the dispersive, lifting, stable, attaching, oscillating, and steady modes under various conditions.
... This may reduce the chemical heat release effectiveness of the leading detonation [2,7,8], which lowers detonation wave stability and degrades thrust performance. In this regard, Pal et al. [16,17] developed a novel combustion diagnostic tool based on chemical explosive mode analysis (CEMA) [18,19] to identify local combustion modes and quantify deflagrative losses in RDEs from high-fidelity large-eddy simulations (LES). ...
... CEMA is a computational combustion diagnostic based on eigenanalysis of the local chemical Jacobian. A chemical explosive mode (CEM) is defined as the eigen-mode associated with a positive eigenvalue, which indicates the tendency of the local mixture to ignite if isolated [18,19]. The zero-crossing of CEM eigenvalue (k e ) is relevant to critical flame features, such as ignition, extinction, and premixed reaction fronts in a variety of flame configurations. ...
In the present work, a first-of-its-kind 3D large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale non-premixed hydrogen-air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen-air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the RDE-NGV configuration exhibits higher total pressure loss compared to RDE without stator across both the mass flux conditions. This study extends the state-of-the-art in numerical modeling of pressure gain combustion systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems relevant to RDE-turbine integration for stationary power generation.
... This may reduce the chemical heat release effectiveness of the leading detonation [2,7,8], which lowers detonation wave stability and degrades thrust performance. In this regard, Pal et al. [16,17] developed a novel combustion diagnostic tool based on chemical explosive mode analysis (CEMA) [18,19] to identify local combustion modes and quantify deflagrative losses in RDEs from high-fidelity large-eddy simulations (LES). ...
... CEMA is a computational combustion diagnostic based on eigen-analysis of the local chemical Jacobian. A chemical explosive mode (CEM) is defined as the eigen-mode associated with a positive eigenvalue which indicates the tendency of the local mixture to ignite if isolated [18,19]. The zero-crossing of CEM eigenvalue (λe) is relevant to critical flame features, such as ignition, extinction, and premixed reaction fronts in a variety of flame configurations. ...
In the present work, a first-of-its-kind 3D large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale non-premixed hydrogen-air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen-air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the RDE-NGV configuration exhibits higher total pressure loss compared to RDE without stator across both the mass flux conditions. This study extends the state-of-the-art in numerical modeling of pressure gain combustion systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems for practical insights pertaining to RDE-turbine integration for stationary power generation.
... Thus, each flamelet is parameterized by a combination of initial (T, ϕ) where T ∈ {1150 K, 1200 K, 1250 K} and ϕ ∈ {0.375, 0.4, 0.425}. The chemistry is represented by a 32-species, 206reactions mechanism [25]. The homogeneous reactor simulations are performed with Cantera [26], and each flamelet is computed for different durations to ensure that the profiles remain nearly similar. ...
... In addition to the chemical reactions that govern the evolution of homogeneous reactors of the previous two cases, this case has effects of convection and diffusion that influence the thermochemical evolution. The chemistry is represented by the same 32-chemical species, 206-reactions mechanism [25], resulting in n v = 33 features. The freelypropagating flame is simulated in a one-dimensional domain of 0.02 m discretized with a grid of around 550 points. ...
For turbulent reacting flows, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, is a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analysis with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA/PCA based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine a priori the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates that are nonlinear functions of the reconstructed state as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: a homogeneous reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional homogeneous charge compression ignition of ethanol. The analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.
... The Jacobian can be eigen-decomposed into the complex eigenvalues , left eigenvector , and right eigenvector . A positive ( ) is defined as a Chemical Explosive Mode (CEM) [48]. ...
... where the value of zero occurs at the transition point from black to white, denoting the point of ignition [48]. It is found that at the low temperature stage (<700 K), the dominant species is HO 2 , same as the methane oxidation process [51]. ...
... The initial condition, shown by the light blue line in Fig. 10, is the steady state solution obtained from the auto-ignition of premixed C 2 H 4 /air mixture at a pressure of 2 atm. A 22 species 18-step reduced mechanism describing the oxidation kinetics of ethylene/air [46] is used. The steady solution is perturbed with sinusoidal temperature fluctuations with a magnitude of 180K and frequency 20K hz at the left boundary using an oscillatory inflow boundary condition [47,48]. ...
... The one-dimensional domain is 4 mm and is discretized with 576 grid points that are distributed across 12 processors. The 22 species, 18-step reduced mechanism from [46] for ethylene/air used in the earlier case is also used here. The initial condition is generated using an auto-ignition case, and non-reflecting inflow and subsonic outflow are imposed at the left and right boundaries, respectively. ...
Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical methods, scalable algorithms and re-design of current state-of-the art numerical solvers are required for scaling to these machines with minimal overheads. One such approach for partial differential equations based solvers involves computation of spatial derivatives with possibly delayed or asynchronous data using high-order asynchrony-tolerant (AT) schemes to facilitate mitigation of communication and synchronization bottlenecks without affecting the numerical accuracy. In the present study, an effective methodology of implementing temporal discretization using a multi-stage Runge-Kutta method with AT schemes is presented. Together these schemes are used to perform asynchronous simulations of canonical reacting flow problems, demonstrated in one-dimension including auto-ignition of a premixture, premixed flame propagation and non-premixed autoignition. Simulation results show that the AT schemes incur very small numerical errors in all key quantities of interest including stiff intermediate species despite delayed data at processing element (PE) boundaries. For simulations of supersonic flows, the degraded numerical accuracy of well-known shock-resolving WENO (weighted essentially non-oscillatory) schemes when used with relaxed synchronization is also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes are derived and tested on linear and non-linear equations. Finally the novel AT-WENO schemes are demonstrated in the propagation of a detonation wave with delays at PE boundaries.
... The ethylene-air chemistry in the training and test datasets is represented by a 32-species, 206-reactions mechanism [28]. PCA and CoK-PCA based lowdimensional manifolds (LDMs) are generated using thermochemical scalar data obtained from 13 distinct initial conditions. ...
A low-dimensional representation of thermochemical scalars based on cokurtosis principal component analysis (CoK-PCA) has been shown to effectively capture stiff chemical dynamics in reacting flows relative to the widely used principal component analysis (PCA). The effectiveness of the reduced manifold was evaluated in a priori analyses using both linear and nonlinear reconstructions of thermochemical scalars from aggressively truncated principal components (PCs). In this study, we demonstrate the efficacy of a CoK-PCA-based reduced manifold using a posteriori analysis. Simulations of spontaneous ignition in a homogeneous reactor that pose a challenge in accurately capturing the ignition delay time as well as the scalar profiles within the reaction zone are considered. The governing ordinary differential equations (ODEs) in the PC space were evolved from the initial conditions using two ODE solvers. First, a standard ODE solver that uses a pre-trained artificial neural network (ANN) to estimate the source terms and integrates the solution in time. Second, a neural ODE solver that incorporates the time integration of PCs into the ANN training. The time-evolved profiles of the PCs and reconstructed thermochemical scalars demonstrate the robustness of the CoK-PCA-based low-dimensional manifold in accurately capturing the ignition process. Furthermore, we observed that the neural ODE solver minimized propagation errors across time steps and provided more accurate results than the standard ODE solver. The results of this study demonstrate the potential of CoK-PCA-based manifolds to be implemented in massively parallel reacting flow solvers.
... Note that the discussion of our experiences are not intended to imply issues with the numerical Jacobian approach used in CVODE or other implicit integrators; such solvers only require approximations to the Jacobian matrix. However, based on our experiences, we recommend taking care when attempting to obtain highly accurate Jacobian matrices, as in the current effort and for analysis techniques such as computational singular perturbation [15,[69][70][71] and chemical explosive mode analysis [72][73][74] that rely on eigendecomposition of the Jacobian matrix. As a result of the aforementioned difficulties with finite differences, we obtained accurate Jacobian matrices via automatic differentiation through expression templates using the Adept software library [64,75]. ...
Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation, then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons.
... Luo [24] p=0.1∼5 MPa; ϕ=0.5∼1.5; ...
To reduce the instability and uncertainty of current linear methods for combustion kinetic model reduction, a new nonlinear method based on artificial intelligence algorithm is proposed to simplify chemical models. This method is applied to reduce the USC-Mech II and JetSurF 2.0 mechanisms, so that the reduced mechanisms can accurately predict the ignition delay time of ethylene and n-decane respectively. The results show that the new reduction method based on particle swarm optimization (PSO) can obtain more compact reduced models. The 22-species ethylene mechanism and the 45-species n-decane combustion mechanism are obtained, which are more compact than those obtained by other reduction methods under similar operating conditions.
... For non-premixed turbulent combustion case, ξ is chosen as the scalar as the mixing process in non-premixed configuration is dominant [44,45]. CEMA is a diagnostic tool used for studying the chemical reaction stability, ignition features, and other aspects of flames in complex flow fields through eigenvalue analysis [46,47]. It calculates the Jacobian of the local chemical source terms as eq. ...
