Finite element solution of an enclosed turbulent diffusion flame

A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity-pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ–? model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi-industrial size, and comparing the results with experiments and finite difference predictions.     

Unsteady boundary layer and its separation over a heated circular cylinder

A numerical method is developed to solve the coupled unsteady laminar momentum and thermal boundary layers over a circular cylinder impulsively started from rest. The present non-iterative finite difference method, which requires relatively fewer grid points in the reversed flow region than any other method, can easily handle the separating boundary layer flows. The results indicate that the present method has accuracy comparable with the earlier methods, while consuming computer time approximately one order of magnitude less. The present numerical method allowed investigation of the effect of buoyancy parameter on the starting boundary layer. The time-dependent behaviour of the boundary layer is studied in terms of the appearance of the singularity, the distribution of skin friction and wall heat flux, and the wall position of the inflection point of the velocity profile. The transient as well as buoyancy-dependent patterns of the streamlines and isotherms are also studied.     

Laminar Heat Transfer Augmentation through A Square Duct and Circular Tube Fitted with Twisted Tapes

Experimental studies on friction factor and heat transfer characteristics for the laminar flow of ethylene glycol in a square duct fitted with twisted tapes of different twist ratios under nearly uniform wall temperature conditions are reported in this article. The Nusselt numbers were found to be 5.44–7.49 and 2.46–4.87 times that of plain square duct forced convection values based on constant flow rate and constant pumping power criteria, respectively, for y = 2.66. The augmented friction factor and Nusselt number for a square duct is about 1.9 and 2.10 times higher than that for an augmented circular tube.     

A numerical study of reignition induced by a diffusion flame

We present a numerical study of the reignition of a cold reactant mixture by the interaction with a nearby diffusion flame. This reignition mechanism may be an important process in turbulent non-premixed flames at high rates of strain where quenched sections of the stoichiometric surface are folded by the turbulent flow and come in close proximity with other burning flame sections. We consider an idealized one-dimensional setup containing the fundamental ingredients that are expected to contribute to this reignition mode. One- and two-step irreversible chemical mechanisms with heat release levels typical of practical hydrocarbon fuels are considered. It is observed that a slow moving reignition kernel originates on the high-temperature region of the burning flame in the one-step chemistry case owing to small leakage of oxidizer from the cold-mixture side. This kernel gradually moves, increasing the local temperature above that provided by diffusion and eventually leads to thermal runaway with the formation of a deflagration wave. The reignition time depends on the chemistry details, the Damköhler number, but in any case it cannot exceed the mixing time. This implies that the flame-induced reignition time is essentially bounded from above by mixing. Unless one of the free streams is hotter, in which case auto-ignition (as opposed to reignition) may proceed first, the reignition time is chemistry dependent. In the case of two-step chemistry, the reignition pathway is different initially owing to leakage of the radical species, but it approaches that of the one-step chemistry case shortly thereafter. It is observed that the only difference between the two cases is in the initial phase of the evolution of the reignition kernel. This phase appears to be very sensitive to the chemistry details, a general aspect of ignition. A parametric study is carried out to elucidate the effect of each non-dimensional quantity on the reignition time for the one-step chemistry case.     

Triple flame: Inherent asymmetries and pentasectional character

A two-dimensional triple-flame numerical model of a laminar combustion process reflects flame asymmetric structural features that other analytical models do not generate. It reveals the pentasectional character of the triple flame, composed of the central pure diffusion-flame branch and the fuel-rich and fuel-lean branches, each of which is divided into two sections: a near-stoichiometric section and a previously unreported near-flammability-limits section with combined diffusion and premixed character. Results include propagation velocity, fuel and oxidiser mass fractions, temperature and reaction rates. Realistic stoichiometric ratios and reaction orders match experimental planar flame characteristics. Constant density, a one-step reaction, and a mixture fraction gradient at the inlet as the simulation parameter are imposed. The upstream equivalence ratio or the upstream reactant mass fractions are linear or hyperbolic functions of the transverse coordinate. The use here of experimental kinetics data differs from previous analytical works and results in flame asymmetry and different flammability limits. Upstream mixture composition gradient affects propagation velocity, flame curvature, diffusion flame reaction rate, and flammability limits. Flammability limits extend beyond those of a planar flame due to transverse heat and mass diffusion causing the pentasectional character.     

Multidimensional chemistry coordinate mapping approach for combustion modelling with finite-rate chemistry

A multidimensional chemistry coordinate mapping (CCM) approach is presented for efficient integration of chemical kinetics in numerical simulations of turbulent reactive flows. In CCM the flow transport is integrated in the computational cells in physical space, whereas the integration chemical reactions are carried out in a phase space made up of a few principal variables. Each cell in the phase space corresponds to several computational cells in the physical space, resulting in a speedup of the numerical integration. In reactive flows with small hydrocarbon fuels two principal variables have been shown to be satisfactory to construct the phase space. The two principal variables are the temperature (T) and the specific element mass ratio of the H atom (J _H). A third principal variable, σ=?J _H·?J _H, which is related to the dissipation rate of J _H, is required to construct the phase space for combustion processes with an initially non-premixed mixture. For complex higher hydrocarbon fuels, e.g. n-heptane, care has to be taken in selecting the phase space in order to model the low-temperature chemistry and ignition process. In this article, a multidimensional CCM algorithm is described for a systematic selection of the principal variables. The method is evaluated by simulating a laminar partially remixed pre-vaporised n-heptane jet ignition process. The CCM approach is then extended to simulate n-heptane spray combustion by coupling the CCM and Reynolds averaged Navier–Stokes (RANS) code. It is shown that the computational time for the integration of chemical reactions can be reduced to only 3–7%, while the result from the CCM method is identical to that of direct integration of the chemistry in the computational cells.     

