Beth Anne V. Bennett

Computational and experimental study of axisymmetric coflow partially premixed ethylene/air flames

Abstract Six coflowing laminar, partially premixed methane/air flames, varying in primary equivalence ratio from ∞ (nonpremixed) to 2.464, have been studied both computationally and experimentally to determine the fundamental effects of partial premixing. Computationally, the local rectangular refinement solution–adaptive gridding method incorporates a damped modified Newton’s method to solve the system of coupled nonlinear elliptic partial differential equations for each flame. The model includes a C2 chemical mechanism, multicomponent transport, and an optically thin radiation submodel. Experimentally, both probe and optical diagnostic methods are used to measure the temperature and species concentrations along each flame’s centerline. Most experimentally measured trends are well predicted by the computational model. Because partial premixing decreases the flame height when the fuel flowrate is held constant, computational and experimental centerline profiles have been plotted against nondimensional axial position to reveal additional effects of partial premixing. Heat release profiles, as well as those of several species, indicate that the majority of the partially premixed flames contain two flame fronts: an inner premixed front whose strength grows with decreasing primary equivalence ratio; and an outer nonpremixed front. As the amount of partial premixing increases, computational results predict a continual reduction in the amount of flow radially inward; the resulting decrease in radial transport is responsible for various effects observed both computationally and experimentally, including a cooling of the gases near the burner surface. At the same time, radiative losses decrease with increasing amounts of premixing, resulting in higher flame temperatures.

Local rectangular refinement with application to axisymmetric laminar flames

Within realistic combustion devices, physical quantities may change by an order of magnitude over an extremely thin flamefront, while remaining nearly unchanged throughout large areas nearby. Such behaviour dictates the use of adaptive numerical methods. The recently developed local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes novel multiple-scale finite-difference discretizations, and incorporates a damped modified Newtons method for simultaneously solving systems of governing elliptic PDEs. Here, the LRR method is applied to two axisymmetric laminar flames: a premixed Bunsen flame with one-step chemistry and a diffusion flame employing various complex chemical mechanisms. The Bunsen flames position is highly dependent upon grid spacing, especially on coarse grids; it stabilizes only with adequate refinement. The diffusion flame results show excellent agreement with experimental data for flame structure, temperature and major sp...

Computational and experimental study of oxygen-enhanced axisymmetric laminar methane flames

Three axisymmetric laminar coflow diffusion flames, one of which is a nitrogen-diluted methane/air flame (the ‘base case’) and the other two of which consist of nitrogen-diluted methane vs. pure oxygen, are examined both computationally and experimentally. Computationally, the local rectangular refinement method is used to solve the fully coupled nonlinear conservation equations on solution-adaptive grids. The model includes C2 chemistry (GRI 2.11 and GRI 3.0 chemical mechanisms), detailed transport, and optically thin radiation. Because two of the flames are attached to the burner, thermal boundary conditions at the burner surface are constructed from smoothed functional fits to temperature measurements. Experimentally, Raman scattering is used to measure temperature and major species concentrations as functions of the radial coordinate at various axial positions. As compared to the base case flame, which is lifted, the two oxygen-enhanced flames are shorter, hotter, and attached to the burner. Computational and experimental flame lengths show excellent agreement, as do the maximum centreline temperatures. For each flame, radial profiles of temperature and major species also show excellent agreement between computations and experiments, when plotted at fixed values of a dimensionless axial coordinate. Computational results indicate peak NO levels in the oxygen-enhanced flames to be very high. The majority of the NO in these flames is shown to be produced via the thermal route, whereas prompt NO dominates for the base case flame.

A mass-conserving vorticity-velocity formulation with application to nonreacting and reacting flows

In a commonly implemented version of the vorticity-velocity formulation, the governing equations for the fluid dynamics are expressed as two Poisson-like velocity equations together with the vorticity transport equation. However, for some flows with large vorticity gradients, spurious mass loss or gain can be observed. In order to conserve mass, a modification to the vorticity-velocity formulation is proposed, involving the substitution of the kinematic definition of vorticity in certain terms of the fluid-dynamic equations. This modified formulation results in a broader computational stencil when the equations are in a second-order-accurate discretized form, and a stronger coupling between the predicted vorticity and the curl of the predicted velocity field. The resulting system of elliptic equations - which includes the energy and species transport equations for the reacting flow case - is discretized with finite differences on a nonstaggered grid and is then solved using Newtons method. Both the unmodified and modified vorticity-velocity formulations are applied to two problems with high vorticity gradients: (1) incompressible, axisymmetric fluid flow through a suddenly expanding pipe and (2) a confined, axisymmetric laminar flame with detailed chemistry and multicomponent transport, generated on a burner whose inner tube extends above the burner surface. The modified formulation effectively eliminates the spurious mass loss in the two test cases to within an acceptable tolerance. The two cases demonstrate the broader range of applicability of the modified formulation, as compared with the unmodified formulation.