Hydrogen-fueled gas turbines play one of the key roles in future carbon-neutral energy structure. Due to hydrogen’s high flame speed and extreme flame temperature, design of burners applying hydrogen as fuel is of challenge. In this work, we conduct direct numerical simulations to investigate a non-premixed steam-diluted oxygen/hydrogen combustion, which is formed by inclined impinging fuel and oxidizer jets injected by sub-millimeter nozzles. This configuration inherently prevent flashback and has a higher mixing efficiency enhanced by jet impingement, thereby leveraging advantages of both conventional premixed and non-premixed configurations. The flame is lifted flame held at the jet impinging position far away from the wall boundary. The most intensive mixing process occurs at the outer sides of the two branches of hydrogen jet after impinging, forming the flame base and resulting in an edge-flame configuration. A larger jet inclination angle leads to more effective bulk turbulence mixing because of the increased mixing volume, thereby enhancing combustion completeness. Simultaneously, it results in lower wall heat flux due to gentler upstream recirculation of burnt products. Chemical explosive mode analysis is conducted to analyze the combustion procedure from ignition to burnt out. The flame is held by the recirculation of high-temperature burnt products upstream of the impingement position, and its structure is primarily formed by the simultaneous ignition of a widespread explosive mixture enhanced by intense turbulence.
... However, their large size leads to high computational cost when solving the corresponding chemical source terms and brings stiff problem to numerical solution. 42,43 Thus, they cannot be directly applied to computationally expensive combustion simulation for ethylenefueled scramjet combustors. ...
The high-fidelity reduced mechanism is one of the key elements in the combustion simulation of scramjet combustors to reveal their combustion and flow phenomena. In the present work, the hierarchically constructed NUIGMech1.2 (2857 species and 11 814 reactions) is applied to the combustion simulation of an ethylene-fueled scramjet combustor using the method of static integrated skeletal reduction and tabulation of dynamic adaptive chemistry (TDAC). The integrated skeletal reduction strategy successively consists of species elimination using the revised directed relation graph with error propagation method of fixed species scheme and improved sensitivity analysis method, and reactions elimination based on computational singular perturbation importance index. A preferred ethylene skeletal mechanism (26 species and 117 reactions) is obtained through the integrated skeletal reduction strategy under target working conditions of temperature range of 900–1800 K, pressure range of 1–4 atm, and equivalence ratio range of 0.25–5.0. The compact skeletal mechanism is comprehensively validated against the experimental results of ignition delay times, laminar flame speeds, and key species concentration profiles. Meanwhile, it shows consistent results with the detailed mechanism on the adiabatic flame temperature profiles and “S”-curves. When applying this skeletal mechanism to combustion simulations of ethylene-fueled scramjet combustor with double parallel cavities, the path flux analysis method and in situ adaptive tabulation algorithm of TDAC is further utilized to speed up the chemical reaction solution process at run-time. Under the scramjet and ramjet modes, the corresponding simulation results in terms of flame luminosity images, schlieren images, and static pressure distributions, coincide well with those of experimental measurements. The combustion and flow characteristics of the two modes are investigated and analyzed comparatively based on above results and combustion performance parameters. Present work contributes to the application of fuel kinetic mechanisms in scramjet combustor combustion simulation.
... To further elaborate on the interactions between fluid dynamics and chemical reactions, Fig. 15 shows the explosion indices for temperature and species CO calculated using the chemical explosive mode analysis (CEMA) [34][35][36][37] for the same case as in Fig. 14. It is found that the mixture behind the detonation front has a strong propensity for thermal runaway, whereas those behind the short-period compression wave and secondary reaction front have a dominant propensity for chemical runaway or chain-branching reactions. ...
One-dimensional numerical simulations based on the hybrid Eulerian–Lagrangian approach are performed to investigate detonation dynamics in two-phase gas-droplet n-heptane/air mixtures with and without liquid fuel pre-vaporization. The reactive Navier–Stokes equations considering the two-way coupling for interphase exchanges of mass, momentum, energy, and species are solved with a skeletal mechanism consisting of 44 species and 112 reactions. The effects of n-heptane droplet diameter and equivalence ratio (ER) on average detonation speed and mode are studied. For pre-vaporization cases, the average detonation speed first decreases and then increases with droplet diameter ranging from 2.5 to 40 μm, which is minimum at 7.5–10 μm due to the competition between fuel vapor addition and droplet evaporative heat absorption. However, the average speed increases monotonically as the droplet ER increases from 0.2 to 1.2. A further increase in the droplet ER (e.g., 2.4) would lead to detonation suppression in the presence of large droplets (e.g., above 30 μm). The detonation is fully quenched when the droplet ER is 3.2. Similar observations are also made for the pure sprayed cases without n-heptane pre-vaporization, where the average speed increases rapidly for droplet ER of 0.2–0.8 and slowly for ER of 0.8–1.6. Various detonation modes are observed with respect to droplet diameter and equivalence ratio, either with or without fuel pre-vaporization. Generally, the pure sprayed cases show more irregular behaviors in detonation propagation. The laden droplets provide a new approach to control the intrinsically unstable or highly irregular behaviors of pure gas or pure sprayed detonations. The finite, small disturbances from the spatially non-uniform droplets, and enrichment from the droplet evaporative mass addition, are two essential mechanisms for the mitigation of the pulsating detonation.
... For grid independence analysis, readers are referred to reference [9,13]. A reduced 22-species ethylene-air chemical mechanism was used for the combustion reaction modeling [14]. The progress variable was defined as a linear combination of the four combustion product species through * = ,"-+ *-" + *-+ ," . ...
Scramjets are a promising air-breathing propulsion technology that can offer efficient, reusable, and safe flights at hypersonic speeds. A scramjet combustor is occupied by a complex flow field where turbulence, shock/rarefaction waves, boundary layers, and combustion kinetics are strongly coupled and interact at various time and length scales. Current simulations of scramjet combustors for design optimization studies are mainly based on the solutions of Reynolds-averaged Navier–Stokes equations (RANS) with finite-rate chemistry (FRC) approach, which omits turbulence-chemistry interactions (TCI). This simulation approach can be computationally expensive in cases that involve detailed chemical mechanisms. In contrast, flamelet-based combustion models are promising solutions for affordable scale- resolved scramjets simulations, including detailed chemical mechanisms and TCI effects. However, using flamelet-based combustion models requires higher dimensional flamelet manifolds, as they are essential in capturing the coupled effects of pressure gradients and unsteady chemical kinetics observed in scramjet combustors. This study examines the Unsteady Flamelet Progress Variable (UFPV) model in VULCAN- CFD in a supersonic mixing layer configuration, followed by the HIFiRE-2 scramjet operating at scramjet mode. UFPV results are compared to FRC simulations and the available experimental surface pressure distribution data for the scramjet simulation. The application of a deep artificial neural network (ANN) approach to compress the higher dimensional manifolds is also presented in the supersonic mixing layer problem. Accuracy, modeling challenges, and different ANN strategies for scramjet simulations as an alternative to the memory-intensive multidimensional flamelet approach are also discussed.
... The datasets generated for training and testing the POUnet models come from solving flamelet equations of varying complexity, which is commonly done for building models in combustion applications (Pope, 2013). The pressure is set to one atmosphere and the fuel and oxidizer are pure ethylene (Luo et al., 2012) and air, respectively. Data generation was performed using Spitfire (Hansen et al., 2020). ...
... In contrast to the computational singular perturbation (CSP) framework [4], CEMA is solely based on the eigen-analysis of the Jacobian of the chemical source term in the transport equations that govern a chemically reactive system. Compared to conventional analysis based on temperature or selected species concentrations, CEMA provides additional insights into key flame features such as ignition, extinction, premixed flame fronts, and flame stabilisation mechanisms [3,5,6]. CEMA has also been successfully applied to segment different flame regions in a dynamic adaptive combustion modelling framework to accelerate turbulent combustion simulation [7]. ...
Grid resolution requirement of chemical explosive mode analysis for large eddy simulations of premixed turbulent combustion, Combustion Theory and Modelling, The grid resolution requirement for trustworthy Chemical Explosive Mode Analysis (CEMA) in Large Eddy Simulation (LES) of premixed turbulent combustion is proposed. Explicit filtering, to emulate the effect of the LES filter, is applied to one-dimensional laminar flame and three-dimensional planar turbulent flames across a wide range of Karlovitz numbers (5 − 239). The identification of the flame front by CEMA is found relatively insensitive to the cell size (), while the combustion mode identification shows more significant sensitivity. Specifically, increasing falsely enhances the auto-ignition and local extinction modes and suppresses the diffusion-assisted mode. Limited dependence of the CEMA performance on the turbulent combustion regime (Karlovitz number) is observed. A simple grid size criterion for reliable CEMA mode identification in LES is proposed as δ L /2; The criterion can be relaxed to δ L in the laminar flame limit. Furthermore, theoretical analysis is conducted on an ide-alised chemistry-diffusion system. The effects of the filtering process and turbulence on the local combustion mode are demonstrated, which is consistent with the numerical observations. By incorporating turbulent combustion models in CEMA, potential improvement in identifying local combustion modes can be expected.
... In contrast to the computational singular perturbation (CSP) framework [4], CEMA is solely based on the eigen-analysis of the Jacobian of the chemical source term in the transport equations that govern a chemically reactive system. Compared to conventional analysis based on temperature or selected species concentrations, CEMA provides additional insights into key flame features such as ignition, extinction, premixed flame fronts, and flame stabilization mechanisms [3,5,6]. CEMA has also been successfully applied to segment different flame regions in a dynamic adaptive combustion modeling framework to accelerate turbulent combustion simulation [7]. ...