Implementation of REDIM reduced chemistry to model an axisymmetric laminar diffusion methane–air flame

The goal of this work is to analyze the use of automatically reduced chemistry by the Reaction–Diffusion Manifold (REDIM) method in simulating axisymmetric laminar coflow diffusion flames. Detailed chemical kinetic models are usually computationally prohibitive for simulating complex reacting flows, and therefore reduced models are required. Automatic reduction model approaches usually exploit the natural multi-scale structure of combustion systems. The novel REDIM approach applies the concept of invariant manifolds to treat also the influence of the transport processes on the reduced model, which overcomes a fundamental problem of model reduction in neglecting the coupling of molecular transport with thermochemical processes. We have considered a previously well studied atmospheric pressure nitrogen-diluted methane–air flame as a test case to validate the methodology presented here. First, one-dimensional and two-dimensional REDIMs were computed and tabulated in lookup tables. Then, the full set of governing equations are projected on the REDIM and implemented in the object-oriented C++ Gascoigne code with a new add-on library to deal with the REDIM tables. The projected set of governing equations have been discretized by the Finite Element Method (FEM) and solved by a GMRES iteration preconditioned by a geometric multigrid method. Local grid refinement, adaptive mesh and parallelization are applied to ensure efficiency and precision. The numerical results obtained using the REDIM approach have shown very good agreement with detailed numerical simulations and experimental data.     

Analysis of RDX-TAGzT pseudo-propellant combustion with detailed chemical kinetics

A detailed model of steady-state combustion of a pseudo-propellant containing cyclotrimethylene trinitramine (RDX) and triaminoguanidinium azotetrazolate (TAGzT) is presented. The physicochemical processes occurring within the foam layer, comprised of a liquid and gas bubbles, and a gas-phase region above the burning surface are considered. The chemical kinetics is represented by a global thermal decomposition mechanism within the liquid by considering 18 species and eight chemical reactions. The reactions governing decomposition of TAGzT were deduced from separate confined rapid thermolysis experiments using Fourier transform infrared spectroscopy and time-of-flight mass spectrometry. Within the gas bubbles and gas-phase region, a detailed chemical kinetics mechanism was used by considering up to 93 species and 504 reactions. The pseudo-propellant burn rate was found to be highly sensitive to the global decomposition reactions of TAGzT. The predicted results of burn rate agree well with experimental burn-rate data. The increase in burn rate by inclusion of TAGzT is due in part from exothermic decomposition of the azotetrazolate within the foam layer, and from fast gas-phase reactions between triaminoguanidine decomposition products, such as hydrazine, and oxidiser products from the nitramine decomposition.     

A computational framework for predicting laminar reactive flows with soot formation

Numerical modeling is an attractive option for cost-effective development of new high-efficiency, soot-free combustion devices. However, the inherent complexities of hydrocarbon combustion require that combustion models rely heavily on engineering approximations to remain computationally tractable. More efficient numerical algorithms for reacting flows are needed so that more realistic physics models can be used to provide quantitative soot predictions. A new, highly-scalable combustion modeling tool has been developed specifically for use on large multiprocessor computer architectures. The tool is capable of capturing complex processes such as detailed chemistry, molecular transport, radiation, and soot formation/destruction in laminar diffusion flames. The proposed algorithm represents the current state of the art in combustion modeling, making use of a second-order accurate finite-volume scheme and a parallel adaptive mesh refinement (AMR) algorithm on body-fitted, multiblock meshes. Radiation is modeled using the discrete ordinates method (DOM) to solve the radiative transfer equation and the statistical narrow-band correlated-k (SNBCK) method to quantify gas band absorption. At present, a semi-empirical model is used to predict the nucleation, growth, and oxidation of soot particles. The framework is applied to two laminar coflow diffusion flames which were previously studied numerically and experimentally. Both a weakly-sooting methane–air flame and a heavily-sooting ethylene–air flame are considered for validation purposes. Numerical predictions for these flames are verified with published experimental results and the parallel performance of the algorithm analyzed. The effects of grid resolution and gas-phase reaction mechanism on the overall flame solutions were also assessed. Reasonable agreement with experimental measurements was obtained for both flames for predictions of flame height, temperature and soot volume fraction. Overall, the algorithm displayed excellent strong scaling performance by achieving a parallel efficiency of 70% on 384 processors. The proposed algorithm proved to be a robust, highly-scalable solution method for sooting laminar flames.     

Effects of buoyancy on turbulent premixed V-flames by large-eddy simulation

Buoyancy effects on turbulent premixed V-flames are investigated under normal gravity (+g) and reversed gravity (–g). Numerical simulations employ large eddy simulation (LES) with a dynamic model for sub-grid scale stress. With the assumption of fast chemistry combustion, a progress variable c-equation is applied to describe the flame front propagation. The equations are solved using a projection-based fractional step method in two dimensions for low-Mach number flows. Computed LES results of buoyancy effects on flame angle and flame brush thickness are consistent with those obtained from experiments. In both +g and –g conditions, the effects of buoyancy become important with increase in Richardson number (Ri). Buoyancy force tends to close up the flame under +g, but has the opposite effect under –g. Buoyancy force also suppresses flame wrinkling in +g and enhances wrinkling in –g. While there is a lack of experimental data available, computed axial velocity is shown to be significantly affected by buoyancy downstream from the flame holder under moderate Reynolds number.