A comparison of the structures of lean and rich axisymmetric laminar Bunsen flames: application of local rectangular refinement solution-adaptive gridding

Axisymmetric laminar methane–air Bunsen flames are computed for two equivalence ratios: lean (Φ=0.776), in which the traditional Bunsen cone forms above the burner; and rich (Φ=1.243), in which the premixed Bunsen cone is accompanied by a diffusion flame halo located further downstream. Because the extremely large gradients at premixed flame fronts greatly exceed those in diffusion flames, their resolution requires a more sophisticated adaptive numerical method than those ordinarily applied to diffusion flames. The local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes multiple-scale finite-difference discretizations, and incorporates Newtons method to solve elliptic partial differential equation systems simultaneously. The LRR method is applied to the vorticity–velocity formulation of the fully elliptic governing equations, in conjunction with detailed chemistry, multicomponent transport and an optically-thin radiation model. The com...

Natural Convection in a Cubic Cavity: Implicit Numerical Solution of Two Benchmark Problems

Natural convection of air within a cubic cavity, two opposite walls of which are differentially heated, is simulated numerically for Rayleigh numbers of 103, 104, 105, and 106. For each Rayleigh number, two benchmark problems are examined: all four remaining walls are either adiabatic or perfectly conducting. The conservation equations, written using a vorticity–velocity formulation, are discretized with second-order finite differences on uniform grids containing up to 813 points. The equations are solved at all points simultaneously using Newtons method. Solutions on an 813 nonuniform grid are also presented. Excellent agreement with published computational and experimental data is observed, and new benchmark data are reported for the second problem.

Distributed-memory parallel computation of a forced, time-dependent, sooting, ethylene/air coflow diffusion flame

Forced, time-varying laminar flames help bridge the gap between laminar and turbulent combustion as they reside in an ever-changing flow environment. A distributed-memory parallel computation of a time-dependent sooting ethylene/air coflow diffusion flame, in which a periodic fluctuation (20 Hz) is imposed on the fuel velocity for four different amplitudes of modulation, is presented. The chemical mechanism involves 66 species, and a soot sectional model is employed with 20 soot sections. The governing equations are discretised using finite differences and solved implicitly using a damped modified Newtons method. The solution proceeds in parallel using strip domain decomposition over 40 central processing units (CPUs) until full periodicity is attained. For forcing amplitudes of 30%, 50%, 70% and 90%, a complete cycle of numerical predictions of the time-resolved soot volume fraction is presented. The 50%, 70% and 90% forcing cases display stretching and pinching off of the sooting region into an isolated oval shape. In the 90% forcing case, a well-defined hollow shell-like structure of the soot volume fraction contours occurs, in which the interior of the isolated sooty region has significantly lower soot concentrations than the shell. Preliminary comparisons are made with experimental measurements of the soot volume fraction for the 50% forcing case. The experimental results are qualitatively consistent with the model predictions.

An adaptive multilevel local defect correction technique with application to combustion

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.

Prediction of electron and ion concentrations in low-pressure premixed acetylene and ethylene flames

Flame stabilisation and extinction in a number of different flows can be affected by application of electric fields. Electrons and ions are present in flames, and because of charge separation, weak electric fields can also be generated even when there is no externally applied electric field. In this work, a numerical model incorporating ambipolar diffusion and plasma kinetics has been developed to predict gas temperature, species, and ion and electron concentrations in laminar premixed flames without applied electric fields. This goal has been achieved by combining the existing CHEMKIN-based PREMIX code with a recently developed methodology for the solution of electron temperature and transport properties that uses a plasma kinetics model and a Boltzmann equation solver. A chemical reaction set has been compiled from seven sources and includes chemiionisation, ion-molecule, and dissociative–recombination reactions. The numerical results from the modified PREMIX code (such as peak number densities of positive ions) display good agreement with previously published experimental data for fuel-rich, non-sooting, low-pressure acetylene and ethylene flames without applied electric fields.

Influence of Strouhal number on pulsating methane–air coflow jet diffusion flames

Four periodically time-varying methane–air laminar coflow jet diffusion flames, each forced by pulsating the fuel jets exit velocity U j sinusoidally with a different modulation frequency w j and with a 50% amplitude variation, have been computed. Combustion of methane has been modeled by using a chemical mechanism with 15 species and 42 reactions, and the solution of the unsteady Navier–Stokes equations has been obtained numerically by using a modified vorticity-velocity formulation in the limit of low Mach number. The effect of w j on temperature and chemistry has been studied in detail. Three different regimes are found depending on the flames Strouhal number S = aw j /U j , with a denoting the fuel jet radius. For small Strouhal number (S = 0.1), the modulation introduces a perturbation that travels very far downstream, and certain variables oscillate at the frequency imposed by the fuel jet modulation. As the Strouhal number grows, the nondimensional frequency approaches the natural frequency of oscillation of the flickering flame (S ≃ 0.2). A coupling with the pulsation frequency enhances the effect of the imposed modulation and a vigorous pinch-off is observed for S = 0.25 and S = 0.5. Larger values of S confine the oscillation to the jets near-exit region, and the effects of the pulsation are reduced to small wiggles in the temperature and concentration values. Temperature and species mass fractions change appreciably near the jet centerline, where variations of over 2 % for the temperature and 15 % and 40 % for the CO and OH mass fractions, respectively, are found. Transverse to the jet movement, however, the variations almost disappear at radial distances on the order of the fuel jet radius, indicating a fast damping of the oscillation in the spanwise direction.