The grid resolution requirement for trustworthy Chemical Explosive Mode Analysis (CEMA) in Large Eddy Simulation (LES) of premixed turbulent combustion is proposed. Explicit filtering, to emulate the effect of the LES filter, is applied to one-dimensional laminar flame and three-dimensional planar turbulent flames across a wide range of Karlovitz numbers (5-239). The identification of the flame front by CEMA is found relatively insensitive to the cell size (∆), while the combustion mode identification shows more significant sensitivity. Specifically, increasing ∆ falsely enhances the auto-ignition and local extinction modes and suppresses the diffusion-assisted mode. Limited dependence of the CEMA performance on the turbulent combustion regime (Karlovitz number) is observed. A simple grid size criterion for reliable CEMA mode identification in LES is proposed as ∆ ≲ δL/2; The criterion can be relaxed to ∆ ≲ δL in the laminar flame limit. Furthermore, theoretical analysis is conducted on an idealized chemistry-diffusion system. The effects of the filtering process and turbulence on the local combustion mode are demonstrated, which is consistent with the numerical observations. By incorporating turbulent combustion models in CEMA, potential improvement in identifying local combustion modes can be expected.
... Validation for the proposed method was performed against a reactive DNS for a premixed ethylene flame in a backward-facing-step configuration show in ref. [27]. While a reduced mechanism consisting of 22 species [43] was used in the DNS solution, a 32 species skeletal mechanism from the same reference was used here for the SG-LEM simulations. 1 The computational domain is shown in Figure 5(a). The LES mesh was created using a multi-block approach and consists of hexagonal cells. ...
... As fast mixing and reaction processes happen simultaneously during jet-induced combustion in the present study, it is interesting to distinguish more precisely between ignition, local extinction, and premixed flame propagation events. For this purpose, the method called chemical explosive mode analysis (CEMA) [56][57][58][59][60] has been used for a systematic identification of these events. CEMA is based on an eigenvalue analysis of the chemical reaction system. ...
The present study investigates turbulent flame dynamics and pollutant emission characteristics in a prechamber/main chamber system. A H2/air turbulent jet flame issued from the prechamber penetrates into the NH3/air mixture found in the main chamber. Recent experimental studies have demonstrated that this configuration is very promising for future NH3 combustion in gas engines. In the present work, 3D direct numerical simulations (DNS) with detailed chemistry have been carried out in the above configuration. The dynamics of the turbulent premixed flame in the prechamber (flame thickness, flame propagation speed) and the structure of the turbulent stratified flame in the main chamber are investigated. It is found that the stratified flame thickness is becoming thicker as the flame propagates within the NH3 /air mixture. The flame displacement speed is slowing down in a first phase, before becoming faster again after jet-induced turbulence starts to decay. A chemical explosive mode analysis (CEMA) has been done to distinguish between ignition, flame propagation, and local extinction events both for the premixed flame in the prechamber and the stratified flame in the main chamber. The temporal evolution of the identified modes are consistent with the flame dynamics and help to explain the later increase in flame displacement speed. NO emission characteristics in the main chamber have also been investigated. The NO production speed first increases, reaches a plateau, before being reduced during later flame propagation; stratification is important to explain the NO emission characteristics. Compared to the laminar NH3 /air flame, the NO production speed is obviously larger in the present configuration, mainly due to the reduced contribution of the NO destruction reactions in the fuel pathway. Compared to premixed NH3/H2/air flames with H2 volume ratios found in practical systems (typically ≥ 0.4), the NO production speed is lower in the present configuration, demonstrating its superiority for practical applications. Finally, conventional heat release rate (HRR) markers are evaluated for the stratified flame. They approximate quite well the general structure of the flame front, but lead to noticeable quantitative errors.
... In particular, simulating simple canonical systems allows to obtain the training dataset, which we also refer to as the thermo-chemical state vector, X ∈ R N ×Q , where N is the number of observations and Q is the number of state variables. In the present work, we generate training data from the steady laminar flamelet model for various fuels: hydrogen [37], syngas [102] and ethylene [140]. We focus on the full state vector defined as X = T, Y 1 , Y 2 , . . . ...
Turbulent multicomponent reacting flows are described by a large number of coupled partial differential equations. With such large systems of equations, the current computational capabilities are insufficient for detailed simulations. At the same time, accurate simulations are crucial to support the rapidly developing combustion technologies. Dimensionality reduction and machine learning approaches appear well-suited for building reduced-order models (ROMs) of complex systems with many degrees of freedom. Dimensionality reduction techniques project a high-dimensional system onto a lower-dimensional basis. Projections can be computed from the available training data and are referred to as low-dimensional manifolds (LDMs). Dimensionality reduction is often coupled with nonlinear regression to bypass the errors associated with the inverse basis transformation. Regression allows to reconstruct the target thermo-chemical state quantities from the LDM parameters. A data-driven reduced-order modeling workflow provides substantial reduction to the number of transport equations solved in combustion simulations, but the quality of the manifold topology is one of the decisive aspects in successful modeling. Numerous manifold challenges of turbulent combustion have been reported in the literature and ought to be addressed. The present work advances the performance of ROMs of reacting flows. Our main focus is in addressing the outstanding manifold challenges. We provide novel tools and algorithms that can help further reduce the order, and improve the predictive capabilities of the model.
... Recently, public awareness of potential hazards regarding the extensive use of chemicals and their effects on the ecosystem has increased [1][2][3]. Operating errors, such as high pressure and excessive critical temperatures in the oil and gas industry, are resulted from chemicals and their potential hazards [4][5][6]. ...
Background:
The present study aimed to consequence modeling and root cause analysis of the real explosion of a methane pressure vessel in separation unit of a gas refinery in Iran.
Method:
ology: This study was performed in a gas refinery in the south of Iran. The studied scenario was the actual scenario that occurred in the studied pressure vessel. Modeling of possible consequences was performed using PHAST 7.2 software. Also, the root causes analysis of the accident was performed using experts' brainstorming.
Results:
At radii of 15 and 45 m, the radiation level reaches 12.5 and 4 kW/m2, respectively. In the late explosion worst-case, the vapor cloud explodes after reaching a distance of 20 m from the pressure vessel. At radii of 20 m, 25 m, and 150 m from the center of the explosion, the pressure reaches 0.2068, 0.1379, and 0.02068 bar, respectively. In the Early Explosion Overpressure, the acceptable pressure is obtained at a distance of 193 m. Moreover, in the Early Explosion Overpressure radiation, at radii of 28 m, 38 m, and 193 m, the pressure reaches 0.2068, 0.1379, and 0.02068 bar, respectively.
Conclusion:
The findings revealed that creating an appropriate risk management algorithm with a focus on consequence modeling can be an effective step towards reducing losses in the process industry. This results can create a novel insight in comparing the two reactive and proactive approaches and also reveal the effectiveness of consequence modeling in reducing the severity of risks.
... (1) usually originate from the chemical kinetics term g(z) [Valorani et al., 2003, Najm et al., 2009, Lu et al., 2010, Luo et al., 2012, Shan et al., 2012, Kooshkbaghi et al., 2015, Tingas et al., 2015. Considering the case where the n-th nonzero eigenvalue λ n of the Jacobian J of g(z) is real (the extension to complex pairs is straightforward [Goussis and Najm, 2006a]), the time scales introduced by the chemical kinetics term are approximated by the relation ...
When designing high-efficiency spark-ignition (SI) engines to operate at high compression ratios, one of the main issues that have to be addressed is detonation development from a pre-ignition front. In order to control this phenomenon, it is necessary to understand the mechanism by which the detonation is initiated. The development of a detonation from a pre-ignition front was analyzed by considering a one-dimensional constant-volume stoichiometric hydrogen/air reactor with detailed chemistry. A spatially linear initial temperature profile near the end-wall was employed, in order to account for the thermal stratification of the bulk mixture. A flame was initiated near the left wall and the effects of its propagation towards the cold end-wall were analyzed. Attention was given on the autoignition that is manifested within the cold-spot ahead of the flame and far from the end-wall, which is followed by detonation. Using CSP tools, the mechanism by which the generated pressure waves influence the autoignition within the cold-spot was investigated. It is found that the pressure oscillations induced by the reflected pressure waves and the pressure waves generated by the pre-ignition front tend to synchronize in the chamber, increasing the reactivity of the system in a periodic manner. The average of the oscillating temperature is greater in the cold-spot, compared to all other points ahead of the flame. As a result, the rate constants of the most important reactions are larger there, leading to a more reactive state that accelerates the dynamics of the cold-spot and to its autoignition.
... (1) usually originate from the chemical kinetics term g(z) [Valorani et al., 2003, Najm et al., 2009, Lu et al., 2010, Luo et al., 2012, Shan et al., 2012, Kooshkbaghi et al., 2015, Tingas et al., 2015. Considering the case where the n-th nonzero eigenvalue λ n of the Jacobian J of g(z) is real (the extension to complex pairs is straightforward [Goussis and Najm, 2006a]), the time scales introduced by the chemical kinetics term are approximated by the relation ...
When designing high-efficiency spark-ignition (SI) engines to operate at high compression ratios, one of the main issues that have to be addressed is detonation development from a pre-ignition front. In order to control this phenomenon, it is necessary to understand the mechanism by which the detonation is initiated. The development of a detonation from a pre-ignition front was analyzed by considering a one-dimensional constant-volume stoichiometric hydrogen/air reactor with detailed chemistry. A spatially linear initial temperature profile near the end-wall was employed, in order to account for the thermal stratification of the bulk mixture. A flame was initiated near the left wall and the effects of its propagation towards the cold end-wall were analyzed. Attention was given on the autoignition that is manifested within the cold-spot ahead of the flame and far from the end-wall, which is followed by detonation. Using CSP tools, the mechanism by which the generated pressure waves influence the autoignition within the cold-spot was investigated. It is found that the pressure oscillations induced by the reflected pressure waves and the pressure waves generated by the pre-ignition front tend to synchronize in the chamber, increasing the reactivity of the system in a periodic manner. The average of the oscillating temperature is greater in the cold-spot, compared to all other points ahead of the flame. As a result, the rate constants of the most important reactions are larger there, leading to a more reactive state that accelerates the dynamics of the cold-spot and to its autoignition.
For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, are a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: zero-dimensional (homogeneous) reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage (low and high temperature) ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Results from the analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.
Detailed chemistry computations are indispensable in numerous complex simulation tasks, which focus on accurately capturing the ignition process or predicting pollutant levels. Machine learning method is a modern data-driven approach for predicting full detailed thermochemical state-to-state behavior in reacting flow simulations. By combining unsupervised clustering algorithms to subdivide the composition space, the complexity of adaptive regression models for temporal dynamics can be significantly reduced. In this article, a more compact dataset is generated, which is essential for the clustering algorithm, by leveraging the adaptive CVODE solver time steps for data augmentation for stiff reactive states. A learning workflow that utilizes a deep residual network model (ResNet) in conjunction with an adaptive clustering algorithm is proposed. This approach aims to replace the stiff ODE direct integration solver traditionally used for computing thermochemical species' state-to-state temporal evolution for detailed chemistry simulations. The learning models are adaptively trained using the K-Means clustering algorithm in the nonlinear transformation space for different subspaces of dynamic systems. Three test cases: (9 species), (32 species), and (53 species), are investigated, each exhibiting varying complexities. The study demonstrates that the iterative predictions of thermochemical states align well with the results obtained from direct numerical integration. Additionally, employing multiple adaptive regression models in subdomains yields superior performance compared to a single regression model prediction case.
Internal combustion engines are the dominant power sources in transport, accounting for significant amounts of fuel consumption and pollutant emissions. Low-temperature combustion is a promising technology for engine combustion, whose main challenge is the complex control of two-stage auto-ignition that determines the performance of a low-temperature combustion engine. This paper systematically reviews the state-of-the-art advances in auto-ignition modeling which is an essential tool to understand auto-ignition mechanisms and provides valuable guidance for designing more efficient and cleaner engines. This paper focuses on turbulence, evaporation and chemistry effects without the consideration of inter-droplet interactions. Five models with increasing complexity are discussed and compared, including homogeneous models without and with evaporation (models 1 and 2), droplet simulation in static environments (model 3), and direct numerical simulation without and with evaporation (models 4 and 5). Rapid mixing leads to homogeneous conditions in models 1 and 2, in which two-stage auto-ignition is divided into low-temperature induction, low-temperature auto-ignition, high-temperature induction and high-temperature auto-ignition. Model 1 only considers chemical reactions and auto-ignition is determined for a certain thermal state. Droplet evaporation affects the auto-ignition evolution in model 2 through evaporation-induced changes in the thermal state. Compared with homogeneous models, droplet evaporation in model 3 leads to compositional and temperature stratifications which cause three new phenomena: preferential auto-ignition, reaction front propagation and non-zero scalar dissipationrate. Models 4 and 5 introduce turbulent effects on induction timescale and front propagation. Finally, challenges and future directions in auto-ignition modeling are outlined.
A lean premixed ethylene–air flame in a backstep configuration is simulated on multiple grids using both direct numerical simulations (DNS) with reduced order kinetic mechanism and large eddy simulations (LES) with flamelet-based thermochemistry. The configuration includes preheated reactants and a recirculation zone that provides radicals and high temperature gases to stabilize the flame. Heat losses are present due to the proximity of cooled walls. The reacting flow obtained from DNS at different resolutions is first analyzed to investigate the property of heat transfer within the recirculation region. LES based on adiabatic flamelets with a correction of the heat capacity is then tested, and its ability to account for heat losses is compared to results obtained using a three-dimensional non-adiabatic flamelet approach. Mean fields and subgrid properties are compared to those obtained from DNS to assess the capability of the LES models. The results show that the non-adiabatic flamelet approach can predict recirculation region and temperature fields with good accuracy. The model with heat capacity correction is able to effectively correct the heat capacity behavior as observed by a priori comparisons. However, in the a posteriori context, it is observed to overestimate the temperature field, although the correct size of the recirculation region is predicted. The combined a priori and a posteriori analyses on the same configuration and at different mesh resolutions allow for a precise separation of modeling effects due to heat transfer at the wall and combustion closure, thus providing indications on the LES performance in the context of flamelets.
In the present work, direct numerical simulation of a laboratory-scale lean premixed reacting jet in cross-flow was performed to explore the flow–flame structures and turbulence–flame interactions. A jet of lean premixed ethylene–air mixtures (equivalence ratio ) was injected into a hot vitiated cross-flow. Both non-reacting and reacting cases were simulated. It was found that the reacting jet penetrates deeper in the cross-flow with a weaker shear layer compared with the non-reacting one. The wake of the non-reacting and reacting jet is characterized by vertical vortices and recirculation zones, respectively. As for the flame structure of the reacting case, the reaction intensity varies considerably in different flame zones. The heat release rate on the leeward side is higher than that on the windward side, but lower than that of the corresponding laminar flame. The analysis of the turbulence–flame interactions of the reacting case showed that the large local Damköhler number ( Da ) related to reaction-induced dilatations results in an increased tendency of the scalar gradient to align with the most extensive strain rate, which is more evident in the regions with high heat release rate on the leeward side. Negative dilatation regions with positive tangential strain rate and negative normal strain rate are observed on the windward side. High positive dilatations appear on the flame front of the leeward side. The tangential strain rate is negatively correlated with the normal strain rate and curvature. Regions with a high local Da on the windward side correspond with high positive curvature regions.
The design of the scramjet‐powered vehicles flown to date relied on varied computational tools, which had to be validated and verified with experimental data obtained from wind tunnel testing. This chapter highlights some of the most important aerothermodynamics flow phenomena that required computational modeling and simulation to predict the performance of closely integrated hypersonic air‐breathing vehicles. To get a sense of the analytical and computational modeling issues present in the flow‐field of such vehicles, it considers the physics of the four major components: vehicle forebody, inlet/isolator, combustor, and nozzle/vehicle afterbody. The origin of today's state‐of‐the‐art computational tools for scramjet research and development began with the Hyper‐X program. The NASA Hyper‐X Program promoted high‐speed computational research and development, placing a greater effort in developing new combustion codes.
In the present work, direct numerical simulation (DNS) of a laboratory-scale lean premixed reacting jet flame in crossflow was performed to understand the flame structures and the flame stabilization mechanism. In the DNS, an ethylene-air jet with an equivalence ratio of 0.6 was injected into a hot vitiated crossflow. The jet Reynolds number reaches 6161. The DNS results were compared with those of the experiment with a good agreement. It was found that the windward and leeward branches of the flame show significantly different behaviors. The windward flame branch, appearing lifted and discontinuous, is located in the shear layer regions with high temperature, low vorticity and low scalar dissipation rate. The location of the peak heat release rate shifts to a higher mixture fraction with increasing distance from the jet exit. The leeward branch of the flame anchors in the shear layer near the jet exit. The recirculation zone in the wake of the jet facilitates the stabilization of the leeward flame. The chemical explosive mode analysis (CEMA) and species budget analysis were employed to characterize the local combustion mode. Auto-ignition plays a key role in the stabilization of the windward flame where a large range of extinction is also found due to the high strain rate. In contrast, premixed flame propagation is dominant on the leeward side.
In the present work, three-dimensional direct numerical simulation (DNS) of n-heptane/air premixed combustion in turbulent boundary layer was performed to explore the near-wall ignition process with low-temperature chemistry. A reduced chemical mechanism with 58 species and 387 elementary reactions for n-heptane combustion was used in the DNS. The general characteristics of the ignition process near the wall were examined. It was found that low-temperature ignition (LTI) dominates the upstream region, and high-temperature ignition (HTI) appears in the downstream region. The ignition process and the low-temperature chemistry pathways of the DNS are compared with those of a corresponding laminar case. It was found that the ignition process was affected by turbulence, which results in thickened reaction zones. However, the carbon flow analysis of low-temperature chemistry showed that turbulence rarely affects the low-temperature chemistry pathway. The combustion modes of various regions were scrutinized based on the budget terms of species transport equations and the chemical explosion mode analysis (CEMA). It was shown that the reaction term of RO2 is significant during the LTI process of the upstream region, and the reaction terms of CH2O and CO2 are evident in the downstream region, indicating the occurrence of HTI. It was also shown that auto-ignition is dominant in the upstream region. With increasing streamwise distance, the contribution of flame propagation increases, which takes over that of auto-ignition in the near-wall region.
Jacobian clustering is proposed to reduce the computational cost associated with matrix operations encountered in the Newton iteration in fully coupled, fully implicit schemes for unsteady reactive flow simulations with detailed chemistry. The iterative solver is based on the Lower-Upper Symmetric Gauss-Seidel (LUSGS) algorithm and sparse matrix technique. The evaluation and sparse Lower-Upper (LU) factorization of the diagonal block of the system Jacobian are performed within clusters rather than individual cells for Computational Fluid Dynamics (CFD) simulations. Cells that are close in the state space are clustered to provide the averaged states for calculating the Jacobians of chemical source terms and transport fluxes. The cells retrieve the factorized sparse matrices from the belonging clusters to perform the necessary iterations. For the purpose of clustering, the spatial dependency of transport Jacobian in the diagonal block is eliminated. To further reduce the computational cost, the sparsity of chemical Jacobian is augmented by removing the insignificant matrix elements. The method is tested in various one-dimensional hydrocarbon flames with both the second order Crank-Nicolson scheme and a third order implicit Runge-Kutta scheme. Various chemical mechanisms with 9 to 111 species are used to test the performance of the iterative solver. Fast convergence of Newton iteration is achieved, and the formal order of accuracy is demonstrated with Jacobian clustering. The overall costs of evaluation and factorization of the block diagonal Jacobian are negligible compared to the cost of calculating transport fluxes and chemical source terms. The averaged costs of Jacobian evaluation, LU factorization and Newton iteration, all increase only linearly with the number of chemical species. The fully coupled, fully implicit Crank-Nicolson scheme with Jacobian clustering shows 4 to 42 times speedup in computational time compared to the decoupled implicit scheme with Strang operator splitting. Jacobian clustering is promising to increase the computational efficiency of high order fully coupled, fully implicit schemes for unsteady reactive flow simulations with detailed chemistry.
This paper presents a joint numerical and experimental study of the ignition process and flame structures in a gasoline partially premixed combustion (PPC) engine. The numerical simulation is based on a five-dimension Flamelet-Generated Manifold (5D-FGM) tabulation approach and large eddy simulation (LES). The spray and combustion process in an optical PPC engine fueled with a primary reference fuel (70% iso-octane, 30% n-heptane by volume) are investigated using the combustion model along with laser diagnostic experiments. Different combustion modes, as well as the dominant chemical species and elementary reactions involved in the PPC engines, are identified and visualized using Chemical Explosive Mode Analysis (CEMA). The results from the LES-FGM model agree well with the experiments regarding the onset of ignition, peak heat release rate and in-cylinder pressure. The LES-FGM model performs even better than a finite-rate chemistry model that integrates the full-set of chemical kinetic mechanism in the simulation, given that the FGM model is computationally more efficient. The results show that the ignition mode plays a dominant role in the entire combustion process. The diffusion flame mode is identified in a thin layer between the ultra fuel-lean unburned mixture and the hot burned gas region that contains combustion intermediates such as CO. The diffusion flame mode contributes to a maximum of 27% of the total heat release in the later stage of combustion, and it becomes vital for the oxidation of relatively fuel-lean mixtures.
A generalized formulation of the characteristic boundary conditions for compressible reacting flows is proposed. The new and improved approach resolves a number of lingering issues of spurious solution behaviour encountered in turbulent reacting flow simulations in the past. This is accomplished (a) by accounting for all the relevant terms in the determination of the characteristic wave amplitudes and (b) by accommodating a relaxation treatment for the transverse gradient terms with the relaxation coefficient properly determined by the low Mach number asymptotic expansion. The new boundary conditions are applied to a comprehensive set of test problems including: vortex-convection; turbulent inflow; ignition front propagation; non-reacting and reacting Poiseuille flows; and counterflow cases. It is demonstrated that the improved boundary conditions perform consistently superior to existing approaches, and result in robust and accurate solutions with minimal acoustic wave interactions at the boundary in hostile turbulent combustion simulation conditions.
Direct numerical simulation (DNS) of the near-field of a three-dimensional spatially-developing turbulent ethylene jet flame in highly-heated coflow is performed with a reduced mechanism to determine the stabilization mechanism. The DNS was performed at a jet Reynolds number of 10,000 with over 1.29 billion grid points. The results show that auto-ignition in a fuel-lean mixture at the flame base is the main source of stabilization of the lifted jet flame. The Damköhler number and chemical explosive mode (CEM) analysis also verify that auto-ignition occurs at the flame base. In addition to auto-ignition, Lagrangian tracking of the flame base reveals the passage of large-scale flow structures and their correlation with the fluctuations of the flame base similar to a previous study (Yoo et al., J. Fluid Mech. 640 (2009) 453–481) with hydrogen/air jet flames. It is also observed that the present lifted flame base exhibits a cyclic ‘saw-tooth’ shaped movement marked by rapid movement upstream and slower movement downstream. This is a consequence of the lifted flame being stabilized by a balance between consecutive auto-ignition events in hot fuel-lean mixtures and convection induced by the high-speed jet and coflow velocities. This is confirmed by Lagrangian tracking of key variables including the flame-normal velocity, displacement speed, scalar dissipation rate, and mixture fraction at the stabilization point.
This paper presents a numerical study of auto-ignition in simple jets of a hydrogen–nitrogen mixture issuing into a vitiated co-flowing stream. The stabilization region of these flames is complex and, depending on the flow conditions, may undergo a transition from auto-ignition to premixed flame propagation. The objective of this paper is to develop numerical indicators for identifying such behavior, first in well-known simple test cases and then in the lifted turbulent flames. The calculations employ a composition probability density function (PDF) approach coupled to the commercial CFD code, FLUENT. The in-situ-adaptive tabulation (ISAT) method is used to implement detailed chemical kinetics. A simple k–ϵ turbulence model is used for turbulence along with a low Reynolds number model close to the solid walls of the fuel pipe.The first indicator is based on an analysis of the species transport with respect to the budget of convection, diffusion and chemical reaction terms. This is a powerful tool for investigating aspects of turbulent combustion that would otherwise be prohibitive or impossible to examine experimentally. Reaction balanced by convection with minimal axial diffusion is taken as an indicator of auto-ignition while a diffusive–reactive balance, preceded by a convective–diffusive balanced pre-heat zone, is representative of a premixed flame. The second indicator is the relative location of the onset of creation of certain radical species such as HO2 ahead of the flame zone. The buildup of HO2 prior to the creation of H, O and OH is taken as another indicator of autoignition.The paper first confirms the relevance of these indicators with respect to two simple test cases representing clear auto-ignition and premixed flame propagation. Three turbulent lifted flames are then investigated and the presence of auto-ignition is identified. These numerical tools are essential in providing valuable insights into the stabilization behaviour of these flames, and the demarcation between processes of auto-ignition and premixed flame propagation.
The lift-off heights and visible-flame lengths of jet diffusion flames in still air have been determined for hydrogen, propane, methane and ethylene.The flame lift-off height varies linearly with the jet exit velocity and is independent of the burner diameter for a given gas. The results support the assumption that if the burner exit flow is choked the burner can be approximated by an equivalent convergent-divergent nozzle at whose exit the flow has expanded to ambient pressure. The data for different gases can be collapsed onto a single curve if they are plotted in terms of the appropriate non-dimensional groupings. These results and previous results for blow-out stability suggest that diffusion flames blow out when the base is lifted to between 0.65 and 0.75 times the height at which stoichiometric concentration is reached at the jet axis. It can be deduced from the experimental results that, at the base of the flame. the ratio of turbulent burning velocity to laminar burning velocity varies as the square root of the local turbulence Reynolds number based on the integral length scale. The predicted correlation for the turbulent burning velocity agrees well with the experimental data presented in the literature.The flame length results for different gases and burner diameters can be collapsed onto a single curve if plotted in terms of the non-dimensional groupings suggested by Becker and Liang (Combust. Flame. 32, p. 115, 1978). The results near the forced convection limit are in line with the theoretical work presented by Becker and Liang but disagree with their final recommendation. Away from the forced convection limit, the flame length correlation is similar to that proposed by Becker and Liang.
Direct numerical simulation (DNS) of the near field of a three-dimensional spatially developing turbulent lifted hydrogen jet flame in heated coflow is performed with a detailed mechanism to determine the stabilization mechanism and the flame structure. The DNS was performed at a jet Reynolds number of 11,000 with over 940 million grid points. The results show that auto-ignition in a fuel-lean mixture at the flame base is the main source of stabilization of the lifted jet flame. A chemical flux analysis shows the occurrence of near-isothermal chemical chain branching preceding thermal runaway upstream of the stabilization point, indicative of hydrogen auto-ignition in the second limit. The Damköhler number and key intermediate-species behaviour near the leading edge of the lifted flame also verify that auto-ignition occurs at the flame base. At the lifted-flame base, it is found that heat release occurs predominantly through ignition in which the gradients of reactants are opposed. Downstream of the flame base, both rich-premixed and non-premixed flames develop and coexist with auto-ignition. In addition to auto-ignition, Lagrangian tracking of the flame base reveals the passage of large-scale flow structures and their correlation with the fluctuations of the flame base. In particular, the relative position of the flame base and the coherent flow structure induces a cyclic motion of the flame base in the transverse and axial directions about a mean lift-off height. This is confirmed by Lagrangian tracking of key scalars, heat release rate and velocity at the stabilization point.
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.
The conventional methods of simplified kinetics modeling through the use of partial-equilibrium and quasi-steady approximations are reviewed and critiqued. The method of computational singular perturbation (CSP) is then presented with special emphasis on the interpretation of CSP data to obtain physical insights on massively complex reaction systems. A simple example is used to demonstrate how CSP deals with complex chemical kinetics problems without the benefits of intuition and experience. 1 Introduction An ideal scenario in the (near) future for the study of chemical kinetics would be that a comprehensive, reliable and up-to-date database of validated reaction rates is readily available to any researcher interested in any reasonable reaction system of interest. Using a suitable sti# solver, one can routinely compute for the numerical solution of a massively complex chemical kinetics system. However, the extraction of physical insights about the # This work is supported by ...
Improved Navier–Stokes characteristic boundary conditions (NSCBC) are formulated for the direct numerical simulations (DNS) of laminar and turbulent counterflow flame configurations with a compressible flow formulation. The new boundary scheme properly accounts for multi-dimensional flow effects and provides nonreflecting inflow and outflow conditions that maintain the mean imposed velocity and pressure, while substantially eliminating spurious acoustic wave reflections. Applications to various counterflow configurations demonstrate that the proposed boundary conditions yield accurate and robust solutions over a wide range of flow and scalar variables, allowing high fidelity in detailed numerical studies of turbulent counterflow flames.
A theoretical analysis of turbulent jet diffusion flames is developed in which the flame is regarded as an ensemble of laminar diffusion flamelets that are highly distorted. The flow inhomogeneities are considered to be sufficiently strong to produce local quenching events for flamelets as a consequence of excessive flame stretch. The condition for flamelet extinction is derived in terms of the instantaneous scalar dissipation rate, which is ascribed a log-normal distribution. Percolation theory for a random network of stoichiometric sheets is used to predict quenching thresholds that define liftoff heights. Predictions are shown to be in reasonably satisfactory agreement with experimentally measured liftoff heights of methane jet diffusion flames, within experimental uncertainties.
A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.
This paper presents a numerical study on the formation of diffusion flame islands in a hydrogen jet lifted flame. A real size hydrogen jet lifted flame is numerically simulated by the DNS approach over a period of about 0.5ms. The diameter of hydrogen injector is 2mm, and the injection velocity is 680m/s. The lifted flame is composed of a stable leading edge flame, a vigorously turbulent inner rich premixed flame, and a number of outer diffusion flame islands. The relatively long-term observation makes it possible to understand in detail the time-dependent flame behavior in rather large time scales, which are as large as the time scale of the leading edge flame unsteadiness. From the observation, the following three findings are obtained concerning the formation of diffusion flame islands. (1) A thin oxygen diffusion layer is developed along the outer boundary of the lifted flame, where the diffusion flame islands burn in a rather flat shape. (2) When a diffusion flame island comes into contact with the fluctuating inner rich premixed flame, combustion is intensified due to an increase in the hydrogen supply by molecular diffusion. This process also works for the production of the diffusion flame islands in the oxygen diffusion layer. (3) When a large unburned gas volume penetrates into the leading edge flame, the structure of the leading edge flame changes. In this transformation process, a diffusion flame island comes near the leading edge flame. The local deficiency of oxygen plays an important role in this production process.
An experimental and numerical investigation is presented of a lifted turbulent H2/N2 jet flame in acollow of hot, vitiated gases. The vitiated coflow burner emulates the coupling of turbulent mixing and chemical kinetics exemplary of the reacting flow in the recirculation region of advanced combustors. It also simplifies numerical investigation of this coupled problem by removing the complexity of recirculating flow. Scalar measurements are reported for a lifted turbulent jet flame of H2/N2 (Re=23,600, H/d=10) in a coflow of hot combustion products from a lean H2/Air flame (=0.25, T=1045 K). The combination of Rayleigh scattering, Raman scattering, and laser-induced fluorescence is used to obtain simultaneous measurements of temperature and concentrations of the major species, OH, and NO. The data attest to the success of the experimental design in providing a uniform vitiated coflow throughout the entire test region. Two combustion models (joint scalar probability density function and eddy dissipation concept) are used in conjunction with various turbulence models to predict the liftoff height (HPDF/d=7, HEDC/d=8.5). Kalghatgi's classic phenomenological theory, which is based on scaling arguments, yields a reasonbly accurate prediction (HK/d=11.4) of the liftoff height for the present flame. The vitiated coflow admits the possibility of autoignition of mixed fluid, and the success of the present parabolic implementation of the PDF model in predicting a stable lifted flame is attributable to such ignition. The measurements indicate a thickened turbulent reaction zone at the flame base. Experimental results and numerical investigations support the plausibility of turbulent premixed flame propagation by small-scale (on the order of the flame thickness) recirculation and mixing of hot products into reactants and subsequent rapid ignition of the mixture.
This article presents experimental and computational results on ignition of nonpremixed, counterflowing jets of nitrogen-diluted methane versus heated air within a wide range of pressures, fuel concentrations, and flow strain rates. The system was brought to ignition by increasing gradually the temperature of the air stream. Each steady-state situation just prior to ignition was experimentally characterized by measuring detailed centerline axial flow velocity and temperature distributions, for ambient pressures between 0.5–8.0 atm, fuel concentrations in the range of 6%–100% methane in nitrogen, and pressure-weighted strain rates between 100–700 s−1. In addition, each situation was modeled numerically, using detailed transport properties and full chemical kinetics based on the GRI (Gas Research Institute) Mech v1.2 mechanism. As in our previous work with hydrogen/air ignition, we have identified computationally the existence of a localized ignition kernel of maximum reactivity and heat release. In contrast to the hydrogen case, however, we have shown that heat release and the thermal feedback are indispensable at ignition in the methane/air system. The ignition temperature, defined as the boundary temperature of the air jet just prior to ignition, was found to increase with increasing flow strain rate at all pressures. This has been shown numerically to be an effect of heat and radical loss out of the ignition kernel by convective-diffusive transport. The ignition temperature decreased abruptly with increasing fuel concentration, for dilute conditions. For CH4 concentrations in excess of 20%–30%, however, the ignition temperature became insensitive to further increase in the fuel concentration. Ignition temperatures at constant pressure-weighted strain rates decreased monotonically with increasing system pressure, similar to the homogeneous explosion limits. Over this range of pressures the numerical simulation indicated that the dominant chemical pathways at ignition do not change significantly. Flux, sensitivity, and the Computational Singular Perturbation (CSP) method were used to identify the ignition chemistry and provide several simplified kinetic mechanisms. The results obtained using a skeletal mechanism M4, with 22 species and 64 irreversible reactions, were found to agree closely with those obtained using the full chemistry. The experimental data were compared with computations using several kinetic mechanisms.
Ignition and extinction characteristics of homogeneous combustion of methane in air near inert surfaces are studied by numerical bifurcation theory for premixed methane/air gases impinging on planar surfaces with detailed chemistry involving 46 reversible reactions and 16 species. One-parameter bifurcation diagrams as functions of surface temperature and two-parameter bifurcation diagrams as functions of equivalence ratio and strain rate are constructed for both isothermal and adiabatic walls. Lean and rich composition limits for ignition and extinction, and energy production are determined from two parameter bifurcation diagrams. For a strain rate of 500 s[sup [minus]1], CH[sub 4]/air mixtures exhibit hysteresis from [approximately] 0.5% up to [approximately] 12.5% and from [approximately] 5.5% up to [approximately] 13.5% near isothermal surfaces and adiabatic walls, respectively. Ignition temperature rises with composition from 1,700 to 1,950 K, without a maximum around the stoichiometric ratio. Under some conditions multiple ignitions and extinctions can occur with up to five multiple solutions, and wall quenching, kinetic limitations, and transport can strongly affect flame stability. Flames near the stoichiometric ratio cannot be extinguished by room temperature surfaces for sufficiently low strain rates. The role of intermediates in enhancing or retarding ignition and extinction is studied, and implications of the effect of catalytic surfaces on homogeneous ignition and extinction are discussed. Removal of H atoms and CH[sub 3] radicals by wall adsorption can increase extinction and ignition temperature of 6% CH[sub 4] in air by up to 300 K for a strain rate of 500 s[sup [minus]1].
Many competing theories have been published to describe the characteristics and blowout of lifted turbulent jet diffusion flames. The assumptions which are made as to the physical processes responsible for these behaviors vary widely. In this paper these assumptions are summarized for each model and compared with the actual turbulent behaviors of unignited fuel jets. As part of this discussion, recent unpublished measurements of real-time concentration fluctuations along a line in a turbulent fuel jet are introduced. To the extent possible, each theory is also assessed as to its capabilities to accurately predict experimentally observed lift off and blowout behaviors. The conclusion of these analyses is that none of the currently-available theories for flame stabilization are satisfactory. Further experimentation is required before the actual physical processes responsible for flame stabilization can be identified and models which are capable of accurate prediction of lift off heights and blowout velocities developed.
Direct numerical simulations of turbulent flames stabilized by hot gases are presented and analysed with the aim of investigating the mechanisms which control turbulent flame stabilization. Even if the simulations are run on an idealized 2D configuration and use a simplified formulation, with single-step chemistry and Le=1 assumptions, they are useful in giving insight in the dynamics of flame stabilization. The current flames are stabilized by instantaneous reignition events triggered by hot gas convected by recirculation, which ignites lean premixed pockets that eventually produce a new triple flame upstream of the otherwise downstream travelling unsteady flame. While the occurrence of these events depends on the level of turbulence imposed to the flame, away from these occasional events the instantaneous flame propagates at a speed given by laminar flame properties, independent of the level of turbulence. This could explain why in some experiments [A. Upatnieks, J.F. Driscoll, Ch.C. Rasmussen, S.L. Ceccio, Combust. Flame 138 (2004) 259–272.] no correlation is found between the local turbulent intensity and the flame propagation speed, but a correlation is found between the mean flame position and the turbulence intensity.
A systematic approach for mechanism reduction was developed and demonstrated. The approach consists of the generation of skeletal mechanisms from detailed mechanism using directed relation graph with specified accuracy requirement, and the subsequent generation of reduced mechanisms from the skeletal mechanisms using computational singular perturbation based on the assumption of quasi-steady-state species. Both stages of generation are guided by the performance of PSR for high-temperature chemistry and auto-ignition delay for low- to moderately high-temperature chemistry. The demonstration was performed for a detailed ethylene oxidation mechanism consisting of 70 species and 463 elementary reactions, resulting in a specific skeletal mechanism consisting of 33 species and 205 elementary reactions, and a specific reduced mechanism consisting of 20 species and 16 global reactions. Calculations for laminar flame speeds and nonpremixed counterflow ignition using either the skeletal mechanism or the reduced mechanism show very close agreement with those obtained by using the detailed mechanism over wide parametric ranges of pressure, temperature, and equivalence ratio.
A chemical explosive mode analysis (CEMA) was developed as a new diagnostic to identify flame and ignition structure in complex flows. CEMA was then used to analyse the near-field structure of the stabilization region of a turbulent lifted hydrogen–air slot jet flame in a heated air coflow computed with three-dimensional direct numerical simulation. The simulation was performed with a detailed hydrogen–air mechanism and mixture-averaged transport properties at a jet Reynolds number of 11000 with over 900 million grid points. Explosive chemical modes and their characteristic time scales, as well as the species involved, were identified from the Jacobian matrix of the chemical source terms for species and temperature. An explosion index was defined for explosive modes, indicating the contribution of species and temperature in the explosion process. Radical and thermal runaway can consequently be distinguished. CEMA of the lifted flame shows the existence of two premixed flame fronts, which are difficult to detect with conventional methods. The upstream fork preceding the two flame fronts thereby identifies the stabilization point. A Damköhler number was defined based on the time scale of the chemical explosive mode and the local instantaneous scalar dissipation rate to highlight the role of auto-ignition in affecting the stabilization points in the lifted jet flame.
The structure and stabilization mechanism of turbulent lifted non-premixed hydrocarbon flames have been investigated using combined laser imaging techniques. The techniques include Rayleigh scattering, laser induced predissociation fluorescence of OH, LIF of PAH, LIF of CH2O, and planar imaging velocimetry. The geometrical structure of multi-reaction zones and flow field at the stabilization region have been simultaneously measured in 16 hydrocarbon flames. The data reveal the existence of triple flame structure at the stabilization region of turbulent lifted flames. Increasing the jet velocity leads to an increase of the lift-off height and to a broadening of the lift-off region. Further analysis of the stabilization criterion at the lift-off height based on the premixed nature of triple-flame propagation and flow field data has been presented and discussed.
Ignition and extinction characteristics of homogeneous combustion of methane in air near inert surfaces are studied by numerical bifurcation theory for premixed methane/air gases impinging on planar surfaces with detailed chemistry involving 46 reversible reactions and 16 species. One-parameter bifuraction diagrams as functions of surface temperature and two-parameter bifurcation diagrams as functions of equivalence ratio and strain rate are constructed for both isothermal and adiabatic walls. Lean and rich composition limits for ignition and extinction, and energy production are determined from two parameter bifurcation diagrams. For a strain rate of 500 s−1, CH4/air mixtures exhibit hysteresis from ∼ 0.5% up to ∼ 12.5% and from ∼ 5.5% up to ∼ 13.5% near isothermal surfaces and adiabatic walls, respectively. Ignition temperature rises with composition from 1,700 to 1,950 K, without a maximum around the stoichiometric ratio. Under some conditions multiple ignitions and extinctions can occur with up to five multiple solutions, and wall quenching, kinetic limitations, and transport can strongly affect flame stability. Flames near the stoichiometric ratio cannot be extinguished by room temperature surfaces for sufficiently low strain rates. The role of intermediates in enhancing or retarding ignition and extinction is studied, and implications of the effect of catalytic surfaces on homogeneous ignition and extinction are discussed. Removal of H atoms and CH3 radicals by wall adsorption can increase extinction and ignition temperature of 6% CH4 in air by up to 300 K for a strain rate of 500 s−1.
The autoignition behaviour of hydrogen in a turbulent co-flow of heated air at atmospheric pressures was examined experimentally. Turbulent flows of air, with temperatures up to 1015 K and velocities up to 35 m/s, were set up in an optically accessible tube of circular cross-section. The fuel, pure or diluted with nitrogen, was continuously injected along the centreline of the tube, with velocities equal to or larger than those of the air, and temperatures that were lower. The fuel mixing patterns hence obtained were akin to diffusion from a point source or to an axisymmetric jet within a co-flow. For a relatively wide range of temperatures and velocities, a statistically steady condition of randomly occurring autoignition kernels was observed, whose axial location was measured by hydroxyl radical chemiluminescence. The probability density function of autoignition location was sharp enough to allow the accurate determination of a minimum autoignition length and smooth enough to allow the mean and variance to be calculated. It was found that both autoignition lengths increased with the air velocity and decreased with the air temperature, as expected. An estimate of the residence time up to autoignition showed that the autoignition delay times increased with the air velocity for the same temperature, suggesting a delaying effect of the turbulence on autoignition. The connection between these findings and previous experimental and direct numerical simulation studies is discussed.
The need and prospect of incorporating realistic fuel chemistry in large-scale simulations of combustion phenomena and combustor performance are reviewed. The review first demonstrates the intricacies of chemical kinetics in homogeneous and diffusive systems, and emphasizes the essential importance of the comprehensiveness of chemical fidelity for mechanisms at the detailed and reduced levels. A systematic approach towards developing detailed reaction mechanisms is then outlined, followed by an extensive discussion on the development of reduced mechanisms and the associated strategies towards facilitated computation. Topics covered include skeletal reduction especially through directed relation graph; time-scale reduction based on the concepts of quasi-steady species enabled through computational singular perturbation; the lumping of isomers and of species with similar diffusivities; on-the-fly stiffness removal; the relative merits of implicit versus explicit solvers; and computation cost minimization achieved through tabulation and the judicious re-sequencing of the computational steps in arithmetic evaluations. Examples are given for laminar flames and direct numerical simulations of turbulent combustion to demonstrate the utility of the integrated strategy and the component methods in incorporating realistic chemistry of practical fuels in large-scale simulations, recognizing that the detailed mechanisms of these fuels may consist of hundreds to thousands of species and thousands to tens of thousands of reactions. Directions for further research are suggested.
Three theories of the liftoff of a turbulent jet flame were assessed using cinema-particle imaging velocimetry movies recorded at 8000 images/s. The images visualize the time histories of the eddies, the flame motion, the turbulence intensity, and streamline divergence. The first theory assumes that the flame base has a propagation speed that is controlled by the turbulence intensity. Results conflict with this idea; measured propagation speeds remains close to the laminar burning velocity and are not correlated with the turbulence levels. Even when the turbulence intensity increases by a factor of 3, there is no increase in the propagation speed. The second theory assumes that large eddies stabilize the flame; results also conflict with this idea since there is no significant correlation between propagation speed and the passage of large eddies. The data do support the “edge flame” concept. Even though the turbulence level and the mean velocity in the undisturbed jet are large (at jet Reynolds numbers of 4300 and 8500), the edge flame creates its own local low-velocity, low-turbulence-level region due to streamline divergence caused by heat release. The edge flame has two propagation velocities. The actual velocity of the flame base with respect to the disturbed local flow is found to be nearly equal to the laminar burning velocity; however, the effective propagation velocity of the entire edge flame with respect to the upstream (undisturbed) flow exceeds the laminar burning velocity. A simple model is proposed which simulates the divergence of the streamlines by considering the potential flow over a source. It predicts the well-established empirical formula for liftoff height, and it agrees with experiment in that the controlling factor is streamline divergence, and not turbulence intensity or large eddy passage. The results apply only to jet flames for Re<8500; for other geometries the role of turbulence could be larger.
A criterion based on computational singular perturbation (CSP) is proposed to effectively distinguish the quasi steady state (QSS) species from the fast species induced by reactions in partial equilibrium. Together with the method of directed relation graph (DRG), it was applied to the reduction of GRI-Mech 3.0 for methane oxidation, leading to the development of a 19-species reduced mechanism with 15 lumped steps, with the concentrations of the QSS species solved analytically for maximum computational efficiency. Compared to the 12-step and 16-species augmented reduced mechanism (ARM) previously developed by Sung, Law & Chen, three species, namely O, CH3OH, and CH2CO, are now excluded from the QSS species list. The reduced mechanism was validated with a variety of phenomena including perfectly stirred reactors, auto-ignition, and premixed and non-premixed flames, with the worst-case error being less than 10% over a wide range of parameters. This mechanism was then supplemented with the reactions involving NO formation, followed by validations in both homogeneous and diffusive systems.
Direct numerical simulations of a two-dimensional, nonpremixed, sooting ethylene flame are performed to examine the effects of soot–flame interactions and transport in an unsteady configuration. A 15-step, 19-species (with 10 quasi-steady species) chemical mechanism was used for gas chemistry, with a two-moment, four-step, semiempirical soot model. Flame curvature is shown to result in flames that move, relative to the fluid, either toward or away from rich soot formation regions, resulting in soot being essentially convected into or away from the flame. This relative motion of flame and soot results in a wide spread of soot in the mixture fraction coordinate. In regions where the center of curvature of the flame is in the fuel stream, the flame motion is toward the fuel and soot is located near the flame at high temperature and hence has higher reaction rates and radiative heat fluxes. Soot–flame breakthrough is also observed in these regions. Fluid convection and flame displacement velocity relative to fluid convection are of similar magnitudes while thermophoretic diffusion is 5–10 times lower. These results emphasize the importance of both unsteady and multidimensional effects on soot formation and transport in turbulent flames.
Simultaneous planar-laser induced fluorescence (PLIF) and particle image velocimetry (PIV) provide a comprehensive view of the molecular mixing and velocity fields in the stabilization region of turbulent, lifted jet diffusion flames. The Mie scattering medium for PIV is a glycerol–water fog, which evaporates at elevated temperatures and allows inference of the location of the high-temperature interface at the flame base. The jet Reynolds numbers vary from 4400 to 10,700. The mixing and velocity fields upstream of the flame base evolve consistently with nonreacting jet scaling. Conditional statistics of the fuel mole fraction at the instantaneous high-temperature interface show that the flame stabilization point does not generally correspond to the most upstream point on the interface (called here the leading point), because the mixture there is typically too lean to support combustion. Instead, the flame stabilization point lies toward the jet centerline relative to the leading point. Conditional axial velocity statistics indicate that the mean axial velocity at the flame front is ≈1.8SL, where SL is the stoichiometric laminar flame speed. The data also permit determination of the scalar dissipation rates, χ, with the results indicating that χ values near the high-temperature interfaces do not typically exceed the quenching value. Thus, the flame stabilization process is more consistent with theories based on partial fuel–air premixing than with those dependent on diffusion flame quenching. We propose a description of flame stabilization that depends on the large-scale organization of the mixing field.
Measurements on gas composition, gas flow velocity, intensity and Eulerian scale of turbulence have been made in a free jet of methane emerging from a conventional circular burner into an unconfined atmosphere. From the experimental data it appears that the base of a lifted diffusion flame anchors in a region where a stoichiometric composition is attained. Accepting the assumption that the turbulent burning velocity Vt equals the gas flow velocity in this region, an experimental relation is obtained between Vt and the parameters of turbulence. Finally the stabilization conditions are discussed; blow off and drop back of the flame are explained by the interaction between aerodynamic flow patterns and burning velocity.
Previous studies on physical boundary conditions for flame–boundary interactions of an ideal, multicomponent, compressible gas have neglected reactive source terms in their boundary condition treatments. By combining analyses of incompletely parabolic systems with those based on the hyperbolic Euler equations, a rational set of boundary conditions is determined to address this shortcoming. Accompanying these conditions is a procedure for implementation into a multidimensional code. In the limits of zero reaction rate or one species, the boundary conditions reduce in a predictable way to cases found in the literature. Application is made to premixed and nonpremixed flames in one and two dimensions to establish efficacy. Inclusion of source terms in boundary conditions derived from characteristic analysis is essential to avoid unphysical generation of pressure and velocity gradients as well as flow reversals. Minor deficiencies in the boundary conditions are attributed primarily to the diffusive terms. Imposing vanishing diffusive boundary-normal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory.
Flame stability of a fuel jet diffusion flame was studied numerically by using finite rate chemistry. The flow is time dependent and plane two-dimensional, and the chemical reaction is described by simplified, overall one-step kinetics. The variable parameters are the jet Reynolds number, PRco and Damköhler number, Dao: and three types of flame stability behavior were observed depending on values of these parameters. The first one is the local and occasional extinction at the transition point from a laminar to a turbulent flame. When Re0 is kept at a rather high value and Da0 is decreased, local extinction at the transition point begins to occur at a certain critical value. The occasional extinction is caused at the instant when the local scalar dissipation rate in the reaction zone becomes too large, producing a rupture in the reaction zone layer. The rupture is quickly connected again to recover the continuous reaction zone layer. As Da0 is decreased further, however, the frequency of rupture increases, and at another critical value, complete extinction is produced at the transition point, leaving a short, residual rim flame immediately downtream of the injector. This is the second type of flame stability. As Da0 is decreased further, the third and final stability characteristic is observed: the blow-off of the whole flame from the injector rim. When the flme is extinguished completely at the transition point, most of the injected fuel flows downstream as a fuel jet entraining the surounding air to produce a lifted, turbulent diffusion flame in the downstream flow. This study of the structure of the flame has shown that it is actually an ensemble of instantaneous local premixed, diffusion., and partially premixed flames.
A general procedure for simplifying chemical kinetics is developed, based on the dynamical systems approach. In contrast to conventional reduced mechanisms no information is required concerning which reactions are to be assumed to be in partial equilibrium nor which species are assumed to be in steady state. The only “inputs” to the procedure are the detailed kinetics mechanism and the number of degrees of freedom required in the simplified scheme. (Four degrees of freedom corresponds to a four-step mechanism, etc.) The state properties given by the simplified scheme are automatically determined as functions of the coordinates associated with the degrees of freedom. Results are presented for the CO/H2/air system. These show that the method provides accurate results even in regimes (e.g., at low temperatures) where conventional mechanisms fail.
Procedures to define boundary conditions for Navier-Stokes equations are discussed. A new formulation using characteristic wave relations through boundaries is derived for the Euler equations and generalized to the Navier-Stokes equations. The emphasis is on deriving boundary conditions compatible with modern non-dissipative algorithms used for direct simulations of turbulent flows. These methods have very low dispersion errors and require precise boundary conditions to avoid numerical instabilities and to control spurious wave reflections at the computational boundaries. The present formulation is an attempt to provide such conditions. Reflecting and non-reflecting boundary condition treatments are presented. Examples of practical implementations for inlet and outlet boundaries as well as slip and no-slip walls are presented. The method applies to subsonic and supersonic flows. It is compared with a reference method based on extrapolation and partial use of Riemann invariants. Test cases described include a ducted shear layer, vortices propagating through boundaries, and Poiseuille flow. Although no mathematical proof of well-posedness is given, the method uses the correct number of boundary conditions required for well-posedness of the Navier-Stokes equations and the examples reveal that it provides a significant improvement over the reference method.
The stabilization point of lifted turbulent hydrogen diffusion flames is investigated by Raman/Rayleigh/laser-induced fluorescence (LIF) spectroscopy. The stabilization point is determined from simultaneously taken planar laser-induced fluorescence (PLIF) images. It is shown from averaged statistics that lift-off height has negligible influence on the flame length and the far region of the jet. Reactants, premixed downstream of the stabilization point, are rapidly consumed over a very short distance. A new method to generate stabilization point conditioned species and temperature data is proposed and applied to the data. With this method it is possible to describe the surrounding of an observer located at the instantaneous stabilization point. The data are presented by constant contour plots of mixture fraction, species, and temperature in a stabilization point fixed coordinate system. The data obtained by this method are used to assess previously proposed theories on the behavior of lifted turbulent diffusion flames. Experimental findings presented are inconsistent with predictions by the concept of premixed flame stabilization as well as with the flamelet concept. The insensitivity of the spatial location of the stabilization point to the variation of the stoichiometric mixture fraction of the fuels investigated suggests a stabilization mechanism through large-scale turbulent structures. Large-scale structures also explain the existence of products upstream of the stabilization point. The conclusion of this analysis is that large-scale turbulent structures play a dominant role in the stabilization mechanisms of the lifted turbulent diffusion flames, subject to this study.
An algorithm is presented for the construction of global reduced mechanisms, based on concepts from the Computational Singular Perturbation method. Input to the algorithm are (i) the detailed mechanism, (ii) a representative numerical solution of the problem under investigation, and (iii) the desired number of steps in the reduced mechanism. The algorithm numerically identifies the “steady-state” species and fast reactions and constructs the reduced mechanism. The stoichiometric coefficients are constant and are connected to the non “steady-state” species, while the related rates involve the slow elementary rates only. The proposed method is applied to a laminar premixed CH4/Air flame and a complex detailed chemical kinetics mechanism, consisting of 279 reactions and 49 species and accounting for both thermal and prompt NOx production. A seven-step mechanism is constructed which is shown to reproduce the species profiles and the laminar burning velocity very accurately over a wide range of values for the initial mixture composition and temperature. In addition, it is shown that the seven-step mechanism introduces much lower time scales than the detailed mechanism does. Since the proposed procedure for constructing reduced mechanisms is fully algorithmic and requires minor computations, it is very much suited for the simplification of large detailed mechanisms.
Computational singular perturbation (CSP) analysis has been used to gain understanding of the complex kinetic behavior associated with two-stage ignition of large hydrocarbon molecules. To this end, available detailed and reduced chemical kinetics models commonly used in numerical simulations of n-heptane oxidation phenomena are directly analyzed to interpret the underlying fundamental steps leading to two-stage ignition. Unlike previous implementations of the CSP methodology, temperature is included as one of the state variables so that factors controlling ignition can be unambiguously determined. The analyzed models show differences in the factors contributing to the initial development and shutdown of the first ignition stage. However, during the second stage, both models show the importance of the degenerate branching decomposition of hydrogen peroxide, which contradicts some previous interpretations of this phenomenon.
A systematic approach was developed to obtain analytic solutions for the concentrations of the quasi steady state (QSS) species in reduced mechanisms. The nonlinear algebraic equations for the QSS species concentrations were first approximated by a set of linear equations, and the linearized quasi steady state approximations (LQSSA) were then analytically solved with a directed graph, namely a QSSG, which was abstracted from the inter-dependence of QSS species. To obtain analytic solutions of high computational efficiency, the groups of strongly connected QSS species were first identified in the QSSG. The inter group couplings were then resolved by a topological sort, and the inner group couplings were solved with variable elimination by substitution. An efficient algorithm was developed to identify a near-optimal sequence for the variable elimination process. The proposed LQSSA-QSSG method was applied to generate a 16-step reduced mechanism for ethylene/air, and good accuracy and high efficiency were observed in simulations of auto-ignition and perfectly stirred reactors with the reduced mechanism.
The Computational Singular Perturbation (CSP) method of simplified kinetics modeling is presented with emphasis on its comparative merits versus conventional methodologies. A new "refinement" procedure for the basis vectors spanning the fast reaction subspace is presented. A simple example is first worked through using the conventional partial-equilibrium and quasi-steady approximations, and is then treated in some detail using CSP.
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